Anomalous diffusion in cerebral glioma assessed using a fractional motion model

Anisotropy of Anomalous Diffusion Improves the Accuracy of Differentiating and Grading Alzheimer's Disease Using Novel Fractional Motion Model

Background and Purpose: Recent evidence shows that the fractional motion (FM) model may be a more appropriate model for describing the complex diffusion process of water in brain tissue and has shown to be beneficial in clinical applications of Alzheimer's disease (AD). However, the FM model averaged the anomalous diffusion parameter values, which omitted the impacts of anisotropy. This study aimed to investigate the potential feasibility of anisotropy of anomalous diffusion using the FM model for distinguishing and grading AD patients. Methods: Twenty-four patients with AD and 11 matched healthy controls were recruited, diffusion MRI was obtained from all participants and analyzed using the FM model. Generalized fractional anisotropy (gFA), an anisotropy metric, was introduced and the gFA values of FM-related parameters, Noah exponent (α) and the Hurst exponent (H), were calculated and compared between the healthy group and AD group and between the mild AD group and moderate AD group. The receiver-operating characteristic (ROC) analysis and the multivariate logistic regression analysis were used to assess the diagnostic performances of the anisotropy values and the directionally averaged values. Results: The gFA(α) and gFA(H) values of the moderate AD group were higher than those of the mild AD group in left hippocampus. The gFA(α) value of the moderate AD group was significantly higher than that of the healthy control group in both the left and right hippocampus. The gFA(ADC) values of the moderate AD group were significantly lower than those of the mild AD group and healthy control group in the right hippocampus. Compared with the gFA(α), gFA(H), α, and H, the ROC analysis showed larger areas under the curves for combination of α + gFA(α) and the combination of H + gFA(H) in differentiating the mild AD and moderate AD groups, and larger area under the curves for combination of α + gFA(α) in differentiating the healthy controls and AD groups. Conclusion: The anisotropy of anomalous diffusion could significantly differentiate and grade patients with AD, and the diagnostic performance was improved when the anisotropy metric was combined with commonly used directionally averaged values. The utility of anisotropic anomalous diffusion may provide novel insights to profoundly understand the neuropathology of AD.

Identification and Classification of Alzheimer's Disease Patients Using Novel Fractional Motion Model

Most diffusion magnetic resonance imaging (dMRI) techniques use the mono-exponential model to describe the diffusion process of water in the brain. However, the observed dMRI signal decay curve deviates from the mono-exponential form. To solve this problem, the fractional motion (FM) model has been developed, which is regarded as a more appropriate model for describing the complex diffusion process in brain tissue. It is still unclear in the identification and classification of Alzheimer's disease (AD) patients using the FM model. The purpose of this study was to investigate the potential feasibility of FM model for differentiating AD patients from healthy controls and grading patients with AD. Twenty-four patients with AD and 11 healthy controls were included. The left and right hippocampus were selected as regions of interest (ROIs). The apparent diffusion coefficient (ADC) values and FM-related parameters, including the Noah exponent (α), the Hurst exponent (H), and the memory parameter (μ=H-1/α), were calculated and compared between AD patients and healthy controls and between mild AD and moderate AD patients using a two-sample t-test. The correlations between FM-related parameters α, H, μ, and ADC values and the cognitive functions assessed by mini-mental state examination (MMSE) and Montreal cognitive assessment (MoCA) scales were investigated using Pearson partial correlation analysis in patients with AD. The receiver-operating characteristic analysis was used to assess the differential performance. We found that the FM-related parameter α could be used to distinguish AD patients from healthy controls (P < 0.05) with greater sensitivity and specificity (left ROI, 0.917 and 0.636; right ROI, 0.917 and 0.727) and grade AD patients (P < 0.05) showed higher sensitivity and specificity (right ROI, 0.917, 0.75). The α was found to be positively correlated with MMSE (P < 0.05) and MoCA (P < 0.05) scores in patients with AD, indicating that the α values in the bilateral hippocampus were a potential MRI-based biomarker of disease severity in AD patients. This novel diffusion model may be useful for further understanding neuropathologic changes in patients with AD.

