A 5-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 make up the LV, taking into account the stationary apex and the moving base. After calculating the LV myocardium volume of the existing beating heart model, we use 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 now available to use with the existing MCAT methodology. To introduce more complex regional LV contraction and perfusion patterns, composites of dynamic heart models are used to create a central region with no or little motion and/or perfusion and a changeover to the normal motion and/or perfusion. Gated cardiac acquisitions for different clinical situations were simulated analytically: 1) a reduced regional motion and perfusion (50% and 75% of normal); 2) same perfusion as in (1) without motion intervention; and 3) washout from the normal myocardium of the LV to 20% of normal, with a reduction to only 40% of normal in the diseased region. Both motion and perfusion can change dynamically during a single rotation or multiple rotations of a simulated SPECT acquisition system.