The Heart - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 126

4.16 Recalculate the stress distribution through the cardiac wall with an inner radius of 3.5 cm and
an outer radius of 4 cm; however, the internal pressure during peak systole is 150 mmHg.
*4.17 Use the Cartesian Navier-Stokes equations to approximate the flow through the left ventri-
cle during peak systole. Assume that the gravitational effects on the flow are negligible
and that the opening orifice for blood to flow through is 25 mm (aorta). The thickness of
the left ventricle can be approximated as 2 cm. Use the pressure gradient during normal
aortic valve opening with a total length from the apex of the heart to the aortic valve of
4 cm. Determine the maximum velocity at both the aorta and within the ventricle.
4.18 During heart valve degeneration, the thickness of the valves can decrease. Calculate the
tension on the inner leaflet to maintain the valve in a closed position. Assume that during
valve closure, there is a pressure difference of 3 mmHg, with an atrial pressure of
5 mmHg. The radii of curvature for the inner leaflet is 1 cm and that for the outer leaflet is
1.05 cm. There is a uniform width of 3 mm across the leaflets.
4.19 Under a condition where the heart valves stiffen, the tension that they can withstand
reduces to 2 mN on the exterior surface and 0.5 mN on the interior surface. What is the
radius of curvature needed for the leaflets to maintain this pressure? Assume that all pres-
sure conditions are the same as in problem 4.18.
4.20 Modeling: Design a two-dimensional aortic valve geometry (including the aorta) using a
computational fluid dynamics program. Compute the velocity field behind the valve at
peak systole (assume that the pressure gradient is 15 mmHg across the section of the valve
shown in Figure 4.12 ).
References
[1] B. Bellhouse, F. Bellhouse, Fluid mechanics of model normal and stenosed aortic valves, Circ. Res. 25 (1969)
693.
[2] B.J. Bellhouse, Fluid mechanics of a model mitral valve and left ventricle, Cardiovasc. Res. 6 (1972) 199.
[3] A.J. Brady, Length dependence of passive stiffness in single cardiac myocytes, Am. J. Physiol. 260 (1991)
H1062.
[4] A.J. Brady, Mechanical properties of isolated cardiac myocytes, Physiol. Rev. 71 (1991) 413.
[5] K.D. Costa, P.J. Hunter, J.M. Rogers, J.M. Guccione, L.K. Waldman, A.D. McCulloch, A three-dimensional
finite element method for large elastic deformations of ventricular myocardium: I-Cylindrical and spherical
polar coordinates, J. Biomech. Eng. 118 (1996) 452.
[6] Y.C. Fung, Mathematical representation of the mechanical properties of the heart muscle, J. Biomech. 3 (1970)
381.
[7] Y.C. Fung, Biorheology of soft tissues, Biorheology 10 (1973) 139.
[8] J.M. Guccione, A.D. McCulloch, L.K. Waldman, Passive material properties of intact ventricular myocardium
determined from a cylindrical model, J. Biomech. Eng. 113 (1991) 42.
[9] J.M. Guccione, L.K. Waldman, A.D. McCulloch, Mechanics of active contraction in cardiac muscle: part II-
Cylindrical models of the systolic left ventricle, J. Biomech. Eng. 115 (1993) 82.
[10] J.M. Guccione, A.D. McCulloch, Mechanics of active contraction in cardiac muscle: part I-Constitutive rela-
tions for fiber stress that describe deactivation, J. Biomech. Eng. 115 (1993) 72.
[11] J.M. Guccione, K.D. Costa, A.D. McCulloch, Finite element stress analysis of left ventricular mechanics in the
beating dog heart, J. Biomech. 28 (1995) 1167.
[12] A.C. Guyton, Determination of cardiac output by equating venous return curves with cardiac response
curves, Physiol. Rev. 35 (1955) 123.