Introduction to Cardiovascular Modeling

In the literature, often the Bergman (1981) minimal model is discussed. This starts with the glucose and insulin balances, similar to Eqns. (18.1) and (18.2). The insulin concentration Cj does not affect the glucose balance directly. Instead, it acts through a separate compartment, the output of the compartment is Ciactive- The relationship suggested, amongst others, by Khoo (2000) is  

This equation is similar to Eqn. (18.5), with t= 1/ 2 and gain K = ki/k2. The gain K can, however, easily be incorporated in the rate constant y, in which case the model discussed in this chapter becomes the Bergman minimal model. 

The human cardiovascular system is very complex and the possibilities for model validation are limited, even though blood flow and pressures at many locations in the body can be measured. The purpose of a model is usually to study the blood circulation, in particular flow and pressure effects. 

In cardiovascular modeling often flow elements are used and it is assumed that the heart pulsates with a particular frequency. This pulsation is called the driving function (Sacca, 2003). 

In another approach in which heart rate variability, variations in cardiac cycle and arterial blood pressure are modeled, also flow elements are used, in addition, a baroreflex model is introduced, affecting the heart rate and the stroke volume of the heart. By introducing a time delay between the baroreflex input and output, an unstable system is created that continues to oscillate and explains the heart rate variability and variations in the cardiac cycle. Both modeling approaches will be briefly discussed in this chapter. 

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