A five-dimensional mathematical model for regional and global changes in cardiac uptake and motion

The objective of this work was to simultaneously introduce known regional changes in contraction pattern and perfusion to the existing gated Mathematical Cardiac Torso (MCAT) phantom heart model. We derived a simple integral to calculate the fraction of the ellipsoidal volume that makes up the left ventricle (LV), taking into account the stationary apex and the moving base. After calculating the LV myocardium volume of the existing beating heart model, we employed the property of conservation of mass to manipulate the LV ejection fraction to values ranging between 13.5% and 68.9%. Multiple dynamic heart models that differ in degree of LV wall thickening, base-to-apex motion, and ejection fraction, are thus available for use with the existing MCAT methodology. To introduce more complex regional LV contraction and perfusion patterns, we used composites of dynamic heart models to create a central region with little or no motion or perfusion, surrounded by a region in which the motion and perfusion gradually reverts to normal. To illustrate this methodology, the following gated cardiac acquisitions for different clinical situations were simulated analytically: 1) reduced regional motion and perfusion; 2) same perfusion as in (1) without motion intervention; and 3) washout from the normal and diseased myocardial regions. Both motion and perfusion can change dynamically during a single rotation or multiple rotations of a simulated single-photon emission computed tomography acquisition system.