Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

Pressure Dependence of Solid Electrolyte Ionic Conductivity: A Particle Dynamics Study

The search for safe, reliable, and compact high-capacity energy storage devices has led to increased interest in all-solid-state battery research. The use of solid electrolytes provides enhanced safety and durability due to their reduced flammability and increased mechanical strength compared to organic liquid electrolytes. Still, the use of solid electrolytes remains challenging. A significant issue is their generally low Li-ion conductivity, which depends on the lattice diffusion of Li ions through the solid phase, as well as on the limited contact area between the electrolyte particles. While the lattice diffusion can be addressed through the chemistry of the solid electrolyte material, the contact area is a mechanical and structural problem of packing and compression of the electrolyte particles depending on their size and shape. This work studies the effect of pressurization on the electrolyte conductivity exploring cases of low as well as high grain boundary (GB) conductivity, compared to the bulk conductivity. Scaling dependence, σ ∼ P^η, of the conductivity σ with pressure P is revealed. For an idealized electrolyte represented as spheres in hexagonal closely packed configuration, η = 2/3 and η = 1/3 have been theoretically calculated for the two cases of low and high GB conductivity, respectively. For randomly packed spheres, the equivalent exponent values were numerically estimated to be approximately 3/4 and 1/2, respectively, which are higher than the closed packed values due to the additional decrease of porosity with the increase in pressure. As demonstrated in the study, experimental measurement of η can indicate which type of bulk or GB conductivity is dominant in a particular electrolyte powder and could be used in addition to electrochemical impedance spectroscopy measurements.

A mathematical model that integrates cardiac electrophysiology, mechanics, and fluid dynamics: Application to the human left heart

We propose a mathematical and numerical model for the simulation of the heart function that couples cardiac electrophysiology, active and passive mechanics and hemodynamics, and includes reduced models for cardiac valves and the circulatory system. Our model accounts for the major feedback effects among the different processes that characterize the heart function, including electro-mechanical and mechano-electrical feedback as well as force-strain and force-velocity relationships. Moreover, it provides a three-dimensional representation of both the cardiac muscle and the hemodynamics, coupled in a fluid-structure interaction (FSI) model. By leveraging the multiphysics nature of the problem, we discretize it in time with a segregated electrophysiology-force generation-FSI approach, allowing for efficiency and flexibility in the numerical solution. We employ a monolithic approach for the numerical discretization of the FSI problem. We use finite elements for the spatial discretization of partial differential equations. We carry out a numerical simulation on a realistic human left heart model, obtaining results that are qualitatively and quantitatively in agreement with physiological ranges and medical images.

A parametric blueprint for optimum cochlear outer hair cell design

The present work examines the hypothesis that cochlear outer hair cell (OHC) properties vary in precise proportions along the tonotopic map to optimize electromechanical power conversion. We tested this hypothesis using a very simple model of a single isolated OHC driving a mechanical load. Results identify three non-dimensional ratios that are predicted to optimize power conversion: the ratio of the resistive-capacitive (RC) corner to the characteristic frequency (CF), the ratio of nonlinear to linear capacitance and the ratio of OHC stiffness to cochlear load stiffness. Optimum efficiency requires all three ratios to be universal constants, independent of CF and species. The same ratios are cardinal control parameters that maximize power output by positioning the OHC operating point on the edge of a dynamic instability. Results support the hypothesis that OHC properties evolved to optimize electro-mechanical power conversion. Identification of the RC corner frequency as a control parameter reveals a powerful mechanism used by medial olivocochlear efferent system to control OHC power output. Results indicate the upper-frequency limit of OHC power output is not constrained by the speed of the motor itself but instead is probably limited by the size of the nucleus and membrane surface area available for ion-channel expression.

Osteochondral Repair and Electromechanical Evaluation of Custom 3D Scaffold Microstructured by Direct Laser Writing Lithography

OBJECTIVE

The objective of this study was to assess a novel 3D microstructured scaffold seeded with allogeneic chondrocytes (cells) in a rabbit osteochondral defect model.

