Smeared multiscale finite element model for electrophysiology and ionic transport in biological tissue

Oscillatory phenomena in electrophysiological networks: The coupling between cell bioelectricity and transcription

Morphogenetic regulation during embryogenesis and regeneration rely on information transfer and coordination between different regions. Here, we explore theoretically the coupling between bioelectrical and transcriptional oscillations at the individual cell and multicellular levels. The simulations, based on a set of ion channels and intercellular gap junctions, show that bioelectrical and transcriptional waves can electrophysiologically couple distant regions of a model network in phase and antiphase oscillatory states that include synchronization phenomena. In this way, different multicellular regionalizations can be encoded by cell potentials that oscillate between depolarized and polarized states, thus allowing a spatio-temporal coding. Because the electric potential patterns characteristic of development and regeneration are correlated with the spatial distributions of signaling ions and molecules, bioelectricity can act as a template for slow biochemical signals following a hierarchy of experimental times. In particular, bioelectrical gradients that couple cell potentials to transcription rates give to each single cell a rough idea of its location in the multicellular ensemble, thus controlling local differentiation processes that switch on and off crucial parts of the genome.

An Insight into Perfusion Anisotropy within Solid Murine Lung Cancer Tumors

Blood vessels are essential for maintaining tumor growth, progression, and metastasis, yet the tumor vasculature is under a constant state of remodeling. Since the tumor vasculature is an attractive therapeutic target, there is a need to predict the dynamic changes in intratumoral fluid pressure and velocity that occur across the tumor microenvironment (TME). The goal of this study was to obtain insight into perfusion anisotropy within lung tumors. To achieve this goal, we used the perfusion marker Hoechst 33342 and vascular endothelial marker CD31 to stain tumor sections from C57BL/6 mice harboring Lewis lung carcinoma tumors on their flank. Vasculature, capillary diameter, and permeability distribution were extracted at different time points along the tumor growth curve. A computational model was generated by applying a unique modeling approach based on the smeared physical fields (Kojic Transport Model, KTM). KTM predicts spatial and temporal changes in intratumoral pressure and fluid velocity within the growing tumor. Anisotropic perfusion occurs within two domains: capillary and extracellular space. Anisotropy in tumor structure causes the nonuniform distribution of pressure and fluid velocity. These results provide insights regarding local vascular distribution for optimal drug dosing and delivery to better predict distribution and duration of retention within the TME.

On the generality of the finite element modeling physical fields in biological systems by the multiscale smeared concept (Kojic transport model)

The biomechanical and biochemical processes in the biological systems of living organisms are extremely complex. Advances in understanding these processes are mainly achieved by laboratory and clinical investigations, but in recent decades they are supported by computational modeling. Besides enormous efforts and achievements in this modeling, there still is a need for new methods that can be used in everyday research and medical practice. In this report, we give a view of the generality of the finite element methodology introduced by the first author and supported by his collaborators. It is based on the multiscale smeared physical fields, termed as Kojic Transport Model (KTM), published in several journal papers and summarized in a recent book (Kojic et al., 2022) [1]. We review relevant literature to demonstrate the distinctions and advantages of our methodology and indicate possible further applications. We refer to our published results by a selection of a few examples which include modeling of partitioning, blood flow, molecular transport within the pancreas, multiscale-multiphysics model of coupling electrical field and ion concentration, and a model of convective-diffusive transport within the lung parenchyma. Two new examples include a model of convective-diffusive transport within a growing tumor, and drug release from nanofibers with fiber degradation.

Cellular communication among smooth muscle cells: The role of membrane potential via connexins

Communication via action potentials among neurons has been extensively studied. However, effective communication without action potentials is ubiquitous in biological systems, yet it has received much less attention in comparison. Multi-cellular communication among smooth muscles is crucial for regulating blood flow, for example. Understanding the mechanism of this non-action potential communication is critical in many cases, like synchronization of cellular activity, under normal and pathological conditions. In this paper, we employ a multi-scale asymptotic method to derive a macroscopic homogenized bidomain model from the microscopic electro-neutral (EN) model. This is achieved by considering different diffusion coefficients and incorporating nonlinear interface conditions. Subsequently, the homogenized macroscopic model is used to investigate communication in multi-cellular tissues. Our computational simulations reveal that the membrane potential of syncytia, formed by interconnected cells via connexins, plays a crucial role in propagating oscillations from one region to another, providing an effective means for fast cellular communication. Statement of Significance: In this study, we investigated cellular communication and ion transport in vascular smooth muscle cells, shedding light on their mechanisms under normal and abnormal conditions. Our research highlights the potential of mathematical models in understanding complex biological systems. We developed effective macroscale electro-neutral bi-domain ion transport models and examined their behavior in response to different stimuli. Our findings revealed the crucial role of connexinmediated membrane potential changes and demonstrated the effectiveness of cellular communication through syncytium membranes. Despite some limitations, our study provides valuable insights into these processes and emphasizes the importance of mathematical modeling in unraveling the complexities of cellular communication and ion transport.

