# Magnetic Microrobotics for Biomedical Applications

David Folio

► To cite this version:

David Folio. Magnetic Microrobotics for Biomedical Applications: Modeling, Simulation, Control and Validations. Automatic. Université d'Orléans, 2021. tel-03483203

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
UNIVERSITÉ D'ORLÉANS

ÉCOLE DOCTORALES MATHÉMATIQUES, INFORMATIQUE, PHYSIQUE THÉORIQUE
ET INGÉNIERIE DES SYSTÈMES

LABORATOIRE PRISME

MÉMOIRE

Par

David FOLIO

Soutenu le 03 décembre 2021

pour obtenir le grade d'Habilitation à Diriger des Recherches

Discipline: Robotique

MAGNETIC MICROROBOTICS FOR BIOMEDICAL APPLICATIONS:
Modeling, Simulation, Control and Validations

Jury:

<table><tr><td>Michaël Gauthier</td><td>Directeur de Recherche, CNRS, FEMTO-ST, Besançon</td><td>Rapporteur</td></tr><tr><td>Sylvain Martel</td><td>Professeur, Polytechnique Montréal, Canada</td><td>Rapporteur</td></tr><tr><td>Philippe Poignet</td><td>Professeur des Universités, Univ. Montpellier</td><td>Rapporteur</td></tr><tr><td>Chantal Pichon</td><td>Professeur des Universités, Univ. Orléans</td><td>Examinatrice</td></tr><tr><td>Christine Prelle</td><td>Professeur des Universités, UTC</td><td>Examinatrice</td></tr><tr><td>Mohammed Samer</td><td>Professeur des Universités, Univ. Paris-Est Creteil Val de Marne</td><td>Examinateur</td></tr><tr><td>Li Zhang</td><td>Professeur, Dept. MAE, CUHK, Hong Kong</td><td>Examinateur</td></tr><tr><td>Antoine Ferreira</td><td>Professeur des Universités, INSA Centre Val de Loire</td><td>Garant</td></tr></table>
<figure><img src="image_2.png" /></figure>
# CONTENTS

<table><tr><td>Contents</td><td>iii</td></tr><tr><td>List of Tables</td><td>vii</td></tr><tr><td>List of Figures</td><td>ix</td></tr><tr><td>Avant Propos (Forewords)</td><td>xiii</td></tr><tr><td><b>PART I ACTIVITIES BACKGROUND</b></td><td><b>1</b></td></tr><tr><td><b>I Presentation</b></td><td><b>3</b></td></tr><tr><td>I.1 Curriculum Vitæ</td><td>3</td></tr><tr><td>I.1.1 Identity</td><td>3</td></tr><tr><td>I.1.2 Current situation</td><td>3</td></tr><tr><td>I.1.3 Experience and Graduate Education</td><td>4</td></tr><tr><td>I.2 Background and Career Overview</td><td>4</td></tr><tr><td>I.2.1 Doctorate degree and post-doctorate</td><td>4</td></tr><tr><td>I.2.2 Tenured as associate professor</td><td>5</td></tr><tr><td><b>II Teaching and Administrative Responsibilities</b></td><td><b>11</b></td></tr><tr><td>II.1 Before Tenure</td><td>11</td></tr><tr><td>II.2 Since Tenured</td><td>11</td></tr><tr><td>II.3 Responsibilities</td><td>13</td></tr><tr><td><b>III Summary of Research Activities</b></td><td><b>15</b></td></tr><tr><td>III.1 Scientific Projects</td><td>15</td></tr><tr><td>III.1.1 European Union (EU) and national funding projects</td><td>15</td></tr><tr><td>III.1.2 Cooperation projects</td><td>16</td></tr><tr><td>III.1.3 Regional projects</td><td>17</td></tr><tr><td>III.2 Student Supervision</td><td>17</td></tr><tr><td>III.2.1 Master students (M2)</td><td>17</td></tr><tr><td>III.2.2 Doctoral students</td><td>18</td></tr><tr><td>III.3 Scientific Collaborations</td><td>19</td></tr></table>
<table><tbody><tr><td>III.3.1 International relationships</td><td>20</td></tr><tr><td>III.3.2 National relationships</td><td>20</td></tr><tr><td>III.4 Scientific Dissemination and Outreach</td><td>20</td></tr><tr><td>III.4.1 Invitations</td><td>21</td></tr><tr><td>III.4.2 Scientific expertise</td><td>21</td></tr><tr><td>III.4.3 Editorial activities</td><td>21</td></tr><tr><td>III.4.4 Awards</td><td>22</td></tr><tr><td><strong>IV Personal References</strong></td><td><strong>23</strong></td></tr><tr><td>IV.1 Articles</td><td>23</td></tr><tr><td>IV.1.1 Articles in International peer-reviewed and referenced journals (ACL)</td><td>23</td></tr><tr><td>IV.1.2 Articles in unreferenced journals (ACLN)</td><td>24</td></tr><tr><td>IV.2 Books</td><td>24</td></tr><tr><td>IV.2.1 Guest Editor (DO)</td><td>25</td></tr><tr><td>IV.2.2 Book Chapter (OS)</td><td>25</td></tr><tr><td>IV.3 Proceedings in International Conferences (ACT)</td><td>25</td></tr><tr><td>IV.4 Oral Communications</td><td>28</td></tr><tr><td>IV.4.1 Invited Speaker in International or National Conferences (INV)</td><td>28</td></tr><tr><td>IV.4.2 Communications in International or National Conferences (COM)</td><td>28</td></tr><tr><td><strong>PART II SCIENTIFIC CONTRIBUTIONS</strong></td><td><strong>29</strong></td></tr><tr><td><strong>V Scientific Context and Organization</strong></td><td><strong>31</strong></td></tr><tr><td>V.1 Introduction</td><td>31</td></tr><tr><td>V.2 Positioning of Main Research Activities</td><td>32</td></tr><tr><td>V.2.1 Working in the microworld</td><td>32</td></tr><tr><td>V.2.2 Microrobotics for biomedical applications</td><td>33</td></tr><tr><td>V.2.3 Biomedical microrobotics challenges</td><td>35</td></tr><tr><td>V.3 Structuring of Activities</td><td>38</td></tr><tr><td>V.3.1 Magnetic microrobotic systems for biomedical applications</td><td>38</td></tr><tr><td>V.3.2 Simulation and navigation strategies</td><td>40</td></tr><tr><td>V.3.3 Evaluation and development of magnetic microrobotic systems</td><td>41</td></tr><tr><td>V.3.4 The others research activities</td><td>42</td></tr><tr><td><strong>VI Modeling Microrobotic Systems for Endovascular Intervention</strong></td><td><strong>45</strong></td></tr><tr><td>VI.1 Introduction</td><td>45</td></tr><tr><td>VI.2 Endovascular Navigation</td><td>46</td></tr><tr><td>VI.2.1 Fluid mechanics</td><td>47</td></tr><tr><td>VI.2.2 Physiology of the cardiovascular system</td><td>50</td></tr><tr><td>VI.2.3 Discussion</td><td>54</td></tr><tr><td>VI.3 Biomedical Microrobot Design</td><td>55</td></tr><tr><td>VI.3.1 Magnetic microrobot</td><td>56</td></tr><tr><td>VI.3.2 Hydrodynamics of microrobot</td><td>63</td></tr><tr><td>VI.3.3 Catalytic micromotor</td><td>66</td></tr><tr><td>VI.4 Magnetic Field Generation</td><td>72</td></tr><tr><td>VI.4.1 Classical electromagnetic coils</td><td>72</td></tr></tbody></table>
<table><tbody><tr><td>VI.4.2 Core-filled electromagnets</td><td>75</td></tr><tr><td>VI.4.3 Electromagnetic actuation setups</td><td>76</td></tr><tr><td>VI.5 Conclusion</td><td>80</td></tr><tr><td><strong>VII Magnetically Actuated Microrobots Navigating in a Vascular Network</strong></td><td><strong>81</strong></td></tr><tr><td>VII.1 Introduction</td><td>81</td></tr><tr><td>VII.2 Microrobot in a Vascular Environment</td><td>82</td></tr><tr><td>VII.2.1 Dynamic of magnetic microrobots in a microchannel</td><td>82</td></tr><tr><td>VII.2.2 Simulation of microrobot navigating in a vascular network</td><td>86</td></tr><tr><td>VII.2.3 Navigation planning in viscous flow</td><td>87</td></tr><tr><td>VII.3 Navigation Control Strategies</td><td>93</td></tr><tr><td>VII.3.1 State-space representation</td><td>93</td></tr><tr><td>VII.3.2 Predictive navigation</td><td>96</td></tr><tr><td>VII.3.3 Nonlinear optimal control</td><td>104</td></tr><tr><td>VII.3.4 Control of multiple magnetic microrobots</td><td>109</td></tr><tr><td>VII.4 Conclusion</td><td>113</td></tr><tr><td><strong>VIII Development of Experimental Platforms and Validations</strong></td><td><strong>115</strong></td></tr><tr><td>VIII.1 Introduction</td><td>115</td></tr><tr><td>VIII.2 Cardiovascular System Simulator</td><td>115</td></tr><tr><td>VIII.3 Magnetic Resonant Navigation (MRN)</td><td>117</td></tr><tr><td>VIII.3.1 The clinical MRI setup</td><td>118</td></tr><tr><td>VIII.3.2 MRI-based sensing</td><td>120</td></tr><tr><td>VIII.3.3 MRN experimental results</td><td>122</td></tr><tr><td>VIII.4 µIRM testbed</td><td>124</td></tr><tr><td>VIII.4.1 Platform descriptions</td><td>124</td></tr><tr><td>VIII.4.2 Results</td><td>126</td></tr><tr><td>VIII.4.3 Discussion</td><td>129</td></tr><tr><td>VIII.5 OctoRob Platform</td><td>130</td></tr><tr><td>VIII.5.1 Platform design specifications</td><td>130</td></tr><tr><td>VIII.5.2 Design of OctoRob</td><td>131</td></tr><tr><td>VIII.5.3 Implementation of the OctoRob prototype</td><td>133</td></tr><tr><td>VIII.6 Conclusion</td><td>135</td></tr><tr><td><strong>Conclusion and Prospects</strong></td><td><strong>137</strong></td></tr><tr><td><strong>APPENDIX</strong></td><td><strong>143</strong></td></tr><tr><td><strong>A Three-dimensional controlled motion of a microrobot using magnetic gradients (ACL3)</strong></td><td><strong>145</strong></td></tr><tr><td><strong>B Simulation and planning of a magnetically actuated microrobot navigating in arteries (ACL6)</strong></td><td><strong>163</strong></td></tr><tr><td><strong>C Catalytic locomotion of core-shell nanowire motors (ACL10)</strong></td><td><strong>173</strong></td></tr></tbody></table>
<table><tr><td>D</td><td>Modeling of optimal targeted therapies using drug-loaded magnetic nanoparticles for the liver cancer (ACL12)</td><td>203</td></tr><tr><td>E</td><td>Mathematical Approach for the Design Configuration of Magnetic System with Multiple Electromagnets (ACL15)</td><td>215</td></tr><tr><td colspan="2">Index of Terms and Notations</td><td>239</td></tr><tr><td colspan="2">Bibliography</td><td>245</td></tr></table>
LIST OF TABLES

<table><tr><td>II.1</td><td>Overview of the various teaching disciplines as associate professor.</td><td>12</td></tr><tr><td>VIII.1</td><td>Standard deviations (SD) of the location of different steel balls size using HASTE and FLASH sequences. [ACL11]</td><td>121</td></tr><tr><td>VIII.2</td><td>Standard deviations (SD) of the position for different k-space reduction. [ACL11]</td><td>121</td></tr><tr><td>VIII.3</td><td>Caracteristics of the μMRI setup coils</td><td>124</td></tr></table>
<figure><img src="image_3.png" /></figure>
LIST OF FIGURES

<table><tr><td>I.1</td><td>Timeline of main events and activities since tenure as Associate Professor</td><td>6</td></tr><tr><td>I.2</td><td>Teaching load progress.</td><td>7</td></tr><tr><td>I.3</td><td>Personal references progress since tenure.</td><td>9</td></tr><tr><td>V.1</td><td>Scaling down to the microworld.</td><td>32</td></tr><tr><td>V.2</td><td>Challenges and opportunities of medical microrobots.</td><td>34</td></tr><tr><td>V.3</td><td>Example of actuation mechanisms envisaged for microrobots</td><td>36</td></tr><tr><td>V.4</td><td>Examples of different microworld imaging modalities</td><td>37</td></tr><tr><td>VI.1</td><td>Overview of the cardiovascular system</td><td>46</td></tr><tr><td>VI.2</td><td>Fluid flow in a pipe</td><td>49</td></tr><tr><td>VI.3</td><td>Relationships among vessel size, cross-sectional area and the blood flow velocity</td><td>51</td></tr><tr><td>VI.4</td><td>Pressure, volume and flow rate relationship in the cardiac cycle.</td><td>52</td></tr><tr><td>VI.5</td><td>Pulsatile flow profiles in a straight tube</td><td>53</td></tr><tr><td>VI.6</td><td>In vivo apparent viscosity using the Pries et al. model</td><td>55</td></tr><tr><td>VI.7</td><td>Examples of magnetic microrobots</td><td>56</td></tr><tr><td>VI.8</td><td>Schematic representation of basic magnetic swimming principle</td><td>57</td></tr><tr><td>VI.9</td><td>Magnetization curves of ferromagnetic and superparamagnetic material</td><td>59</td></tr><tr><td>VI.10</td><td>Representation of spheroidal shapes</td><td>62</td></tr><tr><td>VI.11</td><td>Ellipsoidal and chain-like microrobots in a microchannel.</td><td>65</td></tr><tr><td>VI.12</td><td>Different reported catalytic micro-/nanomotors</td><td>66</td></tr><tr><td>VI.13</td><td>Schematic of the cyclic bubble propulsion mechanism of tubular truncated conical nanorobot</td><td>67</td></tr><tr><td>VI.14</td><td>Representation of the microjet and the inner flow under the simplifying approximations.</td><td>68</td></tr><tr><td>VI.15</td><td>Velocity of the microjets against and along flow rates</td><td>69</td></tr><tr><td>VI.16</td><td>Self-photetic propulsion</td><td>70</td></tr><tr><td>VI.17</td><td>Schematic representation of Ru-Au core-shell nanorod with the different electrokinetic reaction.</td><td>71</td></tr><tr><td>VI.18</td><td>Numerical modeling of Au/Ru core-shell nanorod in the presence of H 2 O 2</td><td>71</td></tr><tr><td>VI.19</td><td>Representation of the Biot-Savart low applied to a circular loop.</td><td>73</td></tr><tr><td>VI.20</td><td>Representation of an Helmholtz (inner red) and Maxwell (outer blue) coils pair.</td><td>74</td></tr><tr><td>VI.21</td><td>The (a) magnetic fields and (b) its gradient induce with Helmholtz coils.</td><td>74</td></tr></table>
<table>
  <tbody>
    <tr>
      <td>VI.22</td>
      <td>The (a) magnetic fields and (b) its gradient induce with Maxwell coils.</td>
      <td>75</td>
    </tr>
    <tr>
      <td>VI.23</td>
      <td>Illustration of the magnetic field due to a theoretical magnetic point-dipole.</td>
      <td>76</td>
    </tr>
    <tr>
      <td>VI.24</td>
      <td>The concept of EMA system applying for various biomedical applications.</td>
      <td>77</td>
    </tr>
    <tr>
      <td>VI.25</td>
      <td>EMA platforms used in our research</td>
      <td>77</td>
    </tr>
    <tr>
      <td>VI.26</td>
      <td>The diagram of the specifications of EMA system design</td>
      <td>79</td>
    </tr>
    <tr>
      <td>VII.1</td>
      <td>Representation of a magnetic microrobot navigating in a microchannel.</td>
      <td>82</td>
    </tr>
    <tr>
      <td>VII.2</td>
      <td>Evolution of microforces acting on a spherical magnetic microrobot in a microchannel and the relevant microforces.</td>
      <td>83</td>
    </tr>
    <tr>
      <td>VII.3</td>
      <td>Hydrodynamic drag forces for spherical, spheroidal and chain-like microrobots.</td>
      <td>83</td>
    </tr>
    <tr>
      <td>VII.4</td>
      <td>Magnetophoretic number and the magnetization rate for spherical microrobot</td>
      <td>84</td>
    </tr>
    <tr>
      <td>VII.5</td>
      <td>Comparison of magnetophoretic number for an ellipsoidal and a chain-like microrobots</td>
      <td>85</td>
    </tr>
    <tr>
      <td>VII.6</td>
      <td>Load volume as function of the equivalent radius when C<sub>mt</sub> = 1</td>
      <td>85</td>
    </tr>
    <tr>
      <td>VII.7</td>
      <td>Clinical MIP image from the MRA obtained for a patient with an isolated stenosis in the iliac artery</td>
      <td>86</td>
    </tr>
    <tr>
      <td>VII.8</td>
      <td>Simulation results of the blood flow velocity field computation.</td>
      <td>87</td>
    </tr>
    <tr>
      <td>VII.9</td>
      <td>Simulation results of the force field</td>
      <td>87</td>
    </tr>
    <tr>
      <td>VII.10</td>
      <td>Pulsatile blood flow simulation</td>
      <td>88</td>
    </tr>
    <tr>
      <td>VII.11</td>
      <td>Illustration of the vessel centerline extraction</td>
      <td>90</td>
    </tr>
    <tr>
      <td>VII.12</td>
      <td>Planning results on varying control action influence for a neodymium microrobot of size 250 µm and 750 µm</td>
      <td>91</td>
    </tr>
    <tr>
      <td>VII.13</td>
      <td>Planning results using the proposed anisotropic cost function for a neodymium microrobot</td>
      <td>92</td>
    </tr>
    <tr>
      <td>VII.14</td>
      <td>Representation of spheroidal magnetic microrobot in x<sub>0</sub>-y<sub>0</sub> plane</td>
      <td>95</td>
    </tr>
    <tr>
      <td>VII.15</td>
      <td>Illustration of the MRI timeline of acquisition and control and the basic concept of predictive navigation.</td>
      <td>97</td>
    </tr>
    <tr>
      <td>VII.16</td>
      <td>Diagram of the SMPC design.</td>
      <td>98</td>
    </tr>
    <tr>
      <td>VII.17</td>
      <td>Microrobot 3D vascular MRN using SMPC.</td>
      <td>99</td>
    </tr>
    <tr>
      <td>VII.18</td>
      <td>3D tracking error with SMPC</td>
      <td>100</td>
    </tr>
    <tr>
      <td>VII.19</td>
      <td>SMPC MRB with blood flow disturbance</td>
      <td>100</td>
    </tr>
    <tr>
      <td>VII.20</td>
      <td>Tracking error with different values of duty cycle</td>
      <td>101</td>
    </tr>
    <tr>
      <td>VII.21</td>
      <td>Navigation based-Generalized Predictive Control (GPC) strategy.</td>
      <td>102</td>
    </tr>
    <tr>
      <td>VII.22</td>
      <td>3D MRN tracking error with GPC</td>
      <td>103</td>
    </tr>
    <tr>
      <td>VII.23</td>
      <td>GPC MRN with blood flow disturbance</td>
      <td>103</td>
    </tr>
    <tr>
      <td>VII.24</td>
      <td>Optimal stabilization of a spheroidal microrobot position</td>
      <td>107</td>
    </tr>
    <tr>
      <td>VII.25</td>
      <td>Optimal stabilization of a spheroidal microrobot with singularity crossing</td>
      <td>107</td>
    </tr>
    <tr>
      <td>VII.26</td>
      <td>Schematic representation of the principle locoregional therapy for the liver cancer.</td>
      <td>108</td>
    </tr>
    <tr>
      <td>VII.27</td>
      <td>Group of magnetic microrobot in a microfluidic environment.</td>
      <td>109</td>
    </tr>
    <tr>
      <td>VII.28</td>
      <td>Interaction forces f<sub>m,12</sub> magnitude between two magnetic microrobot as function of their separation distance d<sub>12</sub>.</td>
      <td>110</td>
    </tr>
    <tr>
      <td>VII.29</td>
      <td>Phase portrait of a pair (x<sub>i1</sub>, v<sub>i1</sub>)</td>
      <td>112</td>
    </tr>
    <tr>
      <td>VII.30</td>
      <td>Optimal stabilization of the three microrobots with different LQI parameters.</td>
      <td>113</td>
    </tr>
    <tr>
      <td>VII.31</td>
      <td>Optimal stabilization of the 2D positions of two magnetic microrobots</td>
      <td>114</td>
    </tr>
    <tr>
      <td>VIII.1</td>
      <td>Illustration of our cardiovascular system simulator</td>
      <td>116</td>
    </tr>
  </tbody>
</table>
<table><tr><td>VIII.2</td><td>Example of pulsatile flow generated by the Harvard Apparatus pump.</td><td>117</td></tr><tr><td>VIII.3</td><td>Viscosity of aqueous mixtures of glycerin: (a) at fixed T = 20 °C, and (b) for 60 wt.% of glycerin</td><td>118</td></tr><tr><td>VIII.4</td><td>The Siemens Magnetom® Verio MRI scanner at Pius Hospital, Oldenburg, Germany,</td><td>119</td></tr><tr><td>VIII.5</td><td>The MRN architecture with the Siemens MRI scanner</td><td>119</td></tr><tr><td>VIII.6</td><td>The MRI experimental setups components</td><td>120</td></tr><tr><td>VIII.7</td><td>MRI susceptibility artifact imaging experiment</td><td>121</td></tr><tr><td>VIII.8</td><td>Navigation along a planned path of a microrobot with standard FLASH sequences</td><td>122</td></tr><tr><td>VIII.9</td><td>MRN along a planned path of a microrobot with optimized FLASH sequence parameters</td><td>123</td></tr><tr><td>VIII.10</td><td>MRN in Y-shaped microfluidic vessel simulator</td><td>123</td></tr><tr><td>VIII.11</td><td>The µIRM EMA platform with its coils pair arrangement.</td><td>124</td></tr><tr><td>VIII.13</td><td>Predictive control in a Y-channel with static flow</td><td>126</td></tr><tr><td>VIII.14</td><td>Predictive control in a Y-channel with a pulsatile flow</td><td>127</td></tr><tr><td>VIII.15</td><td>Predictive control in a W-channel with a pulsatile flow</td><td>127</td></tr><tr><td>VIII.16</td><td>Controlled navigation of soft-magnetic microrobot in W-shaped microchannel</td><td>128</td></tr><tr><td>VIII.17</td><td>Controlled injection of soft-magnetic microrobots</td><td>129</td></tr><tr><td>VIII.18</td><td>Microrobot break-up</td><td>130</td></tr><tr><td>VIII.19</td><td>Illustration of the ophthalmic microrobotic MIS system</td><td>131</td></tr><tr><td>VIII.20</td><td>Representation of the geometric arrangement of electromagnetic coils</td><td>132</td></tr><tr><td>VIII.21</td><td>Evolution of admissible radius and the mobile angle</td><td>133</td></tr><tr><td>VIII.22</td><td>Representation of the coils.</td><td>133</td></tr><tr><td>VIII.23</td><td>The OctoRob prototype</td><td>134</td></tr><tr><td>VIII.24</td><td>Synoptic of OctoRob platform architecture.</td><td>134</td></tr><tr><td>VIII.25</td><td>Representation of the navigation of a magnetic microrobot (TMMC) navigating in a cardiovascular system.</td><td>139</td></tr></table>
<figure><img src="image_4.png" /></figure>
# AVANT PROPOS (FOREWORDS)

Avant de commencer, il est à noter que bien que cet avant-propos soit rédigé en langue française, le reste de ce mémoire est quant à lui écrit en langue anglaise.

