Question

10) In chronic hypertension, vessel radius, r, is reduced due to a thickening of the vessel wall. Poiseuille's Law is stated as follows, 8 xn XL RE- TT X a) According to Poiseuille's Law, state what happens to blood flow resistance, R, when vessel radius, r, is reduced for a person who suffers from chronic hypertension. The equation of fluid flow rate can be stated as follows, LAP 8 XI, X7 x L Хr b) According to the equation of fluid flow rate, state whether the pressure difference, AP, is expected to stay the same, increase, or decrease due to the reduction in the radius, r, of the vessel for a person who suffers from chronic hypertension, c) Given the following factor of change in the vessel radius, r, fill in the rest of the table: Factor of change of vessel radius Factor of change of Resistance, R Factor of change of pressure difference, AP x 1/3 d) Based on your table values, given the average mean arterial pressure, AP, for a healthy adult is 85mm-Hg, provide the numerical value of the mean arterial pressure for an adult who suffers from chronic hypertension.

Answer 1

a) Here , it is given that

$R\propto 1/r^4$

So, as r is reduced, 1/r^4 increases and R increases.

b) The equation for pressure gives that

$\Delta P\propto 1/r^4$

So, as r reduces, 1/r^4 increases and the pressure difference increases.

c) It is given that

$R\propto 1/r^4$

So,

Here, r' = r/3

r/r' = 3

So,

R'/R = 3^4 = 81

So,

R' = R x 81

For the change in pressure also, the relation is same.

So,

$\Delta P' = \Delta P *81$

d) For a healthy adult, the pressure difference is 85 mm Hg

So,

using the equation above,

$\Delta P' = \Delta P *81 = 85*81 = 6885 mm Hg$