Monitoring disease development in arteries, which supply oxygen and nutrients to the body, is crucial and can be assessed using hemodynamic metrics. Hemodynamic metrics can be calculated via computational fluid dynamic simulation of patient-specific geometries. These simulations are known to be heavily influenced by boundary conditions, such as time-dependent inlet flow. However, the effects of…
Virtual planning tools that provide intuitive user interaction and immediate hemodynamic feedback are crucial for cardiologists to effectively treat coronary artery disease. Current FDA-approved tools for coronary intervention planning require days of preliminary processing and rely on conventional 2D displays for hemodynamic evaluation. Immersion offered by extended reality (XR) has been found to benefit intervention…
In mammalian cells, the cohesin protein complex is believed to translocate along chromatin during interphase to form dynamic loops through a process called active loop extrusion. Chromosome conformation capture and imaging experiments have suggested that chromatin adopts a compact structure with limited interpenetration between chromosomes and between chromosomal sections. We developed a theory demonstrating that…
The active loop extrusion hypothesis proposes that chromatin threads through the cohesin protein complex into progressively larger loops until reaching specific boundary elements. We build upon this hypothesis and develop an analytical theory for active loop extrusion which predicts that loop formation probability is a nonmonotonic function of loop length and describes chromatin contact probabilities….
Parallel agent-based models of the adaptive immune response can efficiently recapitulate emerging spatiotemporal properties of T-cell motility during clonal selection across multiple length and time scales. Here, we present a distributed, three-dimensional (3D) computational model of T-cell priming, and associated parallel data structures and algorithms that enable fully deterministic cell simulations at scale. We demonstrate…
In this Note, we address the construction of a class of stochastic Ogden’s stored energy functions associated with incompressible hyperelastic materials. The methodology relies on the maximum entropy principle, which is formulated under constraints arising in part from existence theorems in nonlinear elasticity. More specifically, constraints related to both polyconvexity and consistency with linearized elasticity…
This paper is devoted to the modeling of compressible hyperelastic materials whose response functions exhibit uncertainties at some scale of interest. The construction of parametric probabilistic representations for the Ogden class of stored energy functions is specifically considered and formulated within the framework of Information Theory. The overall methodology relies on the principle of maximum…
In this work, we address the constitutive modeling, in a probabilistic framework, of the hyperelastic response of soft biological tissues. The aim is on the one hand to mimic the mean behavior and variability that are typically encountered in the experimental characterization of such materials, and on the other hand to derive mathematical models that…
This paper deals with the construction of random field models for spatially-dependent anisotropic strain energy functions indexed by complex geometries. The approach relies on information theory and the principle of maximum entropy, which are invoked in order to construct the family of first-order marginal probability distributions in accordance with fundamental constraints such as polyconvexity, coerciveness…