Ce mémoire, rédigé en vue de l'obtention d'une Habilitation à Diriger des Recherches (HDR), décrit mes activités d'enseignement, de recherche, d'encadrement et de collaborations. Ce manuscrit doit donc présenter une synthèse (non exhaustive) de ces activités effectuées depuis ma prise de fonction en qualité de maître de conférences en septembre 2008 à l'ENSI de Bourges (aujourd'hui INSA Centre Val de Loire) et au sein de l'équipe Robotique du laboratoire PRISME. Ce qui est présenté ici est avant tout le résultat d'un travail collectif, issu des interactions avec des collègues enseignant-chercheurs, administratifs et techniques, et aussi d'échange avec des étudiants, avec des scientifiques de divers établissements et des opportunités de projets dans lesquels je me suis investi. Notamment, ce travail n'aurait pas été possible sans l'enthousiasme et l'implication des jeunes chercheurs que j'ai eu l'opportunité de co-encadrer ou de superviser. Leur contribution est mentionnée tout au long de ce mémoire. Depuis mon recrutement, mes travaux de recherche concernent d'une manière générale l'étude de systèmes robotiques, en vue de proposer des solutions innovantes pour réaliser des tâches avancées et fiables pour des applications essentiellement biomédicales. Même si j'ai travaillé dans différents domaines de la robotique, la grande partie de mes contributions concernent l'étude du comportement de ces systèmes aux échelles microscopiques. Cette thématique originale est un domaine de recherche en pleine expansion et fortement pluridisciplinaire, associant entre autre la robotique, le biomédical, la mécanique du solide et des fluides, l'électromagnétisme, les microsystèmes... Les applications et les retombés socio-économiques sont potentiellement très prometteuses. Les futurs robots qu'inspirent ces travaux pourraient transformer significativement la médecine par la possibilité d'aider le diagnostic *in situ* ou de réaliser des thérapies localisées dans des zones aujourd'hui difficiles d'accès autrement que par une chirurgie invasive. Je me suis ainsi fortement investi dans ce nouvel axe de recherche, ayant ainsi un positionnement scientifique original. Je me suis plus particulièrement intéressé à des problématiques, au sens large, de *"modélisation et de commande"* de microrobots magnétiques évoluant dans le corps humain pour du ciblage thérapeutique. L'émergence au sein du laboratoire PRISME de cette thématique coïncide avec le démarrage du projet européen NANOMA dont le laboratoire était coordinateur. Plusieurs enseignants-chercheurs du laboratoire PRISME des groupes de recherche de Robotique et d'Automatique se sont impliqués dans cette thématique autour des aspects de modélisation et de commande.
Ce mémoire est organisé en huit chapitres répartis dans deux parties. Comme tout maître de conférences, mes travaux englobent deux composantes principales qui sont liées aux activités d'enseignement et de recherche. Dans la première partie, quatre chapitres présentent le résumé de ces activités. Ainsi dans le Chapitre I, je présente un bref aperçu de ma carrière et du contexte de mes activités. Le Chapitre II résume mes responsabilités pédagogiques et administratives. La synthèse de mes activités de recherche est introduite au Chapitre III, avec une brève présentation des projets de recherche, des encadrements d'étudiants, des collaborations scientifiques et des actions de rayonnement. La liste complète de mes publications est indiquée dans le Chapitre IV.

Dans la deuxième partie de ce manuscrit, mes principales contributions scientifiques sont présentées. Dans un souci de cohérence, j'ai choisi de ne présenter que les réalisations concernant le développement des microrobots magnétiques pour des thérapies ciblées, en navigant à travers le système cardiovasculaire. Cette problématique, fondamentalement pluridisciplinaire, est globalement abordée selon une approche ascendante (dite "bottom-up"), à savoir de la compréhension et de la modélisation du micromonde à la définition de stratégies de navigation de haut niveau. C'est notamment en suivant cette approche que la présentation de mes contributions scientifiques est organisée.

Le Chapitre V décrit alors le contexte scientifique de mes travaux de recherche. Comme mes principales contributions concernent la microrobotique pour les applications biomédicales, ce thème y est introduit. Puis la manière dont mes activités se sont structurées est présentée. Dans le Chapitre VI, les fondements théoriques qui permettent de décrire et de modéliser les microrobots sont introduis. En effet, pour concevoir un système microrobotique efficace et fiable pour une application biomédicale, une bonne compréhension de leur comportement est une étape importante. Il est nécessaire de bien caractériser la manière dont les microrobots évoluent suivant le type d'environnement biologique et des stimuli externes. Pour cela, nous avons exploré en profondeur les différents éléments qui contribuent majoritairement aux dynamiques dominantes.

Sur cette base, dans le Chapitre VII, nous sommes en mesure de pouvoir simuler le comportement des microrobots. Ces simulations ont pour objectif de bien appréhender les spécificités des systèmes microrobotiques considérés et de tenter d'anticiper les contraintes et difficultés susceptibles de les impacter. Nous avons aussi proposé des stratégies de planification pouvant prendre en compte les contraintes de l'application. Cela nous permet d'obtenir une référence qui est effectivement réalisable par le système microrobotique. Nous avons pu alors définir des stratégies de navigations en fonction des spécificités du système microrobotique et de l'application visée.

Pour tester et valider les modèles et stratégies choisis, nous avons développé différentes plateformes démontrant les preuves-de-concept. Ces réalistions décrites au Chapitre VIII ont été développées essentiellement au sein du laboratoire PRISME, mais ont bénéficié également de collaborations scientifiques avec de nombreux partenaires internationaux (ETH Zurich-Suisse, University of Oldenburgh-Allemagne, KAIST-Corée du Sud...). Notamment, pour évaluer nos stratégies de navigation dans un environnement de type cardiovasculaire, nous avons développé un simulateur qui reproduit au mieux les conditions physiologiques. Puis, pour guider magnétiquement les microbots développés, différentes plateformes d'actionnement magnétiques ont été considérées. Tout cela nous a permis d'évaluer et de démontrer expérimentalement les différents concepts et stratégies que nous avons développés.
En plus des contributions décrites dans ce mémoire, les perspectives que j'ambitionne d'explorer à l'avenir sont également présentées en conclusion de ce mémoire.
# PART I

## ACTIVITIES BACKGROUND
<figure><img src="image_5.png" /></figure>
## I.1 CURRICULUM VITÆ

### I.1.1 Identity

<figure><img src="image_6.png" /><figcaption>**David Folio**</figcaption></figure>

Born September 17, 1979; French nationality

Associate Professor

**Main topic:** Microrobotics for biomedical applications.

**Contact information**

INSA Centre Val de Loire,

Campus de Bourges, 88 bd Lahitolle;

CS 60013; F-18022 Bourges cedex; France

Mobile: +33(0)6 71 30 06 88

Tel.: +33(0)2 48 48 40 75

Fax: +33(0)2 48 48 40 50

email: david.folio@insa-cvl.fr

**Public profiles**

Google Scholar: XQVc6JMAAAAJ

Orcid: 0000-0001-9430-6091

ResearchGate: David_Folio

ResearcherID: D-5808-2013

Scopus: 15924858900

LinkedIn: david-folio-5b8b43a7

### I.1.2 Current situation

**Since 2008 Associate Professor** (maître de conférences), 61st CNU section

**Affiliation:** INSA Centre Val de Loire, University of Orléans, PRISME Laboratory EA4229, Bourges, France.

**Teaching:** member of the teaching team of the Industrial Risk Control (MRI), of the Energy, Risks, and Environment (ERE), and of the Sciences and Techniques for Engineers (STPI) departments on the Bourges campus of INSA Centre Val de Loire.

**Research:** member of the Robotics team of the Images, Robotics, Automatic control and Signal (IRAuS) unit of the PRISME Laboratory.

**Supervision:** 5 Master students (M2) and 6 PhD students, and 3 externals PhD students.

**Publications:** a total of 47 publications, including 15 articles (ACL), 1 guest editorial (DO), 3 books chapter (OS) and 23 proceedings (ACT).

**Since 2014**

* in charge of the Nuclear Energy option of the 5th year of the Industrial Risk Control (MRI) department.

* French outstanding research award (PEDR)

**Since 2020** elected member of the council of the Industrial Risk Control (MRI) department.
### I.1.3 Experience and Graduate Education

**Oct. 2007 – Aug. 2008** Post-Doctorate at Inria Rennes-Bretagne-Atlantique, Rennes, France.
Research on sensory control for unmanned aerial vehicles conducted in Lagadic team,
supervised by François Chaumette.

**Feb. 2007 – Aug. 2007** Teaching assistant (ATER), at Paul Sabatier University of Toulouse,
France.

**Feb. 2004 – Aug. 2007** Doctorate degree at Laboratory for Analysis and Architecture of Systems (LAAS), CNRS, Toulouse, France. "Multi-sensor-based control strategies and visual signal loss management for mobile robots navigation", PhD thesis in Robotic control, of Paul Sabatier University of Toulouse, directed by Viviane Cadenat

**Jury**
* Michel Devy, Senior Research Scientist<fnref n="1" /> LAAS-CNRS, President

* François Chaumette, Senior Research Scientist Inria, Reviewer

* Seth Hutchinson, Professor of University of Illinois, Reviewer

* Bernard Bayle, Associate Professor of University of Strasbourg, Examiner

* Michel Couredesse, Professor of University of Toulouse, Examiner

* Viviane Cadenat, Associate Professor of University of Toulouse, Director

* Philippe Souères, Senior Research Scientist LAAS-CNRS, Guest

**2003 – 2004** Master of Science (DESS) on Intelligent Systems at Paul Sabatier University of Toulouse, France.

**2002 – 2003** Master of Advanced Studies (DEA) on Computer Sciences at Paul Sabatier University of Toulouse, France.

**1999 – 2002** Scholarship (IUP<fnref n="2" />, L2-M1) on Intelligent Systems at Paul Sabatier University of Toulouse, France.

**1997 – 1999** Bachelor's degree (L1-L2) in Science and Technology for the Engineer, at University of Reunion Island, France.

## I.2 BACKGROUND AND CAREER OVERVIEW

### I.2.1 Doctorate degree and post-doctorate

I have defended my PhD in Robotics in 2007 within the Robotics, Action, and Perception (RAP) group of the Laboratory for Analysis and Architecture of Systems<fnref n="3" /> (LAAS), CNRS<fnref n="4" />, under the supervision of Viviane Cadenat, Associate Professor at the Paul Sabatier University of Toulouse, France. Specifically, my PhD thesis was entitled "*Multi-sensor-based control strategies and visual signal loss management for mobile robots' navigation*". My thesis subject was to design multi-sensor-based control strategies allowing a mobile robot to perform vision-based tasks amidst possibly occluding obstacles. Indeed, the improvement of sensors gave rise to the sensor-based control which allows defining the robotic task in the sensor space rather than in the configuration space. As cameras provide high-rate meaningful data, visual servoing has been particularly investigated, and can be used to perform various and accurate navigation tasks [1–3]. My PhD objectives were then to perform reliable navigation tasks,

<footnote n="1">¹Senior Research Scientist refers to in French "Directeur de Recherche".</footnote>

<footnote n="2">²From French "Institut Universitaire Professionnalisé" (IUP)</footnote>

<footnote n="3">³LAAS is a laboratory depending on the CNRS, http://www.laas.fr</footnote>

<footnote n="4">⁴CNRS is the French National Center for Scientific Research, http://www.cnrs.fr</footnote>
despite the presence of obstacles. Thereby, it is necessary to preserve not only the robot safety (i.e. ensuring non-collision), but also the visibility of visual features to ensure the vision-based task feasibility. To achieve these aims, we have first proposed techniques able to fulfill simultaneously the mentioned objectives [ACT1, ACT2, ACT3]. However, avoiding both collisions and occlusions often over-strained the robotic navigation task, reducing the range of realizable missions. This is the reason why we have developed a second approach which let occurs the loss of the visual features if it is necessary for the success of the task. Using the link between vision and motion, we have proposed different methods (analytical and numerical) to compute the visual signal as soon it becomes unavailable [ACT4]. We have then applied them to perform vision-based tasks in cluttered environments, before highlighting their interest to deal with a camera failure during the mission [ACT4, ACT5].

In addition, during my doctorate degree, I also had the opportunity to perform teaching activities, first as temporary teacher (3 years), and then as teaching assistant, specifically in French as "Attaché Temporaire d'Enseignement et de Recherche" (ATER, 1 year), both for the Paul Sabatier University of Toulouse. These global teaching experiences have led to a total volume of 308 hETD<fnref n="5" />.

Between 2007 and 2008, I joined the Lagadic team at Inria<fnref n="6" /> Rennes-Bretagne Atlantique as a post-doctoral fellow on sensory control for unmanned aerial vehicles. My postdoctoral fellow has been supported by *Sensory Control for Unmanned Aerial Vehicles* (SCUAV) ANR project<fnref n="7" />. The main objective was to improve multi-sensor-based servoing tasks for unmanned aerial vehicles. The idea was to design robust control law that combine different sensory data directly at the control level. Especially, I have contributed to the design of a new online sensor self-calibration based on the sensor/robot interaction links [ACT6].

### I.2.2 Tenured as associate professor

In 2008, I was recruited as Associate Professor for the 61st CNU section<fnref n="8" /> at the Graduate Engineering School (ENSI) of Bourges, which is since 2014 the INSA Centre Val de Loire. The INSA Centre Val de Loire was established following the merger of the Val de Loire National Engineering School (ENIVL), Blois and ENSI of Bourges. The Institute was extended in 2015, when it absorbed the National Graduate School for Nature and Landscape, Blois. Like any INSA engineering school, the first two years are a preparatory cycle (L1 and L2) embedded in the Sciences and Techniques for Engineers (STPI) department. From the third to the fifth year, students are enrolled in one of the INSA Centre Val de Loire specialties to became engineer.

<footnote n="5">⁵Equivalent TD hours that is in French heures équivalentes TD (hETD), are the reference hours to calculate the teaching duties. (see also the index of terms and notations for further definition)</footnote>

<footnote n="6">⁶From French: Institut national de recherche en informatique et en automatique. https://www.inria.fr/centre/rennes</footnote>

<footnote n="7">⁷From French "Agence Nationale de la Recherche" (ANR), which is the French National Research Agency, http://www.agence-nationale-recherche.fr</footnote>

<footnote n="8">⁸From French "Conseil National des Université" (CNU), comprises 57 sections covering different scientific disciplines. The 61st section involves IT engineering, automation and signal processing. https://www.conseil-national-des-universites.fr</footnote>
<figure><img src="image_7.png" /><figcaption>**Figure I.1:** Timeline of main events and activities since tenure as Associate Professor. Further information on the different projects, and the supervisions are given in Chapter III.</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure I.2:** Teaching activities progress expressed in equivalent TD hours (hETD).</figcaption></figure>

Since my tenure, I have been regularly involved in the life of the Institute. I contribute at a local level to the scientific animations (e.g. organization of laboratory visits), transfer and training-research relationship. For instance, I regularly attend the international relations division by accompanying the different delegations of schools and universities partners during their visits. In March 2017, the direction of the INSA Centre Val de Loire given to me the mission of referent *racism and antisemitism*. Figure I.1 shows the relevant events related with my activities since tenured as associate professor.

As a lecturer, I am involved, among others, in the development of electronics and electrical sciences teaching activities within the Institute. In particular, I helped to develop all the teaching materials for these courses, tutorials and practices. Since tenured as associate professor, my average teaching load is about 272 hETD per year. Figure I.2 presents the evolution of my teaching duty since 2008. These teaching loads varied depending on the recruitment and the choice of engineering students in the different departments in which I teach. Furthermore, some key events in the life of the Institute have also influenced my teaching loads, as shown in Figure I.1. For instance, since 2012, after the ERE department creation, I have also started to form the apprentices engineers to electrical engineering. In parallel, I took part in the electronics training for the new preparatory cycle which became the Sciences and Techniques for Engineers (STPI) department.

Similarly, various responsibilities entrusted to me have also influenced my teaching duties. Since September 2014, I am in charge of the option entitled *Nuclear Energy* of the 5th year (engineer's degree, M2) of the Industrial Risk Control (MRI) department. Between 2017 and 2020, I have been elected as member of the council department of the Energy, Risks and Environment (ERE); and since November 2020 I am an elected member of the council department of Industrial Risk Control (MRI). Further information on my teaching activities and responsibilities are provided in Chapter II.
Furthermore, I carry out my research activities with the PRISME Laboratory in the Robotics team belonging to the Images, Robotics, Automatic control and Signal (IRAuS) department. The INSA Centre Val de Loire and University of Orléans are jointly responsible for PRISME Laboratory. The laboratory also has hosting agreement with the private School of High Studies in Engineering (HEI) located in Châteauroux. PRISME Laboratory seeks to carry out multidisciplinary research in the general domain of engineering sciences over a broad range of subject areas, including combustion in engines, energy engineering, aerodynamics, mechanics, image and signal processing, control and robotics. One of the specificity of the PRISME Laboratory is that it is spread over 3 departments of the administrative Region Centre Val de Loire, within a total of 7 sites. Within the IRAuS department, the Robotic team is mainly involved in robotics for biomedical and healthcare applications. Specifically, the Robotics team contributes to the development of methods, tools and techniques for the design and control of innovative robotic systems. To achieve these goals, the team comprised 10 researchers. The members of the Robotics team are spread over 3 cities: Bourges (5 with IUT and 2 with INSA Centre Val de Loire), Châteauroux (2) and Orléans (1).

Since I have been an associate professor, my field of scientific research mainly focused on the modeling and control for nano and micro-robots in a biomedical context. It should be noticed that since my PhD degree and post-doctoral fellow, I had to apply a slight evolution on my research topics to address the specificity of the microworld. Hence, during the first years of taking up my position, I deepened my understanding of microrobotics with a particular attention to their biomedical applications. Indeed, one of my first research activities have been mainly related with the European project NANOMA (see also Sections III.1.1 for further detail on projects). This project consisted of designing microrobotic system for targeted drug delivery through the cardiovascular system. Globally, my main contributions focus on the study of **magnetic medical microrobots** for targeted therapies, and this topic will be the common thread in the second part of this manuscript.

Meanwhile, I have also contributed to the development of micromanipulation activities of the laboratory. Firstly, the micromanipulation tasks have been devoted to intracytoplasmic applications [ACT10,ACL5]. Next, these research activities have evolved to micromanipulation of object to be placed in the focus of a light beam within the ANR project PIANHO and the PhD thesis of Nabil Amari [PhD3]. In parallel, I also contributed to projects more related to common robotics topic. Specifically, I have helped the Robotic team in the field of medical robotics with the development of a tele-echographic platform with the ANR project PROSIT [ACL8]; and in the field of mobile robotics with the ANR project PROTEUS. Thanks to the experience acquired in participating in these projects, I subsequently obtained the funding of the US-Probe and BUBBLEBOT project for which I am the principal investigator (PI). These different research projects in which I have been involved are reported in Figure I.1, and are presented in Section III.1. In addition, I have directly supervised the works of 5 Master and 6 PhD students, and I also had the opportunity to follow the research works of 3 external PhD students. Further information about these supervisions are given in Section III.2.

Since tenured in 2008, these various scientific activities have led to 47 publications, including<sup>9</sup> 15 articles (ACL), 1 guest editorial (DO), 3 books chapter (OS) and 23 proceedings (ACT). Figure I.3 illustrates the timeline progress of my publishing activities and the detailed list

<footnote n="9"><sup>9</sup>The bibliography categories follows the nomenclature proposed by the Hcéres which is an independent administrative authority for evaluation of research and higher education. http://www.hceres.fr</footnote>
<figure><img src="image_9.png" /><figcaption>**Figure I.3:** Personal references progress since tenure (see detail in Chapter IV).</figcaption></figure>

of my publications are given in the Chapter IV. My H-index is around 15 based on Google Scholar Citations<fnref n="10" /> (2021).

<footnote n="10">¹⁰See also my Google Scholar profile: http://scholar.google.com/citations?user=XQVc6JMAAAAJ</footnote>
CHAPTER II

---

TEACHING AND ADMINISTRATIVE
RESPONSIBILITIES

In this chapter, the different aspects related to my teaching activities are summarized. My overall teaching activities have been solely related with the 61st CNU section which regroups scientific disciplines from control, IT engineering and signal processing. I taught these teaching activities as a temporary teacher (3 years), teaching assistant (ATER, 1 year), and then as associate professor (since 2008). These different teaching experiences are presented in the following sections.

## II.1 BEFORE TENURE

I have started teaching as a temporary teacher at the Paul Sabatier University of Toulouse, France, during my doctorate (2004 – 2006). Next, I have pursued as teaching assistant, specifically in French as Attaché Temporaire d'Enseignement et de Recherche (ATER, 2007), at the Paul Sabatier University of Toulouse. My teachings were mainly in the fields of robotics, control theory, image processing and real-time systems for students from bachelor's to master degrees. These global teaching experiences have led to a total volume of 308 hETD.

These activities were my first experience in high-graduate education. Those opportunities highlighted my interest in the scientific knowledge transmission. They also allowed me to be familiarized with the different forms of teachings. Indeed, I had then the opportunity to supervise not only tutorials (TD), practical work (TP), and long-term projects (BE); but also few courses. Especially, I also helped the teaching team by writing some TP contents, and in the students' evaluation. This first experience confirmed my interest in teaching, leading me logically to apply for an associate professor position.

## II.2 SINCE TENURED

Until now, my teaching activities have been mainly held at INSA Centre Val de Loire on the Bourges campus. Thus, I am mainly involved in the students' formation of the MRI, ERE, and STPI departments. After having started with teaching of electronics and electrical engineering, I have participated or organized lessons on signal processing, sensors, control and robotics. These various teaching experiences imply very different pedagogical tasks. Especially, those tasks depend on the type of intervention: courses (C), tutorials (TD), practical works (TP), or tutored projects (P); but also according to the different degrees of scientific maturity and specialization of the concerned students: from bachelor's (L1) to
<table><caption>Table II.1: Overview of the various teaching disciplines as associate professor.</caption><thead><tr><th rowspan="2">Disciplines</th><th rowspan="2">LMD<sup>a</sup></th><th rowspan="2">Students<sup>b</sup></th><th colspan="3">Face time</th><th rowspan="2">Dept.</th><th rowspan="2">Years</th></tr><tr><th>C<sup>c</sup></th><th>TD</th><th>TP</th></tr></thead><tbody><tr><td>Electrokinetics</td><td>L1</td><td>100</td><td>18h00</td><td>24h00</td><td></td><td>STPI</td><td>2012-2014</td></tr><tr><td>Analog Electronics (I)</td><td>L2</td><td>80</td><td>8h00</td><td>32h00</td><td></td><td>STPI</td><td>2015-present</td></tr><tr><td>Analog Electronics (II)</td><td>L3</td><td>70</td><td>21h20</td><td>21h20</td><td>6h00</td><td>MRI</td><td>2008-2016</td></tr><tr><td>Analog Electronics (III)</td><td>L3</td><td>70</td><td>10h40</td><td>10h40</td><td></td><td>MRI</td><td>2015-present</td></tr><tr><td>Electrical engineering</td><td>L3</td><td>70</td><td>10h40</td><td>10h40</td><td></td><td>MRI</td><td>2008-2016</td></tr><tr><td>Electricity - Electrical engineering</td><td>L3</td><td>78</td><td>8h00</td><td>14h00</td><td></td><td>ERE</td><td>2016-present</td></tr><tr><td>Electricity - Electrical engineering</td><td>M1</td><td>78</td><td>8h00</td><td>14h00</td><td></td><td>ERE</td><td>2012-2016</td></tr><tr><td>Control and Sensors</td><td>M1</td><td>78</td><td>6h</td><td>9h</td><td></td><td>ERE</td><td>2014-2016</td></tr><tr><td>Control and Diagnostic</td><td>M1</td><td>20</td><td>10h40</td><td>10h40</td><td></td><td>MRI</td><td>2015-present</td></tr><tr><td>Signals and Systems</td><td>M1</td><td>20</td><td>10h40</td><td>10h40</td><td></td><td>MRI</td><td>2014-present</td></tr><tr><td>Perception for robotic</td><td>M2</td><td>25</td><td>4h</td><td></td><td></td><td>MARSS</td><td>2012-2018</td></tr><tr><td>Robotic</td><td>M2</td><td>50</td><td>9h</td><td>9h</td><td></td><td>MRI/3EA</td><td>2019-present</td></tr><tr><td>Students Projects (SA)</td><td>M1</td><td>2</td><td></td><td></td><td></td><td>MRI</td><td>2008-present</td></tr><tr><td>Students Projects (PSI)</td><td>M1</td><td>10</td><td></td><td></td><td></td><td>MRI</td><td>2008-present</td></tr></tbody></table>

master's (M2) degree level. For instance, it can be noticed, that the ERE department trains engineers through an apprenticeship training. Table II.1 illustrates a synthetic overview of the different teaching disciplines for which I am in charge. These responsibilities imply the implementation of teaching materials and the students evaluations, but also the support of teaching assistants (e.g. for the TD). As needed, I also intervened to support the teaching activities of some of my colleagues (e.g. for their TD).

