Rupture of the scapholunate interosseous ligament can cause the dissociation of scaphoid and lunate bones, resulting in impaired wrist function. Current treatments (e.g., tendon-based surgical reconstruction, screw-based fixation, fusion, or carpectomy) may restore wrist stability, but do not address regeneration of the ruptured ligament, and may result in wrist functional limitations and osteoarthritis. Recently a novel multiphasic bone-ligament-bone scaffold was proposed, which aims to reconstruct the ruptured ligament, and which can be 3D-printed using medical-grade polycaprolactone. This scaffold is composed of a central ligament-scaffold section and features a bone attachment terminal at either end. Since the ligament-scaffold is the primary load bearing structure during physiological wrist motion, its geometry, mechanical properties, and the surgical placement of the scaffold are critical for performance optimisation. This study presents a patient-specific computational biomechanical evaluation of the effect of scaffold length, and positioning of the bone attachment sites. Through segmentation and image processing of medical image data for natural wrist motion, detailed 3D geometries as well as patient-specific physiological wrist motion could be derived. This data formed the input for detailed finite element analysis, enabling computational of scaffold stress and strain distributions, which are key predictors of scaffold structural integrity. The computational analysis demonstrated that longer scaffolds present reduced peak scaffold stresses and a more homogeneous stress state compared to shorter scaffolds. Furthermore, it was found that scaffolds attached at proximal sites experience lower stresses than those attached at distal sites. However, scaffold length, rather than bone terminal location, most strongly influences peak stress. For each scaffold terminal placement configuration, a basic metric was computed indicative of bone fracture risk. This metric was the minimum distance from the bone May 22, 2021 1/16Manuscript Click here to access/download;Manuscript;plos_latex_NataliyaPerevoshchiko surface to the internal scaffold bone terminal. Analysis of this minimum bone thickness data confirmed further optimisation of terminal locations is warranted. Introduction 1 The human wrist is a complex joint that includes 8 small carpal bones arranged in two 2 rows (Fig 1). The carpals are interconnected by intrinsic and extrinsic ligaments, and 3 form at least 18 articulations. The scaphoid bone straddles both carpal rows and is 4 bound to the lunate bone by the strong scapholunate interosseous ligament (SLIL). The 5 SLIL is C-shaped and attached to the proximal edges of the scapholunate articulation 6 (Fig 1, top right). The SLIL is comprised of three distinct anatomical regions, i.e. the 7 dorsal, proximal, and volar region [1], which each presents distinct and anisotropic 8 mechanical properties. The thickest and strongest of the three is the dorsal region, 9 which is the primary stabiliser of the scapholunate joint [1{4], and is also mostly 10 commonly injured during violent hyperextension of the wrist, such as during a fall [5]. 11 Figure 1. Wrist anatomy. Within the carpal bones of the wrist are the scaphoid and lunate bones. The scaphoid and lunate are held together by a the interosseous scapholunate ligament. A three-dimensional rendering of the scapholunate interosseous ligament is presented (top right). Removing the scaphoid reveals the dorsal (blue), proximal (yellow), and volar (green) regions of the the interosseous scapholunate ligament. Rupture of the SLIL can cause scapholunate (SL) dissociation, resulting in impaired 12 wrist function and future onset of hand and wrist osteoarthritis. Studies of cadaveric 13 wrists indicate only the dorsal SLIL region needs repair or reconstruction in order to 14 restore normal carpal kinematics [6]. Typically, complete SLIL rupture requires surgical 15 intervention to restore wrist stability, with repair possible in early stages and 16 reconstruction used for delayed presentation. Many different treatments for SLIL 17 rupture have been suggested, with varying clinical results and poor reliability [7{14]. 18 Usually, SLIL reconstruction involves a tendon-based approach [8 {12] aiming to restore 19 wrist stability using a tendon graft replacing the ruptured SLIL. However, tendon-based 20 approaches present with inconsistent and often poor clinical outcomes. Indeed, 20-40 % 21 of patients go on to develop functional limitations and wrist osteoarthritis [15,16]. 22 Moreover, harvesting a portion of the flexor carpi radialis tendon as a graft (as is 23 common) is problematic, as this muscle is important to dynamic wrist stability [17]. 24 Furthermore, tendonous tissue may not accurately mimic the biomechanical properties 25 of the SLIL, thus limiting its effectiveness for treating SLIL rupture [18]. 