Holograms to focus arbitrary ultrasonic fields through the skull
Sergio Jiménez-Gambín, Noé Jiménez, José María Benlloch, Francisco Camarena
HHolograms to focus arbitrary ultrasonic fields through the skull
Sergio Jim´enez-Gamb´ın, No´e Jim´enez, ∗ Jos´e Mar´ıa Benlloch, and Francisco Camarena
Instituto de Instrumentaci´on para Imagen Molecular, Consejo Superior de Investigaciones Cient´ıficas,Universitat Polit`ecnica de Val`encia. Camino de vera s/n 46022 Val`encia, Spain (Dated: May 29, 2019)We report 3D-printed acoustic holographic lenses for the formation of ultrasonic fields of complexspatial distribution inside the skull. Using holographic lenses, we experimentally, numerically andtheoretically produce acoustic beams whose spatial distribution matches target structures of thecentral nervous system. In particular, we produce three types of targets of increasing complexity.First, a set of points are selected at the center of both right and left human hippocampi. Experimentsusing a skull phantom and 3D printed acoustic holographic lenses show that the correspondingbifocal lens simultaneously focuses acoustic energy at the target foci, with good agreement betweentheory and simulations. Second, an arbitrary curve is set as the target inside the skull phantom.Using time-reversal methods the holographic beam bends following the target path, in a similarway as self-bending beams do in free space. Finally, the right human hippocampus is selected asa target volume. The focus of the corresponding holographic lens overlaps with the target volumein excellent agreement between theory in free-media, and experiments and simulations includingthe skull phantom. The precise control of focused ultrasound into the central nervous system ismainly limited due to the strong phase aberrations produced by refraction and attenuation of theskull. Using the present method, the ultrasonic beam can be focused not only at a single pointbut overlapping one or various target structures simultaneously using low-cost 3D-printed acousticholographic lens. The results open new paths to spread incoming biomedical ultrasound applicationsincluding blood-brain barrier opening or neuromodulation.
I. INTRODUCTION
Holographic plates are surfaces that when illuminatedby a wave, typically light, modify the phase of the trans-mitted or reflected wavefront in such a manner that acomplex image can be formed [1–3]. In recent years, sub-wavelength thickness holographic metasurfaces have beendesigned using structured materials with subwavelengthresonances, namely metamaterials [4, 5]. Analogously,in acoustics, a broad range of locally-resonant structureshave been proposed to obtain a precise control of thewavefront at a subwavelength scale [6, 7], including ef-fective negative mass density [8] and/or bulk modulusmetamaterials [9, 10]. Acoustic metamaterials allow anaccurate control of the reflected [11–15] or transmittedwavefronts [16–18]. The use of these structures has beenexploited to design negative-refraction superlenses [19] orhyperbolic dispersion-relation hyperlenses [20] that ex-hibit subwavelength focusing properties in the near field.Holographic lenses have also been reported in acoustics togenerate complex acoustic fields [21–24]. Multi-frequencyholograms have been also reported [25]. Equivalently,using phased-array sources it has been reported the gen-eration of complex beam patterns [26], self-bending andbottle beams[27], or vortex beams for particle levitationand manipulation [28]. Mixed approaches between meta-materials and phased arrays have been also presented[29].In these applications, holographic lenses have demon-strated the ability to manipulate acoustic waves in free ∗ [email protected] media, i.e., without inhomogeneities. However, when us-ing ultrasound in biomedical engineering applications,acoustic beams encounter in their path multiple tissuelayers of complex geometry with non-homogeneous prop-erties. For instance, an accurate control of the focusedbeam is at the basis of focused ultrasound therapy tech-niques, e.g., as in high intensity focused ultrasound hy-perthermia, thermal ablation or histotripsy, or in extra-corporeal shockwave lithotripsy [30, 31]. Focusing di-rectly into human soft-tissues can efficiently be achievedby using conventional systems as ultrasound beam aber-rations are typically small in these media [32]. However,when the target tissue lays behind high-impedance tis-sues, e.g., soft-tissue surrounded by bones, the beam ex-periences strong aberrations due to refraction, reflectionand absorption processes [33]. Some applications makeuse of existing acoustic windows by targeting tissues fromspecific locations. Nevertheless, in the case of transcra-nial propagation skull bones are always present in thepath towards the central nervous system (CNS). In thisway, the precise control of acoustic focus into the CNS ismainly limited due to the strong phase aberrations pro-duced by the refraction and attenuation of the skull [34].To overcome these limitations, minimally-invasivetechniques were developed in the past to design activefocusing systems using the time-reversal invariance of theacoustic propagation [35] or phase conjugation methods[36]. In minimally-invasive techniques, a small acousticsource is introduced into the skull, together with a biopsycatheter. When the catheter reaches the target tissue itradiates a short ultrasonic pulse that travels outwardsand it is recorded by a hemispherical multi-element ar-ray surrounding the patient’s head. Then, the elementsof the phased-array are set to re-emit the time-reversed a r X i v : . [ phy s i c s . a pp - ph ] M a y recorded waveforms (or phase conjugated harmonic sig-nals). Due to spatial reciprocity and time-reversal in-variance of the acoustic media, the generated wavefrontfocuses at the catheter location, i.e., at target tissue [35].Later, it was demonstrated that non-invasive versions ofthese techniques can be obtained using numerical simu-lations [37, 38]. In these techniques a tomographic imageis previously obtained from patient’s head to extract thegeometry of the skull and its acoustic properties [38].Using full-wave simulations the time-reversed wavefrontis calculated by exciting the simulation with a virtualsource at the desired focal spot. Then, a physical hemi-spherical phased-array is excited with the synthetic time-reversed waveforms [39] or phase conjugated signals [37],and sharp focusing through skull-aberration layers is re-trieved. Other techniques include the optimization ofphase-arrays using magnetic resonance imaging (MRI) tomaximize acoustic-radiation-force induced displacementsinto the target focus [40]. However, up-to-date phased-array systems are restricted to a limited number of chan-nels, e.g., 1024 for the Exablate R (cid:13) Model 4000 (InSightec,Ltd)[41], that can be insufficient to fully record the re-quired holographic information in order to conform acomplex beam pattern. In addition, phased-arrays areeffective, but due to its high economical cost it is desir-able to use passive structures to control acoustic beams.Only few theoretical works have tackled the problemof beam focusing through aberrating layers using meta-materials [42] or phase plates [43, 44]. In Ref. [42] a 2Dconfiguration was proposed theoretically using a meta-surface based on membranes. Recently, the use of phaseplates to generate simple focused sources have been re-ported to avoid beam aberrations in transcranial propa-gation [43]. However, the technique was limited to focusthe beam into a single focal spot at the near field of thesource. Besides, in some non-thermal transcranial ultra-sound applications such as blood-brain barrier opening[45] or neuromodulation [46] the ultrasound beam mightbe set to fully-cover a geometrically complex CNS struc-ture rather than focusing over a small focal spot.In this work, we propose the use of 3D-printed holo-graphic phase plates to produce ultrasonic fields of arbi-trary shape into the human brain. The holographic lensesdesigned in this work allow the reconstruction of complexdiffraction-limited acoustic images including the compen-sation of the aberrations produced by a skull phantom.In particular, we theoretically, numerically and exper-imentally demonstrate the generation of several holo-graphic patterns, of increasing complexity, all with di-rect practical application to biomedical ultrasound: anarbitrary set of points, an arbitrary curved line, andan arbitrary volume. First, we provide the conditionsto generate a simple holographic pattern, i.e., a set ofdiffraction-limited focal points, as sketched in Fig. 1 (b).In particular, we extend the use of holographic lensesto generate bifocal beams, matching both foci simulta-neously the location of left and right human hippocam-pus. Second, we demonstrate that ultrasonic beams with
SourceUltrasonic beamHolographic plate(a) Target tissue(arbitrary shape)(b) Multiple point Multiple p (c) Line(c) Line (d) Volumetric) Volume
FIG. 1. (a) Scheme of the holographic lens focusing overa target CNS structure. (b) Focusing on a set of arbitrarypoints (bifocal holographic lens), (c) Focusing over arbitraryline (self-bending holographic lens), (d) Focusing over an ar-bitrary volume (volumetric holographic lens). curved trajectory along the internal CNS tissues can alsobe produced, as Fig. 1 (c) shows. In this way, the acousticbeam can be bent following arbitrary paths producing aself-bending beam inside the CNS. Finally, we report thegeneration of a beam pattern that overlaps with the vol-ume of a specific CNS structure, as shown in Fig. 1 (d),in particular we target the right human hippocampus.