A description of some of these disciplines are summarized hereafter.

**Analog electronics (I), (II) and (III):** The aim is to provide from basic to high level view of the elementary components that are the heart of electronic circuits. It deal with passive components such as resistors, capacitors and inductors as well as an introduction to diodes, transistors and operational amplifiers, and their use in filters, amplifiers, power supply circuits.

First taught to engineering students (L3) of ENSI of Bourges, this discipline has evolved since the creation of INSA Centre Val de Loire and is provided to the STPI (L2) and MRI (L3) departments. This allowed me to develop the teaching of analog electronics from the L3 level to more advanced electronics.

<footnote><sup>a</sup> LMD is the bachelor's, master's, doctorate system (in French License-Master-Doctorat) designed by the Bologna process, with L1-L3: from the 1st to the 3rd year bachelor's degree; M1-M2: from the 1st to the 2nd year master's degree.</footnote>

<footnote><sup>b</sup> the average number of students per year.</footnote>

<footnote><sup>c</sup> refer to face time hours for courses (C), tutorials (TD) and practical works (TP).</footnote>
**Electrical engineering:** After an introduction to fundamental concepts (e.g. electricity, single-phase and three-phase electric power, etc.), this teaching is supplemented by case studies. This allows engineering students to understand the use of tools and models to evaluate the performance of an electrical system, for diagnosis and help in the choice of more efficient and sustainable solutions.

**Robotics:** This course is intended for engineering students from the MRI department (M2) together with the international master degree on Electronics, Electrical Energy and Automatics (3EA) jointly with the University of Tours. This teaching, in English language, allows students to discover new fields of research and to take an interest in the modeling and control of mobile robots.

**Student Projects:**

* Advanced systems projects (SA): a pair have to work over a semester to study an advanced system, such as a microrobotic system, an electromagnetic actuation platform, etc.

* Industrial synthesis projects (PSI): a group of about ten students must divide the workload to study complex processes, such as the viscous flow in channels, the modeling of magnetic fields induced by electromagnetic coils...

## II.3 RESPONSIBILITIES

In addition to teaching tasks, various duties are related to associate professor position. First, I am involved in the life and the scientific animation of the Institute. I also participate in the juries of our engineering students. Similarly, since our establishment have joint the INSA group in 2014, I contribute to select and interview the applying students (about 15 students per year).

Between 2009 and 2013, I have been member of the Hygiene and Security committee of the of ENSI Bourges.

Since September 2014, I am in charge of the Nuclear Energy option of the 5 year (engineer's degree) of the Industrial Risk Control (MRI) department. As such, I coordinate the specific lessons of the option by selecting and recruiting external professional contractors. I also organize visits (nuclear power plant, simulator, etc.) for the engineering students of the option. Since 2018, I took part to panel discussions "support for nuclear training" and "nuclear-jobs-training" which have enabled participants to better understand issues about nuclear energy in France.

Between November 2017 and 2020, I have been an elected member of the ERE department council. Next, since 2020, I am an elected member of the Industrial Risk Control (MRI) department council.

In March 2017, the direction of the INSA Centre Val de Loire given to me the mission of referent "racism and antisemitism".
<figure><img src="image_10.png" /></figure>
CHAPTER III

SUMMARY OF RESEARCH ACTIVITIES

This chapter summarizes the different research activities in which I have been involved. This
includes research projects, student supervision, scientific collaborations, and outreach.

III.1 SCIENTIFIC PROJECTS

My research activities regularly lead me to contribute to scientific projects. These projects aim to obtain funds to either recruit young researchers, to design or improve our experimental platforms, as well as to help to enhance scientific cooperation. Below are listed the different projects in which I have been strongly involved, both in their implementation and in their achievements. Let us notice that all of these projects have been subject to a process with deep scientific reviews. The list of unsuccessful applications is equally important.

III.1.1 European Union (EU) and national funding projects

**NANOMA** Nano-Actuators and Nano-Sensors for Medical Applications

**Date** 06/2008 – 10/2011

**Funding** 3.3M€, supported by the European Commission under FP7 ICT 2007.3.6, Micro/nanosystems

**Summary** The NANOMA was coordinated by Professor Antoine Ferreira, University of Orléans, PRISME Laboratory. This project aimed at proposing novel controlled nanorobotic delivery systems to improve the diagnosis and the administration of drugs in the treatment of breast cancer.

**Role** co-responsible of the workpackage: "object tracking, planning and control in MRI".

**PROSIT** Robotic Platform for an Interactive Tele-echographic Systems

**Date** 01/2009 – 09/2012

**Funding** 230k€, supported by ANR Contint program

**Summary** The PROSIT project was coordinated by Professor Pierre Vieyres, University of Orléans, PRISME Laboratory. The goal was to develop an interactive and complex master-slave robotic platform for a medical diagnosis application (i.e. tele-echography) based on a well-defined modular control architecture.

**Role** co-responsible of the workpackage: "visual servoing".

**PROTEUS** Robotic platform to facilitate transfer between industries

**Date** 12/2009 – 12/2013

**Funding** 2.1M€, supported by ANR ARPEGE program

**Summary** The PROTEUS project motivation was to help to organize interactions between academic and industrial partners of the French robotic community by
providing suitable tools and models. One goal was to create a portal for the French robotic community as embodied by the GDR Robotique and its affiliated industrial partners, in order to facilitate transfer of knowledge and problems among this community. To achieve the PROTEUS project 12 partners have been involved.

**Role** co-responsible of the workpackage: “young challenge”.

**PIANHO** Innovative haptic instrumental platform for 3D nano-manipulation

**Date** 03/2010 – 03/2014

**Funding** 761k€, supported by ANR P3N program.

**Summary** The PIANHO project motivation is to create a nanMANipulation platform capable of pick, hold and place nano-objects in the synchrotron radiation beam of the ESRF<fnref n="1" /> (Grenoble, France) via tuneable tool-object interaction.

**Role** co-responsible of the workpackage: “control of a two-fingered AFM-based nano-manipulation system”.

**MTG** Microrobots Targeting Glioblastoma (MTG)

**Date** 03/2019 – 03/2022

**Funding** 511.4k€, supported by French National Institute of Health and Medical Research<fnref n="2" /> (Inserm) “plan cancer” program

**Summary** The MTG objective is to functionalize magnetic microrobot with NFL peptide<fnref n="3" /> to target glioblastoma (GBM).

**Role** co-responsible of the workpackage: “*in vitro* and *in vivo* distribution and tracking studies using IVIS imaging system to test the capacity of MTG to target glioblastoma cells versus healthy cells of the nervous system”.

### III.1.2 Cooperation projects

**PHC PROCOPE** Franco-German Hubert Curien<fnref n="4" /> partnership (PHC)

**Date** 2010 – 2011

**Summary** Supervision and control of an improved platform for targeted administration of therapeutic Nanorobots.

**Partnership** Division of Microrobotics and Control Engineering<fnref n="5" /> (AMiR), university of Oldenburg, Germany.

**PHC PROCORE** Franco-Hong-Kong Hubert Curien partnership

**Date** 2014 – 2015

**Summary** Design, fabrication and characterization of the swim of enhanced helical microrobots.

**Partnership** Department of Mechanical and Automation Engineering<fnref n="6" /> (MAE), Chinese university of Hong-Kong (CUHK).

<footnote n="1">¹European Synchrotron Radiation Facility (ESRF), https://www.esrf.eu</footnote>

<footnote n="2">²from French: Institut national de la santé et de la recherche médicale (INSERM), https://www.inserm.fr</footnote>

<footnote n="3">³NeuroFilament Light subunit that is binding Tubulin (NFL peptide) is capable to penetrate in GBM, block and inhibit cell division.</footnote>

<footnote n="4">⁴PHC, from French Partenariats Hubert Curien, provides support for international scientific and technological exchange of the Ministry of Foreign Affairs. https://www.campusfrance.org</footnote>

<footnote n="5">⁵AMiR, that is from German Abteilung für Mikrorobotik und Regelungstechnik, is a department of the University of Oldenburg, Germany, headed by Prof. Dr.-Ing. Sergej Fatikov. http://www.amir.uni-oldenburg.de</footnote>

<footnote n="6">⁶MAE is a department of the Chinese University of Hong Kong, with A.Prof. Li Zhang. http://www.mae.cuhk.edu.hk</footnote>
### III.1.3 Regional projects

#### Nano-IRM

**Date** 09/2009 – 08/2012

**Funding** 110k€, supported by Région Centre Val de Loire, the Cher (18) departmental councils and the agglomeration comity of Bourges.

**Summary** Supervision and control of an improved platform for targeted administration of therapeutic nanorobots. This project supports the above project NANOMA, by providing the funding for the PhD thesis of **Karim Belharet**.

**Role** co-supervision of the PhD thesis of **Karim Belharet**.

#### MicroRob

**Date** 10/2013 – 09/2016

**Funding** 110k€, supported by Région Centre Val de Loire and the agglomeration comity of Bourges.

**Summary** Modeling and control of magnetic microcarrier for targeted cancer therapy.

**Role** co-supervision of the PhD thesis of **Lyes Mellal**.

#### US-Probe High Definition Echograph

**Date** 03/2017 – 03/2018

**Funding** 50k€, supported by Région Centre Val de Loire (APR-IA)

**Summary** Design of novel microrobotic platform with ultrasound imaging.

**Role** Principal Investigator (PI).

#### BUBBLEBOT Magnetic microbubbles for the targeted delivery of therapeutic agent in the brain

**Date** 10/2020 – 10/2023

**Funding** 210k€, supported by Région Centre Val de Loire (APR-IR)

**Summary** The aim is to combine the progress made in microrobotics with those made with microbubbles in order to improve the therapeutic targeting of glioblastoma.

**Role** Principal Investigator (PI).

## III.2 STUDENT SUPERVISION

My research work was carried out with the contributions of young researchers whose works I supervised. I had directly supervised 5 Master (M2) and 6 PhD students. The total rate of supervision of defended PhD theses is 200%. In addition, I also had the opportunity to follow the research works of 3 externals PhD students. These different students are listed hereafter, as well as the joint publications.

### III.2.1 Master students (M2)

#### Kamel Ncir

**Date** 03/2010 – 08/2010

**Title** Commande robuste pour le nano-positionnement d'une plateforme instrumentale.

**Situation** Technician at Jubilant HollisterStier LLC, Montréal, Québec, Canada

#### Nabil Amari

**Date** 03/2011 – 08/2011

**Title** Modélisation et Commande d'une plateforme de nano positionnement

**Situation** Associate Professor HEI, Châteauroux, France
**Bruno Sarkis**

**Date** 03/2015 – 08/2015

**Title** Modélisation des microjets catalytiques dans des canaux micro-fluidiques

**References** [ACT22, ACL14]

**Hadjila Mahfoufi**

**Date** 03/2018 – 08/2018

**Title** Modélisation, Simulation et Commande de Microrobot Catalytique

**Situation** Engineer at Alstom, Paris, France

**Oumarou HABOU SOULE**

**Date** 03/2019 – 09/2019

**Title** Suivi de Microrobot par Imagerie Echographique

### III.2.2 Doctoral students

#### III.2.2.1 Defended theses

**[PhD1] Tao Li**

**Date** 03/2009 – 02/2013

**Title** Commande d'un robot de télé-échographie par asservissement visuel. Thesis of university of Rennes 1

**Supervision** 37.5% with Prof. Pierre Veyres (12.5%), François Chaumette (12.5%) and Alexandre Krupa (37.5%)

**References** [ACL8]

**Situation** Engineer at Another Brain, Paris, France

**[PhD2] Karim Belharet**

**Date** 10/2009 – 07/2013

**Title** Navigation prédictive d'un microrobot magnétique : Instrumentation, commande et validation. Thesis of university of Orléans

**Supervision** 50% with Prof. Antoine Ferreira

**References** [ACT8, ACT9, ACT12, ACT14, ACT17, ACT19, ACT21, ACL2, ACL3, ACL6, OS2]

**Situation** Associate Professor HEI, Châteauroux, France

**[PhD3] Nabil Amari**

**Date** 10/2011 – 07/2016

**Title** Développement et Commande d'une Plateforme Microrobotique pour la Synchro-nisation d'un Faisceau de Lumière. Thesis of university of Orléans

**Supervision** 30% with Prof. Antoine Ferreira

**References** [ACT15, ACT16, ACT18, ACT20, ACL7, OS3]

**Situation** Associate Professor HEI, Châteauroux, France

**[PhD4] Lyès Mellal**

**Date** 10/2013 – 12/2016

**Title** Modélisation et commande de microrobots magnétiques pour le traitement ciblé du cancer. Thesis of university of Orléans

**Supervision** 40% with Prof. Antoine Ferreira (30%) and Karim Belharet (30%)

**References** [ACT23, ACT24, ACT25, ACT27, ACL9, ACL12]

**Situation** Teaching assistant at ISEN, Lille, France
[PhD5] Ruipeng Chen

**Date** 11/2016 – 07/2020

**Title** Design Methodology for Electromagnetic Microrobotic Platforms. Thesis of INSA Centre Val de Loire

**Supervision** 50% with Prof. Antoine Ferreira

**References** [ACT27,ACT28,ACT29,ACL15]

**Situation** Post Doctorate, INSA CVL, Bourges, France

### III.2.2.2 Ongoing thesis

[PhD6] Karim Botros

**Date** 04/2021 – 03/2024

**Title** Magnetic Micro-robotic Platform Guided by Robotic Ultrasound for Brain Tumor Targeting. Thesis of INSA Centre Val de Loire

**Supervision** 50% with Prof. Antoine Ferreira

### III.2.2.3 External PhD students

[Ext1] Junsig Kim

**Date** 2008 – 2012

**Title** A Study of Oocyte/Embryo Manipulation Using Microfluidics and Robotics. Thesis of Korea Advanced Institute of Science and Technology (KAIST), South Korea

**References** [ACT10,ACL5]

**Situation** Senior Research Engineer at LG Electronics, South Korea

[Ext2] Christian Dahmen

**Date** 2009 – 2013

**Title** Robust Object Tracking for Micro- and Nanorobotics. Thesis of Carl von Ossietzky Universität Oldenburg

**References** [ACT11,ACT13,ACL11]

**Situation** Dr. Ing. at Carmeq GmbH, Berlin, Germany

[Ext3] Jang Bumjin

**Date** 2015 – 2016

**Title** Magnetic Nano Actuators for Quantitative Analysis. Thesis of ETH Zurich, Switzerland

**References** [ACL10]

**Situation** Engineer at Samsung Electronics, South Korea

## III.3 SCIENTIFIC COLLABORATIONS

My research works have led to various international and national collaborations. These cooperations have made possible to investigate complementary approaches to those I have studied, helping me to benefit from supplementary skills. These exchanges were important in view of the strong multidisciplinary of the achieved works, the variety of physical principles used, and the technologies involved. Hereafter some significant collaborations and partnerships that have resulted in either joint publications or that are still ongoing.
### III.3.1 International relationships

* Department of Mechanical Engineering at Korea Advanced Institute of Science and Technology (KAIST), South Korea

- Team of Prof. Jung Kim

- References: [ACT10, ACL5]

* Division of Microrobotics and Control Engineering (AMiR), university of Oldenburg, Germany

- Team of Prof. Sergej Fatikow

- References: [ACT11, ACT13, ACL11]

* Multi-Scale Robotics Laboratory<fnref n="7" /> (MSRL), ETH<fnref n="8" /> Zurich, Switzerland

- Team of Prof. Bradley Nelson and Prof. Salvador Pané Vidal

- References: [ACT11, ACL10]

* Mechanical and Automation Engineering (MAE) Department of Chinese University of Hong Kong (CUHK), Hong-Kong.

- Team of Prof. Li Zhang

### III.3.2 National relationships

* Inria Rennes-Bretagne Atlantique, IRISA, University of Rennes, France

- Team of senior researcher François Chaumette

- Co-supervision of the PhD thesis of **Tao Li**.

- Reference: [ACL8]

* Translational micro and nanomedicines<fnref n="9" /> (MINT) Laboratory, University of Angers, France

- Team of senior researcher Joël Eyer

* Center for Molecular Biophysics<fnref n="10" /> (CBM), CNRS, Orleans, France

- Team “Innovative therapies and nanomedicine” with Prof. Chantal Pichon

* Vermon<fnref n="11" /> SA, Tours, France

- R&D work on development and industrialization to enhance micro-object perception through ultrasound transducers.

## III.4 SCIENTIFIC DISSEMINATION AND OUTREACH

The appreciation of my research works have been effective through various actions that are reported hereafter.

<footnote n="7">⁷Multi-Scale Robotics Lab (MSRL) is part of Institute of Robotics and Intelligent Systems (IRIS), ETH Zurich, Switzerland. https://msrl.ethz.ch, https://www.iris.ethz.ch</footnote>

<footnote n="8">⁸ETH Zurich is the Swiss Federal Institute of Technology in Zurich, from German "Eidgenössische Technische Hochschule". https://ethz.ch</footnote>

<footnote n="9">⁹From French "Laboratoire Micro et Nanomédecines translationnelles", is funded by the University of Angers, as well as Inserm and the CNRS. http://mint.univ-angers.fr</footnote>

<footnote n="10">¹⁰CBM is a research unit of the CNRS affiliate with the University of Orléans. http://cbm.cnrs-orleans.fr</footnote>

<footnote n="11">¹¹Vermon is a society involved in the design, manufacturing of composite piezoelectric transducer. https://www.vermon.com</footnote>
### III.4.1 Invitations

**June 2010** scientific visit in the AMiR division, university of Oldenburg, Germany

**March 2015** scientific visit in MAE Department of Chinese University of Hong Kong (CUHK), Hong-Kong.

**Others** I have also been invited as a speaker in international or national conferences, [INV1,INV2,INV3] which are reported in Section IV.4.1.

### III.4.2 Scientific expertise

* I have took part in the evaluation process of Generic Call (2019,2020) for the French National Research Agency (ANR).

* I have been member of the recruitment selection committee:

- 2013: associate professor position at University of Orléans;

- 2015: associate professor position at INSA Centre Val de Loire;

- 2021: associate professor position at INSA Centre Val de Loire;

* In addition to the PhD works that I co-supervised, I was also invited as an examiner member of the PhD thesis defense of:

1. Adrien Durand Petiteville, Navigation référencée multi-capteurs d'un robot mobile dans un environnement encombré, university of Toulouse, December, 2011.

2. Moahmed Dkhil, Modélisation, caractérisation et commande d'un système micro-robotique magnétique à l'interface air/liquide, University of Pierre and Marie Curie, Paris, April, 2016

### III.4.3 Editorial activities

**Since 2005** IEEE member (SM'05, AM'08, M'12).

**Since 2013** Editorial Board member of the International Journal of Advanced Robotic Systems (IJARS).

**Since 2015** Member of the program committee of the International Conference on Robotics, Manipulation, and Automation at Small Scales (MARSS)

**2012 Oct.** Session chairman of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Vilamoura, Algarve, Portugal, October 2012

**2021** Associate Editor of the 18th International Conference on Ubiquitous Robots, Gangneung-si, Gangwon-do, Korea, 2021.

**Regular Reviewer** (non-exhaustive list)

* IEEE Transactions on Robotics (TRO);

* IEEE robotics and automation letters (RAL);

* IEEE Transactions on Biomedical Engineering (TBME);

* IEEE/ASME Transactions on Mechatronics (TMECH);

* IEEE Transactions on Automation Science and Engineering (TASE);

* International Journal of Advanced Robotic Systems (IJARS);

* IEEE International Conference on Robotics and Automation (ICRA);

* IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS);

* IEEE International Conference on Biomedical Robotics and Biomechatronics (BioRob), ...
### III.4.4 Awards

French outstanding research award (PEDR) for the periods 2014-2018 and 2018-2022.
My research activities have led to scientific publications that are listed in this chapter. The names of the people for whom I have supervised their works are in **bold face**. Furthermore, the publications list follows the Hcéres proposed nomenclature.

IV.1 ARTICLES

IV.1.1 Articles in International peer-reviewed and referenced journals
(ACL)

**Remark (Remark) —** \iffalse{} Remark (Metrics). Two journal metrics are reported here: journal quartile (Qn) and impact factor (IF). Journal metrics are based on Scopus® data as of April 2020. The reported quartile is the metric of the journal in the year of publishing.

[ ]

[ACL1] David FOLIO, and Viviane Cadenat. "Dealing with visual features loss during a vision-based task for a mobile robot", *International Journal of Optomechatronics*, 2 (3): pp. 185-204, June 2008. doi:10.1080/15599610802301110. Special issue on Visual Servoing. (Q2, IF:0.81)

[ACL2] Karim Belharet, David FOLIO, and Antoine Ferreira. "MRI-based microrobotic system for the propulsion and navigation of ferromagnetic microcapsules", *Mini-mally Invasive Therapy & Allied Technologies*, 19 (3): pp. 157-169, June 2010. doi:10.3109/13645706.2010.481402. (Q2, IF:1.0)

[ACL3] Karim Belharet, David FOLIO, and Antoine Ferreira. "Three-dimensional controlled motion of a microrobot using magnetic gradients", *Advanced Robotics*, 25 (8): pp. 1069-1083(15), May 2011. doi:10.1163/016918611X568657. (Q2, IF:1.24)

In 2013 one of the Advanced Robotics most cited articles from 2011 publications.

[ACL4] Viviane Cadenat, David FOLIO, and Adrien Durand Petiteville. "A comparison of two sequencing techniques to perform a vision-based navigation task in a cluttered environment", *Advanced Robotics*, 26 (5-6): pp. 487-514, March 2012. doi:10.1163/156855311X617470. (Q2, IF:1.24)

[ACL5] Jungsik Kim, Hamid Ladjal, David FOLIO, Antoine Ferreira, and Jung Kim. "Evaluation of telerobotic shared control strategy for efficient single-cell manipulation", *IEEE Transactions on Automation Science and Engineering*, 9 (2): pp. 402-406, April 2012. doi:10.1109/TASE.2011.2174357 (Q1, IF:4.93)

[ACL6] Karim Belharet, David FOLIO, and Antoine Ferreira. "Simulation and planning of a magnetically actuated microrobot navigating in arteries", *IEEE Transactions on Biomedical Engineering*, 60 (4): pp. 994-1001, April 2013. doi:10.1109/TBME.2012.2236092. (Q1, IF:4.42)
[ACL7] **Nabil Amari**, David FOLIO, and Antoine Ferreira. "Motion of a micro/nanMANIPULATOR using a laser beam tracking system", *International Journal of Optomechatronics*, 8 (1): pp. 30–46, April 2014. doi:10.1080/15599612.2014.890813 (Q3, IF:0.81)

[ACL8] Alexandre Kruba, David FOLIO, Cyril Novales, Pierre Vieyres, and Tao Li. "Robotized tele-echography: an assisting visibility tool to support expert diagnostic", *IEEE Systems Journal*, 10 (3): pp. 974–983, April 2014. doi:10.1109/JSYST.2014.2314773 (Q2, IF:3.98)

[ACL9] **Lyes Mellal**, Karim Belharet, David FOLIO, and Antoine Ferreira. "Optimal structure of particles-based superparamagnetic microrobots: application to MRI guided targeted drug therapy", *Journal of Nanoparticle Research*, 17 (2): 64, February 2015. doi:10.1007/s11051-014-2733-3 (Q2, IF:2.13)

[ACL10] **Bumjin Jang**, Wei Wang, Samuel Wiget, Andrew Petruska, Xiangzhong Chen, Chengzhi Hu, Ayoung Hong, David FOLIO, Antoine Ferreira, Salvador Pané, and Bradley Nelson. "Catalytic locomotion of core-shell nanowire motors", *ACS Nano*, 10 (11): pp. 9983–9991, November 2016. doi:10.1021/acsnano.6b04224 (Q1, IF:14.58)

[ACL11] **Christian Dahmen**, Karim Belharet, David FOLIO, Antoine Ferreira, and Sergej Fatikow. "MRI-based dynamic tracking of an untethered ferromagnetic microcapsule navigating in liquid", *International Journal of Optomechatronics*, 10 (2): pp. 73–96, April 2016. doi:10.1080/15599612.2016.1166305 (Q3, IF:0.81)

[ACL12] **Lyes Mellal**, David FOLIO, Karim Belharet, and Antoine Ferreira. "Modeling of optimal targeted therapies using drug-loaded magnetic nanoparticles for the liver cancer", *IEEE Transactions on Nano-Bioscience*, 15 (3): pp. 265–274, April 2016. doi:10.1109/TNB.2016.2535380 (Q2, IF:2.79)

[ACL13] David FOLIO and Antoine Ferreira. "2D robust magnetic resonance navigation of a ferromagnetic microrobot using pareto optimality", *IEEE Transactions on Robotics*, 33 (3): pp. 583–593, 2017. doi:10.1109/TRO.2016.2638446 (Q1, IF:6.12)

[ACL14] **Bruno Sarkis**, David FOLIO and Antoine Ferreira. Catalytic "Tubular Microjet Navigating in Confined Microfluidic Channels: Modeling and Optimization". *IEEE/ASME Journal of Microelectromechanical Systems*, 27 (2): pp.333–343, April 2018. doi:10.1109/JMEMS.2018.2803803 (Q1, IF:2.53)

[ACL15] **Ruipeng Chen**, David FOLIO, and Antoine Ferreira. "Mathematical Approach for the Design Configuration of Magnetic System with Multiple Electromagnets". *Robotic and Autonomous Systems*, 135: p. 103674, 2020. doi:10.1016/j.robot.2020.103674 (Q1, IF:2.82)

[ACL16] **Lyes Mellal**, David FOLIO, Karim Belharet, and Antoine Ferreira. "Modeling and Characterization of Deformable Soft Magnetic Microrobot for Targeted Therapy", *IEEE Robotics and Automation Letters*, vol. 6, no. 4, pp. 8293–8300, Oct. 2021, doi: 10.1109/LRA.2021.3107102 (Q1, IF:3.74)

IV.1.2 Articles in unreferenced journals (ACLN)

[ACLN1] David FOLIO. Les innovations en microrobotique pour le biomédical. *Prospective et Stratégie*, APORS Éditions, 7 (1): pp. 69–78, 2017. doi:10.3917/pstrat.007.0069

IV.2 BOOKS
IV.2.1 Guest Editor (DO)

[DO1] Ashis Banerjee, David FOLIO, Sarthak Misra and Quan Zhou. Guest editors of the Special Issue: “Design, Fabrication, Control, and Planning of Multiple Mobile Microrobots”. *International Journal of Advanced Robotic Systems*, 2014. doi:10.5772/1

IV.2.2 Book Chapter (OS)

[OS1] David FOLIO and Viviane Cadenat. *Treating Image Loss by using the Vision/Motion Link: Generic Framework*, chapter 4, page 538. I-Tech, Vienna, Austria, November 2008. ISBN 978-953-7619-21-3.

