The Problem with NIST Thermodynamics Tables in Continuum Mechanics.

Thermodynamics is a fundamental topic of continuum mechanics and biomechanics, with a wide range of applications to physiological and biological processes. This study addresses two fundamental limitations of current thermodynamic treatments. First, thermodynamics tables distributed online by the U.S. National Institute of Standards and Technology report properties of fluids as a function of absolute temperature T and absolute pressure P. These properties include mass density ρ, specific internal energy u, enthalpy h=u+P/ρ and entropy s. However, formulations of jump conditions across phase boundaries derived from Newton's second law of motion and the first law of thermodynamics employ the gauge pressure p=P-Pr, where Pr is an arbitrarily selected referential absolute pressure. Interchanging p with P is not innocuous as it alters tabulated NIST values for u, while keeping h and s unchanged. Using p for functions of state and governing equations solves the problem with using NIST entries for the specific internal energy u in standard thermodynamics tables, and analyses of phase transformation in continuum mechanics. Second, constitutive models for the free energy of fluids, such as water and air, are not typically provided in standard thermodynamics treatments. This study proposes a set of constitutive models and validates them against suitably modified NIST data.

Continuum Growth Mechanics: Reconciling Two Common Frameworks.

The objective of this study was to investigate whether the two most common growth mechanics modeling frameworks, the constrained-mixture growth model and the kinematic growth model, could be reconciled mathematically. The purpose of this effort was to provide practical guidelines for potential users of these modeling frameworks. Results showed that the kinematic growth model is mathematically consistent with a special form of the constrained-mixture growth model, where only one generation of a growing solid exists at any given time, overturning its entire solid mass at each instant of growth in order to adopt the reference configuration dictated by the growth deformation. The thermodynamics of the kinematic growth model, along with the specialized constrained-mixture growth model, requires a cellular supply of chemical energy to allow deposition of solid mass under a stressed state. A back-of-the-envelope calculation shows that the amount of chemical energy required to sustain biological growth under these models is negligibly small, when compared to the amount of energy normally consumed daily by the human body. In conclusion, this study successfully reconciled the two most popular growth theories for biological growth and explained the special circumstances under which the constrained-mixture growth model reduces to the kinematic growth model.

Erratum: "A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity" [ASME J. Biomech Eng., 2023, 145(1), p. 011004; DOI: 10.1115/1.4054983].

In this erratum, we correct a mistake in a subcomponent of the numerical algorithm proposed in our recent study for modeling anisotropic reactive nonlinear viscoelasticity (doi:10.1115/1.4054983), for the special case where multiple weak bond families may be recruited with loading. This correction overcomes a nonphysical response noted under uni-axial cyclical loading.

Simulating Cerebral Edema and Ischemia After Traumatic Acute Subdural Hematoma Using Triphasic Swelling Biomechanics.

Poor outcome following traumatic acute subdural hematoma (ASDH) is associated with the severity of the primary injury and secondary injury including cerebral edema and ischemia. However, the underlying secondary injury mechanism contributing to elevated intracranial pressure (ICP) and high mortality rate remains unclear. Cerebral edema occurs in response to the exposure of the intracellular fixed charge density (FCD) after cell death, causing ICP to increase. The increased ICP from swollen tissue compresses blood vessels in adjacent tissue, restricting blood flow and leading to ischemic damage. We hypothesize that the mass occupying effect of ASDH exacerbates the ischemic injury, leading to ICP elevation, which is an indicator of high mortality rate in the clinic. Using FEBio (febio.org) and triphasic swelling biomechanics, this study modeled clinically relevant ASDHs and simulated post-traumatic brain swelling and ischemia to predict ICP. Results showed that common convexity ASDH significantly increased ICP by exacerbating ischemic injury, and surgical removal of the convexity ASDH may control ICP by preventing ischemia progression. However, in cases where the primary injury is very severe, surgical intervention alone may not effectively decrease ICP, as the contribution of the hematoma to the elevated ICP is insignificant. In addition, interhemispheric ASDH, located between the cerebral hemispheres, does not significantly exacerbate ischemia, supporting the conservative surgical management generally recommended for interhemispheric ASDH. The joint effect of the mass occupying effect of the blood clot and resulting ischemia contributes to elevated ICP which may increase mortality. Our novel approach may improve the fidelity of predicting patient outcome after motor vehicle crashes and traumatic brain injuries due to other causes.