II. METHODS
The process of hologram generation is composed offour steps. First, we extract the geometry and acous-tic properties of a human skull from X-ray CT images,as shown in Fig. 2 (a), and from MRI tomographic im-ages we identify the target tissue structure, e.g., the righthuman hippocampus as shown Fig. 2 (b). Second, aback-propagation method is used to calculate the acous-tic wavefront generated from a set of virtual sources andimpinging on a holographic surface located outside the y ( mm ) ho l og r aph i c l en s zxy (a) CT + MRI images Virtual sourcesHolographic surfaceSkull phantom Target tissue (acoustic image)Holographic lensSkull phantom(b) Backward propagation (d) Forward propagation(c) Lens design phase ( x , y ) magnitude ( x , y ) -20 -10 0 10 20x (mm)-20-1001020 y ( mm ) -20 -10 0 10 20x (mm)-20-1001020 y ( mm ) -- /20/2 FIG. 2. Hologram generation process. (a) CT+MRI tomographic images. (b) Selected target (red volume) acting as a virtualacoustic source and holographic recording surface (blue area), (c) Lens design using the TR back-propagated field. (d) Forwardpropagation from the holographic lens (red area) to the target tissue (blue volume). skull phantom, as shown in Fig. 2 (b). Third, the phase-plate lens is generated by using the phase and amplitudeof the recorded wavefront at the holographic surface, asshown in Fig. 2 (c). Finally, the lens is excited with a flatand uniform ultrasonic transducer and the target acous-tic image is reconstructed by either theoretical, numericalforward-propagation or experimental methods, as shownin Fig. 2 (d).
A. Tomographic image acquisition
First, in order to model the skull geometry, we usedthe CT Datasets of a female human head with anisotropic resolution of 1 mm (interpolated to 0.22 mm forthe numerical simulation) from the National Library ofMedicine’s Visible Human Project available for generaluse by the University of Iowa. Experiments were con-ducted in a 3D printed skull phantom, while, in addition,we included full-wave simulations using the acousticalproperties of the skull bones. Thus, for the skull phan-tom simulations we used homogeneous acoustical param-eters matching those of the 3D printing material, whilefor the realistic skull simulations we used the same geom-etry but the inhomogeneous acoustical parameters of theskull were derived using the same the CT data, convert-ing the apparent density tomographic data in Hounsfieldunits to density and sound speed distributions using thelinear-piecewise polynomials proposed in Refs. [47, 48].After, we used a human atlas made publicly avail-able by the International Consortium for Brain Mapping(ICBM) from the Laboratory of Neuro Imaging [49]. Thisatlas provided us T1 weighted MRI data that was used toidentify the shape and location of the human hippocam-pus. In particular we used for segmentation the ITK-SNAP software [50] to obtain the shape and location ofthe left and right hippocampi.
B. Calculation methods
We use two methods, of increasing complexity, toestimate the back-and-forward acoustic fields: a semi-analytical method using Rayleigh-Sommerfeld diffractionintegral and a pseudo-spectral time-domain simulationmethod.On the one hand, for theoretical calculations in homo-geneous media, i.e, in water without the skull phantom,the acoustic pressure field given by p ( r ) at point r , gen-erated by a moving surface S of arbitrary shape locatedat coordinates r and vibrating with a complex parti-cle velocity v ( r ) normal to the surface, is given by theRayleigh-Sommerfeld diffraction integral [51]: p ( r , ω ) = iωρ π (cid:90) S v ( r ) exp ( − k | r − r | ) | r − r | dS, (1)where ω = 2 πf ; k = ω/c , c and ρ are the wavenum-ber, sound speed and density of water. Note that inEq. (1) diffraction is captured exactly as compared withangular spectrum methods, so it can be applied to high-aperture sources.On the other hand, for calculations including aberra-tion layers we use a pseudo-spectral simulation methodwith k -space dispersion correction to numerically inte-grate the linearized constitutive relations of acoustics[52, 53]. In an inhomogeneous and absorbing media,the governing equations, i.e., the continuity equation,the momentum conservation equation and the pressure-density relation, can be written as three-coupled first-order partial differential equations as: ∂ρ∂t = − ρ ∇ · u − u · ∇ ρ , (2) ∂ u ∂t = − ρ ∇ p, (3) p = c ( ρ + d · ∇ ρ − L ρ ) , (4)where u is the acoustic particle velocity, d is the acous-tic particle displacement, p is the acoustic pressure, ρ isthe acoustic density, ρ is the ambient (or equilibrium) z xy h ( x , y ) ¢ h z = d , z =0,2 a holographic planesource plane FIG. 3. Geometry of the holographic lens. The lens, of aper-ture 2 a is subdivided in pixels of height h ( x, y ). The sourceis located at z = 0, while the holographic plane is located at z = d . density, c is the sound speed, and L is a linear opera-tor introducing the frequency-dependent absorption anddispersion [52]. Tissue absorption following a power-lawon frequency given by α ( ω ) = α ω γ , where α is the ab-sorption coefficient and γ is the exponent of the frequencypower law, together with its corresponding physical dis-persion are included by the integro-differential operatoras: L = τ ∂∂t (cid:0) −∇ (cid:1) γ − + η (cid:0) −∇ (cid:1) γ +12 − , (5)where τ = − α c γ − and η = 2 α c γ tan ( πγ/
2) and theabsorption and dispersion proportionality coefficients.This operator is solved efficiently using the fractionalLaplacian in the k -space. This simulation method wasselected as it provides low numerical dispersion as com-pared with finite-differences methods [54]. We used anumerical grid with a spatial step of ∆ x = ∆ y = ∆ z =223 µ m and a numerical temporal step of ∆ t = 19 . C. Lens design
Under the assumption of reciprocity, time-invarianceand linearity of the system, a time-reversal (TR) tech-nique together with a direct method was used to designthe only-phase holographic lens.First, we set some virtual sources inside the skull phan-tom and the back-propagated field was estimated at agiven surface outside the skull phantom. For the bifo-cal lens, two virtual sources were set as monopoles withsame phase and amplitude, located at the center of massof the two hippocampi (right and left), as sketched inFig. 1 (a). For the self-bending beam, a set of 50 vir-tual sources were located following an arbitrary curve assketched in Fig. 1 (b), each source compensated by aphase factor of exp( ik z z ) accounting for the direction of arrival of the wavefront. Finally, for the volumetric holo-gram, as sketched in Fig. 1 (c), a set of virtual sourceswere spatially distributed with a separation of λ/ h ( x, y ) and uniform width, ∆ h , as shownin Fig. 3. We assume each elastic column to vibrate lon-gitudinally as a Fabry-P´erot resonator. For each column,the field at the holographic plane located at x = ( x, y, d )is given by the complex transmission coefficient[55]: T ( x ) = 2 Z e − ik [ d − h ( x )] Z cos [ k L h ( x )] + i ( Z + 1) sin [ k L h ( x )] , (6)where d is the distance from the bottom of the lens ( z =0) to the holographic surface, the normalized impedanceis given by Z = Z L /Z , and Z = ρ c is the impedanceof water and Z L = ρ L c L , k L = ω/c L , ρ L and c L , arethe impedance, wavenumber, density and sound speed ofthe lens material. In order to obtain the height of eachpixel of the lens, an analytic inversion of Eq. (6) is notpossible due to the trigonometric terms. Instead, we firstnumerically evaluate the expression for a broad range ofpixel heights ranging from a minimum height that was setto h min = 5 mm to guarantee structural consistency, toa given height that provides a phase of the transmissioncoefficient 2 π greater than for h min , i.e., d = 15 mm,and using steps of 1 µ m, well below the printer accuracy.Finally, we performed interpolation using a cubic-splinemethod to obtain the heigh of the pixel