Calcium dynamics and vasomotion in arteries subject to isometric, isobaric, and isotonic conditions

In vitro, different techniques are used to study the smooth muscle cells’ calcium dynamics and contraction/relaxation mechanisms on arteries. Most experimental studies use either an isometric or an isobaric setup. However, in vivo, a blood vessel is neither isobaric nor isometric nor isotonic, as it is continuously submitted to intraluminal pressure variations arising from heart beat. We use a theoretical model of the smooth muscle calcium and arterial radius dynamics to determine whether results may be considerably different depending on the experimental conditions (isometric, isobaric, isotonic, or cyclic pressure variations). We show that isobaric conditions appear to be more realistic than isometric or isotonic situations, as the calcium dynamics is similar under cyclic intraluminal pressure variations (in vivo-like situation) and under a constant pressure (isobaric situation). The arterial contraction is less pronounced in isotonic than in isobaric conditions, and the vasoconstrictor sensitivity higher in isometric than isobaric or isotonic conditions, in agreement with experimental observations. Interestingly, the model predicts that isometric conditions may generate artifacts like the coexistence of multiple stable states. We have verified this model prediction experimentally using rat mesenteric arteries mounted on a wire myograph and stimulated with phenylephrine.     

Computer simulation of blood flow in the human arm

This paper considers a finite element method to characterize blood flow in the human arm arteries. A set of different pressure waveforms, which represent normal and diseased heart pulses, is used for the proximal boundary conditions, and a modified Windkessel model is used for the distal arterial boundary conditions. A comparison of the distal pressure and flow waveforms, for each different proximal pressure, is made to determine whether such waveforms are significantly altered from normal waveforms. The results show that the distal pressure and/or flow waveforms in certain cases are sufficiently different to be possibly used as a diagnostic indicator of an abnormal heart condition. Also considered is the effect of stenosis, change of compliance, and dilatation of the distal beds on the pressure and flow waveforms. A stenosis which has an area reduction of greater than approximately 75% is found to significantly alter both the distal pressure and flow waveforms. Changes in arterial compliance, however, do not strongly influence the waveforms. Dilatation of distal vascular beds is simulated by reducing the lumped resistance of these beds, and this reduction increases mean flow and decreases mean distal pressure, but has little effect on the basic shape of either the pressure or flow waveform.     

Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid-wall interactions.

Severe stenosis may cause critical flow and wall mechanical conditions related to artery fatigue, artery compression, and plaque rupture, which leads directly to heart attack and stroke. The exact mechanism involved is not well understood. In this paper a nonlinear three-dimensional thick-wall model with fluid-wall interactions is introduced to simulate blood flow in carotid arteries with stenosis and to quantify physiological conditions under which wall compression or even collapse may occur. The mechanical properties of the tube wall were selected to match a thick-wall stenosis model made of PVA hydrogel. The experimentally measured nonlinear stress-strain relationship is implemented in the computational model using an incremental linear elasticity approach. The Navier-Stokes equations are used for the fluid model. An incremental boundary iteration method is used to handle the fluid-wall interactions. Our results indicate that severe stenosis causes considerable compressive stress in the tube wall and critical flow conditions such as negative pressure, high shear stress, and flow separation which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The stress distribution has a very localized pattern and both maximum tensile stress (five times higher than normal average stress) and maximum compressive stress occur inside the stenotic section. Wall deformation, flow rates, and true severities of the stenosis under different pressure conditions are calculated and compared with experimental measurements and reasonable agreement is found.     

Evaluation of a transient,simultaneous, arbitrary Lagrange–Euler based multi-physics method for simulating the mitral heart valve

A transient multi-physics model of the mitral heart valve has been developed, which allows simultaneous calculation of fluid flow and structural deformation. A recently developed contact method has been applied to enable simulation of systole (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the mitral valve within the heart walls in two dimensions. Only the mitral valve undergoes deformation. A moving arbitrary Lagrange–Euler mesh is used to allow true fluid–structure interaction (FSI). The FSI model requires blood flow to induce valve closure by inducing strains in the region of 10–20%. Model predictions were found to be consistent with existing literature and will undergo further development.     

