The Heart - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 124

p o b 3 2r 3 1 a 3 p i a 3 2r 3 1 b 3

ð Þ ð Þ

σ θ ð r Þ 5

Þ 2 2r 3 ð a 3

2 b 3

2r 3 ð a 3

2 b 3

Þ

respectively.
4.5 There are four valves present within the heart: the mitral valve (between the left atrium and
left ventricle), the tricuspid valve (between the right atrium and right ventricle), the aortic
valve (between the left ventricle and the aorta), and the pulmonary valves (between the right
ventricle and the pulmonary artery). The function of the mitral and tricuspid valves is very
similar, and the same is true for the aortic and pulmonary valves. The mitral and the tricus-
pid valves remain open for approximately 75% of the cardiac cycle, so that blood flows freely
from the atria to the ventricles. As the ventricles begin to contract, these valves will close
and the aortic and pulmonary valves will open. The mitral and the tricuspid valves are con-
nected to the chordate tendineae and the papillary muscles which prevent the valves from
bulging (and potentially opening) into the atria. The most important function of the valve
leaflets is to determine the direction of blood flow through the heart. The pressure-tension
relationship for the valve leaflets can be represented as

T e
r e
The Gorlin equation can approximate the aortic valve area as

T i
r i 1

p i 2 p e 5

Cardiac Output

Valve Area 5 p

Mean Pressure Gradient

44 3 ð Heart Rate Þð Systolic Ejection Period Þð Þ

:

4.6 Coronary artery disease is characterized by a reduction in the coronary artery blood flow,
which can eventually lead to cardiac muscle tissue death. The coronary arteries are responsi-
ble for supplying the cardiac tissue with the oxygen/nutrients it needs to contract during the
entire cardiac cycle. Myocardial infarction is characterized by a section of cardiac tissue that
begins to die because it does not receive enough blood. This region will not contract as
strongly as possible, and this can have a drastic effect on the blood delivery to the vascular
system (depending on the size of the infarcted region). Heart valve disease is characterized
by a destruction of the heart valves, which can potentially affect blood flow through the
heart. If the valves do not open fully, there will likely be a reduction in blood flow to the car-
diovascular system, and if the valves do not close fully, then there is the likelihood for back-
flow of blood into the heart.

HOMEWORK PROBLEMS
4.1 Blood returning to the human heart in one of the pulmonary veins will drain first into the
_______, after which it passes into the ______ and then enters the _____ circulation.
4.2 The occurrence of cardiovascular diseases is dependent on the country of origin. For instance,
Greece has a much lower cardiovascular disease rate than the United States. List a few
possible reasons for this dependence. Would it be possible to test the reasons that you list,
and how would you test them?