Systemic modelling of human bioenergetics and blood circulation.

This work reviews the main aspects of human bioenergetics and the dynamics of the cardiovascular system, with emphasis on modelling their physiological characteristics. The methods used to study human bioenergetics and circulation dynamics, including the use of mathematical models, are summarised. The main characteristics of human bioenergetics, including mitochondrial metabolism and global energy balance, are first described, and the systemic aspects of blood circulation and related physiological issues are introduced. The authors also discuss the present status of studies of human bioenergetics and blood circulation. Then, the limitations of the existing studies are described in an effort to identify directions for future research towards integrated and comprehensive modelling. This review emphasises that a multi-scale and multi-physical approach to bioenergetics and blood circulation that considers multiple scales and physiological factors are necessary for the appropriate clinical application of computational models.

New index for categorising cardiac reentrant wave: in silico evaluation.

Based on the similarity between a reentrant wave in cardiac tissue and a vortex in fluid dynamics, the authors hypothesised that a new non-dimensional index, like the Reynolds number in fluid dynamics, may play a critical role in categorising reentrant wave dynamics. Therefore the goal of the present study is to devise a new index to characterise electric wave conduction in cardiac tissue and examined whether this index can be used as a biomarker for categorising the reentrant wave pattern in cardiac tissue. Similar to the procedure used to derive the Reynolds number in fluid dynamics, the authors used a non-dimensionalisation technique to obtain the new index. Its usefulness was verified using a two-dimensional simulation model of electrical wave propagation in cardiac tissue. The simulation results showed that electrical waves in cardiac tissue move into an unstable region when the index exceeds a threshold value.

Modelling Cl- homeostasis and volume regulation of the cardiac cell.

We aim at introducing a Cl- homeostasis to the cardiac ventricular cell model (Kyoto model), which includes the sarcomere shortening and the mitochondria oxidative phosphorylation. First, we examined mechanisms underlying the cell volume regulation in a simple model consisting of Na+/K+ pump, Na+-K+-2Cl- cotransporter 1 (NKCC1), cystic fibrosis transmembrane conductance regulator, volume-regulated Cl- channel and background Na+, K+ and Cl- currents. The high intracellular Cl- concentration of approximately 30 mM was achieved by the balance between the secondary active transport via NKCC1 and passive currents. Simulating responses to Na+/K+ pump inhibition revealed the essential role of Na+/K+ pump in maintaining the cellular osmolarity through creating the negative membrane potential, which extrudes Cl- from a cell, confirming the previous model study in the skeletal muscle. In addition, this model well reproduced the experimental data such as the responses to hypotonic shock in the presence or absence of beta-adrenergic stimulation. Finally, the volume regulation via Cl- homeostasis was successfully incorporated to the Kyoto model. The steady state was well established in the comprehensive cell model in respect to both the intracellular ion concentrations and the shape of the action potential, which are all in the physiological range. The source code of the model, which can reproduce every result, is available from http://www.sim-bio.org/.

Application of the moving-actuator type pump as a ventricular assist device: in vitro and in vivo studies.

A moving actuator type pump has been developed as a multifunctional Korean artificial heart (AnyHeart). The pump consists of a moving actuator as an energy converter, right and left sacs, polymer (or mechanical) valves, and a rigid polyurethane housing. The actuator containing a brushless DC motor moves back and forth on an epicyclical gear train to produce a pendular motion, which compresses both sacs alternately. Of its versatile functions of ventricular assist device and total artificial heart use, we have evaluated the system performance as a single or biventricular assist device through in vitro and in vivo experiments. Pump performance and anatomical feasibility were tested using various animals of different sizes. In the case of single ventricular assist device (VAD) use, one of the sacs remained empty and a mini-compliance chamber was attached to either an outflow or inflow port of the unused sac. The in vitro and in vivo studies show acceptable performance and pump behavior. Further extensive study is required to proceed to human application.

Model-based parameter estimation using cardiovascular response to orthostatic stress.