Design of a system for the accelerated loading of heart valve prostheses

In this paper an equipment is described for the loading of heart valve prostheses under physiological pressure conditions at a frequency of 10 Hz. The system consists essentially of two reservoirs between which a housing is mounted for holding the valve prosthesis. The reservoirs are partly filled with liquid. The physiological pressure variation across the valve is obtained by pressure control within the two reservoirs. A phase difference between the pressures in the two reservoirs compensates for the mass-inertia effects which normally occur at these high frequencies. The system without a valve has been analysed on the basis of simplified relationships between pressure and flow. The predicted values for the phase difference between the flow and the pressure curves within the valve housing, have been verified experimentally for various values of phase difference and amplitude ratios of the pressure variations within the reservoirs. The agreement between theory and experiment is fair. For the system with a valve the experimentally observed patterns closely resemble the theoretically predicted ones. From experiments with a Bj?rk-Shiley ( 21ABP ) and a Hancock (242-A21) valve prosthesis it is concluded that the valves open and close completely and that the pressure and flow patterns around the valves mimic the essential features of the in-vivo signals.     

Biophysical Model of the Spatial Heterogeneity of Myocardial Flow

The blood flow in the myocardium has significant spatial heterogeneity. The objective of this study was to develop a biophysical model based on detailed anatomical data to determine the heterogeneity of regional myocardial flow during diastole. The model predictions were compared with experimental measurements in a diastolic porcine heart in the absence of vessel tone using nonradioactive fluorescent microsphere measurements. The results from the model and experimental measurements showed good agreement. The relative flow dispersion in the arrested, vasodilated heart was found to be 44% and 48% numerically and experimentally, respectively. Furthermore, the flow dispersion was found to have fractal characteristics with fractal dimensions (D) of 1.25 and 1.27 predicted by the model and validated by the experiments, respectively. This validated three-dimensional model of normal diastolic heart will play an important role in elucidating the spatial heterogeneity of coronary blood flow, and serve as a foundation for understanding the interplay between cardiac mechanics and coronary hemodynamics.     

Analysis of blood flow in the entire coronary arterial tree

A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is approximately 2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg.ml(-1).s(-1).g(-1) for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion.     

4D subject-specific inverse modeling of the chick embryonic heart outflow tract hemodynamics

Blood flow plays a critical role in regulating embryonic cardiac growth and development, with altered flow leading to congenital heart disease. Progress in the field, however, is hindered by a lack of quantification of hemodynamic conditions in the developing heart. In this study, we present a methodology to quantify blood flow dynamics in the embryonic heart using subject-specific computational fluid dynamics (CFD) models. While the methodology is general, we focused on a model of the chick embryonic heart outflow tract (OFT), which distally connects the heart to the arterial system, and is the region of origin of many congenital cardiac defects. Using structural and Doppler velocity data collected from optical coherence tomography, we generated 4D (\(\hbox {3D}\,+\,\hbox {time}\)) embryo-specific CFD models of the heart OFT. To replicate the blood flow dynamics over time during the cardiac cycle, we developed an iterative inverse-method optimization algorithm, which determines the CFD model boundary conditions such that differences between computed velocities and measured velocities at one point within the OFT lumen are minimized. Results from our developed CFD model agree with previously measured hemodynamics in the OFT. Further, computed velocities and measured velocities differ by \(<\)15 % at locations that were not used in the optimization, validating the model. The presented methodology can be used in quantifications of embryonic cardiac hemodynamics under normal and altered blood flow conditions, enabling an in-depth quantitative study of how blood flow influences cardiac development.     

Arterial steal phenomenon in femoro-tibial bypass with arterio-venous shunt

Arterio-venous shunts are sometimes constructed at the distal anastomosis of femoro-tibial bypass grafts in order to increase blood flow velocity within the graft. However, the use of such a shunt may "steal' blood from an already ischaemic distal arterial bed. The aim of this study was to determine the conditions under which this might happen. Experiments were carried out on an in vitro model of the femoro-tibial bypass under steady flow conditions. The simple resistance model of Hyman and Brewer (J. Biomechanics 13, 469-675, 1980), modified to take into account the nonlinear pressure flow relationship through a stenosis, was used to interpret experimental data. Good agreement was obtained between measured and calculated steal.     

