Transcranial focusing of arbitrary ultrasonic fields
using acoustic holograms
Sergio Jiménez-Gambín, Noé Jiménez∗ , José María Benlloch, Francisco Camarena
Instituto de Instrumentación para Imagen Molecular, CSIC-UPV, Valéncia, Spain* Corresponding author, nojigon@upv.esAbstract
We present ultrasonic phase plates that are able to produce arbitrary field distributions, i.e., acoustic holograms,
inside the skull. Using 3D printing techniques, we are able to produce lenses that correct the aberrations of theskull and, simultaneously, produce ultrasonic fields whose spatial distribution fits a target organ at the central
nervous system. In particular, using experimental techniques on a human skull phantom and full-wave simulations, several configurations are tested. First, a multiple-point focusing lens is designed to simultaneously
focus at both human hippocampi. Second, a beam following an arbitrary curved trajectory, i.e., a self-bending
beam is presented. Finally, we report a holographic plate producing a broad focus that overlaps with the left
hippocampus. The results show that 3D printed holographic lenses can be used to control the spatial features ofultrasonic beams inside the skull in an unprecedent manner using single-element ultrasonic sources.

Keywords: Acoustic holograms; Transcranial focusing; Biomedical ultrasound.

1INTRODUCTION

Acoustic holographic lenses are complex surfaces that can modify the phase of the transmitted or reflected wavefront in such a manner that a complex image can be formed. Acoustic holographic lenses have demonstrated
the ability to manipulate acoustic waves in free media, i.e., without inhomogeneities [1, 2, 3, 4]. In the contextof biomedical applications, when the target tissue lays behind high-impedance tissues, e.g., soft-tissue surrounded by bones, the beam experiences strong aberrations due to refraction, reflection and absorption processes [5].
In the particular case of transcranial propagation skull bones are always present in the path towards the central
nervous system (CNS). In this way, the precise control of acoustic focus into the CNS is mainly limited due tothe strong phase aberrations produced by the refraction and attenuation of the skull [6].
Only few works have tackled the problem of beam focusing through aberrating layers using metamaterials [7]or phase plates [8]. In Ref. [7] a 2D configuration was proposed theoretically using a metasurface basedon membranes. Recently, the use of phase plates to generate simple focused sources have been reported toavoid beam aberrations in transcranial propagation [8]. However, the technique was limited to focus the beam
into a single focal spot at the near field of the source. Besides, in some non-thermal transcranial ultrasoundapplications such as blood-brain barrier opening [9] or neuromodulation [10] the ultrasound beam might be set
to fully-cover a geometrically complex CNS structure rather than focusing over a small focal spot.
In this work [11], we propose the use of 3D-printed holographic phase plates to produce ultrasonic fields ofarbitrary shape into the human brain. The holographic lenses designed in this work allow the reconstruction ofcomplex diffraction-limited acoustic images including the compensation of the aberrations produced by a skull
phantom. In particular, we theoretically, numerically and experimentally demonstrate the generation of several
holographic patterns, of increasing complexity, all with direct practical application to biomedical ultrasound: anarbitrary set of points, an arbitrary curved line, and an arbitrary volume.

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Self-bending
acoustic beam
Holographic plate
Target structure

z=d, holographic planeh(x, y)Ultrasound source

z=0, source planeyz¢hx
2aFigure 1. (a) Scheme of the holographic lens focusing over a target CNS structure. (b) Geometry of the holographic lens. The
lens, of aperture 2a is subdivided in pixels of height h(x, y). The source is located at z = 0, while the holographic plane is locatedat z = d.

2Results(a)

0 Simulationy (mm)

2.1 Multiple-point holograms
First, two points located at the center of mass of both left and right human hippocampi are selected. The
details about the hologram generation and the methods used can be found in Ref.[11]. The field produced by
the bifocal lens propagating through a human occipital/parietal skull phantom including the compensation for theaberrations of the skull is shown in Figs. 2 (a-f). First, Figs. 2 (a,b) show the axial field cross-section, p(x, y =0, z), using the pseudo-spectral simulation method and measured experimentally, respectively. We observe thatthe reconstructed field accurately matches the target foci, and the experimental results agree with the simulations.
The corresponding transverse field distributions at z = 105 mm are shown in Figs. 2 (c,d) where sharp focusing
is observed.
10.5y (mm)

50

S0m
nto
hall pku-10

Simulation

-20

020

Experiment400.5(d)z = 105 mm-20020x (mm)9040(b)100z (mm)(e)

SimulationExperiment

0Experiment100

1z = 105 mm

10-40-1010-40z (mm)

(c)

00050

100150z (mm)
1(f)

110
1200.5130140 y = 0 mm

150-500x (mm)50-40-200x (mm)20400-40-20020

40x (mm)Figure 2. Axial field cross-section obtained for the bifocal lens using simulations (a) and experiments (b). (c-d)
Corresponding transversal pressure field distributions. Colorbar in units normalized to the peak pressure. (e,f)
Simulated and experimental normalized axial and transversal field cross-sections, respectively.

