Dynamic Models and Parameter Estimation: The Hypoxic Ventilatory Response
Mathematical models of the control of breathing during dynamic changes in various stimuli (e.g., CO2, O2 and exercise) have been extremely useful  in understanding how ventilation is adjusted. In the physical sciences models can often be derived from fundamental physical relationships (e.g., the equations of motion for satellite orbits) but in physiology there are few such relationships to guide the model builder. The building of a model can be divided into two stages. First the structure of the model must be determined. The structure consists of the mathematical equations and any parameters that are not estimated from an individual data set (assumed values and known constants). Secondly, experiments and parameter estimation techniques are used to determine the values of certain parameters from individual experiments. The validation of the model using different data sets and experimental conditions can then be done. Frequently this validation process will suggest modifications to the model and the process starts over. This paper will discuss how some of the assumptions that must go into devising a model for the hypoxic ventilatory response determine the characteristics of such a model. Ultimately a mathematical model is useful to summarize and predict the response and how it is changed by pathological, physiological or pharmacological interventions.
KeywordsSpike Train Ventilatory Response Hypoxic Response Asymmetric Response Hypoxic Ventilatory Response
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