Novel insights into in-vivo diffusion tensor cardiovascular magnetic resonance using computational modeling and a histology-based virtual microstructure

CMRsim-A python package for cardiovascular MR simulations incorporating complex motion and flow

PURPOSE

To present an open-source MR simulation framework that facilitates the incorporation of complex motion and flow for studying cardiovascular MR (CMR) acquisition and reconstruction.

METHODS

CMRsim is a Python package that allows simulation of CMR images using dynamic digital phantoms with complex motion as input. Two simulation paradigms are available, namely, numerical and analytical solutions to the Bloch equations, using a common motion representation. Competitive simulation speeds are achieved using TensorFlow for GPU acceleration. To demonstrate the capability of the package, one introductory and two advanced CMR simulation experiments are presented. The latter showcase phase-contrast imaging of turbulent flow downstream of a stenotic section and cardiac diffusion tensor imaging on a contracting left ventricle. Additionally, extensive documentation and example resources are provided.

RESULTS

The Bloch simulation with turbulent flow using approximately 1.5 million particles and a sequence duration of 710 ms for each of the seven different velocity encodings took a total of 29 min on a NVIDIA Titan RTX GPU. The results show characteristic phase contrast and magnitude modulation present in real data. The analytical simulation of cardiac diffusion tensor imaging with bulk-motion phase sensitivity took approximately 10 s per diffusion-weighted image, including preparation and loading steps. The results exhibit the expected alteration of diffusion metrics due to strain.

CONCLUSION

CMRsim is the first simulation framework that allows one to feasibly incorporate complex motion, including turbulent flow, to systematically study advanced CMR acquisition and reconstruction approaches. The open-source package features modularity and transparency, facilitating maintainability and extensibility in support of reproducible research.

Realistic numerical simulations of diffusion tensor cardiovascular magnetic resonance: The effects of perfusion and membrane permeability

PURPOSE

To study the sensitivity of diffusion tensor cardiovascular magnetic resonance (DT-CMR) to microvascular perfusion and changes in cell permeability.

METHODS

Monte Carlo (MC) random walk simulations in the myocardium have been performed to simulate self-diffusion of water molecules in histology-based media with varying extracellular volume fraction (ECV) and permeable membranes. The effect of microvascular perfusion on simulations of the DT-CMR signal has been incorporated by adding the contribution of particles traveling through an anisotropic capillary network to the diffusion signal. The simulations have been performed considering three pulse sequences with clinical gradient strengths: monopolar stimulated echo acquisition mode (STEAM), monopolar pulsed-gradient spin echo (PGSE), and second-order motion-compensated spin echo (MCSE).

RESULTS

Reducing ECV intensifies the diffusion restriction and incorporating membrane permeability reduces the anisotropy of the diffusion tensor. Widening the intercapillary velocity distribution results in increased measured diffusion along the cardiomyocytes long axis when the capillary networks are anisotropic. Perfusion amplifies the mean diffusivity for STEAM while the opposite is observed for short diffusion encoding time sequences (PGSE and MCSE).

CONCLUSION

The effect of perfusion on the measured diffusion tensor is reduced using an increased reference b-value. Our results pave the way for characterization of the response of DT-CMR to microstructural changes underlying cardiac pathology and highlight the higher sensitivity of STEAM to permeability and microvascular circulation due to its longer diffusion encoding time.

Monte Carlo simulation of water diffusion through cardiac tissue models

Monte Carlo diffusion simulations are commonly used to establish a reliable ground truth of tissue microstructure, including for the validation of diffusion-weighted MRI. However, selecting simulation parameters is challenging and affects validity and reproducibility. We conducted experiments to investigate critical conditions in Monte Carlo simulations, such as tissue representation complexity, simulated molecules, update duration, and compartment size. Results show significant changes in microstructure characteristics when parameters are altered, emphasizing the importance of careful control for a reliable ground truth.

Three-dimensional micro-structurally informed in silico myocardium-Towards virtual imaging trials in cardiac diffusion weighted MRI

