Cardiomyocytes are the functional building blocks of the heart-yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on a homogenized tissue level, assuming that cellular and subcellular structures and processes scale uniformly. Here we present a mathematical and numerical framework for exploring tissue-level cardiac mechanics on a microscale given an explicit three-dimensional geometrical representation of cells embedded in a matrix. We defined a mathematical model over such a geometry and parametrized our model using publicly available data from tissue stretching and shearing experiments. We then used the model to explore mechanical differences between the extracellular and the intracellular space. Through sensitivity analysis, we found the stiffness in the extracellular matrix to be most important for the intracellular stress values under contraction. Strain and stress values were observed to follow a normal-tangential pattern concentrated along the membrane, with substantial spatial variations both under contraction and stretching. We also examined how it scales to larger size simulations, considering multicellular domains. Our work extends existing continuum models, providing a new geometrical-based framework for exploring complex cell-cell and cell-matrix interactions.
Abstract Immature cardiomyocytes, such as those obtained by stem cell differentiation, have been shown to be useful alternatives to mature cardiomyocytes, which are limited in availability and difficult to obtain, for evaluating the behaviour of drugs for treating arrhythmia. In silico models of induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) can be used to simulate the behaviour of the transmembrane potential and cytosolic calcium under drug-treated conditions. Simulating the change in action potentials due to various ionic current blocks enables the approximation of drug behaviour. We used eight machine learning classification models to predict partial block of seven possible ion currents $$ (\textit{I}_{\textit{CaL}},\textit{I}_{\textit{Kr}},\textit{I}_{\textit{to}},\textit{I}_{\textit{K1}},\textit{I}_{\textit{Na}},\textit{I}_{\textit{NaL}} and \textit{I}_{\textit{Ks}}) $$ in a simulated dataset containing nearly 4600 action potentials represented as a paired measure of transmembrane potential and cytosolic calcium. Each action potential was generated under 1 $$ \textit{H}_{\textit{z}} $$ pacing. The Convolutional Neural Network outperformed the other models with an average accuracy of predicting partial ionic current block of 93% in noise-free data and 72% accuracy with 3% added random noise. Our results show that $$ \textit{I}_{\textit{CaL}} $$ and $$ \textit{I}_{\textit{Kr}} $$ current block were classified with high accuracy with and without noise. The classification of $$ \textit{I}_{\textit{to}} $$ , $$ \textit{I}_{\textit{K1}} $$ and $$ \textit{I}_{\textit{Na}} $$ current block showed high accuracy at 0% noise, but showed a significant decrease in accuracy when noise was added. Finally, the accuracy of $$ \textit{I}_{\textit{NaL}} $$ and $$ \textit{I}_{\textit{Ks}} $$ classification were relatively lower than the other current blocks at 0% noise and also showed a significant drop in accuracy when noise was added. In conclusion, these machine learning methods may present a pathway for estimating drug response in adult phenotype cardiac systems, but the data must be sufficiently filtered to remove noise before being used with classifier algorithms.
Computational modeling has increasingly been used to elucidate the effects of heart failure (HF) treatments. Most such models are, however, confined to simulating the acute treatment effects, and do not directly simulate the effects of chronic LV re-modeling (and reverse remodeling). Since left ventricular (LV) remodeling and reverse remodeling are hallmarks of many cardiac diseases and favorable response to HF treatments, the ability to simulate and predict these chronic effects would have significant impact on the use of computational modeling for patient care. Here, we apply a recently proposed reversible cardiac vol-umetric growth model [1] to simulate and predict the chronic effects of an emerging bioinjection therapy that is intended to stiffen the infarct [2].
Abstract In the initial hours following the application of the calcium channel blocker (CCB) nifedipine to microtissues consisting of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), we observe notable variations in the drug’s efficacy. Here, we investigate the possibility that these temporal changes in CCB effects are associated with adaptations in the expression of calcium ion channels in cardiomyocyte membranes. To explore this, we employ a recently developed mathematical model that delineates the regulation of calcium ion channel expression by intracellular calcium concentrations. According to the model, a decline in intracellular calcium levels below a certain target level triggers an upregulation of calcium ion channels. Such an upregulation, if instigated by a CCB, would then counteract the drug’s inhibitory effect on calcium currents. We assess this hypothesis using time-dependent measurements of hiPSC-CMs dynamics and by refining an existing mathematical model of myocyte action potentials incorporating the dynamic nature of the number of calcium ion channels. The revised model forecasts that the CCB-induced reduction in intracellular calcium concentrations leads to a subsequent increase in calcium ion channel expression, thereby attenuating the drug’s overall efficacy. The data and fit models suggests that dynamic changes in cardiac cells in the presence of CCBs may be explainable by induced changes in protein expression, and that this may lead to challenges in understanding calcium based drug effects on the heart unless timings of applications are carefully considered.
Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are an effective tool for studying cardiac function and disease, and hold promise for screening drug effects on human tissue. Changes to motion patterns in these cells are one of the important features to be characterized to understand how an introduced drug or disease may alter the human heart beat. However, quantifying motion accurately and efficiently from optical measurements using microscopy is currently lacking. In this work, we present a unified framework for performing motion analysis on a sequence of microscopically obtained images of tissues consisting of hiPSC-CMs. We provide validation of our developed software using a synthetic test case and show how it can be used to extract displacements and velocities in hiPSC-CM microtissues. Finally, we show how to apply the framework to quantify the effect of an inotropic compound. The described software system is distributed as a python package that is easy to install, well tested and can be integrated into any python workflow.
Abstract Although detailed cell‐based descriptors of cross‐bridge cycling have been applied in finite element (FE) heart models to describe ventricular mechanics, these multiscale models have never been tested rigorously to determine if these descriptors, when scaled up to the organ‐level, are able to reproduce well‐established organ‐level physiological behaviors. To address this void, we here validate a left ventricular (LV) FE model that is driven by a cell‐based cross‐bridge cycling descriptor against key organ‐level heart physiology. The LV FE model was coupled to a closed‐loop lumped parameter circulatory model to simulate different ventricular loading conditions (preload and afterload) and contractilities. We show that our model is able to reproduce a linear end‐systolic pressure volume relationship, a curvilinear end‐diastolic pressure volume relationship and a linear relationship between myocardial oxygen consumption and pressure – volume area. We also show that the validated model can predict realistic LV strain‐time profiles in the longitudinal, circumferential, and radial directions. The predicted strain‐time profiles display key features that are consistent with those measured in humans, such as having similar peak strains, time‐to‐peak‐strain, and a rapid change in strain during atrial contraction at late‐diastole. Our model shows that the myocardial strains are sensitive to not only LV contractility, but also to the LV loading conditions, especially to a change in afterload. This result suggests that caution must be exercised when associating changes in myocardial strain with changes in LV contractility. The methodically validated multiscale model will be used in future studies to understand human heart diseases.
ABSTRACT The specific energy and maximum force required to shear alfalfa stems with a knife and anvil mechanism were determined in a universal testing machine. Subsequently a small rotary cutterhead based on the same type of cutting was evaluated. Specific energy requirement and mean length of cut compared favorably with conventional cutterheads.
In this paper, we describe the application of an integrated electromechanics-growth computational model to simulate the long term effects of cardiac regenerative therapies in a left ventricle (LV). The electromechanics-growth model couples biophysically detailed cellular-based laws that describe the short term events occurring in the excitation-contraction coupling process in the cardiomyocytes, to a phenomenological law that describes the long-term process of growth and remodeling in the cardiac tissue. Two clinically relevant phases depicting the progression and subsequent treatment of heart failure were simulated using this model. These phases are namely, (1) the long-term remodeling process induced by a myocardial infarction and (2) the long-term response following regeneration of the infarct. Our model predictions show that the abnormal myofiber strain values surrounding the infarct can drive the post-infarct LV hypertrophy, whereas a subsequent normalization of the myofiber strain after infarct regeneration can lead to a reduction in the LV size. These findings are consistent with some of the observations found in the experiments and clinical studies of cardiac regenerative therapies.
In order to better locate ischemic regions in the heart using electrical measurements and inverse solutions, we explore the possibility for supplementing BSPM data sets with additional internal electrodes in the esophagus. We investigated whether such internal electrodes closer to the heart's surface could significantly improve the ability to pinpoint ischemic regions. A framework based on exercise ECG testing and a mathematical model for identifying ischemic regions from ECG measurements was implemented to test the effect of potential internal electrodes. This method identifies areas with abnormal perfusion by minimizing the difference between recorded and simulated ECGs. To investigate the effect of the extra electrodes in the esophagus, we computed the location of the ischemic zones with and without the internal electrodes for both synthetic data and using clinically obtained BSPMs. Computations based on pure synthetic data illuminate that, if an ischemic region is close to an electrode in the esophagus, then the use of internal electrodes might improve the result significantly. However, the simulations also indicate that ischemic areas further away from the internal electrodes are not better recovered with the use of such additional ECGs. This study indicates that the use internal electrodes, along with standard BSPMs, might improve the accuracy of the inverse ECG technology.
