Fractional-Order Modeling of Arterial Compliance in Vascular Aging: A Computational Biomechanical Approach for Investigating Cardiovascular Dynamics.

The goal of this study is to investigate the application of fractional-order calculus in modeling arterial compliance in human vascular aging. A novel fractional-order modified arterial Windkessel model that incorporates a fractional-order capacitor (FOC) element is proposed to capture the complex and frequency-dependent properties of arterial compliance. The model's performance is evaluated by verifying it using data collected from three different human subjects, with a specific focus on aortic pressure and flow rates.

Modeling virus transport and dynamics in viscous flow medium.

In this paper, we developed a mathematical model to simulate virus transport through a viscous background flow driven by the natural pumping mechanism. Two types of respiratory pathogens viruses (SARS-Cov-2 and Influenza-A) are considered in this model. The Eulerian-Lagrangian approach is adopted to examine the virus spread in axial and transverse directions.

Recent technologies in cardiac imaging.

Cardiac imaging allows physicians to view the structure and function of the heart to detect various heart abnormalities, ranging from inefficiencies in contraction, regulation of volumetric input and output of blood, deficits in valve function and structure, accumulation of plaque in arteries, and more. Commonly used cardiovascular imaging techniques include x-ray, computed tomography (CT), magnetic resonance imaging (MRI), echocardiogram, and positron emission tomography (PET)/single-photon emission computed tomography (SPECT). More recently, even more tools are at our disposal for investigating the heart's physiology, performance, structure, and function due to technological advancements.

Sea urchin sperm exploit extremum seeking control to find the egg.

Sperm cells perform extremely demanding tasks with minimal capabilities. The cells must quickly navigate in a noisy environment to find an egg within a short time window for successful fertilization without any global positioning information. Many research efforts have been dedicated to derive mathematical principles that explain their superb navigation strategy.

Human Hypertension Blood Flow Model Using Fractional Calculus.

The blood flow dynamics in human arteries with hypertension disease is modeled using fractional calculus. The mathematical model is constructed using five-element lumped parameter arterial Windkessel representation. Fractional-order capacitors are used to represent the elastic properties of both proximal large arteries and distal small arteries measured from the heart aortic root.

Towards Characterization of the Complex and Frequency-dependent Arterial Compliance based on Fractional-order Capacitor.

Arterial compliance is a vital determinant of the ventriculo-arterial coupling dynamic. Its variation is detrimental to cardiovascular functions and associated with heart diseases. Accordingly, assessment and measurement of arterial compliance are essential in the diagnosis and treatment of chronic arterial insufficiency.

Particle swarm optimizer for arterial blood flow models.

Background And Objective: Mathematical modeling and computational simulations of arterial blood flow network can offer an insilico platform for both diagnostics and therapeutic phases of patients that suffer from cardiac diseases. These models are normally complex and involve many unknown parameters. For physiological relevance, these parameters should be optimized using in-vivo human/animal data sets.

Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere.

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction.

An audit of uncertainty in multi-scale cardiac electrophysiology models.

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance.

Quantification of uncertainty in a new network model of pulmonary arterial adventitial fibroblast pro-fibrotic signalling.

Here, we present a novel network model of the pulmonary arterial adventitial fibroblast (PAAF) that represents seven signalling pathways, confirmed to be important in pulmonary arterial fibrosis, as 92 reactions and 64 state variables. Without optimizing parameters, the model correctly predicted 80% of 39 results of input-output and inhibition experiments reported in 20 independent papers not used to formulate the original network. Parameter uncertainty quantification (UQ) showed that this measure of model accuracy is robust to changes in input weights and half-maximal activation levels (EC), but is more affected by uncertainty in the Hill coefficient (), which governs the biochemical cooperativity or steepness of the sigmoidal activation function of each state variable.

Considering discrepancy when calibrating a mechanistic electrophysiology model.

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves.

Quantification of model and data uncertainty in a network analysis of cardiac myocyte mechanosignalling.

Cardiac myocytes transduce changes in mechanical loading into cellular responses via interacting cell signalling pathways. We previously reported a logic-based ordinary differential equation model of the myocyte mechanosignalling network that correctly predicts 78% of independent experimental results not used to formulate the original model. Here, we use Monte Carlo and polynomial chaos expansion simulations to examine the effects of uncertainty in parameter values, model logic and experimental validation data on the assessed accuracy of that model.

