Simulation of the cardiovascular system using equivalent electronic system

This paper describes simulation of the cardiovascular system using a complex electronic circuit. In this study we have taken a slightly different approach to the modeling of the system and tried to advance existing electrical models by increasing more segments and parameters. The model consists of 42 segments representing the arterial system. Anatomical and physiological data for circuit parameters have been extracted from medical articles and textbooks. The frequency of heart is 1 Hz and the system operates in steady state condition. Each artery is modeled by one capacitor, resistor and inductor. The left and right ventricles are modeled using AC power suppliers and diodes. The results of the simulation including pressure and volume graphs exhibit operation of the cardiovascular system under normal condition. The results of the simulation have been compared with the relevant experimental observation and are in good agreement with them.     

Regulation of arterial pressure: role of pressure natriuresis and diuresis

The importance of the renal pressure natriuresis and diuresis mechanisms in long-term control of body fluid volumes and arterial pressure has been controversial and difficult to quantitate experimentally. Recent studies, however, have demonstrated that in several forms of chronic hypertension caused by aldosterone, angiotensin II (AngII), vasopressin, or norepinephrine and adrenocorticotropin, increased renal arterial pressure is essential for maintaining normal excretion of sodium and water in the face of reduced renal excretory capability. When renal arterial pressure was servo-controlled in these models of hypertension, sodium and water retention continued unabated, causing ascites, pulmonary edema, or even complete circulatory collapse within a few days. Apparently, other mechanisms for volume homeostasis, such as the various natriuretic and diuretic factors that have been postulated, are not sufficiently powerful to maintain fluid balance in the absence of increased renal arterial pressure when renal excretory function is reduced in these forms of hypertension. The intrarenal mechanisms responsible for pressure natriuresis and diuresis are not entirely clear, but they seem to involve small increases in glomerular filtration rate and filtered load as well as reductions in fractional reabsorption in proximal and distal tubules. During chronic disturbances of arterial pressure additional factors, especially changes in AngII and aldosterone formation, act to amplify the effectiveness of the basic renal pressure natriuresis and diuresis mechanisms in regulating arterial pressure and body fluid volumes.     

Recent insights into the interactions between the baroreflex and the kidneys in hypertension

Recent findings in chronically instrumented animals challenge the classic concept that baroreflexes do not play a role in the chronic regulation of arterial pressure. As alterations in renal excretory function are of paramount importance in the chronic regulation of arterial pressure, several of these recent studies have focused on the long-term interactions between the baroreflex and the kidneys during chronic perturbations in arterial pressure and body fluid volumes. An emerging body of evidence indicates that the baroreflex is chronically activated in several experimental models of hypertension, but in most cases, the duration of these studies has not exceeded 2 wk. Although these studies suggest that the baroreflex may play a compensatory role in attenuating the severity of the hypertension, possibly even in primary hypertension with uncertain causes of sympathetic activation, there has been only limited assessment of the quantitative importance of this interaction in the regulation of arterial pressure. In experimental models of secondary hypertension, baroreflex suppression of renal sympathetic nerve activity is sustained and chronically promotes sodium excretion. This raises the possibility that the renal nerves may be the critical efferent link for baroreceptor-induced suppression of central sympathetic output through which long-term compensatory reductions in arterial pressure are produced. This contention is supported by strong theoretical evidence but must be corroborated by experimental studies. Finally, although it is now clear that pressure-induced increases in baroreflex activity persist for longer periods of time than previously suggested, studies using new tools and novel approaches and extending beyond 2 wk of hypertension are needed to elucidate the true role of the baroreflex in the pathogenesis of clinical hypertension.     

