Biomedical Engineering Reference
In-Depth Information
intra-atrial pressure, which causes blood within the atrium to push against the valve
inducing valve opening. Once blood begins to enter the ventricle, the intra-ventricular
pressure slowly rises, eventually surpassing the pressure within the atrium. This adverse
pressure gradient slows the blood flow into the ventricles and helps to close the valve leaf-
lets. An interesting occurrence during mitral valve function is that when the ventricles are
in a relaxed state, the valve orifice is larger than that when the ventricles are actively con-
tracting. This aids in blood flow through the valve and aids the valve achieving a secure
closed position. Remember that the papillary muscles do not function to open or close the
valve; instead they prevent the reversing of the valve direction during systole (i.e., into the
atrium). These muscles are also a structural extension of the valve leaflets and can assume
some of the stresses and strains that the leaflets experience during the cardiac cycle. When
both the mitral valve and the aortic valve are closed (isovolumic contraction and isovolu-
mic relaxation), which is coupled to ventricular contraction or relaxation, the papillary
muscles have a small but regulatory role on intra-ventricular pressure. Recall that during
this time, the majority of the pressure is generated from the contraction of the cardiac
muscles or is relieved by the relaxation of the muscle cells. The tension generated by the
papillary muscles can change the radius of curvature of the mitral valve leaflets, which
may change the surface area of the ventricular wall. This is directly related to the pres-
sures that are exerted on the internal and external membrane of the leaflet. Therefore, by
changing the tension in the papillary muscles, the pressure within the ventricle and the
atrium must be changed to balance the forces. The relationship that governs the pressure-
tension relationship of the mitral valve leaflets is
T
i
r
i
1
T
e
r
e
p
i
2
p
e
5
ð
4
4
Þ
:
where p is the pressure, T is the tension, and r is the radius of curvature for the internal
surface (i) or the external surface (e) of the valve leaflet, assuming uniform mechanical and
geometric properties.
Example
Calculate the tension needed on the interior side of the mitral valve leaflet to maintain the
valve in the closed state immediately after valve closure. Assume that at valve closure there is a
pressure difference of 1.5 mmHg between the ventricle and the atrium. The atrial pressure is
3 mmHg, and the radii of curvature for the inner and the outer membrane of the leaflet are 1 cm
and 1.2 cm, respectively. Assume that the mitral valve leaflet is one-third of a spherical shell
with a uniform width of 2 mm.
Solution
To calculate the tension on the outer leaflet we will first need to calculate the exposed area of
the leaflet. With the assumption that the leaflet is a spherical shell, the area of interest is
5
120
360
L
5
2
π
1
:
2cm
2
51 cm
:
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