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.

Spectrum-sine interpolation framework for DTI processing

Diffusion tensor imaging (DTI) data interpolation is important for DTI processing, which could affect the precision and computational complexity in the process of denoising, filtering, regularization, and DTI registration and fiber tracking. In this paper, we propose a novel DTI interpolation framework named with spectrum-sine (SS) focusing on tensor orientation variation in DTI processing. Compared with the state-of-the-art DTI interpolation method using Euler angles or quaternion to represent the orientation of DTI tensors, this method does not need to convert eigenvectors into Euler angles or quaternions, but interpolates each tensor's unit eigenvector directly. The prominent merit of this tensor interpolation method lies in tensor orientation information preservation, which is different from the existing DTI tensor interpolation methods that interpolating tensor's orientation information in a scalar way. The experimental results from both synthetic and real human brain DTI data demonstrated the proposed SS interpolation scheme not only maintains the advantages of Log-Euclidean and Riemannian interpolation frameworks, such as preserving the tensor's symmetric positive definiteness and the monotonic determinant variation, but also preserve the tensor's anisotropy property which was proposed in the spectral quaternion (SQ) method.

Structure Prior Constrained Estimation of Human Cardiac Diffusion Tensors

OBJECTIVE

The purpose of this paper is to increase the accuracy of human cardiac diffusion tensor (DT) estimation in diffusion magnetic resonance imaging (dMRI) with a few diffusion gradient directions.

METHODS

A structure prior constrained (SPC) method is proposed. The method consists in introducing two regularizers in the conventional nonlinear least squares estimator. The two regularizers penalize the dissimilarity between neighboring DTs and the difference between estimated and prior fiber orientations, respectively. A novel numerical solution is presented to ensure the positive definite estimation.

RESULTS

Experiments on ex vivo human cardiac data show that the SPC method is able to well estimate DTs at most voxels, and is superior to state-of-the-art methods in terms of the mean errors of principal eigenvector, second eigenvector, helix angle, transverse angle, fractional anisotropy, and mean diffusivity.

CONCLUSION

The SPC method is a practical and reliable alternative to current denoising- or regularization-based methods for the estimation of human cardiac DT.

SIGNIFICANCE

The SPC method is able to accurately estimate human cardiac DTs in dMRI with a few diffusion gradient directions.

Will the real ventricular architecture please stand up?

Ventricular twisting, essential for cardiac function, is attributed to the contraction of myocardial helical fibers. The exact relationship between ventricular anatomy and function remains to be determined, but one commonly used explanatory model is the helical ventricular myocardial band (HVMB) model of Torrent‐Guasp. This model has been successful in explaining many aspects of ventricular function, (Torrent‐Guasp et al. Eur. J. Cardiothorac. Surg., 25, 376, 2004; Buckberg et al. Eur. J. Cardiothorac. Surg., 47, 587, 2015; Buckberg et al. Eur. J. Cardiothorac. Surg. 47, 778, 2015) but the model ignores important aspects of ventricular anatomy and should probably be replaced. The purpose of this review is to compare the HVMB model with a different model (nested layers). A complication when interpreting experimental observations that relate anatomy to function is that, in the myocardium, shortening does not always imply activation and lengthening does not always imply inactivation.

Multi-output Gaussian processes for enhancing resolution of diffusion tensor fields

Second order diffusion tensor (DT) fields are widely used in several clinical applications: brain fibers connections, diagnosis of neuro-degenerative diseases, image registration, brain conductivity models, etc. However, due to current acquisition protocols and hardware limitations in MRI machines, the diffusion magnetic resonance imaging (dMRI) data is obtained with low spatial resolution (1 or 2 mm3 for each voxel). This issue can be significant, because tissue fibers are much smaller than voxel size. Interpolation has become in a successful methodology for enhancing spatial resolution of DT fields. In this work, we present a feature-based interpolation approach through multi-output Gaussian processes (MOGP). First, we extract the logarithm of eigenvalues (direction) and the Euler angles (orientation) from diffusion tensors and we consider each feature as a separated but related output. Then, we interpolate the features along the whole DT field. In this case, the independent variables are the space coordinates (x, y, z). For this purpose, we assume that all features follow a multi-output Gaussian process with a common covariance matrix. Finally, we reconstruct new tensors from the interpolated eigenvalues and Euler angles. Accuracy of our methodology is better compared to approaches in the state of the art for performing DT interpolation, and it achieves a performance similar to the recently introduced method based on Generalized Wishart processes for interpolation of positive semidefinite matrices. We also show that MOGP preserves important properties of diffusion tensors such as fractional anisotropy.