as a function ofthe required phase. In this way, by tuning the height ofeach Fabry-P´erot resonator the phase at the output ofeach pixel can be tailored to that of a target holographicsurface.However, using this kind of lenses the degree of freedomto modify the magnitude of the field at the holographicsurface is limited. Iterative methods were employed inthe past to obtain equivalent lenses only with phase dis-tributions [21]. In this work, iterative methods are pro-hibitive: the 3D simulations including aberration layersinvolve long calculation times, e.g., 20 hours in a Intel R (cid:13) Xeon R (cid:13) CPU E5-2680 v2 2.80GHz, 256 GB RAM, us-ing a CPU parallel implementation of the code. Instead,we use a direct method to estimate an equivalent holo-graphic lens of uniform field magnitude [56]. The basis ofthis direct method is the sequential scanning of the pix-els to modify the complex transmission coefficient. Themethod work as follows: First, the odd and even rowsare scanned from opposite directions, and a bidirectionalerror of the diffusion process is calculated. The magni-tude of each visited pixel is forced to be a constant valuewhile the exact phase value is preserved. The resultingerror is diffused to the neighboring pixels. Finally, the re-sult gives a surface with a modified phase depending onthe bidirectional error diffusion process [56]. The mainlimitation of this method is that if the pixel width issmall it will appear areas with isolated long pixels, i.e.,columns, that can experience bending modes. Note thisdo not imply that a lens cannot be designed, but thetheory presented here only apply to longitudinal modeson each pixel. The size of the pixels used in this work,5 / a = 50 mm weremanufactured using 3D printing techniques. On the onehand, the bifocal holographic lens was manufactured byadditive 3D printing techniques using Ultimaker 3 Ex-tended (Ultimaker B.V., The Netherlands) with a res-olution of 100 µ m in both, lateral and axial directionsand PLA material. As, in general, the height profile ofthe lens is smooth, we set the square pixel resolution to∆ h = 0 .
22 mm. The acoustical properties of PLA ma-terial were obtained experimentally using a pulse-echotechnique in a test cylinder, resulting in a measuredsound speed of c L = 1818 m/s and a density of ρ L = 1127kg/m , matching with those reported in existing litera-ture [57], and the absorption was set to α = 13 .
72 dB/cmat 1.112 MHz [57]. On the other hand, the self-bendingand volumetric holographic lenses, which needed a moreaccurate printing technique for their complex pattern,were 3D printed using Polyjet techniques with an Ob-jet30 printer (Stratasys, USA), with a resolution of 100 µ m and 28 µ m in lateral and axial directions respectively,and using a photo-resistive polymer (Veroclear R (cid:13) , Strata-sys, USA). As a result of the direct method to obtain theequivalent holographic lens of uniform field magnitude[56], the height distribution presents high spatial modu-lations (see Fig. 2 (c)). Thus, the pixel resolution wasincreased to ∆ h = 1 mm to ensure each column vibratesas a longitudinal Fabry-P´erot resonator avoiding bendingmodes around the working frequency for the volumetrichologram. For this material we experimentally estimated c L = 2312 m/s and ρ L = 1191 kg/m and α = 3 . D. Skull phantom
The geometry of the skull phantom was extractedfrom the 3D CT images as described previously. Thesound speed and density distributions were first esti-mated from the apparent density given by the CT imagesin Hounsfield units [47, 48]. Then, as the 3D printingtechnique results in homogeneous material, the acous-tic properties, including the absorption were considereduniform along the skull bone volume [58–60]. The skullphantom was manufactured by additive 3D printing tech- niques using Ultimaker 3 Extended (Ultimaker B.V., TheNetherlands) with resolution of 100 µ m in both, lateraland axial directions and using PLA material. The acous-tic parameters for the 3D printed phantom are the samethan for the PLA lenses.Finally, for the simulations using a realistic skull, theacoustical parameters were derived using the CT data,converting the apparent density in Hounsfield units todensity and sound speed distributions using the linear-piecewise polynomials proposed in Refs. [47, 48]. Thedensity data ranges between ρ = 1000 kg/m (water)and ρ max = 2206 kg/m (bone), the sound speed valuesrange between c = 1500 m/s and c max = 3117 m/s,matching those reported in literature [31, 61] and thebone absorption was set to 12.6 dB/cm at 1.112 MHz[62].The details about the measurement system can befound in Appendix A. III. MULTIPLE-POINT HOLOGRAMS
We start with the bifocal holographic lens. First, twopoints located at the center of mass of both left andright human hippocampi are selected. Second, we setthis pair of points as the location of virtual sources forthe TR method. For the lens designs in free media,i.e., without the skull, we make use of the Rayleigh-Sommerfeld diffraction integral (see Methods section forfurther details). For the lens designs of holographic sur-faces including the skull-aberration layers we make useof low-numerical-dispersion simulations based on pseudo-spectral methods [52]. In this way the simultaneousback-propagation of the fields irradiated by both virtualmonopoles can be calculated at the holographic surfacewhich is located at the rear part of the skull. The phase-plate lens is designed using the conjugated complex fieldrecorded at the surface. Then, the lens is placed at thelocation of the holographic surface as shown in Fig. 4 (a),and a forward-propagation calculation is carried out totest the quality of the reconstructed acoustic image.The field produced by the bifocal lens propagatingthrough a human occipital/parietal skull phantom in-cluding the compensation for the aberrations of the skullis shown in Figs. 4 (a-f). First, Figs. 4 (a,b) show theaxial field cross-section, p ( x, y = 0 , z ), using the pseudo-spectral simulation method and measured experimen-tally, respectively. We observe that the reconstructedfield accurately matches the target foci, and the exper-imental results agree with the simulations. The corre-sponding transverse field distributions at z = 105 mmare shown in Figs. 4 (c,d) where sharp focusing is ob-served. The focal spots present larger dimensions in theaxial ( z ) direction than in transverse ones, as expectedfrom limited-aperture holographic lenses, where the spa-tial spectral components in axial direction are limitedby the finite-aperture source[63]. Axial (measured at x = 25 mm and y = 0 mm) and transversal (measured z (mm) SimulationExperiment -50 0 50 x (mm) z ( mm ) -40 -20 0 20 40 x (mm) -10010 y ( mm ) -40 -20 0 20 40-10010 y ( mm ) -40 -20 0 20 40 x (mm) -40 -20 0 20 40 x (mm) z ( mm ) ExperimentExperimentSimulation z = 105 mmz = 105 mmy = 0 mmSimulation (a) (e) (f) (b)(d)(c) S k u l l p h a n t o m FIG. 4. Axial field cross-section obtained for the bifocal lens using simulations (a) and experiments (b). (c-d) Correspondingtransversal pressure field distributions. Colorbar in units normalized to the peak pressure. (e,f) Simulated and experimentalnormalized axial and transversal field cross-sections, respectively. at z = 105 mm and y = 0 mm) cross-sections are shownin Figs. 4 (e,f), respectively. Excellent agreement is ob-served between simulation and experiment for the axialfield profile at the focal region. A small secondary lobelocated before the main one appears experimentally. Thetransverse profile shows a small lateral shift of ± x -axis origin.Note that, due to diffraction, the geometrical focus ofa geometrically focused source do not correspond to theacoustic focus of the source [63]. In our case, the targetlocation was set to z = 105 . z = 99 . z = 100 . z = 100 . IV. SELF-BENDING BEAMS