[OS2] **Karim Belharet**, David FOLIO, and Antoine Ferreira. *Real-time software platform for in vivo navigation of magnetic micro-carriers using MRI system*, chapter 11. Number 51 in Biomaterials. Woodhead Publishing, Cambridge, October 2012. ISBN:780857091307.

[OS3] **Nabil Amari**, David FOLIO, and Antoine Ferreira. *Encyclopedia of Nanotechnology*, chapter Nanorobotics for Synchrotron Radiation Applications, pp. 1–19. Springer Netherlands, Dordrecht, 2nd edition, 2016. doi:10.1007/978-94-007-6178-1009270-1

[OS4] **Lyès Mellal**, Karim Belharet, David FOLIO, and Antoine Ferreira. *Modeling Approach of Transcatheter Arterial Delivery of Drug-Loaded Magnetic Nanoparticles*, chapter 10. in The Encyclopedia of Medical Robotics. World Scientific, October 2018. ISBN: 780857091307. doi:10.1142/9789813232280_0010

IV.3 PROCEEDINGS IN INTERNATIONAL CONFERENCES (ACT)

[ACT1] David FOLIO and Viviane Cadenat. Using redundancy to avoid simultaneously occlusions and collisions while performing a vision-based task amidst obstacles. In *European Conference on Mobile Robots (ECMR'05)*, Ancona, Italy, September 2005.

[ACT2] David FOLIO and Viviane Cadenat. A controller to avoid both occlusions and obstacles during a vision-based navigation task in a cluttered environment. In *European Control Conference (ECC'05)*, pages 3898–3903, Seville, Spain, December 2005.

[ACT3] David FOLIO and Viviane Cadenat. A redundancy-based scheme to perform safe vision-based tasks amidst obstacles. In *IEEE/RSJ International Conference on Robotics and Biomimetics (ROBIO'06)*, pages 13–18, Kunming, Yunnan, China, December 2006. doi:10.1109/ROBIO.2006.340252.

Finalist to the T.J. Tarn best paper in Robotics.

[ACT4] David FOLIO and Viviane Cadenat. A new controller to perform safe vision-based navigation tasks amidst possibly occluding obstacles. In *European Control Conference (ECC'07)*, Kos, Greece, July 2007.

[ACT5] David FOLIO and Viviane Cadenat. Using simple numerical schemes to compute visual features whenever unavailable. In *IFAC International Conference on Informatics in Control, Automation and Robotics (ICINCO'07)*, May 2007.

[ACT6] David FOLIO and Viviane Cadenat. A sensor-based controller able to treat total image loss and to guarantee non-collision during a vision-based navigation task. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2008)*, pages 3052–3057, Nice, France, September 2008. doi:10.1109/IROS.2008.4650743.
[ACT7] Olivier Kermorgant, David FOLIO, and François Chaumette. A new sensor self-calibration framework from velocity measurements. In *IEEE International Conference on Robotics and Automation (ICRA'2010)*, pp. 1524-1529, Anchorage, Alaska, May 2010. doi:10.1109/ROBOT.2010.5509219

[ACT8] Karim Belharet, David FOLIO, and Antoine Ferreira. 3D MRI-based predictive control of a ferromagnetic microrobot navigating in blood vessels. In *IEEE RAS and EMBS International Conference on Biomedical Robotics and Biomechatronics (BioRob'2010)*, pp. 808-813, Tokyo, Japan, September 2010. doi:10.1109/BIOROB.2010.5628063

[ACT9] Karim Belharet, David FOLIO, and Antoine Ferreira. Endovascular navigation of a ferromagnetic microrobot using MRI-based predictive control. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2010)*, pp. 2804-2809, Taipei, Taiwan, October 2010. doi:10.1109/IROS.2010.5650803

[ACT10] Jungsik Kim, Dongjune Chang, Hamid Ladjal, David FOLIO, and Antoine Ferreira and Jung Kim. Evaluation of telerobotic shared control for efficient manipulation of single cells in microinjection. In *IEEE International Conference on Robotics and Automation (ICRA'2011)*, pp. 3382-3387, Shanghai, China, May 2011. doi:10.1109/ICRA.2011.5979868

[ACT11] David FOLIO, Christian Dahmen, Tim Wortmann, M. Arif Zeeshan, Kaiyu Shou, Salvador Pane, Bradley J. Nelson, Antoine Ferreira, and Sergej Fatikow. MRI magnetic signature imaging, tracking and navigation for targeted micro/nano-capsule therapeutics. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2011)*, pp. 1297-1303, San Francisco, CA, USA, September 2011. doi:10.1109/IROS.2011.6048651

[ACT12] Karim Belharet, David FOLIO, and Antoine Ferreira. Control of a magnetic microrobot navigating in microfluidic arterial bifurcations through pulsatile and viscous flow. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2012)*, pp. 2559-2564, Vilamoura, Algarve, Portugal, October 2012. doi:10.1109/IROS.2012.6386030

[ACT13] Christian Dahmen, David FOLIO, Tim Wortmann, Alexander Kluge, Antoine Ferreira, and Sergej Fatikow. Evaluation of a MRI based propulsion/control system aiming at targeted micro/nano-capsule therapeutics. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2012)*, pp. 2565-2570, Vilamoura, Algarve, Portugal, October 2012. doi:10.1109/IROS.2012.6386244

[ACT14] Karim Belharet, David FOLIO, and Antoine Ferreira. Untethered microrobot control in fluidic environment using magnetic gradients. In *International Symposium on Optomechatronic Technologies (ISOT'2012)*, pp. 1-5, October 2012.

[ACT15] Nabil Amari, David FOLIO, and Antoine Ferreira. Robust laser beam tracking control using micro/nano dual-stage manipulators. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2013)*, pp. 1543-1548, Tokyo Big Sight, Japan, November 2013. doi:10.1109/IROS.2013.6696554

[ACT16] Nabil Amari, David FOLIO, Karim Belharet, and Antoine Ferreira. Motion of a micro/nanMANIPULATOR using a laser beam tracking system. In *International Symposium on Optomechatronic Technologies (ISOT'2013)*, Jeju Island, Korea, October 2013.

[ACT17] Karim Belharet, Yang Chunbo, David FOLIO, and Antoine Ferreira. Model characterization of magnetic microrobot navigating in viscous environment. In *International*
*Symposium on Optomechatronic Technologies (ISOT'2013)*, Jeju Island, Korea, October 2013.

[ACT18] **Nabil Amari**, David FOLIO, and Antoine Ferreira. Robust tracking of a two-fingered micromanipulation system working through the focus of an optical beam. In *American Control Conference (ACC'2014)*, pp. 1613–1618, Portland, OR, USA, June 2014. doi:10.1109/ACC.2014.6859244

[ACT19] **Karim Belharet**, David FOLIO, and Antoine Ferreira. Vision-based forces characterization of magnetic microrobot in a viscous environment. In *IEEE International Conference on Robotics and Automation (ICRA'2014)*, pp. 2065–2070, Hong Kong, China, May 2014. doi:10.1109/ICRA.2014.6907133

[ACT20] **Nabil Amari**, David FOLIO, and Antoine Ferreira. Robust nanMANipulation control based on laser beam feedback. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2014)*, pp. 4674–4679, Chicago, IL, USA, September 2014. doi:10.1109/IROS.2014.6943226

[ACT21] **Karim Belharet**, David FOLIO, and Antoine Ferreira. Study on rotational and unclogging motions of magnetic chain-like microrobot. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2014)*, pp. 834–839, Chicago, IL, USA, September 2014. doi:10.1109/IROS.2014.6942656

[ACT22] **Bruno Sarkis**, David FOLIO, and Antoine Ferreira. Catalytic tubular microjet propulsion model for endovascular navigation. In *IEEE International Conference on Robotics and Automation (ICRA'2015)*, pp. 3537–3542, Seattle, Washington, USA, May 2015. doi:10.1109/ICRA.2015.7139689

[ACT23] **Lyes Mellal**, David FOLIO, Karim Belharet, and Antoine Ferreira. Magnetic microbot design framework for antiangiogenic tumor therapy. In *IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'2015)*, pp. 1397–1402, Hamburg, Germany, September 2015. doi:10.1109/IROS.2015.7353550

[ACT24] **Lyes Mellal**, David FOLIO, Karim Belharet, and Antoine Ferreira. Optimal control of multiple magnetic microbeads navigating in microfluidic channels. In *IEEE International Conference on Robotics and Automation (ICRA'2016)*, pp. 1921–1926, Stockholm, Sweden, May 2016. doi:10.1109/ICRA.2016.7487338

[ACT25] **Lyes Mellal**, David FOLIO, Karim Belharet, and Antoine Ferreira. Estimation of interaction forces between two magnetic bolus-like microrobots. In *International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS'2016)*, pp. 1–6, Paris, France, July 2016. doi:10.1109/MARSS.2016.7561740

[ACT26] **Lyes Mellal**, David FOLIO, Karim Belharet, and Antoine Ferreira. Motion control analysis of two magnetic microrobots using the combination of magnetic gradient and oscillatory magnetic field. In *International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS'2017)*, pp. 1–6, Montreal, QC, Canada, July 2017. doi:10.1109/MARSS.2017.8001917

[ACT27] **Ruipeng Chen**, David FOLIO, and Antoine Ferreira. Study of robotized electromagnetic actuation system for magnetic microrobots devoted to minimally invasive ophthalmic surgery, in *International Symposium on Medical Robotics (ISMR'2019)*, pp. 1–7, Atlanta, GA, USA, April 2019. doi:10.1109/ISMR.2019.8710208

[ACT28] **Ruipeng Chen**, David FOLIO, and Antoine Ferreira. Computational Electromagnetics Performances of Magnetic Microrobotics Systems, in *International Conference on Robotics and Automation (ICRA'2019)*, Montreal, QC, Canada, May 2019. doi:10.1109/ICRA.2019.8794092
[ACT29] **Ruipeng Chen**, David FOLIO, and Antoine Ferreira Performance Metrics for a Robotic Actuation System using Static and Mobile Electromagnets, in *IEEE International Conference on Computational Electromagnetics (ICCEM'2019)*, pp. 1-3, Shanghai, China, July 2019. doi:10.1109/COMPEM.2019.8778897

## IV.4 ORAL COMMUNICATIONS

### IV.4.1 Invited Speaker in International or National Conferences (INV)

[INV1] David FOLIO. Bio-nanorobotics: A reality for tomorrow? Invited speaker in International R&D Symposium: "biology and communications", Madrid, Spain, March 2012. Fundación Ramón Areces.

[INV2] David FOLIO. Micro/nano-robots thérapeutique pour le traitement cibler du cancer. Invited speaker in Colloque International: "Quelles nanotechnologies pour la médecine", Rabat, Morocco, November 2014.

[INV3] David FOLIO. Innovation en microrobotique pour le biomédical. Invited speaker in Colloque "les futurs de l'innovation", Bourges, France, June 2015. Prospective et Stratégie.

### IV.4.2 Communications in International or National Conferences (COM)

[COM1] David FOLIO and Viviane Cadenat. A method to safely perform a visually guided navigation task amidst occluding obstacles. Presented in the 7th International Workshop on Electronics, Control, Modelling, Measurement and Signals (ECMS'2005), May 2005.

[COM2] David FOLIO évitement d'obstacles et gestion des occultations durant une tâche de navigation référencée vision. Presented in the 6ème Congrès des doctorants EDSYS (EDSYS'05), May 2005.

[COM3] David FOLIO and Viviane Cadenat. Gestion des problèmes d'occultation et de collision durant une tâche référencée vision. Poster presentes in Journées Nationales de la Recherche en Robotique (JNRR'05), October 2005.

[COM4] David FOLIO and Viviane Cadenat. Dealing with visual features occlusions and collisions during a vision-based navigation task in cluttered environments. Presented in the 8th International Workshop on Electronics, Control, Modelling, Measurement and Signals (ECMS'2007), May 2007.

[COM5] **Nabil Amari**, David FOLIO, and Antoine Ferreira. Robust tracking of a two-fingered nanomanipulation system working through the focus of a X-ray beam. Presented in the Workshop on Automation of Assembly and Packaging at the Micro/Nano-scale, Trieste, Italy, August 2011.

[COM6] David FOLIO and Antoine Ferreira. Endovascular navigation of magnetic microcarriers using a MRI system. Presented in the Workshop on Magnetically Actuated Multiscale Medical Robots, Vilamoura, Algarve, Portugal, October 2012.

[COM7] David FOLIO. Dynamic Modeling Of Self-phoretic Magnetic Janus Microrobot. Presented in the Special session Control of bio-hybrid & bio-inspired microrobotic systems of the International Conference on Manipulation, Automation and Robotics at Small Scales (MARSS'2019), Helsinki, Finland, June 2019.
# APPENDIX
<figure><img src="image_11.png" /></figure>
# APPENDIX A

THREE-DIMENSIONAL CONTROLLED MOTION OF
A MICROROBOT USING MAGNETIC GRADIENTS
(ACL3)
# Three-Dimensional Controlled Motion of a Microrobot using Magnetic Gradients

Karim Belharet, David Folio, Antoine Ferreira

► To cite this version:

Karim Belharet, David Folio, Antoine Ferreira. Three-Dimensional Controlled Motion of a Micro-robot using Magnetic Gradients. Advanced Robotics, Taylor & Francis, 2011, 25 (8), pp.1069-1083. 10.1163/016918611X568657. hal-00619080

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# 3D Controlled Motion of a Microrobot using Magnetic Gradients

Karim Belharet,

David Folio

and Antoine Ferreira

Institut PRISME, ENSI de Bourges, 88 boulevard Lahitolle, 18020 Bourges, FRANCE;

{karim.belharet, david.folio, antoine.ferreira} @ensi-bourges.fr

## Abstract

This paper presents an endovascular navigation of a ferromagnetic microdevice using MRI-based predictive control. The concept was studied for future development of microrobot designed to perform minimally invasive interventions in remote sites accessible through the human cardiovascular system. A system software architecture is presented illustrating the different software modules to allow 3D navigation of a microdevice in blood vessels, namely: (i) vessel path extraction, (ii) magnetic gradient steering, (iii) tracking and (iv) closed-loop navigation control. First, the navigation path of the microrobot into the blood vessel is extracted using Fast Marching Method from the pre-operation images (3D MRI imaging) to guide the microrobot from the injection point to the tumor area through the anarchic vessel network. Based on the pre-computed path, a Model Predictive Controller is proposed for robust time-multiplexed navigation along a 3D path in presence of pulsative flow. The simulation results suggest the validation of the proposed image processing and control algorithms.

**keywords:** Microrobot, gradient controlled motion, endovascular navigation

## 1 INTRODUCTION

Microrobots designed to perform targeted therapy by navigating in the cardiovascular system are a prolific research area for minimally invasive surgeries [1][2] and treatments efficiency through early diagnosis of diseases [3]. When microrobots are propelled in the body fluids, especially in the blood circulatory system, a very large number of remote locations in the human body become accessible. Because the method of propulsion should allow such a microrobot to navigate through the cardiovascular system, the use of the normal blood flow itself must be considered only as a complementary means of propulsion when the travel path is along the direction of the blood flow. These untethered microrobots have been mainly developed according to three different designs: magnetic bead pulling [2], biomimetic flagellated robot [4] and magnetotactic bacteria [5]. Furthermore, navigation requires observation of the scene in order either to plan the trajectory by off-line mapping, or to correct on-line the microrobot's pose error between the planned and the observed trajectory. Recently, magnetic resonance imaging (MRI)-based medical microrobotic platforms are investigated to reach locations deep in the human body while enhancing targeting efficacy using real-time navigational and trajectory control [6]. For the position recognition of the microrobot in the blood vessels, from the pre-operation images, 3D path planning and route optimization
solutions have been proposed. The authors in [7] proposed an endovascular path-planning method based on 3D potential fields and enhanced breath-first search algorithms based on MR-imaging. Based on these path-planning techniques, only explorative 2D control strategies have been adopted so far using simple proportional-integral-derivative (PID) controller [8]. However, stability and robustness are not ensured against important perturbations. First, pulsatile flow should be taken into account since variations in waveform, amplitude, and frequency exists from vessels. Second, variation of time-multiplexed sequence parameters (duty cycle of the propulsion gradients, and repetition time of the tracking sequence) produce important trajectory errors during real-time navigation. Finally, random imaging signal noise degrades the localization of the microrobot during tracking.

The main objective of this paper is to propose an automated technique based on image processing and control algorithms for path finding, reconstruction and navigation control of a ferromagnetic microrobot using the MRI system. The MRI-based control of a ferromagnetic microcapsule presented here is dedicated to macroscale navigation, which focuses in conveying a microsphere radius of 300 µm in vessels, such as arteries and arterioles (eg, around 10 to 0.5 mm), as close as possible to the tumor area. Based on slice images provided by an MRI system, relevant information related to detection of blood vessels is extracted using robust Frangi vesselness filtering from the pre-operation images. Then, a set of minimal path is predefined, using Fast Marching Method (FMM), to guide the ferromagnetic microrobot from the injection point to a targeted area through the anarchic vessel network. Based on the precomputed path, a Model Predictive Controller (MPC) is designed. Hence, we proposed a control strategy for robust time-multiplexed navigation along a 3D path even in presence of pulsative flow. The simulation results suggest the validation of the proposed image processing and control algorithms against perturbations.

# 2 MRI-based NAVIGATION SYSTEM

## 2.1 System Overview

The Magnetic Resonant Imaging (MRI)-based microrobotic system is used here for propulsion and navigation of the microdevice. The propulsion of the ferromagnetic microcapsule in the cardiovascular system is realized through the induction of force from magnetic gradients provided by the MRI. This MRI system will guide the microcapsule in vivo through vascular networks to a targeted area. The overview of the software system architecture is given in Fig. 1.

(i) The graphical user interface module, which comprises input command prompt, 3D-visualization, and process supervision tools. (ii) The control module, which comprises (a) the high-level controller responsible for the microcapsule navigation tasks and for the generation of the magnetic field gradients and (b) the low-level controller (manufacturer MRI controller) responsible for the generation of the desired field gradients and for the image acquisition tasks. Then, (iii) the controlled hardware, which comprises (a) the MRI hardware and software systems and (b) the microcapsules that have been injected within the vasculature and are steered by the magnetic gradients. Finally, (iv) the image processing module, which comprises the MRI data rendering, the navigation path extraction, and the microdevice recognition/tracking algorithm. In particular, the tracking
procedure, presented in [9], allows to estimate the position and accumulation of the microdevices within the vasculature, the tissues, and the organs of the human. However as MR-imaging is too slow to gather position of the microrobot and special MR-tracking algorithm, such as MR-SET, must considered to ensure real time control.

## 2.2 Navigation in blood vessels

In our context, the problem of navigation in blood vessels within the MRI data can be formulated as finding the correct way through the data that follows the vessel of interest between its start and end points. Finding a navigation path within the endovascular network is then an essential, primary, and important step that must be addressed prior to the control procedure. The problem of vessels extraction has received considerable attention in the computer vision and medical imaging communities [10]. Hence, several class of methods have been proposed to find a path from a set of medical imaging, such as using tracking methods [11] [6] [12], path extraction methods [13][14][15], and so on. Most works based on in vivo MR-tracking methods usually need many user-defined way points as the input of a controller module for the navigation computation. A major drawback in general remains when the user must define many points (e.g. way or fiducial points) manually. Hence, for a complex structure (e.g. colon, small vessels...) the required interactivity can be very tedious. The path extraction is useful for a range of application domains including medical image analysis, robot navigation, and artificial intelligence. The path extraction technique needs a very simple initialisation and leads to global minimum of a snake-like energy, thus avoiding local minima. Moreover, it is fast and accurate. This path finding problem has been studied for ages by mathematicians, and has been solved numerically using graph theory or dynamic programming. Cohen and Kimmel [16] solved the minimal path problem in 2D with a front propagation equation between the two fixed end points, using the Eikonal equation (that physically models wave-light propagation), with a given initial front. Wink et al. [14] explored different methods to determine the minimum cost path through a pre-defined cost image, for extraction of vessel centrelines from medical image data. Among them are Dijikstra's algorithm, the A\* algorithm, which makes use of additional heuristics to steer the search process, and wave front propagation analysis [15]. Early, Sethian [17] explored the use of Fast Marching Method (FMM) to extract minimal paths. This method relies on the fact that the gradient of the FMM arrival function has only one local minimum, which is guaranteed to be global minimum [13]. Therefore, the minimal path can be extracted by back-propagating from given seeds (e.g. the end point of the desired path) to the starting point implicitly embedded in the arrival function.

In this work the FMM is adopted to design a set of paths to guide the microdevice from the injection point to the tumor area through the vessel network. Our aim is to focus on the automation of the path construction, reducing the need of interaction and improving performance, in a robust way.
# 3 MRI-BASED PREDICTIVE CONTROL

## 3.1 Problem formulation

Navigation in blood vessel requires observation of the scene in order either to plan the path by offline mapping, or to correct online the microrobot pose error between the planned and the observed path. To insure a smooth conveyance of the microcapsule to destination, collisions and the risk to be trapped by the endothelium, optimal navigation performance will be affected by external perturbations and MRI technological constraints:

* Nonnegligible pulsatile flow, whose variations in waveform, amplitude, and frequency exist from one vessel to another (such as arteries and arterioles).

* Magnetic gradients are used both for observation and control purposes in a time-multiplexed sequence. It requires different trade-offs in terms of refresh rate, duty cycle of the propulsion gradients, and repetition time of the tracking sequence.

* MRI overheating avoidance leading to limitations on the MRI duty cycle, tends to increase the dispropor- tional scaling between magnetic forces used for control purpose and perturbation forces (drag forces and net buoyancy forces).

* Limitations on the magnetic gradient amplitude in available MRI devices.

