Spatio-temporal anomalous diffusion imaging: results in controlled phantoms and in excised human meningiomas

Abstract

Recently, we measured two anomalous diffusion (AD) parameters: the spatial and the temporal AD indices, called γ and α, respectively, by using spectroscopic pulse gradient field methods. We showed that γ quantifies pseudo-superdiffusion processes, while α quantifies subdiffusion processes. Here, we propose γ and α maps obtained in a controlled heterogeneous phantom, comprised of packed micro-beads in water and in excised human meningiomas. In few words, α maps represent the multi-scale spatial distribution of the disorder degree in the system, while γ maps are influenced by local internal gradients, thus highlighting the interface between compartments characterized by different magnetic susceptibility. γ maps were already obtained by means of AD stretched exponential imaging and α-type maps have been recently achieved for fixed rat brain with the aim of highlighting the fractal dimension of specific brain regions. However, to our knowledge, the maps representative of the spatial distribution of α and γ obtained on the same controlled sample and in the same excised tissue have never been compared. Moreover, we show here, for the first time, that α maps are representative of the spatial distribution of the disorder degree of the system. In a first phase, γ and α maps of controlled phantom characterized by an ordered and a disordered rearrangement of packed micro-beads of different sizes in water and by different magnetic susceptibility (Δχ) between beads and water were obtained. In a second phase, we investigated excised human meningiomas of different consistency. Results reported here, obtained at 9.4 T, show that α and γ maps are characterized by a different image contrast. Indeed, unlike γ maps, α maps are insensible to (Δχ) and they are sensible to the disorder degree of the microstructural rearrangement. These observations strongly suggest that AD indices α and γ reflect some additional microstructural information which cannot be obtained using conventional diffusion methods based on Gaussian diffusion. Moreover, α and γ maps obtained in excised meningiomas seem to provide more microstructural details above those obtained with conventional DTI analysis, which could be used to improve the classification of meningiomas based on their consistency.

New insight into the contrast in diffusional kurtosis images: Does it depend on magnetic susceptibility?

“…Consistently, opposite behavior is observed in blue‐ROIs. This result is in agreement with in vivo results obtained by De Santis et al , and can be explained by water pseudo‐superdiffusion processes . Indeed, Δ χ H2O‐TISSUE spatial distribution introduces spurious effects on PFG signal decay that can emulate an apparent super diffusion behavior, which in turn affects the quantification of the effective non‐Gaussian diffusion of water in experiments performed by conventional DKI techniques.…”

“…Some authors have recently highlighted that susceptibility tensor imaging (STI) may potentially provide a complementary method, compared with DTI, for fiber tracts reconstruction, thanks to the existence of magnetic susceptibility anisotropy in the WM . Moreover, recent works suggest that non‐Gaussian diffusion of biological water, performed by using diffusion‐gradient strength varying pulsed field gradient (PFG) MRI experiments, is affected by magnetic susceptibility difference between extracellular water and tissue molecules ( Δ χ H2O‐TISSUE ) in a nonnegligible way. As a matter of fact, the spatial distribution of Δ χ H2O‐TISSUE in the brain tissue can provide information about WM spatial distribution, orientation and structural modifications as well as WM and gray matter (GM) different alterations due to specific diseases .…”

Exact solutions to the fractional time-space Bloch–Torrey equation for magnetic resonance imaging

“…The numerical evaluation of the obtained formulas demonstrates that our solutions replicate the super-diffusive and sub-diffusive regimes reported in MRI studies. These have been previously shown to arise from local magnetisation gradients between compartments with different magnetic susceptibility, capillary perfusion, porous media or stationary random flows, intravoxel incoherent motion, and hindered transport in densely packed and heterogeneous structures [14]. Moreover, our solutions at the end of the sequence exhibit residual phase shifts as those associated with the microscopic motion (i.e.…”

“…The main advantage of such an approach is that insights can A C C E P T E D M A N U S C R I P T be derived from generalisations of the physical principles describing the magnetisation of water protons in MRI: the Bloch-Torrey equation [13]. This can have important implications in understanding the different contributions of tissue microstructure to anomalous diffusion [14], compared to the fitting of experimental data to phenomenological signal decays such as bi-exponential [15] or stretched-exponential models [16]. However, an important drawback of the fractional setting is the complexity of its associated non-local operators for the derivation of exact solutions for the acquired signal decay.…”

A fractional motion diffusion model for a twice‐refocused spin‐echo pulse sequence

“…1-3 This deviation, which is often referred to as non-Gaussian diffusion, is accentuated as the b-value increases.Over the past two decades, considerable efforts have been invested to elucidate non-Gaussian diffusion in biological systems. [2][3][4][5][6][7][8][9][10][11][12][13][14] While the efforts by the diffusion MRI community have yielded a wealth of models to improve characterization of the MR signals and probe various aspects of tissue microstructures, it is important to recognize that recent efforts by the biophysics community have also produced valuable new insights into the fundamental diffusion phenomena in biological systems, particularly those related to anomalous diffusion-a sub-class of non-Gaussian diffusion.Anomalous diffusion refers to a diffusion process in which the statistical description of mean squared displacement of the diffusing molecules follows a nonlinear, power-law relationship with time, asymptotically in the limit of infinite times. 15,16 Among numerous anomalous diffusion models, the continuous-time random-walk (CTRW) model and the fractional motion (FM) model are actively pursued by the biophysics community and regarded as the major "archrivals".…”