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.
Mathematical models of the human heart are evolving to become a cornerstone of precision medicine and support clinical decision making by providing a powerful tool to understand the mechanisms underlying pathophysiological conditions. In this study, we present a detailed mathematical description of a fully coupled multi-scale model of the human heart, including electrophysiology, mechanics, and a closed-loop model of circulation. State-of-the-art models based on human physiology are used to describe membrane kinetics, excitation-contraction coupling and active tension generation in the atria and the ventricles. Furthermore, we highlight ways to adapt this framework to patient specific measurements to build digital twins. The validity of the model is demonstrated through simulations on a personalized whole heart geometry based on magnetic resonance imaging data of a healthy volunteer. Additionally, the fully coupled model was employed to evaluate the effects of a typical atrial ablation scar on the cardiovascular system. With this work, we provide an adaptable multi-scale model that allows a comprehensive personalization from ion channels to the organ level enabling digital twin modeling
The human heart is a masterpiece of the highest complexity coordinating multi-physics aspects on a multi-scale range. Thus, modeling the cardiac function to reproduce physiological characteristics and diseases remains challenging. Especially the complex simulation of the blood's hemodynamics and its interaction with the myocardial tissue requires a high accuracy of the underlying computational models and solvers. These demanding aspects make whole-heart fully-coupled simulations computationally highly expensive and call for simpler but still accurate models. While the mechanical deformation during the heart cycle drives the blood flow, less is known about the feedback of the blood flow onto the myocardial tissue. To solve the fluid-structure interaction problem, we suggest a cycle-to-cycle coupling of the structural deformation and the fluid dynamics. In a first step, the displacement of the endocardial wall in the mechanical simulation serves as a unidirectional boundary condition for the fluid simulation. After a complete heart cycle of fluid simulation, a spatially resolved pressure factor (PF) is extracted and returned to the next iteration of the solid mechanical simulation, closing the loop of the iterative coupling procedure. All simulations were performed on an individualized whole heart geometry. The effect of the sequential coupling was assessed by global measures such as the change in deformation and-as an example of diagnostically relevant information-the particle residence time. The mechanical displacement was up to 2 mm after the first iteration. In the second iteration, the deviation was in the sub-millimeter range, implying that already one iteration of the proposed cycle-to-cycle coupling is sufficient to converge to a coupled limit cycle. Cycle-to-cycle coupling between cardiac mechanics and fluid dynamics can be a promising approach to account for fluid-structure interaction with low computational effort. In an individualized healthy whole-heart model, one iteration sufficed to obtain converged and physiologically plausible results.
Individualized computer models of the geometry of the human heart are often based on mag- netic resonance images (MRI) or computed tomography (CT) scans. The stress distribution in the imaged state cannot be measured but needs to be estimated from the segmented geometry, e.g. by an iterative algorithm. As the convergence of this algorithm depends on different geometrical conditions, we system- atically studied their influence. Beside various shape alterations, we investigated the chamber volume, as well as the effect of material parameters. We found a marked influence of passive material parameters: increasing the model stiffness by a factor of ten halved the residual norm in the first iteration. Flat and concave areas led to a reduced robustness and convergence rate of the unloading algorithm. With this study, the geometric effects and modeling aspects governing the unloading algorithm’s convergence are identified and can be used as a basis for further improvement.
In order to be used in a clinical context, numerical simulation tools have to strike a balance between accuracy and low computational effort. For re- producing the pumping function of the human heart numerically, the physical domains of cardiac continuum mechanics and fluid dynamics have a significant relevance. In this context, fluid-structure interaction between the heart muscle and the blood flow is particularly important: Myocardial tension development and wall deformation drive the blood flow. However, the degree to which the blood flow has a retrograde effect on the cardiac mechanics in this multi-physics problem remains unclear up to now. To address this question, we implemented a cycle-to-cycle coupling based on a finite element model of a patient-specific whole heart geometry. The deforma- tion of the cardiac wall over one heart cycle was computed using our mechanical simulation framework. A closed loop circulatory system model as part of the simulation delivered the chamber pressures. The displacement of the endo- cardial surfaces and the pressure courses of one cycle were used as boundary conditions for the fluid solver. After solving the Navier-Stokes equations, the relative pressure was extracted for all endocardial wall elements from the three dimensional pressure field. These local pressure deviations were subsequently returned to the next iteration of the continuum mechanical simulation, thus closing the loop of the iterative coupling procedure. Following this sequential coupling approach, we simulated three iterations of mechanic and fluid simulations. To characterize the convergence, we evaluated the time course of the normalized pressure field as well as the euclidean distance between nodes of the mechanic simulation in subsequent iterations. For the left ventricle (LV), the maximal euclidean distance of all endocardial wall nodes was smaller than 2mm between the first and second iteration. The maximal distance between the second and third iteration was 70μm, thus the limit of necessary cycles was already reached after two iterations. In future work, this iterative coupling approach will have to prove its abil- ity to deliver physiologically accurate results also for diseased heart models. Altogether, the sequential coupling approach with its low computational effort delivered promising results for modeling fluid-structure interaction in cardiac simulations.
E. Kovacheva. Model Based Estimation of the Elastomechanical Properties of the Human Heart. Karlsruher Institut für Technologie (KIT). Dissertation. 2021
The human heart is a complex organ involving the interaction of different phenomena. On the one hand, blood is flowing through the heart chambers and applies pressure on the inner surfaces. On the other hand, the heart is surrounded by a pericardial sac, which influences the chamber motion. Furthermore, electrical waves propagate through the heart tissue to activate a contraction force, which, added to the passive force, works against the chamber pressure and results in the deformation of the myocardium. In the last decades, advanced computational models of the heart phenomena have been created and included in simulation frameworks to study the human heart beat. ....