Prashant K. Purohit

Abstract Background Blood clot contraction/retraction depends on the force-generating actomyosin and on the platelet integrin αIIbβ3, which transmits intracellular forces to fibrin. Before clotting, fibrinogen binds to activated integrin αIIbβ3, mediating platelet aggregation. The relationship between platelet aggregation and subsequent platelet-driven clot contraction remains unclear. Methods We investigated the effects of platelet aggregation on clot contraction by selectively blocking the αIIbβ3-fibrinogen binding using the RGDW peptide. The ability of RGDW to disrupt αIIbβ3-fibrinogen binding was assessed by platelet aggregometry. The time-course of clot contraction was monitored optically in whole blood or platelet-rich plasma and modeled mathematically. Clot stiffness was assessed using Thromboelastography. The effect of the RGDW peptide on the structure of PRP-clots was examined using scanning electron microscopy. Results The RGDW peptide dose-dependently inhibited TRAP-induced platelet aggregation. Both in whole blood and in plasma, the peptide dose-dependently prolonged the lag-period and slowed the rate without affecting the final extent of contraction. Thromboelastography showed that RGDW dose-dependently increased maximum clot stiffness in blood. Scanning electron microscopy revealed that RGDW treatment resulted in formation of smaller fibrin agglomerates surrounding non-aggregated platelets. A theoretical model allowed us to decipher mechanisms underlying the kinetic effects of RGDW. Conclusion Blocking the binding of integrin αIIbβ3 to fibrinogen and preventing platelet aggregation delays and slows subsequent clot contraction without affecting the final degree of shrinkage. These findings indicate a modulatory role of fibrinogen-mediated platelet aggregation in clot contraction and highlight the unforeseen effects of selective inhibitors of platelet aggregation on the contraction of blood clots and thrombi.

Abstract The failure of mechanical metamaterials is a function of the interplay between the properties of the base material and the microstructural geometry. Stochastic failure properties of the base material and disordered microstructural geometries can contribute to variations in the global failure mechanics that are not captured in traditional analyses of ordered, deterministic architected materials. We present a probabilistic framework that couples stochastic material failure and geometric disorder to predict failure in lattice mechanical metamaterials. These predictions are verified through finite element analysis, which confirms that disorder and stochasticity affect both the mean and variance of the damage initiation load in a lattice, with average failure loads being generally reduced and variance increasing with higher levels of disorder and stochasticity. The fracto-cohesive length and representative volume element size are also predicted and constrain the minimum defect and lattice sizes, respectively, for failure to be considered a fracture process. The framework is extended to consider the fracture behaviour of the lattice, the development of damage zones and their impact on the fracture toughness.

Fibrous soft tissues derive their nonlinear mechanical response from networks of extracellular matrix fibers, whose organization gives rise to strain stiffening, the reverse Poynting effect, and anisotropic mechanical behavior. Motivated by these coupled features, we develop an anisotropic hyperelastic model for fibrous biological tissues that accounts for the contribution of the fiber network under both tensile and compressive deformation. We calibrate the model to experimental data for mitral valve leaflets using an inverse finite element approach that is coupled to automatic differentiation to facilitate efficient parameter calibration. Using the calibrated model, we investigate how anisotropy and fiber reorientation affect valve deformation under physiological loading. The results show that greater leaflet compliance in the radial direction yields proper valve closure, whereas localized fiber reorientation leads to stress concentrations that may promote progressive functional degradation. Fiber reorientation that makes the circumferential direction more compliant than the radial direction compromises valve closure and leads to mitral regurgitation. Chordal softening further amplifies the severity of this regurgitant response. These findings suggest that alterations in fiber architecture, especially when accompanied by chordal degradation, can contribute to the onset and progression of mitral valve incompetence.

