Indirect estimation of parameters in a flexible tube, pulsatile flow system
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A mathematical model of pulsatile flow and pressure in a flexible tube with a possible branch and stenosis, or constriction, was formulated. Solution of the model equations was performed by the finite element method and a numerical integration procedure. An in vitro experimental model of pulsatile flow in a flexible tube with a stenosis and a branch was devised to provide observed waveforms and directly measured vessel parameter values. The model response satisfactorily matched the experimental data and exhibited sensitivity to the parameters of interest: vessel compliance, peripheral resistance, and severity and location of the stenosis. The model response was not sensitive to the vessel radius;The Gauss-Newton algorithm was used to minimize the sum of squared error between model response and experimental waveforms by varying the model parameters. Validation of the parameter estimation technique was performed by solving the model equations with measured values assumed for the system parameters and using the resulting waveforms in place of measured data. The vessel radius could not be estimated due to lack of sensitivity. The remaining parameters of interest could be reliably estimated except in the case of a mild stenosis, for which the stenosis location could not be estimated.