The γ-parameter of anomalous diffusion quantified in human brain by MRI depends on local magnetic susceptibility differences

Assessment of Calcaneal Spongy Bone Magnetic Resonance Characteristics in Women: A Comparison between Measures Obtained at 0.3 T, 1.5 T, and 3.0 T

BACKGROUND

There is a growing interest in bone tissue MRI and an even greater interest in using low-cost MR scanners. However, the characteristics of bone MRI remain to be fully defined, especially at low field strength. This study aimed to characterize the signal-to-noise ratio (SNR), T2, and T2* in spongy bone at 0.3 T, 1.5 T, and 3.0 T. Furthermore, relaxation times were characterized as a function of bone-marrow lipid/water ratio content and trabecular bone density.

METHODS

Thirty-two women in total underwent an MR-imaging investigation of the calcaneus at 0.3 T, 1.5 T, and 3.0 T. MR-spectroscopy was performed at 3.0 T to assess the fat/water ratio. SNR, T2, and T2* were quantified in distinct calcaneal regions (ST, TC, and CC). ANOVA and Pearson correlation statistics were used.

RESULTS

SNR increase depends on the magnetic field strength, acquisition sequence, and calcaneal location. T2* was different at 3.0 T and 1.5 T in ST, TC, and CC. Relaxation times decrease as much as the magnetic field strength increases. The significant linear correlation between relaxation times and fat/water found in healthy young is lost in osteoporotic subjects.

CONCLUSION

The results have implications for the possible use of relaxation vs. lipid/water marrow content for bone quality assessment and the development of quantitative MRI diagnostics at low field strength.

Nuclear magnetic resonance signal decay in the presence of a background gradient: Normal and anomalous diffusion

A novel way for calculating the diffusion-weighted nuclear magnetic resonance (NMR) attenuation signal expression in the presence of a background gradient is developed. This method is easily applicable to NMR-attenuated signals arising from any pulse field gradient sequence experiments. Here, we provide detailed calculations for the classical pulsed gradient stimulated echo and the pulsed gradient spin echo, as the particular cases. Within this general theoretical framework, devised for Gaussian processes with stationary increments, we recover and extend the previous Stejskal-Tanner results in the case of normal diffusion and we furnish a new expression in the case of anomalous diffusion.

Differentiation of benign and malignant breast lesions using diffusion-weighted imaging with a fractional-order calculus model

PURPOSE

To assess the feasibility of using three diffusion parameters (D, β, and μ) derived from fractional-order calculus (FROC) diffusion model for improving the differentiation between benign and malignant breast lesions.

METHOD

In this prospective study, 103 patients with breast lesions were enrolled. All subjects underwent diffusion-weighted imaging (DWI) with 12b values. Inter-observer agreement with respect to quantification of parameters by two radiologists was assessed using intraclass coefficient. Conventional apparent diffusion coefficient (ADC) and three FROC model parameters D, β, and μ were compared between the benign lesion and malignant lesion groups using the Mann-Whitney U test. Then, a comprehensive prediction model was created by using binary logistic regression. Receiver operating characteristic (ROC) curve analysis was performed to evaluate the diagnostic performance of the parameters using histopathological diagnosis as the reference standard.

RESULTS

The FROC parameters and ADC all exhibited significant differences between benign lesions and malignant lesions (P＜0.001). Among the individual parameters, the sensitivity of μ was higher than ADC (95.92% for μ vs 91.84% for ADC), and the specificity of β was higher than ADC (72.22% for β vs 70.37% for ADC). The combination of ADC and FROC parameters (D and β) generated the largest area under the ROC curve (0.841) when compared with individual parameters, indicating an improved performance for differentiating benign lesions from malignant lesions.

CONCLUSIONS

This study demonstrated the feasibility of using the FROC diffusion model to improve the accuracy of identifying malignant breast lesions.

