Intramyocardial Injections to De-Stiffen the Heart: A Subject-Specific in Silico Approach

Bayesian optimisation for efficient parameter inference in a cardiac mechanics model of the left ventricle

We consider parameter inference in cardio-mechanic models of the left ventricle, in particular the one based on the Holtzapfel-Ogden (HO) constitutive law, using clinical in vivo data. The equations underlying these models do not admit closed form solutions and hence need to be solved numerically. These numerical procedures are computationally expensive making computational run times associated with numerical optimisation or sampling excessive for the uptake of the models in the clinical practice. To address this issue, we adopt the framework of Bayesian optimisation (BO), which is an efficient statistical technique of global optimisation. BO seeks the optimum of an unknown black-box function by sequentially training a statistical surrogate-model and using it to select the next query point by leveraging the associated exploration-exploitation trade-off. To guarantee that the estimates based on the in vivo data are realistic also for high-pressures, unobservable in vivo, we include a penalty term based on a previously published empirical law developed using ex vivo data. Two case studies based on real data demonstrate that the proposed BO procedure outperforms the state-of-the-art inference algorithm for the HO constitutive law.

Personalization of biomechanical simulations of the left ventricle by in-vivo cardiac DTI data: Impact of fiber interpolation methods

Simulations of cardiac electrophysiology and mechanics have been reported to be sensitive to the microstructural anisotropy of the myocardium. Consequently, a personalized representation of cardiac microstructure is a crucial component of accurate, personalized cardiac biomechanical models. In-vivo cardiac Diffusion Tensor Imaging (cDTI) is a non-invasive magnetic resonance imaging technique capable of probing the heart's microstructure. Being a rather novel technique, issues such as low resolution, signal-to noise ratio, and spatial coverage are currently limiting factors. We outline four interpolation techniques with varying degrees of data fidelity, different amounts of smoothing strength, and varying representation error to bridge the gap between the sparse in-vivo data and the model, requiring a 3D representation of microstructure across the myocardium. We provide a workflow to incorporate in-vivo myofiber orientation into a left ventricular model and demonstrate that personalized modelling based on fiber orientations from in-vivo cDTI data is feasible. The interpolation error is correlated with a trend in personalized parameters and simulated physiological parameters, strains, and ventricular twist. This trend in simulation results is consistent across material parameter settings and therefore corresponds to a bias introduced by the interpolation method. This study suggests that using a tensor interpolation approach to personalize microstructure with in-vivo cDTI data, reduces the fiber uncertainty and thereby the bias in the simulation results.

Establishing the Biofidelity of a Multiphysics Finite Element Model of the Human Heart

PURPOSE

Accelerating development of new therapeutic cardiac devices remains a clinical and technical priority. High-performance computing and the emergence of functional and complex in silico models of human anatomy can be an engine to accelerate the commercialization of innovative, safe, and effective devices.

METHODS

An existing three-dimensional, nonlinear model of a human heart with flow boundary conditions was evaluated. Its muscular tissues were exercised using electrophysiological boundary conditions, creating a dynamic, electro-mechanical simulation of the kinetics of the human heart. Anatomic metrics were selected to characterize the functional biofidelity of the model based on their significance to the design of cardiac devices. The model output was queried through the cardiac cycle and compared to in vivo literature values.

RESULTS

For the kinematics of mitral and aortic valves and curvature of coronary vessels, the model's performance was at or above the 95th percentile range of the in vivo data from large patient cohorts. One exception was the kinematics of the tricuspid valve. The model's mechanical use environment would subject devices to generally conservative use conditions.

CONCLUSIONS

This conservative simulated use environment for heart-based medical devices, and its judicious application in the evaluation of medical devices is justified, but careful interpretation of the results is encouraged.

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.