The previous results show that holographic phaseplates can retain phase information of multiple foci. Us-ing this idea, we can set more complex targets follow-ing the shape of functional structures found in the CNS.Here, we set the target holographic pattern to a beamfollowing a curved trajectory as those reported in ho-mogeneous media without aberrating layers using activesources or metamaterials [17, 27, 64]. As the aberrationlayers will be present in the real application, known an-alytical methods to calculate the phase of the 3D trajec- tory are, in principle, not available [27]. Instead, we makeuse of a TR method: a set of virtual sources were placedalong this trajectory and their back-propagated field werecalculated. We set a factor of ( z/z max ) exp( izk z ) to com-pensate for the amplitude and phase of each source toset the main direction of propagation, being k z the ax-ial component of the wave-vector and z max the distanceto the farthest virtual source (45 mm in this example).A sketch of the target trajectory is shown in Fig. 5 (a).The axial and transversal cross-sections of the forwardpropagated field in water are shown in Figs. 5 (a,b), re-spectively. We observe that using TR method the self-bending beams can be obtained, and the beam accuratelyfollows the target trajectory. Using simulation and a lensmade of elastic material a similar result is obtained, asshown in Figs. 5 (c,d). The experimental tests show asimilar pressure field distribution in comparison with the-ory using the Rayleigh-Sommerfeld integral and simula-tions using pseudo-spectral methods. A lateral shift ofthe peak pressure location of 0.3 mm in the x directionis observed at z = 30 mm and y = 0 mm in the experi-ments.Finally, when the aberration layer of the skull phantomis included the corresponding holographic lens also recon-structs the target acoustic image with curved trajectory,as shown in Figs. 5 (e,f). A similar lateral shift of thepeak pressure location in the experiments, of 0.25 mmin the x direction is observed at z = 30 mm and y = 0mm. The measured pressure field inside the skull phan-tom agree the simulation. Note that the transversal sizeof the curved beam at z = 30 mm is 1.11, 1.07 and 1.19times the wavelength in water for the theoretical calcula- -20 0 20x (mm)01020304050 z ( mm ) lens (c) -20 0 20x (mm)-30-20-100102030 y ( mm ) S o u r c e a p e r t u r e target(d) -20 0 20x (mm)01020304050 z ( mm ) lens (e) -20 0 20x (mm)01020304050 z ( mm ) target trajectory(a) holographic plane -20 0 20x (mm)-30-20-100102030 y ( mm ) S o u r c e a p e r t u r e target(b) -20 0 20x (mm)-30-20-100102030 y ( mm ) S o u r c e a p e r t u r e target(f)z = 30 mm Simulation Experiment Simulation Experiment E x pe r i m en t S i m u l a t i on E x pe r i m en t S i m u l a t i on S k u l l p h a n t o m FIG. 5. Theoretical (a) axial and (b) transverse pressure field distribution for the self-bending beam in water. Simulated (c)axial and (d) transverse pressure field distribution for the self-bending beam in water. Corresponding experimental resultsare shown in the insets in (c) and (d). (e,f) Simulated axial and transversal pressure field including the skull phantom.Corresponding experimental results are shown in the insets in (e) and (f). tion, and for the simulations in water and including theskull phantom, respectively. Both results demonstratethat using TR methods self-bending beams following atarget curve can be obtained inside the skull phantomusing acoustic holographic lenses.
V. VOLUMETRIC HOLOGRAMSOVERLAPPING CNS STRUCTURES
Going further, we designed a holographic lens whichproduces an acoustic image that fits the right human hip-pocampus volume. The holographic surface was placednear the occipital/parietal bones to adapt the acousticimage to the elongated geometry of the hippocampus.However, we locate the lens at the center of the skullsymmetry plane in order to demonstrate the steering ca-pabilities of this holographic lens. The lens generationprocess is based on the TR method with multiple vir-tual sources covering the target area (see Methods sec-tion for further details). Figure 6 summarizes the resultsfor both, water and including the aberration layer of theskull phantom.On the one hand, Figs. 6 (a,b,c) show the forward-propagation field distribution of the holographic lens de-signed for water obtained using the theoretical, experi- mental and simulation results, respectively. First, we ob-serve a good agreement between experiments, simulationand theory in both axial (Figs. 6 (a-c)) and transversalfield distributions (Figs. 6 (f-h)). The beam is steered inthe correct direction and a broad focal spot is generated.The transversal and axial field cross-sections are shownin Figs. 6 (d,e). The diffraction-limited image is recon-structed and the field is enhanced mainly at the targetvolume. To quantify the performance, we define the over-lapping volume as the overlapping volumes of the targetregion and the region of the acoustic pressure field undera threshold corresponding to the half of the peak ampli-tude. In particular, using this lens we obtain in wateran overlapping volume of 29.7%, 20.1% and 19.0% forthe theoretical calculation, simulation and experiment,respectively.On the other hand, the field distribution produced byacoustic holographic lenses including the skull phantomis shown in Figs. 6 (i-n). The experimental forward-propagation field distribution overlaps a similar volumein comparison with simulation result. Both holographicimages present the same qualitative performance andprovide a similar overall covering of the interest zone.In particular, an overlapping volume of of 21.1% and23.2% was obtained in simulation and experiment, re-spectively. In addition, both axial (Fig. 6 (i,j)) and z ( mm ) -40 -20 x (mm) z ( mm ) -50 0 50-20020 y ( mm ) z (mm) TheorySimulationExperiment -50 0 50 x (mm)
TheorySimulationExperiment -40 -20 x (mm) z ( mm ) -40 -20 x (mm) z ( mm ) z ( mm ) -10010 -40 -20 x (mm) -10010 y ( mm ) -10010 y ( mm ) -40 -20 x (mm) -50 0 50 x (mm) SimulationExperiment -40 -20 x (mm) -10010 -50 0 50 x (mm) -20020 y ( mm ) SimulationExperiment (d)(e) (m)(n)(i) (j)(b)(a) (c)(f)(h)(g) (l) (k)Simulation target volume target volume SimulationSimulationSimulation ExperimentExperiment Experiment ExperimentTheory Theory target volumetarget volume target volumeTarget Target TargetTargetTheorySimulationExperiment SimulationExperiment S k u l l p h a n t o m z (mm)x (mm) FIG. 6. Volumetric hologram results. (a,b,c) Theoretical, experimental and simulated axial pressure distribution in water. (d,e)Transversal and axial field cross-sections in water. (f,g,h) Simulated, experimental and theoretical transversal field distributionin water. (i,j) Simulated and experimental axial pressure distribution including the skull phantom. (k,l) Correspondingtransversal pressure distribution and (m,n) transversal and axial cross-section, respectively. transversal (Figs. 6 (k,l)) field distributions are similarof those produced in water without the skull phantom,showing that, first, limited-diffraction holographic vol-umes can be reconstructed and, second, the aberrationsproduced by the skull phantom on these complex beamscan be compensated at the source plane by the acous-tic holographic lenses. Finally, the transversal and axialcross-sections, shown in Figs.6 (m,n), show that the ex-perimental and simulated acoustic holographic lens pro-duces a field enhancement that matches the target dis-tribution.Note that the spatial bandwidth of the image is lim-ited by the diffraction limit and the spatial bandwidthof the acoustic holographic lens [21]. In this case, theholographic lens focuses at z ≈ . λ (100 mm), and itslimited-aperture is only a = 18 . λ (25 mm). Therefore,the transversal components of the wave-vector are band-limited and the performance of the holographic lens atthis distance is restricted. Using lenses with larger aper-ture will improve the quality of the holographic acousticimage, and, therefore, the total overlapping volumes. VI. HOLOGRAM SIMULATION USING AREALISTIC SKULL
