Practical Use of Regularization in Individualizing a Mathematical Model of Cardiovascular Hemodynamics Using Scarce Data

Credibility Assessment of a Subject-Specific Mathematical Model of Blood Volume Kinetics for Prediction of Physiological Response to Hemorrhagic Shock and Fluid Resuscitation

Subject-specific mathematical models for prediction of physiological parameters such as blood volume, cardiac output, and blood pressure in response to hemorrhage have been developed. In silico studies using these models may provide an effective tool to generate pre-clinical safety evidence for medical devices and help reduce the size and scope of animal studies that are performed prior to initiation of human trials. To achieve such a goal, the credibility of the mathematical model must be established for the purpose of pre-clinical in silico testing. In this work, the credibility of a subject-specific mathematical model of blood volume kinetics intended to predict blood volume response to hemorrhage and fluid resuscitation during fluid therapy was evaluated. A workflow was used in which: (i) the foundational properties of the mathematical model such as structural identifiability were evaluated; (ii) practical identifiability was evaluated both pre- and post-calibration, with the pre-calibration results used to determine an optimal splitting of experimental data into calibration and validation datasets; (iii) uncertainty in model parameters and the experimental uncertainty were quantified for each subject; and (iv) the uncertainty was propagated through the blood volume kinetics model and its predictive capability was evaluated via validation tests. The mathematical model was found to be structurally identifiable. Pre-calibration identifiability analysis led to splitting the 180 min of time series data per subject into 50 and 130 min calibration and validation windows, respectively. The average root mean squared error of the mathematical model was 12.6% using the calibration window of (0 min, 50 min). Practical identifiability was established post-calibration after fixing one of the parameters to a nominal value. In the validation tests, 82 and 75% of the subject-specific mathematical models were able to correctly predict blood volume response when predictive capability was evaluated at 180 min and at the time when amount of infused fluid equals fluid loss.

A mathematical model of cardiovascular dynamics for the diagnosis and prognosis of hemorrhagic shock

A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.

Collective Variational Inference for Personalized and Generative Physiological Modeling: A Case Study on Hemorrhage Resuscitation

OBJECTIVE

Individual physiological experiments typically provide useful but incomplete information about a studied physiological process. As a result, inferring the unknown parameters of a physiological model from experimental data is often challenging. The objective of this paper is to propose and illustrate the efficacy of a collective variational inference (C-VI) method, intended to reconcile low-information and heterogeneous data from a collection of experiments to produce robust personalized and generative physiological models.

METHODS

To derive the C-VI method, we utilize a probabilistic graphical model to impose structure on the available physiological data, and algorithmically characterize the graphical model using variational Bayesian inference techniques. To illustrate the efficacy of the C-VI method, we apply it to a case study on the mathematical modeling of hemorrhage resuscitation.

RESULTS

In the context of hemorrhage resuscitation modeling, the C-VI method could reconcile heterogeneous combinations of hematocrit, cardiac output, and blood pressure data across multiple experiments to obtain (i) robust personalized models along with associated measures of uncertainty and signal quality, and (ii) a generative model capable of reproducing the physiological behavior of the population.

CONCLUSION

The C-VI method facilitates the personalized and generative modeling of physiological processes in the presence of low-information and heterogeneous data.

SIGNIFICANCE

The resulting models provide a solid basis for the development and testing of interpretable physiological monitoring, decision-support, and closed-loop control algorithms.

Mathematical Modeling, In-Human Evaluation, and Analysis of Volume Kinetics and Kidney Function after Burn Injury and Resuscitation

OBJECTIVE

Existing burn resuscitation protocols exhibit a large variability in treatment efficacy. Hence, they must be further optimized based on comprehensive knowledge of burn pathophysiology. A physics-based mathematical model that can replicate physiological responses in diverse burn patients can serve as an attractive basis to perform non-clinical testing of burn resuscitation protocols and to expand knowledge on burn pathophysiology. We intend to develop, optimize, validate, and analyze a mathematical model to replicate physiological responses in burn patients.

METHODS

Using clinical datasets collected from 233 burn patients receiving burn resuscitation, we developed and validated a mathematical model applicable to computer-aided in-human burn resuscitation trial and knowledge expansion. Using the validated mathematical model, we examined possible physiological mechanisms responsible for the cohort-dependent differences in burn pathophysiology between younger versus older patients, female versus male patients, and patients with versus without inhalational injury.

RESULTS

We demonstrated that the mathematical model can replicate physiological responses in burn patients associated with wide demographic characteristics and injury severity, and that an increased inflammatory response to injury may be a key contributing factor in increasing the mortality risk of older patients and patients with inhalation injury via an increase in the fluid retention.

CONCLUSION

We developed and validated a physiologically plausible mathematical model of volume kinetic and kidney function after burn injury and resuscitation suited to in-human application.

SIGNIFICANCE

The mathematical model may provide an attractive platform to conduct non-clinical testing of burn resuscitation protocols and test new hypotheses on burn pathophysiology.

Mathematical model of volume kinetics and renal function after burn injury and resuscitation

This paper presents a mathematical model of blood volume kinetics and renal function in response to burn injury and resuscitation, which is applicable to the development and non-clinical testing of burn resuscitation protocols and algorithms. Prior mathematical models of burn injury and resuscitation are not ideally suited to such applications due to their limited credibility in predicting blood volume and urinary output observed in wide-ranging burn patients as well as in incorporating contemporary knowledge of burn pathophysiology. Our mathematical model consists of an established multi-compartmental model of blood volume kinetics, a hybrid mechanistic-phenomenological model of renal function, and novel lumped-parameter models of burn-induced perturbations in volume kinetics and renal function equipped with contemporary knowledge on burn-related physiology and pathophysiology. Using the dataset collected from 16 sheep, we showed that our mathematical model can be characterized with physiologically plausible parameter values to accurately predict blood volume kinetic and renal function responses to burn injury and resuscitation on an individual basis against a wide range of pathophysiological variability. Pending validation in humans, our mathematical model may serve as an effective basis for in-depth understanding of complex burn-induced volume kinetic and renal function responses as well as development and non-clinical testing of burn resuscitation protocols and algorithms.