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We briefly compare the structure of two classes of popular models used to describe poro- and chemo- mechanics wherein a fluid phase is transported within a solid phase. The multiplicative deformation decomposition has been successfully used to model permanent inelastic shape change in plasticity, solid-solid phase transformation, and thermal expansion, which has motivated its application to poro- and chemo- mechanics. However, the energetic decomposition provides a more transparent structure and advantages, such as to couple to phase-field fracture, for models of poro- and chemo- mechanics.

We investigate solution methods for large-scale inverse problems governed by partial differential equations (PDEs) via Bayesian inference. The Bayesian framework provides a statistical setting to infer uncertain parameters from noisy measurements. To quantify posterior uncertainty, we adopt Markov Chain Monte Carlo (MCMC) approaches for generating samples. To increase the efficiency of these approaches in high-dimension, we make use of local information about gradient and Hessian of the target potential, also via Hamiltonian Monte Carlo (HMC). Our target application is inferring the field of soil permeability processing observations of pore pressure, using a nonlinear PDE poromechanics model for predicting pressure from permeability. We compare the performance of different sampling approaches in this and other settings. We also investigate the effect of dimensionality and non-gaussianity of distributions on the performance of different sampling methods.

The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance, that include fracturing or damage of the solid phase, require a nonlinear description of the large deformations that can occur. This paper presents a variational energy-based continuum mechanics framework to model large-deformation poroelasticity. The approach begins from the total free energy density that is additively composed of the free energy of the components. A variational procedure then provides the balance of momentum, fluid transport balance, and pressure relations. A numerical approach based on finite elements is applied to analyze the behavior of saturated and unsaturated porous media using a nonlinear constitutive model for the solid skeleton. Examples studied include the Terzaghi and Mandel problems; a gas-liquid phase-changing fluid; multiple immiscible gases; and unsaturated systems where we model injection of fluid into soil. The proposed variational approach can potentially have advantages for numerical methods as well as for combining with data-driven models in a Bayesian framework., Comment: To appear in International Journal for Numerical and Analytical Methods in Geomechanics

von Willebrand Factor is a mechano-sensitive protein circulating in blood that mediates platelet adhesion to subendothelial collagen and platelet aggregation at high shear rates. Its hemostatic function and thrombogenic effect, as well as susceptibility to enzymatic cleavage, are regulated by a conformational change from a collapsed globular state to a stretched state. Therefore, it is essential to account for the conformation of the vWF multimers when modeling vWF-mediated thrombosis or vWF degradation. We introduce a continuum model of vWF unfolding that is developed within the framework of our multi-constituent model of platelet-mediated thrombosis. The model considers two interconvertible vWF species corresponding to the collapsed and stretched conformational states. vWF unfolding takes place via two regimes: tumbling in simple shear and strong unfolding in flows with dominant extensional component. These two regimes were demonstrated in a Couette flow between parallel plates and an extensional flow in a cross-slot geometry. The vWF unfolding model was then verified in several microfluidic systems designed for inducing high-shear vWF-mediated thrombosis and screening for von Willebrand Disease. The model predicted high concentration of stretched vWF in key regions where occlusive thrombosis was observed experimentally. Strong unfolding caused by the extensional flow was limited to the center axis or middle plane of the channels, whereas vWF unfolding near the channel walls relied upon the shear tumbling mechanism. The continuum model of vWF unfolding presented in this work can be employed in numerical simulations of vWF-mediated thrombosis or vWF degradation in complex geometries. However, extending the model to 3-D arbitrary flows and turbulent flows will pose considerable challenges.

Thromboembolic complications remain a central issue in management of patients on mechanical circulatory support. Despite the best practices employed in design and manufacturing of modern ventricular assist devices, complexity and modular nature of these systems often introduces internal steps and crevices in the flow path which can serve as nidus for thrombus formation. Thrombotic potential is influenced by multiple factors including the characteristics of the flow and surface chemistry of the biomaterial. This study explored these elements in the setting of blood flow over a micro-crevice using a multi-constituent numerical model of thrombosis. The simulations reproduced the platelet deposition patterns observed experimentally and elucidated the role of flow, shear rate, and surface chemistry in shaping the deposition. The results offer insights for design and operation of blood-contacting devices.

Motivated by the complex rheological behaviors observed in small/micro scale blood vessels, such as the Fahraeus effect, plasma-skimming, shear-thinning, etc., we develop a non-linear suspension model for blood. The viscosity is assumed to depend on the volume fraction (hematocrit) and the shear rate. The migration of the red blood cells (RBCs) is studied using a concentration flux equation. A parametric study with two representative problems, namely simple shear flow and a pressure driven flow demonstrate the ability of this reduced-order model to reproduce several key features of the two-fluid model (mixture theory approach), with much lower computational cost.

Thrombosis is a common complication following the surgical implantation of blood contacting devices, and is strongly influenced by the phenomenon of near-wall enrichment of platelets. This paper describes a multi-constituent continuum approach to study this phenomenon. A mixture-theory model is used to describe the motion of the plasma and the red blood cells (RBCs) and the interactions between the two components. A transport model is developed to study the influence of the RBC field on the platelets. The model is used to study blood flow in a rectangular micro-channel, a sudden expansion micro-channel, and a channel containing micro crevices (representing a practical problem encountered in most blood-wetted devices). The simulations show that in the rectangular channel the concentration of platelets near the walls is about five times higher than the concentration near the centerline of the channel. It is also noticed that in the channel with crevices, extremely a large number of platelets accumulate in the deep part of the crevices and this may serve as the nidus for thrombosis occurring in medical devices. Keywords: Platelets; Blood flow; RBCs; Micro-channel; Mixture theory; Two-fluids; Thrombosis

In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined planes. We assume that the granular materials can be represented by a modified form of the second-grade fluid where the viscosity depends on the shear rate and volume fraction and the normal stress coefficients depend on the volume fraction. We also propose a new isotropic (spherical) part of the stress tensor which can be related to the compactness of the (rigid) particles. This new term ensures that the rigid solid particles cannot be compacted beyond a point, namely when the volume fraction has reached the critical/maximum packing value. The numerical results indicate that the newly proposed stress tensor has an obvious and physically meaningful effects on both the velocity and the volume fraction fields., Comment: This manuscript has been submitted to the International Journal of Non-Linear Mechanics

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5mm x 1.6mm x 0.1mm) with small crevices (125{\mu}m x 75{\mu}m and 125{\mu}m x 137{\mu}m). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices., Comment: Submission planned to Biophysical Journal