Microscale acoustic metamaterials as conformal sonotransparent skull prostheses

Microscale acoustic metamaterials as conformal sonotransparent skull prostheses | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Microscale acoustic metamaterials as conformal sonotransparent skull prostheses Gunho Kim, Claire Rabut, Bill Ling, Mikhail Shapiro, Chiara Daraio This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2743580/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Functional ultrasound imaging enables sensitive, high-resolution imaging of neural activity in freely behaving animals and human patients. However, the skull acts as an aberrating and absorbing layer for sound waves, leading to most functional ultrasound experiments being conducted after skull removal. In pre-clinical settings, craniotomies are often covered with a polymethylpentene film, which offers limited longitudinal imaging, due to the film’s poor conformability, and limited mechanical protection, due to the film’s low stiffness. Here, we introduce a skull replacement consisting of a microstructured, conformal acoustic window based on mechanical metamaterials, designed to offer high stiffness-to-density ratio and sonotransparency. We test the acoustic window in vivo, via terminal and survival experiments on small animals. Long-term biocompatibility and lasting signal sensitivity are demonstrated over a long period of time (> 4 months) by conducting ultrasound imaging in mouse models implanted with the metamaterial skull prosthesis. Physical sciences/Physics/Applied physics/Acoustics Biological sciences/Biological techniques/Imaging/Ultrasound Physical sciences/Engineering/Mechanical engineering Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Functional ultrasound imaging (fUSI), the ultrasound analogue of functional magnetic resonance imaging (fMRI), enables the imaging of whole-brain activity with high spatio-temporal resolution and high sensitivity 1 , 2 . Based on the power Doppler technique 3 , fUSI records brain dynamics by measuring the variation of cerebral blood volume, indirectly coupled to cerebral activity through the neurovascular coupling. fUSI has been used in many different animal models from rodent 4 , 5 to primate 6 and in humans 7 , 8 , and it can easily be combined with other brain recording technology such as optical 9 or electrical modalities 10 . Moreover, fUSI can easily be adapted for awake head-fixed or freely-moving animals 11 and it is suitable for pharmacological studies using functional connectivity as a readout 12 . To ensure high sensitivity to smallest blood volume variations, fUSI relies on high frequencies (typically between 5 MHz and 15 MHz), which are sensitive to bone’s attenuation and aberration 13 . This is different from low-frequency focused ultrasounds (typically between 0.2 MHz to 1 MHz) used for therapeutic applications, where transcranial procedures are possible 14 . As a result, most fUSI applications require circumventing the skull, through open craniotomy 4 , 6 or thinned skull procedures 15 . For chronic studies, the skull can be replaced with an acoustically transparent bio-polymeric cranial window, to preserve the integrity of brain tissues over time 10 , 16 . The literature has extensively reported the use of polymethylpentene (PMP) sheets to replace the skull for ultrasound imaging experiments (see references in Table S1 ). However, PMP sheets are thin, not conformal and have a low Young’s modulus (< 2 GPa) 17 , which make them unsuitable to serve as a mechanical protection against external stresses. An improved skull-replacement prosthesis should: (i) be tailorable to match the shape of individual anatomical features, (ii) be stiff to serve as protection for the brain, and (iii) be sonotransparent. Essentially, it is desirable to create conformal acoustic windows, with quasi-static mechanical properties matching the skull and with acoustic impedance matching the brain. Mechanical metamaterials (MMs) are rationally designed materials that derive their properties from the selection of their constitutive materials and from the geometry of their micro- and meso-structures. MMs have been shown to exhibit unprecedented mechanical properties, in both static and dynamic loading regimes. For example, MMs can have very high stiffness and strength at low density 18 – 20 , or are capable of manipulating elastic and acoustic waves beyond naturally defined limits 21 – 23 . Acoustic metamaterials (AMMs) are the subset of MMs aimed at manipulating acoustic waves, capable of achieving selective transmission 24 – 35 , cloaking 36 , 37 , or focusing and lensing 38 , 39 . AMMs can achieve near perfect transmission via resonance 25 , zero or negative density 26 , 27 , narrow apertures 28 , 29 , impedance matching 30 , 31 , and overcome the presence of aberrating layers 32 – 35 . However, most of the proposed solutions only work within a narrow frequency bandwidth, which limits their applications for broader use 24 , 25 , 28 , 29 , 32 – 35 . Earlier works demonstrated the use of MMs to image through a stiff and lossy barrier 33 , 34 , however, these AMMs do not conform to a real skull geometry and do not account for the irregularities and inhomogeneities of bone. As such, existing designs are not readily applicable to solve in vivo problems. Mechanical metamaterials as a conformal cranial windows Here, we focus on the realisation of MMs that can be implanted as custom skull replacements (or “metaskulls”, Fig. 1 a,b). To achieve high effective stiffness along the direction normal to the skull’s surface as protection for the brain, we design a metaskull’s microstructure as a hexagonal, honeycomb lattice with perforated panels (Fig. 1 a). Honeycomb plate lattices are known to reach the highest stiffness values, at constant density for two-phase materials, loaded along the vertical direction (topping the Hashin-Shtrikman bound) 40 . To ensure acoustic transparency around 15 MHz, to meet the requirements for fUSI in small animals 1 , we design structural features in the micrometre scale and fabricate the metaskulls using 2-photon polymerization (2PP) (Fig. 1 c). The metaskulls are composed of polymerized IP-S, which is an acrylic polymer cured from its viscous liquid photoresist state, suitable for fabricating biocompatible microscale materials with intricate inner structures 41 . The unit cells of the honeycomb microlattices consist of vertical panels (Fig. 1 c) that enclose an air filled cavity, to match the acoustic impedance of biological tissue ( Z tissue ~ 1.5 MRayl). To ensure that uncured photoresist trapped inside the cavities can be removed after fabrication, we include horizontal drainage holes (5 µm in diameter) on all vertical panels. To numerically evaluate the quasi-static and dynamic mechanical properties of the metaskulls, we implement finite element (FE) models, which we validate with experiments. We also conduct in vivo tests in mice, to evaluate the brain imaging quality through the metaskulls of varying thickness, by measuring both the total intensity and signal-to-noise ratio (SNR) of the signal. To demonstrate the long-term stability of the metaskulls for brain imaging, we perform longitudinal experiments in vivo via Doppler ultrasound imaging with visual stimulation. Stiffness of metaskulls for mechanical protection We numerically calculate the effective mechanical response of a metaskull’s microstructure under compression using a linear elastic model, with a commercial FE software (COMSOL Multiphysics®) (see SI for more information). The FE model is configured to reproduce the experimental setup (FemtoTools AG, Fig. 2 a). Numerical simulations are used to compute the deformation and stress distribution of a 4-unit-cell-thick, finite-sized honeycomb lattice (Fig. 2 b). To minimise boundary effects, the lattice model is designed to be much larger than the compression tip (Fig. S2). The effective compressive Young’s modulus of the honeycomb lattice evaluated from numerical simulation is E* = 3.08 GPa (see Methods). In comparison, the elastic modulus of the 125-µm-thick PMP is E = 1.5 GPa 17 . As expected, the von Mises stress distribution of the model shows that the stress and deformations are concentrated below the compressed region, especially around the horizontal drainage holes. The presence of the horizontal holes decreases the effective stiffness of the honeycomb plate-lattices by 12.4% (Fig. S4). The mean effective compressive modulus measured from independent compression tests of the 3D-printed honeycomb plate-lattices is 3.02 GPa ± 83.4 MPa (standard deviation), which is in good agreement with the numerical prediction (3.08 GPa) (Fig. 2 d). As a reference, we also measured the compressive response of a PMP film, from which we extracted a Young's modulus of 1.52 GPa ± 112.1 MPa, demonstrating that the mechanical performance of the metaskull is superior to conventional materials used in practice.The dimensions of the honeycomb plate-lattice unit cells were selected so that the metaskulls can be impedance-matched to biological tissue, while preserving the highest possible quasi-static stiffness. As expected, the stiffness of the honeycomb metamaterials lies on the edge of the theoretical limit, which is the Hashin-Shtrikman upper bound for two phase materials 42 (Fig. 2 e). Acoustic characteristics of metaskulls shows sonotransparency We compute the dispersion curves in the 𝚪- A direction in the Brillouin zone when excited by plane acoustic waves in the z -direction, to investigate the wave propagation characteristics of the honeycomb lattices used in metaskulls (Fig. 3 b). The proposed lattice design was selected to have a linear, longitudinal branch around 15 MHz, which allows dispersionless propagation of waves around the fUSI operating frequency. A drawback of acoustic imaging through the skull is the known energy loss in the bone due to the hybridization between the longitudinal and shear modes 43 . We avoid such normal-to-shear coupling by designing the lattice to present a shear mode bandgap between 11.4 and 20.2 MHz, leading to the suppression of shear waves’ conduction through the skull of the subjects 44 . The acoustic impedance of the lattices is matched to biological tissue/water ( Z w = 1.48 MRayl), to reduce reflections from the fluid-metaskull interface. At 15 MHz, the group velocity of the longitudinal waves through the metaskulls’ lattice is c g = 1,938.7 m/s and the effective density of the lattice is ⍴ eff = 775.6 kg/m 3 , resulting in an acoustic impedance along the vertical direction of Z MS = 1.504 MRayl. We investigate the transmission characteristics of the metaskulls by numerically analysing the frequency dependent response (Fig. 3 a). The attenuation through the 4-unit-cell MS at 15 MHz is 1.20 dB, which is significantly smaller than the attenuation at 30 MHz, by 90%. The volumetric strain distribution within the constituent solid as a function of the travelling distance shows that the amplitude of the travelling waves attenuates for both cases, but with much greater loss at the higher frequencies (Fig. S5). The higher transmission loss at 30 MHz is attributed to the presence of a longitudinal band gap between 23.05 and 38.94 MHz, whereas the loss at 15 MHz arises from the viscoelastic dissipation of the polymer itself 45 . With gradually increasing frequency, the slope of the attenuation curve gets steeper and increasingly nonlinear as the frequency surpasses 18 MHz, and the attenuation raises drastically above 20 MHz (Fig. 3 c). We experimentally validate the numerical predictions for the acoustic properties of the metaskulls by measuring the transmission coefficient with respect to the input frequency (Fig. 3 d). Microlattice samples with different thickness (111, 148, 185, 259, and 333 µm) are used for the transmission measurements. The discrepancy between the transmission coefficients at higher frequencies measured in experiments and simulations is due to the finite size of the experimental samples and to boundary effects. To compare results, we average and linear-fit the transmission coefficients between 13.75 and 17.5 MHz for each sample, and compare them to the 125-µm-thick PMP film, as a reference (Fig. 3 c). The curve-fitted transmission loss data extrapolate to the origin, implying zero reflections at the water-metaskull interface, since the metaskulls are acoustically matched to biological tissue. The attenuation coefficient of the metaskulls, 83.0 dB/cm, is larger compared to