Comparison of regularization methods for human cardiac diffusion tensor MRI

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.

Extraction of the 3D local orientation of myocytes in human cardiac tissue using X-ray phase-contrast micro-tomography and multi-scale analysis

This paper presents a methodology to access the 3D local myocyte arrangements in fresh human post-mortem heart samples. We investigated the cardiac micro-structure at a high and isotropic resolution of 3.5 µm in three dimensions using X-ray phase micro-tomography at the European Synchrotron Radiation Facility. We then processed the reconstructed volumes to extract the 3D local orientation of the myocytes using a multi-scale approach with no segmentation. We created a simplified 3D model of tissue sample made of simulated myocytes with known size and orientations, to evaluate our orientation extraction method. Afterwards, we applied it to 2D histological cuts and to eight 3D left ventricular (LV) cardiac tissue samples. Then, the variation of the helix angles, from the endocardium to the epicardium, was computed at several spatial resolutions ranging from 3.6³ mm³ to 112³ µm³. We measure an increased range of 20° to 30° from the coarsest resolution level to the finest level in the experimental samples. This result is in line with the higher values measured from histology. The displayed tractography demonstrates a rather smooth evolution of the transmural helix angle in six LV samples and a sudden discontinuity of the helix angle in two septum samples. These measurements bring a new vision of the human heart architecture from macro- to micro-scale.

On the averaging of cardiac diffusion tensor MRI data: the effect of distance function selection

Diffusion tensor magnetic resonance imaging (DT-MRI) allows a unique insight into the microstructure of highly-directional tissues. The selection of the most proper distance function for the space of diffusion tensors is crucial in enhancing the clinical application of this imaging modality. Both linear and nonlinear metrics have been proposed in the literature over the years. The debate on the most appropriate DT-MRI distance function is still ongoing. In this paper, we presented a framework to compare the Euclidean, affine-invariant Riemannian and log-Euclidean metrics using actual high-resolution DT-MRI rat heart data. We employed temporal averaging at the diffusion tensor level of three consecutive and identically-acquired DT-MRI datasets from each of five rat hearts as a means to rectify the background noise-induced loss of myocyte directional regularity. This procedure is applied here for the first time in the context of tensor distance function selection. When compared with previous studies that used a different concrete application to juxtapose the various DT-MRI distance functions, this work is unique in that it combined the following: (i) metrics were judged by quantitative-rather than qualitative-criteria, (ii) the comparison tools were non-biased, (iii) a longitudinal comparison operation was used on a same-voxel basis. The statistical analyses of the comparison showed that the three DT-MRI distance functions tend to provide equivalent results. Hence, we came to the conclusion that the tensor manifold for cardiac DT-MRI studies is a curved space of almost zero curvature. The signal to noise ratio dependence of the operations was investigated through simulations. Finally, the 'swelling effect' occurrence following Euclidean averaging was found to be too unimportant to be worth consideration.

Ultrafast multi-slice spatiotemporally encoded MRI with slice-selective dimension segmented

As a recently emerging method, spatiotemporally encoded (SPEN) magnetic resonance imaging (MRI) has a high robustness to field inhomogeneity and chemical shift effect. It has been broadened from single-slice scanning to multi-slice scanning. In this paper, a novel multi-slice SPEN MRI method was proposed. In this method, the slice-selective dimension was segmented to lower the specific absorption rate (SAR) and improve the image quality. This segmented method, dubbed SeSPEN method, was theoretically analyzed and demonstrated with phantom, lemon and in vivo rat brain experiments. The experimental results were compared with the results obtained from the spin-echo EPI, spin-echo SPEN method and multi-slice global SPEN method proposed by Frydman and coauthors (abbr. GlSPEN method). All the SPEN images were super-resolved reconstructed using deconvolution method. The results indicate that the SeSPEN method retains the advantage of SPEN MRI with respect to resistance to field inhomogeneity and can provide better signal-to-noise ratio than multi-slice GlSPEN MRI technique. The SeSPEN method has comparable SAR to the GlSPEN method while the T1 signal attenuation effect is alleviated. The proposed method will facilitate the multi-slice SPEN MRI to scan more slices within one scan with better image quality.

