Raul Radovitzky

Computational biology - modeling of primary blast effects on the central nervous system.

OBJECTIVES Recent military conflicts in Iraq and Afghanistan have highlighted the wartime effect of traumatic brain injury (TBI). The reason for the prominence of TBI in these particular conflicts as opposed to others is unclear but may result from the increased survivability of blast due to improvements in body armor. In the military context blunt, ballistic and blast effects may all contribute to CNS injury, however blast in particular, has been suggested as a primary cause of military TBI. While blast effects on some biological tissues, such as the lung, are documented in terms of injury thresholds, this is not the case for the CNS. We hypothesized that using bio-fidelic models, allowing for fluid-solid interaction and basic material properties available in the literature, a blast wave would interact with CNS tissue and cause a possible concussive effect. METHODS The modeling approach employed for this investigation consisted of a computational framework suitable for simulating coupled fluid-solid dynamic interactions. The model included a complex finite element mesh of the head and intra-cranial contents. The effects of threshold and 50% lethal blast lung injury were compared with concussive impact injury using the full head model allowing upper and lower bounds of tissue injury to be applied using pulmonary injury as the reference tissue. RESULTS The effects of a 50% lethal dose blast lung injury (LD(50)) were comparable with concussive impact injury using the DVBIC-MIT full head model. INTERPRETATION CNS blast concussive effects were found to be similar between impact mild TBI and the blast field associated with LD(50) lung blast injury sustained without personal protective equipment. With the ubiquitous use of personal protective equipment this suggests that blast concussive effects may more readily ascertained in personnel due to enhanced survivability in the current conflicts.

In silico investigation of intracranial blast mitigation with relevance to military traumatic brain injury

Blast-induced traumatic brain injury is the most prevalent military injury in Iraq and Afghanistan, yet little is known about the mechanical effects of blasts on the human head, and still less is known about how personal protective equipment affects the brain’s response to blasts. In this study we investigated the effect of the Advanced Combat Helmet (ACH) and a conceptual face shield on the propagation of stress waves within the brain tissue following blast events. We used a sophisticated computational framework for simulating coupled fluid–solid dynamic interactions and a three-dimensional biofidelic finite element model of the human head and intracranial contents combined with a detailed model of the ACH and a conceptual face shield. Simulations were conducted in which the unhelmeted head, head with helmet, and head with helmet and face shield were exposed to a frontal blast wave with incident overpressure of 10 atm. Direct transmission of stress waves into the intracranial cavity was observed in the unprotected head and head with helmet simulations. Compared to the unhelmeted head, the head with helmet experienced slight mitigation of intracranial stresses. This suggests that the existing ACH does not significantly contribute to mitigating blast effects, but does not worsen them either. By contrast, the helmet and face shield combination impeded direct transmission of stress waves to the face, resulting in a delay in the transmission of stresses to the intracranial cavity and lower intracranial stresses. This suggests a possible strategy for mitigating blast waves often associated with military concussion.

Nonlinear compressibility effects in fluid-structure interaction and their implications on the air-blast loading of structures

The impulse imparted by a blast wave to a freestanding solid plate is studied analytically and numerically focusing on the case in which nonlinear compressibility effects in the fluid are important, as is the case for explosions in air. The analysis furnishes, in effect, an extension of Taylor’s pioneering contribution to the understanding of the influence of fluid-structure interaction (FSI) on the blast loading of structures [The Scientific Papers of Sir Geoffrey Ingram Taylor, edited by G. K. Batchelor (Cambridge University Press, Cambridge, 1963), Vol. III, pp. 287–303] to the nonlinear range. The limiting cases of extremely heavy and extremely light plates are explored analytically for arbitrary blast intensity, from where it is concluded that a modified nondimensional parameter representing the mass of compressed fluid relative to the mass of the plate governs the FSI. The intermediate asymptotic FSI regime is studied using a numerical method based on a Lagrangian formulation of the Euler equations of compressible flow and conventional shock-capturing techniques. Based on the analytical and numerical results, an approximate formula describing the entire range of relevant FSI conditions is proposed. The main conclusion of this work is that nonlinear fluid compressibility further enhances the beneficial effects of FSI in reducing the impulse transmitted to the structure. More specifically, it is found that transmitted impulse reductions due to FSI when compared to those obtained ignoring FSI effects are more significant than in the acoustic limit. This result can be advantageously exploited in the design and optimization of structures with increased blast resistance.

