Estimating cardiomyofiber strain in vivo by solving a computational model

Improved computation of Lagrangian tissue displacement and strain for cine DENSE MRI using a regularized spatiotemporal least squares method

Introduction

In displacement encoding with stimulated echoes (DENSE), tissue displacement is encoded in the signal phase such that the phase of each pixel in space and time provides an independent measurement of absolute tissue displacement. Previously for DENSE, estimation of Lagrangian displacement used two steps: first a spatial interpolation and, second, least squares fitting through time to a Fourier or polynomial model. However, there is no strong rationale for such a through-time model,

Methods

To compute the Lagrangian displacement field from DENSE phase data, a minimization problem is introduced to enforce fidelity with the acquired Eulerian displacement data while simultaneously providing model-independent regularization in space and time, enforcing only spatiotemporal smoothness. A regularized spatiotemporal least squares (RSTLS) method is used to solve the minimization problem, and RSTLS was tested using two-dimensional DENSE data from 71 healthy volunteers.

Results

The mean absolute percent error (MAPE) between the Lagrangian displacements and the corresponding Eulerian displacements was significantly lower for the RSTLS method vs. the two-step method for both x- and y-directions (0.73±0.59 vs 0.83 ±0.1, p < 0.05) and (0.75±0.66 vs 0.82 ±0.1, p < 0.05), respectively. Also, peak early diastolic strain rate (PEDSR) was higher (1.81±0.58 (s-1) vs. 1.56±0. 63 (s-1), p<0.05) and the strain rate during diastasis was lower (0.14±0.18 (s-1) vs 0.35±0.2 (s-1), p < 0.05) for the RSTLS vs. the two-step method, with the former suggesting that the two-step method was over-regularized.

Discussion

The proposed RSTLS method provides more realistic measurements of Lagrangian displacement and strain from DENSE images without imposing arbitrary motion models.

A simple and efficient adaptive time stepping technique for low-order operator splitting schemes applied to cardiac electrophysiology

We present a simple, yet efficient adaptive time stepping scheme for cardiac electrophysiology (EP) simulations based on standard operator splitting techniques. The general idea is to exploit the relation between the splitting error and the reaction's magnitude-found in a previous one-dimensional analytical study by Spiteri and Ziaratgahi-to construct the new time step controller for three-dimensional problems. Accordingly, we propose to control the time step length of the operator splitting scheme as a function of the reaction magnitude, in addition to the common approach of adapting the reaction time step. This conforms with observations in numerical experiments supporting the need for a significantly smaller time step length during depolarization than during repolarization. The proposed scheme is compared with classical proportional-integral-differential controllers using state-of-the-art error estimators, which are also presented in details as they have not been previously applied in the context of cardiac EP with operator splitting techniques. Benchmarks show that choosing the time step as a sigmoidal function of the reaction magnitude is highly efficient and full cardiac cycles can be computed with precision even in a realistic biventricular setup. The proposed scheme outperforms common adaptive time stepping techniques, while depending on fewer tuning parameters.

Myocardial mesostructure and mesofunction

The complex and highly organized structural arrangement of some five billion cardiomyocytes directs the coordinated electrical activity and mechanical contraction of the human heart. The characteristic transmural change in cardiomyocyte orientation underlies base-to-apex shortening, circumferential shortening, and left ventricular torsion during contraction. Individual cardiomyocytes shorten ∼15% and increase in diameter ∼8%. Remarkably, however, the left ventricular wall thickens by up to 30-40%. To accommodate this, the myocardium must undergo significant structural rearrangement during contraction. At the mesoscale, collections of cardiomyocytes are organized into sheetlets, and sheetlet shear is the fundamental mechanism of rearrangement that produces wall thickening. Herein, we review the histological and physiological studies of myocardial mesostructure that have established the sheetlet shear model of wall thickening. Recent developments in tissue clearing techniques allow for imaging of whole hearts at the cellular scale, whereas magnetic resonance imaging (MRI) and computed tomography (CT) can image the myocardium at the mesoscale (100 µm to 1 mm) to resolve cardiomyocyte orientation and organization. Through histology, cardiac diffusion tensor imaging (DTI), and other modalities, mesostructural sheetlets have been confirmed in both animal and human hearts. Recent in vivo cardiac DTI methods have measured reorientation of sheetlets during the cardiac cycle. We also examine the role of pathological cardiac remodeling on sheetlet organization and reorientation, and the impact this has on ventricular function and dysfunction. We also review the unresolved mesostructural questions and challenges that may direct future work in the field.

Native-resolution myocardial principal Eulerian strain mapping using convolutional neural networks and Tagged Magnetic Resonance Imaging

BACKGROUND

Assessment of regional myocardial function at native pixel-level resolution can play a crucial role in recognizing the early signs of the decline in regional myocardial function. Extensive data processing in existing techniques limits the effective resolution and accuracy of the generated strain maps. The purpose of this study is to compute myocardial principal strain maps ε_p1 and ε_p2 from tagged MRI (tMRI) at the native image resolution using deep-learning local patch convolutional neural network (CNN) models (DeepStrain).