DESIGN

Direct laser writing lithography in pre-polymers was employed to fabricate custom silicon-zirconium containing hybrid organic-inorganic (HOI) polymer SZ2080 scaffolds of a predefined morphology. Hexagon-pored HOI scaffolds were seeded with chondrocytes (cells), and tissue-engineered cartilage biocompatibility, potency, efficacy, and shelf-life in vitro was assessed by morphological, ELISA (enzyme-linked immunosorbent assay) and PCR (polymerase chain reaction) analysis. Osteochondral defect was created in the weight-bearing area of medial femoral condyle for in vivo study. Polymerized fibrin was added to every defect of 5 experimental groups. Cartilage repair was analyzed after 6 months using macroscopical (Oswestry Arthroscopy Score [OAS]), histological, and electromechanical quantitative potential (QP) scores. Collagen scaffold (CS) was used as a positive comparator for in vitro and in vivo studies.

RESULTS

Type II collagen gene upregulation and protein secretion was maintained up to 8 days in seeded HOI. In vivo analysis revealed improvement in all scaffold treatment groups. For the first time, electromechanical properties of a cellular-based scaffold were analyzed in a preclinical study. Cell addition did not enhance OAS but improved histological and QP scores in HOI groups.

CONCLUSIONS

HOI material is biocompatible for up to 8 days in vitro and is supportive of cartilage formation at 6 months in vivo. Electromechanical measurement offers a reliable quality assessment of repaired cartilage.

Non-invasive Electroarthrography Measures Load-Induced Cartilage Streaming Potentials via Electrodes Placed on Skin Surrounding an Articular Joint

OBJECTIVE

We aimed to demonstrate that electroarthrography (EAG) measures streaming potentials originating in the cartilage extracellular matrix during load bearing through electrodes adhered to skin surrounding an articular joint.

DESIGN

Equine metacarpophalangeal joints were subjected to simulated physiological loads while (1) replacing synovial fluid with immersion buffers of different electrolyte concentrations and (2) directly degrading cartilage with trypsin.

RESULTS

An inverse relationship between ionic strength and EAG coefficient was detected. Compared to native synovial fluid, EAG coefficients increased (P < 0.05) for 5 of 6 electrodes immersed in 0.1X phosphate-buffered saline (PBS) (0.014 M NaCl), decreased (P < 0.05) for 4 of 6 electrodes in 1X PBS (0.14 M NaCl), and decreased (P < 0.05) for all 6 electrodes in 10X PBS (1.4 M NaCl). This relationship corresponds to similar studies where streaming potentials were directly measured on cartilage. EAG coefficients, obtained after trypsin degradation, were reduced (P < 0.05) in 6 of 8, and 7 of 8 electrodes, during simulated standing and walking, respectively. Trypsin degradation was confirmed by direct cartilage assessments. Streaming potentials, measured by directly contacting cartilage, indicated lower cartilage stiffness (P < 10-5). Unconfined compression data revealed reduced Em, representing proteoglycan matrix stiffness (P = 0.005), no change in Ef, representing collagen network stiffness (P = 0.15), and no change in permeability (P = 0.24). Trypsin depleted proteoglycan as observed by both dimethylmethylene blue assay (P = 0.0005) and safranin-O stained histological sections.

CONCLUSION

These data show that non-invasive EAG detects streaming potentials produced by cartilage during joint compression and has potential to become a diagnostic tool capable of detecting early cartilage degeneration.

Intercalated water mediated electromechanical response of graphene oxide films on flexible substrates

The confinement of water between sub-nanometer bounding walls of layered two-dimensional materials has generated tremendous interest. Here, we examined the influence of confined water on the mechanical and electromechanical response of graphene oxide films, prepared with variable oxidative states, casted on polydimethylsiloxane substrates. These films were subjected to uniaxial strain under controlled humid environments (5 to 90% RH), while dc transport studies were performed in tandem. Straining resulted in the formation of quasi-periodic linear crack arrays. The extent of water intercalation determined the density of cracks formed in the system thereby, governing the electrical conductance of the films under strain. The crack density at 5% strain, varied from 0 to 3.5 cracks mm^-1for hydrated films and 8 to 22 cracks mm^-1for dry films, across films with different high oxidative states. Correspondingly, the overall change in the electrical conductance at 5% strain was observed to be ∼5 to 20 folds for hydrated films and ∼20 to 35 folds for the dry films. The results were modeled with a decrease in the in-plane elastic modulus of the film upon water intercalation, which was attributed to the variation in the nature of hydrogen bonding network in graphene oxide lamellae.

