Computational methods for flow in collapsible tubes

Collapsible Tubes can be used as a model to understand the interaction between biological tissues and fluid moving within said tissues. One interaction of paramount importance is the modeling of blood flow through arteries, where it is important to understand precipitating causes of embolisms, flow blockages and other phenomena. Also of interest in blood flow is the flow through arteries under an external load, such a blood pressure cuff, or in the intramyocardial coronary arteries during contraction of the left ventricle. Other important applications include the trachea during exhalation or coughing and the urethera.

In this thesis we formulate a mathematical model for a collapsible tube, deriving some necessary conditions for various tube response laws. Then a new computational methodology is developed to determine the best-fit values for parameters that describe constitutive behavior of the tube. Numerical results of varying multiple parameters are presented for both an expanded and a collapsed tube.