METHODS

For network training, validation, and testing, realistic tMRI datasets were generated and consisted of 53,606 cine images simulating the heart, the liver, blood pool, and backgrounds, including ranges of shapes, positions, motion patterns, noise, and strain. In addition, 102 in-vivo image datasets from three healthy subjects, and three Pulmonary Arterial Hypertension patients, were acquired and used to assess the network's in-vivo performance. Four convolutional neural networks were trained for mapping input tagging patterns to corresponding ground-truth principal strains using different cost functions. Strain maps using harmonic phase analysis (HARP) were obtained with various spectral filtering settings for comparison. CNN and HARP strain maps were compared at the pixel level versus the ground-truth and versus the least-loss in-vivo maps using Pearson correlation coefficients (R) and the median error and Inter-Quartile Range (IQR) histograms.

RESULTS

CNN-based local patch DeepStrain maps at a phantom resolution of 1.1mm × 1.1 mm and in-vivo resolution of 2.1mm × 1.6 mm were artifact-free with multiple fold improvement with ε_p1 ground-truth median error of 0.009(0.007) vs. 0.32(0.385) using HARP and ε_p2 ground-truth error of 0.016(0.021) vs. 0.181(0.08) using HARP. CNN-based strain maps showed substantially higher agreement with the ground-truth maps with correlation coefficients R > 0.91 for ε_p1 and ε_p2 compared to R < 0.21 and R < 0.82 for HARP-generated maps, respectively.

CONCLUSION

CNN-generated Eulerian strain mapping permits artifact-free visualization of myocardial function at the native image resolution.

Using synthetic data generation to train a cardiac motion tag tracking neural network

A CNN based method for cardiac MRI tag tracking was developed and validated. A synthetic data simulator was created to generate large amounts of training data using natural images, a Bloch equation simulation, a broad range of tissue properties, and programmed ground-truth motion. The method was validated using both an analytical deforming cardiac phantom and in vivo data with manually tracked reference motion paths. In the analytical phantom, error was investigated relative to SNR, and accurate results were seen for SNR>10 (displacement error <0.3 mm). Excellent agreement was seen in vivo for tag locations (mean displacement difference = -0.02 pixels, 95% CI [-0.73, 0.69]) and calculated cardiac circumferential strain (mean difference = 0.006, 95% CI [-0.012, 0.024]). Automated tag tracking with a CNN trained on synthetic data is both accurate and precise.

Emerging Techniques in Cardiac Magnetic Resonance Imaging

Cardiovascular disease is the leading cause of death and a significant contributor of health care costs. Noninvasive imaging plays an essential role in the management of patients with cardiovascular disease. Cardiac magnetic resonance (MR) can noninvasively assess heart and vascular abnormalities, including biventricular structure/function, blood hemodynamics, myocardial tissue composition, microstructure, perfusion, metabolism, coronary microvascular function, and aortic distensibility/stiffness. Its ability to characterize myocardial tissue composition is unique among alternative imaging modalities in cardiovascular disease. Significant growth in cardiac MR utilization, particularly in Europe in the last decade, has laid the necessary clinical groundwork to position cardiac MR as an important imaging modality in the workup of patients with cardiovascular disease. Although lack of availability, limited training, physician hesitation, and reimbursement issues have hampered widespread clinical adoption of cardiac MR in the United States, growing clinical evidence will ultimately overcome these challenges. Advances in cardiac MR techniques, particularly faster image acquisition, quantitative myocardial tissue characterization, and image analysis have been critical to its growth. In this review article, we discuss recent advances in established and emerging cardiac MR techniques that are expected to strengthen its capability in managing patients with cardiovascular disease. LEVEL OF EVIDENCE: 5 TECHNICAL EFFICACY: Stage 1.

Arbitrary Point Tracking with Machine Learning to Measure Cardiac Strains in Tagged MRI

Cardiac tagged MR images allow for deformation fields to be measured in the heart by tracking the motion of tag lines throughout the cardiac cycle. Machine learning (ML) algorithms enable accurate and robust tracking of tag lines. Herein, the use of a massive synthetic physics-driven training dataset with known ground truth was used to train an ML network to enable tracking any number of points at arbitrary positions rather than anchored to the tag lines themselves. The tag tracking and strain calculation methods were investigated in a computational deforming cardiac phantom with known (ground truth) strain values. This enabled both tag tracking and strain accuracy to be characterized for a range of image acquisition and tag tracking parameters. The methods were also tested on in vivo volunteer data. Median tracking error was <0.26mm in the computational phantom, and strain measurements were improved in vivo when using the arbitrary point tracking for a standard clinical protocol.