26 Tissue engineering is a promising avenue for replacing injured anatomical structures 27 of the hand [19,20], especially given the limited availability of donor tissue. Recently, a 28 multiphasic bone-ligament-bone (BLB) scaffold [21] has been proposed to reconstruct 29 the dorsal SLIL, and which can be 3D-printed using medical grade polycaprolactone 30 (PCL). In this BLB scaffold, the ligament portion was represented by approximately 31 parallel fibers terminating onto orthogonal plugs that interface with bone (Fig 2). 32 Henceforth, the ligament portion will be referred to as the "ligament-scaffold". In-vivo 33 testing on small- and medium-sized animals demonstrated biocompatibility of the BLB, 34 as evidenced by vascularisation and incorporation into the rabbit knee, as well as 35 collagen deposition in the ligament-scaffold and bone formation within bone 36 plugs [21,22]. Despite these promising results from animal studies, use of BLB scaffold 37 in the human wrist remains a non-trivial challenge due to the limited understanding of 38 the physiological conditions of the human wrist, and the interaction between scaffold 39 design and surgical installation. Indeed, sizing the scaffold for SLIL reconstruction is a 40 May 22, 2021 2/16 careful balance between being small enough to fit in the small bones of the wrist, while 41 being robust enough to avoid failure during physiological wrist motion. 42 Figure 2. Design of multiphasic bone-ligament-bone scaffold. (a) A schematic 2D view and (b) 3D rendering of the scaffold design. This study presents a computational framework for the creation of personalised 43 ligament-scaffold and associated surgical plan using finite element analysis (FEA). 44 Given that the bone terminals are intended to be rigidly attached, or fused, to the 45 bones, the ligament-scaffold portions of the BLB construct are subjected to the highest 46 levels of deformation during physiological wrist motion. As such the focus of this study 47 is a mechanical evaluation of the ligament-scaffold. After manufacturing the BLB 48 scaffold using 3D-printing technique the computational framework encompassed: (1) 49 extracting physiological wrist motions; (2) mechanical testing to determine material 50 properties; (3) identification of material properties using inverse FEA; followed by (4) 51 FEA conducted under physiological motion; and (5) evaluation of the scaffold design. 52 We hypothesized the ligament-scaffold will withstand (i.e., operate below failure stress) 53 physiological wrist motion. Further, we hypothesized surgery positioning the 54 ligament-scaffold distally (i.e., mimicking native SLIL attachment sites) will result in 55 lower stresses during physiological motions compared to installation more proximal. 56 Methods 57 All data processing and visualization were performed using custom MATLAB (R2018b 58 The Mathworks Inc., Natick, MA, USA) codes and the open source MATLAB toolbox 59 GIBBON ( [23], http://www.gibboncode.org/). The FEA was implemented using the 60 open source software FEBio (version 2.8.5, Musculoskeletal Research Laboratories, The 61 University of Utah, USA, http://febio.org/ [24]). 62 Scaffold design and manufacturing 63 The BLB scaffold used in this study was a modification of that developed by Lui and 64 co-workers [21] and is made by 3D-printing of medical grade PCL (PC12). The BLB 65 scaffold design is depicted in Fig 2a and b in 2D and 3D views, respectively. Overall, 66 the scaffold consisted of two terminals orthogonal to the ligament-scaffold portion. The 67 ligament-scaffold portion was composed of parallel PCL fibres mimicking native 68 ligament structure. The terminals are intended to slot into wells drilled into the 69 scaphoid and lunate, and are round cross-sections. 70 The scaffolds were 3D-printed using an 3D-Bioplotter Developer Series 71 (EnvisionTEC GmbH), fitted with a 400 m Tecdia Arqu e needle (ARQ-S-2030; Tecdia 72 INC) attached to a high temperature head. The PCL material was extruded 73 continuously to ensure strong cohesion between scaffold components and host 74 environment which is essential for successful surgical installation and mechanical 75 performance. 76 The BLB scaffold template (i.e., digital object) was loaded into the Perfactory RP 77 software (EnvisionTEC, GmbH) wherein it was processed into 360 m slices (80 % of 78 printer needle diameter). The resulting file was transferred to the main software of the 79 3D-Bioplotter. Therein, the scaffold was assigned an infill comprising 0.7 mm fibre 80 spacing (60 % of porosity) and a 0{90layer-to-layer rotation, resulting in 4 layers of 81 fibres in the ligament compartment (total 28 fibres). The PCL material was placed in a 82 stainless reservoir and heated at 110C through a heated cartridge unit and extruded 83 through a 350 m nozzle to deposit PCL fibres on a programmable stage at 2.5 mm/s. 84 May 22, 2021 3/16 Surgical installation site for scaffold 85 Fig 3 shows an anatomical model of a surgical site for scaffold installation and 86 surrounding bony anatomy. Bright green lines indicate native SLIL attachment sites. In 87 theory, to best approximate biomechanical function of the native SLIL scaffold 88 terminals ("bone plugs") should coincide with these attachment sites. In practice, 89 surgical techniques employ more proximal attachment sites where there is greater bone 90 volume to receive bone plugs and are deemed lower