Generalisation of continuous time random walk to anomalous diffusion MRI models with an age-related evaluation of human corpus callosum

Diffusion MRI measures of the human brain provide key insight into microstructural variations across individuals and into the impact of central nervous system diseases and disorders. One approach to extract information from diffusion signals has been to use biologically relevant analytical models to link millimetre scale diffusion MRI measures with microscale influences. The other approach has been to represent diffusion as an anomalous transport process and infer microstructural information from the different anomalous diffusion equation parameters. In this study, we investigated how parameters of various anomalous diffusion models vary with age in the human brain white matter, particularly focusing on the corpus callosum. We first unified several established anomalous diffusion models (the super-diffusion, sub-diffusion, quasi-diffusion and fractional Bloch-Torrey models) under the continuous time random walk modelling framework. This unification allows a consistent parameter fitting strategy to be applied from which meaningful model parameter comparisons can be made. We then provided a novel way to derive the diffusional kurtosis imaging (DKI) model, which is shown to be a degree two approximation of the sub-diffusion model. This link between the DKI and sub-diffusion models led to a new robust technique for generating maps of kurtosis and diffusivity using the sub-diffusion parameters β_SUB and D_SUB. Superior tissue contrast is achieved in kurtosis maps based on the sub-diffusion model. 7T diffusion weighted MRI data for 65 healthy participants in the age range 19-78 years was used in this study. Results revealed that anomalous diffusion model parameters α and β have shown consistent positive correlation with age in the corpus callosum, indicating α and β are sensitive to tissue microstructural changes in ageing.

Transient Anomalous Diffusion MRI in Excised Mouse Spinal Cord: Comparison Among Different Diffusion Metrics and Validation With Histology

Neural tissue is a hierarchical multiscale system with intracellular and extracellular diffusion compartments at different length scales. The normal diffusion of bulk water in tissues is not able to detect the specific features of a complex system, providing nonlocal, diffusion measurement averaged on a 10-20 μm length scale. Being able to probe tissues with sub-micrometric diffusion length and quantify new local parameters, transient anomalous diffusion (tAD) would dramatically increase the diagnostic potential of diffusion MRI (DMRI) in detecting collective and sub-micro architectural changes of human tissues due to pathological damage. In DMRI, the use of tAD parameters quantified using specific DMRI acquisition protocols and their interpretation has often aroused skepticism. Although the derived formulas may accurately fit experimental diffusion-weighted data, the relationships between the postulated dynamical feature and the underlying geometrical structure remains elusive, or at most only suggestive. This work aimed to elucidate and validate the image contrast and information that can be obtained using the tAD model in white matter (WM) through a direct comparison between different diffusion metrics and histology. Towards this goal, we compared tAD metrics extracted from pure subdiffusion (α-imaging) and super-pseudodiffusion (γ-imaging) in excised mouse spinal cord WM, together with T2 and T2* relaxometry, conventional (normal diffusion-based) diffusion tensor imaging (DTI) and q-space imaging (QSI), with morphologic measures obtained by optical microscopy, to determine which structural and topological characteristics of myelinated axons influenced tAD contrast. Axon diameter (AxDiam), the standard deviation of diameters (SD_ax.diam), axonal density (AxDens) and effective local density (ELD) were extracted from optical images in several WM tracts. Among all the diffusion parameters obtained at 9.4 T, γ-metrics confirmed a strong dependence on magnetic in-homogeneities quantified by R2* = 1/T2* and showed the strongest associations with AxDiam and ELD. On the other hand, α-metrics showed strong associations with SD_ax.diam and was significantly related to AxDens, suggesting its ability to quantify local heterogeneity degree in neural tissue. These results elucidate the biophysical mechanism underpinning tAD parameters and show the clinical potential of tAD-imaging, considering that both physiologic and pathologic neurodegeneration translate into alterations of WM morphometry and topology.

Fractional Diffusion with Geometric Constraints: Application to Signal Decay in Magnetic Resonance Imaging (MRI)

We investigate diffusion in three dimensions on a comb-like structure in which the particles move freely in a plane, but, out of this plane, are constrained to move only in the perpendicular direction. This model is an extension of the two-dimensional version of the comb model, which allows diffusion along the backbone when the particles are not in the branches. We also consider memory effects, which may be handled with different fractional derivative operators involving singular and non-singular kernels. We find exact solutions for the particle distributions in this model that display normal and anomalous diffusion regimes when the mean-squared displacement is determined. As an application, we use this model to fit the anisotropic diffusion of water along and across the axons in the optic nerve using magnetic resonance imaging. The results for the observed diffusion times (8 to 30 milliseconds) show an anomalous diffusion both along and across the fibers.

