Key result
A nonconvex constrained minimisation model solved by a proximal block coordinate descent method successfully determined the 3D position of LV contours using real 2D echocardiography data.
A novel mathematical model using nonconvex constrained minimisation provides a feasible computational approach for recovering 3D left ventricular shapes from standard 2D echocardiography data.
A mathematical model in the form of a nonconvex constrained minimisation problem, aimed to determine the 3D position of LV contours using 2D echocardiography data for the entire cardiac cycle is proposed. It can be considered as a quadratically constrained quadratic program in terms of one of four variables with the others fixed. The model is solved by a proximal block coordinate descent method with cyclic order and the convergence of the algorithm is proved by using the Kurdyka-Lojasiewicz property. The model does not require unsuitable assumptions in practical environments and numerical experiments show its suitability in working with real echocardiography data.
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Ahn et al. (2021) studied Left ventricular shape recovery. Nonconvex constrained minimisation model was evaluated on 3D position of LV contours. A nonconvex constrained minimisation model solved by a proximal block coordinate descent method successfully determined the 3D position of LV contours using real 2D echocardiography data.
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