A population model of integrative cardiovascular physiology

In silico trial of baroreflex activation therapy for the treatment of obesity-induced hypertension

Clinical trials evaluating the efficacy of chronic electrical stimulation of the carotid baroreflex for the treatment of hypertension (HTN) are ongoing. However, the mechanisms by which this device lowers blood pressure (BP) are unclear, and it is uncertain which patients are most likely to receive clinical benefit. Mathematical modeling provides the ability to analyze complicated interrelated effects across multiple physiological systems. Our current model HumMod is a large physiological simulator that has been used previously to investigate mechanisms responsible for BP lowering during baroreflex activation therapy (BAT). First, we used HumMod to create a virtual population in which model parameters (n = 335) were randomly varied, resulting in unique models (n = 6092) that we define as a virtual population. This population was calibrated using data from hypertensive obese dogs (n = 6) subjected to BAT. The resultant calibrated virtual population (n = 60) was based on tuning model parameters to match the experimental population in 3 key variables: BP, glomerular filtration rate, and plasma renin activity, both before and after BAT. In the calibrated population, responses of these 3 key variables to chronic BAT were statistically similar to experimental findings. Moreover, blocking suppression of renal sympathetic nerve activity (RSNA) and/or increased secretion of atrial natriuretic peptide (ANP) during BAT markedly blunted the antihypertensive response in the virtual population. These data suggest that in obesity-mediated HTN, RSNA and ANP responses are key factors that contribute to BP lowering during BAT. This modeling approach may be of value in predicting BAT responses in future clinical studies.

Control-oriented physiological modeling of hemodynamic responses to blood volume perturbation

This paper presents a physiological model to reproduce hemodynamic responses to blood volume perturbation. The model consists of three sub-models: a control-theoretic model relating blood volume response to blood volume perturbation; a simple physics-based model relating blood volume to stroke volume and cardiac output; and a phenomenological model relating cardiac output to blood pressure. A unique characteristic of this model is its balance for simplicity and physiological transparency. Initial validity of the model was examined using experimental data collected from 11 animals. The model may serve as a viable basis for the design and evaluation of closed-loop fluid resuscitation controllers.

Validating the Physiologic Model HumMod as a Substitute for Clinical Trials Involving Acute Normovolemic Hemodilution

BACKGROUND

Blood conservation strategies and transfusion guidelines remain a heavily debated clinical topic. Previous investigational trials have shown that acute isovolemic hemodilution does not limit adequate oxygen delivery; however, a true critical hemoglobin level has never been investigated or defined due to safety concerns for human volunteers. Validated physiologic modeling may be useful to investigate hemodilution at critical hemoglobin levels without the ethical or safety hazards of clinical trials. Our hypothesis is that HumMod, an integrative physiological model, can replicate the cardiovascular and metabolic findings of previous clinical studies of acute isovolemic hemodilution and use coronary blood flow and coronary oxygen delivery in extreme hemodilution to predict a safety threshold.

METHODS

By varying cardiovascular and sizing parameters, unique individuals were generated to simulate a population using HumMod, an integrative mathematical model of human physiology. Hemodilution was performed by simultaneously hemorrhaging 500 mL aliquots of blood while infusing equal volumes of hetastarch, 5% albumin balanced salt solution, or triple volumes of lactated Ringer's solution over 10 minutes. Five hemodilution protocols reported over 3 studies were directly replicated with HumMod to compare and validate essential cardiovascular and metabolic responses to hemodilution in moderately healthy, awake adults. Cardiovascular parameters, mental status, arterial and mixed venous oxygen content, and oxyhemoglobin saturation were recorded after the removal of each aliquot. The outputs of this simulation were considered independent variables and were stratified by hemoglobin concentration at the time of measurement to assess hemoglobin as an independent predictor of hemodynamic and metabolic behavior.

RESULTS

The published reports exhibited discrepancies: Weiskopf saw increased heart rate and cardiac index, while Jones and Ickx saw no change in these variables. In HumMod, arterial pressure was maintained during moderate hemodilution due to decreases in peripheral resistance opposing increases in cardiac index. HumMod showed preserved ventilation through moderate hemodilution, compensated for by an increased oxygen extraction similar to the studies of Jones and Ickx. The simulation results qualitatively followed the clinical studies, but there were statistical differences. In more extreme hemodilution, HumMod had a lesser increase in cardiac index, which led to deficiencies in oxygen delivery and low venous saturation. In the simulations, coronary blood flow and oxygen delivery increase up to a critical hemoglobin threshold of 55-75 g/L in HumMod. In this range, coronary blood flow and oxygen delivery fell, leading to cardiac injury. The allowable amount of hemodilution before reaching the critical point is most closely correlated with nonmuscle mass (r = 0.69) and resting cardiac output (r = 0.67).

CONCLUSIONS

There were significant statistical differences in the model population and the clinical populations, but overall, the model responses lay within the clinical findings. This suggests our model is an effective replication of hemodilution in conscious, healthy adults. A critical hemoglobin range of 5.5-7.5 g/L was predicted and found to be highly correlated with nonmuscle mass and resting cardiac output.

The Creation of Surrogate Models for Fast Estimation of Complex Model Outcomes

A surrogate model is a black box model that reproduces the output of another more complex model at a single time point. This is to be distinguished from the method of surrogate data, used in time series. The purpose of a surrogate is to reduce the time necessary for a computation at the cost of rigor and generality. We describe a method of constructing surrogates in the form of support vector machine (SVM) regressions for the purpose of exploring the parameter space of physiological models. Our focus is on the methodology of surrogate creation and accuracy assessment in comparison to the original model. This is done in the context of a simulation of hemorrhage in one model, “Small”, and renal denervation in another, HumMod. In both cases, the surrogate predicts the drop in mean arterial pressure following the intervention. We asked three questions concerning surrogate models: (1) how many training examples are necessary to obtain an accurate surrogate, (2) is surrogate accuracy homogeneous, and (3) how much can computation time be reduced when using a surrogate. We found the minimum training set size that would guarantee maximal accuracy was widely variable, but could be algorithmically generated. The average error for the pressure response to the protocols was -0.05±2.47 in Small, and -0.3 +/- 3.94 mmHg in HumMod. In the Small model, error grew with actual pressure drop, and in HumMod, larger pressure drops were overestimated by the surrogates. Surrogate use resulted in a 6 order of magnitude decrease in computation time. These results suggest surrogate modeling is a valuable tool for generating predictions of an integrative model’s behavior on densely sampled subsets of its parameter space.