Fibrous soft tissues derive their nonlinear mechanical response from networks of extracellular matrix fibers, whose organization gives rise to strain stiffening, the reverse Poynting effect, and anisotropic mechanical behavior. Motivated by these coupled features, we develop an anisotropic hyperelastic model for fibrous biological tissues that accounts for the contribution of the fiber network under both tensile and compressive deformation. We calibrate the model to experimental data for mitral valve leaflets using an inverse finite element approach that is coupled to automatic differentiation to facilitate efficient parameter calibration. Using the calibrated model, we investigate how anisotropy and fiber reorientation affect valve deformation under physiological loading. The results show that greater leaflet compliance in the radial direction yields proper valve closure, whereas localized fiber reorientation leads to stress concentrations that may promote progressive functional degradation. Fiber reorientation that makes the circumferential direction more compliant than the radial direction compromises valve closure and leads to mitral regurgitation. Chordal softening further amplifies the severity of this regurgitant response. These findings suggest that alterations in fiber architecture, especially when accompanied by chordal degradation, can contribute to the onset and progression of mitral valve incompetence.

Fibrous soft tissues derive their nonlinear mechanical response from networks of extracellular matrix fibers, whose organization gives rise to strain stiffening, the reverse Poynting effect, and anisotropic mechanical behavior. Motivated by these coupled features, we develop an anisotropic hyperelastic model for fibrous biological tissues that accounts for the contribution of the fiber network under both tensile and compressive deformation. We calibrate the model to experimental data for mitral valve leaflets using an inverse finite element approach that is coupled to automatic differentiation to facilitate efficient parameter calibration. Using the calibrated model, we investigate how anisotropy and fiber reorientation affect valve deformation under physiological loading. The results show that greater leaflet compliance in the radial direction yields proper valve closure, whereas localized fiber reorientation leads to stress concentrations that may promote progressive functional degradation. Fiber reorientation that makes the circumferential direction more compliant than the radial direction compromises valve closure and leads to mitral regurgitation. Chordal softening further amplifies the severity of this regurgitant response. These findings suggest that alterations in fiber architecture, especially when accompanied by chordal degradation, can contribute to the onset and progression of mitral valve incompetence.

Abstract Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical mechanics and linear elasticity have yielded deep insights into membrane morphology and the role of thermal fluctuations on cellular function. However, real biological membranes operate far from equilibrium, continuously driven by active processes powered by energy-consuming proteins. In this work, we employ a non-equilibrium statistical mechanics framework to model active membranes and derive analytical expressions for four fundamental properties that characterize their mechanical behavior: (a) the tension–area relation, (b) the mean square amplitude of fluctuations, (c) correlation of normal vectors, and (d) the persistence length. These results collectively highlight the utility of fluctuation spectra as a starting point for elucidating membrane mechanics in both passive and active settings. Moreover, these results provide a theoretical basis for analyzing and interpreting fluctuation-based assays of active membrane behavior.

Abstract Physical modeling of biological matter has conventionally treated them as engineering or physical materials that subscribe to laws of equilibrium physics and are considered “passive” or ”nonliving”. However, biological systems are “active” or “alive” with their own energy source, capable of circumventing equilibrium considerations. In fact, active biological matter including self-propelled particles, filaments, and membranes, is the hallmark of living matter and drives life?s most dynamic processes. Unlike passive soft materials that exhibit only equilibrium thermal fluctuations at the microscopic scales, active systems consume energy to generate unique mechanical behavior. Examples of such behavior include persistent dynamics, stress generation, and large deformations that violate fluctuation?dissipation relations from equilibrium statistical mechanics, placing active matter far from equilibrium. This tutorial introduces a unified approach that combines continuum theory with non-equilibrium statistical mechanics to study soft active biological matter. The discussion is organized by dimensionality: we begin with zero-dimensional active Brownian particles, proceed to one-dimensional active filaments modeled as elastic rods, and conclude with two-dimensional active membranes described using linear curvature elasticity. For each class of active matter, we review equilibrium and non-equilibrium models, illustrate key concepts through simple examples, and provide a concise survey of the literature. Our aim is to emphasize physical interpretation and practical modeling tools, equipping readers with a coherent framework for understanding the existing body of work and pursuing research in non-equilibrium statistical mechanics of living systems.

Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical mechanics and linear elasticity have yielded deep insights into membrane morphology and the role of thermal fluctuations on cellular function. However, real biological membranes operate far from equilibrium, continuously driven by active processes powered by energy consuming proteins. In this work, we employ a nonequilibrium statistical mechanics framework to model active membranes and derive analytical expressions for four fundamental properties that characterize their mechanical behavior: (a) the tension area relation, (b) the mean square amplitude of fluctuations, (c) correlation of normal vectors, and (d) the persistence length. These results collectively highlight the utility of fluctuation spectra as a starting point for elucidating membrane mechanics in both passive and active settings. Moreover, these results provide a theoretical basis for analyzing and interpreting fluctuation based assays of active membrane behavior.

Biological membranes and vesicles play a central role in living systems, forming dynamic interfaces that regulate cellular organization and function. Classical descriptions of membrane mechanics that are rooted in equilibrium statistical mechanics and linear elasticity have yielded deep insights into membrane morphology and the role of thermal fluctuations on cellular function. However, real biological membranes operate far from equilibrium, continuously driven by active processes powered by energy consuming proteins. In this work, we employ a nonequilibrium statistical mechanics framework to model active membranes and derive analytical expressions for four fundamental properties that characterize their mechanical behavior: (a) the tension area relation, (b) the mean square amplitude of fluctuations, (c) correlation of normal vectors, and (d) the persistence length. These results collectively highlight the utility of fluctuation spectra as a starting point for elucidating membrane mechanics in both passive and active settings. Moreover, these results provide a theoretical basis for analyzing and interpreting fluctuation based assays of active membrane behavior.

Abstract Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free energy. To do so, we significantly extend the recent Stochastic Thermodynamics with Internal Variables (STIV) framework, a method for producing macroscopic thermodynamic models far-from-equilibrium from the underlying mesoscopic dynamics and an approximate probability density of states parameterized with so-called internal variables. Though originally explored for Gaussian probability distributions, we here allow for an arbitrary choice of the approximate probability density while retaining a gradient flow dynamics. This greatly extends its range of applicability and automatically ensures consistency with the second law of thermodynamics, without the need for secondary verification. We demonstrate numerical convergence, in the limit of increasing internal variables, to the true probability density of states for both a multi-modal relaxation problem, a protein diffusing on a strand of DNA, and for an externally driven particle in a periodic landscape. Finally, we provide a reformulation of STIV with the quasi-equilibrium approximations in terms of the averages of observables of the mesostate, and show that these, too, obey a gradient flow.

The mechanical properties of the extracellular matrix (ECM) regulate tumor growth and invasion in the tumor microenvironment. Models of biopolymer networks have been used to investigate the impact of elasticity and viscoelasticity of ECM on tumor behavior. Under tumor compression, these networks also show poroelastic behavior that is governed by the resistance to water flow through their pores. This work investigates the hypothesis that poroelastic properties regulate tumor growth. Here, alginate hydrogels with tunable ionic and hybrid ionic/covalent crosslinking are used as a model biopolymer system. Hydrogel stiffness, viscoelasticity, and stress relaxation behavior were characterized using stepwise axial compression. Among these properties, we find poroelastic fluid outflow dominates ECM stress relaxation, as the measured water flux was significantly affected under compression. Continuum mechanics-based modeling was developed to formulate and calculate the chemical potential gradients of water (solvent) in the hydrogels under compression. This framework was extended into an advection-diffusion framework to quantify growth factor (solute) distribution under varying strengths of stress and diffusion indexed by the relative strength of convective to diffusive transport, characterized by the Péclet number. An agent-based computational simulation showed that tumor growth was affected by Péclet number. Together, these results highlight the role of the poroelastic properties of ECM on water flux and transport in the tumor microenvironment.

Natural biopolymer hydrogels often suffer from relatively low moduli and an inability to maintain structure and mechanics under cyclic loading, limiting their utility in dynamic mechanical environments. Here, a cross-linked collagen cryogel scaffold was fabricated by precompression to densify the network. Following lyophilization, the porous scaffolds sustained >90% axial compressive strain with 200 cycles. Ogden hyperelastic modeling and second harmonic generation (SHG) imaging revealed fiber alignment, densification, and strain-stiffening contributing to resilience under repetitive large-scale loading. After rehydration, cross-linked and densified hydrogels showed network stability and recoverability under cyclic loading, with significantly reduced phase transition strains compared to non-cross-linked controls. The scaffolds supported cell encapsulation and maintained cell viability after 50 cycles of 90% strain. Cyclic loading significantly densified the encapsulated cells in the loading direction, comparable to nonloaded controls. Overall, these results suggest that densified, shape memory collagen scaffolds provide a mechanically robust and biocompatible system for dynamic environments.

