Atherosclerosis is a cardiovascular disease that involves the accumulation of cholesterol in the arterial wall in regions with damaged endothelial cells. Assume that the damaged region is a circular hole with radius b. the thickness of the endothelial layer can be neglected. The endothelial layer is impermeable to cholesterol and plasma, except in the damaged region. The subendothelial space can be treated as a semi-infinite porous material with hydraulic conductivity K. The transport of fluid and cholesterol is in the radial direction and is symmetric about the center of the hole. The diffusion coefficient of cholesterol in the subendothelial tissue is D. The concentration of cholesterol and the hydrostatic pressure at r = b are approximately equal to those in the plasma, which are Cp and p0 respectively. The concentration and pressure at r→∞ are assumed to be zero. Determine the distribution of pressure in the subendothelial space in the steady state and evaluate the pressure at r = 0.68 mm. P0 = 135mmHg and Cp = 100 mg/dl, b = 0.2mm. Please give your answer in kPa.

Atherosclerosis is a cardiovascular disease that involves the accumulation of cholesterol in the arterial wall in regions with damaged endothelial cells. Assume that the damaged region is a circular hole with radius b. the thickness of the endothelial layer can be neglected. The endothelial layer is impermeable to cholesterol and plasma, except in the damaged region. The subendothelial space can be treated as a semi-infinite porous material with hydraulic conductivity K. The transport of fluid and cholesterol is in the radial direction and is symmetric about the center of the hole. The diffusion coefficient of cholesterol in the subendothelial tissue is D. The concentration of cholesterol and the hydrostatic pressure at r = b are approximately equal to those in the plasma, which are Cp and p0 respectively. The concentration and pressure at r→∞ are assumed to be zero. Determine the distribution of pressure in the subendothelial space in the steady state and evaluate the pressure at r = 0.68 mm. P0 = 135mmHg and Cp = 100 mg/dl, b = 0.2mm. Please give your answer in kPa.

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