Age-related microstructural and physiological changes in normal brain measured by MRI γ-metrics derived from anomalous diffusion signal representation

Nowadays, increasing longevity associated with declining cerebral nervous system functions, suggests the need for continued development of new imaging contrast mechanisms to support the differential diagnosis of age-related decline. In our previous papers, we developed a new imaging contrast metrics derived from anomalous diffusion signal representation and obtained from diffusion-weighted (DW) data collected by varying diffusion gradient strengths. Recently, we highlighted that the new metrics, named γ-metrics, depended on the local inhomogeneity due to differences in magnetic susceptibility between tissues and diffusion compartments in young healthy subjects, thus providing information about myelin orientation and iron content within cerebral regions. The major structural modifications occurring in brain aging are myelinated fibers damage in nerve fibers and iron accumulation in gray matter nuclei. Therefore, we investigated the potential of γ-metrics in relation to other conventional diffusion metrics such as DTI, DKI and NODDI in detecting age-related structural changes in white matter (WM) and subcortical gray matter (scGM). DW-images were acquired in 32 healthy subjects, adults and elderly (age range 20-77 years) using 3.0T and 12 b-values up to 5000 s/mm². Association between diffusion metrics and subjects' age was assessed using linear regression. A decline in mean γ (Mγ) in the scGM and a complementary increase in radial γ (γ_⊥) in frontal WM, genu of corpus callosum and anterior corona radiata with advancing age were found. We suggested that the increase in γ⊥ might reflect declined myelin density, and Mγ decrease might mirror iron accumulation. An increase in D_// and a decrease in the orientation dispersion index (ODI) were associated with axonal loss in the pyramidal tracts, while their inverted trends within the thalamus were thought to be linked to reduced architectural complexity of nerve fibers. γ-metrics together with conventional diffusion-metrics can more comprehensively characterize the complex mechanisms underlining age-related changes than conventional diffusion techniques alone.

Influence of the size and curvedness of neural projections on the orientationally averaged diffusion MR signal

Neuronal and glial projections can be envisioned to be tubes of infinitesimal diameter as far as diffusion magnetic resonance (MR) measurements via clinical scanners are concerned. Recent experimental studies indicate that the decay of the orientationally-averaged signal in white-matter may be characterized by the power-law, Ē(q) ∝ q^-1, where q is the wavenumber determined by the parameters of the pulsed field gradient measurements. One particular study by McKinnon et al. [1] reports a distinctively faster decay in gray-matter. Here, we assess the role of the size and curvature of the neurites and glial arborizations in these experimental findings. To this end, we studied the signal decay for diffusion along general curves at all three temporal regimes of the traditional pulsed field gradient measurements. We show that for curvy projections, employment of longer pulse durations leads to a disappearance of the q^-1 decay, while such decay is robust when narrow gradient pulses are used. Thus, in clinical acquisitions, the lack of such a decay for a fibrous specimen can be seen as indicative of fibers that are curved. We note that the above discussion is valid for an intermediate range of q-values as the true asymptotic behavior of the signal decay is Ē(q) ∝ q^-4 for narrow pulses (through Debye-Porod law) or steeper for longer pulses. This study is expected to provide insights for interpreting the diffusion-weighted images of the central nervous system and aid in the design of acquisition strategies.

Concerning the matching of magnetic susceptibility differences for the compensation of background gradients in anisotropic diffusion fibre phantoms

Artificial, anisotropic fibre phantoms are nowadays increasingly used in the field of diffusion-weighted MRI. Such phantoms represent useful tools for, among others, the calibration of pulse sequences and validation of diffusion models since they can mimic well-known structural features of brain tissue on the one hand, but exhibit a reduced complexity, on the other. Among all materials, polyethylene fibres have been widely used due to their excellent properties regarding the restriction of water diffusion and surface relaxation properties. Yet the magnetic susceptibility of polyethylene can be distinctly lower than that of distilled water. This difference produces strong microscopic, background field gradients in the vicinity of fibre bundles which are not parallel to the static magnetic field. This, in turn, modulates the MRI signal behaviour. In the present work we investigate an approach to reduce the susceptibility-induced background gradients via reducing the heterogeneity in the internal magnetic susceptibility. An aqueous solution of magnesium chloride hexahydrate (MgCl₂·6H₂O) is used for this purpose. Its performance is demonstrated in dedicated anisotropic fibre phantoms with different geometrical configurations.