Autonomous Experiments in Scanning Probe Microscopy and Spectroscopy: Choosing Where to Explore Polarization Dynamics in Ferroelectrics

Polarization dynamics in ferroelectric materials are explored via automated experiment in piezoresponse force microscopy/spectroscopy (PFM/S). A Bayesian optimization (BO) framework for imaging is developed, and its performance for a variety of acquisition and pathfinding functions is explored using previously acquired data. The optimized algorithm is then deployed on an operational scanning probe microscope (SPM) for finding areas of large electromechanical response in a thin film of PbTiO₃, with results showing that, with just 20% of the area sampled, most high-response clusters were captured. This approach can allow performing more complex spectroscopies in SPM that were previously not possible due to time constraints and sample stability. Improvements to the framework to enable the incorporation of more prior information and improve efficiency further are modeled and discussed.

Mutually Reinforced Polymer-Graphene Bilayer Membranes for Energy-Efficient Acoustic Transduction

Graphene holds promise for thin, ultralightweight, and high-performance nanoelectromechanical transducers. However, graphene-only devices are limited in size due to fatigue and fracture of suspended graphene membranes. Here, a lightweight, flexible, transparent, and conductive bilayer composite of polyetherimide and single-layer graphene is prepared and suspended on the centimeter scale with an unprecedentedly high aspect ratio of 10⁵ . The coupling of the two components leads to mutual reinforcement and creates an ultrastrong membrane that supports 30 000 times its own weight. Upon electromechanical actuation, the membrane pushes a massive amount of air and generates high-quality acoustic sound. The energy efficiency is ≈10-100 times better than state-of-the-art electrodynamic speakers. The bilayer membrane's combined properties of electrical conductivity, mechanical strength, optical transparency, thermal stability, and chemical resistance will promote applications in electronics, mechanics, and optics.

Electromechanically Active As-Electrospun Polystyrene Fiber Mat: Significantly High Quasistatic/Dynamic Electromechanical Response and Theoretical Modeling

Flexible and lightweight pressure sensors have attracted tremendous attention as a promising component of wearable biological motion sensors and artificial electronic skins. Here, the electromechanical response of as-electrospun fiber mats composed of a commodity polymer, atactic polystyrene, which can be applied in low-cost/large-area, flexible, and lightweight pressure sensors is demonstrated. The fiber mat demonstrates a significantly high apparent converse piezoelectric constant of >30 000 pm V^-1 under static measurement and ≈13 000 pm V^-1 even at a high frequency of 1 kHz. The first theoretical model to explain the unique electromechanical response is constructed, which reveals that the softness and moderate charge of the fiber mat are the reasons for the significantly high electromechanical response. Further, apparent piezoelectric constants obtained by direct measurement are lower than those obtained by the converse measurement, which is attributed to the densification and hardening of the fiber mat due to prepressure applied in direct measurement. These findings are likely to serve as a milestone for the development of large-area, flexible, and lightweight pressure sensors at low cost, as well as highly movable actuators like optical modulators without a substantial mechanical load.