Study of myocardial cell inhomogeneity of the human heart: Simulation and validation using polarized light imaging

PURPOSE

The arrangement or architecture of myocardial cells plays a fundamental role in the heart's function and its change was shown to be directly linked to heart diseases. Inhomogeneity level is an important index of myocardial cell arrangements in the human heart. The authors propose to investigate the inhomogeneity level of myocardial cells using polarized light imaging simulations and experiments.

METHODS

The idea is based on the fact that the myosin filaments in myocardial cells have the same properties as those of a uniaxial birefringent crystal. The method then consists in modeling the myosin filaments of myocardial cells as uniaxial birefringent crystal, simulating the behavior of the latter by means of the Mueller matrix, and measuring the final intensity of polarized light and consequently the inhomogeneity level of myocardial cells in each voxel through the use of crossed polarizers. The method was evaluated on both simulated and real tissues and under various myocardial cell configurations including parallel cells, crossed cells, and cells with random orientations.

RESULTS

When myocardial cells run perfectly parallel to each other, all the polarized light was blocked by those parallel myocardial cells, and a high homogeneity level was observed. However, if myocardial cells were not parallel to each other, some leakage of the polarized light was observed, thus causing the decrease of the polarized light amplitude and homogeneity level. The greater the crossing angle between myocardial cells, the smaller the amplitude of the polarized light and the greater the inhomogeneity level. For two populations of myocardial cell crossing at an angle, the resulting azimuth angle of the voxel was the bisector of this angle. Moreover, the value of the inhomogeneity level began to decrease from a nonzero value when the voxel was not totally homogeneous, containing for example cell crossing.

CONCLUSIONS

The proposed method enables the physical information of myocardial tissues to be estimated and the inhomogeneity level of a volume or voxel to be quantified, which opens new ways to study the microstructures of the human myocardium and helps understanding how heart diseases modify myocardial cells and change their mechanical properties.

Global Diffusion Tractography by Simulated Annealing

OBJECTIVE

Our goal is to develop a robust global tractography method for cardiac diffusion imaging.

METHODS

A graph is stretched over the whole myocardium to represent the fiber structure, and the solutions are minima of a graph energy measuring the fidelity to the data along with the fiber density and curvature. The optimization is performed by a variant of simulated annealing that offers increased design freedom without sacrificing theoretical convergence guarantees.

RESULTS

Numerical experiments on synthetic and real data demonstrate the capability of our tractography algorithm to deal with low angular resolution, highly noisy data. In particular, our algorithm outperforms the Bayesian model-based algorithm of Reisert et al. (NeuroImage, vol. 54, no. 2, 2011) and the graph-based algorithm of Frindel et al. (Magn. Reson. Med., vol. 64, no. 4, 2010) at the noise levels typical of in vivo imaging.

CONCLUSION

The proposed algorithm avoids the drawbacks of local techniques and is very robust to noise, which makes it a promising tool for in vivo diffusion imaging of moving organs.

SIGNIFICANCE

Our approach is global in terms of both the fiber structure representation and the minimization problem. It also allows us to adjust the trajectory density by simply changing the vertex-lattice spacing in the graph model, a desirable feature for multiresolution tractography analysis.

Multifiber pathway reconstruction using bundle constrained streamline

Fiber tractography techniques in diffusion magnetic resonance imaging have become a primary tool for studying the fiber architecture of biological tissues both noninvasively and in vivo. Streamline tracking, as a simple and efficient tractography technique, is widely used to reconstruct fiber pathways. It is however very sensitive to noisy estimation of local fiber orientations. In this paper, we propose a bundle constrained streamline method to accurately reconstruct multifiber pathways. The method introduces neighboring fiber consistency constraint in the tracking process and reconstructs fiber pathways that have optimal tradeoff between consistency with local fiber orientation estimations and similarity with neighboring fiber segment orientations. Results on synthetic, physical phantom and real human brain DW images show that the proposed method allows regular fiber pathways to be reconstructed and outperforms existing techniques.

Resolving intravoxel fiber architecture using nonconvex regularized blind compressed sensing

In diffusion magnetic resonance imaging, accurate and reliable estimation of intravoxel fiber architectures is a major prerequisite for tractography algorithms or any other derived statistical analysis. Several methods have been proposed that estimate intravoxel fiber architectures using low angular resolution acquisitions owing to their shorter acquisition time and relatively low b-values. But these methods are highly sensitive to noise. In this work, we propose a nonconvex regularized blind compressed sensing approach to estimate intravoxel fiber architectures in low angular resolution acquisitions. The method models diffusion-weighted (DW) signals as a sparse linear combination of unfixed reconstruction basis functions and introduces a nonconvex regularizer to enhance the noise immunity. We present a general solving framework to simultaneously estimate the sparse coefficients and the reconstruction basis. Experiments on synthetic, phantom, and real human brain DW images demonstrate the superiority of the proposed approach.