risk for bone fracture during 91 surgical drilling. The location chosen for scaffold installation depicted in Fig 3 is a 92 compromise between anatomical (and assumed biomechanical) fidelity and surgical risk. 93 Figure 3. The 3D anatomical model created from computed tomography scan. The model consists of capitate (grey), scaphoid (green), lunate (yellow), and radius (grey) bones. Bone positions in dorsal view of anatomical model correspond to maximum wrist flexion. The attachment sites of the dorsal SLIL are depicted with green dotted lines on both scaphoid and lunate. The dorsal SLIL attachment sites are derived from MRI scan of intact native SLIL with the wrist at neutral position and projected onto the anatomical model created from computed tomography scan. The BLB scaffold is placed at a position proximal to the native attachment sites. Three surgical installation sites for the ligament-scaffold portion (Fig 4a) of the BLB 94 scaffold were assessed using FEA and shown in Fig 4b, c, and d. Due to the regional 95 anatomy, each candidate site required a ligament-scaffold of different length. In total, 96 twelve FEA models were developed based on different candidate installation sites and 97 ligament-scaffold lengths, and subjected to the same motion boundary conditions from 98 one human subject. In Fig 4b, the attachment sites of the dorsal SLIL depicted by 99 green dotted lines on both scaphoid and lunate will be referred to as the distal surgical 100 site. Typical surgical sites are more proximal to the native SLIL footprint in Fig 3 and 101 4d) and will be referred to as such. Finally, the surgical site between distal and 102 proximal (Fig 4c) is proposed, and will be referred to as intermediate. Further, surgical 103 installation of the scaffold should leave an intact wall of bone surrounding the plugs and 104 countersink the ligament-scaffold beneath the surface to prevent impingement with 105 other bones during wrist motion. 106 Figure 4. FEA models. (a) The 28 fibres represent ligament-scaffold where red and black nodes are prescribed boundary conditions. Rigid bones demonstrate (b) distal, (c) intermediate and (d) proximal ligament-scaffold installation sites for finite element analysis. Mechanical testing 107 To determine material behaviour, rectangular 3D-printed samples of PCL were used for 108 uniaxial tensile and cyclic testings. Samples had an overall length of 15 mm, consisting 109 of a ligament-scaffold portion 10 mm in length, and contained 28 fibers each of 350 m 110 diameter (Fig 5). Seven monotonic and five cyclic tensile tests were performed. For 111 these samples, the bone plugs were filled with epoxy resin (Selleys Araldite 5 Minute, 112 Australia) to stiffen them before being inserted into pneumatic grips. This prevented 113 compression and stress concentration at the borders between bone plugs and 114 ligament-scaffold. Tensile mechanical properties of the rectangular sample were 115 measured (5848 Microtester, Instron, USA) fitted with a 500 N load cell operating with 116 a 1/3 mm/seconds cross-head speed at room temperature. Cauchy stress and stretch 117 were calculated. Cyclic testing was performed in phosphate buffer saline (PBS) at 37C 118 May 22, 2021 4/16 by applying 0.1 N preload. Samples were then subjected to 1000 continuous cycles of 119 10% strain at 0.5 Hz. 120 Figure 5. Geometry of rectangular sample. A 3D schematic of the rectangular sample used for uniaxial tensile and cyclic testings that consists of bone plugs and 10 mm length ligament-scaffold with 28 fibers and 350 m in diameter each. Geometry and meshing for computational modelling 121 The 3D contours of the scaphoid, lunate, capitate, and radius were derived from 122 segmenting bone regions from X-ray computed tomography (CT) images. These 123 contours were then converted to triangulated surface models, wherein bones were 124 represented as rigid bodies. The ligament-scaffold, in three length permutations (3-, 5-, 125 7- and 10- mm), was meshed with hexahedral elements. 126 Physiological boundary conditions 127 The kinematic boundary conditions (i.e., rotations and translations of scaphoid, lunate, 128 and capitate) were derived from tri-planar videoradiography. The radius was 129 mathematically fixed and kept static. Wrist motion was defined with reference to the 130 capitate, which moves almost identically with the third metacarpal [42]. Using a similar 131 approach to bi-planar videoradiography, tri-planar videoradiography combines a 132 high-speed X-ray image sequences with 3D bone volumes and contours obtained from 133 static CT scans to track 3D bone motion [43{46]. Motion data were collected from a 134 single cadaveric specimen moved through two sets of flexion/extension rotations and 135 ulnar/radial deviations. The resulting physiological boundary conditions for scaphoid, 136 lunate, and capitate were then applied to the carpal bones individually and applied to 137 the ends of ligament-scaffold (Fig 4a, red and black dots) to simulate a rigid BLB 138 interface. This approach enables prescription of physiological motion directly to the 139 ligament-scaffold (or alternatively the bones to which it is attached) based on motion 140 from medical images. 