that of the PMP film, 36.6 dB/cm, at 15 MHz. We attribute the higher attenuation observed in the metaskull to the presence of interfaces and defects resulting from additive manufacturing. However, we show in the subsequent sections that the fUSI qualities are acceptable even with the slightly increased attenuation. fUSI is based on the ultrafast transmission of plane acoustic waves in tissues to capture subtle blood flow changes caused by neurovascular coupling. To achieve maximum contrast, coherent compounding of tilted plane-waves was performed 46 . Typically for fUSI, four to ten angles between − 10° to + 10° are used to form a single coherently compounded image. We analysed dispersion curves and transmission properties for varying tilting angles and directions of the incident wave fronts (Fig. S8). The incident angles were tilted in the xz -plane based on the Brillouin zone of a hexagonal lattice. Starting from 𝚪- A , the dispersion curves were computed with a gradually increasing incident angle toward the 𝚪- L direction (Fig. S8). With greater tilting angle, the longitudinal modes in the lattice get more hybridised with the shear modes, making it less effective at transmitting the acoustic wave energy. We observe that the original dispersion behaviour in 𝚪- A remains relatively unchanged until 𝚪 -0.2 L , which corresponds to a 14.8° tilting. We numerically investigate the transmission performance of the metaskulls as a function of varying incident angle of plane acoustic waves, at 15 MHz (Fig. S9). The transmission curve of the 4-unit-cell MSs is almost flat up to 14.8° with only 0.16 dB reduction from 0°, but the curve shows steep decrease to -2.55 dB at 30° and to -5.81 dB at 40°. In vivo transmission characteristics through metaskulls show high SNR To validate the fitness of the metaskulls as skull prostheses for high sensitivity fUSI, we conduct in vivo imaging studies using a total of 6 mice. We test four mice to compare the SNR performance of the power Doppler images of the brain through two types of cranial windows of varying thickness (Fig. 4 ), and two for the longitudinal monitoring of fUSI performance after cranial implantation of the metaskulls (Fig. 5 ). We first acquire a transcranial cerebral power Doppler image in anaesthetised mice as a reference. We then perform a craniotomy to open a cranial window and to compare the fUSIe performance through different skull replacement materials. The metaskulls with varying thickness and a PMP film (125 µm) are positioned on top of the brain to cover the cranial opening. The thickness of the metaskull samples are 111, 148, 185, 259, and 333 µm, which correspond to 3, 4, 5, 7, and 9 layers, respectively, along the thickness direction. The size of the metaskull windows is 1 cm x 0.25 cm, consisting of ~ 75,000 honeycomb unit cells per layer. All power Doppler images are acquired on the same coronal plane for all conditions (Bregma − 2.5 mm). The standardised intensity maps obtained from the power Doppler using different types of windows are plotted side by side (Fig. 4 a). We observe strong attenuation of the transcranial power Doppler signal relative to the image acquired after craniotomy. The main arteries (see blue arrows) are indiscernible, also showing poor in-depth signal. Without any covering after craniotomy, cortical vessels are clearly visible, as well as the deeper vessels in the thalamic regions (blue arrows). We then cover the brain with a PMP film or the metaskulls with different thickness, and no clear structural change from the acquired images was noticeable. The average intensity in the power Doppler images is the highest in the case of craniotomy and the lowest in the transcranial case (Fig. 4 b). Taking the intensity from the craniotomy as a reference, the PMP case recovered 60% of the reference intensity, while the metaskulls showed gradual decrease from 50% (111 µm) to 20% (333 µm) of the reference intensity with increasing thickness. We quantitatively assess the signal sensitivity of the ultrasound images through the metaskulls by analysing the SNR of the acquired blood vessel mappings. The normalised SNR in cortical regions and in deeper structures (defined by the white-dotted squares in Fig. 4 a) are shown for all the cases (transcranial, craniotomy, PMP, and metaskulls) (Fig. 4 c). The transcranial SNR is evaluated as a reference, and one can again observe a major loss in SNR in the transcranial case (70% of the craniotomy signal in the cortical region, and 45% in the deeper structures). The SNR obtained after covering the brain with a PMP window is almost 95% of the craniotomy SNR, both in the cortical and deeper regions. Similarly, the metaskulls only cause a slight decrease in SNR for the thinner case (92% at 111 µm) for both cortical and deeper structures, while the SNR gradually decreases to 70% as the thickness of the metaskull increases to 333 µm. We show that the metaskulls induce more than 50% decrease in intensity (this decrease is around 40% for the PMP material) compared to the craniotomy case in the power Doppler images, but that the SNR remained above 80% of the craniotomy SNR. Longitudinal study confirms biocompatibility and functional signal conservation over time We surgically implant the metaskulls in mice ( N = 2) to evaluate the biocompatibility of the constituent polymer, and conservation of the functional signal through the implant over a long period of time is observed (> 4 months). Power Doppler scans are performed at days 10, 20, 34, 82 and 120 after surgery, during which we stimulate the visual system to measure evoked activation in the lateral geniculate nuclei (LGN). At day 10 after the implantation, the power Doppler scan allows visualisation of the brain vessels with great sensitivity from the cortex all the way down to the amygdala. Visually evoked response is clearly visible as the two LGN were activated, which led to a higher volume of blood to flow. Throughout the study, the degradation of the power Doppler signal is observed, resulting in a shallower distinction of the blood vessels in the deeper structures (see Fig. 4 for definition of the deep structures). However, the activation of both LGN is distinguishable throughout the whole functional study from day 10 to day 120 with more than 50% correlation with the stimulation pattern. Advantages, limitations, and outlook In this work, we implanted acoustic metamaterials into living animals for ultrasound imaging and brain protection. The proposed metamaterial cranial window, or “metaskull”, allows for fUSI in small animal brains with long-term stability and lasting signal sensitivity, over 120 days. The metamaterials’ inner geometry was architectured so that the metaskulls can accomplish minimally attenuative transmission of ultrasonic waves at 15 MHz. The high stiffness of the designed microlattices offers robust protection to the brain. Our approach surpasses other widely used solutions for cranial windows, e.g., PMP, since the complex shapes and curvatures of the skull can be easily tailored via 2-photon lithography. The transmission characteristics of the metaskulls could be improved by exploring alternative manufacturing approaches. For example, the viscoelastic nature of the constitutive polymer, IP-S, and the interfacial friction between building blocks cause undesired signal attenuation. To address this issue in future studies, the polymer could be carbonised through pyrolysis to create a more brittle structure 47 . Further research should aim at incorporating additional functionalities into the metaskulls, to adapt its functionalities to other biomedical applications. For instance, the metaskulls could be designed as a focusing lens and/or spatial sound modulator, to manipulate ultrasound waves on demand 48 . The use of metaskulls could also achieve safer photoacoustic imaging, which requires the transmission of ultrasound generated through photonic stimulation 49 . Additionally, the scalability of the metaskulls has a potential to create chronic human skull prostheses, enabling long-term monitoring, treatment, and stimulation using ultrasound 50 . Declarations Acknowledgements We thank Avinoam Bar-Zion, David Maresca, and Daniel Sawyer for the discussion during the early stage of the project. G.K. acknowledges financial support from Kwanjeong Educational Foundation. G. K. and C. D. acknowledge support from the National Science Foundation I-UCRC “Center to Stream Healthcare in Place” at Caltech, and the Donna and Benjamin M. Rosen Bioengineering Center Pilot Research Grant. C.D. acknowledges support from the Heritage Medical Institute at Caltech. C.R. acknowledges Cross-Disciplinary Postdoctoral Fellowship from the Human Frontier Science Program. B.L. acknowledges NIH/NRSA Pre-Doctoral Training Grant (T32GM07616). This project was supported by the Rosen Center for Bioengineering and the National Institute of Health (NIH R01-NS123663 to C.D. and R01-EB018975 to M.G.S.). M.G.S. is an investigator of the Howard Hughes Medical Institute. Author contributions C.D. and M.G.S. conceived the study. G.K. designed, planned and carried out the mechanical characterization experiments, finite element simulation, and analysed data. C.R., B.L., and G.K. designed, planned and carried out the in vivo experiments and analysed data. All authors discussed the results. G.K. and C.R. wrote the manuscript with input from all authors. All authors have given approval to the final version of the manuscript. Competing interests The California Institute of Technology (Caltech) has a patent pending related to the discoveries in this manuscript. Supplementary Information is available for this paper. Methods FEA for the mechanical characterizations We performed the numerical mechanical characterization of a metaskull under quasi-static or dynamic loading via FE analysis (Fig. 2b, 3a). The models used for the simulations consist of a 4-unit-cell thick metaskull with a 300 µm diameter circular face. Mimicking the compression experiment setup shown in Figure 2a, 50 µm X 50 µm square-faced punch was compressed against the plate-lattice domain. Assuming linear elasticity and geometric linearity, we computed the simulation to plot the von Mises stress distribution on xz - and yz -planes, showing the stress concentration along the drainage holes. In addition, we built the transmission models to assess the acoustic characteristics of the travelling pressure waves with respect to the frequency and the angle of incidence (Fig. 3a). Calculation and visualisation of the dispersion curves Numerical simulations were performed using a commercial FE software (COMSOL Multiphysics ® ). The dispersion curves of a metaskull were derived by numerically solving the characteristic equation of the honeycomb unit cell. Bloch-Floquet periodic boundary conditions were applied on all sides, assuming infinite periodicity. With evenly-spaced wavenumbers sweeping within the irreducible Brillouin zone, the eigenfrequencies below 50 MHz were calculated to best represent the behaviour of the metamaterials around the operating frequency of fUSI for small animals (~ 15 MHz). With incident plane waves travelling in the z -direction, 𝚪- A , the volume-averaged displacements in each direction were normalised with the total volume-averaged displacement. We determined the longitudinal polarisation of each normal mode based on the dominant direction of deformation. The longitudinal polarisation factor is defined as where , , and are the displacements in x , y , and z directions, respectively. If the longitudinal polarisation factor of one normal mode is close to 1, the mode has dominant pressure wave behaviour, as opposed to when the transverse mode is dominant and the polarisation factor is close to 0. With blue being purely longitudinal and red being purely transverse, the dispersion curves were plotted to indicate the polarisation of the mode at each solution (Fig. 3b). The dispersion curves of the honeycomb unit cell in different wave directions were calculated by sweeping the Brillouin zone in the reciprocal domain. The wavenumber vectors k = ( k x , k y , k z ) parallel to 𝚪- A, 𝚪- 𝛼 L, 𝚪- 𝛼 H with 𝛼 = 0.2, 0.5, or 1, are used for the dispersion curves. Transmission simulation The input and output pressure field, padded with perfectly matched layers, sandwich a column of honeycomb plate-lattices composed of a finite number of unit cells ( n = 3, 4, 5, 7, and 9). We imposed the Bloch-Floquet periodic boundary conditions on the side faces to