Over the past several decades, phase field modeling has been established as a standard simulation technique for mesoscopic science, allowing for seamless boundary tracking of moving interfaces and relatively easy coupling to other physical phenomena. However, despite its widespread success, phase field modeling remains largely driven by phenomenological justifications except in a handful of instances. In this work, we leverage a recently developed statistical mechanics framework for non-equilibrium phenomena, called Stochastic Thermodynamics with Internal Variables (STIV), to provide the first derivation of a non-conservative phase field model for tracking front propagation in a one dimensional elastic medium without appeal to phenomenology or fitting to experiments or simulation data. In the resulting model, the variables obey a gradient flow with respect to a non-equilibrium free energy, although notably, the dynamics of the strain and phase variables are coupled, and while the free energy functional is non-local in the phase field variable , such non-locality deviates from the traditional form. Moreover, in the systems analyzed here, the model accurately captures stress induced nucleation of transition fronts without the need to incorporate additional physics. We find that the STIV phase field model compares favorably to Langevin simulations of the microscopic system and we provide two numerical implementations enabling one to simulate arbitrary interatomic potentials.

Given a particle system obeying overdamped Langevin dynamics, we demonstrate that it is always possible to construct a thermodynamically consistent macroscopic model which obeys a gradient flow with respect to its non-equilibrium free energy. To do so, we significantly extend the recent Stochastic Thermodynamics with Internal Variables (STIV) framework, a method for producing macroscopic thermodynamic models far-from-equilibrium from the underlying mesoscopic dynamics and an approximate probability density of states parameterized with so-called internal variables. Though originally explored for Gaussian probability distributions, we here allow for an arbitrary choice of the approximate probability density while retaining a gradient flow dynamics. This greatly extends its range of applicability and automatically ensures consistency with the second law of thermodynamics, without the need for secondary verification. We demonstrate numerical convergence, in the limit of increasing internal variables, to the true probability density of states for both a multi-modal relaxation problem, a protein diffusing on a strand of DNA, and for an externally driven particle in a periodic landscape. Finally, we provide a reformulation of STIV with the quasi-equilibrium approximations in terms of the averages of observables of the mesostate, and show that these, too, obey a gradient flow.

A multiscale approach to mechanical testing in silico, which combines discrete particle-based simulations and large-deformation continuum mechanics, is developed to explore the mechanobiology, damage and fracture of fibrous materials. Combined with tensile testing in vitro of fibrin networks, the mechanical scaffold of blood clots, mechanisms of fibrin rupture are investigated that underlie embolization of intravascular blood clots (thrombi), a major cause of ischemic stroke and pulmonary embolism. At moderate strains (<50%), no network damage is observed. At larger strains, damage evolves and the network ruptures when only ∼5% of fibers and branch points break, opening a ∼150 µm rupture zone in silico. A continuum model that predicts macroscopic behavior for arbitrary states of deformation, including damage evolution, is constructed from the mesoscopic simulations with direct correlation of the damage parameter and the number of broken bonds in contrast to phenomenological damage laws. The continuum model can access length- and time-scales that are inaccessible in discrete simulations, which allows prediction of fracture toughness, the material property that determines rupture resistance in the presence of defects. This critical property for a fibrin network at physiological solid volume fraction and accounting for the dramatic decrease in volume (∼90%) under uniform tensile stressing is predicted to be 2.5-7.7 J/m2, in good agreement with experiment. These insights into mechanisms of blood clot fracture can lead to the development of new approaches to predict and prevent embolization of intravascular thrombi. The multiscale approach developed is applicable to a wide range of fibrous network-based biomaterials. STATEMENT OF SIGNIFICANCE: Dummy.