High-Resolution Optical Measurement of Cardiac Restitution, Contraction, and Fibrillation Dynamics in Beating vs. Blebbistatin-Uncoupled Isolated Rabbit Hearts

Optical mapping is a high-resolution fluorescence imaging technique, that uses voltage- or calcium-sensitive dyes to visualize electrical excitation waves on the heart surface. However, optical mapping is very susceptible to the motion of cardiac tissue, which results in so-called motion artifacts in the fluorescence signal. To avoid motion artifacts, contractions of the heart muscle are typically suppressed using pharmacological excitation-contraction uncoupling agents, such as Blebbistatin. The use of pharmacological agents, however, may influence cardiac electrophysiology. Recently, it has been shown that numerical motion tracking can significantly reduce motion-related artifacts in optical mapping, enabling the simultaneous optical measurement of cardiac electrophysiology and mechanics. Here, we combine ratiometric optical mapping with numerical motion tracking to further enhance the robustness and accuracy of these measurements. We evaluate the method's performance by imaging and comparing cardiac restitution and ventricular fibrillation (VF) dynamics in contracting, non-working vs. Blebbistatin-arrested Langendorff-perfused rabbit hearts (N = 10). We found action potential durations (APD) to be, on average, 25 ± 5% shorter in contracting hearts compared to hearts uncoupled with Blebbistatin. The relative shortening of the APD was found to be larger at higher frequencies. VF was found to be significantly accelerated in contracting hearts, i.e., 9 ± 2Hz with Blebbistatin and 15 ± 4Hz without Blebbistatin, and maintained a broader frequency spectrum. In contracting hearts, the average number of phase singularities was N_PS = 11 ± 4 compared to N_PS = 6 ± 3 with Blebbistatin during VF on the anterior ventricular surface. VF inducibility was reduced with Blebbistatin. We found the effect of Blebbistatin to be concentration-dependent and reversible by washout. Aside from the electrophysiological characterization, we also measured and analyzed cardiac motion. Our findings may have implications for the interpretation of optical mapping data, and highlight that physiological conditions, such as oxygenation and metabolic demand, must be carefully considered in ex vivo imaging experiments.

Novel measures of left ventricular electromechanical discoordination predict clinical outcomes in children with pulmonary arterial hypertension

Adverse ventricle-ventricle interaction and resultant left ventricular (LV) dysfunction are a recognized pathophysiological component of disease progression in pulmonary arterial hypertension (PAH) and can be associated with electrical and mechanical dyssynchrony. The purpose of this study was to investigate the clinical and mechanistic implications of LV electromechanical dyssynchrony in children with PAH by using novel systolic stretch and diastolic relaxation discoordination indexes derived noninvasively from cardiac MRI (CMR). In children with PAH referred for CMR (n = 64) and healthy controls (n = 20), we calculated two novel markers of ventricular discoordination, systolic stretch fraction (SSF) and diastolic relaxation fraction (DRF). SSF and DRF were evaluated with respect to 1) electrical dyssynchrony, 2) functional status, and 3) composite clinical outcomes. SSF was increased in patients with PAH compared with controls (P = 0.004). There was no difference in DRF between PAH and control groups. There were no differences between groups in standard mechanical dyssynchrony and LV global circumferential strain. Increased SSF was associated with greater electrical dyssynchrony (QRS duration) as well as worse WHO functional class. SSF, DRF, mechanical dyssynchrony, and right ventricular (RV) volumes were prognostic for worse clinical outcomes. LV dyssynchrony indexes are altered in pediatric patients with PAH compared with controls in proportion with greater degrees of RV dilation. Patients with PAH with greater dyssynchrony have worse clinical outcomes. RV-induced increased LV electromechanical dyssynchrony therefore may be an important link in the causal pathway from PAH to clinically significant LV dysfunction. Since dyssynchrony could precede overt LV dysfunction, addition of ventricular synchrony analysis to CMR postprocessing protocols may be of clinical benefit.NEW & NOTEWORTHY We demonstrate that left ventricular discoordination indexes are altered in pediatric patients with pulmonary arterial hypertension compared with controls and pediatric patients with pulmonary arterial hypertension with greater dyssynchrony have worse clinical outcomes. Furthermore, there is evidence for the mechanism of right ventricular-induced left ventricular discoordination to include a combination of delayed early systolic electromechanical activation, late-systolic septal shift, and prolonged, postsystolic septal thickening.