Multiscale Models of Cardiac Muscle Biophysics and Tissue Remodeling in Hypertrophic Cardiomyopathies.

Myocardial hypertrophy is the result of sustained perturbations to the mechanical and/or neurohormonal homeostasis of cardiac cells and is driven by integrated, multiscale biophysical and biochemical processes that are currently not well defined. In this brief review, we highlight recent computational and experimental models of cardiac hypertrophy that span mechanisms from the molecular level to the tissue level. Specifically, we focus on: (i) molecular-level models of the structural dynamics of sarcomere proteins in hypertrophic hearts, (ii) cellular-level models of excitation-contraction coupling and mechanosensitive signaling in disease-state myocytes, and (iii) organ-level models of myocardial growth kinematics and predictors thereof.

A Stochastic Multiscale Model of Cardiac Thin Filament Activation Using Brownian-Langevin Dynamics.

We use Brownian-Langevin dynamics principles to derive a coarse-graining multiscale myofilament model that can describe the thin-filament activation process during contraction. The model links atomistic molecular simulations of protein-protein interactions in the thin-filament regulatory unit to sarcomere-level activation dynamics. We first calculate the molecular interaction energy between tropomyosin and actin surface using Brownian dynamics simulations.

A hybrid Windkessel-Womersley model for blood flow in arteries.

A hybrid Windkessel-Womersley (WK-W) coupled mathematical model for the study of pulsatile blood flow in the arterial system is proposed in this article. The model consists of the Windkessel-type proximal and distal compartments connected by a tube to represent the aorta. The blood flow in the aorta is described by the Womersley solution of the simplified Navier-Stokes equations.

Tropomyosin dynamics during cardiac muscle contraction as governed by a multi-well energy landscape.

The dynamic oscillations of tropomyosin molecules in the azimuthal direction over the surface of the actin filament during thin filament activation are studied here from an energy landscape perspective. A mathematical model based on principles from nonlinear dynamics and chaos theory is derived to describe these dynamical motions. In particular, an energy potential with three wells is proposed to govern the tropomyosin oscillations between the observed regulatory positions observed during muscle contraction, namely the blocked "B", closed "C" and open "M" states.

Stokes flow patterns induced by a single cardiac cell.

Stokes flow motions induced by a beating single cardiac cell (cardiomyocyte) are obtained numerically using the method of fundamental solutions (MFS). A two-dimensional meshfree-Stokeslets computational framework is used to solve the Stokes governing equations around an isolated cardiomyocyte. An approximate beating kinematical model is derived and used to approximate the cell-length shortening over a complete cardiac cycle.

Acute Optogenetic Modulation of Cardiac Twitch Dynamics Explored Through Modeling.

Optogenetic approaches allow cellular membrane potentials to be perturbed by light. When applied to muscle cells, mechanical events can be controlled through a process that could be termed "optomechanics." Besides functioning as an optical on/off switch, we hypothesized that optomechanical control could include the ability to manipulate the strength and duration of contraction events.

Modeling predicts a connection between sinus vortex effects and aortic compliance.

We submit this letter in order to clarify some methodological issues and concerns raised by Spronck et al. (2015) related to our mathematical modeling of aortic valve dynamics during systole Aboelkassem et al. (2015).

Mathematical modeling of aortic valve dynamics during systole.

We have derived a mathematical model describing aortic valve dynamics and blood flow during systole. The model presents a realistic coupling between aortic valve dynamics, sinus vortex local pressure, and variations in the systemic vascular resistance. The coupling is introduced by using Hill׳s classical semi-spherical vortex model and an aortic pressure-area compliance constitutive relationship.

Selective pumping in a network: insect-style microscale flow transport.

A new paradigm for selective pumping of fluids in a complex network of channels in the microscale flow regime is presented. The model is inspired by internal flow distributions produced by the rhythmic wall contractions observed in many insect tracheal networks. The approach presented here is a natural extension of previous two-dimensional modeling of insect-inspired microscale flow transport in a single channel, and aims to manipulate fluids efficiently in microscale networks without the use of any mechanical valves.