Blood vessels

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Blood circulation is a system of fluids driven by pressure gradients in a network of elastic tubes. Poiseuille's law describes the flow in small vessels (arterioles, capillaries, venules) where Re < 2100 and the flow is laminar. The key element is r: very small changes in radius have a huge effect on resistance (arterioles of 10100 m are the main regulators of peripheral resistance).

In the aorta, Re 30004000 and the flow is transitionally turbulent in systolic. The modified Bernoulli equation quantifies how pressure falls with increasing velocity (arterial stenosis: reduction in r v P_distal, transstenotic gradient threshold of hemodynamic significance when P > 5 mmHg = 667 Pa).

Pulse wave velocity (PWV) measures arterial stiffness: a young, elastic aorta (low E_inc) has PWV 47 m/s; in atherosclerosis, collagen replaces elastin (E_inc increases) and PWV rises to 1015 m/s. Carotid-femoral PWV is the Gold Standard of arterial stiffness and predicts cardiovascular risk regardless of pressure.

Endothelial shear stress (_shear 17 Pa in physiological laminar flow) regulates endothelial biology: it activates eNOS (vasodilator NO production) and suppresses adhesion molecules. In areas of disturbed flow (bifurcations, curvatures: low and oscillatory _shear) atherogenesis is favored. This is the biophysical mechanism that explains the preferential location of atheroma plaques.

Arterial compliance C_art = dV/dP determines how the aorta absorbs the systolic impulse (Windkessel effect): a compliant aorta cushions the pressure wave and produces more continuous capillary flow. With aging and atherosclerosis, C_art decreases increased pulse pressure increased cardiac work left ventricular hypertrophy. The dysfunctional hypertension-arterial stiffness-LVH cycle is one of the most common pathways of heart failure.

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Blood vessels

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gphysics.net - Dr. Willy H. Gerber
Palos Verdes, Costa de Corral, Chile