Stumbling through the Research Wilderness, Standard Methods To Shine Light on Electrically Conductive Nanocomposites for Future Healthcare Monitoring

Electrically conductive nanocomposites are an exciting ever-expanding area of research that has yielded many versatile technologies for wearable health devices. Acting as strain-sensing materials, real-time medical diagnostic tools based on these materials may very well lead to a golden age of healthcare. Currently, the goal in research is to create a material that simultaneously has both a large gauge factor (G) and sensing range. However, a weakness in the area of electromechanical research is the lack of standardization in the reporting of the figure of merit (i.e., G) and the need for other intrinsic metrics to give researchers a more complete view of the research landscape of resistive-type sensors. A paradigm shift in the way in which data are reported is required, to push research in the right direction and to facilitate achieving research goals. Here, we report a standardized method for reporting strain-sensing performance and the introduction of the working factor (W) and the Young's modulus (Y) of a material as figures of merit for sensing materials. Using this standard method, we can define the benchmarks for an optimum sensing material (G > 7, W > 1, Y < 300 kPa) using limits set by standard commercial materials and the human body. Using extrapolated data from 200 publications normalized to this standard method, we can review what composite types meet these benchmark limits, what governs composite performances, the literary trends in composites, and the future prospects of research.

Interaction of the Mechano-Electrical Feedback With Passive Mechanical Models on a 3D Rat Left Ventricle: A Computational Study

In this paper, we are investigating the interaction between different passive material models and the mechano-electrical feedback (MEF) in cardiac modeling. Various types of passive mechanical laws (nearly incompressible/compressible, polynomial/exponential-type, transversally isotropic/orthotropic material models) are integrated in a fully coupled electromechanical model in order to study their specific influence on the overall MEF behavior. Our computational model is based on a three-dimensional (3D) geometry of a healthy rat left ventricle reconstructed from magnetic resonance imaging (MRI). The electromechanically coupled problem is solved using a fully implicit finite element-based approach. The effects of different passive material models on the MEF are studied with the help of numerical examples. It turns out that there is a significant difference between the behavior of the MEF for compressible and incompressible material models. Numerical results for the incompressible models exhibit that a change in the electrophysiology can be observed such that the transmembrane potential (TP) is unable to reach the resting state in the repolarization phase, and this leads to non-zero relaxation deformations. The most significant and strongest effects of the MEF on the rat cardiac muscle response are observed for the exponential passive material law.

Additive Manufacturing of 3D-Architected Multifunctional Metal Oxides

Additive manufacturing (AM) of complex three-dimensional (3D) metal oxides at the micro- and nanoscales has attracted considerable attention in recent years. State-of-the-art techniques that use slurry-based or organic-inorganic photoresins are often hampered by challenges in resin preparation and synthesis, and/or by the limited resolution of patterned features. A facile process for fabricating 3D-architected metal oxides via the use of an aqueous metal-ion-containing photoresin is presented. The efficacy of this process, which is termed photopolymer complex synthesis, is demonstrated by creating nanoarchitected zinc oxide (ZnO) architectures with feature sizes of 250 nm, by first patterning a zinc-ion-containing aqueous photoresin using two-photon lithography and subsequently calcining them at 500 ºC. Transmission electron microscopy (TEM) analysis reveals their microstructure to be nanocrystalline ZnO with grain sizes of 5.1 ± 1.6 nm. In situ compression experiments conducted in a scanning electron microscope show an emergent electromechanical response: a 200 nm mechanical compression of an architected ZnO structure results in a voltage drop of 0.52 mV. This photopolymer complex synthesis provides a pathway to easily create arbitrarily shaped 3D metal oxides that could enable previously impossible devices and smart materials.

A Contemporary Look at Biomechanical Models of Myocardium

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.