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2.2 Self-bending beams
The previous results show that holographic phase plates can retain phase information of multiple foci. Using
this idea, we can set more complex targets following the shape of functional structures found in the CNS. Here,
we set the target holographic pattern to a beam following a curved trajectory. A sketch of the target trajectory
is shown in Fig. 3 (a). The axial cross-sections of the forward propagated field in water is shown in Fig. 3 (a).
We observe that using TR method the self-bending beams can be obtained, and the beam accurately follows
the target trajectory. Using simulation and a lens made of elastic material a similar result is obtained, as shownin Fig. 3 (b). The experimental tests show a similar pressure field distribution in comparison with theory using
the Rayleigh-Sommerfeld integral and simulations using pseudo-spectral methods. Finally, when the aberration
layer of the skull phantom is included the corresponding holographic lens also reconstructs the target acoustic
image with curved trajectory, as shown in Figs. 3 (c). A similar lateral shift of the peak pressure location in theexperiments, of 0.25 mm in the x direction is observed at z = 30 mm and y = 0 mm. Both results demonstratethat using TR methods self-bending beams following a target curve can be obtained inside the skull phantom
using acoustic holographic lenses.
0(b)2020u20 Sk

0.5

40

050-200x (mm)2030
40Simulation

1targettrajectory

10.5050-200x (mm)20z (mm)

10

Experiment1030(c)lens

10antomll ph30140

0.5500-200x (mm)Experimentlens

Simulation0holographic plane(a)z (mm)z (mm)

020

Figure 3. Theoretical (a) axial pressure field distribution for the self-bending beam in water. Simulated (b) axialpressure field distribution for the self-bending beam in water. Corresponding experimental results are shown in
the insets in (b). (c) Simulated axial and transversal pressure field including the skull phantom. Corresponding
experimental results are shown in the insets.

2.3 Volumetric holograms overlapping CNS structures
Going further, we designed a holographic lens which produces an acoustic image that fits the right humanhippocampus volume. The holographic surface was placed near the occipital/parietal bones to adapt the acoustic
image to the elongated geometry of the human hippocampus. However, we locate the lens at the center of theskull symmetry plane in order to demonstrate the steering capabilities of this holographic lens.
The field distribution produced by acoustic holographic lenses including the skull phantom is shown in Figs. 4.
Both holographic images present the same qualitative performance and provide a similar overall covering of theinterest zone. In addition, both axial (Fig. 4 (a,b)) and transversal (Figs. 4 (c,d)) field distributions are similar of
those produced in water without the skull phantom, showing that, first, limited-diffraction holographic volumes
can be reconstructed and, second, the aberrations produced by the skull phantom on these complex beams canbe compensated at the source plane by the acoustic holographic lenses. Finally, the transversal and axial crosssections, shown in Figs.4 (e,f), show that the experimental and simulated acoustic holographic lens produces afield enhancement that matches the target distribution.

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0

Simulation
Experiment (b)

(a)

1 (e)

80z (mm)mnto
haplulSk100-10120z (mm)

(f)

(d)

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target volume-40-20-20
10.5

1500y (mm)target volume

Target0-50

10-40x (mm)1000.5Experiment50

Simulation
Experiment050x (mm)-20x (mm)1 (f)Simulation

(c)

00.5

0.5(h)

20-50

Simulation
Simulation
Experiment
Experiment

100x (mm)50

Target0050

100150200z (mm)Figure 4. Volumetric hologram results. (a,b) Simulated and experimental axial pressure distribution. (c,d)
Transversal field cross-sections. (e) Simulated, experimental transversal field distribution. (f) Simulated andexperimental axial pressure distribution.

3CONCLUSIONS

We have shown that using 3D printed acoustic holograms it is possible to conform diffraction-limited ultrasonicfields of arbitrary shape compensating the aberrations of a the human skull. In particular, experimental tests
using a 3D printed skull phantom and numerical simulations using a realistic skull were performed to accurately
generate multiple focal holograms, self-bending beams and volumetric holographic fields overlapping a target
CNS structure. The proposed approach using holographic lenses represents a step forward when comparedwith the existing solutions using phase arrays, since it opens new venues to develop reliable and cost reduced
ultrasonic applications.
The concept shown in this work opens new doors to optimize and widespread incoming therapy treatments suchas ultrasound-assisted blood-brain barrier opening for drug delivery and neuromodulation, or ultrasonic imagingof the central nervous system using low-cost devices. Considering the emergence of metamaterials [12] andtheir huge flexibility, we also advance incoming biomedical applications of active holographic metasurfaces forthe generation of complex fields in the central nervous system.

ACKNOWLEDGEMENTS
This work was supported by Generalitat Valenciana through grants APOSTD/2017/042, ACIF/2017/045 andGV/2018/11. FC acknowledges financial support from Agència Valenciana de la Innovació through grant INNCON00/18/9 and European Regional Development Fund (IDIFEDER/2018/022).

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