ABSTRACT: Platelet-driven blood clot contraction (retraction) is important for hemostasis and thrombosis. Red blood cells (RBCs) occupy approximately half of the clot volume, but their possible active contribution to contraction is unknown. The work was aimed at elucidating the ability of RBCs to promote clot shrinkage. To distinguish the effects of platelets and RBCs, we formed thrombin-induced clots from reconstituted human samples containing platelet-free plasma and platelet-depleted RBCs, followed by tracking the clot size. The clots before and after RBC-induced shrinkage were analyzed using histology and scanning electron microscopy. Tension developed in the RBC-containing plasma clots was measured with rheometry, and theoretical modeling was used to elucidate the clot shrinkage mechanisms. Platelet-depleted clots formed in the presence of RBCs exhibited >20% volume shrinkage within one hour. This process was insensitive to blebbistatin, latrunculin A, and abciximab. At a higher RBC count, clot shrinkage increased, whereas in the absence of RBCs no plasma clot shrinkage was observed. At low platelet counts, RBCs stimulated clot contraction proportionately to the platelet level. Inside the shrunken clots, RBCs formed aggregates. The average tensile force per 1 RBC was ∼120 ± 100 pN. Clots from purified fibrinogen formed in the presence of RBCs did not change in size, but underwent shrinkage in the presence of osmotically active dextran. Blood clot shrinkage can be caused by RBCs alone, and this effect is because of the RBC aggregation driven mainly by osmotic depletion. The RBC-induced clot shrinkage may reinforce platelet-driven blood clot contraction and promote clot compaction when there are few and/or dysfunctional platelets.

The fracture of polymeric gels has been of growing interest in the last two decades. Well established continuum theories that couple large deformations and fluid diffusion have been applied to gels to determine crack tip fields and the energy release rate. Some studies have combined experiment and calculations to determine the fracture toughness of gels and have shown that fluid effects make a substantial contribution to the toughness. Here we adopt a micro-mechanical view to estimate the fracture toughness of gels, defined as the critical (total) energy release rate, and show how the initiation toughness can be written as a combination of contributions from fiber scission and of fluid-solid demixing at the crack tip. This estimate is based on knowledge of a critical stretch and an associated volumetric strain when fracture is incipient and reveals dependencies on material properties including the solid volume fraction of gels. There have been no known ways to measure the de-mixing contribution directly from experiments, but the results in this paper provide a methodology. We also show how dissipation due to fluid motion as the crack propagates can contribute to the fracture toughness. Detailed results are presented for fibrin gels, which are the main structural component of blood clots.

Mechanisms of blood clot contraction – platelet-driven fibrin network remodeling, are not fully understood. We developed a detailed computational ClotDynaMo model of fibrin network with activated platelets, whose clot contraction rate for normal 450,000/µl human platelets depends on serum viscosity η , platelet filopodia length l , and weakly depends on filopodia traction force f and filopodia extension-retraction speed v . Final clot volume is independent of η , but depends on v , f and l . Analysis of ClotDynaMo output revealed a 2.24 TJ/mol clot contraction free energy change, with ~67% entropy and ~33% internal energy changes. The results illuminate the “optimal contraction principle” that maximizes volume change while minimizing energy cost. An 8-chain continuum model of polymer elasticity containing platelet forces, captures clot contractility as a function of platelet count, η and l . The ClotDynaMo and continuum models can be extended to include red blood cells, variable platelet properties, and mechanics of fibrin network.

Abstract The solution rheology of a fully synthetic, monodisperse mucin that mimics the glycosylated domains of natural mucins, poly(β‐Gal‐Thr) 22 , is studied to systematically explore relationships between polymer structure, solution conditions, and rheological properties. Using standard cone‐plate rheometry, shear thinning is observed over a range of concentrations, with an apparent yield stress—typical for gels—evident at the highest concentrations. This is surprising given the dilute, weakly interacting nature of the solutions and the lack of observable structure in cryogenic electron microscopy and particle tracking microrheology. However, interfacial rheometry demonstrates that the gel‐like behavior is attributable to a thin structured layer at the air–water interface, without any bulk gelation. This is attributed to an interfacial layer formed by inter‐mucin H‐bonds that yields when sheared. A computational model using kinetic Monte Carlo (kMC) simulations qualitatively reproduces the yield stress response of such a network through an intermolecular bonding potential. An analytical model of stochastic bond formation and breaking, validated by the kMC simulations, demonstrates that having multiple bonding sites per mucin with a force‐dependent debonding rate aligns with experiments, consistent with intermolecular interactions for other mucin proteins. This suggests that in mucin solutions, gelation may begin at the air–water interface, and emphasizes the need for multitechnique validation when exploring structural cues of mucus gelation through rheometry.