In silico tissue models (viz. numerical phantoms) provide a mechanism for evaluating quantitative models of magnetic resonance imaging. This includes the validation and sensitivity analysis of imaging biomarkers and tissue microstructure parameters. This study proposes a novel method to generate a realistic numerical phantom of myocardial microstructure. The proposed method extends previous studies by accounting for the variability of the cardiomyocyte shape, water exchange between the cardiomyocytes (intercalated discs), disorder class of myocardial microstructure, and four sheetlet orientations. In the first stage of the method, cardiomyocytes and sheetlets are generated by considering the shape variability and intercalated discs in cardiomyocyte-cardiomyocyte connections. Sheetlets are then aggregated and oriented in the directions of interest. The morphometric study demonstrates no significant difference (p>0.01) between the distribution of volume, length, and primary and secondary axes of the numerical and real (literature) cardiomyocyte data. Moreover, structural correlation analysis validates that the in-silico tissue is in the same class of disorderliness as the real tissue. Additionally, the absolute angle differences between the simulated helical angle (HA) and input HA (reference value) of the cardiomyocytes (4.3°±3.1°) demonstrate a good agreement with the absolute angle difference between the measured HA using experimental cardiac diffusion tensor imaging (cDTI) and histology (reference value) reported by (Holmes et al., 2000) (3.7°±6.4°) and (Scollan et al. 1998) (4.9°±14.6°). Furthermore, the angular distance between eigenvectors and sheetlet angles of the input and simulated cDTI is much smaller than those between measured angles using structural tensor imaging (as a gold standard) and experimental cDTI. Combined with the qualitative results, these results confirm that the proposed method can generate richer numerical phantoms for the myocardium than previous studies.

Development of a cardiovascular magnetic resonance-compatible large animal isolated heart model for direct comparison of beating and arrested hearts

Cardiac motion results in image artefacts and quantification errors in many cardiovascular magnetic resonance (CMR) techniques, including microstructural assessment using diffusion tensor cardiovascular magnetic resonance (DT-CMR). Here, we develop a CMR-compatible isolated perfused porcine heart model that allows comparison of data obtained in beating and arrested states. Ten porcine hearts (8/10 for protocol optimisation) were harvested using a donor heart retrieval protocol and transported to the remote CMR facility. Langendorff perfusion in a 3D-printed chamber and perfusion circuit re-established contraction. Hearts were imaged using cine, parametric mapping and STEAM DT-CMR at cardiac phases with the minimum and maximum wall thickness. High potassium and lithium perfusates were then used to arrest the heart in a slack and contracted state, respectively. Imaging was repeated in both arrested states. After imaging, tissue was removed for subsequent histology in a location matched to the DT-CMR data using fiducial markers. Regular sustained contraction was successfully established in six out of 10 hearts, including the final five hearts. Imaging was performed in four hearts and one underwent the full protocol, including colocalised histology. The image quality was good and there was good agreement between DT-CMR data in equivalent beating and arrested states. Despite the use of autologous blood and dextran within the perfusate, T2 mapping results, DT-CMR measures and an increase in mass were consistent with development of myocardial oedema, resulting in failure to achieve a true diastolic-like state. A contiguous stack of 313 5-μm histological sections at and a 100-μm thick section showing cell morphology on 3D fluorescent confocal microscopy colocalised to DT-CMR data were obtained. A CMR-compatible isolated perfused beating heart setup for large animal hearts allows direct comparisons of beating and arrested heart data with subsequent colocalised histology, without the need for onsite preclinical facilities.

Random walk diffusion simulations in semi-permeable layered media with varying diffusivity

In this paper we present random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a novel transit model for solving the interaction of random walkers with a membrane. This hybrid model is based on treating the membrane permeability and the step change in diffusion coefficient as two interactions separated by an infinitesimally small layer. By conducting an extensive analytical flux analysis, the performance of our hybrid model is compared with a commonly used membrane transit model (reference model). Numerical simulations demonstrate the limitations of the reference model in dealing with step changes in diffusivity and show the capability of the hybrid model to overcome this limitation and to offer substantial gains in computational efficiency. The suitability of both random walk transit models for the application to simulations of diffusion tensor cardiovascular magnetic resonance (DT-CMR) imaging is assessed in a histology-based domain relevant to DT-CMR. In order to demonstrate the usefulness of the new hybrid model for other possible applications, we also consider a larger range of permeabilities beyond those commonly found in biological tissues.

Cardiac Diffusion Tensor Biomarkers of Chronic Infarction Based on In Vivo Data

In vivo cardiac diffusion tensor imaging (cDTI) data were acquired in swine subjects six to ten weeks post-myocardial infarction (MI) to identify microstructural-based biomarkers of MI. Diffusion tensor invariants, diffusion tensor eigenvalues, and radial diffusivity (RD) are evaluated in the infarct, border, and remote myocardium, and compared with extracellular volume fraction (ECV) and native T1 values. Additionally, to aid the interpretation of the experimental results, the diffusion of water molecules was numerically simulated as a function of ECV. Finally, findings based on in vivo measures were confirmed using higher-resolution and higher signal-to-noise data acquired ex vivo in the same subjects. Mean diffusivity, diffusion tensor eigenvalues, and RD increased in the infarct and border regions compared to remote myocardium, while fractional anisotropy decreased. Secondary (e₂) and tertiary (e₃) eigenvalues increased more significantly than the primary eigenvalue in the infarct and border regions. These findings were confirmed by the diffusion simulations. Although ECV presented the largest increase in infarct and border regions, e₂, e₃, and RD increased the most among non-contrast-based biomarkers. RD is of special interest as it summarizes the changes occurring in the radial direction and may be more robust than e₂ or e₃ alone.

