Thomas G. Coleman’s research while affiliated with University of Mississippi Medical Center and other places

Mathematical modeling is an important tool for understanding quantitative relationships among components of complex physiological systems and for testing competing hypotheses. We used HumMod, a large physiological model, to test hypotheses of blood pressure (BP) salt sensitivity. Systemic hemodynamics, renal, and neurohormonal responses to chronic changes in salt intake were examined during normal renal function, fixed low or high plasma angiotensin II (Ang II) levels, bilateral renal artery stenosis, increased renal sympathetic nerve activity (RSNA), and decreased nephron numbers. Simulations were run for 4 weeks at salt intakes ranging from 30 to 1000 mmol/day. Reducing functional kidney mass or fixing Ang II increased salt sensitivity. Salt sensitivity, associated with inability of Ang II to respond to changes in salt intake, occurred with smaller changes in renal blood flow but greater changes in glomerular filtration rate, renal sodium reabsorption, and total peripheral resistance (TPR). However, clamping TPR at normal or high levels had no major effect on salt sensitivity. There were no clear relationships between BP salt sensitivity and renal vascular resistance or extracellular fluid volume. Our robust mathematical model of cardiovascular, renal, endocrine, and sympathetic nervous system physiology supports the hypothesis that specific types of kidney dysfunction, associated with impaired regulation of Ang II or increased tubular sodium reabsorption, contribute to BP salt sensitivity. However, increased preglomerular resistance, increased RSNA, or inability to decrease TPR does not appear to influence salt sensitivity. This model provides a platform for testing competing concepts of long-term BP control during changes in salt intake.

Background: Evidence suggests that morbid obesity may be an independent risk factor for adverse outcomes in patients with traumatic injuries. Objectives: In this study, a theoretic analysis using a derivation of the Guyton model of cardiovascular physiology examines the expected impact of obesity on hemodynamic changes in Mean Arterial Pressure (MAP) and Cardiac Output (CO) during Hemorrhagic Shock (HS). Patients and methods: Computer simulation studies were used to predict the relative impact of increasing Body Mass Index (BMI) on global hemodynamic parameters during HS. The analytic procedure involved recreating physiologic conditions associated with changing BMI for a virtual subject in an In Silico environment. The model was validated for the known effect of a BMI of 30 on iliofemoral venous pressures. Then, the relative effect of changing BMI on the outcome of target cardiovascular parameters was examined during simulated acute loss of blood volume in class II hemorrhage. The percent changes in these parameters were compared between the virtual nonobese and obese subjects. Model parameter values are derived from known population distributions, producing simulation outputs that can be used in a deductive systems analysis assessment rather than traditional frequentist statistical methodologies. Results: In hemorrhage simulation, moderate increases in BMI were found to produce greater decreases in MAP and CO compared to the normal subject. During HS, the virtual obese subject had 42% and 44% greater falls in CO and MAP, respectively, compared to the nonobese subject. Systems analysis of the model revealed that an increase in resistance to venous return due to changes in intra-abdominal pressure resulting from obesity was the critical mechanism responsible for the differences. Conclusions: This study suggests that obese patients in HS may have a higher risk of hemodynamic instability compared to their nonobese counterparts primarily due to obesity-induced increases in intra-abdominal pressure resulting in reduced venous return.

Insufficient pre-oxygenation before emergency intubation, and hyperventilation after intubation are mistakes that are frequently observed in and outside the operating room, in clinical practice and in simulation exercises. Physiological parameters, as appearing on standard patient monitors, do not alert to the deleterious effects of low oxygen saturation on coronary perfusion, or that of low carbon dioxide concentrations on cerebral perfusion. We suggest the use of HumMod, a computer-based human physiology simulator, to demonstrate beneficial physiological responses to pre-oxygenation and the futility of excessive minute ventilation after intubation. We programmed HumMod, to A.) compare varying times (0-7 minutes) of pre-oxygenation on oxygen saturation (SpO2) during subsequent apnoea; B.) simulate hyperventilation after apnoea. We compared the effect of different minute ventilation rates on SpO2, acid-base status, cerebral perfusion and other haemodynamic parameters. A.) With no pre-oxygenation, starting SpO2 dropped from 98% to 90% in 52 seconds with apnoea. At the other extreme, following full pre-oxygenation with 100% O2 for 3 minutes or more, the SpO2 remained 100% for 7.75 minutes during apnoea, and dropped to 90% after another 75 seconds. B.) Hyperventilation, did not result in more rapid normalization of SpO2, irrespective of the level of minute ventilation. However, hyperventilation did cause significant decreases in cerebral blood flow (CBF). HumMod accurately simulates the physiological responses compared to published human studies of pre-oxygenation and varying post intubation minute ventilations, and it can be used over wider ranges of parameters than available in human studies and therefore available in the literature.