A mathematical model to investigate the effects of intravenous fluid administration and fluid loss

The optimal fluid administration protocol for critically ill perioperative patients is hard to estimate due to the lack of tools to directly measure the patient fluid status. This results in the suboptimal clinical outcome of interventions. Previously developed predictive mathematical models focus on describing the fluid exchange over time but they lack clinical applicability, since they do not allow prediction of clinically measurable indices. The aim of this study is to make a first step towards a model predictive clinical decision support system for fluid administration, by extending the current fluid exchange models with a regulated cardiovascular circulation, to allow prediction of these indices. The parameters of the model were tuned to correctly reproduce experimentally measured changes in arterial pressure and heart rate, observed during infusion of normal saline in healthy volunteers. With the resulting tuned model, a different experiment including blood loss and infusion could be reproduced as well. These results show the potential of using this model as a basis for a decision support tool in a clinical setting.     

Modeling of Kidney Hemodynamics: Probability-Based Topology of an Arterial Network

Through regulation of the extracellular fluid volume, the kidneys provide important long-term regulation of blood pressure. At the level of the individual functional unit (the nephron), pressure and flow control involves two different mechanisms that both produce oscillations. The nephrons are arranged in a complex branching structure that delivers blood to each nephron and, at the same time, provides a basis for an interaction between adjacent nephrons. The functional consequences of this interaction are not understood, and at present it is not possible to address this question experimentally. We provide experimental data and a new modeling approach to clarify this problem. To resolve details of microvascular structure, we collected 3D data from more than 150 afferent arterioles in an optically cleared rat kidney. Using these results together with published micro-computed tomography (μCT) data we develop an algorithm for generating the renal arterial network. We then introduce a mathematical model describing blood flow dynamics and nephron to nephron interaction in the network. The model includes an implementation of electrical signal propagation along a vascular wall. Simulation results show that the renal arterial architecture plays an important role in maintaining adequate pressure levels and the self-sustained dynamics of nephrons.     

Control of the contractility of the myocardium in a feedback system

Experimental evidence strongly suggests that the contractility of the intact heart in situ, in contrast to that of striated muscle elsewhere in the body, is controlled in a close-cycle system. Thus, the variation of intraventricular pressure during systole follows a complex pattern, whose relative form remains quite constant regardless of the duration of ejection. By use of the single-chambered model of the cardiovascular system, a mathematical representation of a feasible feedback mechanism is developed. The requirement that the feedback system must satisfy mathematical principles eliminates relationships apparently reasonable from a physiological viewpoint. A clinical application which the mathematical development suggests is that early arterial hypertension may arise from an abnormal feedback mechanism with excessively large cardiac output in the initial portion of systole.     

Hemodynamic effects of atrial natriuretic hormone

The atrial natriuretic hormone (ANH) alters cardiovascular function independent of changes in body fluid volume. Most investigators agree that ANH decreases mean arterial pressure (MAP). However, although some investigators have observed a decrease in total peripheral resistance in association with the decrease in MAP, a more frequent observation has been decreased cardiac output (CO). The mechanism whereby ANH decreases CO is unknown, but does not appear to be the result of direct myocardial depression, reductions in intravascular or cardiopulmonary volumes, or venodilation. Alterations in skeletal muscle and splanchnic blood flow have been reported by some but not all investigators. Although increases in renal blood flow have been reported, they are transitory and have not been consistently observed by all researchers. The cardiovascular effects of ANH appear to be influenced not only by the dose, but also by the cardiovascular control mechanisms that operate at the time of ANH administration. Non-renin-dependent hypertensive models exhibit a decrease in MAP associated with decreased CO, whereas in renin-dependent animals this hypotension is associated with a decrease in total peripheral resistance.     

Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation.

Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system, which regulates blood pressure, and cerebral autoregulation, which maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes in beat-to-beat arterial blood pressure and middle cerebral artery blood flow velocity during postural change from sitting to standing. Our cardiovascular model utilizes 11 compartments to describe blood pressure, blood flow, compliance, and resistance in the heart and systemic circulation. To include dynamics due to the pulsatile nature of blood pressure and blood flow, resistances in the large systemic arteries are modeled using nonlinear functions of pressure. A physiologically based submodel is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: 1) autonomic regulation mediated by sympathetic and parasympathetic responses, which affect heart rate, cardiac contractility, resistance, and compliance, and 2) autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and CO(2) concentration, which affect cerebrovascular resistance. Finally, we formulate an inverse least-squares problem to estimate parameters and demonstrate that our mathematical model is in agreement with physiological data from a young subject during postural change from sitting to standing.     

