Marco Palombo

Non-Gaussian diffusion imaging: a brief practical review

The departure from purely mono-exponential decay of the signal, as observed from brain tissue following a diffusion-sensitized sequence, has prompted the search for alternative models to characterize these unconventional water diffusion dynamics. Several approaches have been proposed in the last few years. While multi-exponential models have been applied to characterize brain tissue, several unresolved controversies about the interpretations of the results have motivated the search for alternative models that do not rely on the Gaussian diffusion hypothesis. In this brief review, diffusional kurtosis imaging (DKI) and anomalous diffusion imaging (ADI) techniques are addressed and compared with diffusion tensor imaging. Theoretical and experimental issues are briefly described to allow readers to understand similarities, differences and limitations of these two non-Gaussian models. However, since the ultimate goal is to improve specificity, sensitivity and spatial localization of diffusion MRI for the detection of brain diseases, special attention will be paid on the clinical feasibility of the proposed techniques as well as on the context of brain pathology investigations.

Spatio-temporal anomalous diffusion in heterogeneous media by nuclear magnetic resonance

In this paper, we describe nuclear magnetic resonance measurements of water diffusion in highly confined and heterogeneous colloidal systems using an anomalous diffusion model. For the first time, temporal and spatial fractional exponents, α and μ, introduced within the framework of continuous time random walk, are simultaneously measured by pulsed gradient spin-echo NMR technique in samples of micro-beads dispersed in aqueous solution. In order to mimic media with low and high level of disorder, mono-dispersed and poly-dispersed samples are used. We find that the exponent α depends on the disorder degree of the system. Conversely, the exponent μ depends on both bead sizes and magnetic susceptibility differences within samples. The new procedure proposed here may be a useful tool to probe porous materials and microstructural features of biological tissue.

Structural disorder and anomalous diffusion in random packing of spheres

Nowadays Nuclear Magnetic Resonance diffusion (dNMR) measurements of water molecules in heterogeneous systems have broad applications in material science, biophysics and medicine. Up to now, microstructural rearrangement in media has been experimentally investigated by studying the diffusion coefficient (D(t)) behavior in the tortuosity limit. However, this method is not able to describe structural disorder and transitions in complex systems. Here we show that, according to the continuous time random walk framework, the dNMR measurable parameter α, quantifying the anomalous regime of D(t), provides a quantitative characterization of structural disorder and structural transition in heterogeneous systems. To demonstrate this, we compare α measurements obtained in random packed monodisperse micro-spheres with Molecular Dynamics simulations of disordered porous media and 3D Monte Carlo simulation of particles diffusion in these kind of systems. Experimental results agree well with simulations that correlate the most used parameters and functions characterizing the disorder in porous media.

Fractional Order Generalization of Anomalous Diffusion as a Multidimensional Extension of the Transmission Line Equation

In this paper, a new fractional order generalization of the diffusion equation is developed to describe the anisotropy of anomalous diffusion that is often observed in brain tissues using magnetic resonance imaging (MRI). The new model embeds three different fractional order exponents-corresponding to the principal directions of water diffusion-into the governing Bloch-Torrey equation. The model was used to analyze diffusion weighted MRI data acquired from a normal human brain using a 3T clinical MRI scanner. Analysis of the data revealed normal Gaussian diffusion in the cerebral spinal fluid (isotropic fractional order exponent of (0.90 ±0.1), and anomalous diffusion in both the white (0.67 ±0.1) and the gray (0.77 ±0.1) matter. In addition, we observed anisotropy in the fractional exponent values for white mater (0.59 ±0.1) along the fibers versus 0.68 ±0.1 across the fibers), but not for gray matter. This model introduces new parameters to describe the complexity of the tissue microenvironment that may be sensitive biomarkers of the structural changes arising in neural tissues with the onset of disease.

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

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 9.4T, 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.

The γ parameter of the stretched-exponential model is influenced by internal gradients: validation in phantoms.

In this paper, we investigate the image contrast that characterizes anomalous and non-gaussian diffusion images obtained using the stretched exponential model. This model is based on the introduction of the γ stretched parameter, which quantifies deviation from the mono-exponential decay of diffusion signal as a function of the b-value. To date, the biophysical substrate underpinning the contrast observed in γ maps, in other words, the biophysical interpretation of the γ parameter (or the fractional order derivative in space, β parameter) is still not fully understood, although it has already been applied to investigate both animal models and human brain. Due to the ability of γ maps to reflect additional microstructural information which cannot be obtained using diffusion procedures based on gaussian diffusion, some authors propose this parameter as a measure of diffusion heterogeneity or water compartmentalization in biological tissues. Based on our recent work we suggest here that the coupling between internal and diffusion gradients provide pseudo-superdiffusion effects which are quantified by the stretching exponential parameter γ. This means that the image contrast of Mγ maps reflects local magnetic susceptibility differences (Δχ(m)), thus highlighting better than T(2)(∗) contrast the interface between compartments characterized by Δχ(m). Thanks to this characteristic, Mγ imaging may represent an interesting tool to develop contrast-enhanced MRI for molecular imaging. The spectroscopic and imaging experiments (performed in controlled micro-beads dispersion) that are reported here, strongly suggest internal gradients, and as a consequence Δχ(m), to be an important factor in fully understanding the source of contrast in anomalous diffusion methods that are based on a stretched exponential model analysis of diffusion data obtained at varying gradient strengths g.

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

In this MRI study, diffusional kurtosis imaging (DKI) and T2* multiecho relaxometry were measured from the white matter (WM) of human brains and correlated with each other, with the aim of investigating the influence of magnetic‐susceptibility (ΔχH2O‐TISSUE) on the contrast.