Description of the deformation of the left ventricle by a kinematic model

A model of left ventricular (LV) kinematics is essential to identify the fundamental physiological models of LV deformation during a complete cardiac cycle as observed from the motion of a finite number of markers embedded in the LV wall. Kinematics can be described by a number of modes of motion and deformation in succession. An obvious mode of LV deformation is the ejection of cavity volume while the wall thickens. In the more sophisticated model of LV kinematics developed here, seven time-dependent parameters were used to describe not only volume change but also torsion and shape changes throughout the cardiac cycle. Rigid-body motion required another six parameters. The kinematic model employed a deformation field that had no singularities within the myocardium, and all parameters describing the modes of deformation were dimensionless. Note that torsion, volume and symmetric shape changes all require the definition of a cardiac coordinate system, which has generally been related to the measured cardiac geometry by reference to approximate anatomical landmarks. However, in the present study the coordinate system was positioned objectively by a least-squares fit of the kinematic model to the measured motion of markers. Theoretically, at least five markers are needed to find a unique set of parameters. In a computer simulation for 6, 14 and 100 markers, the stability of the parameter estimates was investigated. In a realistic case of normal cardiac deformation, 60 frames in time, 14 markers and a measuring error of ± 0.3 mm (S.D.), the standard error in the determination of the location of the coordinate origin and the direction of the torsion axis were ± 0.24 mm and ± 0.015 rad, respectively. For a simulated 100 g LV, errors per frame in the estimated parameters were: ± 0.6 ml in volume, ± 0.005 rad in torsion, and ± 0.002 in long-axis shape. Furthermore, in an experimental trial the kinematic model described the motion of 14 radiopaque markers implanted in a canine LV with a small r.m.s. error in the fit to each marker: ± 0.2 mm during ejection and ± 0.5 mm in the rest of the cycle. The time courses of all 13 kinematic parameters were obtained with high signal/noise ratios. During ejection, the major modes of deformation were torsion and axially symmetric shape change in conjunction with volume change.