assume infinite periodicity in the lateral directions. The viscoelastic dissipation of the constituent polymer was incorporated by feeding an isotropic structural loss factor ( η = 0.075) to the materialistic model 45 . We evaluated the amplitude of the travelling pressure waves in the output pressure field, and showed the transmission curves in dB, (Fig. 3d). Micro fabrication process of metaskulls We adopted the microscale 2PP technique for the fabrication of the metaskulls with intricate inner structures (Nanoscribe GmbH & Co. KG). The photoresist, IP-S, in the form of highly viscous liquid becomes acrylic when cured under laser irradiation. After printing the desired MS geometry, we develop the MS using propylene glycol monomethyl ether acetate (PGMEA) and isopropyl alcohol (IPA). The presence of the drainage holes allows the remaining photoresist to be thoroughly removed from the cavities. We measured the mass of the MS samples before and after underwater tests to confirm that the cavities are saturated with air, trapped inside the structure due to surface tension. For microscopic images, only 25 X 24 X 4 arrays of unit cells were printed, which resulted in a sample with outer dimensions of 590 µm X 574 µm X 148 µm (Fig. 2a). Since the single printing size of the Nanoscribe Photonic Professional GT (300 µm X 300 µm X 300 µm) is smaller than the final dimension, smaller blocks were stitched together to form a larger final structure. Compression experiments on metaskull samples The quasi-static characterization was performed using a micromechanical testing tool (FemtoTools AG, FT-MTA02) (Fig. 2a). A displacement-controlled probe tip with a square end (FT-S100,000) was compressed against a metaskull sample composed of honeycomb unit cells for force measurement. The size of the sample used for testing (700 µm X 700 µm X 148 µm) is larger than the front end of the tip (50 µm X 50 µm), so that boundary effects could be neglected (Fig. S2). The probe tip recorded the force signal as the measuring arm travelled downward 2 µm from the top surface. Calibration test against a rigid substrate surface was done prior to the measurements to offset the deformation of the measuring arm under given force. The reference stiffness of the measuring system, K ref = 28,000 N/m, was then used for the calibration. We took the sample’s effective stiffness from the beginning of the unloading curve, which indicates the global response of the lattice. Acoustic transmission experiments We used zero-padded, Hann-windowed single-cycle sinusoidal bursts as input waves for the underwater transmission tests. The signals centred at multiple different frequencies were sent through the metaskull samples using an immersion transducer (Olympus, V356-SU). The output signals were recorded by a hydrophone (Precision Acoustics, 0.2 mm needle) and Fourier-transformed for the evaluation in the frequency domain. We plotted the transmission coefficients of the metaskulls with varying thickness (111, 148 ,175, 259, and 333 µm) and a PMP film (125 µm) in Fig. 3b. Animal surgeries for in vivo experiments All animal experiments were conducted under protocols approved by the Institutional Animal Care and Use Committee of the California Institute of Technology. The in vivo experiments presented were performed on C57BL/6J mice (Jackson Laboratory) aged between 6 to 8 weeks. No randomization or blinding were necessary in this study. Side-by-side comparison of different skull replacement material Four mice were used for the cranial window characterization study. Mice were anaesthetised with 2–3% isoflurane with their heads fixed on a stereotaxic frame. After the incision and stabilisation of the skin, the skull was exposed and rinsed with sterile saline. Ultrasound coupling gel is applied on top of the skull, then we acquired a first transcranial power Doppler image set (“Transcranial” case in Figure 4a) following the parameters described in the fUSI acquisition section. A skull window (1 cm x 0.4 cm) was then removed by drilling (Foredom) at low speed using a micro drill steel burr (Burr number 19007-07, Fine Science Tools). Care was taken not to damage the dura and to prevent inflammatory processes in the brain. We acquired a second transcranial power Doppler image set where only ultrasound coupling gel is applied on top of the brain (“Craniotomy” case in Figure 4a). Then, successive implant sheets for PMP and metalskull cases were positioned on top of the brain for additional power Doppler acquisitions. Surgical implantation of honeycomb lattices for chronic imaging of the brain in mice Two mice were implanted with the metaskull and used for the longitudinal study. Mice were anaesthetised with 2%–3% isoflurane, with their heads fixed on a stereotaxic frame. After the incision and stabilisation of the skin, we removed a rectangular skull window (1 cm x 0.4 cm) by drilling at low speed using a micro drill steel burr. The window corresponds to the coronal planes from Bregma -2 mm to Bregma -2.5 mm. Care was taken not to damage the dura and to prevent inflammatory processes in the brain. We dropped 20 µl of artificial dura on top of the exposed brain to provide an aqueous layer between the brain tissue and the implant. A 1 cm x 0.5 cm metaskull window was sealed in place with the layer of acrylic resin.The surgical procedure took 45 min to 1 h. Animals recovered quickly, and after a conservative 10 days resting period, they were used for the data acquisition via fUSI. fUSI acquisition fUSI visualises neural activity by mapping local changes in cerebral blood volume (CBV). CBV variations are tightly linked to neuronal activity through the neurovascular coupling and are evaluated by calculating power Doppler variations in the brain. fUSI was performed using a 15 MHz ultrasonic probe (L22-14vX, 15 MHz, 64 elements, 0.11 mm pitch, Verasonics) connected to a Verasonics Vantage ultrasound system (Verasonics) driven by custom MATLAB (MathWorks) transmission scripts. Each power Doppler image was obtained from the temporal integration of 300 compounded frames acquired at 500 Hz frame rate, using 5 tilted plane waves separated by 3° (−6°, −3°, 0°, 3°, and 6°) acquired at a 2,500 Hz pulse repetition frequency. Power Doppler images were then repeated every second (1 Hz image framerate). Each block of 300 images was processed using a SVD clutter filter to separate tissue signal from blood signal to obtain a final power Doppler image exhibiting CBV in the whole imaging plane. Functional activation of mice visual system To evaluate the sensitivity of fUSI through metaskull long-term, we stimulated the visual system of the metaskull-implanted mice over multiple days (day 10, 20, 34, …). We delivered visual stimuli using a blue LED positioned at 3 cm in front of the eyes of the mice. Stimulation runs consisted of periodic flickering of the blue LED using the following parameters: 30 s of rest followed by 30 s of a flicker. Activation maps Correlation maps were computed individually from the normalised correlation between each pixel’s temporal signal with the visual stimulus patterns (Pearson’s product moment) using MATLAB (MathWorks). SNR calculation For the SNR performance through different materials and thicknesses study (Fig/ 4), we delimited two regions: one region in the cortex (region i.) and one region in the deeper structures (region ii.). Each region was of dimensions: 10 x 5 (lateral x depth) pixels. For each depth, we measured the intensity profile and calculated the local minima and maxima along the lateral axis (Fig. S10). SNR was calculated as: References Macé E et al (2011) Functional ultrasound imaging of the brain. Nat Methods 8:662–664 Deffieux T, Demené C, Tanter M (2021) Functional ultrasound imaging: A new imaging modality for neuroscience. Neuroscience 474:110–121 Rubin JM, Bude RO, Carson PL, Bree RL, Adler RS (1994) Power Doppler US: a potentially useful alternative to mean frequency-based color Doppler US. Radiology 190:853–856 Gesnik M et al (2017) 3D functional ultrasound imaging of the cerebral visual system in rodents. 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Appl Phys Lett 103:063509 Lee SH, Park CM, Seo YM, Wang ZG, Kim CK (2009) Acoustic metamaterial with negative density. Phys Lett A 373:4464–4469 Fleury R, Alù A (2013) Extraordinary Sound Transmission through Density-Near-Zero Ultranarrow Channels. Phys Rev Lett 111:055501 Zhang X (2005) Acoustic resonant transmission through acoustic gratings with very narrow slits: Multiple-scattering numerical simulations. Phys Rev B 71:241102 Lu M-H et al (2007) Extraordinary Acoustic Transmission through a 1D Grating with Very Narrow Apertures. Phys Rev Lett 99:174301 D’Aguanno G et al (2012) Broadband metamaterial for nonresonant matching of acoustic waves. Sci Rep 2:340 Xie Y, Konneker A, Popa B-I, Cummer SA (2013) Tapered labyrinthine acoustic metamaterials for broadband impedance matching. Appl Phys Lett 103:201906 Shen C, Xu J, Fang NX, Jing Y (2014) Anisotropic Complementary Acoustic Metamaterial for Canceling out Aberrating Layers. Phys Rev X 4:041033 Craig SR, Welch PJ, Shi C (2019) Non-Hermitian complementary acoustic metamaterials for lossy barriers. Appl Phys Lett 115:051903 Craig SR, Welch PJ, Shi C (2020) Non-Hermitian Complementary Acoustic Metamaterials for Imaging Through Skull With Imperfections.Frontiers in Mechanical Engineering6, Wang J, Allein F, Boechler N, Friend J, Vazquez-Mena O (2021) Design and Fabrication of Negative-Refractive-Index Metamaterial Unit Cells for Near-Megahertz Enhanced Acoustic Transmission in Biomedical Ultrasound Applications. Phys Rev Applied 15:024025 Chen H, Chan CT (2007) Acoustic cloaking in three dimensions using acoustic metamaterials. Appl Phys Lett 91:183518 Zhang S, Xia C, Fang N (2011) Broadband Acoustic Cloak for Ultrasound Waves. Phys Rev Lett 106:024301 Yang S et al (2004) Focusing of Sound in a 3D Phononic Crystal. Phys Rev Lett 93:024301 Li J, Fok L, Yin X, Bartal G, Zhang X (2009) Experimental demonstration of an acoustic magnifying hyperlens. Nat Mater 8:931–934 Wadley HNG (2006) Multifunctional periodic cellular metals. Philosophical Trans Royal Soc A: Math Phys Eng Sci 364:31–68 Moussi K, Bukhamsin A, Hidalgo T, Kosel J (2020) Biocompatible 3D Printed Microneedles for Transdermal, Intradermal, and Percutaneous Applications. Adv Eng Mater 22:1901358 Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11:127–140 Tian Y, Shen Y, Qin X, Yu Z (2021) Enabling the complete mode conversion of Lamb waves into shear horizontal waves via a resonance-based elastic metamaterial. Appl Phys Lett 118:014101 Salahshoor H, Shapiro MG, Ortiz M (2020) Transcranial focused ultrasound generates skull-conducted shear waves: Computational model and implications for neuromodulation. Appl Phys Lett 117:033702 Ashby MF (2017) Materials Selection in Mechanical Design. 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Supplementary Files Microscaleacousticmetamaterialsasconformalsonotransparentskullprosthesessupplementary.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2743580","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":187435338,"identity":"83847e54-bd0b-41a3-8ebc-a60de825eab6","order_by":0,"name":"Gunho Kim","email":"","orcid":"","institution":"California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Gunho","middleName":"","lastName":"Kim","suffix":""},{"id":187435339,"identity":"b958412c-5f01-4158-9668-db2c881745ea","order_by":1,"name":"Claire Rabut","email":"","orcid":"","institution":"California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Claire","middleName":"","lastName":"Rabut","suffix":""},{"id":187435340,"identity":"8c29e52a-9710-4e05-b85e-a2d0984cfc7d","order_by":2,"name":"Bill Ling","email":"","orcid":"","institution":"California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Bill","middleName":"","lastName":"Ling","suffix":""},{"id":187435341,"identity":"03a554cf-e940-4e17-a336-6eba9197bb64","order_by":3,"name":"Mikhail Shapiro","email":"","orcid":"https://orcid.org/0000-0002-0291-4215","institution":"California Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Mikhail","middleName":"","lastName":"Shapiro","suffix":""},{"id":187435342,"identity":"889b70c7-ef57-4144-bb55-576a271584ca","order_by":4,"name":"Chiara Daraio","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIie3PMQuCQBTA8ScPdLNVCfQrKC4N0mc5CewruFUEt7nXt6it0bjB5crVcNHF2VFp6YamCC+3hvvBwfG4P48DUJR/lIlDIAQwxEXbvic/JDEA4pQEgE1IzPzWdHVSuLP97FoPF3DMkownNl8HFuGVf2CIfsohsGWJl8VgRbQiwFCfaxSikzQpWuwjeicuQ+Mpko08KWNdbMmIJ7agSIgn/UvZ6gvCV/6ZYWCn1PKPvB5PzCLGR58sXSffNd1AQ9fMJVs+WdOeK4qiKN+9AJYGRv9OSp56AAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-5296-4440","institution":"California Institute of Technology","correspondingAuthor":true,"prefix":"","firstName":"Chiara","middleName":"","lastName":"Daraio","suffix":""}],"badges":[],"createdAt":"2023-03-27 18:35:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2743580/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2743580/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":36788749,"identity":"131f31ca-78d7-47b2-84a1-f10789cadb23","added_by":"auto","created_at":"2023-05-10 19:47:17","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1978555,"visible":true,"origin":"","legend":"\u003cp\u003eDesign and structure of a metaskull. a, Concept schematic illustrating ultrasound brain imaging through a metaskull. A 3D model of the inner structures of the metamaterials shows a periodic tessellation of honeycomb unit cells, with h = 37 µm, w = 32.3 µm, th = 7.5 µm, and tw = 4.5 µm. b, The metaskulls can fit an arbitrarily shaped region in a curved parietal lobe of the mouse skull (dashed blue region). c, The metaskulls are fabricated with a microscale 2-photon polymerization technique. SEM images of a metaskull’s sections, from the top and isometric views. Scale bars: b, 1 cm; c, 200 µm (left), 100 µm (bottom right), and 20 µm (top right).