Region-Dependent Mechanical Properties of Human Brain Tissue Under Large Deformations Using Inverse Finite Element Modeling.

This study aims to facilitate intracranial simulation of traumatic events by determining the mechanical properties of different anatomical structures of the brain. Our experimental indentation paradigm used fresh, post-operative human tissue, which is highly advantageous in determining mechanical properties without being affected by postmortem time. This study employed an inverse finite element approach coupled with experimental indentation data to characterize mechanical properties of the human hippocampus (CA1, CA3, dentate gyrus), cortex white matter, and cortex grey matter. We determined that an uncoupled viscoelastic Ogden constitutive formulation was most appropriate to represent the mechanical behavior of these different regions of brain. Anatomical regions were significantly different in their mechanical properties. The cortex white matter was stiffer than cortex grey matter, and the CA1 and dentate gyrus were both stiffer than cortex grey matter. Although no sex dependency was observed, there were trends indicating that male brain regions were generally stiffer than corresponding female regions. In addition, there were no statistically significant age dependent differences. This study provides a structure-specific description of fresh human brain tissue mechanical properties, which will be an important step toward explicitly modeling the heterogeneity of brain tissue deformation during TBI through finite element modeling.

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis.

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

Modeling Inelastic Responses Using Constrained Reactive Mixtures.

This study reviews the progression of our research, from modeling growth theories for cartilage tissue engineering, to the formulation of constrained reactive mixture theories to model inelastic responses in any solid material, such as theories for damage mechanics, viscoelasticity, plasticity, and elasto-plastic damage. In this framework, multiple solid generations α can co-exist at any given time in the mixture. The oldest generation is denoted by α=s and is called the master generation, whose reference configuration Xs is observable. The solid generations α are all constrained to share the same velocity vs, but may have distinct reference configurations Xα. An important element of this formulation is that the time-invariant mapping Fαs=∂Xα/∂Xs between these reference configurations is a function of state, whose mathematical formulation is postulated by constitutive assumption. Thus, reference configurations Xα are not observable (α≠s). This formulation employs only observable state variables, such as the deformation gradient Fs of the master generation and the referential mass concentrations ρrα of each generation, in contrast to classical formulations of inelastic responses which rely on internal state variable theory, requiring evolution equations for those hidden variables. In constrained reactive mixtures, the evolution of the mass concentrations is governed by the axiom of mass balance, using constitutive models for the mass supply densities ρˆrα. Classical and constrained reactive mixture approaches share considerable mathematical analogies, as they both introduce a multiplicative decomposition of the deformation gradient, also requiring evolution equations to track some of the state variables. However, they also differ at a fundamental level, since one adopts only observable state variables while the other introduces hidden state variables. In summary, this review presents an alternative foundational approach to the modeling of inelastic responses in solids, grounded in the classical framework of mixture theory.

Finite Element Implementation of Computational Fluid Dynamics With Reactive Neutral and Charged Solute Transport in FEBio.

The objective of this study was to implement a novel fluid-solutes solver into the open-source finite element software FEBio, that extended available modeling capabilities for biological fluids and fluid-solute mixtures. Using a reactive mixture framework, this solver accommodates diffusion, convection, chemical reactions, electrical charge effects, and external body forces, without requiring stabilization methods that were deemed necessary in previous computational implementations of the convection-diffusion-reaction equation at high Peclet numbers. Verification and validation problems demonstrated the ability of this solver to produce solutions for Peclet numbers as high as 1011, spanning the range of physiological conditions for convection-dominated solute transport. This outcome was facilitated by the use of a formulation that accommodates realistic values for solvent compressibility, and by expressing the solute mass balance such that it properly captured convective transport by the solvent and produced a natural boundary condition of zero diffusive solute flux at outflow boundaries. Since this numerical scheme was not necessarily foolproof, guidelines were included to achieve better outcomes that minimize or eliminate the potential occurrence of numerical artifacts. The fluid-solutes solver presented in this study represents an important and novel advancement in the modeling capabilities for biomechanics and biophysics as it allows modeling of mechanobiological processes via the incorporation of chemical reactions involving neutral or charged solutes within dynamic fluid flow. The incorporation of charged solutes in a reactive framework represents a significant novelty of this solver. This framework also applies to a broader range of nonbiological applications.

