Thomas G. Coleman

Subpressor angiotensin infusion, renal sodium handling, and salt-induced hypertension in the dog.

We studied the combined effect of subpressor amounts of angiotensin and long-term sodium chloride infusion on arterial pressure in 16 dogs for periods of 2-8 weeks. In dogs receiving 3.5 liters of isotonic NaCl daily, but no angiotensin, the arterial pressure increased an average of only 3 mm Hg. When angiotensin was infused continuously at a rate of 5 ng/kg per min (a rate too small to cause an observable immediate increase in pressure), subsequent infusion of 3.5 liters of saline daily then increased the pressure by 39 mm Hg. The urinary output of sodium increased to the same extent in both instances, that is, there was no extra sodium loss because of the elevated pressure. This suggests that the angiotensin significantly blocked the normal ‘pressure natriuresis’ usually seen with such large increases in pressure. However, the plasma aldosterone levels during angiotensin infusion were not found to be different from those in the absence of angiotensin. Therefore, we have suggested that the tendency of the kidneys to retain sodium under the influence of angiotensin was probably caused mainly by a direct effect of angiotensin on the kidney itself. Such a direct renal sodium-retaining effect also could be a contributing factor in the marked hypertension that results from salt administration in the presence of small amounts of angiotensin.

HumMod: A Modeling Environment for the Simulation of Integrative Human Physiology

Mathematical models and simulations are important tools in discovering key causal relationships governing physiological processes. Simulations guide and improve outcomes of medical interventions involving complex physiology. We developed HumMod, a Windows-based model of integrative human physiology. HumMod consists of 5000 variables describing cardiovascular, respiratory, renal, neural, endocrine, skeletal muscle, and metabolic physiology. The model is constructed from empirical data obtained from peer-reviewed physiological literature. All model details, including variables, parameters, and quantitative relationships, are described in Extensible Markup Language (XML) files. The executable (HumMod.exe) parses the XML and displays the results of the physiological simulations. The XML description of physiology in HumMods modeling environment allows investigators to add detailed descriptions of human physiology to test new concepts. Additional or revised XML content is parsed and incorporated into the model. The model accurately predicts both qualitative and quantitative changes in clinical and experimental responses. The model is useful in understanding proposed physiological mechanisms and physiological interactions that are not evident, allowing one to observe higher level emergent properties of the complex physiological systems. HumMod has many uses, for instance, analysis of renal control of blood pressure, central role of the liver in creating and maintaining insulin resistance, and mechanisms causing orthostatic hypotension in astronauts. Users simulate different physiological and pathophysiological situations by interactively altering numerical parameters and viewing time-dependent responses. HumMod provides a modeling environment to understand the complex interactions of integrative physiology. HumMod can be downloaded at http://hummod.org

Validation of a computational platform for the analysis of the physiologic mechanisms of a human experimental model of hemorrhage

Computational models of integrative physiology may serve as a framework for understanding the complex adaptive responses essential for homeostasis in critical illness and resuscitation and may provide insights for design of diagnostics and therapeutics. In this study a computer model of human physiology was compared to results obtained from experiments using Lower Body Negative Pressure (LBNP) analog model of human hemorrhage. LBNP has been demonstrated to produce physiologic changes in humans consistent with hemorrhage. The computer model contains over 4000 parameters that describe the detailed integration of physiology based upon basic physical principles and established biologic interactions. The LBNP protocol consisted of a 5min rest period (0mmHg) followed by 5min of chamber decompression of the lower body to -15, -30, -45, and -60mmHg and additional increments of -10mmHg every 5min until the onset of hemodynamic decompensation (n=20). Physiologic parameters recorded include mean arterial pressure (MAP), cardiac output (CO), and venous oxygen saturation (SVO(2); from peripheral venous blood), during the last 30s at each LBNP level. The computer model analytic procedure recreates the investigational protocol for a virtual individual in an In Silico environment. After baseline normalization, the model predicted measurements for MAP, CO, and SVO(2) were compared to those observed through the entire range of LBNP. Differences were evaluated using standard statistical performance error measurements (median performance error (PE) <5%). The simulation results closely tracked the average changes observed during LBNP. The predicted MAP fell outside the standard error measurement for the experimental data at only LBNP -30mmHg while CO was more variable. The predicted SVO(2) fell outside the standard error measurement for the experimental data only during the post-LBNP recovery point. However, the statistical median PE measurement was found to be within the 5% objective error measure (1.3% for MAP, -3.5% for CO, and 3.95% for SVO(2)). The computer model was found to accurately predict the experimental results observed using LBNP. The model should be explored as a platform for studying concepts and physiologic mechanisms of hemorrhage including its diagnosis and treatment.

Numerical integration: A method for improving solution stability in models of the circulation

Compartmentalized models of the circulatory system are used to investigate the dynamics of the movement of blood from one region of the circulation to another. When these models are studied using numerical methods—viz., numerical integration—solution stability can often be achieved only at integration step sizes that are far less than the time intervals of interest. Hence, obtaining solution stability at much larger integration step sizes is desirable. Instability results from a (one-iteration) delay between calculation of the derivative and calculation of the integral. The method described here, applied locally within a model, replaces the usual method of estimating flow at the beginning of the interval only, with an estimated average value for the whole interval. The “flow predictor” method is not general; it requires a knowledge of local resistances and capacitances and their effect on flow. But, only one subroutine call is required when a flow is calculated; the expense in computing time is minimal. Using an example four-compartment model, the maximum stable integration interval with rectangular integration (0.0005 min) was improved by a factor of 106 (to 1000 min) with this method.