* Proper delay in the image processing algorithms that renders the navigation control unstable.

## 3.2 Real-Time Sequence Design

The overall concept of the in-vivo MRI-tracking system is based on the fact that both tracking and propulsion is possible with the gradient coils of the MRI system. Software based upgrading of a clinical MRI system is the least expensive approach to convert a platform that is used for imaging to an effective interventional platform. At any instant only one of the functions could be applied (i.e. either tracking or propulsion), but both will be executed over the same MRI interface. The MRI interface has therefore to be shared and a time-division-multiple-access scheme for it has to be developed. Fig. 2 shows an overview of the real-time sequence with time-multiplexed positioning and propulsion phases introduced by Martel et al. [6]. The main aspect relevant to the controller's performance is (i) the duty cycle $T_{Prop}/T_s$ that stands for the ratio between the propulsion time and the time between two successive position requests, and (ii) the synchronization event delay $T_{Sync}$ that stands for the minimum time allowed for image processing and real-time control feedback. First, the duty cycle should be adapted to apply sufficient magnetic propulsion gradients during a predefined propulsion time $T_{Prop}$ to prevent the microrobot from drifting away from the path. Second, a large time delay $T_{Sync}$ produces oscillations as the microrobot approaches the reference path w leading to position instabilities. Such limitations have been pointed out by Mathieu et al. [8] when implementing simple proportional-integral-derivative (PID) controller. We proposed a Model Predictive Controller (MPC) including microrobot's motion and dynamics with estimation of the pulsative blood flow and time-multiplexed positioning. A predictive path-tracking control consider a prediction window (cf. Fig. 2). The
propulsion phase starts during $T_{Prop}$ seconds at the same initial condition as the prediction phase, recording the performance of the system according to a prediction horizon. After this phase the system ends after a imaging-propulsion sequence at a final position Y which is set as the new initial condition of the next prediction output $\hat{Y}$. The proposed navigation based predictive controller offers stability by design and allows the designer to trade-off performance for (computation) speed, stability margins according to the MRI application and technological requirements outlined in section 3.1.

### 3.3 Model description

The linear model used in this work is derived from the nonlinear model developed in a previous study [18]. The authors used this model to combine the backstepping controller and high-gain observer in order to control the path of the microrobot inside a vessel using the MRI gradients.

The different forces acting on the microrobot are (see Fig. 3): drag force $\vec{F}_d$, apparent weight $\vec{W}_a$ and magnetic force $\vec{F}_m$. The application of Newton's third law and the projection on the $(\vec{x}, \vec{y}, \vec{z})$ axes leads to:

$$ 
\left\{ 
\begin{aligned}
m\ddot{x} &= \vec{F}_{dx} + \vec{F}_{mx} \\
m\ddot{y} &= \vec{F}_{dy} + \vec{F}_{my} \\
m\ddot{z} &= \vec{F}_{dz} + \vec{F}_{mz} + \vec{W}_a
\end{aligned}
\right. 
\qquad (1) $$

where m is the mass of the microrobot modeled by a ferromagnetic sphere with a high saturation magnetization.

Let $\vec{v} = (v_{fx}, v_{fy}, v_{fz})$ denotes the blood flow velocity, and $(x, y, z)$ the robot location in the blood vessel wrt. to a given frame $\mathcal{F}(O, \vec{x}, \vec{y}, \vec{z})$. Taking the drag coefficient $C_d = \frac{24}{Re}$, the linear model can be written as follow:

$$ 
\left\{ 
\begin{aligned}
\ddot{x} &= \alpha_1 (\dot{x} - v_{fx}) + \alpha_2 u_x \\
\ddot{y} &= \beta_1 (\dot{y} - v_{fy}) + \beta_2 u_y \\
\ddot{z} &= \gamma_1 (\dot{z} - v_{fz}) + \gamma_2 u_z
\end{aligned}
\right. 
\qquad (2) $$

with the following parameters $\alpha_i, \beta_i$ and $\gamma_i$, and the magnetic gradients considered as control inputs $u_x, u_y$ and $u_z$, that is:

$$ 
\left\{ 
\begin{aligned}
\alpha_1 &= -4.5 \frac{\eta \cos \varphi \cos \theta}{r^2 \rho}, & u_x &= \| \vec{\nabla} B_x \| \\
\beta_1 &= -4.5 \frac{\eta \cos \varphi \sin \theta}{r^2 \rho}, & u_y &= \| \vec{\nabla} B_y \| \\
\gamma_1 &= -4.5 \frac{\eta \sin \varphi}{r^2 \rho}, & u_z &= \| \vec{\nabla} B_z \| \\
\alpha_1 &= \beta_2 = \gamma_2 = \frac{m}{\rho}
\end{aligned}
\right. 
\qquad (3) $$

where $\rho$ is the density of the fluid; $\eta$ is the fluid viscosity; $r$ is the spherical radius of the microrobot; and $\mathbf{B} = (B_x, B_y, B_z)^T$ is the magnetic field generated by the MRI system.

Finally, the state-space representation is deduced from (2):

$$ 
\left( S \right) 
\left\{ 
\begin{aligned}
\dot{x} &= v_x \\
\dot{v}_x &= \alpha_1 v_x - \alpha_1 v_{fx} + \alpha_2 u_x \\
\dot{y} &= v_y \\
\dot{v}_y &= \beta_1 v_y - \beta_1 v_{fy} + \beta_2 u_y \\
\dot{z} &= v_z \\
\dot{v}_z &= \gamma_1 v_z - \gamma_1 v_{fz} + \gamma_2 u_z
\end{aligned}
\right\} 
\qquad (4) $$
where $(v_x, v_y, v_z)^T$ denotes the robot velocity along $\vec{x}$-axis, $\vec{y}$-axis and $\vec{z}$-axis. Assuming that the microrobot location $(x, y, z)$ can be measured thanks to the MRI system, we denote by $Y = (x, y, z)^T$ the process measure. We can notice that system $(S)$ can be divided into three subsystems $(S_x)$, $(S_y)$ and $(S_z)$, which allow us to define three independent MPC schemes to track the reference path $w$ in 3D MRI data.

In this paper, we aim to use the system model defined in (4) in a high level MPC scheme in order to follow efficiently a pre-planned path extracted with the method proposed in section 2.2. The proposed MPC controller is intended to embed the low level robust controller designed in [18][19] (see Fig. 4). Let us notice that the low level controller provides<fnref n="1" /> robustness performances against MRI system constraints (as pulsatile flow, limited gradient amplitude, and image noise) while the MPC controller is designed to tradeoff time-multiplexed sequence constraints in terms of refresh-rate, duty cycle of the propulsion gradients, and repetition time of the tracking sequence.

## 3.4 Predictive Control

Model Predictive Control (MPC) has become an area of significant research interest over the last past twenty years. This interest has been powered by a stream of successful industrial applications [21]. When focusing on linear (and unconstrained) discrete time transfer function models and quadratic cost functions, some of the best known approaches include the Generalized Predictive Control (GPC) introduced by Clarck et al. [22], and the inner loop stabilizing Stable Predictive Control [23].

MPC refers to a class of computer control algorithms which use an explicit process model to predict the future response of the system. One way to design MPC is to use an extended state-space representation, which is given by:

$$ \begin{cases} \dot{X}_{k+1} = AX_k + B\Delta u_k \\ Y_k = CX_k \end{cases} \qquad (5) $$

where $\Delta u_k = u_k - u_{k-1}$ is the discrete difference operator. The predicted state vector at time $k+i$ is then computed from [24]:

$$ \hat{X}_{k+i|k} = A^i X_{k|k-1} + \sum_{j=0}^{i-1} A^j B u_{k-j-1} \qquad (6) $$

Then, the future outputs $Y_{k+j|k}$ can be computed based on the plant for future times starting at time $k$ using a recursion procedure, defined by:

$$ \hat{Y}_{k+i|k} = C \left( A^i X_k + \sum_{j=1}^{i} A^{i-j-1} B u_{k+i-j|k} \right) \qquad (7) $$

Design criterion is defined for certain interval of predictions (several steps to future). It includes the part of control error, in which the model of system is covered (insertion of equations of prediction (7)) and the part of control actions, where the input energy (control actions) is weighted. This part redistributes control errors to individual steps of predictions and provides coupling within intervals of predictions. Usual form of the criterion

<footnote n="1">¹The interested reader is invited to refer to [18][19][20].</footnote>
for predictive design is written as follows:

$$J_k = \sum_{j=N_1+1}^{N_2} [Y_{k+j} W_{k+j}^T Q_Y Y_{k+j} W_{k+j}] + \sum_{j=1}^{N_u} [u_{k+j-1}^T Q_u u_{k+j-1}] \quad (8)$$

The criterion is expressed in step k. $N = N_2 - N_1$ is a horizon of prediction, $N_u$ is the control horizon. $Q_Y$ and $Q_u$ are output and input penalizations. $Y_{k+j}$ and $u_{k+j-1}$ are output and input (full or incremental) values.

Finally, let us note how to construct real control actions at incremental algorithm: after computing a vector for whole horizon, only first control $u_k$ is used; then to obtain the full control actions the second line of equation (5) is applied.

When using MPC in the state-space formulation, and generally at the use of whichever state-space control, it is necessary to solve the question of availability of the state of the system (state vector). If it is not available, and only system output from the measurement are known, then some state-space estimation has to be considered. Suitable well-known solution of such estimation is the state-space observer based on Kalman filter.

# 4 Results

## 4.1 Navigation Path Extraction

The FMM algorithm, introduced by Sethian [17] is applied here to extract a targeted navigation path within the vessel network. From the set of 3D MRI data, a speed map is computed (ie. a weighting image map) in order to enhance the relevant intravascular network. Choosing an appropriate and efficient image cost function is the most difficult part of the entire process.

We describe in the sequel presented in Fig. 5, the process used to extract the navigation path. First, we need a relevant cost function which allow to enhance vessel in the image. To this aim, we used some a priori knowledge about vessel shape and intensity in MRI data (cf. Fig. 5). Vessels are expected to appear as bright tubular structures in a darker environment. One way to account for the varying size of vessels is by multiscale analysis. It allows us to detect structures of different sizes according to the scale at which they give maximal response. In this context, a typical speed image is produced by using a Frangi vesselness filter [25] which uses the eigenvectors of the Hessian matrix at each voxel of the image to compute the likeliness of an image region to vessels. This mapping is selected in such a way that vessels regions will have higher speed (high level in speed image, see Fig. 5). Once the speed map is generated, the user has to select a start and end points (ie. seed points) in the viewer of the input original image. The FFM will then propagate a front from the start seed and traveling to the targeted area, thanks to the speed map. Thus, this approach allow to find a minimal navigation path between the start and targeted seed (cf. Fig. 5).

## 4.2 Microdevice Navigation using Predictive Control

Simulations conducted here are performed within the scope of actual commonly spread MRI system abilities. Actually, MRI systems are able to generate magnetic gradients with an intensity of some tens of mT.m⁻¹. Let us note that this limitation is additionally affected by the gradient coils duty-cycle and by the time-multiplexing
sequence ($T_{Prop}/T_s$) needed both for controlling and observing sequences. In order to make sure that the amplitude of the control inputs remains bounded by physical actuators limits $u_{i,max}$, and to protect the system, we applied a simple time-scaling factor defined by $\frac{u_i}{k(t)}$, with $k(t) = \max\{1, \frac{u_i}{u_{i,max}}\}$. The following set of simulations corresponds to a microcapsule radius of $r = 300$ µm and a time scaling settled at $k(t) = 0.55$. Different situations are considered to illustrate and to validate the performance of the proposed MRI-based predictive controller.

We validated the proposed control strategy on a 3D endovascular navigation path $w$ extracted from MRI-data with the previously presented method without any disturbance. Then, to evaluate the efficiency of the proposed MRI-based predictive controller, we performed some tests with a white Gaussian noise on the system output measure $Y$. The noise is about 10% of the measured signal which is motivated by the common precision of clinical MRI devices.

Fig. 6 describes the navigation path followed by the microrobot, and Fig. 7 presents the relative error norm between the current position $Y$ and the reference $w$, for a time horizon $N = 5$. As shown, the system output $Y$ follows perfectly the reference path $w$. In particular, the microdevice is able to reach quickly the navigation path, in spite of a gap between the initial position $Y$ and the reference $w$. Let us notice that the 3D tracking is not too much affected by the Gaussian noise since position standard deviation (STD) and root mean square (RMS) error are quite satisfactory.

Fig. 8 simulates the impact of the time horizon $N$ on the system tracking error for optimized time horizon values between $3 \le N \le 10$. Comparing the error statistics, the nature of anticipation of the MPC scheme is well illustrated - important values of $N$ improve greatly the anticipation nature of the path behavior but increases at the same time the path tracking error-. Hence, a great value of $N$ does not necessarily guarantee good performances, and classically increase the complexity of the scheme.

To evaluate the robustness of our control strategies, we have also applied an external disturbance which represent the pulsatile blood flow behavior.

Hence, we have modeled the blow flow as a time-sinusoidal profile with spatial parabolic form $\sigma_{flow}(t)$. In case of an artery, to model the action of flow (positive) and reflux of blood (negative) $\sigma_{flow}(t)$ were shifted up, leading to:

$$ \sigma_{flow}(t) = 0.025 \left( 1 + 1.15 \sin \left( 2\pi t + \frac{\pi}{8} \right) \right) \qquad (9) $$

where amplitude of 0.025 is representative of maximum blood flow speed. In the following, the performance and stability of the predictive controller with respect to physiological parameters variations are demonstrated in Fig. 9. It appears that the system is robust to uncertain physiological parameters (disturbance applied at $t = 13$ seconds) since the 3D position tracking error norm is bounded to 0.2%.

Finally, we have evaluated the robustness of our controller for different duty cycle values: 25%, 50% and 75%, respectively. The error curves and statistics for the three scenario are illustrated on Fig. 10. As one can see for a duty cycle of 50%, that is the MRI system propels during the first half-period, and acquires 3D images on the other half-period, the path tracking is quite satisfactory. It corresponds to the real-time navigational and trajectory control constraints reported in [8]. Nevertheless for a duty cycle of 25% (ie. the MRI propels during 1/4 period, and image during 3/4 period) the microrobot can not properly track the reference path $w$ leading
to great tracking error. The time-multiplexing duty cycle is optimized for a value around 40 %. In the optimal case, the simulated predictive behavior of the MPC controller suggests better tracking results compared to those obtained by [8] that should be confirmed by experimentation.

# 5 CONCLUSIONS

The proposed MRI-based ferromagnetic microcapsule steering and navigation strategy has been developed at milli and microscale, where endovascular navigation path extraction and predictive controller have been designed. The main drawback of MRI-based navigation stems from the strong limitations on the magnetic gradient amplitude of available MRI devices. As magnetic forces used for propelling are volumetric, whereas the drag force is at best dependent on the microcapsule's area, the smaller the capsule, the higher the required control forces with respect to hydrodynamic perturbations. Consequently, this approach is well conditioned for beads whose radius is up to a few dozen micrometers with actual MRI devices. Targeting aims at focusing these microcarriers and stopping them through embolization at the arterioles entry close to the occluded blood vessels. Possible releasing mechanisms could rely on biodegradable polymer and techniques used in hyperthermia where aggregates of nanocapsules can be heated to melt polymer. Such a solution is actually under experimentation for validation of the proposed minimally invasive MRI-based microrobotic system.

# 6 ACKNOWLEDGMENTS

This work was supported by European Union's 7th Framework Program and its research area ICT-2007.3.6 Micro/nanosystems under the project NANOMA (Nano-Actuators and Nano-Sensors for Medical Applications). The PhD student K. Belharet is supported by the Nano-IRM project, funded by Conseil Général du Cher and Agglomération de Bourges.

# References

[1] K. Ishiyama, M. Sendoh, and K. I. Arai, "Magnetic micromachines for medical applications," *J. of Magnetism and Magnetic Materials*, vol. 242-245, pp. 41-46, 2002.

[2] J. Abbott, Z. Nagy, F. Beyeler, and B. Nelson, "Robotics in the Small," *IEEE Robot. Automat. Mag.*, p. 92, 2007.

[3] T. A. Cavalcanti, B. Shirinzadeh and S. Ikeda, "Nanorobot for Brain Aneurysm," *Int. J. of Robotic Research*, vol. 28, no. 4, pp. 558-570, 2009.

[4] B. Behkam and M. Sitti, "Design methodology for biomimetic propulsion of miniature swimming robots," *ASME J. Dyn. Syst. Meas. Control*, pp. 36-43, 2006.
[5] S. Martel, M. Mohammadi, O. Felfoul, Z. Lu, and P. Pouponneau, "Flagellated magnetotactic bacteria as controlled MRItrackable propulsion and steering systems for medical nanorobots operating in the human microvasculature," *Int. J. Robot. Res.*, vol. 28, no. 4, pp. 571–582, 2009.

[6] O. Felfoul, J. Mathieu, G. Beaudoin, and S. Martel, "In vivo MR-tracking based on magnetic signature selective excitation," *IEEE Trans. Med. Imag.*, vol. 27, no. 1, pp. 28–35, Jan. 2008.

[7] W. Sabra, M. Khousam, and S. Martel, "Use of 3D potential field and an enhanced breath-first search algorithms for path-planning of microdevices propelled in the cardiovascular system," in *27th IEEE EMBS Annual Int. Conf.*, Shangai, China, 2005, pp. 91–100.

[8] S. Tamaz, A. Chanu, J.-B. Mathieu, R. Gourdeau, and S. Martel, "Real-time mri-based control of a ferro-magnetic core for endovascular navigation," *IEEE Trans. Bio-Med. Eng.*, vol. 55, no. 7, pp. 1854–1863, July 2008.

[9] T. Wortmann, C. Dahmen, and S. Fatikow, "Study of MRI susceptibility artifacts for nanomedical applications," *Journal of Nanotechnology in Engineering and Medicine*, vol. 1, no. 4, p. 041002, 2010.

[10] C. Kirbas and F. Quek, "A review of vessel extraction techniques and algorithms," *ACM Comput. Surv.*, vol. 36, no. 2, pp. 81–121, 2004.

[11] P. Reuzé, J. Coatrieux, L. Luo, and J. Dillenseger, "A 3D moment based approach for blood vessel detection and quantification in MRA," *Technology and Health Care*, vol. 1, pp. 181–188, 1993.

[12] J. Tokuda, G. S. Fischer, S. P. DiMaio, D. G. Gobbi, C. Csoma, P. W. Mewes, G. Fichtinger, C. M. Tempany, and N. Hata, "Integrated navigation and control software system for mri-guided robotic prostate interventions," *Computerized Medical Imaging and Graphics*, vol. 34, no. 1, pp. 3–8, 2010.

[13] T. Deschamps, "Curve and shape extraction with minimal path and level-sets techniques: Applications to 3d medical imaging," Ph.D. dissertation, University of Paris Dauphine, 2001.

[14] O. Wink, W. J. Niessen, and M. A. Viergever, "Minimum cost path determination using a simple heuristic function," *Int. Conf. on Pattern Recognition*, vol. 3, p. 7010, 2000.

[15] O. Wink, W. Niessen, B. Verdonck, and M. Viergever, "Vessel axis determination using wave front propagation analysis," *Medical Image Computing and Computer-Assisted Intervention*, vol. 2208, pp. 845–853, 2001, lecture Notes in Computer Science.

[16] L. Cohen and R. Kimmel, "Global minimum for active contour models: A minimal path approach," *Int. J. of Computer Vision*, vol. 24, no. 1, pp. 57–78, 1997.

[17] J. A. Sethian, *Level set methods and fast marching methods*. Cambridge University Press, 1999.

[18] L. Arcèse, M. Fruchard, and A. Ferreira, "Nonlinear modeling and robust controller-observer for a magnetic microrobot in a fluidic environment using MRI gradients," in *IEEE/RSJ Int. Conf. on Intel. Robots and Systems*, St. Louis, MO, USA, Oct. 2009, pp. 534–539.
[19] L. Arcese, A. Cherry, M. Fruchard, and A. Ferreira, "High gain observer for backstepping control of a mri-guided therapeutic microrobot in blood vessels," in *IEEE/RAS-EMBS Int. Conf. on Biomedical Robotics and Biomechatronics*, Tokyo, Japan, Sep. 2010, pp. 349–354.

[20] L. Arcese, A. Cherry, M. Fruchard, and A. Ferreira, "Dynamic behavior investigation for trajectory control of a microrobot in blood vessels," in *IEEE/RSJ Int. Conf. on Intel. Robots and Systems*, Taipei, Taiwan, Oct. 2010, pp. 5774–5779.

[21] S. Qin and T. Badgwell, "A survey of industrial model predictive control technology," *Control engineering practice*, vol. 11, no. 7, pp. 733–764, 2003.

[22] D. Clarke, C. Mohtadi, and P. Tuffs, "Generalized predictive control – Part I & II," *Automatica*, vol. 23, pp. 137–160, 1987.

[23] B. Kouvaritakis, J. Rossiter, and A. Chang, "Stable generalised predictive control: an algorithm with guaranteed stability," *IEE Proceedings Part D Control Theory and Applications*, vol. 139, no. 4, pp. 349–362, 1992.

[24] E. Camacho and C. Bordons, *Model predictive control*. Springer Verlag, 2004.

[25] A. Frangi, W. Niessen, K. Vincken, and M. Viergever, "Multiscale vessel enhancement filtering," *Lecture Notes in Computer Science*, pp. 130–137, 1998.
<figure><img src="image_12.png" /><figcaption>Figure 1: Overall system overview.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 2: Timeline of acquisition and control prediction.</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 3: Forces applied on microrobot navigating in blood vessel.</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>Figure 4: MRI-based Predictive Control strategy.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 5: 3D Navigation path extraction processing: a) Original MRI data; b) Computed cost function using Frangi filter (here displayed in red volume); c) Extracted navigation path between the start and end seeds using FFM.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Figure 6: 3D MRI-based microrobot endovascular navigation (N = 5, in mm).</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>Figure 7: 3D tracking error: $||Y - w||$ for N = 5.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>Figure 8: Tracking error statistics for different time horizons N.</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>Figure 9: MRI-based navigation with blood flow disturbance.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Figure 10: Tracking error with different values of duty cycle.</figcaption></figure>
# APPENDIX B

## SIMULATION AND PLANNING OF A
MAGNETICALLY ACTUATED MICROROBOT
NAVIGATING IN ARTERIES (ACL6)
# Simulation and Planning of a Magnetically Actuated Microrobot Navigating in Arteries

Karim Belharet, David Folio, Antoine Ferreira

<figure><img src="image_22.png" /></figure>

## To cite this version:

Karim Belharet, David Folio, Antoine Ferreira. Simulation and Planning of a Magnetically Actuated Microrobot Navigating in Arteries. IEEE Transactions on Biomedical Engineering, Institute of Electrical and Electronics Engineers, 2013, 60 (4), pp.994-1001. 10.1109/TBME.2012.2236092. hal-00767787

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# Simulation and Planning of a Magnetically Actuated Microrobot Navigating in the Arteries

Karim Belharet, David Folio, *Member, IEEE*, and Antoine Ferreira, *Member, IEEE*

***Abstract***—This work presents a preoperative microrobotic surgical simulation and planning application. The main contribution is to support computer-aided minimally invasive surgery (MIS) procedure using untethered microrobots that have to navigate within the arterial networks. We first propose a fast interactive application (with endovascular tissues) able to simulate the blood flow and microrobot interaction. Secondly, we also propose a microrobotic surgical planning framework, based on the anisotropic Fast Marching Method (FMM), that provides a feasible pathway robust to biomedical navigation constraints. We demonstrate the framework performance in a case study of the treatment of peripheral arterial diseases (PAD).