Computational study of biomechanical drivers of renal cystogenesis.

Renal cystogenesis is the pathological hallmark of autosomal dominant polycystic kidney disease, caused by PKD1 and PKD2 mutations. The formation of renal cysts is a common manifestation in ciliopathies, a group of syndromic disorders caused by mutation of proteins involved in the assembly and function of the primary cilium. Cystogenesis is caused by the derailment of the renal tubular architecture and tissue deformation that eventually leads to the impairment of kidney function. However, the biomechanical imbalance of cytoskeletal forces that are altered in cells with Pkd1 mutations has never been investigated, and its nature and extent remain unknown. In this computational study, we explored the feasibility of various biomechanical drivers of renal cystogenesis by examining several hypothetical mechanisms that may promote morphogenetic markers of cystogenesis. Our objective was to provide physics-based guidance for our formulation of hypotheses and our design of experimental studies investigating the role of biomechanical disequilibrium in cystogenesis. We employed the finite element method to explore the role of (1) wild-type versus mutant cell elastic modulus; (2) contractile stress magnitude in mutant cells; (3) localization and orientation of contractile stress in mutant cells; and (4) sequence of cell contraction and cell proliferation. Our objective was to identify the factors that produce the characteristic tubular cystic growth. Results showed that cystogenesis occurred only when mutant cells contracted along the apical-basal axis, followed or accompanied by cell proliferation, as long as mutant cells had comparable or lower elastic modulus than wild-type cells, with their contractile stresses being significantly greater than their modulus. Results of these simulations allow us to focus future in vitro and in vivo experimental studies on these factors, helping us formulate physics-based hypotheses for renal tubule cystogenesis.

Toward defining the role of the synovium in mitigating normal articular cartilage wear and tear.

Cartilage repair has been studied extensively in the context of injury and disease, but the joint's management of regular sub-injurious damage to cartilage, or 'wear and tear,' which occurs due to normal activity, is poorly understood. We hypothesize that this cartilage maintenance is mediated in part by cells derived from the synovium that migrate to the worn articular surface. Here, we demonstrate in vitro that the early steps required for such a process can occur. First, we show that under physiologic mechanical loads, chondrocyte death occurs in the cartilage superficial zone along with changes to the cartilage surface topography. Second, we show that synoviocytes are released from the synovial lining under physiologic loads and attach to worn cartilage. Third, we show that synoviocytes parachuted onto a simulated or native cartilage surface will modify their behavior. Specifically, we show that synoviocyte interactions with chondrocytes lead to changes in synoviocyte mechanosensitivity, and we demonstrate that cartilage-attached synoviocytes can express COL2A1, a hallmark of the chondrogenic phenotype. Our findings suggest that synoviocyte-mediated repair of cartilage 'wear and tear' as a component of joint homeostasis is feasible and is deserving of future study.

Pulse wave imaging of a stenotic artery model with plaque constituents of different stiffnesses: Experimental demonstration in phantoms and fluid-structure interaction simulation.

