Mechanisms of blood pressure salt sensitivity: new insights from mathematical modeling.

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 wk at salt intakes ranging from 30 to 1,000 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.

Theoretical Analysis of the Relative Impact of Obesity on Hemodynamic Stability During Acute Hemorrhagic Shock.

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.

Preventing and Treating Hypoxia: Using a Physiology Simulator to Demonstrate the Value of Pre-Oxygenation and the Futility of Hyperventilation.

INTRODUCTION: 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. METHODS: 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. RESULTS: 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). CONCLUSIONS: 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.

A population model of integrative cardiovascular physiology.

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.

The apparent hysteresis in hormone-agonist relationships.

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.

Theoretical analysis of the effect of positioning on hemodynamic stability during pregnancy.

OBJECTIVES: 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. METHODS: 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. 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. CONCLUSIONS: 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.

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 HumMod's 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.

Systems biology and integrative physiological modelling.

Over the last 10 years, 'Systems Biology' has focused on the integration of biology and medicine with information technology and computation. The current challenge is to use the discoveries of the last 20 years, such as genomics and proteomics, to develop targeted therapeutical strategies. These strategies are the result of understanding the aetiologies of complex diseases. Scientists predict the data will make personalized medicine rapidly available. However, the data need to be considered as a highly complex system comprising multiple inputs and feedback mechanisms. Translational medicine requires the functional and conceptual linkage of genetics to proteins, proteins to cells, cells to organs, organs to systems and systems to the organism. To help understand the complex integration of these systems, a mathematical model of the entire human body, which accurately links the functioning of all organs and systems together, could provide a framework for the development and testing of new hypotheses that will be important in clinical outcomes. There are several efforts to develop a 'Human Physiome', with the strengths and weaknesses of each being presented here. The development of a 'Human Model', with verification, documentation and validation of the underlying and integrative responses, is essential to provide a usable environment. Future development of a 'Human Model' requires integrative physiologists working in collaboration with other scientists, who have expertise in all areas of human biology, to develop the most accurate and usable human model.

Ventricular chamber sphericity during spaceflight and parabolic flight intervals of less than 1 G.

INTRODUCTION: Pathology driven alterations in the geometric shape of the heart have been found to result in regional changes in ventricular wall stress and a remodeling of the myocardium. If reductions in the gravitational forces acting on the heart produce similar changes in the overall contour of the ventricles, this modification might also induce adaptations in the cardiac structure during long-term spaceflight. In this study we examined the changes in left ventricle (LV) shape in spaceflight and during parabolic flights. METHODS: The diastole dimensions of the human LV were assessed with echocardiography during spaceflight and in parabolic flights which replicated the gravity of the Moon, Mars, and spaceflight and were compared to findings in Earth's gravity. LV dimensions were translated into circularity indices and geometric aspect ratios and correlated with their corresponding gravitational conditions. RESULTS: During parabolic flight, a linear relationship (r = 0.99) was found between both the circularity index and geometric aspect ratio values and the respective gravitational fields in which they were measured. During spaceflight (N = 4) and parabolic flights (N = 3), there was an average 4.1 and 4.4% higher circularity index and a 5.3 and 8.1% lower geometric aspect ratio, respectively. CONCLUSIONS: A correlative trend was found between the degree of LV sphericity and the amount of gravitational force directed caudal to the longitudinal orientation of the body. The importance of this finding is uncertain, but may have implications regarding physiologic adaptations in the myocardial structure secondary to changes in LV wall stress upon prolonged exposure to microgravity.

Theoretical analysis of the mechanisms of a gender differentiation in the propensity for orthostatic intolerance after spaceflight.

BACKGROUND: A tendency to develop reentry orthostasis after a prolonged exposure to microgravity is a common problem among astronauts. The problem is 5 times more prevalent in female astronauts as compared to their male counterparts. The mechanisms responsible for this gender differentiation are poorly understood despite many detailed and complex investigations directed toward an analysis of the physiologic control systems involved. METHODS: In this study, a series of computer simulation studies using a mathematical model of cardiovascular functioning were performed to examine the proposed hypothesis that this phenomenon could be explained by basic physical forces acting through the simple common anatomic differences between men and women. In the computer simulations, the circulatory components and hydrostatic gradients of the model were allowed to adapt to the physical constraints of microgravity. After a simulated period of one month, the model was returned to the conditions of earth's gravity and the standard postflight tilt test protocol was performed while the model output depicting the typical vital signs was monitored. CONCLUSIONS: The analysis demonstrated that a 15% lowering of the longitudinal center of gravity in the anatomic structure of the model was all that was necessary to prevent the physiologic compensatory mechanisms from overcoming the propensity for reentry orthostasis leading to syncope.

Simulations of exercise and brain effects of acute exposure to carbon monoxide in normal and vascular-diseased persons.

At some level, carboxyhemoglobin (COHb) due to inhalation of carbon monoxide (CO) reduces maximum exercise duration in both normal and ischemic heart patients. At high COHb levels in normal subjects, brain function is also affected and behavioral performance is impaired.These are findings from published experiments that are, due to ethical or practical considerations, incomplete in that higher or lower ranges of COHb, and exercise have not been well studied. To fill in this knowledge base, a whole-body human physiological model was used to make estimates of physiological functioning by the simulation of parametric exposures to CO and various exercise levels. Ischemic heart disease was simulated by introducing a stenosis in the left heart arterial supply. Brain blood flow was also limited by such a stenosis. To lend credibility to such estimation, the model was tested by simulating experiments from the published literature. Simulations permitted several new conclusions. Increases in COHb produced the largest decreases in exercise duration when exercise was least strenuous and when COHb was smallest. For ischemic heart disease subjects, the greatest change in exercise duration produced by COHb increase was when ischemia and COHb was smallest. Brain aerobic metabolism was unaffected until COHb exceeded 25%, unless the maximum brain blood supply was limited by a stenosis greater than 50% of normal. For higher levels of stenosis, aerobic brain metabolism was reduced for any increase in COHb level, implying that behavior would be impaired with no "threshold" for COHb.