Soft biopolymer networks play pivotal roles in governing cellular mechanics, tissue structure, and physiological processes such as blood coagulation. Understanding their permeability and mechanical responses under compression is crucial for elucidating mass transport phenomena and their impact on extra- and intra-cellular behavior as well as processes affecting functionality of blood clots, cartilage and other fibrous tissues. The nonlinear responses of these networks to mechanical stresses prevent application of established linear poro-elasticity models. Despite extensive studies of fibrous network viscoelastic properties under shear deformations, their dynamic responses to compressive deformations remain poorly understood, particularly in physiological contexts of growth and collective migration of solid bodies. Conventional experimental techniques face challenges in accurately evaluating the permeability of these networks, hindering comprehensive understanding of their poromechanical behavior. In this study, we employ a novel poroelastic hybrid approach combining rheometer-based compression rheology with camera-facilitated sample shape detection to directly measure fluid flux and network permeability under controlled compressive strains. Accompanying experimental investigations, a continuum model implemented in finite elements, and an analytical model are developed to interpret the findings. The experimental data align well with the analytical model, revealing the emergence and disappearance of distinct densification regimes within the gel under mechanical stress. This study advances our understanding of the intricate interplay between mechanical forces, fluid flow, and structural properties in soft biopolymer networks, with a specific focus on fibrin- and collagen-based gels which represent the most abundant protein networks in the extracellular environment.

We study the dynamics and pattern formation of ordered arrays of active semi-flexible filaments, each of which is pinned at one end and free at the other. The filaments are modeled as connected chains of polar active particles with activity incorporated through local follower forces acting along their local tangent. Using Brownian dynamics simulations in two dimensions, we show that for a range of activity and filament separation, the filament array self-assembles into regularly spaced, kinetically arrested compact clusters. Activity, array geometry, filament elasticity, and grafting density are each seen to crucially influence the show size, shape, and spacing of these emergent clusters. Furthermore, cluster shapes for different grafting densities can be rescaled into self-similar forms with activity-dependent scaling exponents. We derive theoretical expressions that relate the number of filaments in a cluster and the spacing between adjacent clusters to filament activity, filament elasticity, and grafting density. Our results provide insight into the physical mechanisms involved in the initiation of clustering and suggest that steric contact forces and friction balance active forces and filament elasticity to shape and stabilize emergence clusters.

a network Laplacian; a matrix object which couples the motions of the structure joints. We show that this method is equivalent to the continuum limit of linear finite element methods as well as capable of reproducing natural frequencies and modes determined by more complex and computationally costlier methods. Our results show that balls-and-springs models inadequately describe dynamics, especially at short times relative to wave propagation time through rods. Furthermore, we illustrate the method's utility in optimizing target joint displacements using impedance matching and resonance-based schemes, offering a computationally efficient approach for analyzing large, complex truss structures.

We use Brownian dynamics simulations and theory to study the over-damped spatiotemporal dynamics and pattern formation in a fluid-permeated array of equally spaced, active, elastic filaments that are pinned at one end and free at the other. The filaments are modeled as connected colloidal chains with activity incorporated via compressive follower forces acting along the filament backbone. The length of the chains is smaller than the thermal persistence length. For a range of filament separation and activity values, we find that the filament array eventually self-assembles into a series of regularly spaced, kinetically arrested, compact clusters. Filament activity, geometry, elasticity, and grafting density are each seen to crucially influence the size, shape, and spacing of emergent clusters. Furthermore, cluster shapes for different grafting densities can be rescaled into self-similar forms with activity-dependent scaling exponents. We derive theoretical expressions that relate the number of filaments in a cluster and the spacing between clusters, to filament activity, filament elasticity, and grafting density. Our results provide insight into the physical mechanisms involved in the initiation of clustering and suggest that steric contact forces and friction balance active forces and filament elasticity to stabilize the clusters. Our simulations suggest design principles to realize filament-based clusters and similar self-assembling biomimetic materials using active colloids or synthetic microtubule-motor systems.

