Nonhomogeneous Strain From Sparse Marker Arrays for Analysis of Transmural Myocardial Mechanics

Background: Knowledge of normal cardiac kinematics is important when attempting to understand the mechanisms that impair the contractile function of the heart during disease. The complex kinematics of the heart can be studied by inserting radiopaque markers in the cardiac wall and study the pumping heart with biplane cineradiography. In order to study the local strain, the bead array was developed where small radiopaque beads are inserted along three columns transmurally in the left ventricle. Method: This paper suggests a straightforward method for strain computation, based on polynomial least-squares fitting and tailored for combined marker and bead array analyses. Results: This polynomial method gives small errors for a realistic bead array on an analytical test case. The method delivers an explicit expression of the Lagrangian strain tensor as a polynomial function of the coordinates of material points in the reference configuration. The method suggested in this paper is validated with analytical strains on a deforming cylinder resembling the heart, compared to a previously suggested finite element method, and applied to in vivo ovine data. The errors in the estimated strain components are shown to remain unchanged on an analytical test case when evaluating the effects of one missing bead. In conclusion, the proposed strain computation method is accurate and robust, with errors smaller or comparable to the current gold standard when applied on an analytical test case.