Calculating Stress Strain Curves in Nonlinear Arterial Mechanics

• Samuel Cash, Mathematics, University of Delaware

• Pak-Wing Fok, Mathematics, University of Delaware

In this presentation, we seek to understand the effects of uniaxial tension on coronary arteries through the calculation of stress-strain curves. While the arterial wall is composed of three layers (adventitia, media and intima), a single layer model is used in order to represent these individual layers separately. Stress-strain models of these arterial layers prove useful in hemodynamics simulations and cardiovascular disease. Mechanical models of an artery are integral to the understanding of Glagov Remodeling: which describes how arteries change their shape in response to an increased atherosclerotic burden.

 Using MatLab, we have created a script that can compute the stress-strain curves for the arterial layer given its mechanical properties. We then compute the circumferential stretch and hoop stress as a function of radius for different blood pressures. For these blood pressures, we average the hoop stress and circumferential stretch over the radius of the arterial wall in order to derive a stress-strain curve. The collagen fibers present in arteries contribute to their stiffness, noticeably increasing the exponential growth of hoop stress in relation to the stretch. In contrast, removal of collagen fibers from the model produces a significantly more linear stress-strain curve. Our simulated stress strain curves agree with the empirical curves from previously published data for individual arterial layers.