141 For the tri-planar videoradiography, X-ray sources were oriented 120relatively, with 142 one parallel to the floor resting atop a trestle table. The cadaveric forearm was placed 143 on the trestle table, and a wooden dowel used to manipulate the hand from outside the 144 field-of-view. The hand was manipulated throughout flexion-extension and radial-ulnar 145 deviation over one continuous 10 second data capture. The capitate, scaphoid, and 146 lunate were tracked within the videoradiographic images, and were analyzed in a 147 2D-to-3D image registration software, Autoscoper (Brown University) [47]. Following 148 registration, their 3D postures were calculated. Since surgical installation of the scaffold 149 will be performed with the wrist flexed, wrist flexion was used as the reference frame 150 and the path of flexion-extension-neutral-radial deviation-ulnar deviation was then used 151 for FEA. 152 The experimental work to acquire the carpal database was approved by the 153 Institutional Review Board (IRB) of Lifespan-Rhode Island Hospital, an AAHRPP 154 accredited IRB. 155 Constitutive modelling 156 Constitutive equations were used to describe the mechanical behavior of 157 ligament-scaffold portion of BLB scaffold (Fig 4a) through specification of the 158 dependence of force-displacement and force-time experimental data (see section above 159 May 22, 2021 5/16 on Mechanical testing). The arithmetic average of force-displacement and force-time 160 experimental curves were used for subsequent optimisation (described below). 161 The ligament-scaffold is modeled as isotropic hyperelastic and viscoelastic material. 162 The purely elastic behavior is represented by the following uncoupled hyperelastic strain 163 energy density formulation : 164 = dev+ vol (1) which features an additive decoupling of the deviatoric (shape changing) strain energy 165 density dev, and the volumetric strain energy density vol. The former is here defined 166 as: 167 dev(~1;~2;~3) =c m23X i=1~m i+~m i2 (2) The variable J=123, withithe principal stretches, represents the Jacobian or 168 volume ratio. The variables ~i=J1 3iare the deviatoric principal stretches. The 169 parametercis a shear-modulus-like material parameter with units of stress, and mis a 170 parameter controlling the degree of non-linearity. Note that Eq 2 represents a second 171 order Ogden formulation [48] (see also FEBio's Ogden implementation), with the 172 constraints c=c1=c2,m=m1=m2as motivated by [49]. Furthermore, note that if 173 J1 andm= 2 Eq 2 reduces to the well-known Mooney-Rivlin formulation. The 174 volumetric strain energy density volin equation 1is given by: 175 vol(J) = 2ln (J)2(3) whererepresents the material bulk-modulus. The 3D printed PCL material was 176 assumed to be nearly incompressible, as such the bulk modulus was here set at 177 = 100 c, which was found to be sufficient to keep volume changes below 1%. Using 178 the strain energy density function the elastic second Piola-Kirchoff stress tensor S 179 can be derived from: 180 S= 2@ C= 2@ dev C+pJC1=J2 3Dev~S + pJC1(4) withp=d vol dJthe hydrostatic pressure, Cthe right Cauchy green tensor, and ~San 181 elastic stress contribution given by: 182 ~S= 2@ dev @~C(5) where ~C=J2 3Cis the deviatoric right Cauchy-Green tensor. In Eq 4 use was made of 183 the deviatoric operator in the Lagrangian description: Dev~S =~S1 3(~S:C)C1. 184 The above expressions are for purely elastic behaviour. To extend the formulation to 185 capture the rate dependant viscoelastic behaviour of PCL the quasi-linear viscoelastic 186 theory is used here (see also [50] and FEBio's Uncoupled viscoelastic implementation). 187 In this case the time dependant second Piola-Kirchoff stress tensor is now written: 188 S(t) =J2=3tZ 1G(ts)d Dev~S dsds + pJ C1(6) whereGrepresents the following discrete relaxation function: 189 G(t) = 1 +NX a=1 aexpt a (7) May 22, 2021 6/16 The viscoelastic parameters ahave units of stress and represent proportional 190 parameters, and ahave units of time and are relaxation time parameters. In this study 191 a single relaxation term is used leading to N= 1, and the definition 1= and 1= . 192 Note that the relaxation function Gallows for the viscoelastic stresses to decay as a 193 function of time (as per the chosen parameters and ), such that once decayed, Eq 6 194 reduced to the purely elastic response defined by Eq 4. 195 Fitting constitutive law parameters 196 To identify PCL material parameters for the constitutive laws presented in Eq 1 and 197 viscoelasticity, an inverse iterative FEA technique was used. This technique involved 198 optimisation the parameters within constitutive equations to fit experimental data from 199 mechanical testing of the rectangular scaffold (Fig 5). In the optimisation, a single fibre 200 (Fig 6) of 10 mm in length and 0.35 mm in diameter was used to produce total force in 201 28 fibers of the ligament-scaffold. We assumed displacement applied to one end of the 202 fibre (red nodes) was uniform, causing uniform fibre deformation and force. Force 203 multiplied by the number of fibres gives total scaffold force subject to uniaxial loading. 