The left ventricle of the heart is a fundamental structure in the human cardiac system that pumps oxygenated blood into the systemic circulation. Several valvular conditions can cause the aortic and mitral valves associated with the left ventricle to become severely diseased and require replacement. However, the clinical outcomes of such operations, specifically the postoperative ventricular hemodynamics of replacing both valves, are not well understood. This work uses computational fluid-structure interaction (FSI) to develop an improved understanding of this effect by modeling a left ventricle with the aortic and mitral valves replaced with bioprostheses. We use a hybrid Arbitrary Lagrangian-Eulerian/immersogeometric framework to accommodate the analysis of cardiac hemodynamics and heart valve structural mechanics in a moving fluid domain. The motion of the endocardium is obtained from a cardiac biomechanics simulation and provided as an input to the proposed numerical framework. The results from the simulations in this work indicate that the replacement of the native mitral valve with a tri-radially symmetric bioprosthesis dramatically changes the ventricular hemodynamics. Most significantly, the vortical motion in the left ventricle is found to reverse direction after mitral valve replacement. This study demonstrates that the proposed computational FSI framework is capable of simulating complex multiphysics problems and can provide an in-depth understanding of the cardiac mechanics.

In this work, we present a computational fluid-structure interaction (FSI) study for a healthy patient-specific pulmonary arterial tree using the unified continuum and variational multiscale (VMS) formulation we previously developed. The unified framework is particularly well-suited for FSI, as the fluid and solid sub-problems are addressed in essentially the same manner and can thus be uniformly integrated in time with the generalized- method. In addition, the VMS formulation provides a mechanism for large-eddy simulation in the fluid sub-problem and pressure stabilization in the solid sub-problem. The FSI problem is solved in a quasi-direct approach, in which the pressure and velocity in the unified continuum body are first solved, and the solid displacement is then obtained via a segregated algorithm and prescribed as a boundary condition for the mesh motion. Results of the pulmonary arterial FSI simulation are presented and compared against those of a rigid wall simulation.

An analysis is presented of the equilibrium response of a radially deformed cylinder of isotropic, incompressible bio-elastic material swollen by an infused liquid satisfying a static diffusive balance law.

Untreated tricuspid valve regurgitation (TR) is associated with increased rates of mortality, morbidity, and hospitalization. Current pharmacological and surgical treatment options for TR are limited. MitraClip (MC), an edge-to-edge percutaneous intervention, has been reported to be effective for treatment of TR. The goal of this study was to examine the effects of MC position on TR, using a multiphysics fluid-structure-interaction (FSI) analysis. The computational set up included the tricuspid valve (TV), the chordae tendineae, the blood particles, and a tube that surrounded the leaflets and blood particles. The leaflets and chordae were modeled as hyperelastic materials, and blood was modeled using smoothed particle hydrodynamics. FSI analysis was conducted for blood flow through the closed valve for multiple simulations that account for normal, diseased, and treated conditions of the TV. To simulate the diseased TV, a group of chordae between septal and pulmonary leaflets were removed from the normal TV, which produced increased regurgitation. Four MC treated scenarios were considered: i) one MC near the annulus, ii) one MC approximately midway between the annulus and leaflet tip, iii) one MC near the leaflet tip, iv) two MCs: one approximately midway between the annulus and leaflet tip, and one close to the leaflet tip. The TR increased in diseased TV (7.5%) compared to normal TV (2.5%). All MC treated scenarios decreased TR. The MC located near the midway point between the annulus and leaflet tip led to largest decrease in TR (75.2% compared to the untreated condition). The MC located near the leaflet tip was associated with lowest reduction in TR (2.2% compared to the untreated condition). When two MCs were used, reduction in TR was relatively high (68.7%), but TR was not improved compared to the optimal single MC. MC caused high stresses in the vicinity of the clipping area in all conditions; the highest occurred when the MC was near the leaflet tips. Using a quantitative computational approach, we confirm previous clinical reports on the efficacy of MC for treatment of TR. The results of this study could lead to the design of more efficient MC interventions for TR.