***Index Terms***—Microrobotics, minimally invasive surgery, blood flow simulation, anisotropic path planning.

## I. INTRODUCTION

PREOPERATIVE surgical simulation and planning is a critical stage in medical decision-making and in the design of novel microrobotic minimally invasive surgery (MIS) techniques [1,2]. Due to the lack of anatomic consistency, preoperative planning with virtual and physical models of the system could improve the chances of achieving predictable intraoperative results. To this aim, it is mandatory to cope with potential conflicts between the intervention purposes of the microrobotic surgical system and the biological laws governing the patient body. To improve microrobotic MIS procedure significant progress has been made in three dimensional (3D) imagers [3]; modeling software for anatomy and vascular networks representation [4]; and biomechanical modeling of interactions between tissues and MIS tools. These advances have been mainly developed for catheter or guidewire-based operations [5,6], or gastrointestinal endoscopic capsules [7,8]. In contrast, there has been fewer works in the area of untethered microrobots for cardiovascular interventions [1,9]. To date, even in the case of a successfully performed procedure, the choice of a microrobot's design (shape, size, materials, locomotion abilities...) plays a key role. Indeed, these factors affect the microrobot propulsion that depends mainly on the motile, fluidic and friction forces between the endovascular device and the vessel. Therefore, the development of training applications or interactive planning systems, where the robotician or physician is able to design different microrobots and then test their behaviors in a patient-specific context, will be very helpful. A few applications focusing on interventional MIS have been developed or commercialized [10,11] until now. These applications include interactive models of catheters [5], endoscopic capsules [7], but do not address

the challenging topic of modeling untethered microrobots [12] and their complex interactions with the blood flow and vessels walls [1]. Most proposed solutions use finite element modeling (FEM)-based representations, or computational fluid dynamics (CFD) simulations. Such approaches are suitable when accurate modeling or simulation are a primary concern. However, they usually rely on commercial software (such as Fluents or Comsol), and the computation time (usually in hours) is incompatible with interactive simulation or clinical practice. Moreover, planning a reliable and feasible path against the blood flow and vessel networks constraints is an important issue to be addressed for innovative microrobot-aided MIS applications. For instance, S. Martel et al. propose to use potential fields and the breadth-first search algorithm to find a pre-planned path [13] which are then delimited by waypoints [9]. A first drawback in such discrete graph-search algorithms is that they suffer from metrication errors [14]. Moreover, it is difficult to cope explicitly with the anisotropy. Finally, most untethered microrobot propulsion schemes based on magnetic pulling have to face important constraints related to coils technology. The planned path has to reduce the maximum pulling gradients being applied to the coils, the operation time and to maintain the rising temperature of the coils within operating limits. It actually impacts different endovascular magnetic actuation systems based on Magnetic Resonance Navigation (MRN) [9], or Octomag system [15]. Thus, the planned pathway must satisfy these considerations to be reliable.

This work aims to propose a preoperative microrobotic surgical planning application with blood flow simulation that may use patient-specific data. In particular, the computer-aided optimization of the untethered microrobots for innovative MIS procedure is the main focus of our work. First, in Section II, after introducing the system model used by the microrobotic surgical simulation, we present the surgical planning framework. The proposed framework is based on the Fast Marching Method (FMM) [16]. In our previous work [17,18], the classical FMM with isotropic cost function has been proposed to extract the vessel centerline path. This first solution is suitable mainly to navigate far away from the vessel wall. However, as navigation in real vascular networks is directionally constrained by the biological environment, a new framework based on the *anisotropic* FMM [19] is proposed in this paper. Furthermore, the proposed method allows a multi-parameter optimization of the navigation path that takes into account: i) the technology of the magnetic system; ii) the microrobot design; and iii) the physiology of the patient. Finally, our approach ensures a smooth conveyance of the microrobot to destination robust to cardiovascular navigation

<footnote>The authors are with Laboratoire PRISME, ENSI de Bourges, 88 boulevard Lahitolle, 18020 Bourges, France.
E-mail: firstname.name@ensi-bourges.fr</footnote>
<figure><img src="image_23.png" /><figcaption>Fig. 1. Modeling scheme example in case of bead pulled microrobot.</figcaption></figure>

constraints while minimizing the energy expenditure, to reduce the gradient pulling and system overheating. Specifically, we aim to get a feasible path by finding the min-energy pathway (which is not necessarily the shortest). Section III briefly describes our developed microrobotic surgical simulation and planning application, before illustrating its performance. As an illustration, we consider the treatment of peripheral arterial diseases (PAD), such as artery narrowing (stenosis). For instance, one possible surgical application is to target atherosclerotic plaques in stenosed arteries. One of the most common strategies is angioplasty, occasionally with stent implantation. Despite the high success rate, these solutions are not satisfactory, as vessel damage, infection and restenosis can appear at a later stage. Otherwise, a surgical microrobot for such vascular applications offers some novel solutions [1]. Specifically, microrobotic intervention based on chemical, mechanical or mechano-chemical could be achieved to treat vascular obstructions [2]. Finally, we discuss some open issues, evaluate the computational efficiency, and outline some future extends in Section IV. This study is concluded in Section V.

## II. METHODS

### A. A modeling overview

Different types of devices could be used for MIS interventions from catheter and guidewires, to wireless microcapsules or microcarriers [1]. In this framework, any kind of untethered microdevice (termed as microrobot throughout the text) that has to perform endovascular navigation within blood flow is considered. More precisely, we consider any microsystem that could be modeled as:

$$m\dot{\mathbf{v}} = \mathbf{f}_a(\mathbf{a}) + \mathbf{f}_d(\mathbf{v}) + \mathbf{f}_{\text{Ext}}(\mathbf{x}) \quad (1)$$

where $\mathbf{v}$ is the velocity of the device; $m$ its mass; $\mathbf{f}_a(\mathbf{a})$ is the controlled force, that is related to the control action $\mathbf{a} \in \mathcal{A}$, with $\mathcal{A}$ the admissible controls set; $\mathbf{f}_d(\mathbf{v})$ denotes the fluid flow hydrodynamic drag force; and $\mathbf{f}_{\text{Ext}}(\mathbf{x})$ are all other external forces, as depicted Fig. 1. Different external forces could be added to the model (1), such as the weight ($\mathbf{f}_g$), electrostatic ($\mathbf{f}_e$), van der Waals ($\mathbf{f}_v$), contact or steric forces. The interested reader may refer to [20] for detailed formulation of microforces. Fig.2 illustrates the evolution of these microforces with varying microrobot radius $r$ and wrt. its distance to vessel wall $\delta$. In particular, Fig. 2(f) shows that close to the centerline of the vessel ($\delta = R$) the electrostatic

<figure><img src="image_24.png" /><figcaption>Fig. 2. Microforces evolution: (a) apparent weight $\mathbf{f}_g$ (b) magnetic force $\mathbf{f}_a$ (with $\nabla B = 200 \text{ mT/m}$), (c) drag force $\mathbf{f}_d$ (with $\|\bar{\mathbf{v}}_f\| = 400 \text{ mm/s}$), (d) electrostatic force $\mathbf{f}_e$, (e) van der Waals force $\mathbf{f}_v$, as function of the distance to the vessel wall $\delta$ in artery ($R = 5 \text{ mm}$) and wrt. the microrobot radius $r$. (f) Microforces acting on a microrobot with $r = 1 \text{ mm}$ wrt. the distance to the vessel wall $\delta$ in artery ($R = 5 \text{ mm}$).</figcaption></figure>

and the van der Waals microforces are negligible compared to the other relevant forces. In addition, if the microrobot is never in contact with the vessel wall, the contact force could be omitted. Finally, most of the time because of the size of the microsphere, the effect of Brownian motion is also neglected.

### B. Navigation Planning in Flow

1) **Minimal Path Planning:** Classically, a navigation pathway could be defined as a curve $\mathcal{P}$ linking a starting point $\mathbf{x}_0$ to any point $\mathbf{x}$. In the general case, a curve is a minimal path, also called a geodesic, wrt. the metric $\varpi$, if it globally minimizes the energy functional:

$$\mathcal{E}_{\varpi}(\mathcal{P}) = \int_{\mathcal{P}} \varpi(\mathcal{P}(l), \dot{\mathcal{P}}(l))dl, \quad (2)$$

with $l$ the arclength parameter. The solution to the minimum path finding problem (2) could be obtained through the computation of the distance map $\mathcal{U}: \mathcal{C} \mapsto \mathbb{R}^+$, defined as: $\mathcal{U}(\mathbf{x}) = \min_{\mathcal{P}} \mathcal{E}(\mathcal{P})$, for any $\mathcal{P}$ linking $\mathbf{x}$ to $\mathbf{x}_0$ in the domain $\mathcal{C} \subset \mathbb{R}^d$ (with $d = 2, 3, 4...$). In this context, Sethian [16] has proposed the Fast Marching Method (FMM). Indeed, the FMM converges to a smooth solution in the continuous domain even when it is implemented on a sampled environment, contrary to discrete graph-search algorithms. Especially, in the isotropic case, the FMM satisfies the Eikonal equation:

$$\left\{ \begin{array}{l} \|\nabla \mathcal{U}(\mathbf{x})\| = w(\mathbf{x}), \quad \forall \mathbf{x} \in \mathcal{C} \\ \mathcal{U}(\mathbf{x}_0) = 0 \end{array} \right. \quad (3)$$

where the isotropic cost function $w: \mathbf{x} \in \mathcal{C} \mapsto w(\mathbf{x}) \in \mathbb{R}^+$ is the metric. As the map $\mathcal{U}$ has a single local minimum, the geodesic can be retrieved with a simple gradient descent on $\mathcal{U}$ from a targeted seed $\mathbf{x}_g$ to $\mathbf{x}_0$. The FMM provides a continuous solution to the minimum path problem by employing upwind differences and a causality condition [16]. The key issue of
the FMM is then to get an appropriate metric $w(\mathbf{x})$ which drives the front expansion efficiently to find a geodesic $\mathcal{P}$. In previous works [17,18], we have proposed to design such a metric on spatial consideration:

$$w: \mathbf{x} \in \mathcal{C} \mapsto \text{Vesselness}(\mathbf{x}) \in \mathbb{R}^{+} \quad (4)$$

where Vesselness($\mathbf{x}$) is a vesselness enhancement function. A typical Vesselness($\mathbf{x}$) function could be designed using a multi-scale analysis of the Hessian matrix, as proposed by Frangi [21] or Sato [22]. This approach then allows to find the vessel centerline geodesic $\mathcal{P}_c$, as the considered vesselness filter gives their maximal response in the vessel center. We have applied this procedure to different sets of data, in 2D [17] as well as in 3D [18].

As mentioned previously the contact, electrostatic and van der Waals microforces are negligible when the microrobot navigates close to the centerline $\mathcal{P}_c$ (cf. Fig. 2). $\mathcal{P}_c$ is then the best solution to navigate far away from the vessels wall. However, navigation in real vascular networks is constrained by the biological environment, and can strongly modify the system behavior, leading to incompleteness in real intra-operative applications.

2) Anisotropic Path Planning: Navigating in blood flow implies some directional constraints. When the path finding problem has some preferred directions of travel it becomes anisotropic, i.e. the solutions depend on the configuration and directional constraints. In [19], the authors noticed that the FMM could be applied to isotropic or anisotropic problems, and they provided a numerical scheme to solve static Hamilton-Jacobi equations of the form:

$$\left\{ \begin{array}{l} \|\nabla U(\mathbf{x})\| = \varpi(\mathbf{x}, \frac{\nabla U(\mathbf{x})}{\|\nabla U(\mathbf{x})\|}), \quad \forall \mathbf{x} \in \mathcal{C} \\ U(\mathbf{x}_0) = 0 \end{array} \right. \quad (5)$$

where the anisotropy expansion is the result of the dependence of $\varpi$ on $\nabla U(\mathbf{x})$. Nevertheless, the computational complexity of the FMM in the anisotropic case is growing significantly with the amount of anisotropy. The literature provides different variants of the FMM to deal with anisotropy, such as using a recursive approach [23], or iterative schemes [24]. Furthermore, in [14] anisotropic cost functions have been also proposed. The proposed basic idea is to take advantage of the original FMM efficiency, and to model the anisotropy thanks to a vector $\mathbf{f}$ of a field of force $\mathcal{F}$, leading to the following anisotropic metric:

$$\varpi: (\mathbf{x}, \mathbf{f}) \in \mathcal{C} \times \mathcal{F} \mapsto \varpi(\mathbf{x}, \mathbf{f}) \in \mathbb{R}^{+} \quad (6)$$

Such an anisotropic cost function leads to anisotropic front-propagation, and gives better geodesic than isotropic FMM. To embed the directional constraints $\mathbf{f}$ within such an anisotropic FMM different specific cost functions have been proposed mainly for autonomous underwater vehicles (AUVs) [14,25]. The drag and flow forces have a significant effect on the motion of the AUV, which is a common problem with our microrobot planning problem. However, the proposed solution mainly deals with either the min-distance or the min-time path finding problem, and not minimizing directly neither the dynamics nor the motion applied to the system. Moreover,

most existing approaches classically simplify the problem by assuming constant vehicle speed, or only spatially varying flow fields without time variation. Such limitations can generate physically unfeasible paths. Especially, in the presence of strong flows, incompleteness or incorrectness issues are reported [25].

3) Minimum-feasible-energy Planning: Most microrobot propulsion schemes usually require a limitation of the power consumption, and have a maximum available power. Moreover, considering only either the min-time or min-distance problem usually leads to compute high motion forces, that is reach the goal as fast as possible. But in our context, high motion implies high drag forces, and then high motion force $f_a$ (limited by the maximum available magnetic forces) to be able to reach the targeted area. To minimize the energy expenditure, a basic idea is to use a classical power functional expression, that is:

$$p(\mathbf{x}, \mathbf{a}) = \langle \mathbf{f}(\mathbf{x}, \mathbf{a}) \cdot \mathbf{v}(\mathbf{x}) \rangle \quad (7)$$

where $\langle \cdot, \cdot \rangle$ is the inner product of $\mathbb{R}^d$; $\mathbf{v}$ is a velocity; and $\mathbf{f}(\mathbf{x}, \mathbf{a})$ is the applied resultant force that embeds the controlled action $\mathbf{a} \in \mathcal{A}$. Using the optimal control approach, we propose the following anisotropic cost function:

$$\varpi(\mathbf{x}, \mathbf{f}) = \max_{\mathbf{a} \in \mathcal{A}} \langle \mathbf{f}(\mathbf{x}, \mathbf{a}) \cdot \mathbf{v}(\mathbf{x}) \rangle \quad (8)$$

This anisotropic cost formulation, as in [14,25], naturally incites the device to move in the direction of the force $\mathbf{f}$. Especially, $\varpi(\mathbf{x}, \mathbf{f})$ will imply that the FMM propagation (5) follows the force field constraints, that is $\frac{\nabla U(\mathbf{x})}{\|\nabla U(\mathbf{x})\|} \propto \mathbf{f}$. Finally, this new anisotropic formulation (8) using optimal control aspects embeds the system motion wrt. a finite defined admissible control set $\mathcal{A}$. This ensures that the given geodesic $\mathcal{P}$ is really feasible by the system and minimizes energy expenditure. Indeed, the metric $\varpi(\mathbf{x}, \mathbf{f})$ allows to consider both the biological constraints and the microrobot capabilities.

### III. RESULTS

#### A. Simulation and Planning Tool

The proposed framework has been integrated in a dedicated interactive microrobot surgical simulation and planning application. This application, depicted on Fig. 3, is based on the Visualization Toolkit (VTK) [26], the Insight Segmentation and Registration Toolkit (ITK) [27], and the Qt Toolkit [28]. Through the user interface (Fig. 3(b)), the surgeon realizes the following operating mode iteratively:

a) Specifications: The surgeon provides different parameters in the software (in the left panel on Fig. 3(b)) related to: i) the physiology of the patient (blood flow and viscosity, vessel's size and topology); ii) the technology of the magnetic system (coil's slew rate, maximum magnetic gradients, power limitations); and iii) the microrobot design (size, density, magnetic saturation).

b) Simulations: The surgeon initiates the simulation and planning process wrt. the specification constraints.

c) Data analysis: The surgeon analyses the power functional mapping and force field wrt. microrobot specifications. This iterative process is conducted until the preoperative planning of plaque removal specifications are satisfied. We
<figure><img src="image_25.png" /><figcaption>Fig. 3. Preoperative microrobot surgical simulation and planning application: (a) application workflow; (b) vessel centerline extraction example.</figcaption></figure>

focus in the sequel on the main contributions of this paper that is the simulation and reliable vascular navigation planning.

## B. Case study: peripheral arterial diseases

To assess the overall framework, we have performed a series of tests for both the microrobot within blood vessel model simulation and preoperative microrobotic MIS planning. We illustrate the proposed application for the treatment of peripheral arterial diseases (PAD). One possible application is to locate atherosclerotic plaque in stenosed arteries. In particular, stenosis implies an abnormal narrowing of the vessel which causes a decrease in blood flow. Different plaque removal tasks have already been realized by magnetically actuated microrobots navigating in occluded blood vessels [2]. In [29], shear-targeting of a thrombolytic drug in a mouse arterial thrombosis model using a microcarrier has been successfully tested. In [30], the rotation of the magnetic microrobot is at the origin of a drilling action through an occlusion in a vessel. In the following, we propose a preoperative planning of a magnetic microrobot navigating within the vasculature to the stenosed artery for plaque removal. We will consider here as case study the real Magnetic Resonance Angiogram (MRA) clinical dataset depicted on Fig. 4. As the proposed framework works in $C \subset \mathbb{R}^d$ (with $d = 2, 3...$), for the sake of clarity of the representation, we will only show here a Maximum Intensity Projection (MIP) image of the MRA. Here, the patient has a single level disease represented by an isolated stenosis in the iliac artery. As it is still a challenging issue to identify automatically the patient pathology and its location, the PAD is manually defined by the user.

## C. Simulation Results

As previously mentioned, the simulation is based on a physics-based model (presented in details in [20]). When

<figure><img src="image_26.png" /><figcaption>Fig. 4. Real MIP image from MRA (resolution of $N = 384 \times 384$ nodes) obtained in a patient with an isolated stenosis in the iliac artery (the white (A)-arrow), used to illustrate microrobotic MIS treatment simulation and planning.</figcaption></figure>

interactive simulation is required (for training, intervention planning, etc.), a trade-off between computation time and accuracy has to be found. In our application, computational efficiency is more important than small-scale details, as we aim to increase the users interaction capabilities, whereas precision could be achieved using FEM or CFD simulation. To speed-up either the blood flow velocity or the force fields simulation computation, the basic FMM is extended to be able to compute these vector fields during the front propagation (see Fig. 3(a)). Indeed, using Vesselness($x$) isotropic cost function, the FMM front will extend only within the vascular structure. This allows to take advantage of the FMM efficiency, without using the whole dataset grids, and significantly reduce the overall computational time.

The blood flow velocity field simulation of the considered case study is illustrated on Fig. 5. The interactive simulation tool takes into account that blood flow velocity intensity $\bar{v}_f$ on the vessel centerline decreases wrt. vessels radii, that is from about $||\bar{v}_f^{ad}|| \approx 400$ mm/s in descending aorta with a radius $R \approx 6.5$ mm, to $||\bar{v}_f^{ei}|| \approx 250$ mm/s in external iliac artery with a radius $R \approx 3.5$ mm. As one can see, the blood flow velocity field is modified in the considered stenosis case (narrowed vessel on Fig. 5). The corresponding force field that will act on a neodymium microrobot with a radius $r = 500$ µm is shown on Fig. 6. In this simulation, only the weight $f_g$ (in the $\vec{g}$-axis direction), drag $f_d$ and electrostatic $f_e$ forces are calculated. Let us notice that any force that can have an analytical expression and can be embedded in (1) can easily be added to the application. Finally, the realized interactive simulation application is also able to deal with periodic time-varying pulsatile blood flows, as presented on Fig. 7. The user defines the periodic pulsatile blood flow parameters [20], a number of time-steps, and can then browse the time-frame of either the blood flow velocity or the applied force field. Fig. 7(a) illustrates a typical periodic time-varying pulsatile blood flow that takes place in the descending aorta, and the row 7(b) describes the corresponding velocity field. Fig. 7(c) and 7(d) show the resulting force fields applied on the microrobot for two case studies, a microrobot of radius of $r = 250$ µm and $r = 1.5$ mm, respectively. This demonstrates that when the microrobot’s radius $r$ or weight $f_g$ increases, the resultant force becomes more important.
<figure><img src="image_27.png" /><figcaption>Fig. 5. Simulation results of the blood flow velocity field computation.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Fig. 6. Simulation results of the force field: $\mathbf{f} = \mathbf{f}_d(\mathbf{v}) + \mathbf{f}_e(\mathbf{x}) + \mathbf{f}_g$, applied on a microrobot of $r = 500$ µm radius.</figcaption></figure>

### D. Microrobotic surgical planning demonstration

Once the microrobot is specified (size, materials, etc.), the system's planning step only requires as user's input the starting $\mathbf{x}_0$ and ending points $\mathbf{x}_g$. Next, to deal with the anisotropy of the media, the blood flow and force fields simulation results are used to compute the power functional map (7). The key issue is then to generate the controlled force field $\mathbf{f}_a(\mathbf{a})$, $\forall \mathbf{a} \in A$. First, the action magnitude has to be defined wrt. available actuation command. The action magnitude is usually the controlled magnetic gradient ($\mathbf{a} = \nabla B$), which implies the following magnetic force on a spherical device:

$$ \mathbf{f}_a(\nabla B) = D \tau_m \frac{4}{3} \pi r^3 (\mathbf{M} \cdot \nabla) \nabla B, \quad (9) $$

where $r$ is the microsphere radius; $\tau_m \in [0; 1]$ is the volume ratio of the magnetic material; $\mathbf{M}$ its magnetization; and $D \in [0; 1]$ is the duty-cycle, i.e., the ratio between the duration of the applied magnetic gradient for propulsion to the total period $T$.

The magnetic gradient used to propel a magnetic microrobot is assumed to be generated from various medical magnetic steering systems: ElectroMagnetic based Actuation (EMA) systems such as the Magnetic Catheter Steering System (a larger version of the Octomag system [15]) or the one developed in [30]; and Magnetic Resonance Navigation (MRN). The EMA systems are capable of generating maximum magnetic gradient fields up to $a_{max} = 350$ mT/m in closed-loop navigation control. In this case, the duty cycle is considered equal to $D = 1$ since the imaging modality is provided by either optical microscopy or X-ray imaging. These systems are more suitable for the navigation of millimeter-sized hard magnetic microrobots. The MRN system is based on clinical MRI systems, without any hardware upgrades. Such magnetic systems are usually limited to maximum values to $a_{max} = 80$ mT/m in closed-loop navigation control. Generally, the

<figure><img src="image_29.png" /><figcaption>Fig. 7. Pulsatile blood flow simulation: (a) the periodic time-varying velocity in the descending aorta; (b) zoomed view of the blood flow velocity field; (c-d) zoomed view of the force field $\mathbf{f} = \mathbf{f}_d + \mathbf{f}_e + \mathbf{f}_g$ acting on a microrobot of: (c) $r = 250$ µm, and (d) $r = 1500$ µm for different time instants.</figcaption></figure>

duty cycle is $D < 1$, since MR-imaging sequences and MR-tracking are provided by the same scanner to gather feedback positional information during MRN [9]. The MRN approach is more suitable for micrometer-sized soft magnetic microrobots. However, it should be noticed that experimental results have shown that therapeutic particles (known as TMMC), 50-60 µm diameter were navigated in arteries (rabbit models) and that MRN was done with gradient coils (capable of 450 mT/m with inner diameter suitable for limbs or head interventions) installed in the tunnel of clinical MRI scanners [31].

Our proposed FMM strategy can be adapted to each specific case by taking into account the duty-cycle $D$, the slew rate of the magnetic coils, and the maximum temperature coils. Secondly, the action direction should be defined. To this aim, we used some a priori knowledge about the goal direction, defined between $\mathbf{x}_0$ and $\mathbf{x}_g$, provided by the isotropic FMM using Vesselness($\mathbf{x}$) cost function (see Fig. 3(a)). Indeed, this FMM step provides the distance map $U_c$ between $\mathbf{x}_0$ and $\mathbf{x}_g$ (or reciprocally), and then the goal direction field $\nabla U_c(\mathbf{x})$. This helps to define the appropriate guidance field $G(\mathbf{x}) \propto \nabla U_c(\mathbf{x})$. Some variations could be added on the goal direction field to enlarge the guidance field set. The admissible control set $A$ can then be defined as:

$$ A = \{ \mathbf{A} \times \mathbf{G} \}, \quad (10) $$

where $\mathbf{A} \subset ]0; a_{max}]$ is a finite set of action magnitudes, and $\mathbf{G} = \{G(\mathbf{x}) \sim [0; \frac{\pi}{2}]\}$ is the guidance field set. Let us recall that $A$ could be filtered to consider some technological constraints (such as the duty-cycle, or the magnetic slew rate).