204 Figure 6. A single fibre. The hexahedral mesh of a single fibre (left) used for inverse FEA, and two close-ups for the top two and bottom two element layers. The top surface nodes (red) feature a prescribed z-displacement and a zero x, and y displacement constraint. The bottom surface nodes (black) are fully constrained from moving. In total, two optimisations were conducted. First, elastic properties of PCL material 205 were optimised. Then, optimised elastic constants were used to optimise viscoelastic 206 properties. The final optimised material constants were used to evaluate mechanical 207 response of the ligament-scaffold under load from physiological wrist motion. Each 208 iteration of the optimisation involves creating an FEBio input file with the appropriate 209 material parameters, starting FEA, importing and analyzing results, comparing FEA 210 results to the experimental boundary conditions (from mechanical testing) to formulate 211 the objective function, and finally, performing inverse FEA based optimisation of the 212 objective function using a chosen optimisation algorithm. The inverse parameter 213 identification employed Levenberg-Marquardt [51] based optimisation (the MATLAB 214 lsqnonlin implementation). 215 The constitutive parameters were estimated by minimizing the following objective 216 function : 217 (`) =1 nnX i=1 Fexp iFsim i2(8) where,Fexp iare the experimentally forces and Fsim ithe simulated forces, and nis the 218 number of experimental data points over time. 219 The optimisation was deemed to have converged if either parameters or objective 220 functions did not vary >0.01. 221 During the first optimisation step, a single material behavior was assumed leading to 222 the material parameter vector `=[c m ]. In a second step, the material optimisation 223 employs parameter vector `=[c m ]. 224 In silico failure criteria for ligament-scaffold 225 To assess ligament-scaffold performance, candidate surgical installation sites were 226 subject to physiological wrist motion and calculated maximum and 3D von Mises 227 stresses were calculated and used as failure criteria. Yield strength of PCL was derived 228 from the average of the experimental force-displacement curve and used as critical stress. 229 May 22, 2021 7/16 Evaluation of scaffold design 230 A process to select the optimal configuration of scaffold was implemented, based on 231 FEA numerical evaluation, from the described subset of ligament-scaffold lengths and 232 surgical placements. Based on outcomes of the FEA, the ligament-scaffold portion of 233 BLB scaffold was optimised in terms of its length. The BLB scaffold was then digitally 234 placed at candidate surgical sites. Complying with optimisation and assessing safety of 235 installation, the 3D closest point distance was calculated from the surfaces of the 236 optimised scaffold and bone. Based on the experience of co-author RB (specialist wrist 237 surgeon), we considered proximity less than 2 mm as high risk for bone wall fracture 238 during drilling. 239 Results 240 Inverse finite element based mechanical properties 241 Cauchy stress-stretch curves ending in fracture and after yield are shown (Fig 7a and b, 242 respectively). Reproducibility of tensile curves is good. Average force-displacement and 243 force-time curves are plotted (Fig 8 and 9, respectively). Minimum and maximum 244 experimental curves are shaded gray, showing averages are good representations of 245 experimental data. 246 Results of material constant optimisation are summarized (Table 1). 247 Figure 7. The Cauchy stress-stretch curves. (a) The 3D-printed samples. The zoom in (b) locates the elastic-plastic region from Cauchy stress-stretch curves depicted in (a). Figure 8. Experimental and simulated force-displacement curves. This is the force-displacement curve using the material constants from the optimisation of the elastic properties. The area between minimum and maximum force-displacement experimental curves are shaded grey. Figure 9. Experimental and simulated force-time curves. This is the force-time curve using the material constants from the optimisation of the viscoelastic properties. The area between minimum and maximum force-time experimental curves are shaded grey. Table 1. Optimised material parameters for finite element models. c(kPa) 57.05317 m 2.0008 (MPa) 1.23339 25.365 Physiological boundary conditions 248 Rotation (0) and translation (mm) against time are plotted (Fig 10). Wrist flexion, 249 extension, neutral, radial deviation, and ulnar deviation were demarcated using color 250 coding (Fig 10). 251 May 22, 2021 8/16 Figure 10. Filtered motion of wrist, scaphoid, and lunate for flexion (first frame) acquired from tri-planar video-radiography [43]. Times 0; 1.11; 2.355; 3.42; 3.67 and 4.485 seconds correspond to flexion (red), extension (purple), radial deviation (green), neutral (yellow), ulnar deviation (cyan) and radial deviation again (green), respectively. Ligament-scaffold stresses during physiological motion 252 The maximum von Mises stresses from each of the three candidate surgical installation 253 sites and their associated ligament-scaffold lengths are plotted (Fig 11). Critical stress 254 (y) is 17 MPa (Fig 7b). There is no obvious effect of surgical installaiton site on stress 255 in the ligament-scaffold (Fig 11). The percentage of mesh elements exceeding critical 256 stress was calculate at a selected time for a representative ligament-scaffold (i.e., 3 mm 257 length) (Fig 11). The ligament-scaffold with 3 mm length shows highest stress profile 258 among different lengths assessed. 