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-2743580/v1/3874e42096f056704e0e0f3a.png"},{"id":36788641,"identity":"b9001764-c101-4aa7-9524-413d128efdef","added_by":"auto","created_at":"2023-05-10 19:39:17","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":774786,"visible":true,"origin":"","legend":"\u003cp\u003eQuasi-static mechanical characterization of a metaskull (MS). a, Optical microscopy image of a metaskull section used for compression testing, showing the probe tip of the measurement system. b, Von Mises stress distribution calculated with the FE model compressed with a 50 µm X 50 µm square-faced probe tip. Only a quarter of the model and its side views are shown. c, Experimental stress-strain curves showing a single loading-unloading cycle of the metaskull and of a PMP film under indentation. Dashed lines indicate the slopes at the onset of the unloading curve, which are used to calculate the effective Young's moduli. d, The average and standard deviation of the Young's modulus obtained from experiments, for both the honeycomb plate-lattices and a PMP film. Red lines indicate the predicted values from the numerical simulations (MS) or the known material properties (PMP). e, Theoretical upper bound for the modulus (E+HS) of a two-phase, isotropic material (gray line) crossed by an isoline matching the acoustic impedance of the brain (blue line), both as a function of the Young's modulus and density of the constituent solid. Black point indicates the properties of the metaskull: (EMS = 3.02 GPa, 𝜌MS = 775.6 kg/m3). The acoustic impedance of water (Zw) is constant at 1.48 MRayl and follows a relation, Z=√𝜌E . The normalised Young's modulus (E*/Es) and relative density (𝜌*/𝜌s) are normalised with the Young's modulus, 5.5 GPa, and density, 1100 kg/m3, of IP-S, respectively.\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-2743580/v1/0ccf6fd30d5116486773eabf.png"},{"id":36788766,"identity":"1f6cbaa4-0bdb-4c5b-9a32-0fb053cf8edd","added_by":"auto","created_at":"2023-05-10 19:55:17","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":775334,"visible":true,"origin":"","legend":"\u003cp\u003eCharacterization of dynamic mechanical properties of metaskulls. a, FE model for the ultrasonic wave propagation at 15 and 30 MHz through 4 unit cells of the honeycomb plate-lattices in water, assuming infinite periodicity in the lateral directions. (Left) Pressure distribution within the water surrounding a metaskull and the air inside the cavities. Both water and air pressures are normalised by the peak pressures in each medium. (Right) The volumetric strain distribution within the honeycomb metamaterials. b, The dispersion curves of the honeycomb metamaterials in both 𝚪-A and 𝚪-0.2L directions. Curves’ colours indicate the longitudinal polarisation (see SI) of each mode (blue: pressure mode, red: shear mode, and purple: hybridised mode). The graphical representation of each wavevector in the corresponding Brillouin zone is shown in the SI. c, Experimental transmission coefficients of the MS samples with different thickness (111, 148, 195, 259, and 333 µm) averaged between 13.75 and 17.5 MHz, shown with error bars. The slope of the linear regression plot (blue, solid, r2 = 0.99) is -83.0 dB/cm, whereas the attenuation coefficient of a 125-µm-thick PMP film (black, dashed) is -36.6 dB/cm. d, Experimental (dotted) and numerical (solid) transmission curves of PMP films (black, dotted) and the metaskulls with varying thickness, with respect to frequency. Discrepancies between experimental and numerical results are attributed to the finite size of the experimental samples.\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-2743580/v1/e45002839bc967a4891a5b69.png"},{"id":36788494,"identity":"2950e3d1-d630-4b3e-987a-fc68c1f562e7","added_by":"auto","created_at":"2023-05-10 19:31:17","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":891481,"visible":true,"origin":"","legend":"\u003cp\u003eSide-by-side comparison of different skull replacement material for high sensitive cerebral power Doppler imaging in mice (N = 4). a, Cerebral power Doppler imaging of one mouse through the intact skull, after craniotomy without any material, and through a layer of PMP (125 μm) or MSs (111, 148, 185, 259, and 333 μm) (Representative mouse). b, Standardised total intensity of the power Doppler images with respect to the skull replacement material. c, Standardised SNR of the power Doppler in i. the cortex and ii. the deeper structures. Scale bar: 5mm. PD = Power Doppler.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-2743580/v1/1141142dd690c0dd5bc532e8.png"},{"id":36788491,"identity":"80632cf1-4a20-4457-9663-f13a260136c1","added_by":"auto","created_at":"2023-05-10 19:31:17","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1141326,"visible":true,"origin":"","legend":"\u003cp\u003eLongitudinal fUSI study in mice after metaskull implantation. a, Longitudinal study protocol: mice are implanted with a metaskull (148 µm) at day 0. They are then examined at day 10, 20, 34, 82 and 120, during which visually evoked activity is recorded. b, Power Doppler images are acquired around coronal plane B-2.2 mm showing the structure of the vascular network (top, hot colours) and the activated LGN following visual stimulation (bottom, cold colours)\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-2743580/v1/88f5f56e76b78c2431cc939c.png"},{"id":40478141,"identity":"3af2c70e-a11e-4469-a544-7a8321566333","added_by":"auto","created_at":"2023-07-24 14:19:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3654270,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2743580/v1/4e6e7337-befd-4e52-a980-8901612136f7.pdf"},{"id":36788496,"identity":"bee15dfd-c1f6-4cbb-9147-32e4278dd665","added_by":"auto","created_at":"2023-05-10 19:31:18","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1515533,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"Microscaleacousticmetamaterialsasconformalsonotransparentskullprosthesessupplementary.docx","url":"https://assets-eu.researchsquare.com/files/rs-2743580/v1/d6f120e5ffa4f4c30a8283ec.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Microscale acoustic metamaterials as conformal sonotransparent skull prostheses","fulltext":[{"header":"Introduction","content":"\u003cp\u003eFunctional ultrasound imaging (fUSI), the ultrasound analogue of functional magnetic resonance imaging (fMRI), enables the imaging of whole-brain activity with high spatio-temporal resolution and high sensitivity\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Based on the power Doppler technique\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, fUSI records brain dynamics by measuring the variation of cerebral blood volume, indirectly coupled to cerebral activity through the neurovascular coupling. fUSI has been used in many different animal models from rodent\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e to primate\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e and in humans\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, and it can easily be combined with other brain recording technology such as optical\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e or electrical modalities\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. Moreover, fUSI can easily be adapted for awake head-fixed or freely-moving animals\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e and it is suitable for pharmacological studies using functional connectivity as a readout\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTo ensure high sensitivity to smallest blood volume variations, fUSI relies on high frequencies (typically between 5 MHz and 15 MHz), which are sensitive to bone\u0026rsquo;s attenuation and aberration\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. This is different from low-frequency focused ultrasounds (typically between 0.2 MHz to 1 MHz) used for therapeutic applications, where transcranial procedures are possible\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. As a result, most fUSI applications require circumventing the skull, through open craniotomy\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e or thinned skull procedures\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. For chronic studies, the skull can be replaced with an acoustically transparent bio-polymeric cranial window, to preserve the integrity of brain tissues over time\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. The literature has extensively reported the use of polymethylpentene (PMP) sheets to replace the skull for ultrasound imaging experiments (see references in Table \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e). However, PMP sheets are thin, not conformal and have a low Young\u0026rsquo;s modulus (\u0026lt;\u0026thinsp;2 GPa)\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e, which make them unsuitable to serve as a mechanical protection against external stresses.\u003c/p\u003e \u003cp\u003eAn improved skull-replacement prosthesis should: (i) be tailorable to match the shape of individual anatomical features, (ii) be stiff to serve as protection for the brain, and (iii) be sonotransparent. Essentially, it is desirable to create conformal acoustic windows, with quasi-static mechanical properties matching the skull and with acoustic impedance matching the brain.\u003c/p\u003e \u003cp\u003eMechanical metamaterials (MMs) are rationally designed materials that derive their properties from the selection of their constitutive materials and from the geometry of their micro- and meso-structures. MMs have been shown to exhibit unprecedented mechanical properties, in both static and dynamic loading regimes. For example, MMs can have very high stiffness and strength at low density\u003csup\u003e\u003cspan additionalcitationids=\"CR19\" citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, or are capable of manipulating elastic and acoustic waves beyond naturally defined limits\u003csup\u003e\u003cspan additionalcitationids=\"CR22\" citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Acoustic metamaterials (AMMs) are the subset of MMs aimed at manipulating acoustic waves, capable of achieving selective transmission\u003csup\u003e\u003cspan additionalcitationids=\"CR25 CR26 CR27 CR28 CR29 CR30 CR31 CR32 CR33 CR34\" citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e, cloaking\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e,\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e, or focusing and lensing\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e,\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. AMMs can achieve near perfect transmission via resonance\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, zero or negative density\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e,\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e, narrow apertures\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e, impedance matching\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e, and overcome the presence of aberrating layers\u003csup\u003e\u003cspan additionalcitationids=\"CR33 CR34\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. However, most of the proposed solutions only work within a narrow frequency bandwidth, which limits their applications for broader use\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e,\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan additionalcitationids=\"CR33 CR34\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. Earlier works demonstrated the use of MMs to image through a stiff and lossy barrier\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, however, these AMMs do not conform to a real skull geometry and do not account for the irregularities and inhomogeneities of bone. As such, existing designs are not readily applicable to solve in vivo problems.