Over the past several decades, phase field modeling has been established as a standard simulation technique for mesoscopic science, allowing for seamless boundary tracking of moving interfaces and relatively easy coupling to other physical phenomena. However, despite its widespread success, phase field modeling remains largely driven by phenomenological justifications except in a handful of instances. In this work, we leverage a recently developed statistical mechanics framework for non-equilibrium phenomena, called Stochastic Thermodynamics with Internal Variables (STIV), to provide the first derivation of a phase field model for front propagation in a one dimensional elastic medium without appeal to phenomenology or fitting to experiments or simulation data. In the resulting model, the variables obey a gradient flow with respect to a non-equilibrium free energy, although notably, the dynamics of the strain and phase variables are coupled, and while the free energy functional is non-local in the phase field variable, it deviates from the traditional Landau-Ginzburg form. Moreover, in the systems analyzed here, the model accurately captures stress induced nucleation of transition fronts without the need to incorporate additional physics. We find that the STIV phase field model compares favorably to Langevin simulations of the microscopic system and we provide two numerical implementations enabling one to simulate arbitrary interatomic potentials.

Embolization is a leading cause of mortality, yet we know little about clot rupture mechanics. Fibrin provides the main structural and mechanical stability to blood clots. Previous studies have shown that altering the concentration of coagulation activators (thrombin or tissue factor (TF)) has a significant impact on fibrin structure and viscoelastic properties, but their effects on rupture properties are mostly unknown. Toughness, which corresponds to the ability to resist rupture, is independent of viscoelastic properties. We used varying TF concentrations to alter the structure and toughness of human plasma clots. We performed single-edge notch rupture tests to examine fibrin toughness under a constant strain rate and we assessed viscoelastic mechanics using rheology. We utilized fluorescent confocal and scanning electron microscopy (SEM) to quantify the fibrin network structure under varying TF concentrations. Our results revealed that increased TF concentration resulted in increased number of fibrin fibers with a reduction in network pore size, thinner and shorter fibrin fibers. Increasing TF concentration yielded a maximum toughness at mid-TF concentration, such that fibrin diameter and number of fibers underlie a complex role in influencing the rupture resistance of blood clots, resulting in a nonmonotonic relationship between TF and toughness. A simple mechanical model, built on our findings from our Fluctuating Spring (FS) computational model, adopted to estimate the fracture toughness (critical energy release rate) as a function of TF predicts trends that are in good agreement with experiments. The differences in mechanical responses point to the importance of studying the structure-function relationships of fibrin networks, which may be predictive of the tendency for embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the main mechanical and structural scaffold of blood clots that provides the necessary strength and stability to the clot, ensuring effective stemming of bleeding. The rupture of blood clots can result in the blockage of downstream vessels thereby blocking blood flow and oxygen supply. The fibrin network structure has been shown to influence the viscoelastic mechanical properties of clots, but has not been explored for fracture mechanics. Here, we modulate the fibrin network structure by varying the concentration of Tissue Factor (TF). Interestingly, the association between TF concentration and maximum toughness of the clots is non-monotonic. The variations in mechanical responses highlight the importance of studying the structure-function relationships of fibrin networks, as these may predict the tendency for embolization.

the critical energy release rate, is relatively independent of the type of loading and is therefore a fundamental property of the gel. Ultrastructural studies and finite element simulations demonstrate that cracks propagate perpendicular to the direction of maximum stretch at the crack tip. These observations indicate that locally, the mechanism of rupture is predominantly tensile. Knowledge gained from this study will aid in the development of methods for prediction/prevention of thrombotic embolization.

