Construction of a two-parameter empirical model of left ventricle wall motion using cardiac tagged magnetic resonance imaging data

Abstract

Background: A one-parameter model was previously proposed to characterize the short axis motion of the LV wall at the mid-ventricle level. The single parameter of this model was associated with the radial contraction of myocardium, but more comprehensive model was needed to account for the rotation at the apex and base levels. The current study developed such model and demonstrated its merits and limitations with examples.

Materials and methods: The hearts of five healthy individuals were visualized using cardiac tagged magnetic resonance imaging (tMRI) covering the contraction and relaxation phases. Based on the characteristics of the overall dynamics of the LV wall, its motion was represented by a combination of two components - radial and rotational. Each component was represented by a transformation matrix with a time-dependent variable α or β.Image preprocessing step and model fitting algorithm were described and applied to estimate the temporal profiles of α and β within a cardiac cycle at the apex, mid-ventricle and base levels. During this process, the tagged lines of the acquired images served as landmark reference for comparing against the model prediction of the motion. Qualitative and quantitative analyses were performed for testing the performance of the model and thus its validation.

Results: The α and β estimates exhibited similarities in values and temporal trends once they were scaled by the radius of the epicardium (r(epi))and plotted against the time scaled by the period of the cardiac cycle (T(cardiac)) of each heart measured during the data acquisition. α/repi peaked at about Δt/T(cardiac)=0.4 and with values 0.34, 0.4 and 0.3 for the apex, mid-ventricle and base level, respectively. β/r(epi) similarly maximized in amplitude at about Δt/T(cardiac)=0.4, but read 0.2 for the apex and - 0.08 for the base level. The difference indicated that the apex twisted more than the base.

Conclusion: It is feasible to empirically model the spatial and temporal evolution of the LV wall motion using a two-parameter formulation in conjunction with tMRI-based visualization of the LV wall in the transverse planes of the apex, mid-ventricle and base. In healthy hearts, the analytical model will potentially allow deriving biomechanical entities, such as strain, strain rate or torsion, which are typically used as diagnostic, prognostic or predictive markers of cardiovascular diseases including diabetes.

Figure 1

Tagged MRI of a human heart. Magnetization tag lines are the dark lines forming a uniform two dimensional mesh in the image. The square window identified with the red colored edges and is used for cropping the image at the center of the LV.

Figure 2

Selection of slices for viewing the LV from its short-axis. Slice numbering starts from the apex and increased towards the base. Slice thickness is adjusted so that twelve slices cover the LV fully.

Figure 3

Example of an annular mesh of simulated tag lines used in model fitting process. (a) Initial uniform mesh. (b) Deformed mesh calculated with specific values of the model parameters α and β.

Figure 4

LV wall at the (a) beginning and (b) end of systole as it twists at the base (slice # 9) and apex (slice # 4) levels in opposite orientations. The background images on the left are the tagged images of the LV wall and those on the right are the corresponding binary images. The LV wall rotates counter clockwise at the base and clockwise at the apes when viewed from the head-to-toe direction. The meshes of the red lines superimposed on the tagged images are the model predictions of the motions.

Figure 5

The variation of the radial displacement parameter (α) as a function of time within a cardiac cycle at the base (slice # 9), mid-ventricle (slice # 6) and apex (slice # 4) levels.r_epi is the end-diastolic radius of the LV wall at the epicardium at the indicated level. T_cardiac is the cardiac period. The error bars represent the intragroup (n=5) standard deviations.

Figure 6

The variation of the rotation parameter β as a function of time within a cardiac cycle at the base (slice # 9), mid-ventricle (slice # 6) and apex (slice # 4) levels.