Multiple modeling in the study of interaction of hemodynamics and gas exchange
Introduction
Grodins [1] presented the first mathematical dynamic model of the respiratory system in 1954. Horgan, Grodins, Milhorn, Fincham, and Lorenzo followed this work [2], [3], [4], [5], [6], [7]. Many comprehensive mathematical models of the human respiratory system as well as cardiovascular system were published in the past years. Many of these models are dealing only with either gas exchange process or hemodynamics. Only a few works represent the comprehensive functions of both ventilatory and circulatory hemodynamics. Further understanding of the mechanism of the interaction of respiration and circulation may play an important rule in the protection technique development for some special environment, such as flight conditions of hypobaric hypoxia and hypobaric oxygen inhalation.
The purpose of this paper is to develop an integrated model of cardio-pulmonary system and to study the interaction of hemodynamics and gas exchange. To be able to present the systemic interaction of the two physiological systems, an integrated model is developed. It consists of two human physiological systems: respiratory and circulatory systems. This model can be depicted as follows: (1) the process of gas transport, exchange and storage; (2) a pressure-flow model; (3) an alveolar ventilation controller; (4) a cardiac output controller; and (5) a controller of frequency of breathing.
Using the model presented in this paper, normal and hypoxic physiological conditions are simulated. Results referring to steady-state and transient conditions are presented and compared with the data previously reported.
Section snippets
Model description
Fig. 1 shows a schematic diagram of the model of hemodynamics and gas exchange. This model consists of five parts: the multi-element, nonlinear mathematical model of human circulatory system, the model of oxygen (O2) and carbon dioxide (CO2) exchange, transport and storage, the model of respiratory frequency and the controllers that adjust cardiac output (Q) and alveolar ventilation . Each part of the model is depicted in this section. A full list of the symbol used is given in the
Simulation results
This model was implemented using an IBM compatible personal computer. Relevant parameters in this model are given in Table 1 in terms of [5], [6], [9], [10], [11], [12]. The model was adjusted to present a subject with a resting heart rate of 72 beats per second. It was assumed that oxygen metabolic rates in body tissues and brain tissue are constant. A comprehensive set of simulations was performed in order to test the model under the normal and hypoxic physiological conditions. Steady-state
Discussion
Responses in the respiratory and circular systems to hypoxia are given. Fig. 2, Fig. 3 describe their mutual interactions during 15 min hypoxia ) and subsequent recovery. The ratio of alveolar ventilation to cardiac output decides whether gas pump can accord with blood pump. Its normal range is from 0.7 to 1. Fig. 5 shows that it is higher than the normal range during hypoxia. This result illustrates that there is not enough Q that all gas in the lung can exchange with,
Summary
The interaction of hemodynamics and gas exchange is studied with the model presented in this paper. It consists of both respiratory and circulatory systems. Model simulations provide results of both dynamic and steady-state responses for different PI,O2. Steady-state results agree with the data reported in the literature. Dynamic results reflect the interaction of hemodynamics and gas exchange.
Using this model, the changes of pulmonary arterial pressure Ppula and left ventricular pressure Plv
Acknowledgements
The Chinese National Natural Science Foundation and The Ministry of Science and Technology supported this work.
Anqi Qiu was born in 1976 and received the B.S. degree in Biomedical Engineering from Tsinghua University, Beijing, China, in 1999. Since then she has been a graduate student in Biomedical Engineering at Tsinghua University. Her main areas are mathematical modeling of metabolism.
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Anqi Qiu was born in 1976 and received the B.S. degree in Biomedical Engineering from Tsinghua University, Beijing, China, in 1999. Since then she has been a graduate student in Biomedical Engineering at Tsinghua University. Her main areas are mathematical modeling of metabolism.
Jing Bai received her B.S. in Physics at Jilin University, Changchun, People's Republic of China, in 1982. She then obtained the M.S. and Ph.D. from Drexel University, Philadelphia, in 1983 and 1985. From 1985 to 1987 she was a Research Associate and Assistant Professor with the Biomedical Engineering and Science Institute of Drexel University. In 1988 and 1991, she become an Associate Professor and Professor of Electrical Engineering Department of Tsinghua University, Beijing, China. She is appointed as Deputy Director of Biomedical Engineering Program of Tsinghua University since 1988 and the Vice Dean of the School of Life Science and Engineering of Tsinghua University since 1994. Her research activities have included mathematical modeling and simulation of cardiovascular system, optimization of cardiac assist devices, medical ultrasound, telemedicine, home health care network and home monitoring devices, and medical informatics. She has published two books, over 80 journal papers and over 60 conference proceedings papers. She become a senior member of IEEE since 1991. From 1997, she become Associate Editor for IEEE Transactions on Information Technology in Biomedicine. She is also a committee member of China Association for Science and Technology, Vice Dean of the academic committee of the Chinese Society of Biomedical Engineers, Secretary in General of Chinese Bioelectronics Society, and Council member of Beijing Biomedical Engineering Society.