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Keywords: numerical optimization, inverse problems, sensitivity analysis, cardiovascular, compartmental models.
This volume synthesizes theoretical and practical aspects of both the mathematical and life science viewpoints needed for modeling of the cardiovascular-respiratory system specifically and physiological systems generally. Theoretical points include model design, model complexity and validation in the light of available data, as well as control theory approaches to feedback delay and Kalman filter applications to parameter identification. State of the art approaches using parameter sensitivity are discussed for enhancing model identifiability through joint analysis of model structure and data. Practical examples illustrate model development at various levels of complexity based on given physiological information. The sensitivity-based approaches for examining model identifiability are illustrated by means of specific modeling examples. The themes presented address the current problem of patient-specific model adaptation in the clinical setting, where data is typically limited.
Experimentalists tend to revel in the complexity and multidimensionality of biological processes. Modelers, on the other hand, generally look towards parsimony as a guiding prin ciple in their approach to understanding physiological systems. It is therefore not surprising that a substantial degree of miscommunication and misunderstanding still exists between the two groups of truth-seekers. However, there have been numerous instances in physiology where the marriage of mathematical modeling and experimentation has led to powerful in sights into the mechanisms being studied. Respiratory control represents one area in which this kind of cross-pollination has proven particularly fruitful. While earlier modeling ef forts were directed primarily at the chemical control of ventilation, more recent studies have extended the scope of modeling to include the neural and mechanical aspects pertinent to respiratory control. As well, there has been a greater awareness of the need to incorpo rate interactions with other organ systems. Nevertheless, it is necessary from time to time to remind experimentalists of the existence of modelers, and vice versa. The 4th Annual Biomedical Simulations Resource (BMSR) Short Course was held in Marina Del Rey on May 21-22,1989, to acquaint respiratory physiologists and clinical researchers with state-of-the art methodologies in mathematical modeling, experiment design and data analysis, as well as to provide an opportunity for experimentalists to challenge modelers with their more recent findings.
Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control uses a principle-based modeling approach and analysis of feedback control regulation to elucidate the physiological relationships. Models are arranged around specific questions or conditions, such as exercise or sleep transition, and are generally based on physiological mechanisms rather than on formal descriptions of input-output behavior. The authors ask open questions relevant to medical and clinical applications and clarify underlying themes of physiological control organization. Current problems, key issues, developing trends, and unresolved questions are highlighted. Researchers and graduate students in mathematical biology and biomedical engineering will find this book useful. It will also appeal to researchers in the physiological and life sciences who are interested in mathematical modeling.
Keywords: lumped compartment models, parameter estimation, subset selection, non-linear least squares optimization, cardiovascular models, respiratory models.