@article{chandrasekaran_santibanez_tripathi_deruiter_bruegge_pinton_2022, title={In situ ultrasound imaging of shear shock waves in the porcine brain}, volume={134}, ISSN={["1873-2380"]}, DOI={10.1016/j.jbiomech.2021.110913}, abstractNote={Direct measurement of brain motion at high spatio-temporal resolutions during impacts has been a persistent challenge in brain biomechanics. Using high frame-rate ultrasound and high sensitivity motion tracking, we recently showed shear waves sent to the ex vivo porcine brain developing into shear shock waves with destructive local accelerations inside the brain, which may be a key mechanism behind deep traumatic brain injuries. Here we present the ultrasound observation of shear shock waves in the acoustically challenging environment of the in situ porcine brain during a single-shot impact with sinusoidal and haversine time profiles. The brain was impacted to generate surface amplitudes of 25-33g, and to propagate a 40-50 Hz shear waves into the brain. Simultaneously, images of the moving brain were acquired at 2193 images/s, using a custom sequence with 8 interleaved ultrasound propagation events. For a long field-of-view, wide-beam emissions were designed using time-reversal ultrasound simulations and no compounding was used to avoid motion blurring. For a 40 Hz, 25g sinusoidal impact, a shock-front acceleration of 102g was measured 7.1 mm deep inside the brain. Using a haversine pulse that models a realistic impact more closely, a shock acceleration of 113g was observed 3.0 mm inside the brain, from a 50 Hz, 33g excitation. The experimental velocity, acceleration, and strain-rate waveforms in brain for the monochromatic impact are shown to be in excellent agreement with theoretical predictions from a custom higher-order finite volume method hence demonstrating the capabilities to measure rapid brain motion despite strong acoustical reverberations from the porcine skull.}, journal={JOURNAL OF BIOMECHANICS}, author={Chandrasekaran, Sandhya and Santibanez, Francisco and Tripathi, Bharat B. and DeRuiter, Ryan and Bruegge, Ruth Vorder and Pinton, Gianmarco}, year={2022}, month={Mar} }
 @article{chandrasekaran_tripathi_espindola_pinton_2021, title={Modeling Ultrasound Propagation in the Moving Brain: Applications to Shear Shock Waves and Traumatic Brain Injury}, volume={68}, ISSN={["1525-8955"]}, DOI={10.1109/TUFFC.2020.3022567}, abstractNote={Traumatic brain injury (TBI) studies on the living human brain are experimentally infeasible due to ethical reasons and the elastic properties of the brain degrade rapidly postmortem. We present a simulation approach that models ultrasound propagation in the human brain, while it is moving due to the complex shear shock wave deformation from a traumatic impact. Finite difference simulations can model ultrasound propagation in complex media such as human tissue. Recently, we have shown that the fullwave finite difference approach can also be used to represent displacements that are much smaller than the grid size, such as the motion encountered in shear wave propagation from ultrasound elastography. However, this subresolution displacement model, called impedance flow, was only implemented and validated for acoustical media composed of randomly distributed scatterers. Herein, we propose a generalization of the impedance flow method that describes the continuous subresolution motion of structured acoustical maps, and in particular of acoustical maps of the human brain. It is shown that the average error in simulating subresolution displacements using impedance flow is small when compared to the acoustical wavelength ( $\lambda $ /1702). The method is then applied to acoustical maps of the human brain with a motion that is imposed by the propagation of a shear shock wave. This motion is determined numerically with a custom piecewise parabolic method that is calibrated to ex vivo observations of shear shocks in the porcine brain. Then the fullwave simulation tool is used to model transmit-receive imaging sequences based on an L7-4 imaging transducer. The simulated radio frequency data are beamformed using a conventional delay-and-sum method and a normalized cross-correlation method designed for shock wave tracking is used to determine the tissue motion. This overall process is an in silico reproduction of the experiments that were previously performed to observe shear shock waves in fresh porcine brain. It is shown that the proposed generalized impedance flow method accurately captures the shear wave motion in terms of the wave profile, shock front characteristics, odd harmonic spectrum generation, and acceleration at the shear shock front. We expect that this approach will lead to improvements in image sequence design that takes into account the aberration and multiple reflections from the brain and in the design of tracking algorithms that can more accurately capture the complex brain motion that occurs during a traumatic impact. These methods of modeling ultrasound propagation in moving media can also be applied to other displacements, such as those generated by shear wave elastography or blood flow.}, number={1}, journal={IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL}, author={Chandrasekaran, Sandhya and Tripathi, Bharat B. and Espindola, David and Pinton, Gianmarco F.}, year={2021}, month={Jan}, pages={201–212} }