GEMS: A Fully Integrated PETSc-Based Solver for Coupled Cardiac Electromechanics and Bidomain Simulations

Cardiac contraction is coordinated by a wave of electrical excitation which propagates through the heart. Combined modeling of electrical and mechanical function of the heart provides the most comprehensive description of cardiac function and is one of the latest trends in cardiac research. The effective numerical modeling of cardiac electromechanics remains a challenge, due to the stiffness of the electrical equations and the global coupling in the mechanical problem. Here we present a short review of the inherent assumptions made when deriving the electromechanical equations, including a general representation for deformation-dependent conduction tensors obeying orthotropic symmetry, and then present an implicit-explicit time-stepping approach that is tailored to solving the cardiac mono- or bidomain equations coupled to electromechanics of the cardiac wall. Our approach allows to find numerical solutions of the electromechanics equations using stable and higher order time integration. Our methods are implemented in a monolithic finite element code GEMS (Ghent Electromechanics Solver) using the PETSc library that is inherently parallelized for use on high-performance computing infrastructure. We tested GEMS on standard benchmark computations and discuss further development of our software.

A Multiphysics Biventricular Cardiac Model: Simulations With a Left-Ventricular Assist Device

Computational models have become essential in predicting medical device efficacy prior to clinical studies. To investigate the performance of a left-ventricular assist device (LVAD), a fully-coupled cardiac fluid-electromechanics finite element model was developed, incorporating electrical activation, passive and active myocardial mechanics, as well as blood hemodynamics solved simultaneously in an idealized biventricular geometry. Electrical activation was initiated using a simplified Purkinje network with one-way coupling to the surrounding myocardium. Phenomenological action potential and excitation-contraction equations were adapted to trigger myocardial contraction. Action potential propagation was formulated within a material frame to emulate gap junction-controlled propagation, such that the activation sequence was independent of myocardial deformation. Passive cardiac mechanics were governed by a transverse isotropic hyperelastic constitutive formulation. Blood velocity and pressure were determined by the incompressible Navier-Stokes formulations with a closed-loop Windkessel circuit governing the circulatory load. To investigate heart-LVAD interaction, we reduced the left ventricular (LV) contraction stress to mimic a failing heart, and inserted a LVAD cannula at the LV apex with continuous flow governing the outflow rate. A proportional controller was implemented to determine the pump motor voltage whilst maintaining pump motor speed. Following LVAD insertion, the model revealed a change in the LV pressure-volume loop shape from rectangular to triangular. At higher pump speeds, aortic ejection ceased and the LV decompressed to smaller end diastolic volumes. After multiple cycles, the LV cavity gradually collapsed along with a drop in pump motor current. The model was therefore able to predict ventricular collapse, indicating its utility for future development of control algorithms and pre-clinical testing of LVADs to avoid LV collapse in recipients.

Bilayer Implants: Electromechanical Assessment of Regenerated Articular Cartilage in a Sheep Model

OBJECTIVE

To compare the regenerative capacity of 2 distinct bilayer implants for the restoration of osteochondral defects in a preliminary sheep model.

METHODS

Critical sized osteochondral defects were treated with a novel biomimetic poly-ε-caprolactone (PCL) implant (Treatment No. 2; n = 6) or a combination of Chondro-Gide and Orthoss (Treatment No. 1; n = 6). At 19 months postoperation, repair tissue (n = 5 each) was analyzed for histology and biochemistry. Electromechanical mappings (Arthro-BST) were performed ex vivo.

RESULTS

Histological scores, electromechanical quantitative parameter values, dsDNA and sGAG contents measured at the repair sites were statistically lower than those obtained from the contralateral surfaces. Electromechanical mappings and higher dsDNA and sGAG/weight levels indicated better regeneration for Treatment No. 1. However, these differences were not significant. For both treatments, Arthro-BST revealed early signs of degeneration of the cartilage surrounding the repair site. The International Cartilage Repair Society II histological scores of the repair tissue were significantly higher for Treatment No. 1 (10.3 ± 0.38 SE) compared to Treatment No. 2 (8.7 ± 0.45 SE). The parameters cell morphology and vascularization scored highest whereas tidemark formation scored the lowest.

CONCLUSION

There was cell infiltration and regeneration of bone and cartilage. However, repair was incomplete and fibrocartilaginous. There were no significant differences in the quality of regeneration between the treatments except in some histological scoring categories. The results from Arthro-BST measurements were comparable to traditional invasive/destructive methods of measuring quality of cartilage repair.