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMechanical metamaterials as a conformal cranial windows\u003c/p\u003e \u003cp\u003eHere, we focus on the realisation of MMs that can be implanted as custom skull replacements (or \u0026ldquo;metaskulls\u0026rdquo;, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea,b). To achieve high effective stiffness along the direction normal to the skull\u0026rsquo;s surface as protection for the brain, we design a metaskull\u0026rsquo;s microstructure as a hexagonal, honeycomb lattice with perforated panels (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). Honeycomb plate lattices are known to reach the highest stiffness values, at constant density for two-phase materials, loaded along the vertical direction (topping the Hashin-Shtrikman bound)\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e. To ensure acoustic transparency around 15 MHz, to meet the requirements for fUSI in small animals\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, we design structural features in the micrometre scale and fabricate the metaskulls using 2-photon polymerization (2PP) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec).\u003c/p\u003e \u003cp\u003eThe metaskulls are composed of polymerized IP-S, which is an acrylic polymer cured from its viscous liquid photoresist state, suitable for fabricating biocompatible microscale materials with intricate inner structures\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e. The unit cells of the honeycomb microlattices consist of vertical panels (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec) that enclose an air filled cavity, to match the acoustic impedance of biological tissue (\u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003etissue\u003c/em\u003e\u003c/sub\u003e ~ 1.5 MRayl). To ensure that uncured photoresist trapped inside the cavities can be removed after fabrication, we include horizontal drainage holes (5 \u0026micro;m in diameter) on all vertical panels.\u003c/p\u003e \u003cp\u003eTo numerically evaluate the quasi-static and dynamic mechanical properties of the metaskulls, we implement finite element (FE) models, which we validate with experiments. We also conduct in vivo tests in mice, to evaluate the brain imaging quality through the metaskulls of varying thickness, by measuring both the total intensity and signal-to-noise ratio (SNR) of the signal. To demonstrate the long-term stability of the metaskulls for brain imaging, we perform longitudinal experiments in vivo via Doppler ultrasound imaging with visual stimulation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eStiffness of metaskulls for mechanical protection\u003c/p\u003e \u003cp\u003eWe numerically calculate the effective mechanical response of a metaskull\u0026rsquo;s microstructure under compression using a linear elastic model, with a commercial FE software (COMSOL Multiphysics\u0026reg;) (see SI for more information). The FE model is configured to reproduce the experimental setup (FemtoTools AG, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea). Numerical simulations are used to compute the deformation and stress distribution of a 4-unit-cell-thick, finite-sized honeycomb lattice (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb). To minimise boundary effects, the lattice model is designed to be much larger than the compression tip (Fig. S2). The effective compressive Young\u0026rsquo;s modulus of the honeycomb lattice evaluated from numerical simulation is \u003cem\u003eE*\u003c/em\u003e = 3.08 GPa (see Methods). In comparison, the elastic modulus of the 125-\u0026micro;m-thick PMP is \u003cem\u003eE\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.5 GPa\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. As expected, the von Mises stress distribution of the model shows that the stress and deformations are concentrated below the compressed region, especially around the horizontal drainage holes. The presence of the horizontal holes decreases the effective stiffness of the honeycomb plate-lattices by 12.4% (Fig. S4).\u003c/p\u003e \u003cp\u003eThe mean effective compressive modulus measured from independent compression tests of the 3D-printed honeycomb plate-lattices is 3.02 GPa\u0026thinsp;\u0026plusmn;\u0026thinsp;83.4 MPa (standard deviation), which is in good agreement with the numerical prediction (3.08 GPa) (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). As a reference, we also measured the compressive response of a PMP film, from which we extracted a Young's modulus of 1.52 GPa\u0026thinsp;\u0026plusmn;\u0026thinsp;112.1 MPa, demonstrating that the mechanical performance of the metaskull is superior to conventional materials used in practice.The dimensions of the honeycomb plate-lattice unit cells were selected so that the metaskulls can be impedance-matched to biological tissue, while preserving the highest possible quasi-static stiffness. As expected, the stiffness of the honeycomb metamaterials lies on the edge of the theoretical limit, which is the Hashin-Shtrikman upper bound for two phase materials\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ee).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAcoustic characteristics of metaskulls shows sonotransparency\u003c/p\u003e \u003cp\u003eWe compute the dispersion curves in the \u003cem\u003e\u0026#120490;-\u003c/em\u003e\u003cspan type=\"BoldItalic\" class=\"BoldItalic\" name=\"Emphasis\"\u003eA\u003c/span\u003e direction in the Brillouin zone when excited by plane acoustic waves in the \u003cem\u003ez\u003c/em\u003e-direction, to investigate the wave propagation characteristics of the honeycomb lattices used in metaskulls (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The proposed lattice design was selected to have a linear, longitudinal branch around 15 MHz, which allows dispersionless propagation of waves around the fUSI operating frequency. A drawback of acoustic imaging through the skull is the known energy loss in the bone due to the hybridization between the longitudinal and shear modes\u003csup\u003e\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. We avoid such normal-to-shear coupling by designing the lattice to present a shear mode bandgap between 11.4 and 20.2 MHz, leading to the suppression of shear waves\u0026rsquo; conduction through the skull of the subjects\u003csup\u003e\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. The acoustic impedance of the lattices is matched to biological tissue/water (\u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003ew\u003c/em\u003e\u003c/sub\u003e = 1.48 MRayl), to reduce reflections from the fluid-metaskull interface. At 15 MHz, the group velocity of the longitudinal waves through the metaskulls\u0026rsquo; lattice is \u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eg\u003c/em\u003e\u003c/sub\u003e = 1,938.7 m/s and the effective density of the lattice is \u003cem\u003e⍴\u003c/em\u003e\u003csub\u003e\u003cem\u003eeff\u003c/em\u003e\u003c/sub\u003e = 775.6 kg/m\u003csup\u003e3\u003c/sup\u003e, resulting in an acoustic impedance along the vertical direction of Z\u003csub\u003eMS\u003c/sub\u003e= 1.504 MRayl.\u003c/p\u003e \u003cp\u003eWe investigate the transmission characteristics of the metaskulls by numerically analysing the frequency dependent response (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). The attenuation through the 4-unit-cell MS at 15 MHz is 1.20 dB, which is significantly smaller than the attenuation at 30 MHz, by 90%. The volumetric strain distribution within the constituent solid as a function of the travelling distance shows that the amplitude of the travelling waves attenuates for both cases, but with much greater loss at the higher frequencies (Fig. S5). The higher transmission loss at 30 MHz is attributed to the presence of a longitudinal band gap between 23.05 and 38.94 MHz, whereas the loss at 15 MHz arises from the viscoelastic dissipation of the polymer itself\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e. With gradually increasing frequency, the slope of the attenuation curve gets steeper and increasingly nonlinear as the frequency surpasses 18 MHz, and the attenuation raises drastically above 20 MHz (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec).\u003c/p\u003e \u003cp\u003eWe experimentally validate the numerical predictions for the acoustic properties of the metaskulls by measuring the transmission coefficient with respect to the input frequency (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). Microlattice samples with different thickness (111, 148, 185, 259, and 333 \u0026micro;m) are used for the transmission measurements. The discrepancy between the transmission coefficients at higher frequencies measured in experiments and simulations is due to the finite size of the experimental samples and to boundary effects. To compare results, we average and linear-fit the transmission coefficients between 13.75 and 17.5 MHz for each sample, and compare them to the 125-\u0026micro;m-thick PMP film, as a reference (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). The curve-fitted transmission loss data extrapolate to the origin, implying zero reflections at the water-metaskull interface, since the metaskulls are acoustically matched to biological tissue. The attenuation coefficient of the metaskulls, 83.0 dB/cm, is larger compared to that of the PMP film, 36.6 dB/cm, at 15 MHz. We attribute the higher attenuation observed in the metaskull to the presence of interfaces and defects resulting from additive manufacturing. However, we show in the subsequent sections that the fUSI qualities are acceptable even with the slightly increased attenuation.\u003c/p\u003e \u003cp\u003efUSI is based on the ultrafast transmission of plane acoustic waves in tissues to capture subtle blood flow changes caused by neurovascular coupling. To achieve maximum contrast, coherent compounding of tilted plane-waves was performed\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e. Typically for fUSI, four to ten angles between \u0026minus;\u0026thinsp;10\u0026deg; to +\u0026thinsp;10\u0026deg; are used to form a single coherently compounded image. We analysed dispersion curves and transmission properties for varying tilting angles and directions of the incident wave fronts (Fig. S8). The incident angles were tilted in the \u003cem\u003exz\u003c/em\u003e-plane based on the Brillouin zone of a hexagonal lattice. Starting from \u003cem\u003e\u0026#120490;-\u003c/em\u003e\u003cspan type=\"BoldItalic\" class=\"BoldItalic\" name=\"Emphasis\"\u003eA\u003c/span\u003e, the dispersion curves were computed with a gradually increasing incident angle toward the \u003cem\u003e\u0026#120490;-\u003c/em\u003e\u003cspan type=\"BoldItalic\" class=\"BoldItalic\" name=\"Emphasis\"\u003eL\u003c/span\u003e direction (Fig. S8). With greater tilting angle, the longitudinal modes in the lattice get more hybridised with the shear modes, making it less effective at transmitting the acoustic wave energy. We observe that the original dispersion behaviour in \u003cem\u003e\u0026#120490;-\u003c/em\u003e\u003cspan type=\"BoldItalic\" class=\"BoldItalic\" name=\"Emphasis\"\u003eA\u003c/span\u003e remains relatively unchanged until \u003cem\u003e\u0026#120490;\u003c/em\u003e-0.2\u003cspan type=\"BoldItalic\" class=\"BoldItalic\" name=\"Emphasis\"\u003eL\u003c/span\u003e, which corresponds to a 14.8\u0026deg; tilting. We numerically investigate the transmission performance of the metaskulls as a function of varying incident angle of plane acoustic waves, at 15 MHz (Fig. S9). The transmission curve of the 4-unit-cell MSs is almost flat up to 14.8\u0026deg; with only 0.16 dB reduction from 0\u0026deg;, but the curve shows steep decrease to -2.55 dB at 30\u0026deg; and to -5.81 dB at 40\u0026deg;.