Jerry J. Batzel

Cardiovascular and respiratory systems : modeling, analysis, and control

Preface 1. The cardiovascular system under an ergometric workload 2. Respiratory modeling 3. Cardio-Respiratory Modeling 4. Blood volume and the venous system 5. Future directions Appendix A. Supplemental calculations B. A Nonlinear feedback law C. Retarded functional differential equations: Basic theory Bibliography Index.

Modelling and disentangling physiological mechanisms: linear and nonlinear identification techniques for analysis of cardiovascular regulation

Cardiovascular (CV) regulation is the result of a number of very complex control interactions. As computational power increases and new methods for collecting experimental data emerge, the potential for exploring these interactions through modelling increases as does the potential for clinical application of such models. Understanding these interactions requires the application of a diverse set of modelling techniques. Several recent mathematical modelling techniques will be described in this review paper. Starting from Grangers causality, the problem of closed-loop identification is recalled. The main aspects of linear identification and of grey-box modelling tailored to CV regulation analysis are summarized as well as basic concepts and trends for nonlinear extensions. Sensitivity analysis is presented and discussed as a potent tool for model validation and refinement. The integration of methods and models is fostered for a further physiological comprehension and for the development of more potent and robust diagnostic tools.

Time delay in physiological systems: analyzing and modeling its impact.

This article examines the functional and clinical impact of time delays that arise in human physiological systems, especially control systems. An overview of the mathematical and physiological contexts for considering time delays will be illustrated, from the system level to cell level, by examining models that incorporate time delays. This examination will highlight how such delays in combination with other system structures and parameters influence system dynamics. Model analysis that reveals the influence of delays can also reveal related physiological effects which may have medical consequences and clinical applications.

Maximizing information from space data resources: a case for expanding integration across research disciplines

Regulatory systems are affected in space by exposure to weightlessness, high-energy radiation or other spaceflight-induced changes. The impact of spaceflight occurs across multiple scales and systems. Exploring such interactions and interdependencies via an integrative approach provides new opportunities for elucidating these complex responses. This paper argues the case for increased emphasis on integration, systematically archiving, and the coordination of past, present and future space and ground-based analogue experiments. We also discuss possible mechanisms for such integration across disciplines and missions. This article then introduces several discipline-specific reviews that show how such integration can be implemented. Areas explored include: adaptation of the central nervous system to space; cerebral autoregulation and weightlessness; modelling of the cardiovascular system in space exploration; human metabolic response to spaceflight; and exercise, artificial gravity, and physiologic countermeasures for spaceflight. In summary, spaceflight physiology research needs a conceptual framework that extends problem solving beyond disciplinary barriers. Administrative commitment and a high degree of cooperation among investigators are needed to further such a process. Well-designed interdisciplinary research can expand opportunities for broad interpretation of results across multiple physiological systems, which may have applications on Earth.

Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia.

This study develops a lumped cardiovascular-respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO(2) partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO(2) reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO(2) induced challenges. It is difficult to characterize cerebral CO(2) reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO(2) reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO(2) and O(2)) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO(2) partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.

Modeling the Cardiovascular-Respiratory Control System: Data, Model Analysis, and Parameter Estimation

Several key areas in modeling the cardiovascular and respiratory control systems are reviewed and examples are given which reflect the research state of the art in these areas. Attention is given to the interrelated issues of data collection, experimental design, and model application including model development and analysis. Examples are given of current clinical problems which can be examined via modeling, and important issues related to model adaptation to the clinical setting.

Sensitivity analysis of a model of the cardiovascular system

In this paper we consider the sensitivity analysis of a model of the cardiovascular system (CVS) simulating the transition to aerobic exercise and where the control for the system is implemented via an optimal control. Classical and generalized sensitivity analysis are discussed and compared and their application to the CVS model is analyzed

Bridging different perspectives of the physiological and mathematical disciplines

The goal of this report is to discuss educational approaches for bridging the different perspectives of the physiological and mathematical disciplines. These approaches can enhance the learning experience for physiology, medical, and mathematics students and simultaneously act to stimulate mathematical/physiological/clinical interdisciplinary research. While physiology education incorporates mathematics, via equations and formulas, it does not typically provide a foundation for interdisciplinary research linking mathematics and physiology. Here, we provide insights and ideas derived from interdisciplinary seminars involving mathematicians and physiologists that have been conducted over the last decade. The approaches described here can be used as templates for giving physiology and medical students insights into how sophisticated tools from mathematics can be applied and how the disciplines of mathematics and physiology can be integrated in research, thereby fostering a foundation for interdisciplinary collaboration. These templates are equally applicable to linking mathematical methods with other life and health sciences in the educational process.

Application of the Unscented Kalman Filtering to Parameter Estimation

Filtering is a methodology used to combine a set of observations with a model to obtain the optimal state. This technique can be extended to estimate the state of the system as well as the unknown model parameters. Estimating the model parameters given a set of data is often referred to as the inverse problem. Filtering provides many benefits to the inverse problem by providing estimates in real time and allowing model errors to be taken into account. Assuming a linear model and Gaussian noises, the optimal filter is the Kalman filter. However, these assumptions rarely hold for many problems of interest, so a number of extensions have been proposed in the literature to deal with nonlinear dynamics. In this chapter, we illustrate the application of one approach to deal with nonlinear model dynamics, the so-called unscented Kalman filter. In addition, we will also show how some of the tools for model validation discussed in other chapters of this volume can be used to improve the estimation process.

Space physiology IV: mathematical modeling of the cardiovascular system in space exploration.

Mathematical modeling represents an important tool for analyzing cardiovascular function during spaceflight. This review describes how modeling of the cardiovascular system can contribute to space life science research and illustrates this process via modeling efforts to study postflight orthostatic intolerance (POI), a key issue for spaceflight. Examining this application also provides a context for considering broader applications of modeling techniques to the challenges of bioastronautics. POI, which affects a large fraction of astronauts in stand tests upon return to Earth, presents as dizziness, fainting and other symptoms, which can diminish crew performance and cause safety hazards. POI on the Moon or Mars could be more critical. In the field of bioastronautics, POI has been the dominant application of cardiovascular modeling for more than a decade, and a number of mechanisms for POI have been investigated. Modeling approaches include computational models with a range of incorporated factors and hemodynamic sophistication, and also physical models tested in parabolic and orbital flight. Mathematical methods such as parameter sensitivity analysis can help identify key system mechanisms. In the case of POI, this could lead to more effective countermeasures. Validation is a persistent issue in modeling efforts, and key considerations and needs for experimental data to synergistically improve understanding of cardiovascular responses are outlined. Future directions in cardiovascular modeling include subject-specific assessment of system status, as well as research on integrated physiological responses, leading, for instance, to assessment of subject-specific susceptibility to POI or effects of cardiovascular alterations on muscular, vision and cognitive function.