Slow oscillations in blood pressure via a nonlinear feedback model

Blood pressure is well established to contain a potential oscillation between 0.1 and 0.4 Hz, which is proposed to reflect resonant feedback in the baroreflex loop. A linear feedback model, comprising delay and lag terms for the vasculature, and a linear proportional derivative controller have been proposed to account for the 0.4-Hz oscillation in blood pressure in rats. However, although this model can produce oscillations at the required frequency, some strict relationships between the controller and vasculature parameters must be true for the oscillations to be stable. We developed a nonlinear model, containing an amplitude-limiting nonlinearity that allows for similar oscillations under a very mild set of assumptions. Models constructed from arterial pressure and sympathetic nerve activity recordings obtained from conscious rabbits under resting conditions suggest that the nonlinearity in the feedback loop is not contained within the vasculature, but rather is confined to the central nervous system. The advantage of the model is that it provides for sustained stable oscillations under a wide variety of situations even where gain at various points along the feedback loop may be altered, a situation that is not possible with a linear feedback model. Our model shows how variations in some of the nonlinearity characteristics can account for growth or decay in the oscillations and situations where the oscillations can disappear altogether. Such variations are shown to accord well with observed experimental data. Additionally, using a nonlinear feedback model, it is straightforward to show that the variation in frequency of the oscillations in blood pressure in rats (0.4 Hz), rabbits (0.3 Hz), and humans (0.1 Hz) is primarily due to scaling effects of conduction times between species.     

Effects of arterial wall stress on vasomotion

Smooth muscle and endothelial cells in the arterial wall are exposed to mechanical stress. Indeed blood flow induces intraluminal pressure variations and shear stress. An increase in pressure may induce a vessel contraction, a phenomenon known as the myogenic response. Many muscular vessels present vasomotion, i.e., rhythmic diameter oscillations caused by synchronous cytosolic calcium oscillations of the smooth muscle cells. Vasomotion has been shown to be modulated by pressure changes. To get a better understanding of the effect of stress and in particular pressure on vasomotion, we propose a model of a blood vessel describing the calcium dynamics in a coupled population of smooth muscle cells and endothelial cells and the consequent vessel diameter variations. We show that a rise in pressure increases the calcium concentration. This may either induce or abolish vasomotion, or increase its frequency depending on the initial conditions. In our model the myogenic response is less pronounced for large arteries than for small arteries and occurs at higher values of pressure if the wall thickness is increased. Our results are in agreement with experimental observations concerning a broad range of vessels.     

Steady flow of a viscous fluid through a network of tubes with applications to the human arterial system

The paper presents a finite-element model for the analysis of steady flow of a viscous fluid through a connected system of elastic tubes with the aim of simulating the conditions of blood flow through the human arterial system. The governing equations of the model are non-linear in character and are solved through an iterative computational procedure. This model is capable of incorporating the effects of stenosis on flow and pressure. Typical results are presented and discussed. Quantitative results have been obtained on blood flow through a model of the human arterial system corresponding to the sets of prescribed conditions at the terminations. Also computational results on the effect of stenosis in typical arteries of the system are presented.     

The effect of environmental factors on circulation and respiration in teleost fish

Summary Anesthesia, handling and activity can produce large variations in some of the parameters of circulation and breathing movements in fish. Handling and MS222 anesthesis cause a large increase in heart rate in the tench, but have the reverse effect on the trout. Hypoxia causes a decreased heart rate and changes in dorsal aortic blood pressure. Serial sampling of the blood appears to have little effect on the parameters of circulation if the blood is replaced with saline. Removal of blood without replacement causes a decrease in blood pressure and a slowing of the heart. It is suggested that much of the variability observed in the measurement of circulatory parameters in fish can be accounted for by the experimental procedure, rather than demonstrating large inter-specific variations in teleost fish.     

