Application of feed forward and recurrent neural networks in simulation of left ventricular mechanics.

An understanding of left ventricle (LV) mechanics is fundamental for designing better preventive, diagnostic, and treatment strategies for improved heart function. Because of the costs of clinical and experimental studies to treat and understand heart function, respectively, in-silico models play an important role. Finite element (FE) models, which have been used to create in-silico LV models for different cardiac health and disease conditions, as well as cardiac device design, are time-consuming and require powerful computational resources, which limits their use when real-time results are needed. As an alternative, we sought to use deep learning (DL) for LV in-silico modeling. We used 80 four-chamber heart FE models for feed forward, as well as recurrent neural network (RNN) with long short-term memory (LSTM) models for LV pressure and volume. We used 120 LV-only FE models for training LV stress predictions. The active material properties of the myocardium and time were features for the LV pressure and volume training, and passive material properties and element centroid coordinates were features of the LV stress prediction models. For six test FE models, the DL error for LV volume was 1.599 ± 1.227 ml, and the error for pressure was 1.257 ± 0.488 mmHg; for 20 LV FE test examples, the mean absolute errors were, respectively, 0.179 ± 0.050 for myofiber, 0.049 ± 0.017 for cross-fiber, and 0.039 ± 0.011 kPa for shear stress. After training, the DL runtime was in the order of seconds whereas equivalent FE runtime was in the order of several hours (pressure and volume) or 20 min (stress). We conclude that using DL, LV in-silico simulations can be provided for applications requiring real-time results.

Prediction of Left Ventricular Mechanics Using Machine Learning.

The goal of this paper was to provide a real-time left ventricular (LV) mechanics simulator using machine learning (ML). Finite element (FE) simulations were conducted for the LV with different material properties to obtain a training set. A hyperelastic fiber-reinforced material model was used to describe the passive behavior of the myocardium during diastole. The active behavior of the heart resulting from myofiber contractions was added to the passive tissue during systole. The active and passive properties govern the LV constitutive equation. These mechanical properties were altered using optimal Latin hypercube design of experiments to obtain training FE models with varied active properties (volume and pressure predictions) and varied passive properties (stress predictions). For prediction of LV pressures, we used eXtreme Gradient Boosting (XGboost) and Cubist, and XGBoost was used for predictions of LV pressures, volumes as well as LV stresses. The LV pressure and volume results obtained from ML were similar to FE computations. The ML results could capture the shape of LV pressure as well as LV pressure-volume loops. The results predicted by Cubist were smoother than those from XGBoost. The mean absolute errors were as follows: XGBoost volume: 1.734 ± 0.584 ml, XGBoost pressure: 1.544 ± 0.298 mmHg, Cubist volume: 1.495 ± 0.260 ml, Cubist pressure: 1.623 ± 0.191 mmHg, myofiber stress: 0.334 ± 0.228 kPa, cross myofiber stress: 0.075 ± 0.024 kPa, and shear stress: 0.050 ± 0.032 kPa. The simulation results show ML can predict LV mechanics much faster than the FE method. The ML model can be used as a tool to predict LV behavior. Training of our ML model based on a large group of subjects can improve its predictability for real world applications.