\u003c/p\u003e \u003cp\u003eIn vivo transmission characteristics through metaskulls show high SNR\u003c/p\u003e \u003cp\u003eTo validate the fitness of the metaskulls as skull prostheses for high sensitivity fUSI, we conduct in vivo imaging studies using a total of 6 mice. We test four mice to compare the SNR performance of the power Doppler images of the brain through two types of cranial windows of varying thickness (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e), and two for the longitudinal monitoring of fUSI performance after cranial implantation of the metaskulls (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eWe first acquire a transcranial cerebral power Doppler image in anaesthetised mice as a reference. We then perform a craniotomy to open a cranial window and to compare the fUSIe performance through different skull replacement materials. The metaskulls with varying thickness and a PMP film (125 \u0026micro;m) are positioned on top of the brain to cover the cranial opening. The thickness of the metaskull samples are 111, 148, 185, 259, and 333 \u0026micro;m, which correspond to 3, 4, 5, 7, and 9 layers, respectively, along the thickness direction. The size of the metaskull windows is 1 cm x 0.25 cm, consisting of ~\u0026thinsp;75,000 honeycomb unit cells per layer. All power Doppler images are acquired on the same coronal plane for all conditions (Bregma \u0026minus;\u0026thinsp;2.5 mm).\u003c/p\u003e \u003cp\u003eThe standardised intensity maps obtained from the power Doppler using different types of windows are plotted side by side (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). We observe strong attenuation of the transcranial power Doppler signal relative to the image acquired after craniotomy. The main arteries (see blue arrows) are indiscernible, also showing poor in-depth signal. Without any covering after craniotomy, cortical vessels are clearly visible, as well as the deeper vessels in the thalamic regions (blue arrows). We then cover the brain with a PMP film or the metaskulls with different thickness, and no clear structural change from the acquired images was noticeable. The average intensity in the power Doppler images is the highest in the case of craniotomy and the lowest in the transcranial case (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). Taking the intensity from the craniotomy as a reference, the PMP case recovered 60% of the reference intensity, while the metaskulls showed gradual decrease from 50% (111 \u0026micro;m) to 20% (333 \u0026micro;m) of the reference intensity with increasing thickness.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe quantitatively assess the signal sensitivity of the ultrasound images through the metaskulls by analysing the SNR of the acquired blood vessel mappings. The normalised SNR in cortical regions and in deeper structures (defined by the white-dotted squares in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) are shown for all the cases (transcranial, craniotomy, PMP, and metaskulls) (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). The transcranial SNR is evaluated as a reference, and one can again observe a major loss in SNR in the transcranial case (70% of the craniotomy signal in the cortical region, and 45% in the deeper structures). The SNR obtained after covering the brain with a PMP window is almost 95% of the craniotomy SNR, both in the cortical and deeper regions. Similarly, the metaskulls only cause a slight decrease in SNR for the thinner case (92% at 111 \u0026micro;m) for both cortical and deeper structures, while the SNR gradually decreases to 70% as the thickness of the metaskull increases to 333 \u0026micro;m.\u003c/p\u003e \u003cp\u003eWe show that the metaskulls induce more than 50% decrease in intensity (this decrease is around 40% for the PMP material) compared to the craniotomy case in the power Doppler images, but that the SNR remained above 80% of the craniotomy SNR.\u003c/p\u003e \u003cp\u003eLongitudinal study confirms biocompatibility and functional signal conservation over time\u003c/p\u003e \u003cp\u003eWe surgically implant the metaskulls in mice (\u003cem\u003eN\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2) to evaluate the biocompatibility of the constituent polymer, and conservation of the functional signal through the implant over a long period of time is observed (\u0026gt;\u0026thinsp;4 months). Power Doppler scans are performed at days 10, 20, 34, 82 and 120 after surgery, during which we stimulate the visual system to measure evoked activation in the lateral geniculate nuclei (LGN).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAt day 10 after the implantation, the power Doppler scan allows visualisation of the brain vessels with great sensitivity from the cortex all the way down to the amygdala. Visually evoked response is clearly visible as the two LGN were activated, which led to a higher volume of blood to flow. Throughout the study, the degradation of the power Doppler signal is observed, resulting in a shallower distinction of the blood vessels in the deeper structures (see Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e for definition of the deep structures). However, the activation of both LGN is distinguishable throughout the whole functional study from day 10 to day 120 with more than 50% correlation with the stimulation pattern.\u003c/p\u003e \u003cp\u003eAdvantages, limitations, and outlook\u003c/p\u003e \u003cp\u003eIn this work, we implanted acoustic metamaterials into living animals for ultrasound imaging and brain protection. The proposed metamaterial cranial window, or \u0026ldquo;metaskull\u0026rdquo;, allows for fUSI in small animal brains with long-term stability and lasting signal sensitivity, over 120 days. The metamaterials\u0026rsquo; inner geometry was architectured so that the metaskulls can accomplish minimally attenuative transmission of ultrasonic waves at 15 MHz. The high stiffness of the designed microlattices offers robust protection to the brain. Our approach surpasses other widely used solutions for cranial windows, e.g., PMP, since the complex shapes and curvatures of the skull can be easily tailored via 2-photon lithography.\u003c/p\u003e \u003cp\u003eThe transmission characteristics of the metaskulls could be improved by exploring alternative manufacturing approaches. For example, the viscoelastic nature of the constitutive polymer, IP-S, and the interfacial friction between building blocks cause undesired signal attenuation. To address this issue in future studies, the polymer could be carbonised through pyrolysis to create a more brittle structure\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFurther research should aim at incorporating additional functionalities into the metaskulls, to adapt its functionalities to other biomedical applications. For instance, the metaskulls could be designed as a focusing lens and/or spatial sound modulator, to manipulate ultrasound waves on demand\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e\u003c/sup\u003e. The use of metaskulls could also achieve safer photoacoustic imaging, which requires the transmission of ultrasound generated through photonic stimulation\u003csup\u003e\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. Additionally, the scalability of the metaskulls has a potential to create chronic human skull prostheses, enabling long-term monitoring, treatment, and stimulation using ultrasound\u003csup\u003e\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eAcknowledgements\u003c/p\u003e\n\u003cp\u003eWe thank Avinoam Bar-Zion, David Maresca, and Daniel Sawyer for the discussion during the early stage of the project. G.K. acknowledges financial support from Kwanjeong Educational Foundation. G. K. and C. D. acknowledge support from the National Science Foundation I-UCRC \u0026ldquo;Center to Stream Healthcare in Place\u0026rdquo; at Caltech, and the Donna and Benjamin M. Rosen Bioengineering Center Pilot Research Grant. C.D. acknowledges support from the Heritage Medical Institute at Caltech. C.R. acknowledges Cross-Disciplinary Postdoctoral Fellowship from the Human Frontier Science Program. B.L. acknowledges NIH/NRSA Pre-Doctoral Training Grant (T32GM07616). This project was supported by the Rosen Center for Bioengineering and the National Institute of Health (NIH R01-NS123663 to C.D. and R01-EB018975 to M.G.S.). M.G.S. is an investigator of the Howard Hughes Medical Institute.\u003c/p\u003e\n\u003cp\u003eAuthor contributions\u003c/p\u003e\n\u003cp\u003eC.D. and M.G.S. conceived the study. G.K. designed, planned and carried out the mechanical characterization experiments, finite element simulation, and analysed data. C.R., B.L., and G.K. designed, planned and carried out the in vivo experiments and analysed data. All authors discussed the results. G.K. and C.R. wrote the manuscript with input from all authors. All authors have given approval to the final version of the manuscript.\u003c/p\u003e\n\u003cp\u003eCompeting interests\u003c/p\u003e\n\u003cp\u003eThe California Institute of Technology (Caltech) has a patent pending related to the discoveries in this manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eSupplementary Information is available for this paper. \u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eFEA for the mechanical characterizations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe performed the numerical mechanical characterization of a metaskull under quasi-static or dynamic loading via FE analysis (Fig. 2b, 3a). The models used for the simulations consist of a 4-unit-cell thick metaskull with a 300 µm diameter circular face. Mimicking the compression experiment setup shown in Figure 2a, 50 µm X 50 µm square-faced punch was compressed against the plate-lattice domain. Assuming linear elasticity and geometric linearity, we computed the simulation to plot the von Mises stress distribution on \u003cem\u003exz\u003c/em\u003e- and \u003cem\u003eyz\u003c/em\u003e-planes, showing the stress concentration along the drainage holes. In addition, we built the transmission models to assess the acoustic characteristics of the travelling pressure waves with respect to the frequency and the angle of incidence (Fig. 3a).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCalculation and visualisation of the dispersion curves\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNumerical simulations were performed using a commercial FE software (COMSOL Multiphysics\u003csup\u003e®\u003c/sup\u003e). The dispersion curves of a metaskull were derived by numerically solving the characteristic equation of the honeycomb unit cell. Bloch-Floquet periodic boundary conditions were applied on all sides, assuming infinite periodicity. With evenly-spaced wavenumbers sweeping within the irreducible Brillouin zone, the eigenfrequencies below 50 MHz were calculated to best represent the behaviour of the metamaterials around the operating frequency of fUSI for small animals (~ 15 MHz). With incident plane waves travelling in the \u003cem\u003ez\u003c/em\u003e-direction, \u003cem\u003e𝚪-\u003cstrong\u003eA\u003c/strong\u003e\u003c/em\u003e, the volume-averaged displacements in each direction were normalised with the total volume-averaged displacement. We determined the longitudinal polarisation of each normal mode based on the dominant direction of deformation. The longitudinal polarisation factor is defined as\u0026nbsp;\u0026nbsp;where\u0026nbsp;,\u0026nbsp;, and\u0026nbsp;\u0026nbsp;are the displacements in \u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e, and \u003cem\u003ez\u003c/em\u003e directions, respectively. If the longitudinal polarisation factor of one normal mode is close to 1, the mode has dominant pressure wave behaviour, as opposed to when the transverse mode is dominant and the polarisation factor is close to 0. With blue being purely longitudinal and red being purely transverse, the dispersion curves were plotted to indicate the polarisation of the mode at each solution (Fig. 3b). The dispersion curves of the honeycomb unit cell in different wave directions were calculated by sweeping the Brillouin zone in the reciprocal domain. The wavenumber vectors \u003cem\u003ek\u003c/em\u003e = (\u003cem\u003ek\u003csub\u003ex\u003c/sub\u003e, k\u003csub\u003ey\u003c/sub\u003e, k\u003csub\u003ez\u003c/sub\u003e\u003c/em\u003e) parallel to \u003cem\u003e𝚪-\u003cstrong\u003eA,\u0026nbsp;\u003c/strong\u003e𝚪-\u003c/em\u003e𝛼\u003cstrong\u003e\u003cem\u003eL,\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003cem\u003e𝚪-\u003c/em\u003e𝛼\u003cstrong\u003e\u003cem\u003eH\u003c/em\u003e\u003c/strong\u003e with 𝛼 = 0.2, 0.5, or 1, are used for the dispersion curves.