Abstract
This chapter introduces the main theoretical and practical topics which arise in the mathematical modeling of the human cardiovascular–respiratory system. These topics and ideas, developed in detail in the text, also represent a template for considering interdisciplinary research involving mathematical and life science disciplines in general. The chapter presents a multi-sided view of the modeling process which synthesizes the mathematical and life science viewpoints needed for developing and validating models of physiological systems. Particular emphasis is placed on the problem of coordinating model design and experimental design and methods for analyzing the model identification problem in the light of restricted data. In particular a variety of approaches based on information derived from parameter sensitivity are examined. The themes presented seek to provide a coordinated view of modeling that can aid in considering the current problem of patient-specific model adaptation in the clinical setting where data is in particular typically limited.
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Notes
- 1.
Aelius Galenus, born 129 or 131 ad in Pergamon, died 199, 201 or 216 in Rome(?).
- 2.
For simplicity of presentation we assume that the sampling times are the same for all measurable system outputs which in general is not case.
- 3.
In abuse of language we frequently find the statement that the parameter θ i is sensitive in a neighborhood of θ0.
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Batzel, J.J., Bachar, M., Karemaker, J.M., Kappel, F. (2013). Merging Mathematical and Physiological Knowledge: Dimensions and Challenges. In: Batzel, J., Bachar, M., Kappel, F. (eds) Mathematical Modeling and Validation in Physiology. Lecture Notes in Mathematics(), vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32882-4_1
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