Three-dimensional phase field model for actin-based cell membrane dynamics

The interface dynamics of a 3D cell immersed in a 3D extracellular matrix is investigated. We suggest a 3D generalization of a known 2D minimal phase field model suggested in [1] for the description of keratocyte motility. Our model consists of two coupled evolution equations for the order parameter and a three-dimensional vector field describing the actin network polarization (orientation). We derive a closed evolutionary integro-differential equation governing the interface dynamics of a 3D cell. The equation includes the normal velocity of the membrane, its curvature, cell volume relaxation, and a parameter that is determined by the non-equilibrium effects in the cytoskeleton. This equation can be considered as a 3D generalization of the 2D case that was studied in [2].

Localizing Clinical Patterns of Blast Traumatic Brain Injury Through Computational Modeling and Simulation

Blast traumatic brain injury is ubiquitous in modern military conflict with significant morbidity and mortality. Yet the mechanism by which blast overpressure waves cause specific intracranial injury in humans remains unclear. Reviewing of both the clinical experience of neurointensivists and neurosurgeons who treated service members exposed to blast have revealed a pattern of injury to cerebral blood vessels, manifested as subarachnoid hemorrhage, pseudoaneurysm, and early diffuse cerebral edema. Additionally, a seminal neuropathologic case series of victims of blast traumatic brain injury (TBI) showed unique astroglial scarring patterns at the following tissue interfaces: subpial glial plate, perivascular, periventricular, and cerebral gray-white interface. The uniting feature of both the clinical and neuropathologic findings in blast TBI is the co-location of injury to material interfaces, be it solid-fluid or solid-solid interface. This motivates the hypothesis that blast TBI is an injury at the intracranial mechanical interfaces. In order to investigate the intracranial interface dynamics, we performed a novel set of computational simulations using a model human head simplified but containing models of gyri, sulci, cerebrospinal fluid (CSF), ventricles, and vasculature with high spatial resolution of the mechanical interfaces. Simulations were performed within a hybrid Eulerian—Lagrangian simulation suite (CTH coupled via Zapotec to Sierra Mechanics). Because of the large computational meshes, simulations required high performance computing resources. Twenty simulations were performed across multiple exposure scenarios—overpressures of 150, 250, and 500 kPa with 1 ms overpressure durations—for multiple blast exposures (front blast, side blast, and wall blast) across large variations in material model parameters (brain shear properties, skull elastic moduli). All simulations predict fluid cavitation within CSF (where intracerebral vasculature reside) with cavitation occurring deep and diffusely into cerebral sulci. These cavitation events are adjacent to high interface strain rates at the subpial glial plate. Larger overpressure simulations (250 and 500kPa) demonstrated intraventricular cavitation—also associated with adjacent high periventricular strain rates. Additionally, models of embedded intraparenchymal vascular structures—with diameters as small as 0.6 mm—predicted intravascular cavitation with adjacent high perivascular strain rates. The co-location of local maxima of strain rates near several of the regions that appear to be preferentially damaged in blast TBI (vascular structures, subpial glial plate, perivascular regions, and periventricular regions) suggest that intracranial interface dynamics may be important in understanding how blast overpressures leads to intracranial injury.