The effects of noise in cardiac diffusion tensor imaging and the benefits of averaging complex data

There is growing interest in cardiac diffusion tensor imaging (cDTI), but, unlike other diffusion MRI applications, there has been little investigation of the effects of noise on the parameters typically derived. One method of mitigating noise floor effects when there are multiple image averages, as in cDTI, is to average the complex rather than the magnitude data, but the phase contains contributions from bulk motion, which must be removed first. The effects of noise on the mean diffusivity (MD), fractional anisotropy (FA), helical angle (HA) and absolute secondary eigenvector angle (E2A) were simulated with various diffusion weightings (b values). The effect of averaging complex versus magnitude images was investigated. In vivo cDTI was performed in 10 healthy subjects with b = 500, 1000, 1500 and 2000 s/mm(2). A technique for removing the motion-induced component of the image phase present in vivo was implemented by subtracting a low-resolution copy of the phase from the original images before averaging the complex images. MD, FA, E2A and the transmural gradient in HA were compared for un-averaged, magnitude- and complex-averaged reconstructions. Simulations demonstrated an over-estimation of FA and MD at low b values and an under-estimation at high b values. The transition is relatively signal-to-noise ratio (SNR) independent and occurs at a higher b value for FA (b = 1000-1250 s/mm(2)) than MD (b ≈ 250 s/mm(2)). E2A is under-estimated at low and high b values with a transition at b ≈ 1000 s/mm(2), whereas the bias in HA is comparatively small. The under-estimation of FA and MD at high b values is caused by noise floor effects, which can be mitigated by averaging the complex data. Understanding the parameters of interest and the effects of noise informs the selection of the optimal b values. When complex data are available, they should be used to maximise the benefit from the acquisition of multiple averages. The combination of complex data is also a valuable step towards segmented acquisitions.

Reducing Individual Variation for fMRI Studies in Children by Minimizing Template Related Errors

Spatial normalization is an essential process for group comparisons in functional MRI studies. In practice, there is a risk of normalization errors particularly in studies involving children, seniors or diseased populations and in regions with high individual variation. One way to minimize normalization errors is to create a study-specific template based on a large sample size. However, studies with a large sample size are not always feasible, particularly for children studies. The performance of templates with a small sample size has not been evaluated in fMRI studies in children. In the current study, this issue was encountered in a working memory task with 29 children in two groups. We compared the performance of different templates: a study-specific template created by the experimental population, a Chinese children template and the widely used adult MNI template. We observed distinct differences in the right orbitofrontal region among the three templates in between-group comparisons. The study-specific template and the Chinese children template were more sensitive for the detection of between-group differences in the orbitofrontal cortex than the MNI template. Proper templates could effectively reduce individual variation. Further analysis revealed a correlation between the BOLD contrast size and the norm index of the affine transformation matrix, i.e., the SFN, which characterizes the difference between a template and a native image and differs significantly across subjects. Thereby, we proposed and tested another method to reduce individual variation that included the SFN as a covariate in group-wise statistics. This correction exhibits outstanding performance in enhancing detection power in group-level tests. A training effect of abacus-based mental calculation was also demonstrated, with significantly elevated activation in the right orbitofrontal region that correlated with behavioral response time across subjects in the trained group.

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.

Assessment of cardiac motion effects on the fiber architecture of the human heart in vivo

The use of diffusion tensor imaging (DTI) for studying the human heart in vivo is very challenging due to cardiac motion. This paper assesses the effects of cardiac motion on the human myocardial fiber architecture. To this end, a model for analyzing the effects of cardiac motion on signal intensity is presented. A Monte-Carlo simulation based on polarized light imaging data is then performed to calculate the diffusion signals obtained by the displacement of water molecules, which generate diffusion weighted (DW) images. Rician noise and in vivo motion data obtained from DENSE acquisition are added to the simulated cardiac DW images to produce motion-induced datasets. An algorithm based on principal components analysis filtering and temporal maximum intensity projection (PCATMIP) is used to compensate for motion-induced signal loss. Diffusion tensor parameters derived from motion-reduced DW images are compared to those derived from the original simulated DW images. Finally, to assess cardiac motion effects on in vivo fiber architecture, in vivo cardiac DTI data processed by PCATMIP are compared to those obtained from one trigger delay (TD) or one single phase acquisition. The results showed that cardiac motion produced overestimated fractional anisotropy and mean diffusivity as well as a narrower range of fiber angles. The combined use of shifted TD acquisitions and postprocessing based on image registration and PCATMIP effectively improved the quality of in vivo DW images and subsequently, the measurement accuracy of fiber architecture properties. This suggests new solutions to the problems associated with obtaining in vivo human myocardial fiber architecture properties in clinical conditions.