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.     

3D models of blood flow in the cerebral vasculature

The circle of Willis (CoW) is a ring-like arterial structure located in the base of the brain and is responsible for the distribution of oxygenated blood throughout the cerebral mass. To investigate the effects of the complex 3D geometry and anatomical variability of the CoW on the cerebral hemodynamics, a technique for generating physiologically accurate models of the CoW has been created using a combination of magnetic resonance data and computer-aided design software. A mathematical model of the body's cerebral autoregulation mechanism has been developed and numerous computational fluid dynamics simulations performed to model the hemodynamics in response to changes in afferent blood pressure. Three pathological conditions were explored, namely a complete CoW, a fetal P1 and a missing A1. The methodology of the cerebral hemodynamic modelling is proposed with the potential for future clinical application in mind, as a diagnostic tool.     

A neural set point for the long-term control of arterial pressure: beyond the arterial baroreceptor reflex

Arterial baroreceptor reflex control of renal sympathetic nerve activity (RSNA) has been proposed to play a role in long-term control of arterial pressure. The hypothesis that the "set point" of the acute RSNA baroreflex curve determines the long-term level of arterial pressure is presented and challenged. Contrary to the hypothesis, studies on the long-term effects of sinoaortic denervation (SAD) on arterial pressure and RSNA, as well as more recent studies of chronic baroreceptor "unloading" on arterial pressure, suggest that the basal levels of sympathetic nerve activity and arterial pressure are regulated independent of arterial baroreceptor input to the brainstem. Studies of the effect of SAD on the long-term salt sensitivity of arterial pressure are consistent with a short-term role, rather than a long-term role for the arterial baroreceptor reflex in regulation of arterial pressure during changes in dietary salt intake. Renal denervation studies suggest that renal nerves contribute to maintenance of the basal levels of arterial pressure. However, evidence that baroreflex control of the kidney plays a role in the maintenance of arterial pressure during changes in dietary salt intake is lacking. It is proposed that a "baroreflex-independent" sympathetic control system must exist for the long-term regulation of sympathetic nerve activity and arterial pressure. The concept of a central nervous system "set point" for long-term control of mean arterial pressure (CNS-MAP set point), and its involvement in the pathogenesis of hypertension, is discussed.     

Theoretical considerations in the dynamic closed-loop baroreflex and autoregulatory control of total peripheral resistance

The most important goal of this study is to enhance our understanding of the crucial functional relationships that determine the behavior of the systemic circulation and its underlying physiological regulatory mechanisms with minimal modeling. To the present day, much has been said about the indirect hydraulic effects of right atrial pressure (PRA) via cardiac output (CO) on arterial pressure (Pa) through the heart and pulmonary circulation or the direct regulatory effects of PRA on Pa through the cardiopulmonary baroreflex; however, very little attention has been given to the hydraulic influence that PRA exerts directly through the systemic circulation. The experimental data reported by Guyton et al. in 1957 demonstrated that steady-state PRA and the rate at which blood passes through the systemic circulation are locked in a functional relationship independent of any consequence of altered PRA on cardiac function. With this in mind, we emphasize the analytic algebraic analysis of the systemic circulation composed of arteries, veins, and its underlying physiological regulatory mechanisms of baroreflex and autoregulatory modulation of total peripheral resistance (TPR), where the behavior of the system can be analytically synthesized from an understanding of its minimal elements. As a result of this analysis, we present a novel mathematical method to determine short-term TPR fluctuations, which accounts for the entirety of observed Pa fluctuations, and propose a new cardiovascular system identification method to delineate the actual actions of the physiological mechanisms responsible for the dynamic couplings between CO, Pa, PRA, and TPR in an individual subject.     

