| The cardiovascular system can be numerically modeled as
a series of reservoirs with resistance to flow between reservoirs
and with capacitances describing the ability of the reservoirs to
expand with pressure. The addition of the heart valves introduces
nonlinear elements into the model which can be mode led as
piecewise-linear combinations of multiple linear functions. The
medium, blood, is actively transported between the reservoirs by the
active contraction of the pump, the heart, with the system dynamics
defined by the particular system parameters. Passive transport
mechanisms, such as diffusion, and active mechanisms, such as
molecular pumps, move the components of blood between the
cardiovascular system and the rest of the body.
I will go through the history of the model, my additions to the
model as an interactive experimental testbed, and show my latest
additions of (1) valve malfunction, presence, and absence, along
with (2) selectable changes in the network topology. This will
demonstrate what the model predicts for how valve function and
malfunction affects the system dynamics of the cardiovascular
physiology. I will show animated functional models of flow dynamics,
and show how the state space diagram allows for cardiovascular
physiological parameters to be read from the graphical output, and
how these models can be used for "personalized medicine" for
patient care. An extension of this model into the cerebrovascular
system for one particular patient of neurosurgical interest will
also be described along with further work to be done on this
model. |