DAVIS, OLGHA BASSAM. Refining an Elastic Constitutive Equation to Predict Aortic Pressure Distributions for Normotensive and Hypertensive Aortas. (Under the direction of Dr. Brooke N. Steele).
Constitutive equations are used to mathematically represent arterial wall mechanical properties. Accurate vascular wall models are crucial for providing acceptable simulation results of arterial blood pressure (ABP) wave propagation. An important consideration when determining the constitutive equation is the effect of ABP on vessel wall compliance; the tendency of the arteries to expand and contract in response to ABP. The goal of this work is to model the compliance of normotensive and hypertensive aortas to mathematically describe vessel distensibility. While large vessels exhibit a viscoelastic characteristic, the determination of pure elastic modulus is a reasonable first approximation. The arterial stiffness is expressed in terms of pressure-strain elastic modulus (Eo) and stress-strain Young’s modulus (E). The elastic modulus may be computed directly from gradients of pressure and diameter measurements. In addition to strain and pressure, Young’s modulus requires the cross-sectional area of the vessel wall to compute stress. Wall thickness (h) and vessel undeformed radius (ro) vary due to numerous factors including, but not limited to age and morbidity. In this work, three methods are used to approximate , compute the corresponding pressure for a given diameter, and compare the computed pressure to experimental data. The first method uses an empirical model by Olufsen to approximate with a decaying exponential function of and a constant offset . This term is used to compute pressure using an elastic constittive equation. For the second method, it is noted that for large vessels (ro>0.6cm), including the aorta, the previous empirical method relies only on the constant offset term. Therefore, this parameter is optimized for normotensive and hypertensive data using the Nelder-Mead method. Lastly, the third method incorporates patient-specific pulse pressure and diastolic radii, which are readily available from clinical diagnostic data, with an approximation of the pulsatile change in radius as a percentage of the undeformed radius. This percentage is different for normotensive and hypertensive models. All three methods are applied to data found in the literature including human and canine normotensive aortas and human hypertensive aortas. Based on this work, using patient-specific approach in estimating the pressure distributions for corresponding diameter measurements appears to be the best to approximate the normotensive pressure distribution for a given patient’s diameter measurements and pulse pressure readings. However, no conclusive evidence was found to determine a best-fit model to approximate pressure distribution for hypertensive subjects.