Assessment of MRI-based anomalous diffusion changes in brain ischemic stroke with a fractional motion model

The actual diffusion process in human brain has been shown to be anomalous comparing to that predicted with traditional diffusion MRI (dMRI) theory. Recently, dMRI based on fractional motion (FM) model has demonstrated the potential to accurately describe anomalous diffusion in vivo. In this work, we explored the potential value of FM model-based dMRI in quantificational identification of ischemic stroke and compared that with the traditional apparent diffusion coefficient (ADC). We included 23 acute stroke patients, 8 of whom finished a follow-up scan, and 22 matched healthy controls. The dMRI images were acquired by using a Stejskal-Tanner single-shot spin-echo echo-planar-imaging sequence (diffusion gradients were applied in three orthogonal directions with 25 non-zero b values ranging from 248 to 4474 s/mm²) at 3.0 T MRI. We calculated the coefficient of variation (CV) for FM-related parameters in stroke lesions, and compared the mean values for FM-related parameters and ADC by using two-sample t-tests. Correlation analysis was achieved using Pearson correlation coefficient test. In acute stroke lesions, CV for FM-related parameters showed significant increase compared with normal tissues (P < 0.01), while those of ADC didn't appear statistical difference. Mean values for FM-related parameters showed significant decrease in acute lesion (P < 0.01) and their changing pattern during follow-up was positively correlated with ADC (P < 0.005). Our results initially verified the utility of the FM-model in detecting ischemic stroke compared with traditional dMRI.

Detection of axonal degeneration in a mouse model of Huntington's disease: comparison between diffusion tensor imaging and anomalous diffusion metrics

OBJECTIVE

The goal of this work is to study the changes in white matter integrity in R6/2, a well-established animal model of Huntington's disease (HD) that are captured by ex vivo diffusion imaging (DTI) using a high field MRI (17.6 T).

MATERIALS AND METHODS

DTI and continuous time random walk (CTRW) models were used to fit changes in the diffusion-weighted signal intensity in the corpus callosum of controls and in R6/2 mice.

RESULTS

A significant 13% decrease in fractional anisotropy, a 7% increase in axial diffusion, and a 33% increase in radial diffusion were observed between R6/2 and control mice. No change was observed in the CTRW beta parameter, but a significant decrease in the alpha parameter (- 21%) was measured. Histological analysis of the corpus callosum showed a decrease in axonal organization, myelin alterations, and astrogliosis. Electron microscopy studies demonstrated ultrastructural changes in degenerating axons, such as an increase in tortuosity in the R6/2 mice.

CONCLUSIONS

DTI and CTRW diffusion models display quantitative changes associated with the microstructural alterations observed in the corpus callosum of the R6/2 mice. The observed increase in the diffusivity and decrease in the alpha CTRW parameter providing support for the use of these diffusion models for non-invasive detection of white matter alterations in HD.

Improved stimulated echo in diffusion magnetic resonance imaging: introducing a π pulse for SNR enhancement

PURPOSE

Anomalous diffusion in biological tissues can be examined by diffusion MRI for various applications, including tumor diagnosis and measurement of brain fiber pathways. However, the measurement of anomalous diffusion requires high b-values for the diffusion gradient in MRI, and current MRI methods cannot provide a high SNR. This study aimed to improve on the standard stimulated echo (STE) to enhance the SNR in diffusion MRI with high b-values.

METHODS

Because of hardware limitations and human safety considerations, prolonging the diffusion time (Δ) is 1 of the few methods available to realize high b-values. Here, we propose a new echo mechanism for diffusion MRI to enhance SNRs under long Δ. By introducing a π pulse at the midpoint between 2nd and 3rd π/2 pulses of STE, we refocus the magnetic moment vectors in the longitudinal plane before the third π/2 pulse is applied, which preserves the full echo signals. This sequence was compared with STE and spin echo (SE). Nine Δs were tested in a phantom. Multi b-values with 2 Δs were tested in a mouse liver, brain, and tumor.

RESULTS

Compared with STE and SE, the proposed improved STE (ISTE) exhibited an improved SNR in the phantom experiment and improved performance in the in vivo experiments.

CONCLUSION

By using the proposed echo mechanism in diffusion MRI, we enhanced the SNR of the images, which enables us to investigate diffusion behavior at higher b-values and further facilitates the development of quantitative diffusion MRI and radiomics.

