Adaptive motion estimation of shear shock waves in soft solids and tissue with ultrasound

Shear shock wave injury in vivo: High frame-rate ultrasound observation and histological assessment

Using high frame-rate ultrasound and ¡1μm sensitive motion tracking we previously showed that shear waves at the surface of ex vivo and in situ brains develop into shear shock waves deep inside the brain, with destructive local accelerations. However post-mortem tissue cannot develop injuries and has different viscoelastodynamic behavior from in vivo tissue. Here we present the ultrasonic measurement of the high-rate shear shock biomechanics in the in vivo porcine brain, and histological assessment of the resulting axonal pathology. A new biomechanical model of brain injury was developed consisting of a perforated mylar surface attached to the brain and vibrated using an electromechanical shaker. Using a custom sequence with 8 interleaved wide beam emissions, brain imaging and motion tracking were performed at 2900 images/s. Shear shock waves were observed for the first time in vivo wherein the shock acceleration was measured to be 2.6 times larger than the surface acceleration ( 95g vs. 36g). Histopathology showed axonal damage in the impacted side of the brain from the brain surface, accompanied by a local shock-front acceleration of >70g. This shows that axonal injury occurs deep in the brain even though the shear excitation was at the brain surface, and the acceleration measurements support the hypothesis that shear shock waves are responsible for deep traumatic brain injuries.

Modeling Ultrasound Propagation in the Moving Brain: Applications to Shear Shock Waves and Traumatic Brain Injury

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 ( λ /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.

Simultaneous electrophysiological and morphological assessment of functional damage to neural networks in vitro after 30-300 g impacts

An enigma of mild traumatic brain injury are observations of substantial behavior and performance deficits in the absence of bleeding or other observable structural damage. Altered behavior and performance reflect changes in action potential (AP) patterns within neuronal networks, which could result from subtle subcellular responses that affect synaptic efficacy and AP production. The aim of this study was to investigate and quantify network activity changes after simulated concussions in vitro and therewith develop a platform for simultaneous and direct observations of morphological and electrophysiological changes in neural networks. We used spontaneously active networks grown on microelectrode arrays (MEAs) to allow long-term multisite monitoring with simultaneous optical observations before and after impacts delivered by a ballistic pendulum (30 to 300 g accelerations). The monitoring of AP waveshape templates for long periods before and after impact provided an internal control for cell death or loss of cell-electrode coupling in the observed set of neurons. Network activity patterns were linked in real-time to high power phase contrast microscopy. There was no overt loss of glial or neuronal adhesion, even at high-g impacts. All recording experiments showed repeatable spike production responses: a loss of activity with recovery to near reference in 1 hr, followed by a slow activity decay to a stable, level plateau approximately 30–40% below reference. The initial recovery occurred in two steps: a rapid return of activity to an average 24% below reference, forming a level plateau lasting from 5 to 20 min, followed by a climb to within 10% of reference where a second plateau was established for 1 to 2 hrs. Cross correlation profiles revealed changes in firing hierarchy as well as in Phase 1 in spontaneous network oscillations that were reduced by as much as 20% 6–8 min post impact with only a partial recovery at 30 min. We also observed that normally stable nuclei developed irregular rotational motion after impact in 27 out of 30 networks. The evolution of network activity deficits and recovery can be linked with microscopically observable changes in the very cells that are generating the activity. The repeatable electrophysiological impact response profiles and oscillation changes can provide a quantitative basis for systematic evaluations of pharmacological intervention strategies. Future expansion to include fluorescent microscopy should allow detailed investigations of damage mechanisms on the subcellular level.

Piecewise parabolic method for propagation of shear shock waves in relaxing soft solids: One-dimensional case

Shear 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.

Subresolution Displacements in Finite Difference Simulations of Ultrasound Propagation and Imaging

Time domain finite difference simulations are used extensively to simulate wave propagation. They approximate the wave field on a discrete domain with a grid spacing that is typically on the order of a tenth of a wavelength. The smallest displacements that can be modeled by this type of simulation are thus limited to discrete values that are integer multiples of the grid spacing. This paper presents a method to represent continuous and subresolution displacements by varying the impedance of individual elements in a multielement scatterer. It is demonstrated that this method removes the limitations imposed by the discrete grid spacing by generating a continuum of displacements as measured by the backscattered signal. The method is first validated on an ideal perfect correlation case with a single scatterer. It is subsequently applied to a more complex case with a field of scatterers that model an acoustic radiation force-induced displacement used in ultrasound elasticity imaging. A custom finite difference simulation tool is used to simulate propagation from ultrasound imaging pulses in the scatterer field. These simulated transmit-receive events are then beamformed into images, which are tracked with a correlation-based algorithm to determine the displacement. A linear predictive model is developed to analytically describe the relationship between element impedance and backscattered phase shift. The error between model and simulation is λ/ 1364 , where λ is the acoustical wavelength. An iterative method is also presented that reduces the simulation error to λ/ 5556 over one iteration. The proposed technique therefore offers a computationally efficient method to model continuous subresolution displacements of a scattering medium in ultrasound imaging. This method has applications that include ultrasound elastography, blood flow, and motion tracking. This method also extends generally to finite difference simulations of wave propagation, such as electromagnetic or seismic waves.

Numerical Simulation of Focused Shock Shear Waves in Soft Solids and a Two-Dimensional Nonlinear Homogeneous Model of the Brain

Shear waves that propagate in soft solids, such as the brain, are strongly nonlinear and can develop into shock waves in less than one wavelength. We hypothesize that these shear shock waves could be responsible for certain types of traumatic brain injuries (TBI) and that the spherical geometry of the skull bone could focus shear waves deep in the brain, generating diffuse axonal injuries. Theoretical models and numerical methods that describe nonlinear polarized shear waves in soft solids such as the brain are presented. They include the cubic nonlinearities that are characteristic of soft solids and the specific types of nonclassical attenuation and dispersion observed in soft tissues and the brain. The numerical methods are validated with analytical solutions, where possible, and with self-similar scaling laws where no known solutions exist. Initial conditions based on a human head X-ray microtomography (CT) were used to simulate focused shear shock waves in the brain. Three regimes are investigated with shock wave formation distances of 2.54 m, 0.018 m, and 0.0064 m. We demonstrate that under realistic loading scenarios, with nonlinear properties consistent with measurements in the brain, and when the shock wave propagation distance and focal distance coincide, nonlinear propagation can easily overcome attenuation to generate shear shocks deep inside the brain. Due to these effects, the accelerations in the focal are larger by a factor of 15 compared to acceleration at the skull surface. These results suggest that shock wave focusing could be responsible for diffuse axonal injuries.