This planning framework has been validated on the case study dataset considering different microrobot sizes navigating within arteries. First, Fig. 8 demonstrates the influence of the
<figure><img src="image_30.png" /><figcaption>Fig. 8. Planning results on varying control action influence for a neodymium microrobot of size 250 µm and 750 µm: (a) the energy functional $\mathcal{E}_{\infty}(\mathcal{P})$ wrt. the action magnitude (i.e. the magnetic gradient) and (b) zoomed view of the corresponding geodesics: $\mathcal{P}_c$ the vessel centerline and $\mathcal{P}_a$ the min-energy path for the varying action magnitude.</figcaption></figure>

<figure><img src="image_31.png" /><figcaption>Fig. 9. Planning results on varying control action influence for a neodymium microrobot of size 1.5 mm and 2.5 mm in clinical MRI context.</figcaption></figure>

motion force magnitude on finding the minimum-feasible-energy path. We noticed that as the motion force magnitude increased, the required energy $\mathcal{E}_{\infty}(\mathcal{P})$ increased exponentially. This is significant for important microrobot size ($r = 750$ µm on Fig. 8(a)). Indeed, Fig. 8(b) shows that with much power the microrobot is more able to leave the vessel's centerline $\mathcal{P}_c$ (provided by the isotropic FMM) to reach the goal faster. If limited magnetic gradient magnitudes are available to propel the microrobot, such as in clinical MRI, Fig. 9 shows that increasing its size should overcome the power limitation. Therefore, the proposed min-energy path planning has been evaluated for various microrobot sizes and for EMA and MRN systems, as reported on Fig. 10. We can notice that for a microrobot radius bigger than 1.5 mm the curve length increases slightly, and starts to decrease significantly below 1 mm (cf. Fig. 10(a)). Furthermore, Fig. 10(b) depicts that the energy functional decreases significantly with the microrobot radius. In fact, the action force $f_a(a)$ decreases following a cubic power ($L^3$), minimizing the power budget. Therefore, it is more difficult for neodymium microrobots with a size below 750 µm to overcome the blood flow constraints that take place in the artery. Finally, as an illustration of the blood flow

<figure><img src="image_32.png" /><figcaption>Fig. 10. Planning results with varying microrobot radii, for an EMA system ($a_{max} = 350$ mT/m) and a MRN ($a_{max} = 80$ mT/m): (a) the geodesic curvature length (in mm); and (b) the energy functional.</figcaption></figure>

<figure><img src="image_33.png" /><figcaption>Fig. 11. Planning results using the proposed anisotropic cost function for a neodymium microrobot with $r = 1.5$ mm: three targeted point are specified ($x_{g1}$, $x_{g2}$ and $x_{g3}$). The colored map depicted the power functional level.</figcaption></figure>

<table><caption>TABLE I
PLANNING RESULTS OF MINIMUM-FEASIBLE-PATH FOR THREE TARGETED POINT ($x_{g1}$, $x_{g2}$ AND $x_{g3}$) DEPICTED ON FIG. 11</caption><thead><tr><th>Geodesic #</th><th>Length (mm)</th><th>Energy E<sub>&infin;</sub>(P)</th></tr></thead><tbody><tr><td>P<sub>1</sub></td><td>360.086</td><td>0.6765</td></tr><tr><td>P<sub>2</sub></td><td><strong>359.612</strong></td><td>0.5118</td></tr><tr><td>P<sub>3</sub></td><td>361.735</td><td><strong>0.4879</strong></td></tr></tbody></table>

influence, Fig. 11 shows the planning results of our minimum-feasible-path finder for three targeted points ($x_{g1}$, $x_{g2}$ and $x_{g3}$), and Table I lists the curve lengths of their geodesics ($P_1$, $P_2$ and $P_3$) and the energy functional $\mathcal{E}_{\infty}(\mathcal{P})$. The min-energy geodesic is curve $P_3$, while the shortest length is $P_2$. This means that although $P_3$ is longer than $P_2$, $P_3$ consumes less energy.

IV. DISCUSSION

The most computationally intensive part of the microrobotic surgical application is the vesselness filter (that provides Vesselness(x) cost function) based on a multiscale analysis of the Hessian matrix [21]. This multiscale interpretation of eigenvalues of the Hessian matrix could be improved thanks to parallelization through GPU implementation. Furthermore, as mentioned, instead of using the overall dataset grid (in the case study $N = 147 456$), the vector fields simulations are performed on only 18 941 nodes corresponding to the vasculature. Thus, on an Intel Core2 3Ghz processor, one simulation time
takes less than 150 ms. For the periodic pulsatile blood flow, this allows to compute one cardiac cycle with 50 time-steps in less than 8 s. Therefore, the combination of the microrobot and the car cardiovascular model together with the FMM may become accurate enough to support interactive microrobotic surgical planning applications. Finally, in the planning step, the main computational aspect remains on action set A generation. This set A is related to the dimension of the action magnitude set A and guidance field set G, specified by the users. For the case study with dim A = {10 × 10}, the overall planning procedure needs a calculation time of about 36 s. This computational efficiency ensures a high level of interactivity for preoperative simulation, planning and navigation.

In the simulation process we have chosen to focus on computational efficiency, rather than on accurate blood flow simulations. Nonetheless, the vasculature and blood flow modeling are still strongly investigated by the communities, and remain an open issue. In future extends, we will use some analytical modeling of vessel bifurcation as in [20], to improve the blood flow simulation accuracy. Although the visualization of vector fields is still a challenging issue (especially in 3D), more intuitive flow rendering (such as streamline, streamribbon, etc.) could also be helpful for the microrobotic surgery applications.

## V. CONCLUSION

In this study, a microrobotic surgical simulation and planning has been presented for the treatment of peripheral arterial diseases. However, the proposed framework could also be applied to other regions of the body, different therapy and various MIS microrobots. Especially, the results shows that interactive applications can be helpful to design the suitable microrobot design (e.g. shape, size, materials, etc.) wrt. anatomic consistency to improve microrobotic surgical applications. Hence, preoperative surgical planning with blood flow simulation provides useful information for understanding cardiovascular pathologies, predicting their onset and choosing an optimal therapy strategy for innovative microrobotic MIS procedure.

## ACKNOWLEDGMENT

The PhD student K. Belharet is supported by the Nano-IRM project, founded by Region Centre and City of Bourges.

## REFERENCES

[1] B. J. Nelson, I. K. Kaliakatsos, and J. J. Abbott, "Microrobots for minimally invasive medicine," *Annual Review of Bio.med. Eng.*, vol. 12, no. 1, pp. 55–85, 2010.

[2] P. Miloro, E. Sinibaldi, A. Menciassi, and P. Dario, "Removing vascular obstructions: a challenge, yet an opportunity for interventional micro devices," *Bio.med. Microdevices*, vol. 14, pp. 511–532, 2012.

[3] R. M. Satava, "Virtual reality, telesurgery, and the new world order of medicine," *Computer Aided Surgery*, vol. 1, no. 1, pp. 12–16, 1995.

[4] K. Sun, Z. Chen, and S. Jiang, "Local morphology fitting active contour for automatic vascular segmentation," *IEEE Trans. Biomed. Eng.*, vol. 59, no. 2, pp. 464–473, Feb. 2012.

[5] Y. Ganji and F. Janabi-Sharifi, "Catheter kinematics for intracardiac navigation," *IEEE Trans. Biomed. Eng.*, vol. 56, no. 3, pp. 621–632, Mar. 2009.

[6] W. Tang, T. R. Wan, D. A. Gould, T. How, and N. W. John, "A stable and real-time nonlinear elastic approach to simulating guide-wire and catheter insertions based on cosserat rod," *IEEE Trans. Biomed. Eng.*, vol. PP, no. 99, p. 1, 2012.

[7] F. Carpi, N. Kastelein, M. Talcott, and C. Pappone, "Magnetically controllable gastrointestinal steering of video capsules," *IEEE Trans. Biomed. Eng.*, vol. 58, no. 2, pp. 231–234, Feb. 2011.

[8] G. Ciuti, M. Salerno, G. Lucarini, P. Valdastri, A. Arezzo, A. Menciassi, M. Morino, and P. Dario, "A comparative evaluation of control interfaces for a robotic-aided endoscopic capsule platform," *IEEE Trans. Robot.*, vol. 28, no. 2, pp. 534–538, Apr. 2012.

[9] S. Tamaz, A. Chanu, J.-B. Mathieu, R. Gourdeau, and S. Martel, "Real-time MRI-based control of a ferromagnetic core for endovascular navigation," *IEEE Trans. Biomed. Eng.*, vol. 55, no. 7, pp. 1854–1863, Jul. 2008.

[10] (2012) Stereotaxis Inc. [Online]. Available: http://www.stereotaxis.com

[11] (2012) Sensei(r) x robotic catheter system. Hansen Medical. [Online]. Available: http://www.hansenmedical.com

[12] C. Pawashe, S. Floyd, and M. Sitti, "Modeling and experimental characterization of an untethered magnetic micro-robot," *The Int. J. of Robot. Research*, vol. 28, no. 8, pp. 1077–1094, 2009.

[13] W. Sabra, M. Khouzam, and S. Martel, "Use of 3D potential field and an enhanced breadth-first search algorithms for the path planning of microdevices propelled in the cardiovascular system," in *IEEE Int. Conf. of the Eng. in Med. and Bio. Soc.*, Apr. 2005.

[14] C. Pêtrès, Y. Pailhas, P. Patron, Y. Petilot, J. Evans, and D. Lane, "Path planning for autonomous underwater vehicles," *IEEE Trans. Robot.*, vol. 23, no. 2, pp. 331–341, 2007.

[15] M. Kummer, J. J. Abbott, B. E. Kratochvil, R. Borer, A. Sengul, and B. J. Nelson, "Octomag: An electromagnetic system for 5-dof wireless micromanipulation," *IEEE Trans. Robot.*, vol. 26, no. 6, pp. 1006–1017, Sep. 2010.

[16] J. A. Sethian, *Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science*. Cambridge University Press, 1999.

[17] K. Belharet, D. Folio, and A. Ferreira, "Endovascular navigation of a ferromagnetic microrobot using MRI-based predictive control," in *IEEE/RSJ Int. Conf. on Intel. Robots and Syst.*, Taiwan, Oct. 2010.

[18] ——, "3D MRI-based predictive control of a ferromagnetic microrobot navigating in blood vessels," in *IEEE RAS & EMBS Int. Conf. on BioMed. Robot. and BioMechatron.*, Tokyo, Japan, Sep. 2010.

[19] J. A. Sethian and A. Vladimirsky, "Ordered upwind methods for static hamilton-jacobi equations: theory and algorithms," *SIAM J. on Numerical Analysis*, vol. 41, no. 1, pp. 325–363, 2003.

[20] L. Arcèse, M. Fruchard, and A. Ferreira, "Endovascular Magnetically-Guided Robots: Navigation Modeling and Optimization," *IEEE Trans. Biomed. Eng.*, no. 99, pp. 1–12, Sep. 2011.

[21] A. Frangi, W. Niessen, K. Vincken, and M. Viergever, "Multiscale vessel enhancement filtering," *Lect. Notes in Comp. Scie.*, pp. 130–137, 1998.

[22] Y. Sato, S. Nakajima, H. Atsumi, T. Koller, G. Gerig, S. Yoshida, and R. Kikinis, "Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images," *Med. Imag. Anal.*, vol. 2, no. 2, pp. 143–168, 1998.

[23] E. Konukoglu, M. Sermesant, O. Clatz, J.-M. Peyrat, H. Delingette, and N. Ayache, "A recursive anisotropic fast marching approach to reaction diffusion equation: Application to tumor growth modeling," in *Inf. Processing in Med. Imag.*, N. Karssemeijer and B. Lelieveldt, Eds., vol. 4584. Springer, 2007, pp. 687–699.

[24] F. Bornemann and C. Rasch, "Finite-element discretization of static hamilton-jacobi equations based on a local variational principle," *Computing and Visualization in Science*, vol. 9, pp. 57–69, 2006.

[25] M. Soulignac, "Feasible and optimal path planning in strong current fields," *IEEE Trans. Robot.*, no. 99, pp. 1–10, Feb. 2011.

[26] (2012) The visualization toolkit (VTK). Kitware. [Online]. Available: http://www.vtk.org

[27] (2012) Insight segmentation and registration toolkit (ITK). Kitware. [Online]. Available: http://www.itk.org

[28] (2012) Qt-a cross-platform application and UI framework. Nokia. [Online]. Available: http://qt.nokia.com/

[29] N. Korin, M. Kanapathipillai, B. Matthews, M. Crescente, A. Brill, T. Mammoto, K. Ghosh, S. Jurek, S. Bencherif, D. Bhatta et al., "Shear-activated nanotherapeutics for drug targeting to obstructed blood vessels," *Science*, vol. 337, no. 6095, pp. 738–742, 2012.

[30] C. Yu, J. Kim, H. Choi, J. Choi, S. Jeong, K. Cha, J. oh Park, and S. Park, "Novel electromagnetic actuation system for three-dimensional locomotion and drilling of intravascular microrobot," *Sensors and Actuators A: Physical*, vol. 161, no. 1-2, pp. 297–304, 2010.

[31] P. Pouponneau, J.-C. Leroux, G. Soulez, L. Gaboury, and S. Martel, "Co-encapsulation of magnetic nanoparticles and doxorubicin into biodegradable microcarriers for deep tissue targeting by vascular MRI navigation," *Biomaterials*, vol. 32, no. 13, pp. 3481–3486, 2011.
APPENDIX C

CATALYTIC LOCOMOTION OF CORE-SHELL NANOWIRE MOTORS (ACL10
# Catalytic locomotion of Au/Ru core-shell nanowire motors

Bumjin Jang,, Wang Wei, Samuel Wiget,, Petruska Andrew, Xiangzhong Chen,, Chengzhi Hu,, Ayoung Hong,, David Folio, Antoine Ferreira, Salvador Pané, et al.

<figure><img src="image_34.png" /></figure>

## ► To cite this version:

Bumjin Jang,, Wang Wei, Samuel Wiget,, Petruska Andrew, Xiangzhong Chen,, et al., Catalytic locomotion of Au/Ru core-shell nanowire motors. ACS Nano, American Chemical Society, 2016, 10 (11), 10.1021/acsnano.6b04224. [http://dx.doi.org/10.1021/acsnano.6b04224](http://dx.doi.org/10.1021/acsnano.6b04224)

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# Catalytic locomotion of Au/Ru core-shell nanowire motors

Bumjin Jang*, \*† Wei Wang, ‡ Samuel Wiget, † Andrew J. Petruska, † Xiang-Zhong Chen, † Chenzhi Hu, † David Folio, § Antoine Ferreira, § Salvador Pané, \*† and Bradley J. Nelson†

†Institute of Robotics and Intelligent Systems, ETH Zurich, Zurich, CH-8092, Switzerland

‡Shenzhen Key Laboratory for Advanced Materials, School of Material Sciences and Engineering, Shenzhen Graduate School, Harbin Institute of Technology, University Town, Shenzhen 518055, China

§ INSA Centre Val de Loire, Universite d'Orleans, PRISME EA 4229, Bourges, France.

KEYWORDS: core-shell nanowires, catalytic micro-nanomotors, self-electroosmosis, self-diffusiophoresis, net propulsive force

Fifteen years ago, Whitesides et al. pioneered a work on self-propelled catalytic millimeter-scale ships,¹ triggering a mighty development of synthetic micro- and nanomotors. These devices move autonomously in the presence of a fuel solution by converting chemical to mechanical energy.² Most of reported catalytic micro- and nanomotors are driven by the decomposition of hydrogen peroxide, although there are other recent examples using glucose and urea as fuels.³⁻⁵ Several applications for these miniaturized motors have been demonstrated such
as electronic circuit healing,⁶ biosensing,⁴,⁷ nanolithography,⁸ microfluidic pumping,⁹ nanocargo transport¹⁰, or environmental remediation (for details, see recent review articles¹¹⁻¹⁶). Most of these applications require a precise control over the speed and directionality of the motors.¹⁷, which are highly dependent on the motor design parameters, such as its geometry, size and composition. Understanding the mechanisms involved in the propulsion of catalytic micro- and nanomotors as a function of their design is crucial for controlling their motion. Different propulsion mechanisms have been identified, such as bubble propulsion, self-electroosmosis, self-diffusiophoresis or interfacial tension.¹⁶ In the first mechanism, bubbles are formed on the catalytic surface and impart momentum to the motor. For example, tubular microjets¹⁸, ¹⁹ are driven by oxygen bubble propulsion, caused by the decomposition of H₂O₂ at the inner catalytic surface. While bubble propulsion seems at first glance the most intuitive way to explain the motion of these motors, this mechanism cannot be used to rationalize, for instance, the motion of bimetallic structures such as Pt/Au or Cu/Pt nanowires (NWs) in H₂O₂ and I₂ solutions respectively.²⁰, ²¹ For bimetallic NWs, self-electroosmosis ²², ²³ is generally the most accepted mechanism compared to others²¹, ²⁴. In this case, a self-induced electric field is generated by redox reactions occurring on the two different metallic segments. The motion of other micro- and nanomotors has been explained in terms of self-diffusiophoresis. Several works suggest that micro- and nanoparticles asymmetrically coated with Pt move due to an O₂ concentration gradient, caused by the asymmetric decomposition of H₂O₂ along the body of the motor.²⁵⁻²⁷ ²⁸, ²⁹ Recent investigations evaluating more complex motor architectures are pointing towards a concomitant occurrence of mechanisms.³⁰, ³¹
Among all micro- and nanomotors' structures, NWs are particularly appealing due to their unique physical properties.32 Additionally, NWs can be compartmentalized in several functional modules by means of segmentation33 or coaxial lithography34 to increase their capabilities and functionalities. For instance, the trajectory of catalytic NW motor consisting of Pt/Ni/Au/Ni/Au segments can be controlled by means of magnetic fields.35 However, interfacing certain building blocks can be detrimental for several applications. For example, the combination of two dissimilar metallic segments such as Au and Ni can lead to an increase of the corrosion rate of the magnetic part due to galvanic coupling.36 Also, the interaction of certain materials (e.g. Ni) with the surrounding environment (e.g. biological or aquatic media) must be avoided to prevent undesired leakage of toxic ions. Alternatively, core-shell arrangements can provide an inert housing to prevent certain components to be in direct contact to the surrounding environment. Core-shell NWs have been manufactured using a wide variety of methods, and usually they imply two or more steps.37-42

In this work, we capitalize on a recently developed method, which allows for the batch fabrication of freestanding NWs based on template-assisted electrodeposition and wafer bonding. As the NWs are self-supported on the wafer after template removal, a second electrodeposition step can be realized to produce a core-shell architecture. This newly developed method can be adopted to fabricate core-shell NWs with various material combinations. Here, we have produced different types of bimetallic core-shell NWs such as Au/Ru, Rh/Au, Au/Rh and we have investigated for the first time their motion in H₂O₂ solutions. We observed abnormal behaviors of these core-shell devices including a speed increase with the length of Au/Ru core-shell NWs and a large speed difference among Au/Ru, Rh/Au and Au/Rh, which have not been
observed for the segmented (conventional bimetallic) NWs. The experimental results suggest that self-electroosmosis cannot be the sole mechanism for the locomotion of these architectures. Indeed, we suggest that self-diffusiophoresis is additionally playing a role as well. Additionally, magnetically guided motion of a (Au-Ni)/Ru core-shell NW is demonstrated. In this configuration, the magnetic component is enclosed within the shell, thus preventing the Ni core to be in contact with the surrounding solution.

## Results

**Numerical model of electroosmotic mechanism on core-shell NWs.** It has previously been established that the electroosmotic force is the main driving force for locomotion of nanomotors based on surface redox reactions.43, 44 The redox reaction consists of an oxidation reaction and reduction reaction as illustrated in Figure 1a. Protons, oxygen molecules, and electrons are generated in the oxidation process at the anode (Au) by decomposing $H_2O_2$. The generated protons travel by convection, diffusion, and migration to the cathode (Ru), where they react with electrons, oxygen and $H_2O_2$ molecules to produce $H_2O$ in the reduction process. As a consequence of this redox reaction, protons are asymmetrically distributed around the nanomotor and, accordingly, an asymmetric electric field is developed. This self-generated electric field causes protons to migrate inside the electrical double layer that naturally formed when the nanomotor is immersed in a water solution. The proton migration leads to an electroosmotic flow, which eventually causes the motion of the nanomotor. The influence of the electroosmotic mechanism on the locomotion of our newly designed nanomotor is simulated using commercial multiphysics simulation package COMSOL (5.1). Figure S1a shows that the proton concentration around the Au/Ru core-shell NW is highly asymmetric, as expected. The protons are highly concentrated at the Au (anode) end the NW, where they are generated, and have a low
concentration at the Ru (cathode) end, where they are consumed. As expected, Figure S1b
shows that the electric potential is also asymmetric because of the asymmetric distribution of
protons. Figure 1b shows that the fluid flows from the anode to the cathode, translating to a
directional motion of the Au/Ru core-shell NW with the anode forward. The simulation also
reveals that the fluid speed is highest at the interface between the cathode and anode of the core-
shell NW, where the majority of the electroosmosis flow occurs.

We notice in our simulation (Figure 1b) that near the opposite tip to the anode there is a
convergent flow loop on each side of the rod due to the coupling between the electrosmotic flow
moving from the anode to the cathode, and a flow from the surrounding solution due to the
electric field pointing towards the cathode. We further investigate how the length of Au/Ru core-
shell NW affects the convergent flow. When the length is small enough (~ 500 nm, Figure 1b
(i)), the electric field generated at the anode dominates the overall electroosmotic flow (Figure
S1c), and the disturbance to the fluid flow at the tip of the cathode is negligible. At
approximately 1.5 µm, a flow reversal at the tip occurs, which is caused by the migration of
protons from the surrounding solution to the cathode (Figure 1b (ii)). The reverse flow gains
enough strength to create vortices near the surface of the NW tip. Further increase in length
increase the size of vortices (Figure 1b (iii), (iv)). These vortices represent a local increase in the
fluidic drag at the tail of the NW, according to the observed negative fluidic speed at the tip of
the cathode as seen from the fluid profile along the NW long axis (Figure S1d).

The nanomotor speeds are calculated from the fluid velocities around the core-shell NWs
using the Solomentsev and Anderson model.⁴⁵ Figure 1c shows the speed as a function of length
of the core-shell NW. The decreased speed with length in the numerical simulation can be
attributed to the increase in drag force of the nanomotor as its length increases, since no-slip boundary condition was chosen for the nanomotor surface in the simulation.

**Design and fabrication of the Au/Ru core shell NWs.** The fabrication process is illustrated in Figure 2a. First, an anodic aluminium oxide (AAO) membrane was transferred onto a Si substrate via the Au/Au compressive bonding technique previously developed in our group.⁴⁶ Next, Au was electrodeposited into the pores of the AAO. The AAO was then chemically etched to obtain a freestanding Au NW array on the Si substrate. Ru was then electrochemically deposited on the freestanding Au NW array, hence the formation of a core-shell structure. The strong adhesion between the freestanding array and the Si substrate is able to withstand the electrophoretic and fluidic forces exerted on the NWs during Ru electrodeposition. We importantly note that the freestanding NWs must be kept in solution to prevent drying, because the surface tension forces during drying will cause severe NW aggregation ⁴⁷ and result in a non-uniform deposition of the Ru shell. After the Ru deposition, the NWs are released by sonication.

A scanning electron microscope (SEM) image obtained using a back-scattered electron (BSE) detector in Figure 2b shows a typical Au/Ru core-shell NW with an approximate diameter and a length of 350 nm and 2.5 µm, respectively, where the length varies with the deposition time of the Au core. Since the intensity of the BSE signal is proportional to the atomic number, the bright area and the dark area can be assigned to Au and Ru, respectively. The Au core appears only at the base (left end) as a consequence of being released from the Si substrate. No obvious defects are observed in the Au/Ru core-shell NW structure as is seen in the high-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) image (Figure 2c). The corresponding energy dispersive X-ray (EDX) mapping verifies that the core-shell NW is
composed of Au and Ru (Figure 2d). For a better understanding of the Ru distribution, we further selectively etched the Au core in Au etchant. Representative SEM and STEM images (Figure 2e,f) show that the remaining structure after etching is a Ru shell. The Ru shell has an approximate diameter of 350 nm, which is similar to that of a Au/Ru core-shell NW. A smooth surface of the nanoshell without holes or cracks on the rod is observed and confirms the uniform distribution and the conformal growth of the Ru shell. Subsequent EDX mapping verifies that the nanoshell solely consists of Ru (Figure 2g).