Anisotropy of anomalous diffusion improves the accuracy of differentiating low- and high-grade cerebral gliomas

BACKGROUND

Anomalous diffusion model has been introduced and shown to be beneficial in clinical applications. However, only the directionally averaged values of anomalous diffusion parameters were investigated, and the anisotropy of anomalous diffusion remains unexplored. The aim of this study was to demonstrate the feasibility of using anisotropy of anomalous diffusion for differentiating low- and high-grade cerebral gliomas.

METHODS

Diffusion MRI images were acquired from brain tumor patients and analyzed using the fractional motion (FM) model. Twenty-two patients with histopathologically confirmed gliomas were selected. An anisotropy metric for the FM-related parameters, including the Noah exponent (α) and the Hurst exponent (H), was introduced and their values were statistically compared between the low- and high-grade gliomas. Additionally, multivariate logistic regression analysis was performed to assess the combination of the anisotropy metric and the directionally averaged value for each parameter. The diagnostic performances for grading gliomas were evaluated using a receiver operating characteristic (ROC) analysis.

RESULTS

The Hurst exponent H was more anisotropic in high-grade than in low-grade gliomas (P = 0.015), while no significant difference was observed for the anisotropy of α. The ROC analysis revealed that larger areas under the ROC curves were produced for the combination of α (1) and the combination of H (0.813) compared with the directionally averaged α (0.979) and H (0.594), indicating an improved performance for tumor differentiation.

CONCLUSION

The anisotropy of anomalous diffusion can provide distinctive information and benefit the differentiation of low- and high-grade gliomas. The utility of anisotropic anomalous diffusion may have an improved effect for investigating pathological changes in tissues.

Fractional cable equation for general geometry: A model of axons with swellings and anomalous diffusion

Different experimental studies have reported anomalous diffusion in brain tissues and notably this anomalous diffusion is expressed through fractional derivatives. Axons are important to understand neurodegenerative diseases such as multiple sclerosis, Alzheimer's disease, and Parkinson's disease. Indeed, abnormal accumulation of proteins and organelles in axons is a hallmark of these diseases. The diffusion in the axons can become anomalous as a result of this abnormality. In this case the voltage propagation in axons is affected. Another hallmark of different neurodegenerative diseases is given by discrete swellings along the axon. In order to model the voltage propagation in axons with anomalous diffusion and swellings, in this paper we propose a fractional cable equation for a general geometry. This generalized equation depends on fractional parameters and geometric quantities such as the curvature and torsion of the cable. For a cable with a constant radius we show that the voltage decreases when the fractional effect increases. In cables with swellings we find that when the fractional effect or the swelling radius increases, the voltage decreases. Similar behavior is obtained when the number of swellings and the fractional effect increase. Moreover, we find that when the radius swelling (or the number of swellings) and the fractional effect increase at the same time, the voltage dramatically decreases.

Directional sensitivity of anomalous diffusion in human brain assessed by tensorial fractional motion model

Anisotropic diffusion in the nervous system is most commonly modeled by apparent diffusion tensor, which is based on regular diffusion theory. However, the departure of diffusion-induced signal attenuation from a mono-exponential form implies that there is anomalous diffusion. Recently, a novel diffusion NMR theory based on the fractional motion (FM) model, which is an anomalous diffusion model, has been proposed. While the FM model has been applied to both healthy subjects and tumor patients, its anisotropy in the nervous system remains elusive. In this study, this issue was addressed by measuring the FM-related parameters in 12 non-collinear directions. A metric to quantify the directional deviation was derived. Furthermore, the FM-related parameters were modeled as tensors and analyzed in analogy with the conventional diffusion tensor imaging (DTI). Experimental results, which were obtained for 15 healthy subjects at 3T, exhibited pronounced anisotropy of the FM-related parameters, although the effects were smaller than the apparent diffusion coefficient (ADC). The tensorial nature for α, which is the Noah exponent in the FM model, showed behavior similar to the ADC, especially the principal eigenvector for α aligned with the dominant white matter fiber directions. The Hurst exponent H in the FM model, however, showed no correlation with the major fiber directions. The anisotropy of the FM model may provide complementary information to DTI and may have potential for tractography and detecting brain abnormalities.