Feature-preserving smoothing of diffusion weighted images using nonstationarity adaptive filtering

Although promising for studying the microstructure of in vivo tissues, the performance and the potentiality of diffusion tensor magnetic resonance imaging are hampered by the presence of high-level noise in diffusion weighted (DW) images. This paper proposes a novel smoothing approach, called the nonstationarity adaptive filtering, which estimates the intensity of a pixel by averaging intensities in its adaptive homogeneous neighborhood. The latter is determined according to five constraints and spatiodirectional nonstationarity measure maps. The proposed approach is compared with an anisotropic diffusion method used in DW image smoothing. Experimental results on both synthetic and real human DW images show that the proposed method achieves a better compromise between the smoothness of homogeneous regions and the preservation of desirable features such as boundaries, even for highly noisy data, thus leading to homogeneously consistent tensor fields and consequently more coherent fibers.

Human atlas of the cardiac fiber architecture: study on a healthy population

Cardiac fibers, as well as their local arrangement in laminar sheets, have a complex spatial variation of their orientation that has an important role in mechanical and electrical cardiac functions. In this paper, a statistical atlas of this cardiac fiber architecture is built for the first time using human datasets. This atlas provides an average description of the human cardiac fiber architecture along with its variability within the population. In this study, the population is composed of ten healthy human hearts whose cardiac fiber architecture is imaged ex vivo with DT-MRI acquisitions. The atlas construction is based on a computational framework that minimizes user interactions and combines most recent advances in image analysis: graph cuts for segmentation, symmetric log-domain diffeomorphic demons for registration, and log-Euclidean metric for diffusion tensor processing and statistical analysis. Results show that the helix angle of the average fiber orientation is highly correlated to the transmural depth and ranges from -41° on the epicardium to +66° on the endocardium. Moreover, we find that the fiber orientation dispersion across the population (±13°) is lower than for the laminar sheets (±31°) . This study, based on human hearts, extends previous studies on other mammals with concurring conclusions and provides a description of the cardiac fiber architecture more specific to human and better suited for clinical applications. Indeed, this statistical atlas can help to improve the computational models used for radio-frequency ablation, cardiac resynchronization therapy, surgical ventricular restoration, or diagnosis and followups of heart diseases due to fiber architecture anomalies.

Detecting structure in diffusion tensor MR images

We derive herein first and second-order differential operators for detecting structure in diffusion tensor MRI (DTI). Unlike existing methods, we are able to generate full first and second-order differentials without dimensionality reduction and while respecting the underlying manifold of the data. Further, we extend corner and curvature feature detectors to DTI using our differential operators. Results using the feature detectors on diffusion tensor MR images show the ability to highlight structure within the image that existing methods cannot.

Diffusion-weighted magnetic resonance imaging for the healthy cervical multifidus: a potential method for studying neck muscle physiology following spinal trauma

STUDY DESIGN

Cross-sectional.

OBJECTIVE

To develop a new magnetic resonance imaging (MRI) measure for the diffusive properties of the healthy cervical multifidus and to determine the interrater and intrarater reliability of the measurement.

BACKGROUND

Diffusion-weighted MRI, via calculation of the apparent diffusion coefficient (ADC), provides a representation of microscopic movements of water molecules in human tissues and may be useful to assess structural changes in neck muscle, as has been observed following whiplash. The optimal imaging parameters, however, have not been established.

METHODS

A diffusion-weighted MRI measure was developed, and, for the basic examination, the right cervical multifidus muscle at the C5 level was studied. A total of 6 asymptomatic volunteer individuals (3 females and 3 males) underwent a single diffusion-weighted MRI scan. Interrater and intrarater agreement was evaluated using Bland-Altman plots and intraclass correlation coefficients.

RESULTS

Mean ADCb0-b50 and ADCb50-250 were significantly different from one another (P=.03). The plots confirmed the agreement of raters for ADC of the right cervical multifidus at C5.

CONCLUSIONS

A quantitative and reliable diffusion-weighted MRI measure of cervical multifidus ADC has been described. There appears to be a fast and slow component ADC for the healthy multifidus, suggesting changes in extracellular and intracellular volume. Further comparative study is needed to quantify ADCs in the neck muscles in patients with traumatic whiplash.