An Ultrasound-Driven Kinematic Model for Deformation of the Infarcted Mouse Left Ventricle Incorporating a Near-Incompressibility Constraint

Mathematical models of varying complexity have proved useful in fitting and interpreting regional cardiac displacements obtained from imaging methods such as ultrasound speckle tracking or MRI tagging. Simpler models, such as the classic thick-walled cylinder model of the left ventricle (LV), can be solved quickly and are easy to implement, but they ignore regional geometric variations and are difficult to adapt to the study of regional pathologies like myocardial infarctions. Complex, anatomically accurate finite-element models work well, but are computationally intensive and require specialized expertise to implement. We developed a kinematic model that offers a compromise between these two traditional approaches, assuming only that displacements in the left ventricle are polynomial functions of initial position and that the myocardium is nearly incompressible, while allowing myocardial motion to vary spatially as would be expected in an ischemic or dyssynchronous LV. Model parameters were determined using an objective function with adjustable weights to account for confidence in individual displacement components and desired strength of the incompressibility constraint. The model accurately represented the motion of both normal and infarcted mouse LVs during the cardiac cycle, with normalized root mean square errors in predicted deformed positions of 8.2 ± 2.3% and 7.4 ± 2.1% for normal and infarcted hearts, respectively.