Lumped parameter model for computing the minimum pressure during mechanical heart valve closure

The cavitation inception threshold of mechanical heart valves has been shown to be highly variable. This is in part due to the random distribution of the initial and final conditions that characterize leaflet closure. While numerous hypotheses exist explaining the mechanisms of inception, no consistent scaling laws have been developed to describe this phenomenon due to the complex nature of these dynamic conditions. Thus in order to isolate and assess the impact of these varied conditions and mechanisms on inception, a system of ordinary differential equations is developed to describe each system component and solved numerically to predict the minimum pressure generated during valve closure. In addition, an experiment was conducted in a mock circulatory loop using an optically transparent size 29 bileaflet valve over a range of conditions to calibrate and validate this model under physiological conditions. High-speed video and high-response pressure measurements were obtained simultaneously to characterize the relationship between the valve motion, fluid motion, and negative pressure transients during closure. The simulation model was calibrated using data from a single closure cycle and then compared to other experimental flow conditions and to results found in the literature. The simulation showed good agreement with the closing dynamics and with the minimum pressure trends in the current experiment. Additionally, the simulation suggests that the variability observed experimentally (when using dP/dt alone as the primary measure of cavitation inception) is predictable. Overall, results from the current form of this lumped parameter model indicate that it is a good engineering assessment tool.     

An experimental study of pressure losses in pulsatile flows through rigid and pulsating stenosis

The time-dependent pressure curves of a pulsatile flow across rigid and pulsating stenoses were investigated experimentally in a laboratory simulator of the outflow tract of the heart right ventricle. The experiments were performed within the range of physiological conditions of frequency and flow rate. The experimental setup consisted of a closed flow system which was operated by a pulsatile pump, and a test chamber which enabled checking different modes of stenosis. Rigid constrictions were simulated by means of axisymmetric blunt-ended annular plugs with moderate-to-severe area reductions. The pulsating stenosis consisted of a short starling resistor device operated by a pulsating external pressure which was synchronized by the pulsatile flow. It was found that the shape of the time-dependent pressure curve upstream of the stenosis was different in the case of rigid stenosis than in the pulsating one. Potential clinical applications of the work may relate to diagnosis of the type of stenosis in the congenital heart disease known as Tetralogy of Fallot.     

A thick walled viscoelastic model for the mechanics of arteries

A knowledge of the mechanics of arteries is of importance in the determination of vessel rheological properties and in the studies of blood flow and certain arterial diseases. Most existing arterial models treat only wave motions; however, other types of motion, in particular those associated with flow development and other end effects, occur in the vascular system. Thus, a model is needed which can be applied to a variety of possible types of motion.

An arterial model is described which includes the effects of thick walls, linear viscoelasticity, and wall tethering. The forms of the displacements and stresses are found independently of the exact form of the applied fluid stresses; thus, the results are applicable to a range of possible dynamical conditions. Displacements and stress states can then be found from experimental or theoretical knowledge of the blood pressure and flow. The results are applied to flow development and wave propagation regions in the arteries.     

A model of human cardiovascular system containing a loop for the autonomic control of mean blood pressure

We propose a model for the human cardiovascular system that describes the cardiac cycle, the autonomic regulation of heart and vessels, the baroreflex, and the formation of blood pressure. The model also allows for the influence of respiration on these processes. It has been found that an allowance for nonlinearity and insertion of a loop for the autonomic control of mean blood pressure (having the form of selfoscillating time-delay system) enables obtaining model signals with statistical and spectral characteristics that are qualitatively and quantitatively similar to those for experimental signals. The model reproduces the phenomenon of synchronization of the loop for mean blood pressure regulation with a basic frequency of approximately 10 s by the signal of respiration.     