Fundamentals of turbulent flow spectrum imaging

PURPOSE

To introduce a mathematical framework and in-silico validation of turbulent flow spectrum imaging (TFSI) of stenotic flow using phase-contrast MRI, evaluate systematic errors in quantitative turbulence parameter estimation, and propose a novel method for probing the Lagrangian velocity spectra of turbulent flows.

THEORY AND METHODS

The spectral response of velocity-encoding gradients is derived theoretically and linked to turbulence parameter estimation including the velocity autocorrelation function spectrum. Using a phase-contrast MRI simulation framework, the encoding properties of bipolar gradient waveforms with identical first gradient moments but different duration are investigated on turbulent flow data of defined characteristics as derived from computational fluid dynamics. Based on theoretical insights, an approach using velocity-compensated gradient waveforms is proposed to specifically probe desired ranges of the velocity autocorrelation function spectrum with increased accuracy.

RESULTS

Practical velocity-encoding gradients exhibit limited encoding power of typical turbulent flow spectra, resulting in up to 50% systematic underestimation of intravoxel SD values. Depending on the turbulence level in fluids, the error due to a single encoding gradient spectral response can vary by 20%. When using tailored velocity-compensated gradients, improved quantification of the Lagrangian velocity spectrum on a voxel-by-voxel basis is achieved and used for quantitative correction of intravoxel SD values estimated with velocity-encoding gradients.

CONCLUSION

To address systematic underestimation of turbulence parameters using bipolar velocity-encoding gradients in phase-contrast MRI of stenotic flows with short correlation times, tailored velocity-compensated gradients are proposed to improve quantitative mapping of turbulent blood flow characteristics.

Magnetic Resonance-Based Characterization of Myocardial Architecture

Advances in technology have made it possible to image the microstructure of the heart with diffusion-weighted magnetic resonance. The technique provides unique insights into the cellular architecture of the myocardium and how this is perturbed in a range of disease contexts. In this review, the physical basis of diffusion MRI and the challenges of implementing it in the beating heart are discussed. Cutting edge acquisition and analysis techniques, as well as the results of initial clinical studies, are reported.

Lattice Boltzmann method for simulation of diffusion magnetic resonance imaging physics in multiphase tissue models

We report an implementation of the lattice Boltzmann method (LBM) to integrate the Bloch-Torrey equation, which describes the evolution of the transverse magnetization vector and the fate of the signal of diffusion magnetic resonance imaging (dMRI). Motivated by the need to interpret dMRI experiments in biological tissues, and to offset the small time-step limitation of classical LBM, a hybrid LBM scheme is introduced and implemented to solve the Bloch-Torrey equation. A membrane boundary condition is presented which is able to accurately represent the effects of thin curvilinear membranes typically found in biological tissues. As implemented, the hybrid LBM scheme accommodates piece-wise uniform transport, dMRI parameters, periodic and mirroring outer boundary conditions, and finite membrane permeabilities on non-boundary-conforming inner boundaries. By comparing with analytical solutions of limiting cases, we demonstrate that the hybrid LBM scheme is more accurate than the classical LBM scheme. The proposed explicit LBM scheme maintains second-order spatial accuracy, stability, and first-order temporal accuracy for a wide range of parameters. The parallel implementation of the hybrid LBM code in a multi-CPU computer system, as well as on GPUs, is straightforward and efficient. Along with offering certain advantages over finite element or Monte Carlo schemes, the proposed hybrid LBM constitutes a flexible scheme that can by easily adapted to model more complex interfacial conditions and physics in heterogeneous multiphase tissue models and to accommodate sophisticated dMRI sequences.

Motion and eddy current-induced signal dephasing in in vivo cardiac DTI

PURPOSE

To address motion in cardiac DWI, stimulated-echo acquisition mode (STEAM) and second-order motion-compensated spin-echo (SE) sequences have been proposed. Despite applying motion-compensation strategies, residual motion can cause misleading signal attenuation. The purpose of this study is to estimate the motion-induced error in both sequences by analysis of image phase.

METHODS

Diffusion-weighted motion-compensated SE sequences and STEAM imaging was applied in vivo with diffusion encoding along 3 orthogonal directions. A b-value range of 100 to 600 s/mm² and trigger delays of 25%, 50%, and 75% of end systole and middiastole were used. Eddy-current contributions were obtained from phantom measurements. After computation of motion-induced phase maps, the amount of signal dephasing was computed from phase gradients, and the resulting errors in diffusion tensor parameters were calculated.