A data-driven model to study utero-ovarian blood flow physiology during pregnancy

In this paper, we describe a mathematical model of the cardiovascular system in human pregnancy. An automated, closed-loop 1D–0D modelling framework was developed, and we demonstrate its efficacy in (1) reproducing measured multi-variate cardiovascular variables (pulse pressure, total peripheral resistance and cardiac output) and (2) providing automated estimates of variables that have not been measured (uterine arterial and venous blood flow, pulse wave velocity, pulsatility index). This is the first model capable of estimating volumetric blood flow to the uterus via the utero-ovarian communicating arteries. It is also the first model capable of capturing wave propagation phenomena in the utero-ovarian circulation, which are important for the accurate estimation of arterial stiffness in contemporary obstetric practice. The model will provide a basis for future studies aiming to elucidate the physiological mechanisms underlying the dynamic properties (changing shapes) of vascular flow waveforms that are observed with advancing gestation. This in turn will facilitate the development of methods for the earlier detection of pathologies that have an influence on vascular structure and behaviour.

     

慢性动脉血压调节与原发性高血压病——Ⅰ.慢性动脉血压调节

机体在不同条件下维持动脉血压恒定的机理是不相同的。目前认为,长时程或慢性血压调节的关键器官是肾脏,这种调节与机体的水盐平衡有密切的关系。动脉血压的升高可以导致肾脏排尿量（或排钠量）的升高,即动脉血压与肾脏的排尿量（或排钠量）呈明显的正相关关系,称之为“压力-利尿作用”。当血容量升高时,通过肾脏的压力-利尿作用,可以排出过多的容量,维持动脉血压的恒定。只有在肾脏功能受到损伤的条件下,高血容量才可能引起高血压。     

Human tissue-engineered blood vessels for adult arterial revascularization

There is a crucial need for alternatives to native vein or artery for vascular surgery. The clinical efficacy of synthetic, allogeneic or xenogeneic vessels has been limited by thrombosis, rejection, chronic inflammation and poor mechanical properties. Using adult human fibroblasts extracted from skin biopsies harvested from individuals with advanced cardiovascular disease, we constructed tissue-engineered blood vessels (TEBVs) that serve as arterial bypass grafts in long-term animal models. These TEBVs have mechanical properties similar to human blood vessels, without relying upon synthetic or exogenous scaffolding. The TEBVs are antithrombogenic and mechanically stable for 8 months in vivo. Histological analysis showed complete tissue integration and formation of vasa vasorum. The endothelium was confluent and positive for von Willebrand factor. A smooth muscle-specific alpha-actin-positive cell population developed within the TEBV, suggesting regeneration of a vascular media. Electron microscopy showed an endothelial basement membrane, elastogenesis and a complex collagen network. These results indicate that a completely biological and clinically relevant TEBV can be assembled exclusively from an individual's own cells.     

Mesor-hypertension: hints by chronobiologists

Circadian systems are intermodulated by networks of specialized neural, hormonal and cellular functions, with time structures that are interdependent. In cardiovascular pathophysiology, circadian and ultradian rhythms of clinical interest have been demonstrated. Cardiac output, heart rate, arterial pressure and blood volume are the best known. Systolic and diastolic blood pressure and heart rate have circadian patterns in health and therefore arterial pressure cannot be evaluated by a single measurement during a 24-h span. With correct monitoring for at least 48-h it is possible to detect the mesor-hypertension and the possible amplitude-hypertension that precedes the mesor-hypertension. Prolonged elevation of blood pressure can cause irreparable harm to sensitive tissues. To quantify the damage, the concept of hyperbaric impact has been introduced. This is a measure of the excess load exerted upon the arterial walls. Studies of the beta-blocker penbutolol with correct automatic monitoring have shown the persistence of the physiological circadian variation in the cardiovascular parameters during penbutolol administration. The so-called elimination of the circadian rhythm in blood pressure, which would not really be desirable, was not seen in any of our patients, whose cardiovascular parameters were monitored continuously, day and night, while taking penbutolol. The amplitudes of the rhythms were always prominent. A phase shift, a delay of about 100 degrees, was demonstrated in the heart rate of one 63-year-old mesor-normotensive woman.     