It is worth noting here that the impedance of the avail-able 3D printing material used to manufacture the skull phantom is soft compared with the skull bone. In thisway, the phase aberrations produced by a real skull willbe stronger than the ones observed in the previous ex-periments. To demonstrate the focusing performance ofthe proposed lenses in a realistic situation a set of sim-ulations were performed using the acoustical parametersof skull bones. The parameters were derived using thesame the CT data and were listed in Section II D.First, the results of the bifocal lens simulation using arealistic skull are summarized in Fig 7. First, the sagittalcross-section of the absolute value of the pressure fieldat y = 0 mm is shown in Fig. 7 (a). We can see thatthe lens focuses at two clear spots, almost at the tar-get distance. The corresponding traversal cross-sectionis shown in Fig. 7 (b) measured at z = 100 mm. In fact,good agreement is found between the simulations usinga realistic skull and the calculations using the Rayleigh-Sommerfeld integral considering homogeneous water me-dia. These two focal spots are generated together withsmall amplitude secondary lobes. The amplitude of theside lobes is -8.86 dB below the peak pressure in the the-ory in water and -5.16 dB in the simulation includingthe skull. To quantify the focusing performance of thelens, we show in Fig. 7 (c) the transversal cross-sectionat z = 100 mm and y = 0 mm. The lateral shift of theleft focus is -26.3 mm and -26.0 mm for the theoreticalprediction and for the simulation, respectively. A relativeerror of 1.1% was committed. These small lateral shifts -20 0 20 x (mm) -20-1001020 y ( mm ) -50 0 50 x (mm) SimulationTheory -20 0 20 y (mm)
SimulationTheory
50 100 150 z (mm)
SimulationTheory -20 0 20 x (mm) z ( mm ) (a) (c) (d)(e)(b) (c)(d)(c)(e) Simulation Simulation S k u l l lens (water) (water) (water) FIG. 7. Simulation results for the bifocal holographic lens designed for a realistic skull. (a) Axial cross-section of the pressuredistribution at y = 0 mm. (b) Transversal cross-section at z = 100 mm. (c) Lateral cross-section at z = 100 mm and y = 0mm. (d) Lateral cross-section at z = 100 mm and x = −
26 = 0 mm. (e) Axial cross-section at x = −
26 = 0 mm and y = 0mm. are of the order of the experimental test shown previouslywith the 3D printed phantom. Moreover, the amplitudeof the side lobes in the simulation using a realistic skullare 0.3 times the peak pressure. These side-lobes presenthigher amplitude in the lateral cross-section joining bothfoci (Fig 7 (c)) than in the lateral cross-section measuredat x = 0 mm, as shown in Fig 7 (d). Finally, Fig. 7 (e)shows the axial pressure distribution measured at the lo-cation of the right hippocampus. The axial peak locationof the simulation including a realistic skull ( z = 99 . z = 99 . y = 0mm, together with the location of the target marked inred dashed line. In this case the performance of the lensto produce such a complex beam is reduced as comparedwith the previous cases, as can be seen by the presence ofsecondary lobes. This is mainly caused by the generationof strong stationary waves between the skull bone andthe lens. However, the peak pressure follows the targettrajectory and the location of the peak pressure matchesthe center of the curve. A clearer picture is given inFig. 8 (b), that shows the transversal field distributionmeasured at z = 35 mm. Here, a sharp focal spot is visi-ble and location of the peak pressure almost matches the location of the target focus. A lateral shift of +0 .
22 mm,that corresponds to one numerical grid step in the sim-ulation was found in the x direction. The correspondingtransversal field distributions are shown in Fig. 8 (c) forthe x direction and in Fig. 8 (d) for the y direction, re-spectively. Here, the reference calculations using theoret-ical methods in a homogeneous medium (water) are also -30 -20 -10 0 10 20 30x (mm)-30-20-100102030 y ( mm ) -30 -20 -10 0 10 20 30x (mm)01020304050 z ( mm ) S k u l l -30 -20 -10 0 10 20 30y (mm)00.51 SimulationTheory -30 -20 -10 0 10 20 30x (mm)00.51
SimulationTheory target trajectory L e n s a p e r t u r e target Lens (b)(a) (c) (d)
SimulationSimulation(water) (water)
FIG. 8. Simulation results for the self-bending holographicbeam designed for a realistic skull. (a) Axial cross-section ofthe pressure distribution at y = 0 mm. (b) Transversal cross-section at z = 35 mm. (c) Lateral cross-section at z = 35 mmand y = 0 mm. (d) Lateral cross-section at z = 35 mm and x = 2 mm. -20 0 20y (mm)00.51 SimulationTheory
50 100 150z (mm)00.51
SimulationTheorySimulation -50 0 50x (mm)00.51
SimulationTheory -40 -20 0 20 40x (mm)-20020 y ( mm ) -40 -20 0 20 40x (mm)050100150 z ( mm ) (a) (c) (e)(d)(b) (c)(d)(e) (c) Target TargetSimulationSimulation S k u l l (water) (water)(water) FIG. 9. Simulation results for the volumetric hologram designed for a realistic skull. (a) Axial cross-section of the pressuredistribution at y = 0 mm. (b) Transversal cross-section at z = 95 mm. (c) Lateral cross-section at z = 95 mm and y = 0 mm.(d) Lateral cross-section at z = 95 mm and x = −
26 = 0 mm. (e) Axial cross-section at x = −
26 = 0 mm and y = 0 mm. shown for comparison. The location of the focal spotsobserved in both lateral directions for the simulations in-cluding the realistic skull are in excellent agreement withthe corresponding focal spots in water. The width of thefocal spot obtained using both calculation methods alsois in agreement. The main discrepancy is the presence ofsecondary lobes in the simulated field, presenting a peakamplitude of 0.36 times the pressure at the focus. Theamplitude of these lobes is 1.7 times larger in directionin which the beam is bent.Third, a holographic lens was designed with the tar-get of producing a volumetric hologram overlapping withthe right hippocampus volume, and in this case includingthe acoustic properties of a realistic skull. The resultingforward-simulated pressure field is shown in Figs. 9 (a-e). First, the sagittal cross-section of the magnitude ofthe pressure field at y = 0 mm is shown in Fig. 9 (a).The produced field focuses around the target volume,shown in dashed white lines. The beam is steered in thedirection of the right hippocampus while the transduceraxis remains normal to the skull surface. The transversalcross-section at z = 95 mm is shown in Fig. 9 (b). Whilethe acoustic field is focused into the target volume, thereexists areas not covered by the beam, mainly in the outer-most regions away from the transducer source. To quan-tify the focusing performance, field cross-sections alongthe corresponding dashed lines are given in Figs. 9 (c-e).The lateral cross-section at z = 95 mm and y = 0 mmis shown in Fig. 9 (c). As a comparison, we also plotthe corresponding cross-section of a holographic lens de-signed to produce the same hologram in water using thetheoretical Rayleigh-Sommerfeld integration. The sim-ulated beam using the realist skull and the theoretical prediction in water mostly overlaps, being the energy ofthe beam concentrated into the target volume. Smallside-lobes with an amplitude 5.3 times smaller than thepeak pressure are observed in the simulations includingthe realistic skull. Note that the corresponding acousticintensity of the side lobes is about 30 times smaller thanthe intensity at the focus. The volume of the beam, de-fined as the total volume of the beam under a thresholdof 0.5 times the peak pressure, roughly overlaps with thetarget volume. The overlapping volume between the tar-get and the volumetric acoustic hologram is 29.7% for thetheoretical calculation in water and 21.4% for the simu-lation including the skull. The transversal cross-sectionalong the y axis is given in Fig. 9 (d), where excellentagreement is found between the two configurations. Fi-nally, the axial cross-section along the z axis is shownin Fig. 9 (e). In this case, the field presents remark-able side-lobes before and after the target region, but itsamplitude is lower than half of the maximum pressure.Note this direction corresponds to the beam axis and thepressure distribution of the corresponding focused beampresents an elongated shape due to the limited apertureof the source. In this case, a good agreement is also foundbetween the axial pressure distribution of the simulationincluding the realistic skull and the theoretical predictionin water. VII. CONCLUSIONS
