Musings of a Compulsive Thinker

Modeling the cardiovascular system

There are several popular models of the cardiovascular (CV) system. Depending on your training and experience, one may make more sense than others. Personally, I prefer the fluid flow model; incidentally, this is probably the closest analog to the actual CV system itself, because blood behaves largely as a fluid.

The Windkessel fluid flow model is relatively straight-forward, with elements representing the aorta and the peripheral circulation (i.e., all of the other veins, arteries, etc. in the body). The aorta is modeled by an elastic chamber, exerting pressure on the fluid it contains, and the peripheral circulation is modeled as a rigid tube of constant resistance; the system input is given as a volume inflow rate.

Another analog to this model is that of an electrical circuit:


The circuit can be laid out as follows:

The heart will be represented by an alternating-current (AC) current source, providing a current (blood flow rate) of specified period and amplitude (ranging from zero to a positive value). The flow will then pass through a diode (valve) to prevent backflow into the source (heart). Here, current (blood flow) can pass through the diode (valve) in one direction only.

The flow then encounters an inductor (arterial element) and resistor (aorta) in parallel. Here, the resistance is the proportionality of the voltage (pressure) across the element to the current (blood flow rate) through it; the inductor (inertial component) induces a voltage (pressure) that opposes any change in current (blood flow rate).

Following this, the flow encounters a capacitor (systemic/arterial compliance) and resistor (systemic resistance) in parallel. Here, the capacitor (compliance/elasticity) stores an amount of charge (blood volume) proportional to the voltage (pressure) across the element (aorta); i.e., it stores an amount of energy proportional to one-half the square of the voltage (pressure). Resistance here is the same as described above.

The circuit after this point goes back to the source, with a branch to common ground (blood supply, "reservoir"). Here, ground (supply) merely provides a reference "low" voltage (pressure) for the rest of the circuit.

>> Cole et al. (2005): "A LabVIEW Model Incorporating an Open-Loop Arterial Impedance and a Closed-Loop Circulatory System," Annals of Biomedical Engineering.

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Labels: engineering, science

posted by the alygator @ 1:21 PM