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.
Student Theses (1)
L. Thämer. The Inverse Problem of the Heart Mechanics - Reconstruction of the Active Tension. Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT). Masterarbeit. 2019
To support clinical analytics, knowledge of the heart’s wall stress is seen as an important parameter to analyse the failing heart. As this stress cannot be measured directly, it needs to be derived from other indicators. The deformation of the wall of the left ventricle, obtained from medical imaging methods, is widely used to estimate the stress. This is called the inverse problem of the heart mechanics. This thesis targeted the use of short-axis cine Magnetic Resonance Imaging (MRI) data to reconstruct the active tension in the left ventricle and to detect inhomogeneities in the myocardial wall. Based on the simulation framework CardioMechanics, it covered a sensitivity analysis of the inverse solver to enable accurate reconstruction of active tension and deformation of the left ventricle. The selected input parameters for the forward solver were considered to be ground truth. The input data used for the inverse solver were whole endocardial surface data. The results showed a good reconstruction of small infarction areas down to 1 % of the total number of elements. The system tolerated misalignment of fibre angles of up to 10◦. Statistical variability of up to 20 % of wall thickness as input data were successfully processed. A post-processing was introduced, as well as a border zone to improve active tension reconstruction in case of infarction areas. For preliminary assessment of active tension estimation based on clinical data, synthetic slice data were used to analyse the performance of the inverse solver. From the output of the forward simulation, slice data were generated. These data were remeshed to be processed by the inverse solver. Results of this analysis were not promising yet. Several possible approaches were proposed and discussed to improve the behaviour of the inverse solver. In summary, this thesis was used to explore the limits of the inverse solver showing promising results for the use of whole endocardial surface data and provided basics for the use of slice data.