**Catalytic propulsion of the Au/Ru core-shell NWs.** The catalytic locomotion of the Au/Ru core-shell NWs (approximate length of 2.5 µm) in H₂O₂ solution was investigated at various concentrations (0, 0.1, 0.3, 2.5, 5, 10 and 20 wt %). As expected, the speed of the core-shell NW increases with the concentration of H₂O₂ (Figure 3a), showing the maximum speed of 41 ± 7.6 µm/s at 20 wt % H₂O₂. The positive correlation between the speed of the motor and the concentration of H₂O₂ is in accordance with previous findings.⁴⁸⁻⁵¹ A representative core-shell-NW trajectory is shown in Figure 3a (i). A large displacement is observed over 4.55 sec in the presence of H₂O₂ (5 wt %) in contrast to the control experiment, conducted in the absence of H₂O₂, which shows Brownian motion and a very small displacement (Figure 3a (ii)).

To systematically understand the locomotion, we studied the dynamic motion behavior of the core-shell NW with different lengths (1.8, 2.6 and 3.4 µm). We calculated the mean-square displacement (MSD) from the recorded motion trajectory (see also supporting movie1) using:

$$ \Delta L^2(t) = \langle [r(t) - r(0)]^2 \rangle \qquad (1) $$

where $r(t) = (x(t), y(t))$.
Similar to catalytic motors of other shapes, the MSD curves in Figure 3b and S2a,b show sinusoidal oscillations, which indicate that our motors exhibit a circular motion.⁴⁸, ⁵², ⁵³ The translational velocity (v), rotational velocity (ω), translational diffusivity (D) and rotational diffusivity (D<sub>r</sub>) for a moving particle can be extracted by fitting the MSD curves with⁵³:

$$ \Delta L^2(t) = 4 D_t + \frac{2v^2 D_r t}{D_r^2 + \omega^2} + \frac{2v^2(\omega^2 - D_r^2)}{D_r^2 + \omega^2} + \frac{2v^2 e^{D_r t}}{(D_r^2 + \omega^2)^2} \left[ (D_r^2 - \omega^2) \cos \omega t - 2\omega D_r \sin \omega t \right] $$

For comparison, the translational diffusivity D<sub>t,b</sub> and the rotational diffusivity D<sub>r,b</sub> of passive Brownian motion (i.e. in the absence of H<sub>2</sub>O<sub>2</sub>) of our core-shell NW are calculated by the Einstein relation:

$$ D_{t,b} = \frac{k_B T}{f_t^{\parallel}} \qquad (3) $$

$$ \ln \left( \frac{1}{L} \right) = \frac{3 \ln \left( \frac{D_t}{D_r} \right) + 3 \ln \left( \frac{D_r}{D_t} \right)}{6} \qquad (4) $$

where k<sub>B</sub> is the Boltzmann constant, T is the absolute temperature, f<sub>t</sub><sup>||</sup> is the translational frictional drag force and f<sub>r</sub><sup>||</sup> is the rotational frictional drag force parallel to the long axis of NW with a length (L) and a diameter (d) in a viscous media b<sub>t</sub>/c<sub>t</sub><sup>J</sup>/L. D<sub>r,b</sub> = k<sub>B</sub>T/f<sub>r</sub><sup>||</sup> are defined as:⁵⁴

$$ f_t^{\parallel} = \frac{2 \pi \eta L}{\ln(L/d) - 0.207 + \frac{0.980}{(L/d)} - \frac{0.133}{(L/d)^2}} \qquad (5) $$

$$ K_B \qquad (6) $$

All of the values, as summarized in Table 1, vary as the length changes. The translational diffusivity D<sub>t</sub>, rotational diffusivity D<sub>r</sub>, and rotational velocity decrease with increasing length
which are easy to understood by the Einstein law; as the length increases, both translational and
rotational drag forces increase, which results in a decrease in both the diffusivity and velocity.
However, while $D_t$ is quite close to $D_{t,b}$, a discrepancy of several orders of magnitude is observed
between $D_r$ and $D_{r,b}$ for longer core-shell NWs. The vortices at the tail of the cathode, found in
the numerical modelling (see again Figure 1b) may explain the observed discrepancy between $D_r$
and $D_{r,b}$ for a longer NW. This additional fluidic drag caused by the vortices, electrochemically
formed contributes to the large reduction in the rotational diffusivity, hence reducing its
tendency to rotate and, therefore, increasing its motion stability (or directionality.) For a detailed
elucidation, we example macro-scaled flying objects, such as rockets or airplanes. For those
flying objects, it is commonly known that the center of drag force should locate behind the center
of thrust for a directional stability, and the stability further increases with the distance of the two
centers. In our case, the center of thrust locates at the tip of the anode, while the center of drag
force, supposed to be at the center for this rectangular shaped-nanomotor is actually shifted to the
side of the cathode tip due to the additional drag force. The distance of the two centers further
increases with the size of vortex as the length increases.

In addition, the increase in translational velocity (v) with increasing length is unexpected
and somewhat counter-intuitive. Previous study conducted on Cu/Pt nanomotors show a decrease
in velocity with increasing nanomotor length, most likely due to the increased drag force for a
longer length.²⁰ However, in our experiments the speed of Au-Ru core-shell nanomotor increased
with the nanomotor length, as shown by the averaged measured velocities in Figure 3c for
lengths of 1.5, 2.5 and 3.5 µm (N>8 for each length). Our experimental values show a dissimilar
trend with the numerical simulations (Figure 1c). The increase in speed with length in the
experimental data implies that there might be an extra driving force that increases with length.
This extra driving force superimposes on the main driving force (electroosmotic force), resulting in increase in the net propulsive force of the nanomotor (Figure 3d). We can assume that the extra driving force can be related to a self-diffusiophoresis mechanism because O₂ concentration gradient around the motor surface is reinforced as the catalytically reactive surface area (Ru) increases with length. Although it is intuitively compelling that self-diffusiophoresis due to the generated O₂ concentration on the Ru surface leads to a speed enhancement, the exact magnitude of such enhancement remains unknown, and it is therefore difficult to directly compare the relative contribution from the enhanced force due to O₂ generation, and the larger viscous drag that a longer rod would experience slowing down the motor.

**Catalytic propulsion of the core-shell NWs with various material combinations and the prediction of their propulsive force.** In order to further investigate the role of diffusiophoresis in the catalytic propulsion of core-shell nanomotors, we fabricated Au/Rh and Rh/Au core-shell NWs with a length of 2.5 µm. Their motion in the presence of 20 wt% H₂O₂ were compared with that of Au/Ru core-shell NW. We note that Ru/Au core-shell NW was not fabricated due to the growth limit of Ru cores beyond 200 nm in a length. The trajectories of the core-shell NWs are represented in Figure 4. The speed comparison of these three types of nanomotors was Au/Ru >> Rh/Au > Au/Rh (See the Supplementary movie2).

Such a trend cannot be explained by existing theory on self-electroosmosis, and we reason as follows. The speed of a self-electroosmotic nanomotor is in general correlated to a combination of the surface charge of the nanomotor (zeta potential), and the self-generated electric field as a result of surface electrochemical reactions. To understand the effects of these two factors, we first measured the zeta potential of Au/Ru, Rh/Au and Au/Rh core-shell NWs, all
yielding results around ~ -26 mV. This indicates that the observed speed difference among these three samples cannot be explained solely by the differences in their zeta potential. Secondly, as far as self-generated electric field is concerned, we believe that the difference among these three samples are to be insignificant, supported by a previous study by Wang et al.²² showing similar speed of Au-Ru, Rh-Au and Au-Rh segmented NW motors. To briefly summarize, self-electroosmosis mechanism would predict similar speeds for these three samples, which is in clear contrast to what we have experimentally observed.

Given the inadequacy of self-electroosmosis in explaining the observed speed trend, we attempt to reconcile our results with self-diffusiophoresis. The magnitude of the self-diffusiophoretic force (extra driving force) depends on the $O_2$ concentration gradient, developed by the decomposition of $H_2O_2$ on the catalytically active layer. According to the previous studies, the decomposition rate of $H_2O_2$ on Ru is twice as high as Rh, while it is 10 times slower on Au than on Rh.⁵⁵ This implies that the predicted magnitude of the self-diffusiophoretic forces on the core-shell NWs are in the order of Au/Rh >> Rh/Au > Au/Ru core-shell NWs, provided that the total number of $H_2O_2$ decomposition is defined as the product of the decomposition rate and the reactive surface area. With the regards, diffusiophoretic force directions on Au/Rh, Rh/Au, Au/Ru core-shell nanomotors can be predicted as Au → Rh, Rh → Au and Au → Ru respectively. The predicted force magnitudes and directions are illustrated in the left column of Figure 4. We note that the arrow sizes are relative among three core-shell samples.

To this end, the relative speeds among three nanomotors are predicted by comparing the magnitudes of the propulsive forces that is the sum of the self-electroosmotic force and self-diffusiophoretic force. Since the Au/Ru and Au/Rh core-shell NW exhibits the highest and lowest propulsive force respectively, the expected speeds for the core-shell NWs decrease in the
following order: Au/Ru > Rh/Au > Au/Rh. This prediction is in accordance with our
experimental observation, confirming our propulsion mechanism.

Magnetic guided motion of (Au-Ni)/Ru core-shell NWs.

In this section, we demonstrate that the trajectory of our core-shell NWs can be
controlled under an applied magnetic field in H₂O₂ solution. For a magnetically guided motion, a
Ni segment was additionally deposited on a Au segment, and subsequently coated with a Ru shell
(see **Figure S3** for SEM images and EDX mapping of the (Au-Ni)/Ru core-shell NWs). A
magnetic guided motion was performed under the magnetic field (,**B**̅) of 1mT with a
negligible magnetic field gradient. **Supplementary movie 3** shows rectangular trajectories of two
(Au-Ni)/Ru core-shell NWs when the field orientation is switched counterclockwise with a step
of 90°. Interestingly, the magnetic field only serves to align the motors parallel to the magnetic
field lines, but it does not determine the heading direction along them.

In conclusion, core-shell NWs composed Au/Ru have been fabricated and studied as a
potential catalytic nanomotor when submerged in H₂O₂. Their maximum speed was observed to
be 41±7.6 µm/s at a 20% H₂O₂ concentration. Moreover, decreased rotational diffusivity or,
equivalently, enhanced directionality is observed with increased length, which results from the
formation of vortices at the end of the cathode as revealed by the electroosmotic mechanism
based numerical simulation. Experimentally, this nanomotor design exhibits a positive length-
speed correlation, which is contrary to what occurs in other designs or in our simulation. In the
case of our core-shell nanostructures, we assume that the propulsion comes from two
simultaneous mechanisms: self-diffusiophoresis and self-electroosmosis. When the catalytic
active surface area (Ru) increases with length, the self-diffusiophoretic force increases due to a higher O₂ concentration gradient. For a core-shell Au/Ru NW, the generated self-diffusiophoretic force is superimposed to the self-electroosmotic force with the same force direction. Therefore, the net propulsion force is reinforced. The suggested propulsion mechanism also justifies the large difference in speed among Au/Rh, Rh/Au and Au/Ru core-shell NWs, which has not been observed for conventional bimetallic NWs. Finally, we have successfully demonstrated magnetically guided motion of core-shell NWs by inserting a Ni segment in the core-shell architecture as a magnetic responsive material. The core-shell fabrication method presented here also allows for the integration of materials within the shell such as magnetic parts, and prevent them to be in direct contact with the surrounding environment.
Figures
<figure><img src="image_35.png" /><figcaption>**Figure 1.** Numerical modeling of Au/Ru core-shell NW in the presence of H₂O₂: (a) A schematic drawing of the self-electroosmotic model for our Au/Ru core-shell NW. We note the force arrow is represented from the point of view of the nanomotor, rather than fluid. b) Magnitude of fluid velocity (background), fluid velocity (magenta arrows) and electroosmotic flux (red arrows) of Au/Ru core-shell NW with a length of 2.5 µm; the inserts are the magnified images of the magnitude of fluid velocity (background) and fluid velocity field (magenta arrows) for the length of (i) 0.5 µm, (ii) 1.5 µm, (iii) 2.5 µm and (iv) 3.5 µm; the diameter of NWs are fixed to 300 nm, and (c) Speed as a function of lengths.</figcaption></figure>
<figure><img src="image_36.png" /><figcaption>**Figure 2.** (a) A schematic drawing of the fabrication of core-shell NWs: the fabrication process includes AAO/Si substrate bonding and electrodeposition. BSE images of (b) a Au/Ru core-shell NW and (e) a Ru shell. *Inserts in (b) and (e) are schematic drawings of Au/Ru core-shell NW and Ru shell, respectively. HAADF STEM images of (c) a Au/Ru core-shell NW and (f) a Ru shell. TEM-edx maps of (d) a Au/Ru core-shell NW and (g) a Ru shell, respectively.</figcaption></figure>
<figure><img src="image_37.png" /><figcaption>(c)</figcaption></figure>

<figure><img src="image_38.png" /><figcaption>(b)</figcaption></figure>

<figure><img src="image_39.png" /><figcaption>(d)</figcaption></figure>

<figure><img src="image_40.png" /></figure>

**Figure3.** Experimental data of Au/Ru core-shell NW in the presence of H₂O₂. (a) Averaged speed as a function of the concentration of H₂O₂. Speed was averaged from at least 11 samples with an approximate length of 2.5 µm. Inset (i): A tracked path of a core-shell NW at 5 wt % H₂O₂. And inset (ii): A tracked path of a core-shell NW at 0 wt % H₂O₂. (b) a MSD curve of Au/Ru core-shell NWs at the approximate length of 2.5 µm. (c) Speed of Au/Ru core-shell NWs as a function of a length of NWs in the presence of 5 wt % H₂O₂. *The length of core-shell NWs ranges from 1 to 2 µm, 2 to 3 µm and 3 to 4 µm. Averaged speed from at least eight samples for each range. (d) A schematic drawing of our proposed mechanism for the propulsion of the Au/Ru core-shell NWs. We note the force arrows are represented from the point of view of the nanomotor, rather than fluid.
<table><caption>**Table 1.** Measured parameters ($D_t$, $v$, $D_r$ and $\omega$) and theoretical values ($D_{t,b}$ and $D_{r,b}$) of Au/Ru core-shell NWs</caption><thead><tr><th>Parameters<br>Length</th><th>D<sub>t</sub> (µm<sup>2</sup>/s)</th><th>D<sub>t,b</sub><br>(µm<sup>2</sup>/s)</th><th>v (µm/s)</th><th>D<sub>r</sub> (µm<sup>2</sup>/rad)</th><th>D<sub>r,b</sub><br>(µm<sup>2</sup>/rad)</th><th>Ω<br>(rad/s)</th></tr></thead><tbody><tr><td>1.8 µm</td><td>0.97</td><td>0.71</td><td>9.83</td><td>1.84</td><td>2.13</td><td>6.97</td></tr><tr><td>2.6 µm</td><td>0.58</td><td>0.58</td><td>16.35</td><td>0.44</td><td>1.52</td><td>5.73</td></tr><tr><td>3.4 µm</td><td>0.31</td><td>0.50</td><td>27.88</td><td>0.0015</td><td>1.18</td><td>1.43</td></tr></tbody></table>

<figure><img src="image_41.png" /><figcaption>**Figure 4.** The predictions of the magnitude and direction of self-electroosmotic and self-diffusiophoretic forces, and the experimentally observed tracked paths of (a) Au/Rh, (b) Rh/Au and (c) Au/Ru core-shell NWs over 4.8 sec.
* The arrow size are relatively predicted in three samples and force arrows are represented from the point of view of the nanomotor, rather than fluid.</figcaption></figure>
<figure><img src="image_42.png" /><figcaption>TOC</figcaption></figure>
## REFERENCES

(1) Ismagilov, R. F.; Schwartz, A.; Bowden, N.; Whitesides, G. M. Autonomous Movement and Self-Assembly. *Angew. Chem. Int. Ed. Engl.* 2002, 41, 652-654.

(2) Wang, W.; Duan, W.; Ahmed, S.; Mallouk, T. E.; Sen, A. Small power: Autonomous nano- and micromotors propelled by self-generated gradients. *Nano Today* 2013, 8, 531-554.

(3) Mano, N.; Heller, A. Bioelectrochemical Propulsion. *J. Am. Chem. Soc.* 2005, 127, 11574-11575.

(4) Ma, X.; Jannasch, A.; Albrecht, U. R.; Hahn, K.; Miguel-Lopez, A.; Schaffer, E.; Sanchez, S. Enzyme-Powered Hollow Mesoporous Janus Nanomotors. *Nano Lett.* 2015, 15, 7043-7050.

(5) Gaspar, S. Enzymatically induced motion at nano- and micro-scales. *Nanoscale* 2014, 6, 7757-7763.

(6) Li, J.; Shklyaev, O. E.; Li, T.; Liu, W.; Shum, H.; Rozen, I.; Balazs, A. C.; Wang, J. Self-Propelled Nanomotors Autonomously Seek and Repair Cracks. *Nano Lett.* 2015, 15, 7077-7085.

(7) Dey, K. K.; Zhao, X.; Tansi, B. M.; Mendez-Ortiz, W. J.; Cordova-Figueroa, U. M.; Golestanian, R.; Sen, A. Micromotors Powered by Enzyme Catalysis. *Nano Lett.* 2015, 15, 8311-8315.

(8) Li, J.; Gao, W.; Dong, R.; Pei, A.; Sattayasamitsathit, S.; Wang, J. Nanomotor lithography. *Nat. Commun.* 2014, 5, 5026.

(9) Kline, T. R.; Paxton, W. F.; Wang, Y.; Velegol, D.; Mallouk, T. E.; Sen, A. Catalytic Micropumps: Microscopic Convective Fluid Flow and Pattern Formation. *J. Am. Chem. Soc.* 2005, 127, 17150-17151.
(10) Sundararajan, S.; Lammert, P. E.; Zudans, A. W.; Crespi, V. H.; Sen, A. Catalytic Motors for Transport of Colloidal Cargo. *Nano Lett.* 2008, 8, 1271-1276.

(11) Dey, K. K.; Wong, F.; Altemose, A.; Sen, A. Catalytic Motors—Quo Vadimus? *Curr. Opin. Colloid Interface Sci.* 2016, 21, 4-13.

(12) Yadav, V.; Duan, W.; Butler, P. J.; Sen, A. Anatomy of Nanoscale Propulsion. *Annu. Rev. Biophys.* 2015, 44, 77-100.

(13) Sanchez, S.; Soler, L.; Katuri, J. Chemically powered micro- and nanomotors. *Angew. Chem. Int. Ed. Engl.* 2015, 54, 1414-1444.

(14) Wang, W.; Duan, W.; Ahmed, S.; Sen, A.; Mallouk, T. E. From one to many: dynamic assembly and collective behavior of self-propelled colloidal motors. *Acc. Chem. Res.* 2015, 48, 1938-1946.

(15) Guix, M.; Mayorga-Martinez, C. C.; Merkoci, A. Nano/micromotors in (bio)chemical science applications. *Chem. Rev.* 2014, 114, 6285-6322.

(16) Zhou, C.; Zhang, H.; Li, Z.; Wang, W. Chemistry pumps: a review of chemically powered micropumps. *Lab Chip* 2016, 16, 1791-1811.

(17) Colberg, P. H.; Reigh, S. Y.; Robertson, B.; Kapral, R. Chemistry in motion: tiny synthetic motors. *Acc. Chem. Res.* 2014, 47, 3504-3511.

(18) Solovev, A. A.; Mei, Y.; Bermudez Urena, E.; Huang, G.; Schmidt, O. G. Catalytic microtubular jet engines self-propelled by accumulated gas bubbles. *Small* 2009, 5, 1688-1692.

(19) Huang, W.; Manjare, M.; Zhao, Y. Catalytic Nanoshell Micromotors. *J. Phys. Chem. C* 2013, 117, 21590-21596.
(20) Liu, R.; Sen, A. Autonomous nanomotor based on copper-platinum segmented nanobattery.

*J. Am. Chem. Soc.* 2011, 133, 20064-20067.

(21) Paxton, W. F.; Kistler, K. C.; Olmeda, C. C.; Sen, A.; St. Angelo, S. K.; Cao, Y.; Mallouk, T. E.; Lammert, P. E.; Crespi, V. H. Catalytic Nanomotors: Autonomous Movement of Striped Nanorods. *J. Am. Chem. Soc.* 2004, 126, 13424-13431.

(22) Wang, Y.; Hernandez, R. M.; Bartlett, D. J.; Bingham, J. M.; Kline, T. R.; Sen, A.; Mallouk, T. E. Bipolar Electrochemical Mechanism for the Propulsion of Catalytic Nanomotors in Hydrogen Peroxide Solutions†. *Langmuir* 2006, 22, 10451-10456.

(23) Pumera, M. Electrochemically powered self-propelled electrophoretic nanosubmarines. *Nanoscale* 2010, 2, 1643-1649.

(24) Fournier-Bidoz, S.; Arsenault, A. C.; Manners, I.; Ozin, G. A. Synthetic self-propelled nanorotors. *Chem. Commun.* 2005, 4, 441-443.

(25) Ma, X.; Hahn, K.; Sanchez, S. Catalytic mesoporous Janus nanomotors for active cargo delivery. *J. Am. Chem. Soc.* 2015, 137, 4976-4979.

(26) Yamamoto, D.; Takada, T.; Tachibana, M.; Iijima, Y.; Shioi, A.; Yoshikawa, K. Micromotors working in water through artificial aerobic metabolism. *Nanoscale* 2015, 7, 13186-13190.

(27) Howse, J. R.; Jones, R. A.; Ryan, A. J.; Gough, T.; Vafabakhsh, R.; Golestanian, R. Self-motile colloidal particles: from directed propulsion to random walk. *Phys. Rev. Lett.* 2007, 99, 048102.

(28) Frankel, A. E.; Khair, A. S. Dynamics of a self-diffusiophoretic particle in shear flow. *Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys.* 2014, 90, 013030.
(29) Golestanian, R.; Liverpool, T. B.; Ajdari, A. Propulsion of a molecular machine by asymmetric distribution of reaction products. *Phys. Rev. Lett.* 2005, 94, 220801.

(30) Wilson, D. A.; Nolte, R. J.; van Hest, J. C. Autonomous movement of platinum-loaded stomatocytes. *Nat. Chem.* 2012, 4, 268-274.

(31) Wang, S.; Wu, N. Selecting the swimming mechanisms of colloidal particles: bubble propulsion versus self-diffusiophoresis. *Langmuir* 2014, 30, 3477-3486.

(32) Hu, J.; Odom, T. W.; Lieber, C. M. Chemistry and Physics in One Dimension: Synthesis and Properties of Nanowires and Nanotubes. *Acc. Chem. Res.* 1999, 32, 435-445.

(33) Nicewarner-Pena, S. R.; Freeman, R. G.; Reiss, B. D.; He, L.; Pena, D. J.; Walton, I. D.; Cromer, R.; Keating, C. D.; Natan, M. J. Submicrometer metallic barcodes. *Science* 2001, 294, 137-141.

(34) Ozel, T.; Bourret, G. R.; Mirkin, C. A. Coaxial lithography. *Nat. Nanotechnol.* 2015, 10, 319-324.

(35) Kline, T. R.; Paxton, W. F.; Mallouk, T. E.; Sen, A. Catalytic Nanomotors: Remote-Controlled Autonomous Movement of Striped Metallic Nanorods. *Angew. Chem. Int. Ed. Engl.* 2005, 117, 754-756.

(36) Hangarter, C. M.; Lee, Y. I.; Hernandez, S. C.; Choa, Y. H.; Myung, N. V. Nanopeapods by galvanic displacement reaction. *Angew. Chem. Int. Ed. Engl.* 2010, 49, 7081-7085.

(37) Lauhon, L. J.; Gudiksen, M. S.; Wang, D.; Lieber, C. M. Epitaxial core-shell and core-multishell nanowire heterostructures. *Nature* 2002, 420, 57-61.