(G-270) High-Speed Cardiac Pressure-Volume Simulations Using a Neural Network Finite Element Approach

Introduction:: With advances in imaging and computational capabilities, personalized patient-specific computational models for cardiac simulations could become vital tools for personalized clinical diagnosis and treatment. However, traditional finite element methods are too slow for clinical applications of these models due to the complex nature of cardiac biomechanical function, which involves multiple physical and multiscale factors. Moreover, reduced order models do not provide sufficient speed improvements for patient-specific simulations and may cause loss of detail and accuracy, making them unsuitable for clinical applications.

We have developed and utilized a novel neural network finite element (NNFE) approach for soft organ simulations that can produce simulation results within clinically relevant timeframes. This approach utilizes a neural network (NN) to represent the map from boundary conditions to nodal displacements. Finite elements are used to define and map the displacement output from the NN on the organ geometry, enforce boundary conditions, and perform numerical integrations. This approach does not rely on data generated from physical experiments or simulations for training, but rather, is trained to learn the solutions for the governing PDEs themselves. In this study, the NNFE approach was utilized for complete organ-level cardiac simulations to predict the left ventricle's responses for any P-V loop within the functional range of pressures, considering active contraction and transmural fiber distributions. The NNFE approach was first implemented on a simplified prolate spheroid geometry of a healthy heart and is being extended to capture effects of myocardial infarction in a human left ventricle geometry captured from transesophageal echocardiogram (TEE).


Materials and Methods:: To develop a functioning cardiac model, we incorporated spatially varying fiber structures into a prolate spheroidal model of the left ventricle as a first step. We developed a Google-JAX based training scheme, using differentiable finite elements to compute the residual force vector of the governing PDE, that determines neural network (NN) parameters so that the system potential energy is minimized. We constrained the basal plane to in-plane motion only, fixed one point on the basal plane entirely, and constrained an adjacent point radially while applying pressure to the endocardium surface. We described the fiber distributions with a rules-based approach to approximate the transmural gradient of -60 to 60 degrees. We modeled the passive mechanical properties of the myocardium using an incompressible transversely isotropic Fung-based hyperelastic material model, and modeled the active contraction using an additional stress based on the Hunter-McCulloch-Ter Keurs model with minor modifications. We took the material constants from an ovine heart model. Our NNFE model took pressure p and active contraction T_Ca as inputs and predicted nodal displacements U in the output layer, from which the myocardial volume V was determined. We designed the NN with three hidden layers and 1024 neurons and trained it using the first-order gradient-based optimization algorithm Adam with learning rate scheduling. Unique to this model was that we trained the model over the entire functional training space of boundary conditions at once. We compared model results against those of the traditional finite element method using an identical model simulated in FEniCS.


Results, Conclusions, and Discussions:: The NNFE model predicted the displacement field for any p-V loop in the physiological training space with a mean nodal error of 64.4 microns. The trained NNFE model could accurately produce the twisting experienced by the left ventricle under active contraction. The model took 40 hours for training, but a trained NNFE model took 300 microseconds for producing the results for any loading, whereas FEniCS took 10-20 min for a single loading path. It is important to note that the NNFE model was trained over all possible p-V-T_Ca combinations in the entire functional space at once and can produce results for any loading path without need for retraining. Consequentially, the NNFE approach is well-suited for many-query problems, such as patient-specific surgical planning, where one needs to solve very similar problems repeatedly with only small changes to the inputs. For such applications, the training can be done in advance, and when presented with the patient-specific data, rapid simulation results can be produced with the trained model.

Our results showcase the first practical application of the NNFE approach for a biomedical application at an organ level. The approach is currently being extended to use spline-based geometry for rapid use of patient specific human left ventricle geometries developed from TEE imaging data for both healthy and diseased hearts. We note that TEE was selected as the imaging modality since this model will serve as an intermediate step towards a final goal of a combined LV-MV model and TEE is preferred for obtaining MV data. We are also extending this model to study the effect of infarcts in different locations of the ventricle on cardiac behavior. Ultimately, while still in its early stages, this approach paves the pathway for high-speed patient-specific clinical simulations.


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