Validation of a Numerical Simulation of Elastomechnics of the Human Heart and Parameter Estimation using Clinical Data
This work is a part of a project, which aim is to combine cardiovascular magnetic resonance imaging (CMR) with computational modeling of cardiac biomechanics in order to improve diagnosis of cardiomyopathy, a group of diseases that affect the heart muscle. Before a cardiomyopathy case can be examined a healthy case needs to be correctly represented in- silico.
The contraction of the human heart is a complex process involving the interaction of the passive properties of the tissue and the active tension development, which is elicited by the electrical activation of the cells. Each of these processes is mathematically modeled and implemented in a computational framework, which simulates the contraction of the heart. At the Institute of Biomedical Engineering (IBT) such a framework has been developed during the last ten years. This framework, called CardioMechanics, calculates the deformation of a geometrical mesh by using the second order finite element method and solving non-linear differential equations.
At present, the evaluation of the simulated results is done by a comparison with literature data. The strongly coupled circulatory model delivers blood pressure and blood volume curves, which are referenced to generalized values found in literature. Furthermore, a study to verify computational frameworks for numerical heart simulations was undertaken by Land et al. in 2015. Here, the CardioMechanics framework was among the eleven participants. In this study the results of three simulations with predefined setups were compared between all participants. Nevertheless, only simple geometries were used, a bar and an ellipsoid, the latter representing a simplified left ventricle.
In this work, a patient specific geometrical heart model will be simulated and validated using clinical data. Furthermore, the data will be used to estimate parameters for the mathematical models involved in a computational framework.
The clinical data were acquired from a healthy volunteer at the Heidelberg University Hospital. The following cardiovascular magnetic resonance imaging data were acquired: 3D whole heart, 2 chamber view, 4 chamber view, 12 short axis slices Cine and strain encoded MRI (SENC).
In this work, a validation framework will be developed, which compares the Cine MRI and the simulation results. Here two different options should be examined. On the one hand, the segmented Cine MRI slices of the left ventricle will be imported in CardioMechanics and deliver a similarity value. The Cine MRI will be segmented beforehand and will be provided for the master student. The similarity value will represent the overlap between the surface of segmented slices and in the same plane, the surface of the simulated ventricle. On the other hand, based on the simulation output, a virtual MRI will be computed (pseudo MRI) and will be compared to the acquired MRI with methods of imaging processing. This will not require any segmentation of the Cine MRI data. Both comparison methods will be compared regarding their performance, accuracy and time needed for preprocessing. It will be decided which should be used in the future.
Additionally to using the methods for validation, it will be also considered to use the method of choice for an estimate of global material properties of the left ventricle. Here, the clinical data during the diastole will be used, where the passive stiffness of the tissue dominates the behavior. In present, the model of the global passive behavior comprises four parameters, which are defined based on generalized values. These parameters will be estimated by solving an optimization problem, which maximizes the overlap between the measured data and the simulated data. Furthermore, an estimate of local tissue properties will be made. For this purpose, the left ventricle will be divided in subdomains and the estimation method will be extended to deliver the tissue properties on each subdomain.
Furthermore, if there is enough time left until the end of the master thesis, following will be considered: For validation purposes, the SENC measurement will be compared with the strain from the computational model. The strain in the simulated data is delivered on a local scale for each finite element. Therefore, the simulation results based on the estimated material properties on both global and local scale will be validated.