A Mathematical Model of Valveless Pumping: A Lumped Model with Time-Dependent Compliance,Resistance, and Inertia

A new lumped model of flow driven by pumping without valves is presented, motivated by biomedical applications: the circulation of the human fetus before the development of the heart valves and mechanism of blood flow during the external cardiopulmonary resuscitation (CPR). The phenomenon of existence of a unidirectional net flow around a loop of tubing that consists of two different compliances is called valveless pumping. The lumped parameter model of valveless pumping in this paper is governed by the ordinary differential equations for pressure and flow, with time-dependent compliance, resistance, and inertia. This simple model can represent the essential features of valveless pumping we observed in earlier mathematical models and physical experiments of valveless pumping. We demonstrate that not only parameters of the driving function, such as frequency or amplitude, but also physical parameters, such as wall thickness and tube stiffness, are important in determining the direction and magnitude of a net flow. In this system, we report two new and interesting phenomena of valveless pumping: One is that the shifted peak frequency can be predicted by the pulsewave speed and the other is that time-dependent resistance is a crucial factor in generating valveless pumping. We also demonstrate that this lumped model can be extended to a one-dimensional flow model of valveless pumping and explain why a linear case, the case of the constant compliance, resistance, and inertia, generates almost zero net flow. This emphasizes that the nonlinearity of valveless pumping is also an important factor to generate a net flow in a closed loop model of valveless pumping.     

Mechanisms of blood flow during pneumatic vest cardiopulmonary resuscitation

Mechanisms of blood flow during cardiopulmonary resuscitation (CPR) were studied in a canine model with implanted mitral and aortic flow probes and by use of cineangiography. Intrathoracic pressure (ITP) fluctuations were induced by a circumferential pneumatic vest, with and without simultaneous ventilation, and by use of positive-pressure ventilation alone. Vascular volume and compression rate were altered with each CPR mode. Antegrade mitral flow was interpreted as left ventricular (LV) inflow, and antegrade aortic flow was interpreted as LV outflow. The pneumatic vest was expected to elevate ITP uniformly and thus produce simultaneous LV inflow and LV outflow throughout compression. This pattern, the passive conduit of "thoracic pump" physiology, was unequivocally demonstrated only during ITP elevation with positive-pressure ventilation alone at slow rates. During vest CPR, LV outflow started promptly with the onset of compression, whereas LV inflow was delayed. At compression rates of 50 times/min and normal vascular filling pressures, the delay was sufficiently long that all LV filling occurred with release of compression. This is the pattern that would be expected with direct LV compression or "cardiac pump" physiology. During the early part of the compression phase, catheter tip transducer LV and left atrial pressure measurements demonstrated gradients necessitating mitral valve closure, while cineangiography showed dye droplets moving from the large pulmonary veins retrograde to the small pulmonary veins. When the compression rate was reduced and/or when intravascular pressures were raised with volume infusion, LV inflow was observed at some point during the compressive phase. Thus, under these conditions, features of both thoracic pump and cardiac pump physiology occurred within the same compression. Our findings are not explained by the conventional conceptions of either thoracic pump or cardiac compression CPR mechanisms alone.     

Some factors affecting oxygen uptake by red blood cells in the pulmonary capillaries

In this study we investigate the equations governing the transport of oxygen in pulmonary capillaries. We use a mathematical model consisting of a red blood cell completely surrounded by plasma within a cylindrical pulmonary capillary. This model takes account of convection and diffusion of oxygen through plasma, diffusion of oxygen through the red blood cell, and the reaction between oxygen and haemoglobin molecules. The velocity field within the plasma is calculated by solving the slow flow equations. We investigate the effect on the solution of the governing equations of: (i) mixed-venous blood oxygen partial pressure (the initial conditions); (ii) alveolar gas oxygen partial pressure (the boundary conditions); (iii) neglecting the convection term; and (iv) assuming an instantaneous reaction between the oxygen and haemoglobin molecules. It is found that: (a) equilibrium is reached much more rapidly for high values of mixed-venous blood and alveolar gas oxygen partial pressure; (b) the convection term has a negligible effect on the time taken to reach a prescribed degree of equilibrium; and (c) an instantaneous reaction may be assumed. Explanations are given for each of these results.