Vulnerable plaques associated with softer components may rupture, releasing thrombotic emboli to smaller vessels in the brain, thus causing an ischemic stroke. Pulse Wave Imaging (PWI) is an ultrasound-based method that allows for pulse wave visualization while the regional pulse wave velocity (PWV) is mapped along the arterial wall to infer the underlying wall compliance. One potential application of PWI is the non-invasive estimation of plaque's mechanical properties for investigating its vulnerability. In this study, the accuracy of PWV estimation in stenotic vessels was investigated by computational simulation and PWI in validation phantoms to evaluate this modality for assessing future stroke risk. Polyvinyl alcohol (PVA) phantoms with plaque constituents of different stiffnesses were designed and constructed to emulate stenotic arteries in the experiment, and the novel fabrication process was described. Finite-element fluid-structure interaction simulations were performed in a stenotic phantom model that matched the geometry and parameters of the experiment in phantoms. The peak distension acceleration of the phantom wall was tracked to estimate PWV. PWVs of 2.57 ms-1, 3.41 ms-1, and 4.48 ms-1 were respectively obtained in the soft, intermediate, and stiff plaque material in phantoms during the experiment using PWI. PWVs of 2.10 ms-1, 3.33 ms-1, and 4.02 ms-1 were respectively found in the soft, intermediate, and stiff plaque material in the computational simulation. These results demonstrate that PWI can effectively distinguish the mechanical properties of plaque in phantoms as compared to computational simulation.

Damage Mechanics of Biological Tissues in Relation to Viscoelasticity.

This study examines the theoretical foundations for the damage mechanics of biological tissues in relation to viscoelasticity. Its primary goal is to provide a mechanistic understanding of well-known experimental observations in biomechanics, which show that the ultimate tensile strength of viscoelastic biological tissues typically increases with increasing strain rate. The basic premise of this framework is that tissue damage occurs when strong bonds, such as covalent bonds in the solid matrix of a biological tissue, break in response to loading. This type of failure is described as elastic damage, under the idealizing assumption that strong bonds behave elastically. Viscoelasticity arises from three types of dissipative mechanisms: (1) Friction between molecules of the same species, which is represented by the tissue viscosity. (2) Friction between fluid and solid constituents of a porous medium, which is represented by the tissue hydraulic permeability. (3) Dissipative reactions arising from weak bonds breaking in response to loading, and reforming in a stress-free state, such as hydrogen bonds and other weak electrostatic bonds. When a viscoelastic tissue is subjected to loading, some of that load may be temporarily supported by those frictional and weak bond forces, reducing the amount of load supported by elastic strong bonds and thus, the extent of elastic damage sustained by those bonds. This protective effect depends on the characteristic time response of viscoelastic mechanisms in relation to the loading history. This study formalizes these concepts by presenting general equations that can model the damage mechanics of viscoelastic tissues.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

Superficial zone chondrocytes can get compacted under physiological loading: A multiscale finite element analysis.

Recent in vivo and in vitro studies have demonstrated that superficial zone (SZ) chondrocytes within articular layers of diarthrodial joints die under normal physiologic loading conditions. In order to further explore the implications of this observation in future investigations, we first needed to understand the mechanical environment of SZ chondrocytes that might cause them to die under physiological sliding contact conditions. In this study we performed a multiscale finite element analysis of articular contact to track the temporal evolution of a SZ chondrocyte's interstitial fluid pressure, hydraulic permeability, and volume under physiologic loading conditions. The effect of the pericellular matrix modulus and permeability was parametrically investigated. Results showed that SZ chondrocytes can lose ninety percent of their intracellular fluid after several hours of intermittent or continuous contact loading, resulting in a reduction of intracellular hydraulic permeability by more than three orders of magnitude. These findings are consistent with loss of cell viability due to the impediment of cellular metabolic pathways induced by the loss of fluid. They suggest that there is a simple mechanical explanation for the vulnerability of SZ chondrocytes to sustained physiological loading conditions. Future studies will focus on validating these specific findings experimentally. STATEMENT OF SIGNIFICANCE: As with any mechanical system, normal 'wear and tear' of cartilage tissue lining joints is expected. Yet incidences of osteoarthritis are uncommon in individuals younger than 45. This counter-intuitive observation suggests there must be an intrinsic repair mechanism compensating for this wear and tear over many decades of life. Recent experimental studies have shown superficial zone chondrocytes die under physiologic loading conditions, suggesting that this repair mechanism may involve cell replenishment. To better understand the mechanical environment of these cells, we performed a multiscale computational analysis of articular contact under loading. Results indicated that normal activities like walking or standing can induce significant loss of intracellular fluid volume, potentially hindering metabolic activity and fluid transport properties, and causing cell death.