259 Figure 11. Summary of von Mises stress. The 10-, 7-, 5- and 3-mm ligament-scaffold inserted at distal (Fig 4b), intermediate (Fig 4c), and proximal (Fig 4d) surgical sites. The von Mises stress depicted maximum values of stress distribution in ligament-scaffold. The percentage of mesh elements exceeding critical stress ( y=17 MPa) for 3 mm ligament-scaffold length was calculated at times 0; 1.11; 2.355; 3.42; 3.67 and 4.485 seconds, which correspond to flexion (red), extension (purple), radial deviation (green), neutral (yellow), ulnar deviation (cyan) and radial deviation (green), respectively. The lowest and highest stresses consistently developed when the ligament-scaffold 260 was placed at proximal and distal sites, respectively, and independent of 261 ligament-scaffold length. Only when wrist was at full extension, highest stress developed 262 when ligament-scaffold installed at proximal rather than distal site. The stress in the 263 ligament-scaffold at the intermediate position interposes between those developed from 264 proximal and distal sites. 265 The percentage of mesh elements with ligament-scaffold with stress above critical 266 value demonstrated lower risk of failure at the proximal site (5 to 30 % of mesh 267 elements) and higher risk at distal site (10 to 50 % of mesh elements). The 268 ligament-scaffold placed at the intermediate site demonstrated an percentage of 269 elements above critical stress (from 5 to 20 %). 270 Maximum stress in 7- and 10- mm ligament-scaffolds was always beneath critical 271 stress. In contrast, the 3- and 5- mm lengths occasioned maximum stress above critical 272 stress. 273 The 3D von Mises stress distribution patterns for 3- and 7- mm ligament-scaffold 274 lengths and three candidate surgical installation sites are presented for 3 mm (Fig 12) 275 and 7 mm (Fig 13). The 7 mm ligament-scaffold length had a more consistent stress 276 distribution pattern compared to the 3 mm length variant. For the 7 mm length, and 277 across the candidate installation sites and wrist activities, high levels of stress developed 278 in both middle and sides of the ligament-scaffold. For 3 mm length, overall stress 279 development was scattered depending on installation site and wrist activity. 280 The von Mises stress patterns on the 3 mm scaffold (Fig 12) corresponded to certain 281 wrist motions (Fig 14). Specifically, stress peaks develop during radial deviation, as the 282 wrist transitioned between maximal wrist positions. 283 May 22, 2021 9/16 Figure 12. Von Mises stress distribution on the 3 mm ligament-scaffold at three surgical installation sites. (a) The distal (Fig 4b); (b) intermediate (Fig 4c); (c) proximal (Fig 4d) in the dorsal view of the wrist being in positions of extension, neutral, ulnar deviation, and radial deviation. The von Mises stress scale bar is from 1 to 18 MPa. Figure 13. Von Mises stress distribution on the 7 mm ligament-scaffold at three surgical installation sites. (a) The distal (Fig 4b); (b) intermediate (Fig 4c); (c) proximal (Fig 4d) in the dorsal view of the wrist being in positions of extension, neutral, ulnar deviation, and radial deviation. The von Mises stress scale bar is from 1 to 18 MPa. Figure 14. Von Mises stress distribution on the 3 mm ligament-scaffold at three installation surgical sites. Chosen time corresponds to maximum peaks in von Mises stress (Fig 12). (a) The distal (Fig 4b); (b) intermediate (Fig 4c); (c) proximal (Fig 4d) in the dorsal view of the wrist. Design evaluation 284 The 3D closest point distance was calculated from optimised scaffold's surface to bone 285 surfaces (Fig 15). The distance less than 2 mm is coded in blue and presented on the 286 scaphoid side in the scaffold. 287 Figure 15. Closest point distance (mm) from an optimised scaffold to scaphoid and lunate. The length of the ligament-scaffold is 7 mm. The scaffold is placed at the proximal site according to Fig 4d. The scale bar is in the range from 0 to 2 mm. Discussion 288 Reconstruction of the scapholunate interosseous ligament remains a challenge for hand 289 surgeons with various procedures proposed but no reliable solution. An engineered 290 scaffold providing mechanical support to the dissociated scaphoid and lunate bones 291 while also encouraging ligament formation has shown promising results in animal 292 models. However, use in the human wrist requires precision design, manufacture, and 293 installation. The aim of this paper was to develop a computational framework to design 294 a personalised scaffold and further, assist the surgeon plan the optimal site for scaffold 295 installation based on in silico modelling of the ligament-scaffolds performance in the 296 wrist. 