Free-breathing diffusion tensor imaging and tractography of the human heart in healthy volunteers using wavelet-based image fusion

Free-breathing cardiac diffusion tensor imaging (DTI) is a promising but challenging technique for the study of fiber structures of the human heart in vivo. This work proposes a clinically compatible and robust technique to provide three-dimensional (3-D) fiber architecture properties of the human heart. To this end, 10 short-axis slices were acquired across the entire heart using a multiple shifted trigger delay (TD) strategy under free breathing conditions. Interscan motion was first corrected automatically using a nonrigid registration method. Then, two post-processing schemes were optimized and compared: an algorithm based on principal component analysis (PCA) filtering and temporal maximum intensity projection (TMIP), and an algorithm that uses the wavelet-based image fusion (WIF) method. The two methods were applied to the registered diffusion-weighted (DW) images to cope with intrascan motion-induced signal loss. The tensor fields were finally calculated, from which fractional anisotropy (FA), mean diffusivity (MD), and 3-D fiber tracts were derived and compared. The results show that the comparison of the FA values (FA(PCATMIP) = 0.45 ±0.10, FA(WIF) = 0.42 ±0.05, P=0.06) showed no significant difference, while the MD values ( MD(PCATMIP)=0.83 ±0.12×10(-3) mm (2)/s, MD(WIF)=0.74±0.05×10(-3) mm (2)/s, P=0.028) were significantly different. Improved helix angle variations through the myocardium wall reflecting the rotation characteristic of cardiac fibers were observed with WIF. This study demonstrates that the combination of multiple shifted TD acquisitions and dedicated post-processing makes it feasible to retrieve in vivo cardiac tractographies from free-breathing DTI acquisitions. The substantial improvements were observed using the WIF method instead of the previously published PCATMIP technique.

Cardiac fiber unfolding by semidefinite programming

Diffusion-tensor imaging allows noninvasive assessment of the myocardial fiber architecture, which is fundamental in understanding the mechanics of the heart. In this context, tractography techniques are often used for representing and visualizing cardiac fibers, but their output is only qualitative. We introduce here a new framework toward a more quantitative description of the cardiac fiber architecture from tractography results. The proposed approach consists in taking three-dimensional (3-D) fiber tracts as inputs, and then unfolding these fibers in the Euclidean plane under local isometry constraints using semidefinite programming. The solution of the unfolding problem takes the form of a Gram matrix which defines the two-dimensional (2-D) embedding of the fibers and whose spectrum provides quantitative information on their organization. Experiments on synthetic and real data show that unfolding makes it easier to observe and to study the cardiac fiber architecture. Our conclusion is that 2-D embedding of cardiac fibers is a promising approach to supplement 3-D rendering for understanding the functioning of the heart.

Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI

Diffusion tensor interpolation is an important issue in the application of diffusion tensor magnetic resonance imaging (DT-MRI) to the human heart, all the more as the points representing the myocardium of the heart are often sparse. We propose a feature-based interpolation framework for the tensor fields from cardiac DT-MRI, by taking into account inherent relationships between tensor components. In this framework, the interpolation consists in representing a diffusion tensor in terms of two tensor features, eigenvalues and orientation, interpolating the Euler angles or the quaternion relative to tensor orientation and the logarithmically transformed eigenvalues, and reconstructing the tensor to be interpolated from the interpolated eigenvalues and tensor orientations. The results obtained with the aid of both synthetic and real cardiac DT-MRI data demonstrate that the feature-based schemes based on Euler angles or quaternions not only maintain the advantages of Log-Euclidean and Riemannian interpolation as for preserving the tensor's symmetric positive-definiteness and the monotonic determinant variation, but also preserve, at the same time, the monotonicity of fractional anisotropy (FA) and mean diffusivity (MD) values, which is not the case with Euclidean, Cholesky and Log-Euclidean methods. As a result, both interpolation schemes remove the phenomenon of FA collapse, and consequently avoid introducing artificial fiber crossing, with the difference that the quaternion is independent of coordinate system while Euler angles have the property of being more suitable for sophisticated interpolations.