Bendable osteochondral allografts for patellar resurfacing: A finite element analysis of congruence.

Osteochondral allograft (OCA) transplantation provides a safe and effective treatment option for large cartilage defects, but its use is limited partly due to the difficulty of matching articular surface curvature between donor and recipient. We hypothesize that bendable OCAs may provide better curvature matching for patella transplants in the patellofemoral joint (PFJ). This finite element study investigates PFJ congruence for unbent and bendable OCAs, at various flexion angles. Finite element models were created for 12 femur-patella OCA pairings. Two grooves were cut in each OCA bony substrate, allowing the articular layer to bend. PFJs with either unbent (OCA) or permanently bent (BOCA) allografts were articulated from 40 to 70 degrees flexion and contact area was calculated. OCAs and BOCAs were then shifted 6 mm distally toward the tibia (S-OCA, S-BOCA) to investigate the influence of proximal-distal alignment on congruence. On average, no significant difference in contact area was found between native PFJs and either OCAs or BOCAs (p > 0.25), indicating that both types of allografts restored native congruence. This result provides biomechanical support in favor of an emerging surgical procedure. S-BOCAs resulted in a significant increase in contact area relative to the remaining groups (p < 0.02). The fact that BOCAs produced equally good results implies that bendable allografts may prove useful in future surgical procedures, with the possibility of transplanting them with a small distal shift. Surgeons who are reluctant to use OCAs for resurfacing patellae based on curvature matching capabilities may be more amenable to adopting BOCAs.

A Friction Testing-Bioreactor Device for Study of Synovial Joint Biomechanics, Mechanobiology, and Physical Regulation.

In primary osteoarthritis (OA), normal 'wear and tear' associated with aging inhibits the ability of cartilage to sustain its load-bearing and lubrication functions, fostering a deleterious physical environment. The frictional interactions of articular cartilage and synovium may influence joint homeostasis through tissue level wear and cellular mechanotransduction. To study these mechanical and mechanobiological processes, a device capable of replicating the motion of the joint is described. The friction testing device controls the delivery of reciprocal translating motion and normal load to two contacting biological counterfaces. This study adopts a synovium-on-cartilage configuration, and friction coefficient measurements are presented for tests performed in a phosphate-buffered saline (PBS) or synovial fluid (SF) bath. The testing was performed for a range of contact stresses, highlighting the lubricating properties of SF under high loads. This friction testing device can be used as a biomimetic bioreactor for studying the physical regulation of living joint tissues in response to applied physiologic loading associated with diarthrodial joint articulation.

Toward Development of a Diabetic Synovium Culture Model.

Osteoarthritis (OA) is a degenerative joint disease characterized by articular cartilage degradation and inflammation of synovium, the specialized connective tissue that envelops the diarthrodial joint. Type 2 diabetes mellitus (DM) is often found in OA patients, with nearly double the incidence of arthritis reported in patients with diabetes (52%) than those without it (27%). The correlation between OA and DM has been attributed to similar risk factors, namely increasing age and joint loading due to obesity. However, a potential causative link is not well understood due to comorbidities involved with treating diabetic patients, such as high infection rates and poor healing response caused by hyperglycemia and insulin resistance. The purpose of this study was to investigate the effect of hyperglycemic and insulin culture conditions on synovium properties. It was hypothesized that modeling hyperglycemia-induced insulin resistance in synovium would provide novel insights of OA pathogenesis in DM patients. To simulate DM in the synovial joint, healthy synovium was preconditioned in either euglycemic (EG) or hyperglycemic (HG) glucose concentrations with insulin in order to induce the biological response of the diseased phenotype. Synovium biochemical composition was evaluated to determine ECM remodeling under hyperglycemic culture conditions. Concurrent changes in AKT phosphorylation, a signaling pathway implicated in insulin resistance, were measured along with gene expression data for insulin receptors, glucose transporters, and specific glycolysis markers involved in glucose regulation. Since fluid shear stress arising during joint articulation is a relevant upstream stimulus for fibroblast-like synoviocytes (FLS), the predominant cell type in synovium, FLS mechanotransduction was evaluated via intracellular calcium ([Ca2+]i). Incidence and length of primary cilia, a critical effector of cell mechanosensing, were measured as potential mechanisms to support differences in [Ca2+]i responses. Hyperglycemic culture conditions decreased collagen and GAG content compared to EG groups, while insulin recovered ECM constituents. FLS mechanosensitivity was significantly greater in EG and insulin conditions compared to HG and non-insulin treated groups. Hyperglycemic treatment led to decreased incidence and length of primary cilia and decreased AKT phosphorylation, providing possible links to the mechanosensing response and suggesting a potential correlation between glycemic culture conditions, diabetic insulin resistance, and OA development.