Control of cardiac output by regional blood flow distribution

Most data indicate that cardiac output is normally controlled by the systemic circulation rather than by the heart. This manuscript extends that concept by analyzing the systemic circulation with a mathematical model comprised of two dissimilar blood flow channels. The concept and the model are not new and have, in fact, a strong anatomical and historical basis. However, re-examination using a quantitative, computerized analysis scaled to human dimensions is made in the face of new experimental data.The crux of the model is that two parallel blood flow channels have dissimilar compliances. Regional blood flows distribute total blood volume between the two primary blood storage areas, where the blood is more or less effective in promoting venous return according to its location. Changes in cardiac output can theoretically be achieved solely by changes in arterial resistance, without alteration of venous compliance or resistance; this is the situation that is analyzed in detail.The performance of the model was correlated with experimental data that describe the hemodynamic responses to thoracic aortic constriction, exercise, circulatory shock following endotoxin administration, and other situations. The correlation indicates that redistribution of blood flow following arterial resistance changes can theoretically have a very strong effect on the level of cardiac output, either in a direct causal role or in an ancillary role in conjunction with other, more dominant control mechanisms.

A simulation support system for solving large physiological models on microcomputers

Although physiological modeling and computer simulation have become useful research tools to test new scientific theories and to design and analyze laboratory experiments, developing a new model can be a tedious process because the investigator must often write very complex and specific routines for data input and output. To facilitate the design of new models (as well as the use of existing models), we have developed MODSIM, a FORTRAN-based simulation support system for the IBM PC computer than can accommodate very large dynamic models having up to several thousand equations. It provides the investigator with utilities for continuous on-line graphical and/or tabular output, as well as facilities for dynamic interaction with the model. The user must only supply a model as a list of mathematical equations written in FORTRAN, along with the initial values of the model variables and parameters. The model is precompiled, compiled, and then linked to the MODSIM utilities. Without further programming, the user can then solve the model, select variables for graphical output, and stop the model at any time to analyze the data or to change a parameter before resuming the simulation. This simulation system makes it very easy to develop new models that actively interact with the experimental research of the investigator.

The renin-angiotensin system. Normal physiology and changes in older hypertensives.

The long‐term effects of angiotensin (ANGII) on arterial pressure regulation appear to be closely linked to volume homeostasis, via the renal‐pressure natriuresis mechanism, both in normal humans and in older hypertensives. In response to disturbances such as increased sodium intake, suppression of ANGII and aldosterone formation greatly amplifies the effectiveness of the pressure natriuresis mechanism, thereby preventing large increases in body fluid volumes and minimizing the rise in blood pressure needed to maintain sodium balance. When ANGII levels are inappropriately elevated, the antinatriuretic effects of ANGII cause increased arterial pressure, which then serves to maintain sodium and water balance via the pressure natriuresis mechanism. The primary intrarenal and extrarenal mechanisms by which ANGII controls renal excretion and arterial pressure include: (1) a direct effect of ANGII on tubular sodium transport; (2) a preferential constrictor action of ANGII on efferent arterioles, which increases sodium reabsorption by altering peritubular capillary physical forces (efferent arteriolar constriction also prevents excessive decreases in glomerular filtration rate when renal perfusion is compromised, such as in renal artery stenosis); and (3) extrarenal effects of ANGII, including stimulation of aldosterone secretion. Current evidence suggests that the direct effects of ANGII on the kidney are quantitatively more important than indirect effects mediated by aldosterone. In older hypertensives, plasma renin activity and aldosterone concentration are often suppressed, perhaps due to loss of functional nephrons and increased sodium chloride delivery to the macula densa of the remaining nephrons. The observation that converting enzyme inhibition lowers arterial pressure in older hypertensives, even when plasma renin activity is normal or slightly reduced, suggests that even small amounts of ANGII may be important in maintaining arterial pressure.

Mathematical Analysis of Cardiovascular Function

This paper identifies several published models of cardiovascular function, and attempts to analyze them in terms of the physiological processes which are embedded in their structure. It appears that representative models have increased in size and complexity in direct proportion to increases in the power and suitability of available computing machinery. An early focus on pulsatile hemodynamics within a single vascular compartment has evolved into analyses of ventricular filling and ejection, the function of the circulatory system as a closed system, longterm cardiovascular control, and the interaction of the circulatory system with other organ systems.

The role of the kidney in essential hypertension.

1. Many forms of human and experimental hypertension begin with compromised renal function. Essential hypertension may be another such case.

Some problems and solutions for modeling overall cardiovascular regulation

Abstract A brief history of the development of mathematical models of the cardiovascular system is presented. Until the advent of computers, very little modeling of transient physiological phenomena was done, but this is now commonplace. The problem of stability in complex physiological models fortunately is averted by the fact that the physiological controls are themselves highly stable. The reason for this is that evolution has eliminated unstable feedback loops because they are lethal. Indeed, enough safety factor has been provided in the design of the body so that even poor mathematical models are often quite stable. An especially important use of complex cardiovascular models has been to derive new concepts of cardiovascular function. One such concept is the “principle of infinite gain” for long-term control of arterial pressure, which states that the long-term level of arterial pressure is controlled by a balance between the fluid intake and the output of fluid by the kidneys, not by the level of total peripheral resistance as has been a long-standing misconception based on acute rather than chronic animal experiments.