Pulmonary arterial hypertension (PAH) is a heart disease that is characterized by an abnormally high pressure in the pulmonary artery (PA). While right ventricular assist device (RVAD) has been considered recently as a treatment option for the end-stage PAH patients, its effects on biventricular mechanics are, however, largely unknown. To address this issue, we developed an image-based modeling framework consisting of a biventricular finite element (FE) model that is coupled to a lumped model describing the pulmonary and systemic circulations in a closed-loop system. The biventricular geometry was reconstructed from the magnetic resonance images of two PAH patients showing different degree of RV remodeling and a normal subject. The framework was calibrated to match patient-specific measurements of the left ventricular (LV) and RV volume and pressure waveforms. An RVAD model was incorporated into the calibrated framework and simulations were performed with different pump speeds. Results showed that RVAD unloads the RV, improves cardiac output and increases septum curvature, which are more pronounced in the PAH patient with severe RV remodeling. These improvements, however, are also accompanied by an adverse increase in the PA pressure. These results suggest that the RVAD implantation may need to be optimized depending on disease progression.

The mechanical bidomain model is a mathematical description of the elastic properties of cardiac tissue. The unique feature of the bidomain model is that it is a macroscopic continuum representation of tissue that nevertheless accounts for the intracellular and extracellular spaces individually, thereby focusing on mechanical forces arising across the cell membrane. In this paper, the mechanical bidomain model describes a two-dimensional sheet of cardiac tissue undergoing a uniform active tension. At the boundary, the tissue sheet is free to move. Analytical solutions are found for the intracellular and extracellular displacements and pressures. The model predicts that membrane forces, which may be responsible for phenomena such as mechanotransduction and remodeling, are large near the tissue boundary, and fall off rapidly with distance from the boundary.

Adult cardiac muscle adapts to mechanical changes in the environment by growth and remodeling (G&R) via a variety of mechanisms. Hypertrophy develops when the heart is subjected to chronic mechanical overload. In ventricular pressure overload (e.g. due to aortic stenosis) the heart typically reacts by concentric hypertrophic growth, characterized by wall thickening due to myocyte radial growth when sarcomeres are added in parallel. In ventricular volume overload, an increase in filling pressure (e.g. due to mitral regurgitation) leads to eccentric hypertrophy as myocytes grow axially by adding sarcomeres in series leading to ventricular cavity enlargement that is typically accompanied by some wall thickening. The specific biomechanical stimuli that stimulate different modes of ventricular hypertrophy are still poorly understood. In a recent study, based on in-vitro studies in micropatterned myocyte cell cultures subjected to stretch, we proposed that cardiac myocytes grow longer to maintain a preferred sarcomere length in response to increased fiber strain and grow thicker to maintain interfilament lattice spacing in response to increased cross-fiber strain. Here, we test whether this growth law is able to predict concentric and eccentric hypertrophy in response to aortic stenosis and mitral valve regurgitation, respectively, in a computational model of the adult canine heart coupled to a closed loop model of circulatory hemodynamics. A non-linear finite element model of the beating canine ventricles coupled to the circulation was used. After inducing valve alterations, the ventricles were allowed to adapt in shape in response to mechanical stimuli over time. The proposed growth law was able to reproduce major acute and chronic physiological responses (structural and functional) when integrated with comprehensive models of the pressure-overloaded and volume-overloaded canine heart, coupled to a closed-loop circulation. We conclude that strain-based biomechanical stimuli can drive cardiac growth, including wall thickening during pressure overload.

Hypothesis testing via numerical models has emerged as a powerful tool which permits the verification of theoretical frameworks against canonical experimental and clinical observations. Cleverly designed computational experiments also inspire new methodologies by elucidating important biological processes and restricting parametric spaces. Constrained mixture models of arterial growth and remodeling (G&R) can facilitate the design of computational experiments which can bypass technical limitations in the laboratory, by considering illustrative special cases. The resulting data may then inform the design of focused experimental techniques and the development of improved theories. This work is a survey of computational hypothesis-testing studies, which exploit the unique abilities offered by the constrained mixture theory of arterial G&R. Specifically, we explore the core hypotheses integrated in these models, review their basic mathematical conceptualizations, and recapitulate their most salient and illuminating findings. We then assess how a decade's worth of constrained mixture models have contributed to a lucid, emerging picture of G&R mechanisms.

Cardiac growth and remodeling in the form of chamber dilation and wall thinning are typical hallmarks of infarct-induced heart failure. Over time, the infarct region stiffens, the remaining muscle takes over function, and the chamber weakens and dilates. Current therapies seek to attenuate these effects by removing the infarct region or by providing structural support to the ventricular wall. However, the underlying mechanisms of these therapies are unclear, and the results remain suboptimal. Here we show that myocardial infarction induces pronounced regional and transmural variations in cardiac form. We introduce a mechanistic growth model capable of predicting structural alterations in response to mechanical overload. Under a uniform loading, this model predicts non-uniform growth. Using this model, we simulate growth in a patient-specific left ventricle. We compare two cases, growth in an infarcted heart, pre-operative, and growth in the same heart, after the infarct was surgically excluded, post-operative. Our results suggest that removing the infarct and creating a left ventricle with homogeneous mechanical properties does not necessarily reduce the driving forces for growth and remodeling. These preliminary findings agree conceptually with clinical observations.

