By Jerry J. Batzel, Franz Kappel, Daniel Schneditz, Hien T. Tran
The human cardiovascular and breathing keep an eye on platforms symbolize a huge point of interest for constructing physiological regulate conception a result of complexity of the keep watch over mechanisms concerned, the interplay among cardiovascular and respiration funcÂtion, and the significance of this interplay in lots of medical events. This quantity brings jointly the diversity of keep watch over approaches serious about the potent legislation of those structures and develops modeling subject matters, techniques, and key scientific purposes utilizing modern mathematical and keep watch over methodologies. The reader will achieve an appreciation of the way analytical options and ideas from optimum keep an eye on thought, platforms conception, and numerical research can be used to higher comprehend the legislation techniques in human cardiovascular and respiration platforms.
Cardiovascular and respiration structures: Modeling, research, and regulate makes use of a principle-based modeling method and research of suggestions keep an eye on rules to clarify the physiological relationships. types are prepared round particular questions or stipulations, equivalent to workout or sleep transition, and are mostly according to physiological mechanisms instead of on formal descriptions of input-output habit. The authors ask open questions correct to clinical and medical functions and make clear underlying issues of physiological keep watch over association. present difficulties, key matters, constructing developments, and unresolved questions are highlighted.
Researchers and graduate scholars in mathematical biology and biomedical engineering will locate this ebook important. it's going to additionally attract researchers within the physiological and lifestyles sciences who're drawn to mathematical modeling.
checklist of Symbols and Abbreviations; Preface; bankruptcy 1: The Cardiovascular process below an Ergometric Workload; bankruptcy 2: respiration Modeling; bankruptcy three: Cardiorespiratory Modeling; bankruptcy four: Blood quantity and the Venous procedure; bankruptcy five: destiny instructions; Appendix A:
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Extra info for Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control (Frontiers in Applied Mathematics)
Sample text
Because of the inherent modeling errors, an optimal control for the model system would not be an optimal control for the real cardiovascular system in general. 2 of Appendix A, we provide formulas for the elements of the matrix A. Under the transformation x -> £ the cost functional J takes the form where 24 Chapter 1. The Cardiovascular System under an Ergometric Workload with C = (q^, 0 , . . 49) with the given control u(t). 53) has a unique positive definite solution X if the pair (A, B) is stabilizable and the pair (C, A) is detectable.
3: The complete closed-loop model for the cardiovascular system. model validation based on the data obtained from bicycle ergometer tests with test persons in an upright sitting position. Data recordings began 10 minutes before the exercise phase started. The workload VTexer for the exercise phase, which also lasted for 10 minutes, was constant. In order to meet the assumptions of the modeling process, a rather low workload was chosen, Initially, only measurements for the heart rate H and the arterial systemic pressure P& were made.
Doppler echocardiographic devices, as for instance the Vingmed CFM 800 system, determine v(t) by directly measuring the velocity of the red blood cells relative to the sonar head of the device (using the Doppler effect) and then determine the VTI by numerical integration. In order that the Doppler echocardiographic measurements give a sufficiently good approximation for v(t), the following requirements have to be satisfied (see Fehske, 1988): • The axis of the sonar head has to be orthogonal to the cross section of the aorta, where the average flow velocity is determined.