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.
Background: Hypertrophic cardiomyopathy (HCM) is typically caused by mutations in sarcomeric genes leading to cardiomyocyte disarray, replacement fibrosis, impaired contractility, and elevated filling pressures. These varying tissue properties are associ- ated with certain strain patterns that may allow to establish a diagnosis by means of non-invasive imaging without the necessity of harmful myocardial biopsies or con- trast agent application. With a numerical study, we aim to answer: how the variability in each of these mechanisms contributes to altered mechanics of the left ventricle (LV) and if the deformation obtained in in-silico experiments is comparable to values reported from clinical measurements. Methods: We conducted an in-silico sensitivity study on physiological and pathologi- cal mechanisms potentially underlying the clinical HCM phenotype. The deformation of the four-chamber heart models was simulated using a finite-element mechanical solver with a sliding boundary condition to mimic the tissue surrounding the heart. Furthermore, a closed-loop circulatory model delivered the pressure values acting on the endocardium. Deformation measures and mechanical behavior of the heart mod- els were evaluated globally and regionally. Results: Hypertrophy of the LV affected the course of strain, strain rate, and wall thickening—the root-mean-squared difference of the wall thickening between control (mean thickness 10 mm) and hypertrophic geometries (17 mm) was >10%. A reduc- tion of active force development by 40% led to less overall deformation: maximal radial strain reduced from 26 to 21%. A fivefold increase in tissue stiffness caused a more homogeneous distribution of the strain values among 17 heart segments. Fiber disarray led to minor changes in the circumferential and radial strain. A combination of pathological mechanisms led to reduced and slower deformation of the LV and halved the longitudinal shortening of the LA. Conclusions: This study uses a computer model to determine the changes in LV deformation caused by pathological mechanisms that are presumed to underlay HCM. This knowledge can complement imaging-derived information to obtain a more accu- rate diagnosis of HCM.