Cell growth describes an essential feature of biological tissues. This growth process may be modeled by using a set of relatively simple governing equations based on the axioms of mass and momentum balance, and using a continuum framework that describes cells and tissues as mixtures of a solid matrix, a solvent and multiple solutes. In this model the mechanics of cell growth is driven by osmotic effects, regulated by the cells' active uptake of solutes and passive uptake of solvent. By accounting for the anisotropy of the cells' cytoskeletal structures or extracellular matrix, as well as external constraints, a wide variety of growing shapes may be produced as illustrated in various examples.

Unlike common engineering materials, living matter can autonomously respond to environmental changes. Living structures can grow stronger, weaker, larger, or smaller within months, weeks, or days as a result of a continuous microstructural turnover and renewal. Hard tissues can adapt by increasing their density and grow strong. Soft tissues can adapt by increasing their volume and grow large. For more than three decades, the mechanics community has actively contributed to understand the phenomena of growth and remodeling from a mechanistic point of view. However, to date, there is no single, unified characterization of growth, which is equally accepted by all scientists in the field. Here we shed light on the continuum modeling of growth and remodeling of living matter, and give a comprehensive overview of historical developments and trends. We provide a state-of-the-art review of current research highlights, and discuss challenges and potential future directions. Using the example of volumetric growth, we illustrate how we can establish and utilize growth theories to characterize the functional adaptation of soft living matter. We anticipate this review to be the starting point for critical discussions and future research in growth and remodeling, with a potential impact on life science and medicine.

Glaucoma is a blinding diseases in which damage to the axons results in loss of retinal ganglion cells. Experimental evidence indicates that chronic intraocular pressure elevation initiates axonal insult at the level of the lamina cribrosa. The lamina cribrosa is a porous collagen structure through which the axons pass on their path from the retina to the brain. Recent experimental studies revealed the extensive structural changes of the lamina cribrosa and its surrounding tissues during the development and progression of glaucoma. In this perspective paper we review the experimental evidence for growth and remodeling mechanisms in glaucoma including adaptation of tissue anisotropy, tissue thickening/thinning, tissue elongation/shortening and tissue migration. We discuss the existing predictive computational approaches that try to elucidate the potential biomechanical basis of theses growth and remodeling mechanisms and highlight open questions, challenges, and avenues for further development.

The electroosmotic flow (EOF) rate in fused silica microchannels is experimentally found to decrease when trace quantities of salts containing the divalent cations Ca(2+) and Mg(2+) are added to a constant ionic strength background electrolytic solution (BGE) flowing in a channel having negatively charged walls. Moreover, the observed effect is quantitatively different for the two ions Ca(2+) and Mg(2+). Since electrostatic interactions are identical for ions of the same valence modeled as point charges, a description of the electric double layer (EDL) based on the Poisson-Boltzmann equation alone cannot account for these experimental observations. New experimental observations on electroosmotic flow in presence of Ca(2+) and Mg(2+) are reported in this work. A site binding model that accounts for the chemical interactions of the BGE ions with the silica surface is developed. The model predictions are in good agreement with the experimental observations on divalent cations as well as data from the literature on how properties such as pH and ionic strength affect electroosmotic flow rates for a BGE with monovalent cations.

In microfluidic devices, it is necessary to propel samples and reagents from one part of the device to another, stir fluids, and detect the presence of chemical and biological targets. Given the small size of these devices, the above tasks are far from trivial. Magnetohydrodynamics (MHD) offers an elegant means to control fluid flow in microdevices without a need for mechanical components. In this paper, we review the theory of MHD for low conductivity fluids and describe various applications of MHD such as fluid pumping, flow control in fluidic networks, fluid stirring and mixing, circular liquid chromatography, thermal reactors, and microcoolers.

Cell and microparticle separation in microfluidic systems has recently gained significant attention in sample preparations for biological and chemical studies. Microfluidic separation is typically achieved by applying differential forces on the target particles to guide them into different paths. This paper reviews basic concepts and novel designs of such microfluidic separators with emphasis on the use of non-inertial force fields, including dielectrophoretic force, optical gradient force, magnetic force, and acoustic primary radiation force. Comparisons of separation performances with discussions on physiological effects and instrumentation issues toward point-of-care devices are provided as references for choosing appropriate separation methods for various applications.