A New MRI-Based Model of Heart Function with Coupled Hemodynamics and Application to Normal and Diseased Canine Left Ventricles

A methodology for the simulation of heart function that combines an MRI-based model of cardiac electromechanics (CE) with a Navier–Stokes-based hemodynamics model is presented. The CE model consists of two coupled components that simulate the electrical and the mechanical functions of the heart. Accurate representations of ventricular geometry and fiber orientations are constructed from the structural magnetic resonance and the diffusion tensor MR images, respectively. The deformation of the ventricle obtained from the electromechanical model serves as input to the hemodynamics model in this one-way coupled approach via imposed kinematic wall velocity boundary conditions and at the same time, governs the blood flow into and out of the ventricular volume. The time-dependent endocardial surfaces are registered using a diffeomorphic mapping algorithm, while the intraventricular blood flow patterns are simulated using a sharp-interface immersed boundary method-based flow solver. The utility of the combined heart-function model is demonstrated by comparing the hemodynamic characteristics of a normal canine heart beating in sinus rhythm against that of the dyssynchronously beating failing heart. We also discuss the potential of coupled CE and hemodynamics models for various clinical applications.

An electromechanical model of neuronal dynamics using Hamilton's principle

Damage of the brain may be caused by mechanical loads such as penetration, blunt force, shock loading from blast, and by chemical imbalances due to neurological diseases and aging that trigger not only neuronal degeneration but also changes in the mechanical properties of brain tissue. An understanding of the interconnected nature of the electro-chemo-mechanical processes that result in brain damage and ultimately loss of functionality is currently lacking. While modern mathematical models that focus on how to link brain mechanics to its biochemistry are essential in enhancing our understanding of brain science, the lack of experimental data required by these models as well as the complexity of the corresponding computations render these models hard to use in clinical applications. In this paper we propose a unified variational framework for the modeling of neuronal electromechanics. We introduce a constrained Lagrangian formulation that takes into account Newton's law of motion of a linear viscoelastic Kelvin-Voigt solid-state neuron as well as the classic Hodgkin-Huxley equations of the electronic neuron. The system of differential equations describing neuronal electromechanics is obtained by applying Hamilton's principle. Numerical simulations of possible damage dynamics in neurons will be presented.

Toward GPGPU accelerated human electromechanical cardiac simulations

In this paper, we look at the acceleration of weakly coupled electromechanics using the graphics processing unit (GPU). Specifically, we port to the GPU a number of components of CHeart--a CPU-based finite element code developed for simulating multi-physics problems. On the basis of a criterion of computational cost, we implemented on the GPU the ODE and PDE solution steps for the electrophysiology problem and the Jacobian and residual evaluation for the mechanics problem. Performance of the GPU implementation is then compared with single core CPU (SC) execution as well as multi-core CPU (MC) computations with equivalent theoretical performance. Results show that for a human scale left ventricle mesh, GPU acceleration of the electrophysiology problem provided speedups of 164 × compared with SC and 5.5 times compared with MC for the solution of the ODE model. Speedup of up to 72 × compared with SC and 2.6 × compared with MC was also observed for the PDE solve. Using the same human geometry, the GPU implementation of mechanics residual/Jacobian computation provided speedups of up to 44 × compared with SC and 2.0 × compared with MC.

Computational modeling of chemo-electro-mechanical coupling: a novel implicit monolithic finite element approach

Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of 4 days on a standard desktop computer.

A fully implicit finite element method for bidomain models of cardiac electromechanics

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes.

Review on the modeling of electrostatic MEMS

Electrostatic-driven microelectromechanical systems devices, in most cases, consist of couplings of such energy domains as electromechanics, optical electricity, thermoelectricity, and electromagnetism. Their nonlinear working state makes their analysis complex and complicated. This article introduces the physical model of pull-in voltage, dynamic characteristic analysis, air damping effect, reliability, numerical modeling method, and application of electrostatic-driven MEMS devices.