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.

Quantitative Circulatory Physiology: an integrative mathematical model of human physiology for medical education.

We have developed Quantitative Circulatory Physiology (QCP), a mathematical model of integrative human physiology containing over 4,000 variables of biological interactions. This model provides a teaching environment that mimics clinical problems encountered in the practice of medicine. The model structure is based on documented physiological responses within peer-reviewed literature and serves as a dynamic compendium of physiological knowledge. The model is solved using a desktop, Windows-based program, allowing students to calculate time-dependent solutions and interactively alter over 750 parameters that modify physiological function. The model can be used to understand proposed mechanisms of physiological function and the interactions among physiological variables that may not be otherwise intuitively evident. In addition to open-ended or unstructured simulations, we have developed 30 physiological simulations, including heart failure, anemia, diabetes, and hemorrhage. Additional stimulations include 29 patients in which students are challenged to diagnose the pathophysiology based on their understanding of integrative physiology. In summary, QCP allows students to examine, integrate, and understand a host of physiological factors without causing harm to patients. This model is available as a free download for Windows computers at http://physiology.umc.edu/themodelingworkshop.

Computer systems analysis of spaceflight induced changes in left ventricular mass.

Circulatory adaptations resulting in postflight orthostasis have frequently been observed in response to space travel. It has been postulated that a decrement in left ventricular mass (LVM) found after microgravity exposure may be the central component in this cardiovascular deconditioning. However, a physiologic mechanism responsible for these changes in the myocardium has not been determined. In this study, we examined the sequential alterations in echocardiographic measured LVM from preflight to landing day and 3 days into the postflight recovery period. In a previous study in returning astronauts we found a comparative 9.1% reduction in postflight LVM that returned to preflight values by the third day of recovery. This data was further evaluated in a systems analysis approach using a well-established advanced computer model of circulatory functioning. The computer model incorporates the physiologic responses to changes in pressures, flows and hydraulics within the circulatory system as affected by gravitational forces. Myocardial muscle progression to atrophy or hypertrophy in reaction to the circulatory load conditions is also included in the model. The integrative computer analysis suggests that these variations in LVM could be explained by simple fluid shifts known to occur during spaceflight and can reverse within a few days after reentry into earth's gravity. According to model predictions, the reductions in LVM found upon exposure to microgravity are a result of a contraction of the myocardial interstitial fluid space secondary to a loss in the plasma volume. This hypothesis was additionally supported by the published ground-based study in which we followed the alterations in LVM and plasma volume in normal subjects in which hypovolemia was induced by simple dehydration. In the hypovolemic state, plasma volume was reduced in these subjects and was significantly correlated with echocardiographic measurements of LVM. Based on these experimental findings and the performance of the computer systems analysis it appears that reductions in LVM observed after spaceflight may be secondary to fluid exchanges produced by common physiologic mechanisms. Reductions in LVM observed after microgravity exposure have been previously postulated to be a central component of spaceflight-induced cardiovascular deconditioning. However, a recent study has demonstrated a return of astronauts' LVM to preflight values by the third day after landing through uncertain mechanisms. A systems analysis approach using computer simulation techniques allows for a dissection of the complex physiologic control processes and a more detailed examination of the phenomena. From the simulation studies and computer analysis it appears that microgravity induced reductions in LVM may be explained by considering physiologic fluid exchanges rather than cardiac muscle atrophy.

Mechanism of spaceflight-induced changes in left ventricular mass.

Decrements in left ventricular (LV) mass observed after microgravity exposure have been previously postulated to be a central component of spaceflight-induced cardiovascular deconditioning. In this study, echocardiographic measurements of LV mass in astronauts demonstrated a comparative 9.1% reduction in postflight LV mass that returned to preflight values by the third day of recovery. A ground-based study in normal subjects determined that these pre- to postflight LV mass changes could be reproduced by simple dehydration. Reductions in LV mass observed immediately after spaceflight may be secondary to simple physiologic fluid exchanges.

Bench to bedside: electrophysiologic and clinical principles of noninvasive hemodynamic monitoring using impedance cardiography.

The evaluation of the hemodynamic state of the severely ill patient is a common problem in emergency medicine. While conventional vital signs offer some insight into delineating the circulatory pathophysiology, it is often impossible to determine the true clinical state from an analysis of blood pressure and heart rate alone. Cardiac output measurements by thermodilution have been the criterion standard for the evaluation of hemodynamics. However, this technology is invasive, expensive, time-consuming, and impractical for most emergency department environments. Impedance cardiography (ICG) is a noninvasive method of obtaining continuous measurements of hemodynamic data such as cardiac output that requires little technical expertise. ICG technology was first developed by NASA in the 1960s and is based on the idea that the human thorax is electrically a nonhomogeneous, bulk conductor. Variation in the impedance to flow of a high-frequency, low-magnitude alternating current across the thorax results in the generation of a measured waveform from which stroke volume can be calculated by a modification of the pulse contour method. To adequately judge the possible role of this technology in the practice of emergency medicine, it is important to have a sufficient understanding of the basic scientific principles involved as well as the clinical validity and limitations of the technique.