Nonhomogeneous distributions of strains are simulated and utilized to determine two potential errors in the measurement of cardiac strains. First, the error associated with the use of single-plane imaging of myocardial markers is examined. We found that this error ranges from small to large values depending on the assumed variation in stretch. If variations in stretch are not accompanied by substantial regional changes in ventricular radius, the associated error tends to be quite small. However, if the nonuniform stretch field is a result of substantial variations in local curvature from their reference values, large errors in stretch and strain occur. For canine hearts with circumferential radii of 2 to 4 cm, these errors in stretch may be as great as 30 percent or more. Moreover, gradients in stretch may be over- or underestimated by as much as 100 percent. In the second part of this analysis, the influence of random measurement errors in the coordinate positions of markers on strains computed from them is studied. Arrays of markers covering about 16 cm2 of ventricular epicardium are assumed and nonuniform stretches imposed. The reference and deformed positions of the markers are perturbed with Gaussian noise with a standard deviation of 0.1 mm, and then strains are computed using either homogeneous strain theory or a nonhomogeneous finite element method. For the strain distributions prescribed, it is found that the finite element method reduces the error resulting from noise by about 50 percent over most of the region. Accurate measurements of cardiac strain distributions are needed for correlation with and validation of realistic three-dimensional stress analyses of the heart. Moreover, with the advent of increasingly effective noninvasive methods to measure cardiac deformation such as magnetic resonance imaging, the use of nonhomogeneous strain analysis to determine more accurate strain distributions has increasing clinical significance.
Three Dimensional Stress-Strain Analysis of a Typical Gas Turbine Blade using Finite Element Method
