Lumped parameter estimation for the embryonic chick vascular system: a time-domain approach using MLAB

We have evaluated several lumped parameter analog models for the early chick embryonic vascular system that may be used to infer loading characteristics of the developing heart. We measured dorsal aortic pressure and flow simultaneously with a servo-null pressure system and a pulsed Doppler velocimeter. Four different analog circuit models were chosen for comparisons. We formulated the time-domain differential equations specifying the relations between pressure and flow in the models, and then estimated the lumped parameters that produced the best fit. The MLAB mathematical modeling software was used for solving differential equations, and for minimizing the difference between model-predicted values and experimental data. The traditional three-element Windkessel model with an added inductance term was most often the best-fitting model. This is compatible with the previous study using a frequency-domain approach. The procedures developed for the current study are adaptable for the study of a variety of nonlinear models, and distributed parameter models for mammalian cardiovascular development with mechanically, pharmacologically, or genetically altered conditions.