 @article{tripathi_espindola_pinton_2019, title={Modeling and simulations of two dimensional propagation of shear shock waves in relaxing soft solids}, volume={395}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2019.06.014}, abstractNote={Soft solids, such as gelatin or soft tissue, have a shear wave speed that is smaller than the compressional wave speed. Recent observations of shear shock wave generation in the brain, which can easily reach a large Mach number regime, suggest that the cubic nonlinear behavior of soft solids could be responsible for traumatic brain injury. However, currently there are no two-dimensional (2D) models describing the propagation of linearly-polarized shear shock waves in relaxing soft solids. These models are required to model the fundamental wave propagation physics like diffraction, focusing etc., and are related to traumatic brain injuries as it can be used to model the skull/brain morphology. In this work, we present a two-dimensional system of first-order equations modeling the propagation of shear shock waves in a relaxing soft solid, and then this system is solved numerically using the piecewise parabolic method, a high-order finite volume method. The numerical solutions are validated in two parts. First, the nonlinear component, which is designed for large Mach numbers, is validated with a step-shock Riemann problem. Then relaxation mechanisms based on a generalized Maxwell body, which model the non-classical attenuation that occurs in soft tissue, are compared to analytical solutions with an error of 5%-10%. The validation of attenuation also includes dispersion due to causality which is determined by the Kramers-Kronig relations. Finally, the full numerical method, which includes nonlinearity, attenuation, and dispersion, is compared to ultrasonic measurements of shear shock wave propagation in tissue-mimicking phantoms. Two experiments were performed based on high frame-rate ultrasound imaging and tracking in a gelatin phantom 1) planar shear shock waves, and 2) focused shear shock wave propagation. The experimental and numerical waveforms closely match, e.g. the RMS amplitude error is between 12.05% and 12.27%. Moreover, the frequency-content of the temporal signal was compared for third and fifth multiples of fundamental harmonic validating the generation of odd-harmonics due to cubic nonlinearity. Furthermore, the numerical tool was able to estimate the nonlinear parameter in the phantom (β=4.4) using a grid-parameter-search. In context of traumatic brain injury, the current method can be used to study the shear shock formation in 2D-sections of human skull, and can also be used for nonlinear parameter estimation in brain.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Tripathi, Bharat B. and Espindola, David and Pinton, Gianmarco F.}, year={2019}, month={Oct}, pages={205–222} }
 @article{tripathi_espindola_pinton_2019, title={Piecewise parabolic method for propagation of shear shock waves in relaxing soft solids: One-dimensional case}, volume={35}, ISSN={["2040-7947"]}, DOI={10.1002/cnm.3187}, abstractNote={AbstractShear shock waves can be generated spontaneously deep within the brain during a traumatic injury. This recently observed behavior could be a primary mechanism for the generation of traumatic brain injuries. However, shear shock wave physics and its numerical modeling are relatively unstudied. Existing numerical solvers used in biomechanics are not designed for the extremely large Mach numbers (greater than 1) observed in the brain. Furthermore, soft solids, such as the brain, have a complex nonclassical viscoleastic response, which must be accurately modeled to capture the nonlinear wave behavior. Here, we develop a 1D inviscid velocity‐stress–like system to model the propagation of shear shock waves in a homogeneous medium. Then a generalized Maxwell body is used to model a relaxing medium that can describe experimentally determined attenuation laws. Finally, the resulting system is solved numerically with the piecewise parabolic method, a high‐order finite volume method. The nonlinear and the relaxing components of this method are validated with theoretical predictions. Comparisons between numerical solutions obtained for the proposed model and the experiments of plane shear shock wave propagation based on high frame‐rate ultrasound imaging and tracking are shown to be in excellent agreement.}, number={5}, journal={INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING}, author={Tripathi, Bharat B. and Espindola, David and Pinton, Gianmarco F.}, year={2019}, month={May} }