A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading

A virtual test facility (VTF) for studying the three-dimensional dynamic response of solid materials subject to strong shock and detonation waves has been constructed as part of the research program of the Center for Simulating the Dynamic Response of Materials at the California Institute of Technology. The compressible fluid flow is simulated with a Cartesian finite volume method and treating the solid as an embedded moving body, while a Lagrangian finite element scheme is employed to describe the structural response to the hydrodynamic pressure loading. A temporal splitting method is applied to update the position and velocity of the boundary between time steps. The boundary is represented implicitly in the fluid solver with a level set function that is constructed on-the-fly from the unstructured solid surface mesh. Block-structured mesh adaptation with time step refinement in the fluid allows for the efficient consideration of disparate fluid and solid time scales. We detail the design of the employed object-oriented mesh refinement framework AMROC and outline its effective extension for fluid–structure interaction problems. Further, we describe the parallelization of the most important algorithmic components for distributed memory machines and discuss the applied partitioning strategies. As computational examples for typical VTF applications, we present the dynamic deformation of a tantalum cylinder due to the detonation of an interior solid explosive and the impact of an explosion-induced shock wave on a multi-material soft tissue body.

Fluid-structure interaction effects in the dynamic response of free-standing plates to uniform shock loading

The problem of uniform shocks interacting with free-standing plates is studied analytically and numerically for arbitrary shock intensity and plate mass. The analysis is of interest in the design and interpretation of fluid-structure interaction (FSI) experiments in shock tubes. In contrast to previous work corresponding to the case of incident blast profiles of exponential distribution, all asymptotic limits obtained here are exact. The contributions include the extension of Taylors FSI analysis for acoustic waves, the exact analysis of the asymptotic limits of very heavy and very light plates for arbitrary shock intensity, and a general formula for the transmitted impulse in the intermediate plate mass range. One of the implications is that the impulse transmitted to the plate can be expressed univocally in terms of a single nondimensional compressible FSI parameter.

Porcine Head Response to Blast

Recent studies have shown an increase in the frequency of traumatic brain injuries related to blast exposure. However, the mechanisms that cause blast neurotrauma are unknown. Blast neurotrauma research using computational models has been one method to elucidate that response of the brain in blast, and to identify possible mechanical correlates of injury. However, model validation against experimental data is required to ensure that the model output is representative of in vivo biomechanical response. This study exposes porcine subjects to primary blast overpressures generated using a compressed-gas shock tube. Shock tube blasts were directed to the unprotected head of each animal while the lungs and thorax were protected using ballistic protective vests similar to those employed in theater. The test conditions ranged from 110 to 740 kPa peak incident overpressure with scaled durations from 1.3 to 6.9 ms and correspond approximately with a 50% injury risk for brain bleeding and apnea in a ferret model scaled to porcine exposure. Instrumentation was placed on the porcine head to measure bulk acceleration, pressure at the surface of the head, and pressure inside the cranial cavity. Immediately after the blast, 5 of the 20 animals tested were apneic. Three subjects recovered without intervention within 30 s and the remaining two recovered within 8 min following respiratory assistance and administration of the respiratory stimulant doxapram. Gross examination of the brain revealed no indication of bleeding. Intracranial pressures ranged from 80 to 390 kPa as a result of the blast and were notably lower than the shock tube reflected pressures of 300–2830 kPa, indicating pressure attenuation by the skull up to a factor of 8.4. Peak head accelerations were measured from 385 to 3845 G’s and were well correlated with peak incident overpressure (R2 = 0.90). One SD corridors for the surface pressure, intracranial pressure (ICP), and head acceleration are presented to provide experimental data for computer model validation.