The aim of this paper is to place the cell locomotion problem within the general framework of classical continuum mechanics, and while doing so, to account for the deformation of the actin network in the cytoskeleton; the myosin activity on the lamellum including its effect on depolymerization at the trailing edge; model the stress-dependent driving forces and kinetic laws controlling polymerization at the leading edge, depolymerization at the trailing edge and ATP hydrolysis consistently with the dissipation inequality; and, based on the observations in Gardel et al. (Gardel et al. 2008 J. Cell Biol. 183 , 999–1005 ( doi:10.1083/jcb.200810060 )), include a biphasic velocity-dependent traction stress acting on the actin network. While we chose certain specific models for each of these, in part to allow for an analytical solution, the generality of the framework allows one to readily introduce different constitutive laws to describe these phenomena as might be needed, for example, to study some different type of cells. As described in §5, the predictions of the model compare well with observations such as the magnitude of the very different actin retrograde speeds in the lamellum and lamellipodium including their jump at the interface, the magnitude of the cell speed, and the relative lengths of the lamellipodium and lamellum.

Abstract The material point method (MPM) enables large‐deformation simulations of complex material behaviors with natural multi‐material coupling. However, MPM struggles to accurately capture fields related to material discontinuities, for example, traction‐free surfaces, making MPM fracture simulation challenging. Many MPMs seek to alleviate this challenge, but comparing these approaches has been elusive. This work presents a benchmarking process for evaluating and comparing discontinuous MPM approaches. The benchmarks focus field quantities near a circular hole in a plate and a planar crack with comparisons to accurate finite element solutions.

Abstract Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of nonequilibrium systems. But despite tremendous efforts, a universal theory of nonequilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex nonequilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data or on running concurrent simulations at the particle level. Instead, we provide a novel framework for deriving stand-alone macroscopic thermodynamic models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework’s effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double-stranded DNA, thus producing, to the authors’ knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers.

Fibrous gels such as cartilage, blood clots, and carbon-nanotube-based sponges with absorbed oils suffer a reduction in volume by the expulsion of liquid under uniaxial tension, and this directly affects crack-tip fields and energy release rates. A continuum model is formulated for isotropic fibrous gels that exhibit a range of behaviors from volume increasing to volume decreasing in uniaxial tension by changing the ratio of two material parameters. The motion of liquid in the pores of such gels is modeled using poroelasticity. The direction of liquid fluxes around cracks is shown to depend on whether the gel locally increases or decreases in volume. The energy release rate for cracks is computed using a surface-independent integral and it is shown to have two contributions - one from the stresses in the solid network, and another from the flow of liquid. The contribution to the integral from liquid permeation tends to be negative when the gel exhibits volume decrease, which effectively is a crack shielding mechanism.

Far-from-equilibrium phenomena are critical to all natural and engineered systems, and essential to biological processes responsible for life. For over a century and a half, since Carnot, Clausius, Maxwell, Boltzmann, and Gibbs, among many others, laid the foundation for our understanding of equilibrium processes, scientists and engineers have dreamed of an analogous treatment of non-equilibrium systems. But despite tremendous efforts, a universal theory of non-equilibrium behavior akin to equilibrium statistical mechanics and thermodynamics has evaded description. Several methodologies have proved their ability to accurately describe complex non-equilibrium systems at the macroscopic scale, but their accuracy and predictive capacity is predicated on either phenomenological kinetic equations fit to microscopic data, or on running concurrent simulations at the particle level. Instead, we provide a framework for deriving stand-alone macroscopic thermodynamics models directly from microscopic physics without fitting in overdamped Langevin systems. The only necessary ingredient is a functional form for a parameterized, approximate density of states, in analogy to the assumption of a uniform density of states in the equilibrium microcanonical ensemble. We highlight this framework's effectiveness by deriving analytical approximations for evolving mechanical and thermodynamic quantities in a model of coiled-coil proteins and double stranded DNA, thus producing, to the authors' knowledge, the first derivation of the governing equations for a phase propagating system under general loading conditions without appeal to phenomenology. The generality of our treatment allows for application to any system described by Langevin dynamics with arbitrary interaction energies and external driving, including colloidal macromolecules, hydrogels, and biopolymers.