A model for the relationship between the arterial pressure and the heart period

This paper provides a simple model for predicting the relationship between steady-state heart rate and arterial blood pressure. Two current state-of-the-art models of the cardiovascular system as a pump operating in its circuit are reformulated and combined in order to highlight the role of the duration of the heart cycle. The proposed model establishes that the cardiac cycle lengthens linearly with the inverse of the average blood pressure. Experimental data are reported for sixteen preoperated conscious dogs resting quietly on their sides. Vagal and sympathetic blocks have been produced in four dogs in order to obtain a wide range of sympathetic and parasympathetic tones, namely, to cover the entire range of physiological values of the heart rate. For these dogs a comparison between the experimental values and the theoretical predictions shows a good agreement, the results of the linear regression model being statistically significant at the p = 0.001 level for three dogs and at the p = 0.01 level for the fourth dog.     

Effect of stellate ganglionectomy on basal cardiovascular function and responses to beta1-adrenoceptor blockade in the rat

Cardiac sympathetic nerve activity is an important short-term controller of cardiac function and arterial pressure. Studies also suggest that long-term increases in cardiac sympathetic nerve activity may contribute to hypertension, coronary artery disease, and cardiac remodeling in heart failure. However, our understanding of the role of cardiac sympathetic nerves in chronic models of cardiovascular disease has been limited by inadequate experimental approaches. The present study was conducted to develop a surgical method to surgically denervate the sympathetic nerves of the rat heart for long-term cardiovascular studies. We characterized the effect of cardiac sympathetic denervation on basal levels of mean arterial pressure (MAP) and heart rate (HR) and the responses to a chronic administration of atenolol, a beta1-adrenoceptor antagonist. Rats were instrumented with telemetry transmitters for continuous recording of MAP and HR. After a 4-day baseline period, the rats were subjected to bilateral stellate ganglionectomy (SGX; n=9) or sham surgery (Sham; n=8). Seven days following SGX or Sham, the rats were administered atenolol for 5 days, followed by a 7-day recovery period. Following a transient decrease, SGX had no effect on basal MAP but decreased HR compared with baseline and Sham rats. Five days of atenolol treatment decreased MAP similarly in SGX and Sham rats. Atenolol resulted in a marked bradycardia in Sham rats but had a neglible effects on HR in SGX rats. The measurement of the content of cardiac catecholamines in all cardiac chambers at the end of the study verified a successful sympathetic denervation. This study confirms that bilateral SGX is a useful method to study the contribution of cardiac sympathetic nerves on the regulation of cardiac function. Moreover, these results suggest that cardiac sympathetic nerves are relatively unimportant in maintaining the basal level of MAP or the depressor response to atenolol in conscious, unrestrained rats.     

A viscoelastic model for use in predicting arterial pulse waves

In nonlinear mathematical models of the arterial circulation, the viscoelasticity of the vessel walls has generally been neglected or only taken into account in a highly approximate manner. A new method is proposed to simulate the nonlinear viscoelastic properties of the wall material with the aid of a convolution integral of the creep function and the pressure history. With this simulation it is possible to properly describe the measured characteristics of arterial viscoelasticity. Moreover, it is utilized in a mathematical model of arterial pulse propagation to study the influence of the internal wall friction on the shape, amplitude and mean value of pressure and flow pulses. The corresponding predictions are in much better agreement with in-vivo measurements, especially for the distal part of the circulation, than those obtained without viscoelasticity.     

From inverse problems in mathematical physiology to quantitative differential diagnoses

The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses. We outline possible steps toward translating this computational approach to the bedside, to supplement today's evidence-based medicine with a quantitatively founded model-based medicine that integrates mechanistic knowledge with patient-specific information.