297 We studied the 3D-printed PCL multiphasic scaffold design previously developed by 298 our colleagues for animal models (Fig 2, [21]). The goal of reconstruction with a printed 299 multiphasic scaffold is to implant the bone plugs into drilled holes in the scaphoid and 300 lunate with the longitudinal fibers aligned on the dorsal surface of the scapholunate 301 articulation. Over time, bone plugs ideally fully incorporate into scaphoid and lunate 302 while the ligament-scaffold bridge is replaced with collagen aligned to form a novel 303 biologically restored SLIL. The scaffold is designed to enable bone growth into its pores 304 (i.e., voids) within the terminal bone plugs, which also provide rigid fixation required for 305 bone in-growth into an implant. We assumed the ligament-scaffold will bear the major 306 loads produced by wrist motion. Therefore, it is important the stress developed in the 307 ligament-scaffold does not lead to failure. Consequently, FEA models were created to 308 evaluate maximum and 3D stress development by varying ligament-scaffold lengths and 309 May 22, 2021 10/16 positioning at feasible surgical sites, all subjected to physiologic wrist motion. The 310 power of studied FEA was the incorporation of subject-specific anatomy, coupled with 311 dynamic motion data derived from tri-planar videoradiography [43], and optimised 312 material parameters of PCL material model. Many previous studies used two X-ray 313 sources (i.e., biplanar videoradiography), but in this study three X-ray sources were 314 used to achieve a higher accuracy in tracking the motion of carpal bones, specifically, 315 capitate, scaphoid, and lunate used for FEA simulations. 316 FEA models of the wrist have been previously developed for various purposes to 317 study load transmission [25{29], behavior of a bone after fracture fixation [30{34], 318 vibration transmission [35,36], carpal bone replacement [37] and fingertip-object 319 interaction [38,39]. One of the strategies that has been used for studying wrist motion 320 in 3D FEA is load transfer to metacarpal bones at single or multiple points while 321 reproducing critical wrist postures in a quasi-static manor. In this approach, a model of 322 the entire wrist is constructed, including (e.g. [27{29]) or excluding (e.g. [40]) their 323 articulations. Another strategy has been focused on quasi-static 2D (e.g. [25,32,37]) or 324 3D (e.g. [26,30,31,33]) FEA of particular joint(s) with force or displacement control 325 modes mimicking particular physiological states. 326 Conversely, the 3D FEA models of SL joints developed in this study feature 327 displacement control to capture detailed wrist kinematics with a high temporal 328 resolution. This approach enables accurate analysis across a multitude of time points 329 during the motion cycle. 330 Calculated maximum and 3D von Mises stress were use as a failure criterion. The 331 proximal surgical site generated von Mises stress below critical levels using 7 to 10 mm 332 ligament-scaffolds, whereas 3- and 5- mm lengths will fail is subjected to physiologic 333 wrist motion. Under physiological wrist motion, the ligament-scaffold stresses appear to 334 be more influenced by ligament-scaffold length and wrist posture than surgical 335 installation sites. The 7 mm length demonstrates consistency in stress distribution in 336 the ligament-scaffold whereas stress is scattered in the 3 mm length. 337 Our numerical results show that stresses were larger in shorter specimens and, 338 therefore, generated larger strains for a given displacement. The mechanics of the native 339 SLIL have not received as much research focus as hand-wrist tendon, but tendons and 340 ligaments possess similar ultrastructure and physiology, as well as fulfilling similar 341 functions in particular cases ( [52]). Uniaxial tensile experiments on rat-tail 342 tendon [53,54] demonstrate larger total strains at short compared to long specimen 343 lengths. Stresses, on the other hand, were insensitive to specimen length. Further 344 experimental studies suggested this strain sensitivity might be a technical artifact (i.e., 345 "end-effect"), where extra unseen sample length within the grips of a mechanical testing 346 machine contributes dramatically to overall strain measurements in short specimens, 347 whereas the response of longer samples more closely reflects true material properties 348 ( [55,56]). Therefore, acquiring both simulation and experimental results for validation 349 is necessary. Experiments on cadaver is our target for future studies. 350 The wrist in a flexed posture was used as the reference position for studied FEA 351 modelling. Therefore, scaffold stress at this position was low. In all simulations the 352 different scaffold lengths, the maximum von Mises stress were substantially greater at 353 the position of maximum wrist extension and the transition motions: from flexion to 354 extension; from extension to radial deviation; from radial deviation to neutral; from 355 neutral to ulnar deviation; from ulnar to radial deviation. The transition motions show 356 pics in stress. These observations concur with a previous study [3] and suggest patients 357 should limit their wrist extension and transition motions in the early period after 358 surgery involving SLIL reconstruction. 