A Hybrid Biphasic Mixture Formulation for Modeling Dynamics in Porous Deformable Biological Tissues.

The primary aim of this study is to establish the theoretical foundations for a solid-fluid biphasic mixture domain that can accommodate inertial effects and a viscous interstitial fluid, which can interface with a dynamic viscous fluid domain. Most mixture formulations consist of constituents that are either all intrinsically incompressible or compressible, thereby introducing inherent limitations. In particular, mixtures with intrinsically incompressible constituents can only model wave propagation in the porous solid matrix, whereas those with compressible constituents require internal variables, and related evolution equations, to distinguish the compressibility of the solid and fluid under hydrostatic pressure. In this study, we propose a hybrid framework for a biphasic mixture where the skeleton of the porous solid is intrinsically incompressible but the interstitial fluid is compressible. We define a state variable as a measure of the fluid volumetric strain. Within an isothermal framework, the Clausius-Duhem inequality shows that a function of state arises for the fluid pressure as a function of this strain measure. We derive jump conditions across hybrid biphasic interfaces, which are suitable for modeling hydrated biological tissues. We then illustrate this framework using confined compression and dilatational wave propagation analyses. The governing equations for this hybrid biphasic framework reduce to those of the classical biphasic theory whenever the bulk modulus of the fluid is set to infinity and inertia terms and viscous fluid effects are neglected. The availability of this novel framework facilitates the implementation of finite element solvers for fluid-structure interactions at interfaces between viscous fluids and porous-deformable biphasic domains, which can include fluid exchanges across those interfaces.

A Hybrid Reactive Multiphasic Mixture With a Compressible Fluid Solvent.

Mixture theory is a general framework that has been used to model mixtures of solid, fluid, and solute constituents, leading to significant advances in modeling the mechanics of biological tissues and cells. Though versatile and applicable to a wide range of problems in biomechanics and biophysics, standard multiphasic mixture frameworks incorporate neither dynamics of viscous fluids nor fluid compressibility, both of which facilitate the finite element implementation of computational fluid dynamics solvers. This study formulates governing equations for reactive multiphasic mixtures where the interstitial fluid has a solvent which is viscous and compressible. This hybrid reactive multiphasic framework uses state variables that include the deformation gradient of the porous solid matrix, the volumetric strain and rate of deformation of the solvent, the solute concentrations, and the relative velocities between the various constituents. Unlike standard formulations which employ a Lagrange multiplier to model fluid pressure, this framework requires the formulation of a function of state for the pressure, which depends on solvent volumetric strain and solute concentrations. Under isothermal conditions the formulation shows that the solvent volumetric strain remains continuous across interfaces between hybrid multiphasic domains. Apart from the Lagrange multiplier-state function distinction for the fluid pressure, and the ability to accommodate viscous fluid dynamics, this hybrid multiphasic framework remains fully consistent with standard multiphasic formulations previously employed in biomechanics. With these additional features, the hybrid multiphasic mixture theory makes it possible to address a wider range of problems that are important in biomechanics and mechanobiology.