A Virtual Test Facility for the Simulation of Dynamic Response in Materials

The Center for Simulating Dynamic Response of Materials at the California Institute of Technology is constructing a virtual shock physics facility for studying the response of various target materials to very strong shocks. The Virtual Test Facility (VTF) is an end-to-end, fully three-dimensional simulation of the detonation of high explosives (HE), shock wave propagation, solid material response to pressure loading, and compressible turbulence. The VTF largely consists of a parallel fluid solver and a parallel solid mechanics package that are coupled together by the exchange of boundary data. The Eulerian fluid code and Lagrangian solid mechanics model interact via a novel approach based on level sets. The two main computational packages are integrated through the use of Pyre, a problem solving environment written in the Python scripting language. Pyre allows application developers to interchange various computational models and solver packages without recompiling code, and it provides standardized access to several data visualization engines and data input mechanisms. In this paper, we outline the main components of the VTF, discuss their integration via Pyre, and describe some recent accomplishments in large-scale simulation using the VTF.

Direct visualization of laser-driven focusing shock waves.

Direct real-time visualization and measurement of laser-driven shock generation, propagation, and 2D focusing in a sample are demonstrated. A substantial increase of the pressure at the convergence of the cylindrical acoustic shock front is observed experimentally and simulated numerically. Single-shot acquisitions using a streak camera reveal that at the convergence of the shock wave in water the supersonic speed reaches Mach 6, corresponding to the multiple gigapascal pressure range ∼30 GPa.

An animal-to-human scaling law for blast-induced traumatic brain injury risk assessment

Significance A physics-based animal-to-human scaling law for the effects of a blast wave on brain tissue is proposed. This scaling law, or transfer function, enables the translation of animal-based assessments of injury to the human, thus effectively enabling the derivation of human injury criteria based on animal tests. This is critical both in the diagnosis of traumatic brain injury as well as in the design of blast-protective helmets. Despite recent efforts to understand blast effects on the human brain, there are still no widely accepted injury criteria for humans. Recent animal studies have resulted in important advances in the understanding of brain injury due to intense dynamic loads. However, the applicability of animal brain injury results to humans remains uncertain. Here, we use advanced computational models to derive a scaling law relating blast wave intensity to the mechanical response of brain tissue across species. Detailed simulations of blast effects on the brain are conducted for different mammals using image-based biofidelic models. The intensity of the stress waves computed for different external blast conditions is compared across species. It is found that mass scaling, which successfully estimates blast tolerance of the thorax, fails to capture the brain mechanical response to blast across mammals. Instead, we show that an appropriate scaling variable must account for the mass of protective tissues relative to the brain, as well as their acoustic impedance. Peak stresses transmitted to the brain tissue by the blast are then shown to be a power function of the scaling parameter for a range of blast conditions relevant to TBI. In particular, it is found that human brain vulnerability to blast is higher than for any other mammalian species, which is in distinct contrast to previously proposed scaling laws based on body or brain mass. An application of the scaling law to recent experiments on rabbits furnishes the first physics-based injury estimate for blast-induced TBI in humans.

Advances in Cohesive Zone Modeling of Dynamic Fracture

In this chapter, we review the state of the-art in computational methods for modeling dynamic fracture of brittle solids based on the popular cohesive element approach. The discussion includes a detailed review of the underlying theory, its implementation via interface elements in its two different flavors: the intrinsic and extrinsic approach, as well as the application of the method to different concrete problems in dynamic fracture. Limitations and numerical issues are discussed in detail. As a means to address some of these issues, we describe an alternative approach based on a discontinuous Galerkin (DG) reformulation of the continuum problem that exploits the virtues of the existing cohesive element methods. The scalability and accuracy of the DG method for fracture mechanics is demonstrated through wave propagation and spall tests in ceramics. Lastly, some unresolved open problems and numerical issues pertaining to cohesive zone modeling of fracture are briefly discussed.