We have shown that using 3D printed acoustic holo-grams it is possible to conform diffraction-limited ultra-sonic fields of arbitrary shape compensating the aberra-1tions of a the human skull. In particular, experimentaltests using a 3D printed skull phantom and numericalsimulations using a realistic skull were performed to ac-curately generate multiple focal holograms, self-bendingbeams and volumetric holographic fields overlapping atarget CNS structure. The proposed approach usingholographic lenses represents a step forward when com-pared with the existing solutions using phase arrays, sinceit opens new venues to develop reliable and cost reducedultrasonic applications.The quality of the reconstructed acoustic images is re-lated to the diffraction limit and the spatial bandwidth ofthe holographic lens, which depends on the spatial aper-ture of the lens, the number of pixels of the lens, andthe frequency of the beam [21]. In this work, we targeta human hippocampus using a single holographic lens ofonly 50 mm aperture and operating at a frequency of 1.1MHz. The reported experimental results inside a skullphantom are in good agreement with theory and simula-tions. Only small shifts, of the order of one wavelength(1.4 mm in water), were found between the target lo-cation and the field produced by the holographic lens.These shifts can be caused by experimental reasons thatinclude small positioning error between the lens and thecurved surface of the phantom and can be corrected us-ing optimization methods during lens design. It is worthnoting here that the phantom used in the experimentspresents a smaller acoustic impedance than a real skull.However, full-wave simulations performed using the den-sity, sound speed and attenuation values of skull-boneshow that these arbitrary fields can also be produced ina realistic situation. The generated acoustic fields insidethe skull were in good agreement with those produced inwater. This shows that the aberrations produced by theskull can be mitigated by using holographic lenses evenwhen a complex field is required.Moreover, using the proposed methodology diffractionis captured exactly as compared with Fraunhofer or an-gular spectrum methods, leading to a better accuracyof the generated acoustic fields. In addition, the holo-graphic lens design is based on resonating slabs, whichinclude not only the refraction over a curved plate, butthe resonating waves inside the lens.Phased-arrays are efficient but their high-cost can beprohibitive to spread out some of the incoming ultrasonictranscranial therapy treatments. Using phased arraysthe ultrasonic beams can be adjusted in real time andmonitored using MRI, obtaining a precise location of theacoustic focus into de CNS. Nevertheless, the number ofelements of the phased-array systems can be insufficientto produce a complex volumetric ultrasonic field thatmatches a specific CNS structure. The use of holographiclenses present several advantages to produce complex vol-umetric patterns. First, the cost of a 3D printed lensis low as compared with phased-array systems. Second,each pixel in a holographic lens acts as an element of thephased-array with fixed phase. Due to the high numberof passive sources in a holographic lens, more than 4000 for the small lenses considered here, complex patternscan be generated. However, once the lens is designed itsfocal distance and the spatial features of the holographicimage remains fixed and, in principle, it is not possibleto steer the ultrasonic beam in real time with accuracy.For this reason, the technique is specially relevant for thetreatment using a single sonification of structures or inthe sonification of large volumes.The concept shown in this paper opens new doors tooptimize and widespread incoming therapy treatmentssuch as ultrasound-assisted blood-brain barrier openingfor drug delivery and neuromodulation, or ultrasonicimaging of the central nervous system using low-cost de-vices. Considering the emergence of metamaterials andtheir huge flexibility, we also advance incoming biomed-ical applications of active holographic metasurfaces forthe generation of complex fields in the central nervoussystem.
ACKNOWLEDGMENTS
This work was supported by the Spanish Ministry ofEconomy and Innovation (MINECO) through ProjectTEC2016-80976-R. NJ and SJ acknowledge financialsupport from Generalitat Valenciana through grantsAPOSTD/2017/042, ACIF/2017/045 and GV/2018/11.FC acknowledges financial support from Ag`encia Valen-ciana de la Innovaci´o through grant INNCON00/18/9and European Regional Development Fund (ID-IFEDER/2018/022).
Appendix A: Measurement setup
The experiments were conducted inside a 1 × . × ,
5m water tank filled with degassed and distilled water at26 ◦ . The ultrasonic transducer was composed by a sin-gle element circular piezoceramic crystal (PZT26, Fer-roperm Piezoceramics, Denmark) mounted in a customdesigned stainless-steel housing with aperture 2 a = 50mm as shown in Fig. 10 (e). The transducer was drivenwith a 50 cycles sinusoidal pulse burst at a frequencyof f = 1 .
112 MHz by a signal generator (14 bits, 100MS/s, model PXI5412, National Instruments) and am-plified by a linear RF amplifier (ENI 1040L, 400 W, 55dB, ENI, Rochester, NY). The pressure field was mea-sured by a needle hydrophone with a 500 µ m active di-ameter (149.6 mV/MPa sensitivity at 1.112 MHz, ModelHNR-500, Onda) calibrated from 1 MHz to 20 MHz. Thesource amplitude was set low enough to avoid any non-linear effects in the propagation, we measure 1.8 kPa atthe focus for the bifocal lens. The hydrophone signalswere digitized at a sampling rate of 64 MHz by a dig-itizer (model PXI5620, National Instruments) averaged100 times to increase the signal to noise ratio.An 3D micro-positioning system (OWIS GmbH) wasused to move the hydrophone in three orthogonal direc-2 HologramTransducerHydrophoneSkull phantomz xy 3D MicropositioningSystemDigitizerPXI5620PXI ControllerNI8176Function GeneratorPXI5412AmplifierENI 1040L
FIG. 10. Experimental setup showing the block diagram andskull phantom inside the water tank with the ultrasonic sourceand the acoustic hologram at the bottom. tions with an accuracy of 10 µ m. For the bifocal lensexperiment the scanning an area for the sagittal cross-sections, p ( x, z ), covers from -40 mm to 40 mm in the x direction and from 82 mm to 143 mm in the z direc-tion, using a step of 0.5 mm in both directions, for thetransversal cross-section planes, p ( x, y ), covers from -40to 40 mm in the x direction and from -10 mm to 10 mmin the y direction, using a step of 0.3 mm. For the self-bending lens, the scanned area covers from 20 to 50 mmin the z direction, from -5 to 5 mm in the x direction, andfrom -5 to 5 mm in the y direction, using the same spatialsteps. Finally, for the volumetric holograms the scannedarea covers from 65 to 135 mm in the z direction, from-45 to -5 mm in the x direction, and from -10 to 10 mm inthe y direction, using the same spatial steps. All the sig-nal generation and acquisition processes were based on aNI8176 National Instruments PXI-Technology controller,which also controlled the micro-positioning system. Tem-perature measurements were performed throughout thewhole process to ensure no temperature changes of 0.5 ◦ C. [1] Dennis Gabor. A new microscopic principle. Nature ,161:777–778, 1948.[2] Dionys Gabor et al. Microscopy by reconstructed wave-fronts.