RESULTS

Motion-induced dephasing from the STEAM sequence showed less dependency on the b-value and no dependency on the heart phase, whereas SE imaging performed best at 75% end systole followed by 50% end systole and middiastole. For a typical experimental setting, errors of 3.3%/3.0% mean diffusivity, 4.9%/4.8% fractional anisotropy, 2.9º/3.2º helix angulation, 0.8º/0.7º transverse angulation, and 9.9º/10.0º sheet angulation (SE/STEAM) were calculated.

CONCLUSION

Image phase contains valuable information regarding uncompensated motion and eddy currents in cardiac DTI. Although the trigger delay window for SE is narrower compared with the STEAM-based approach, imaging in both systole and diastole is feasible and both sequences perform similarly if the trigger delays are selected carefully with SE.

Diffusion tensor cardiovascular magnetic resonance in hypertrophic cardiomyopathy: a comparison of motion-compensated spin echo and stimulated echo techniques

Objectives

Diffusion tensor cardiovascular magnetic resonance (DT-CMR) interrogates myocardial microstructure. Two frequently used in vivo DT-CMR techniques are motion-compensated spin echo (M2-SE) and stimulated echo acquisition mode (STEAM). Whilst M2-SE is strain-insensitive and signal to noise ratio efficient, STEAM has a longer diffusion time and motion compensation is unnecessary. Here we compare STEAM and M2-SE DT-CMR in patients.

Materials and methods

Biphasic DT-CMR using STEAM and M2-SE, late gadolinium imaging and pre/post gadolinium T1-mapping were performed in a mid-ventricular short-axis slice, in ten hypertrophic cardiomyopathy (HCM) patients at 3 T.

Results

Adequate quality data were obtained from all STEAM, but only 7/10 (systole) and 4/10 (diastole) M2-SE acquisitions. Compared with STEAM, M2-SE yielded higher systolic mean diffusivity (MD) (p = 0.02) and lower fractional anisotropy (FA) (p = 0.02, systole). Compared with segments with neither hypertrophy nor late gadolinium, segments with both had lower systolic FA using M2-SE (p = 0.02) and trend toward higher MD (p = 0.1). The negative correlation between FA and extracellular volume fraction was stronger with STEAM than M2-SE (r² = 0.29, p < 0.001 STEAM vs. r² = 0.10, p = 0.003 M2-SE).

Discussion

In HCM, only STEAM reliably assesses biphasic myocardial microstructure. Higher MD and lower FA from M2-SE reflect the shorter diffusion times. Further work will relate DT-CMR parameters and microstructural changes in disease.

Electronic supplementary material

The online version of this article (10.1007/s10334-019-00799-3) contains supplementary material, which is available to authorized users.

Novel insights into in-vivo diffusion tensor cardiovascular magnetic resonance using computational modeling and a histology-based virtual microstructure

Purpose

To develop histology‐informed simulations of diffusion tensor cardiovascular magnetic resonance (DT‐CMR) for typical in‐vivo pulse sequences and determine their sensitivity to changes in extra‐cellular space (ECS) and other microstructural parameters.

Methods

We synthesised the DT‐CMR signal from Monte Carlo random walk simulations. The virtual tissue was based on porcine histology. The cells were thickened and then shrunk to modify ECS. We also created idealised geometries using cuboids in regular arrangement, matching the extra‐cellular volume fraction (ECV) of 16–40%. The simulated voxel size was 2.8 × 2.8 × 8.0 mm³ for pulse sequences covering short and long diffusion times: Stejskal–Tanner pulsed‐gradient spin echo, second‐order motion‐compensated spin echo, and stimulated echo acquisition mode (STEAM), with clinically available gradient strengths.

Results

The primary diffusion tensor eigenvalue increases linearly with ECV at a similar rate for all simulated geometries. Mean diffusivity (MD) varies linearly, too, but is higher for the substrates with more uniformly distributed ECS. Fractional anisotropy (FA) for the histology‐based geometry is higher than the idealised geometry with low sensitivity to ECV, except for the long mixing time of the STEAM sequence. Varying the intra‐cellular diffusivity (D_IC) results in large changes of MD and FA. Varying extra‐cellular diffusivity or using stronger gradients has minor effects on FA. Uncertainties of the primary eigenvector orientation are reduced using STEAM.

Conclusions

We found that the distribution of ECS has a measurable impact on DT‐CMR parameters. The observed sensitivity of MD and FA to ECV and D_IC has potentially interesting applications for interpreting in‐vivo DT‐CMR parameters.