SILICOFCM platform, multiscale modeling of left ventricle from echocardiographic images and drug influence for cardiomyopathy disease

BACKGROUND AND OBJECTIVE

In silico clinical trials are the future of medicine and virtual testing and simulation are the future of medical engineering. The use of a computational platform can reduce costs and time required for developing new models of medical devices and drugs. The computational platform, which is one of the main results of the SILICOFCM project, was developed using state-of-the-art finite element modeling for macro simulation of fluid-structure interaction with micro modeling at the molecular level for drug interaction with the cardiac cells. SILICOFCM platform is using for risk prediction and optimal drug therapy of familial cardiomyopathy in a specific patient.

METHODS

In order to obtain 3D image reconstruction, the U-net architecture was used to determine geometric parameters for the left ventricle which were extracted from the echocardiographic apical and M-mode views. A micro-mechanics cellular model which includes three kinetic processes of sarcomeric proteins interactions was developed. It allows simulation of the drugs which are divided into three major groups defined by the principal action of each drug. Fluid-solid coupling for the left ventricle was presented. A nonlinear material model of the heart wall that was developed by using constitutive curves which include the stress-strain relationship was used.

RESULTS

The results obtained with the parametric model of the left ventricle where pressure-volume (PV) diagrams depend on the change of Ca2+ were presented. It directly affects the ejection fraction. The presented approach with the variation of the left ventricle (LV) geometry and simulations which include the influence of different parameters on the PV diagrams are directly interlinked with drug effects on the heart function. It includes different drugs such as Entresto and Digoxin that directly affect the cardiac PV diagrams and ejection fraction.

CONCLUSIONS

Computational platforms such as the SILICOFCM platform are novel tools for risk prediction of cardiac disease in a specific patient that will certainly open a new avenue for in silico clinical trials in the future.

Preparation and modeling of three-layered PCL/PLGA/PCL fibrous scaffolds for prolonged drug release

The authors present the preparation procedure and a computational model of a three‐layered fibrous scaffold for prolonged drug release. The scaffold, produced by emulsion/sequential electrospinning, consists of a poly(d,l-lactic-co-glycolic acid) (PLGA) fiber layer sandwiched between two poly(ε-caprolactone) (PCL) layers. Experimental results of drug release rates from the scaffold are compared with the results of the recently introduced computational finite element (FE) models for diffusive drug release from nanofibers to the three-dimensional (3D) surrounding medium. Two different FE models are used: (1) a 3D discretized continuum and fibers represented by a simple radial one-dimensional (1D) finite elements, and (2) a 3D continuum discretized by composite smeared finite elements (CSFEs) containing the fiber smeared and surrounding domains. Both models include the effects of polymer degradation and hydrophobicity (as partitioning) of the drug at the fiber/surrounding interface. The CSFE model includes a volumetric fraction of fibers and diameter distribution, and is additionally enhanced by using correction function to improve the accuracy of the model. The computational results are validated on Rhodamine B (fluorescent drug l) and other hydrophilic drugs. Agreement with experimental results proves that numerical models can serve as efficient tools for drug release to the surrounding porous medium or biological tissue. It is demonstrated that the introduced three-layered scaffold delays the drug release process and can be used for the time-controlled release of drugs in postoperative therapy.

Smeared Multiscale Finite Element Models for Mass Transport and Electrophysiology Coupled to Muscle Mechanics

Mass transport represents the most fundamental process in living organisms. It includes delivery of nutrients, oxygen, drugs, and other substances from the vascular system to tissue and transport of waste and other products from cells back to vascular and lymphatic network and organs. Furthermore, movement is achieved by mechanical forces generated by muscles in coordination with the nervous system. The signals coming from the brain, which have the character of electrical waves, produce activation within muscle cells. Therefore, from a physics perspective, there exist a number of physical fields within the body, such as velocities of transport, pressures, concentrations of substances, and electrical potential, which is directly coupled to biochemical processes of transforming the chemical into mechanical energy and further internal forces for motion. The overall problems of mass transport and electrophysiology coupled to mechanics can be investigated theoretically by developing appropriate computational models. Due to the enormous complexity of the biological system, it would be almost impossible to establish a detailed computational model for the physical fields related to mass transport, electrophysiology, and coupled fields. To make computational models feasible for applications, we here summarize a concept of smeared physical fields, with coupling among them, and muscle mechanics, which includes dependence on the electrical potential. Accuracy of the smeared computational models, also with coupling to muscle mechanics, is illustrated with simple example, while their applicability is demonstrated on a liver model with tumors present. The last example shows that the introduced methodology is applicable to large biological systems.