Proc. R. Soc. Lond. A , 197(1051):454–487, 1949.[3] Emmett N Leith and Juris Upatnieks. Recon-structed wavefronts and communication theory.
JOSA ,52(10):1123–1130, 1962.[4] Xingjie Ni, Alexander V Kildishev, and Vladimir M Sha-laev. Metasurface holograms for visible light.
NatureCommunications , 4:2807, 2013.[5] Lingling Huang, Xianzhong Chen, Holger M¨uhlenbernd,Hao Zhang, Shumei Chen, Benfeng Bai, Qiaofeng Tan,Guofan Jin, Kok-Wai Cheah, Cheng-Wei Qiu, et al.Three-dimensional optical holography using a plasmonicmetasurface.
Nature Communications , 4:2808, 2013.[6] Guancong Ma and Ping Sheng. Acoustic metamateri-als: From local resonances to broad horizons.
Scienceadvances , 2(2):e1501595, 2016.[7] Steven A Cummer, Johan Christensen, and Andrea Al`u.Controlling sound with acoustic metamaterials.
NatureReviews Materials , 1:16001, 2016.[8] Zhengyou Liu, Xixiang Zhang, Yiwei Mao, YY Zhu,Zhiyu Yang, Che Ting Chan, and Ping Sheng. Locallyresonant sonic materials.
Science , 289(5485):1734–1736,2000.[9] Nicholas Fang, Dongjuan Xi, Jianyi Xu, MuralidharAmbati, Werayut Srituravanich, Cheng Sun, and XiangZhang. Ultrasonic metamaterials with negative modulus.
Nature Materials , 5(6):452, 2006.[10] Min Yang, Guancong Ma, Zhiyu Yang, and PingSheng. Coupled membranes with doubly negative massdensity and bulk modulus.
Physical Review Letters ,110(13):134301, 2013.[11] Yong Li, Bin Liang, Zhong-ming Gu, Xin-ye Zou, andJian-chun Cheng. Reflected wavefront manipulation based on ultrathin planar acoustic metasurfaces.
Sci-entific Reports , 3:2546, 2013.[12] Yangbo Xie, Wenqi Wang, Huanyang Chen, Adam Kon-neker, Bogdan-Ioan Popa, and Steven A Cummer. Wave-front modulation and subwavelength diffractive acousticswith an acoustic metasurface.
Nature Communications ,5:5553, 2014.[13] No´e Jim´enez, Trevor J Cox, Vicent Romero-Garc´ıa,and Jean-Philippe Groby. Metadiffusers: Deep-subwavelength sound diffusers.
Scientific Reports ,7(1):5389, 2017.[14] No´e Jim´enez, Vicent Romero-Garc´ıa, Vincent Pagneux,and Jean-Philippe Groby. Rainbow-trapping absorbers:Broadband, perfect and asymmetric sound absorption bysubwavelength panels for transmission problems.
Scien-tific Reports , 7(1):13595, 2017.[15] Shuibao Qi, Yong Li, and Badreddine Assouar. Acous-tic focusing and energy confinement based on multilat-eral metasurfaces.
Physical Review Applied , 7(5):054006,2017.[16] Eun Bok, Jong Jin Park, Haejin Choi, Chung Kyu Han,Oliver B Wright, and Sam H Lee. Metasurface forwater-to-air sound transmission.
Physical review letters ,120(4):044302, 2018.[17] Yong Li, Xue Jiang, Bin Liang, Jian-chun Cheng, andLikun Zhang. Metascreen-based acoustic passive phasedarray.
Physical Review Applied , 4(2):024003, 2015.[18] Yong Li and M Badreddine Assouar. Three-dimensionalcollimated self-accelerating beam through acousticmetascreen.
Scientific reports , 5:17612, 2015.[19] Nad`ege Kaina, Fabrice Lemoult, Mathias Fink, and Ge-offroy Lerosey. Negative refractive index and acoustic su-perlens from multiple scattering in single negative meta-materials.
Nature , 525(7567):77, 2015.[20] Jensen Li, Lee Fok, Xiaobo Yin, Guy Bartal, and Xi- ang Zhang. Experimental demonstration of an acousticmagnifying hyperlens. Nature Materials , 8(12):931, 2009.[21] Kai Melde, Andrew G Mark, Tian Qiu, and Peer Fischer.Holograms for acoustics.
Nature , 537(7621):518, 2016.[22] Yangbo Xie, Chen Shen, Wenqi Wang, Junfei Li, DingjieSuo, Bogdan-Ioan Popa, Yun Jing, and Steven ACummer. Acoustic holographic rendering with two-dimensional metamaterial-based passive phased array.
Scientific Reports , 6:35437, 2016.[23] Yifan Zhu, Jie Hu, Xudong Fan, Jing Yang, Bin Liang,Xuefeng Zhu, and Jianchun Cheng. Fine manipulationof sound via lossy metamaterials with independent andarbitrary reflection amplitude and phase.
Nature com-munications , 9(1):1632, 2018.[24] Gianluca Memoli, Mihai Caleap, Michihiro Asakawa,Deepak R Sahoo, Bruce W Drinkwater, and Sriram Sub-ramanian. Metamaterial bricks and quantization of meta-surfaces.
Nature communications , 8:14608, 2017.[25] Michael D Brown, Ben T Cox, and Bradley E Treeby.Design of multi-frequency acoustic kinoforms.
AppliedPhysics Letters , 111(24):244101, 2017.[26] Y Hertzberg and G Navon. Bypassing absorbing objectsin focused ultrasound using computer generated holo-graphic technique.
Medical Physics , 38(12):6407–6415,2011.[27] Peng Zhang, Tongcang Li, Jie Zhu, Xuefeng Zhu, SuiYang, Yuan Wang, Xiaobo Yin, and Xiang Zhang. Gener-ation of acoustic self-bending and bottle beams by phaseengineering.
Nature Communications , 5:4316, 2014.[28] Asier Marzo, Sue Ann Seah, Bruce W Drinkwater,Deepak Ranjan Sahoo, Benjamin Long, and Sriram Sub-ramanian. Holographic acoustic elements for manip-ulation of levitated objects.
Nature Communications ,6:8661, 2015.[29] Mohd Adili Norasikin, Diego Martinez Plasencia, Spy-ros Polychronopoulos, Gianluca Memoli, Yutaka Tokuda,and Sriram Subramanian. Soundbender: dynamic acous-tic control behind obstacles. In
The 31st Annual ACMSymposium on User Interface Software and Technology ,pages 247–259. ACM, 2018.[30] Gail ter Haar and Constantin Coussios. High intensityfocused ultrasound: physical principles and devices.
In-ternational journal of hyperthermia , 23(2):89–104, 2007.[31] Ayache Bouakaz and Jean-Michel Escoffre.
Therapeuticultrasound: From biophysics concepts to clinical applica-tions , volume 880 of
Advances in Experimental Medicineand Biology . Springer International Publishing, 2016.[32] Thomas L Szabo.
