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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. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

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. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue Uncertainty quantification in cardiac and cardiovascular modelling and simulation.

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 (EC50), but is more affected by uncertainty in the Hill coefficient (n), which governs the biochemical cooperativity or steepness of the sigmoidal activation function of each state variable. Epistemic uncertainty in model structure, due to the reliance of some network components and interactions on experiments using non-PAAF cell types, suggested that this source of uncertainty had a smaller impact on model accuracy than the alternative of reducing the network to only those interactions reported in PAAFs. UQ highlighted model parameters that can be optimized to improve prediction accuracy and network modules where there is the greatest need for new experiments. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

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. The prediction accuracy of the model was robust to parameter changes over a wide range being least sensitive to uncertainty in time constants and most affected by uncertainty in reaction weights. Quantifying epistemic uncertainty in the reaction logic of the model showed that while replacing 'OR' with 'AND' reactions greatly reduced model accuracy, replacing 'AND' with 'OR' reactions was more likely to maintain or even improve accuracy. Finally, data uncertainty had a modest effect on assessment of model accuracy. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

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. This energy profile is then generalized to account for the observed tropomyosin transitions between its regulatory stable states. The generalized energy landscape then served as a basis for developing a filament-scale model using Langevin dynamics. This integrated analysis, spanning molecular to thin-filament scales, is capable of tracking the events of the tropomyosin conformational changes as it moves over the actin surface. The tropomyosin coil with flexible overlap regions between adjacent tropomyosins is represented in the model as a system of coupled stochastic ordinary differential equations. The proposed multiscale approach provides a more detailed molecular connection between tropomyosin dynamics, the trompomyosin-actin interaction-energy landscape, and the generated force by the sarcomere.

A two-cell vortex solution to the Navier–Stokes equations is derived in this article. The theoretical analysis provides expressions for the velocity components, vorticity, and pressure distributions of the two-cell vortex flow. A key feature of this new modeling approach is the presence of a "vortex eye" region, which is absent in classical single-cell vortex models. The derived tangential velocity profile is kept general, allowing for the recovery of the single-cell profile as a special case. The model parameters are constrained by the boundary conditions inherent to two-cell vortices. The model explicitly demonstrates that the two-cell vortex flow exhibits two regions of recirculating flow structures in the meridional plane. The analysis shows that near the vortex core, fluid descends from above and diverges outward. This downward flow meets the incoming flow from the vortex's outer region at a distance known as the "eye-wall" radius. The merging of these two streams results in an upward deflection, generating the two-cell fluid motion. Unlike in single-cell vortices, where vorticity reaches its maximum at the vortex center, the present results indicate that in two-cell vortices, the vorticity peaks at the eye-wall radius. [ABSTRACT FROM AUTHOR]

This study investigates the effects of slip boundary conditions on the electroosmotic flow of an electrolyte solution in a microchannel with a squeezing upper wall and a charged lower wall. The mathematical model is derived by utilizing a tight coupling between the nonlinear Poisson–Boltzmann equation and the flow Navier–Stokes equations. An analytical solution to the problem is acquired through the application of lubrication theory, enabling the resolution of the Poisson–Boltzmann equation without resorting to any approximation techniques. The study thoroughly investigates the impact of various electrokinetic parameters, including the Helmholtz–Smoluchowski velocity, wall zeta potential, Debye length, and electric field, on fluid shear stress, pressure distributions, velocity field, and net flow rate. The results demonstrate that the time-averaged net flow rate is significantly influenced by the collective impact of wall slip velocity, Helmholtz–Smoluchowski velocity, zeta potential, and electric double layer. The data clearly show that altering the Helmholtz–Smoluchowski velocity direction can also impact the direction of the net flow rate, regardless of the slip effects. These results further confirm that applying slip boundary conditions to both walls can improve pumping efficiency. [ABSTRACT FROM AUTHOR]

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. The Basset–Boussinesq–Oseen equation is considered to study the effects of gravity, virtual mass, Basset force, and drag forces on the viruses transport velocity. The results indicate that forces acting on the spherical and non-spherical particles during the motion play a significant role in the transmission process of the viruses. It is observed that high viscosity is responsible for slowing the virus transport dynamics. Small sizes of viruses are found to be highly dangerous and propagate rapidly through the blood vessels. Furthermore, the present mathematical model can help to better understand the viruses spread dynamics in a blood flow. [ABSTRACT FROM AUTHOR]

In this article, we extend the space-time analogy shared by viscous vortices to generalize the dissipation of intense vortices Vatistas and Aboelkassem (Am. Inst. Aeronaut. Astronaut. J. 44, 912 (2006)). The main objective is to layout a mathematical algorithm that can be used to transform vortices into their dissipative phase or into a steady-state counterpart via a similarity transformation to Navier--Stokes equations. The method is applied to examine the time decay of eddies that belong to the Oseen-like concentrated type of viscous vortices. The steady-state Burgers' vortex model was used to validate the transformation approach. This analysis shows that, upon variable transformation, Burgers' vortex model has changed into the Oseen--Lamb class of decaying vortices. The approach is simple, general, and applicable to all kinds of viscous incompressible vortices like those of Sullivan, Rott, Bellamy-Knights, Vatistas, and Scully. PACS No: 47.32.C Nous etendons ici l'analogie espace-temps partagee par les vortex visqueux pour generaliser la dissipation des vortex intenses Vatistas et Aboelkassem (Am. Inst. Aeronaut. Astronaut. J. 44, 912 (2006)). L'objectif principal est de presenter un algorithme mathematique qui peut e tre utilise pour transformer des vortex dans leur phase dissipative en leur contrepartie stationnaire via une transformation de similarite aux equations de Navier--Stokes. La methode est utilisee pour examiner la desintegration dans le temps des tourbillons qui sont des vortex visqueux de type Oseen. Nous avons utilise le mode'le de vortex stationnaire de Burger pour valider l'approche par transformation. Cette analyse montre que, sous transformation, le modele du vortex stationnaire de Burger se change en classe de vortex en voie de se dissiper de Oseen--Lamb. L'approche est simple, generale et applicable a tous les types de vortex visqueux incompressibles, comme ceux de Sullivan, Rott, Bellamy-Knights, Vatistas et Scully. [Traduit par la Redaction], 1. Introduction Vortex flows are complex and are difficult to understand and analyze. However, some classical theoretical models and elementary algebraic solutions aimed at describing the phenomena were proposed in [...]

A new analytical solution for self-similar compressible vortices is derived in this paper. Based on the previous incompressible formulation of intense vortices, we derived a theoretical model that includes density and temperature variations. The governing equations are simplified assuming strong vortex conditions. Part of the hydrodynamic problem (mass and momentum) is shown to be analogous to the incompressible kind and as such the velocity is obtained through a straightforward variable transformation. Since all the velocity components are bounded in the radial direction, the density and pressure are then determined by standard numerical integration without the usual stringent simplification for the radial velocity. While compressibility is shown not to affect the tangential velocity, it influences only the meridional flow (radial and axial velocities). The temperature, pressure, and density are found to decrease along the converging flow direction. The traditional homentropic flow hypothesis, often employed in vortex stability and optical studies, is shown to undervalue the density and greatly overestimate the temperature. Comparable to vorticity diffusion balance for the incompressible case, the incoming flow carries the required energy to offset the contributions of conduction, viscous dissipation, and material expansion, thus keeping the temperature steady. This model is general and can be used to obtain a compressible version for all classical previous incompressible analysis from the literature such as Rankine, Burgers, Taylor, and Sullivan vortices. [DOI: 10.1115/1.2746897]