Question 3: Medical Case Study ALL PARTS WITH WORK SHOWN

(f) Estimate how much addit 3. Medical Case Study: Flux of Fluid from a Capillary20 The heart pumps blood throughout the body, the arteries are the blood vessels carrying blood away from the heart, and the veins return blood to the heart. Close to the heart, arteries are very large. As they progress toward tissues (such as the brain), the arteries branch repeatedly, getting smaller as they do. The smallest blood vessels are capillaries- microscopic, living tubes that link the smallest arteries to the smallest veins. The capillary is where nutrients and fluids move out of the blood into the adjacent tissues and waste products from the tissues move into the blood. The key to this process is the capillary wall, which is only one cell thick, allowing the unfettered passage of small molecules, such as water, ions, oxygen, glucose, and amino acids, while preventing the passage of large components of the blood (such as large proteins and blood cells). Precise measurements demonstrate that the flux (rate of flow) of fluid through the capillary wall is not constant over the length of the capillary. Fluids in and around the capillary are subjected to two forces. The hydrostatic pressure, resulting from the hearts pumping, pushes fluid out of the capillary into the surrounding tissue. The oncotic pressure drives absorption in the other direction. At the start of a capillary, where the capillary branches off the small artery, the hydrostatic pressure is high while the oncotic pressure is low. Along the length of the capillary, the hydrostatic pressure decreases while the oncotic pressure is approximately constant. See Figure 5.92. Hydrostatic pressure vector Oncotic pressure vector Tissue Capillary wall Artery Blood StreamDirection of blood flow Vein Figure 5.92: Vectors representing pressure in and out of capillary For most capillaries there is a net positive value for flow: more fluid flows from the capillaries into the surrounding tissue than the other way around. This presents a major problem for maintaining fluid balance in the body. How is the fluid left in the tissues to get back into circulation? If it cannot, the tissues progressively swell (a condition called aAIJedemaaAl). Evolution's solution is to provide humans and other mammals with a second set of vessels, the lymphatics, that absorb extra tissue fluid and provide one-way routes back to the bloodstream. 330 Along a cylindrical capillary of length L = 0.1 cm and radius r = 0.0004 cm, the hydrostatic pressure, ph, varies from 35 mm Hg at the artery end to 15 mm Hg at the vein end. (mm Hg, millimeters of mercury, is a unit of pressure.) The oncotic pressure, Po, is approximately 23 mm Hg throughout the length of the capillary. 391 (a) Find a formula for Ph as a function of x, the distance in centimeters from the artery end of the capillary, assuming that Ph is a linear function of x. (b) Find a formula for p, the net outward pressure, as a function of x. (c) Write and evaluate an integral for the average outward net pressure in the capillary. D-1 (d) The rate of movement, j, of fluid volume per capillary wall area across the capillary wall is proportional to the net pressure. We have j = k . p where k, the hydraulic conductivity, has value A-T k = 10-7 cm E-T sec . mm Hg Check that j has units of volume per time per area. 1-7 (e) Estimate the net volume flow rate (volume per unit time) through the wall of the entire capillary using the average pressure. 4. Medical Case Study: Testing for Kidney Disease21