Diagnostic ultrasound imaging: insideout . Academic Press, 2004.[33] P G´elat, G Ter Haar, and N Saffari. A comparison ofmethods for focusing the field of a hifu array transducerthrough human ribs.
Physics in Medicine & Biology ,59(12):3139, 2014.[34] FJ Fry and JE Barger. Acoustical properties of thehuman skull.
The Journal of the Acoustical Society ofAmerica , 63(5):1576–1590, 1978.[35] J-L Thomas and Mathias A Fink. Ultrasonic beam focus-ing through tissue inhomogeneities with a time reversalmirror: application to transskull therapy.
IEEE Transac-tions on Ultrasonics, Ferroelectrics, and Frequency Con-trol , 43(6):1122–1129, 1996.[36] Kullervo Hynynen and Ferenc A Jolesz. Demonstration ofpotential noninvasive ultrasound brain therapy throughan intact skull.
Ultrasound in Medicine and Biology , 24(2):275–283, 1998.[37] Jie Sun and Kullervo Hynynen. Focusing of thera-peutic ultrasound through a human skull: a numericalstudy.
The Journal of the Acoustical Society of America ,104(3):1705–1715, 1998.[38] J-F Aubry, M Tanter, M Pernot, J-L Thomas, andM Fink. Experimental demonstration of noninvasivetransskull adaptive focusing based on prior computed to-mography scans.
The Journal of the Acoustical Societyof America , 113(1):84–93, 2003.[39] Micka¨el Tanter, Jean-Louis Thomas, and Mathias Fink.Focusing and steering through absorbing and aberratinglayers: Application to ultrasonic propagation through theskull.
The Journal of the Acoustical Society of America ,103(5):2403–2410, 1998.[40] Y Hertzberg, A Volovick, Y Zur, Y Medan, S Vitek,and G Navon. Ultrasound focusing using magnetic res-onance acoustic radiation force imaging: applicationto ultrasound transcranial therapy.
Medical Physics ,37(6Part1):2934–2942, 2010.[41] Ferenc A Jolesz.
Intraoperative imaging and image-guidedtherapy . Springer Science & Business Media, 2014.[42] Chen Shen, Jun Xu, Nicholas X Fang, and Yun Jing.Anisotropic complementary acoustic metamaterial forcanceling out aberrating layers.
Physical Review X ,4(4):041033, 2014.[43] Guillaume Maimbourg, Alexandre Houdouin, ThomasDeffieux, Mickael Tanter, and Jean-Fran¸cois Aubry. 3d-printed adaptive acoustic lens as a disruptive technol-ogy for transcranial ultrasound therapy using single-element transducers.
Physics in Medicine & Biology ,63(2):025026, 2018.[44] Marcelino Ferri, Jos M. Bravo, Javier Redondo, andJuan V. Snchez-Prez. Enhanced numerical method forthe design of 3-d-printed holographic acoustic lenses foraberration correction of single-element transcranial fo-cused ultrasound.
Ultrasound in Medicine & Biology ,45(3):867 – 884, 2019.[45] Kullervo Hynynen, Nathan McDannold, NataliaVykhodtseva, and Ferenc A Jolesz. Noninvasive mrimaging–guided focal opening of the blood-brain barrierin rabbits.
Radiology , 220(3):640–646, 2001.[46] William J Tyler, Yusuf Tufail, Michael Finsterwald,Monica L Tauchmann, Emily J Olson, and CassondraMajestic. Remote excitation of neuronal circuits us-ing low-intensity, low-frequency ultrasound.
PloS one ,3(10):e3511, 2008.[47] Uwe Schneider, Eros Pedroni, and Antony Lomax. Thecalibration of ct hounsfield units for radiotherapy treat-ment planning.
Physics in Medicine & Biology , 41(1):111,1996.[48] T Douglas Mast. Empirical relationships between acous-tic parameters in human soft tissues.
Acoustics ResearchLetters Online , 1(2):37–42, 2000.[49] John C Mazziotta, Arthur W Toga, Alan Evans, PeterFox, Jack Lancaster, et al. A probabilistic atlas of thehuman brain: theory and rationale for its development.
Neuroimage , 2(2):89–101, 1995.[50] Paul A Yushkevich, Joseph Piven, Heather Cody Hazlett,Rachel Gimpel Smith, Sean Ho, James C Gee, and GuidoGerig. User-guided 3d active contour segmentation ofanatomical structures: significantly improved efficiencyand reliability.
Neuroimage , 31(3):1116–1128, 2006.[51] David T. Blackstock.
Fundamentals of physical acoustics . John Wiley & Sons, 2000.[52] Bradley E Treeby and BT Cox. Modeling power lawabsorption and dispersion for acoustic propagation usingthe fractional laplacian.
The Journal of the AcousticalSociety of America , 127(5):2741–2748, 2010.[53] Bradley E Treeby, Jiri Jaros, Alistair P Rendell, andBT Cox. Modeling nonlinear ultrasound propagationin heterogeneous media with power law absorption us-ing ak-space pseudospectral method.
The Journal of theAcoustical Society of America , 131(6):4324–4336, 2012.[54] No´e Jim´enez, Francisco Camarena, Javier Redondo,V´ıctor S´anchez-Morcillo, Yi Hou, and Elisa E Konofagou.Time-domain simulation of ultrasound propagation in atissue-like medium based on the resolution of the nonlin-ear acoustic constitutive relations.
Acta Acustica unitedwith Acustica , 102(5):876–892, 2016.[55] No´e Jim´enez, Vicent Romero-Garc´ıa, Vincent Pagneux,and Jean-Philippe Groby. Quasiperfect absorption bysubwavelength acoustic panels in transmission using ac-cumulation of resonances due to slow sound.
PhysicalReview B , 95(1):014205, 2017.[56] Peter Wai Ming Tsang and T-C Poon. Novel method forconverting digital fresnel hologram to phase-only holo-gram based on bidirectional error diffusion.
Optics Ex-press , 21(20):23680–23686, 2013.[57] Robert Lirette and Joel Mobley. Focal zone characteris-tics of stepped fresnel and axicon acoustic lenses.
Pro-ceedings of Meetings on Acoustics , 31(1):045001, 2017. [58] Matteo Gatto, Gianluca Memoli, Adam Shaw, NeelakshSadhoo, Pierre Gelat, and Russell A Harris. Three-dimensional printing (3dp) of neonatal head phantom forultrasound: Thermocouple embedding and simulation ofbone.
Medical Engineering and Physics , 34(7):929–937,2012.[59] James Robertson, Eleanor Martin, Ben Cox, andBradley E Treeby. Sensitivity of simulated transcra-nial ultrasound fields to acoustic medium property maps.
Physics in Medicine & Biology , 62(7):2559, 2017.[60] Chen Bai, Meiling Ji, Ayache Bouakaz, Yujin Zong, andMingxi Wan. Design and characterization of an acousti-cally and structurally matched 3d-printed model for tran-scranial ultrasound imaging.
IEEE Transactions on Ul-trasonics, Ferroelectrics, and Frequency Control , 2018.[61] Christopher Rowland Hill, JC Bamber, andGR Ter Haar.
Physical principles of medical ultrasonics .John Wiley & Sons New YorkChichesterBrisbane-Toronto, 2004.[62] Richard SC Cobbold.
Foundations of biomedical ultra-sound . Oxford University Press, 2006.[63] HoT O’Neil. Theory of focusing radiators.
The Journal ofthe Acoustical Society of America , 21(5):516–526, 1949.[64] Di-Chao Chen, Xing-Feng Zhu, Qi Wei, Da-Jian Wu, andXiao-Jun Liu. Broadband acoustic focusing by airy-likebeams based on acoustic metasurfaces.