Although Eq. (3.41) was derived for a thin-walled cylinder, it can be shown that

Question

Although Eq. (3.41) was derived for a thin-walled cylinder, it can be shown that it provides a reasonable estimate of the mean circumferential stress in a thick-walled tube as well. Note, therefore, that in hypertension (i.e., a persistent increase in blood pressure), the aorta distends (i.e., a increases) and the wall thins (i.e., h decreases). Hence, sigma_theta_theta increases tremendously. If the hypertensive pressure PH = nP, where n is a number and the luminal radius returns to sigma_theta_theta due to smooth muscle contraction and a shear-stress-mediated vaso-constriction, how much does the aorta need to thicken to restore sigma_theta_theta back to its original value? Find data in the literature on aortic morphology in hypertension to see if this is borne out of data.

Reference: Eq. (3.41) is sigma_theta_theta = Pa/h

o thin wan Eq. (3.41) was derived for a thin-walled cylinder, it can be Although shown that it provides a reasonable estimate of the mean

Explanation / Answer

restoration of thickness of walls of aorta-

if luminal radius and wall thickness are dictated by flow and pressure, then restoring z to its original value requires a change in axial force f, which typically would cause a change in length (e.g., possible tortuosity). That responses to all stresses must be considered together is reinforced by observed, coupled effects of pressure (e.g., cyclic circumferential stress or strain) and flow (wall shear stress) induced changes at cellularand tissue levels

following can be an added information regarding above phenomena-

As the pressure increases above physiologic values, more collagen fibers become load bearing and their stiffness limits arterial distension, providing the classic nonlinear behavior observed in arterial mechanics.Elastin is organized into elastic fibers in the wall during arterial development in a complex process that requires spatial and temporal coordination of numerous proteins.

Hypertension causes and is caused by significant changes in the structure and function of arteries.

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