The action potential is a pivotal electrical phenomenon that governs the contraction of cardiac muscle cells, known as cardiomyocytes. This rapid shift in membrane potential is orchestrated by the precise movement of ions across the cell membrane through specific ion channels. In the heart, action potentials are indispensable for initiating and coordinating the contractions of cardiac chambers, ensuring effective blood circulation throughout the body. The left ventricle, responsible for propelling oxygenated blood into the aorta and systemic circulation, is particularly critical. Deviations in the left ventricular action potential can result in severe cardiac conditions, including arrhythmias, heart failure, and sudden cardiac death. Consequently, an accurate understanding and modeling of the left ventricular action potential are essential for elucidating the mechanisms underlying these diseases and developing effective treatments. This paper provides a comprehensive overview of methodologies used to simulate the action potential within the left ventricle. It examines the historical evolution of electrophysiological models, foundational theories of cardiac action potentials, and their specific application to the left ventricle. The review encompasses the clinical relevance of these models and an analysis of simulation outcomes. This paper also explores the application of machine learning (ML) to enhance the accuracy and efficiency of action potential calculations within the left ventricle, highlighting various ML techniques and their potential impact on cardiology.

Within the multi-stage process of metastasis, there is a separation of cancer cells, so-called circulating tumor cells (CTCs), from the primary tumor, and their journey to the target organ where they remain. On the way to the target organs, CTCs pass through the circulatory system where they interact with host cells. Recent studies have suggested that platelets have a crucial role in enhancing the survival of circulating tumor cells in the bloodstream and aggravating cancer metastasis. The main physiological function of platelets is to create a blood clot by binding to the injured sites on the vessel to stop bleeding. However, in cancer patients, activated platelets adhere to circulating tumor cells and exacerbate metastatic spreading. To examine the biophysical conditions needed for CTC arrest, we used a custombuilt viscoelastic solid-fluid 2D computational model that enables the calculation of the limiting cases for which CTC will get stacked into the capillary by the influence of platelets. Two representative examples were developed a) cell in narrowing with platelets and b) cell in wide capillary with platelets attached to the cell. By exploring the parameter space, a relationship between the capillary blood pressure gradient and the CTC mechanical properties (size and stiffness) and platelet size, is determined. Based on the results obtained using the presented software and platform, it can be concluded that the platform can be a useful tool in studying biological conditions for CTC arrest, studying the mechanism of interaction between cells and platelets, as well as predicting disease progression.

Huxley's muscle model, originally devised for modeling non-uniform contractions, possesses a noteworthy drawback rooted in its substantial computational demands, particularly evident in the context of multi-scale finite element simulations. In order to address this limitation, we have created surrogate models of Huxley's muscle model. These surrogate models emulate the behavior of the original model while reducing the computational demands in terms of execution time. In this paper, we present the construction of surrogate models using physics-informed neural networks. Besides the precision of neural network predictions, it is also important for the neural network to have a small number of weights in order to be computationally efficient. To optimize the size of the neural network along with the precision of its predictions, we performed Bayesian Optimization. Our physics-informed neural network predicts the probabilities of cross-bridge formation, based on which, force and stiffness can be calculated and used during finite element analysis. In our work, we also present the procedure to integrate a physics-informed neural network into the finite element analysis framework at the micro-level of multi-scale simulation.

Most cardiac diseases and disorders occur in the left ventricle. Numerical methods can give an insight into the mechanical response of the left ventricle under different conditions, before the execution of clinical trials and experiments. Before we use the finite element method to analyze the behavior of the left ventricle, a geometrical model has to be generated. In our work, we generated a left ventricle model from echocardiographic data. We manually extracted contours of the inner and outer surface of the left ventricle and applied our algorithm to generate the 3D model. This semi-automatic model generation enables the usage of patient-specific geometries for finite element analysis of the left ventricle.

The heart is a complex organ which produces mechanical force needed for the blood flow. Electrical signals are transformed into active stresses which contract the heart muscle and pump the blood out from the left ventricle. Therefore, comprehensive numerical procedure has to be established in order to simulate this process and to investigate the effects of different drugs on heart behavior. We here present application of the finite element (FE) computational model for simulation of heart beat cycle of the parametric left ventricle model. We are using Hunter excitation model for active, and direct experimental constitute relations for passive mechanical stresses. Additionally, computational model includes hysteretic and compressible behavior according to the experimental investigations. Applicability of our computational model is demonstrated using parametric left ventricle model which includes inlet mitral and outlet aortic valve cross-sections. With using different boundary conditions and prescribed values, this model has potential to mimic the effects of different drugs on heart beat cycle.

In this report we present basic steps in the 3D reconstruction process of DICOM images and application of our finite element (FE) numerical procedure for loose coupling solid-fluid interaction, to simulate a complete heartbeat cycle for a realistic model of the left heart side. Passive mechanical stresses are calculated using an orthotropic material model based on the experimental investigation of passive material properties of the myocardium, while active stresses are calculated using the Hunter material model. The basic equations for solid mechanics, fluid dynamics, and muscle activation are summarized and model applicability is illustrated on a complex realistic model which includes a left atrium, ventricle, mitral and aortic valves (which serve as fluid domain) coupled with solid wall with realistic fiber directions.

In this report we implement our smeared model for electrical and calcium concentration field within a heart tissue and couple it to muscle mechanics. The basic equations are summarized and applicability of this model, coupling neural excitation and mechanics, is illustrated on one numerical example.

In this report we summarize computational models for convective and diffusive drug transport within small blood vessels (capillaries) and tissue. The presented methodology is primarily focused on drug transport via micro-nanoparticles designed for nanotherapeutics in cancer. Our original multiscale hierarchical models couple nanoscale molecular dynamics (MD) and macroscale continuum finite element (FE) discretization. The convective part relies on a FE solution of the solid-fluid interaction problem of moving bodies within fluid, with a remeshing procedure. In diffusion, MD is used to evaluate the effective diffusivity of a porous continuum, where the physico-chemical interaction between transported molecules and microstructural surface is included, and the mass release curves are considered as the constitutive curves. Several representative examples illustrate effectiveness of our methodology and developed software PAK.