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTransmission simulation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe input and output pressure field, padded with perfectly matched layers, sandwich a column of honeycomb plate-lattices composed of a finite number of unit cells (\u003cem\u003en\u003c/em\u003e = 3, 4, 5, 7, and 9). We imposed the Bloch-Floquet periodic boundary conditions on the side faces to assume infinite periodicity in the lateral directions. The viscoelastic dissipation of the constituent polymer was incorporated by feeding an isotropic structural loss factor (\u003cem\u003eη\u003c/em\u003e = 0.075) to the materialistic model\u003ca href=\"https://www.zotero.org/google-docs/?FJxH4X\"\u003e\u003csup\u003e45\u003c/sup\u003e\u003c/a\u003e. We evaluated the amplitude of the travelling pressure waves in the output pressure field, and showed the transmission curves in dB,\u0026nbsp;\u0026nbsp;(Fig. 3d).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMicro fabrication process of metaskulls\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe adopted the microscale 2PP technique for the fabrication of the metaskulls with intricate inner structures (Nanoscribe GmbH \u0026amp; Co. KG). The photoresist, IP-S, in the form of highly viscous liquid becomes acrylic when cured under laser irradiation. After printing the desired MS geometry, we develop the MS using propylene glycol monomethyl ether acetate (PGMEA) and isopropyl alcohol (IPA). The presence of the drainage holes allows the remaining photoresist to be thoroughly removed from the cavities. We measured the mass of the MS samples before and after underwater tests to confirm that the cavities are saturated with air, trapped inside the structure due to surface tension. For microscopic images, only 25 X 24 X 4 arrays of unit cells were printed, which resulted in a sample with outer dimensions of 590 µm X 574 µm X 148 µm (Fig. 2a). Since the single printing size of the Nanoscribe Photonic Professional GT (300 µm X 300 µm X 300 µm) is smaller than the final dimension, smaller blocks were stitched together to form a larger final structure.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompression experiments on metaskull samples\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe quasi-static characterization was performed using a micromechanical testing tool (FemtoTools AG, FT-MTA02) (Fig. 2a). A displacement-controlled probe tip with a square end (FT-S100,000) was compressed against a metaskull sample composed of honeycomb unit cells for force measurement. The size of the sample used for testing (700 µm X 700 µm X 148 µm) is larger than the front end of the tip (50 µm X 50 µm), so that boundary effects could be neglected (Fig. S2). The probe tip recorded the force signal as the measuring arm travelled downward 2 µm from the top surface. Calibration test against a rigid substrate surface was done prior to the measurements to offset the deformation of the measuring arm under given force. The reference stiffness of the measuring system, \u003cem\u003eK\u003csub\u003eref\u003c/sub\u003e\u003c/em\u003e = 28,000 N/m, was then used for the calibration. We took the sample’s effective stiffness from the beginning of the unloading curve, which indicates the global response of the lattice.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcoustic transmission experiments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe used zero-padded, Hann-windowed single-cycle sinusoidal bursts as input waves for the underwater transmission tests. The signals centred at multiple different frequencies were sent through the metaskull samples using an immersion transducer (Olympus, V356-SU). The output signals were recorded by a hydrophone (Precision Acoustics, 0.2 mm needle) and Fourier-transformed for the evaluation in the frequency domain. We plotted the transmission coefficients of the metaskulls with varying thickness (111, 148 ,175, 259, and 333 µm) and a PMP film (125 µm) in Fig. 3b.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAnimal surgeries for in vivo experiments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll animal experiments were conducted under protocols approved by the Institutional Animal Care and Use Committee of the California Institute of Technology. The in vivo experiments presented were performed on C57BL/6J mice (Jackson Laboratory) aged between 6 to 8 weeks. No randomization or blinding were necessary in this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSide-by-side comparison of different skull replacement material\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFour mice were used for the cranial window characterization study. Mice were anaesthetised with 2–3% isoflurane with their heads fixed on a stereotaxic frame. After the incision and stabilisation of the skin, the skull was exposed and rinsed with sterile saline. Ultrasound coupling gel is applied on top of the skull, then we acquired a first transcranial power Doppler image set (“Transcranial” case in Figure 4a) following the parameters described in the fUSI acquisition section. A skull window (1 cm x 0.4 cm) was then removed by drilling (Foredom) at low speed using a micro drill steel burr (Burr number 19007-07, Fine Science Tools). Care was taken not to damage the dura and to prevent inflammatory processes in the brain. We acquired a second transcranial power Doppler image set where only ultrasound coupling gel is applied on top of the brain (“Craniotomy” case in Figure 4a). Then, successive implant sheets for PMP and metalskull cases were positioned on top of the brain for additional power Doppler acquisitions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSurgical implantation of honeycomb lattices for chronic imaging of the brain in mice\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTwo mice were implanted with the metaskull and used for the longitudinal study. Mice were anaesthetised with 2%–3% isoflurane, with their heads fixed on a stereotaxic frame. After the incision and stabilisation of the skin, we removed a rectangular skull window (1 cm x 0.4 cm) by drilling at low speed using a micro drill steel burr. The window corresponds to the coronal planes from Bregma -2 mm to Bregma -2.5 mm. Care was taken not to damage the dura and to prevent inflammatory processes in the brain. We dropped 20 µl of artificial dura on top of the exposed brain to provide an aqueous layer between the brain tissue and the implant. A 1 cm x 0.5 cm metaskull window was sealed in place with the layer of acrylic resin.The surgical procedure took 45 min to 1 h. Animals recovered quickly, and after a conservative 10 days resting period, they were used for the data acquisition via fUSI.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003efUSI acquisition\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003efUSI visualises neural activity by mapping local changes in cerebral blood volume (CBV). CBV variations are tightly linked to neuronal activity through the neurovascular coupling and are evaluated by calculating power Doppler variations in the brain. fUSI was performed using a 15 MHz ultrasonic probe (L22-14vX, 15 MHz, 64 elements, 0.11 mm pitch, Verasonics) connected to a Verasonics Vantage ultrasound system (Verasonics) driven by custom MATLAB (MathWorks) transmission scripts. Each power Doppler image was obtained from the temporal integration of 300 compounded frames acquired at 500 Hz frame rate, using 5 tilted plane waves separated by 3° (−6°, −3°, 0°, 3°, and 6°) acquired at a 2,500 Hz pulse repetition frequency. Power Doppler images were then repeated every second (1 Hz image framerate). Each block of 300 images was processed using a SVD clutter filter to separate tissue signal from blood signal to obtain a final power Doppler image exhibiting CBV in the whole imaging plane.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunctional activation of mice visual system\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eTo evaluate the sensitivity of fUSI through metaskull long-term, we stimulated the visual system of the metaskull-implanted mice over multiple days (day 10, 20, 34, …). We delivered visual stimuli using a blue LED positioned at 3 cm in front of the eyes of the mice. Stimulation runs consisted of periodic flickering of the blue LED using the following parameters: 30 s of rest followed by 30 s of a flicker.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eActivation maps\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eCorrelation maps were computed individually from the normalised correlation between each pixel’s temporal signal with the visual stimulus patterns (Pearson’s product moment) using MATLAB (MathWorks).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSNR calculation\u003cbr\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFor the SNR performance through different materials and thicknesses study (Fig/ 4), we delimited two regions: one region in the cortex (region i.) and one region in the deeper structures (region ii.). Each region was of dimensions: 10 x 5 (lateral x depth) pixels. For each depth, we measured the intensity profile and calculated the local minima and maxima along the lateral axis (Fig. S10). SNR was calculated as:\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cimg 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fXZRi3ScFGpkB2+EPpGL/NUUBBO6DFrKI5kktWH8v7YqSs1mcld1piO3QjnJXiSAGg/JrSoLmJK8NdToSVLPxIV+VEtunF3tzf8EMi/+EEJHSaAgCDRx6cd5O8v2YlBO4755wXQxNaFj5z58fFBXtrKxYvPg5/ljbFYV6Wl47KsRbGEuEChKU1Db03PsYu5JKb+tTE7dwGltzChAoCCItHIfyc8isihnhHKKi6roWdOm7D9vN4v2wt1G1qrQRvD1DipC3Zlzo4zy1ydyoZ+6yALwQHkLwFt/v8qOZgIhCJRsPDnl69jS/SB3JrOWh/+vLVUQKNl15Vv7bhbva9Lz7JcDaSeCgiCyQYcZ/D3ZqBRyKn8Z40yVIFAQ1Gzc81VuSdY9BOWpqaL/eQSS1YzB9bgR/wfW/bYDYfHncDXrFqg2h5WdM5q37QTfoGAM6OOPZg2MnzHgango9p4pKI37IKjd0GN0jyoWavU4/9dvOHxZLosRITSAe9/hCGxi1MUzXEfUlt1IyqsopgBBlKA2s4JDU3d4eLuj0SPr/AYAChD1377o+14Gxm86hK8eb1T1MFF7Ap881hWvhvng07N78EIzEYAe8Qu6IGDhTUzdnoiVA4v/tIItmOI2Amtbv4/jB1+He8l/pI/BO35dsThrKrYfX4mBloD24h94feR4fJUzGX/ErED/knW/rJ8xwnUKtqgfw5fRWzGzhQRAj2PvBsJ34UWM3ZCCn0OK+lsZq4fDbdoe9PzmPLZOd6wsf8ZqDG8+FX80mobQqG8wxF4slXFdh49xet8cNK+q0IYMnI46iTRdzdNJgpkzOvm0hHWNIwgZJxZ1gde7N/HUriSs6PMg7VU0uByxB1FpdvAO7ooWVbirz78cjcNR55El2aG5hz/8WljXOF1QcCUGB8PPIc/UCW18A+HRpJqwjbln8fe+OGQ2bIcu3TrBqfhb0l6OwK7INDj49EFQC+OP/fay3jsybhzfh7CzKrj36IkOFeMS11pmA27E78RfZyW06RYMr8bGDUUezh7YjaNZTgjo3xVuFb2haK8gancErtp4IrhrK1jd0+jzfpWnjqlSleTG87upXrSVBApqB3YIHs7xU6Zw7CAvNjYRinpuggUHf5tW4UEND38UQg8HFYWSHp6qDef8XUWPTb7ObW/2ZSvL4h6ioKaT7yz+eqFCf0UbyWWjPemgEmroRQpUWbdhvxd+YkLu/dClDx+Z+15iJzOBom079uzfn/2rOvr1pn8La0oCKJgN5Y8l3RhdBN/oqKLkOou7jf4KXew79FRLbPn8X+U2E2kPv8p2KoEWnqM457npHNPfiy52LvQdNY+hZ8v/l5q9s9lckug2ey/L9hdruHe2GyV1J6NemIY7n25KSd2Fi5Oq7pNqdj9DV0lNv/8eL+21aiPeYEeViu1ePcIHsxOlrkYaCgr1g8r2KfJ5/DB5MGZtToWZ50ysW/8xxriXqF8ZV36bgq7/+QWXxDbw9ato/22KoFc2YKfZALg9txeFAKC/gD82RmBJj57lbYxFRzzx/v/gaPBGt6UnIXi+hm2HFsG/YkfIxB8v/LYb5o81x8ydt0C1P+aH/YE57SygkvNx4+Ix/LXuYyz45E/s+XwaHksFDq+fBNdHabUm90/MfeoLJGoIapLw9+6k2z4iNmiIhuqi34b0GMSclaEK9kaZSb2M09v/xEnZCkOCvIzmZA1IP3oU52VT+PYZju697OAw+VUs79gGThYVK1XGhfBopNIe4wd0KZu/lS8gPPoK4DwDwSVeQfWncCT6OoTmI9G1SisQGecjYnAVTTG0R8mCroxLf/2N0wY7jO/mUb0X1cIj+GjyIuzLqXmkITo9gfe+nQ1PxU2ngsJdU+nzydzyLt7eegWyWRDmrvkcY9yNb5HgMvxZjGm9Hp9kesLXveqvT5IkQLRDh/bmOJV4BcnbNyFiaU/0rDTSFyFKIgRBBZ8xE+FTzcgZUEEUixZUpaaB6O3hCBtTALCEpY0TWnh2h7vOG70/TsKVzUvwZdRYLAl8hOaqTNrhyRVbMOQOzIcEc1f4F1cBs3OQZwAk8wYoUf+Gy+vw7lcxKJQCEeBvCUCGbJAgiURB/i1QMEeLbiMxcljZn1J4+RQu27ZFq9KpiGyER5yAXuUDLy+j+2JWY22sCM83n0LvktP5CUg4rYcY1LbYosSA7MwcWNraFCuIHERGnYRsHgxfj5IXJQdhh49Bb9YN3bqYAbIMWZKqiGeghkVDa1gLt1EaVuaKW2cFhXukwjeUhz2/b8c1GVB5D8fodlV8YiYd0Gt4XyTcehwBVTbyepw8eQ4GqQMmvOCOL2evwpXkP7AxfCl69qqoNTQ4fzYFeqkFuvWsaL1jRGESTp2XQQho4NWl8s5MmMHv8b5o+lkSkvVnERlxAwh0qUXx6wmmzREwsPldPy45NYOzBRB9OgHHNBPgn7kb7766F7beTpB2m0LIjMB3019GaOefsH2OO5p0ag9HIRKxYZHIHdkTVoY8nN72AZ5/ZT2clxzA96MaF82ja2MQHnsLhAnMSt6FrDAsevFLJHd+Cdv/z7v0BTPkZCCrkDCkJCLqbBIs/lyEl761wtKwrzDICkVutmMLILl7w6fE5l1/BRdTNBAsLKFK2Y+Pn30b8aO24KdxjuULaOKH2d/8itl3XUPG5OBcchoMzEHqpUwY0FgxMVRQMKbcZJX+JN8PVBMATQesZMUVi1qhP8+PephQcpnB/11fz7H2IgEVWz2/v7LflGILBNF2LNfXsBYhX1nBfmYCATWDlpyp0kpDG/YK3VUgYMKeH1+4G8kfYTK5a05HWggq2jRzZ/ugqfwuIYdnP+9X5FRNsqXvrHU8U2pVdYY/jGtNc9GMjq3bs42LI5t3m87PDqSWq3vdsQX0VQtUm1nSJXA0Z0wfy54tG7PtsAXceaXCv6Q7xk+C7SgJIASJ1p0m8dv4Mhsq/Yn3GKAW6fTkVqO1kRzumN2aJgIoqJsw+K0dTP2nHLZlbuAzPu3ZsrElVULRWpmgakDHFu3oNXYlzzwEjuIUFB4GKiiNc/ywe5HSkFymcktN/o6rI2ctR9uINO37Ba/o07lmpC1FgFLL51nRr5mc8jn7mAo06fkJL9RgRpYfOomNRNToHC1t1RBaCiBEJ07ZnF/lPf9u8nghYi/3hZ9lRmkDmMPz4fsZdiq9CkV8i6nxB7hr9988eiGrSkWd9t3jbCCYsPenSUyJ/5u7dv3NuOTMKuMEkCR1aTxxcDf3HD5jJMNt0Kfz5KG/GHnhEbVwUFCoZ5Sff5KaoltQK6jCkqBPXYu5r4+A/xdPoMkdjM8L48IRmyfCzcsbDpIdBg3tjYabQpF1cTs2Hv4QvYPL5pZuRUYgQSfBzS8AztXmUYjj4THINACCtRe6eFdhAikn4/d1B5BPQHIejBG9bx9FrHYU4Pr5FGTdxpSzZgRYOrWCi01duwBoALeAPnArd84KLQJ7o0WV95uhiUdPNKk2PQ2ij8RBI7nCy7cFXDza4rYTgqpGaN+9H9rfidiSHdp163UnTygoKPyTVNQicsoajnaWikxmBQu6j1vBqMza7ibR8+wH3ag2DliS9iOH2wgEJLZ4bp/RFJWW4a93oEq05dga56ZSuDzYlAJAddelPFuph6pl0jdD2UQCBcmZIT9cuK1v/1qj2cGnXKTbbhqr+TBhn8+vPHpBknRxnOetJlTunL7+BG8qntkVFP4VVFrpFl3GY+Wak7g8cjHCMwtwet1z6B17EB+sWYnZfrfzc5SHyIhE6FVt4eNdZGIjNhqMkGBrbAnNwqXtGxH2YTD6mAEw3EBk5DnIqkAEBNQwMrgVgYhjOhAquPp1QbNSN8P5uBK/Hxu/XYol34XhmkkrDF+yDqufdKt+Qf1OkZzgOeAJDLl5L16PVPBsYfYILqaawe/J9/GBlkBKLM4VtIf9I2SwpqCgUA3VaZOcuG85pXNDisU9ZtEmgK/tul5zj1n7F59vKVFq+jSNQ9mmrQ6hjQBCcuPsvcXLnHkbOcFBvG18Ye2RV9leVbSBz9TGiU2aNGFjRztamYgUAAqmjekz6i3+Gp/56PXmFRQUFB4yavY9lXuMPzzZsWiBGaDoMJgrK88PlaI/s5Rd1QIbPP49ywUXS1vNEBuRgES32Xt4i6Qu4g12VIm0Hbue1U9Oyby4LJimAghVCz7+8jzOm/cO33huDP0cVRQEM3rM2cOb/wJtgXuaIlMO5VCOR+2os7botnfIV7l1ZruihhsV3UWUJ3NNCBsKavpWCGVI3uRPITZFVlRuz3KvRua1lQNoJhSZx1bf5ufy9/F2Rc81Le+wLnPHTLZSgZBc+J/fbjMCegSo6xdUOZRDOR6uo664/VS72BhDln6IiU0lADKuHD6AU1V6QNYiNjwO+aIjvAPcK+watMfgkGA0FAE5ZSe2hOcjNiYROskNfoHO1c/3FyYg4mgODBBg7tMFvkaGUzZ9JmN4SxUgpyL0q7W49IhHBmWRglcO5VAO5QDJOmuLaudVwToY/btYYtXlbDA3C1lVNdByMiKiU2Aw7Y9AX3Wly/aDQxDccAtCsy5i17b/welEGmgZggCP6ldPDVcjEXVBBqBCh8Au5YMEmfigV1d7fHr6OjTRB3Aw50W42VST0N1SeBDv9J2BddfuRSOpETTvL/w4qQqvrgoKCgr1DBUAaGN/wnsbC9D/lafRo8rYkBLUJhIEAIJtIzSqyjwpJxKRJ/RQtfWDf1Wxne0HIyS4IbaEZuHc9uXYekOGyiMQgTV4+i2IjECCnoDkAr8uLSpYRZnA168T1KuvQ3srEbHHCzGp+30236EWWdevIjX1XkKemCC94GEfBuUj/JvPcKnXGxjTtq73kygoKDzMqAA9jm/8CEs+IOThM9DDr4oGX38aCSdzYYAEt6DuaFVFu6KNOYKYfAFWHTzRpsrxS/EU1ZZQZCUdRgRUcPeteVNf3JEY5BoAoUFn+FVyOCXCwdcHLaS9SJKTcTQqFYbubve3N2/aD5+fzsHn9zPNuqYwHItHvoTNaUaKzJCN5EQBU/a+ijH3z2BZQUHhEUQEMhEXew56/Rns2326igDrBlzd8hF+iNdBsOqGZ2b1QOU92YWI33MAqbKIJs2aVuvC2n7wCAQ3LG7WRUt4BXpW7+5an4TdfyVDD0Bs5Aq3KkYkJp0C4GMtAtQhdv9+3NN2in8LzMKF2BicvpqF7OzsoiMXsG3VAc0rBoVRUFBQqIAIbQJiErUgtYj8YArmrIlBWmHRxcL0E9j+0SQMmPYLLovNMPyTr/FCh8oNi+b0z1i65hT0MODmmVO4Xl2oYPvHMKJPQ4gABFVnBFa7qU+Ds78swqoEHQCA2ck4nVpY+TaLIAR5mUAAkbv7Uyz88xoUvVELBHsM+yIeSUlJZcexjXjWXVEaCgoKNaMy5KSj0LQhTIQsFGZFY8Ukf6ycYYWG5kR+bh4KDSo4eI7CwsUf4vVBrpVWzvXxC9A9cAFitEWr+dc3TYF7/3Qc2zMHLSu1QfZ4LKQPGm7ehLzmfghwqToYT9LSvvB+8zA0xQYChszteMbdBYfWJuPnUUZDDrExBg30hXpfGAo1x7BiWEfsn/UjjiwfAqsqUn4U0Oydj5HvH8St2hpPCNbot2A95t7v9R6FfxRDQSbSsjUgAAgqWDo0gtXDGgzEUIDMtOzi71WAytIBjR60sIZUrJ8zFV8nNkD/BWvxZvf7EKb3n0jzEaA4RrgBBWlncPzYSZy7mIrrGbm4pRNgbu+K9gG90MurCaqNj6TwYMnajWcDH8dXp/WQWozFJ8sno3UF3UtdFk5tX4b3votAOuwwYcMVrCmO0w3tTjzdegwOd3oMLbQpSMsXYdcmCMNnvYwZ3RsrKxoPBQZc+2M+Zr3zNbbH34BsEoxlZ/bg+WYPp/2d4dofmD/rHXy9PR43ZBMELzuDPc83e7DWgvmhmOQ2Cmuyg/DByQN4taqF14chzUeA4u6ACAvHtgjo2xYBdSuPwu2w6YuFH0qfjFUAABP+SURBVE/GjpBVuHBxJ0LPzseuOe0qjQAHP9EHTbK9MfF3bfkLan9MXzQf7WVXtHIyhebSIaxa8hme2fg/nNkRjo96W0KhrhHR+ImF+K1hDjr0XY6LLf3g7/RwKgwAEBs/gYW/NUROh75YfrEl/PydHrh5uSHPHJ3GPIVnrLrhseb3p3H/J9J8JKBC/UO+xt8nNqUEULQbwC+qiRB0a++zbKG244RN1e3hLyJrwwQ6iiIbT91W7W5/hQdP5k/DaSWItBv/ew2udh4SMn/icCuBot14/v7QC6twLzyss6QKNSE6YcTSJRixdwp+v7oH7875Ho9tebrSGpJZl2EY7nEEtBBKz8m513A5rwGaNbEqnYpq4OoKRwm4qtM9uDIo3AYtjkbEoQAqdA/wR3UmI3LWKRzYsR9xFzNBO3f0eGIIApxrWr/SIjVmF3aFJSIl2wBTW2e09uiOkJ6tK6aMtPjt2LY3Edd0lnD17YchvR2Q9PtWZAdMwsBW5fPQHo1AXAGg6h4A/9uEs9GnxWDbpn04g84Y+eQgtDIDgDyc3huKnTGpkFoNwLgQb9iLRefP7g3FjpirEFv2x7gRJeeLMKQfwqoVu3FZBiCo4T7s/zDB26xcXls37sNZoXJef8ZchdhqAMaHeMHuDtO8X/LfS53XGXWttRTuFj2Tvx9GRxGE6Mjhq5JrEUdE5pXP+9CsUQh/TCnx1qXnuWV9aCk5cvSv1x55H171Bn0iF/oVxSt5uSo30PJ1HvhwNDtYm9Gly2jOfO4pDve0o8rai8+GplT5P+afXMsXezVlA/sOHDDhac4Y3JaWAqj2nlc+6fTDXDbRi3bmjekbMp3Pzf4Pu7lY0NbJgSZSUz69s2L0TD0TF/pRDRXdXz7E6p1W65i8+WV2dbalg40pBcGUPvNjqb15kO8PbkkHJydaqwVCsGLPD09Qe/MgFw92o429I22Kz3dfery8X7vc8zz47WS6qwRC1YZz/i6NWcwLm14yysuEPvOOUpt+kO8/1py2DmVp9vgwsdZp3nf577rO6w5FadRn9Ge5YmCxQ8cmo/hzyu2afJk31z3Jlg3VbNCiF8c9PZszRnVhM4c2fGLBHl5TNMbDQ/oPHGIpULAZzbUVwy7Ladz5sjetxAb0nbODpeHY0zdyorNEyXkyQzPLP3Ir7jMObKyiabtpXH+uuAHKD+VkRxWdp28vuzH3CBd0taFk6cOXdlwt7Yjk/D6eDiIoWA7hqpusQDp/GGJJQbDh6ErCGol9bS0n+D7Bj8IzqPnrBbZSibQd8S7f7e/H8StjmUU9k5f3obkg0LTvK3xngB9HLw/nTVnmxc/70kIQaNr/q8rv6c1v+JiZQMF6JItjv1WZl93IBZzfz5djPo9g+n1K877If1d1XncoSqOeozvxCYOti9zOu4xfx9TaNPzadJ6PP8L9u3Zw98F4puQq2uJhQ7N7Fl0lUN3tg0rRKtO3TKWrJNAi8L+MNe6Aytf51QATQnLhUzuMLuQf5lwvM4rmvpwXmV92Xn+JO5cv5PdhGSU38tBrnWgqmDNgYVy5EYNm59NsKoFq/4VMrDik1ezmLFeJUHfjBzWETiBJWS56125tmUJHUaCpVWuO/uF8ae87/7extBZAQdWIg5YnlsqQt240rQWBliE/M6tCmtqwV+iuAtVBS3jKKPvSvLY+SSdRoJmVG4d8ebI0zfz1Y2kjCGwwbPWdp3nf5L/LOq9DFKVR79Ey/v2utBRAQWrGyRsffTfxjz56nnwvkGpIbPn8fpabmNCf4kc9zCmI9hz9a4Xup3yNX/Y3IQQLhvxSohxkpnw9mNaCyMYTNjCD1SOnfs8hNiJFhzFcm17+Wtq3g2kuSHSdtZuVJqdOvsdANSi1fJ77azWLomPcPG+qIdLmsZW8UNog6pn0fiDVEGjV+xMm6cvuj5/vQzXU9KkUdkHmlS/60lSQ2Hz23kqyGedl3e9znjNKM+HdojQ7vhl512neq/x3W+d1ycNrx6dQS0zg8dIyvOJrAchXcfjvU1W4glGoX+QiOvok9IIFPP09y7ntkS9tx9ZIDWDZHY8PtC//mOESLqcSEBrCtsRdj+EqNv++HzmCAwaMGgTbavM04MYfG7Avm2jYaygG2hlf0yAmMgGFsIBPkG8lN0K50dE4qRdg4ekPz9rsfzOkIyIyCXrREUNn/gdupQYctxAXdwqy2AhDn5uGUt+Zhoyi+yVH+AS0qWBerkFkRAJ0MIdngFdlF0elednj8ZmTyoxFDOkIj0iCXrSCh0/7u0zzXuW/+zqvSxSl8SigsoS9jRlULsMw76Wu1fvzqhY94lfNwgBPN7g2a4mhX5zDvfj1vWc0EVjxZB90au4K1zYT8HPav8w5TGE8ohIKQFV7+Po1LHdJdyweSTpC1doLPuUvwXA9ClHn9RDU7dC5c/FbUBiLmONaUNURfv7mNWSqQ2xUAjRUwd3bB+WSLjiMP/ZehazqgICACpmiEPFRCSigCu19/VDxatXli0J4nBaw8EdwDyPfDYUJiIrLA8380LunUSCEgkM4EK0BLHzRLaDCNuPC44g4mgmDqh38/KxRiZK8TL3Ro7tRXgWHcCBKA6g9EFjR3Ku2ad6z/Hdb53WLojTqPQWIXjwNb/9th8lffokJd7UJSQXPacvwcqAeqVd1aNKm6QPZGV4Q/jVemfMR/rxeQSmYBeLZL2fDIycF1yxaokNVrvYfYeQr0Th6SQ/JyQt+FeyoDbk5yCUgOrrAuVz32ICUzaEI1wBmgUPwRNPiOtNnID2LEEzt0ajKsAcl6JCWlgEDRNg7GXsGMODSr5/i12QZkosfAltUeDPkK4g+egl6yQlefi1r9d7oE8MRnW6Aqq0fjHWinHIEEckyVK194Gs0JNJG/4UjGQaoOndD9woxcwwZMYg5J0Ny9IJfRdcIxnm18Ye/Q1n5C48eRESWAVKrQHRpUr5eap3mPct/l3Vex/y7vsZHkOy/5mHa4ji4vfAdPh56D4Ge5IuIP54Gg7kPgvwfxGA4E9uXz8PyX+JRYFlZajk5CWfzRTgGdEXHOtlNJCM95he8M2EMFh+uwlnmP4ju5EmckwWoO/rCxxSAJgMZeUXXJIdGsBMB6nXQGeva/DAsW3EA+ZIbJr42tcy1jKoBLM0FoDAHWbnGDxhwff+nWLrpYvGoUoRaJQEgCvJySx1/FiZ9g5dWxEMlCFC19yyaftJkICO/VFicPCdDUHeEb5GwyCgRtkoMuBERiTN6EY28/NDa6L/NPXIYx3QCrD180FZVdv+12HikyBKa+gSgmQQYMtORWTwU1iWdwFkdIbXzgpcagDYD6aXlLMvL1jsA7Y3SvJlwDJdkEbZ+QehsUpRmxh2mee/y32Wd1zGK0qjHGK5vwSszluOi91ysWtgLVQyka3g4HdFr/ovnJo/E8JFTMGfx59h5QoaqQwACq0pIexmHVi/CC1NGY9jQkZixYCOSCkouZiNh7XxMHzUKM5cfRoYBMNyIxI/vzMDo4aMw8+N9MA5+qLl2DDuXPYO3Nt4AG2TgyLLFWLx4CT7alFi6HpMdFYWTsgV8u/khJ2IV5k4dgWGjn8Gygzf+YU/GeqRFrsYbIR5o3WUSFq2PwKWCBxta05Cbi3wCKpUE3bWDWDoiCMO/OA49ANOuwzG4qQR97E5sTylu5bTnsO65GVhxyhJBc3/E0seNurkmXdAryAooDMP3H+/GFa2MgtRo/DZ/OLqFLEP4tSwUOZoxQWePtlAJOsRtXY/E3Dwk7/0A4yZuReAr49BYBCQaoEndj/eGBWHUypNFysaQi9wiYSHpruHg0hEIGv4Fjle7sKZBRHgcCmGKzv6+RlOpWkSHRSMPKnT09THydWdAVlYuCAEmagk5iWvwdHBXzNmSDgBgdg5yKUAUAP2Nw/hkTBAe+zCmuEwleZnAI8DfKE0iKysHpAhbO1vcSlqHZ/p0xUub7yTN+yH/XdZ5XVPXK/EKd4k+matHOlPlMIgrkqraLkRSTuPWt8fy+dVJ5Tf+ZR3m4n7ObNhmBBeHRvB47Fa+HmRFARKbz95TyVJDe+pnTvewp3PvV/nTgViGfzeOzVUm9H03ntRf4dYX/dnKewB7t2lA0awPlx3+hVM6taDPoCcY1MyUgtiIo39NK05Nx7hvn+OE4NY0FUQ28h3OCRMncuLEyZzzQ8nGJw13z3KlpPbjMwvG0at9Dw593IeNJIHqTnMZVU1xyTxePXuKSUlJNR6nzl9nfjUpZG6ZTg/f//C9DWHc9GxbqiQ3zt77YG1X5Is/MMRRoiAIFExc2G/ezrK9GJSZtm8eg11MaeLYmX0eH8SurWxo1TyYz/8YW8l0lCQ1x77iiBbmFICiNAU17T3HcvGelAqWPBs4rY0ZBQgUBJFW7iP5WUQW5YxQTnFRFT1r2pT95+0uM+2WL/KHEEdKgkBBMKFLv3nceaUG+1BtBF/voCLUnTnX+I8s3czYmi8eKL898Nbfr7KjmUAIAiUbT075OpYlu0Hk1F84xrlYNnVj9nx1C5N1FfPqxDcjy780t8Lm0suiJE0PTv766B2meb/kv4s6r2MUpVEv0fLEsn60U7twzC+XqjexzdnICY4m9F1wrKxxkNO4eZob1Ta9+eGxsp2u0W95UC00ZMhP5XeFyTe3c5a7KRv4z2NEXvHJm99wkKnEZjN3kZoTXLf8N57S6Hj0bQ+qpSZs492Hb+wpMv3N3z6dLpJEl6d2GKWqZ9L7XagWHTkpNI+V0Cdykb+6qBEatJRHMklqw/h/bVWUms3krura8FuhnGQvEkCNh+Q2m9XqAb2GGn2RjIkL/aiuA6VBkrcuhXPbxq0MO1+NI6e8S4zatZHrf9vM3RHnmXW7BiU/hdE7N3D9hm38Kz61eh9jOWd4YPPv3LzvGK8ZtX2aS+HcumErD5+v4v+6dYnh2zZya9j5f8hHlp5px3YxNHQfE29WVkialEhu27iFB8/m3IG5ucyME3sZunkvj9+3NKujZvnvqs7rEEVp1EPyIxewi5UJ3Z/+g2nVvtEaJn4cTGvRhMHLyhSLLu5d+ppIbD5zJ8texXxuntyIojqIS4x3MlHH6Lc9aSI158ydxc2BJpnbXvSlpUkbzt5lvPs3kz+FWFEQ7Th45fnSkY0uYT591CLtJ24yujedPw6zotjgcX53vYoCpP/IYZYCpRbTufVm8fX8zZzcSKRJr0+ZXF2Z5XSeCj/EgwcP1ngcijp3+0a2jpWGgsLDiuKwsL6RtR9vT1uMiPwGaJu0DBMGLaviJkKXdQ6xR5ORTVNYWdsUL17pcXTd74iXXTBjVG+UhrPSn0ZMfBaEZn7o4mZkqVEYhfUbEqEz7Yj0nW9ixqpTiAmLwY3GffDy+iWY29/I3FB7FOFHCyC6zsQrU1qUWoLIN24gwyChiWszo3ujcDimAFLn7uhehfc27dEIxN5SwXvqSxhcfL3weDhiMkW0DOiCJtWtxIl2cA/sBvfa1KOCgsJdoSiNekUu/pz7FL5I1IDUIOnv3Ui63SNiAzRsqC76bUhHTMxZyKpgeBvtwpJPb8efJ2VYDQmCl9EmD0P6URw9L8PUtw+Gd+8FO4fJeHV5R7RxsqhkQSFfCEd0KmE/fgC6lK4CyrgQHo0rcMaM4E6l9+pPHUH0dQHNR3ZFZWtCGecjYnAVTTG0R+ti5SPj0l9/47TBDuO7eVS/D6XwCD6avAj7cmpeuBadnsB7386Gp/L2KyjcMcpnU68wQbsnV2DLkDuwHxLM4epf3MwyGzl5BkAyR4OS/UyGy1j37leIKZQQGOAPSwCybIAkiWBBPm5RgHmLbhg5cliZRUjhZZy6bIu2rcoCNmWHR+CEXgUfLy+j+2Kwem0sRM838VTvMnuS/IQEnNaLCGrbtugFNGQjM8cStjYSgBxERp2EbB4MX48SxZaDsMPHoDfrhm5dzABZhixJVewJUMOioTWshdsoDStz5cVXULhLlG+nXmGK5gED0fxuH5ec0MzZAog+jYRjGkzwz8Tud1/FXltvOEm7YSpkIuK76Xg5tDN+2joH7k06ob2jgMjYMETmjkRPKwPyTm/DB8+/gvXOS3Dg+1FoLAKAFjHhsbhFwMSsRDlkIWzRi/gyuTNe2v5/8DayW8/JyEIhDUhJjMLZJAv8ueglfGu1FGFfDYKV9igiYgsguXuX7XjWX8HFFA0EC0uoUvbj42ffRvyoLfhpnGP58pn4YfY3v2L23dZPOXJwLjkNBuYg9VImDGis2KcrKACKye2/jcxdc9jRQqDKphnd2wdx6ncJzDn7OftZC4Qg0dZ3FtedKbOqOvPDOLY2F2nm2Jrt27jQsXk3Tv/sAFPLrZcf4wJfNQW1GS1dAjl6xnSO7dmSjdsO44KdVyrF+dAd+4TBdlKRCahkzU6TvmV88aq8/sR7DFCLdHpyq5GFTw53zG5NEwEU1E0Y/NaO8vnf1wrawGd82rNlY0uqhCJrK0HVgI4t2tFr7EpWEyRRQeFfg0Dywe5cUqhz8pMjEXGBaO7lh1a2RZM8uRciEHPVFh6B7rCrMO+juZqAyONpEBxaw8PDDdYV54VufI8nWjyF3f6fIGFNH6SduA44uqNzx+awqWYsq79xEuHxqZDcfBDQ2vb27ifkDCSFH0Ouiy/83ZQ45goKdYWiNBTuGc2OGWg9ZDXMn9+HxE973IXDRAUFhfqCMk2rcI/ocSr8KNJkQMy9inPpD9ZPk4KCwoNFWQhXuGfM/J7E+x9oQaQg9lwB2tsrYw0FhUcVZXpKQUFBQaHWKNNTCgoKCgq1RlEaCgoKCgq1RlEaCgoKCgq1RlEaCgoKCgq1RlEaCgoKCgq15v8BxSWTVh+67tcAAAAASUVORK5CYII=\"\u003e\u003cbr\u003e\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n 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Science 335:1458\u0026ndash;1462\u003c/span\u003e\u003c/li\u003e\n \u003cli\u003e\u003cspan\u003eYaqoob Z, Psaltis D, Feld MS, Yang C Optical phase conjugation for turbidity suppression in biological samples.Nature\u003c/span\u003e\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-2743580/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2743580/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eFunctional ultrasound imaging enables sensitive, high-resolution imaging of neural activity in freely behaving animals and human patients. However, the skull acts as an aberrating and absorbing layer for sound waves, leading to most functional ultrasound experiments being conducted after skull removal. In pre-clinical settings, craniotomies are often covered with a polymethylpentene film, which offers limited longitudinal imaging, due to the film’s poor conformability, and limited mechanical protection, due to the film’s low stiffness. Here, we introduce a skull replacement consisting of a microstructured, conformal acoustic window based on mechanical metamaterials, designed to offer high stiffness-to-density ratio and sonotransparency. We test the acoustic window in vivo, via terminal and survival experiments on small animals. Long-term biocompatibility and lasting signal sensitivity are demonstrated over a long period of time (\u0026gt; 4 months) by conducting ultrasound imaging in mouse models implanted with the metamaterial skull prosthesis.\u003c/p\u003e","manuscriptTitle":"Microscale acoustic metamaterials as conformal sonotransparent skull prostheses","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-05-10 19:31:12","doi":"10.21203/rs.3.rs-2743580/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"6c07f442-59d8-4b28-a458-f9c5494ef1c7","owner":[],"postedDate":"May 10th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":20293184,"name":"Physical sciences/Physics/Applied physics/Acoustics"},{"id":20293185,"name":"Biological sciences/Biological techniques/Imaging/Ultrasound"},{"id":20293186,"name":"Physical sciences/Engineering/Mechanical engineering"}],"tags":[],"updatedAt":"2023-07-24T14:18:56+00:00","versionOfRecord":[],"versionCreatedAt":"2023-05-10 19:31:12","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2743580","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2743580","identity":"rs-2743580","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}