We present a small integrative model of human cardiovascular physiology. The model is population-based; rather than using best fit parameter values, we used a variant of the Metropolis algorithm to produce distributions for the parameters most associated with model sensitivity. The population is built by sampling from these distributions to create the model coefficients. The resulting models were then subjected to a hemorrhage. The population was separated into those that lost less than 15 mmHg arterial pressure (compensators), and those that lost more (decompensators). The populations were parametrically analyzed to determine baseline conditions correlating with compensation and decompensation. Analysis included single variable correlation, graphical time series analysis, and support vector machine (SVM) classification. Most variables were seen to correlate with propensity for circulatory collapse, but not sufficiently to effect reasonable classification by any single variable. Time series analysis indicated a single significant measure, the stressed blood volume, as predicting collapse in situ, but measurement of this quantity is clinically impossible. SVM uncovered a collection of variables and parameters that, when taken together, provided useful rubrics for classification. Due to the probabilistic origins of the method, multiple classifications were attempted, resulting in an average of 3.5 variables necessary to construct classification. The most common variables used were systemic compliance, baseline baroreceptor signal strength and total peripheral resistance, providing predictive ability exceeding 90%. The methods presented are suitable for use in any deterministic mathematical model.

It has been noted in multiple studies that the calcium-PTH axis, among others, is subject to an apparent hysteresis. We sought to explain a major component of the observed phenomenon by constructing a simple mathematical model of a hormone and secretagogue system with concentration dependent secretion and containing two delays. We constructed profiles of the hormone-agonist axis in this model via four types of protocols, three of which emulating experiments from the literature, and observed a delay- and load-dependent hysteresis that is an expected mathematical artifact of the system described. In particular, the delay associated with correction allows for over-secretion of the hormone influencing the corrective mechanism; thus rate dependence is an artifact of the corrective mechanism, not a sensitivity of the gland to the magnitude of change. From these observations, the detected hysteresis is due to delays inherent in the systems being studied, not in the secretory mechanism.

A left lateral tilt of 15° has been advocated during trauma resuscitation of near-term pregnant patients to avoid the potential for hemodynamic compromise caused by aortocaval compression in the supine position. This recommendation is supported by limited objective evidence, and an experimental determination of the optimal tilt required would be very difficult to accomplish logistically. A derivation of the Guyton/Coleman/Summers computer model of cardiovascular physiology was used to analyze the theoretically expected hemodynamic responses to varying degrees of lateral tilt for a normal pregnancy and during a simulated hemorrhagic shock. Computer simulation studies were used to predict the degree of left lateral tilt required to restore hemodynamic normalcy during the final 20 weeks of gestation. The analytic procedure involved recreating the clinical conditions for a virtual subject through a simulated reenactment of the clinical transfer of a pregnant patient from a lateral to a supine positioning. An analysis of model validity in the context of this particular clinical condition found the model predictions to be within 5% to 12% of experimental results. During the simulated lateral to supine position transfer, the virtual patient with Class I hemorrhage had a 7% greater fall in cardiac output and a 17% greater fall in mean arterial pressure (MAP) than the corresponding nonhemorrhagic patient. The model suggests that 15° of tilt will result in hemodynamic normalization only up to 26 weeks of gestation. In addition, 13% greater tilt is required to achieve hemodynamic normalcy in the hemorrhaged term pregnant patient. Current trauma guidelines suggest that the pregnant trauma patient be placed in a 15° left lateral tilt position to prevent aortocaval compression. A computer simulation study suggests that this tilt may be inadequate to offload the vena cava and normalize the circulation.

An example of a mathematical model of a typical physiological system is presented in this chapter. The example is followed by a description of several mathematical tools which we have found to be useful in the study of such systems.