I.
Introduction.
Mr Aiman has met a cardiologist at Hospital Seberang Jaya after suffering from
shortness of breath and chest pain. After examination from a doctor, the blood
pressure of Mr Aiman is higher compare than normal blood pressure. He was
diagnosed with arteriosclerosis where the lumen part of his artery was accumulated
with lipid and cholesterol. This caused the rate of changed of blood flow in Mr Aiman
is slow. The study shows that the rate of changed of blood flow for normal artery is
100𝑐𝑚3 /𝑚𝑖𝑛.
II.
Objective.
To measure the related rate of blood flow for arteriosclerosis patient with radius of
lumen 0.05cm and length of artery 20cm.
III.
Problem statement.
The rate of change of blood flow for normal artery is 100𝑐𝑚3 /𝑚𝑖𝑛 with radius of
lumen 0.2cm and the length of artery is 20cm. What is the rate of change of blood
flow for atherosclerosis patient with the radius of lumen 0.05cm.
IV.
Solution:
dv
dt
=
dv
dr
dr
× dt
Let r = 0.2 cm and l= 20 cm
𝑟
=
𝑙
𝑟
=
𝑙
0.2
20
1
100
𝚤 = 100𝑟
Let
𝑣 = 𝜋𝑟 2 𝑙
= 𝜋𝑟 2 (100𝑟)
= 100𝜋𝑟 3
Where
𝑑𝑣
𝑑𝑟
= 300𝜋𝑟 2
𝑑𝑟
To find 𝑑𝑡 = ? for normal person.
𝑑𝑟
100𝑐𝑚3 /𝑚𝑖𝑛 = 300𝜋(0.2)2 × 𝑑𝑡
𝑑𝑟
𝑑𝑡
25
= 3𝜋 𝑐𝑚𝑚𝑖𝑛−1
Hence, the rate of change of blood flow for atherosclerosis is
𝑑𝑣
𝑑𝑡
= ? when radius
0.05cm
let
𝑑𝑣
𝑑𝑡
=
𝑑𝑣
𝑑𝑟
×
𝑑𝑟
𝑑𝑡
25
= 300𝜋𝑟 2 × 3𝜋
25
= 300𝜋(0.05)2 × 3𝜋
= 6.25𝑐𝑚3 /𝑚𝑖𝑛
V.
Conclusion.
Hence, the rate of changed of blood flow on Mr Aiman who diagnosed
arteriosclerosis is 6.25𝑐𝑚3 /𝑚𝑖𝑛.