359 Using anatomical models created from CT, we performed a semi-quantitative 360 analysis of risks for bone fracture at the candidate surgical installation sites. In this 361 May 22, 2021 11/16 approach, the closest distance between scaffold bone plugs and scaphoid and lunate out 362 surfaces was quantified . Based on the extensive experience of co-author RB (specialist 363 wrist surgeon), the proximity less than 2 mm was considered as high risk for bone wall 364 fracture. Moreover, there is a concern that the height of bone plug of 3 mm or less will 365 not provide a secure bone-plug interface and resulting micromotion will have a negative 366 impact on bone regeneration. The proximal site for SLIL reconstruction (i.e., scaffold 367 installation) offers more bone volume for drilling and subsequent plug insertion, 368 however, the location is proximal to the native SLIL footprint and this may impair 369 regeneration and potentially intrude on other tissues. In contrast, the distal site offers 370 comparatively limited bone volume to accommodate the current scaffold design, but 371 perhaps ideal mechanical and functional properties. A balance between installation 372 safety and mechanical function is suggested. 373 The scaffold design (Fig 2) warrants further optimisation to enhance bone plug 374 fixation into the proximal position to be safely placed proximally in the dorsal view of 375 the wrist. 376 Limitations 377 The major limitation of the current work is the motion data used to drive the FEA 378 simulations were collected from a single cadaveric specimen. At present, acquiring both 379 motion and force data from the small wrist bones, such as the scaphoid and lunate, 380 during dynamic activities is exceedingly difficult using 3D optical motion capture or 381 biplanar videoradiography. This difficulty is primarily due to the small size of these 382 bones and how they move relative to the other bones and tissues, often occluding line of 383 sight or causing collision between stand-off marker frames. Although wrist motion has 384 previously be calculated from other types of medical imaging, such as those found on 385 the Carpal Database (wrist anatomy and kinematics, created using static CT wrist 386 positions, [57]), kinematics generated using the Carpal Database are not comparable to 387 tri-planar videoradiography due to the different wrists studied and methods for 388 computing kinematics. The Carpal Database uses a mathematical model that describes 389 wrist motion based on quadratic surface models generated based on static bone poses. 390 The current data were collected using tri-planar videoradiography, which we contend is 391 the most appropriate and comprehensive data collected on wrist motion. Therefore, we 392 are confident with the results computed tri-planar videoradiography and FEA 393 simulations. 394 Another limitation of this study is the challenge of optimising the ligament-scaffold 395 fibre number and diameter. This is the outside of our scope. We anticipate changing 396 fibre number will constrain bone motions, which in turn will wrist function. 397 Finally, finite element models were not directly validated against measures of strain 398 in vivo or in situ. Ongoing experiments in our laboratory will explore whether 399 robotically actuated cadaveric wrists, when implanted with the scaffold, can provide 400 insight into scaffold mechanics under physiological motion and force boundary 401 conditions. Although the developed models can be used to provide insight into scaffold 402 mechanics when experimental data are not available, the validity of our predictive 403 simulations will only be as good as the assumptions and approximations used. 404 Conclusion 405 In conclusion, it is advisable to use longer scaffolds whenever possible to reduce the 406 stresses and strains and their variability during physiological wrist motion. The choice 407 of surgical installation site can be very sensitive to the patient's bone anatomy and 408 May 22, 2021 12/16 natural wrist motion. Therefore, the choice of surgical installation site should be 409 evaluated using individual wrist motion and bone anatomy of the patient. It is 410 recommended to avoid full extension of the wrist and transition motions between wrist 411 critical positions avoiding development of high stress and strain in scaffold. Future 412 mechanical evaluation is needed to experimentally confirm these findings. 413 Acknowledgments 414 The authors would like to acknowledge funding support for this project from the 415 Australian Medical Research Futures Fund: BioMedTech Horizons program, delivered 416 by the MTPConnect, grant # LIL BMTH 07. 417 We thank Dr. Steve A. Maas (lead software developer of the FEBio and 418 FEBioStudio projects, University of Utah) for useful discussions. 419 We also thank Amy M. Morton and Dr. Elizabeth L. Brainerd (Brown University) 420 for their help throughout tri-planar videoradiography data acquisition. 421