Estimating cardiac active tension from wall motion-An inverse problem of cardiac biomechanics

The contraction of the human heart is a complex process as a consequence of the interaction of internal and external forces. In current clinical routine, the resulting deformation can be imaged during an entire heart beat. However, the active tension development cannot be measured in vivo but may provide valuable diagnostic information. In this work, we present a novel numerical method for solving an inverse problem of cardiac biomechanics-estimating the dynamic active tension field, provided the motion of the myocardial wall is known. This ill-posed non-linear problem is solved using second order Tikhonov regularization in space and time. We conducted a sensitivity analysis by varying the fiber orientation in the range of measurement accuracy. To achieve RMSE <20% of the maximal tension, the fiber orientation needs to be provided with an accuracy of 10°. Also, variation was added to the deformation data in the range of segmentation accuracy. Here, imposing temporal regularization led to an eightfold decrease in the error down to 12%. Furthermore, non-contracting regions representing myocardial infarct scars were introduced in the left ventricle and could be identified accurately in the inverse solution (sensitivity >0.95). The results obtained with non-matching input data are promising and indicate directions for further improvement of the method. In future, this method will be extended to estimate the active tension field based on motion data from clinical images, which could provide important insights in terms of a new diagnostic tool for the identification and treatment of diseased heart tissue.