This paper presents a cardiovascular model that is capable of simulating the short-term (< or approximately equal to 3 min) transient hemodynamic response to gravitational stress and a gradient-based optimization method that allows for the automated estimation of model parameters from simulated or experimental data. We perform a sensitivity analysis of the transient heart rate response to determine which parameters of the model impact the heart rate dynamics significantly. We subsequently include only those parameters in the estimation routine that impact the transient heart rate dynamics substantially. We apply the estimation algorithm to both simulated and real data and showed that restriction to the 20 most important parameters does not impair our ability to match the data.

Numerical analysis of blood flow through a stenosed artery using a coupled, multiscale simulation method.

A global system model of the systemic circulation is combined with a local finite element solution to simulate blood flow in a stenosed coronary artery. Local fluid dynamic issues arise in connection with the detailed flow patterns within the stenosed coronary artery while the global system model is used to simulate the response of the rest of the circulation to the local perturbation. A PISO type finite element technique is employed to compute the local blood flow. The Navier-Stokes equations are solved with the assumption of viscous incompressible flow across the stenosed coronary artery. A detailed lumped parameter model simulates the characteristics of the coronary circulation and is imbedded in a coarse-grained lumped parameter model of the entire cardiovascular system. These two methods are coupled in that the lumped parameter calculations provide the time-dependent boundary conditions for the local finite element calculation. In turn, the local fluid dynamical computation provides estimates for the pressure drop across the stenosis, which is subsequently used to refine the lumped parameter calculation. Results are obtained for an axisymmetric coronary artery model with a stenosis of 90% area reduction over one cardiac cycle. Numerical results show that the flow rate and resistance are strongly coupled. Compared with the flow rate distribution computed from the global simulation with constant resistance, the coupled solution predicts a flow rate with only slight changes. The high flow rate during diastole increases the stenosis pressure drop and resistance. In turn, this increased resistance of the stenosis slightly reduces the flow rate computed in the lumped parameter simulation.

Computational model of cardiovascular function during orthostatic stress.

Orthostatic intolerance following spaceflight remains a critical problem in the current life-science space program. The study presented in this paper is part of an ongoing effort to use mathematical models to investigate the effects of gravitational stresses on the cardiovascular system of normals and microgravity adapted individuals. We employ a twelve compartment lumped parameter representation of the hemodynamic system coupled to set-point models of the arterial baroreflex and the cardiopulmonary reflex to investigate the transient response of heart rate to orthostatic stress. We simulate current hypotheses concerning the mechanisms underlying post-spaceflight orthostatic intolerance over a range of physiologically reasonable values and compare the simulations to astronaut stand-test data pre- and post-flight. Furthermore, we explore the effects of a potential countermeasure.

Computational models of cardiovascular function for analysis of post-flight orthostatic intolerance.

The work presented in this paper is part of an ongoing effort to use mathematical models to investigate the effects of microgravity on the cardiovascular system. In particular, a thirteen compartment lumped parameter representation of the cardiovascular system is used to simulate some of the current hypotheses concerning the mechanism of post-flight orthostatic intolerance. Simulations are compared to astronaut stand test data pre - and post-flight in an effort to quantitatively evaluate alternative hypotheses.

Numerical analysis of three-dimensional Björk-Shiley valvular flow in an aorta.

Laminar vortical flow around a fully opened Björk-Shiley valve in an aorta is obtained by solving the three-dimensional incompressible Navier-Stokes equations. Used is a noniterative implicit finite-element Navier-Stokes code developed by the authors, which makes use of the well-known finite difference algorithm PISO. The code utilizes segregated formulation and efficient iterative matrix solvers such as PCGS and ICCG. Computational results show that the three-dimensional vortical flow is recirculating with large shear in the sinus region of the valve chamber. Passing through the valve, the flow is split into major upper and lower jet flows. The spiral vortices generated by the disk are advected in the wake and attenuated rapidly downstream by diffusion. It is shown also that the shear stress becomes maximum near the leading edge of the disk valve.