Linear Multi-scale Modeling of diffusion MRI data: A framework for characterization of orientational structures across length scales
Barbara Wichtmann1,2, Susie Huang1, Qiuyun Fan1, Thomas Witzel1, Elizabeth Gerstner3, Bruce Rosen1, Lothar Schad2, Lawrence Wald1,4, and Aapo Nummenmaa1

1A. A. Martinos Center for Biomedical Imaging, Department of Radiology, Massachusetts General Hospital, Charlestown, MA, United States, 2Computer Assisted Clinical Medicine, Medical Faculty Mannheim, Heidelberg University, Mannheim, Germany, 3Department of Neurology, Massachusetts General Hospital, Harvard Medical School, Boston, MA, United States, 4Harvard-MIT Division of Health Sciences and Technology, Massachusetts Institute of Technology, Cambridge, MA, United States


We propose a new analysis technique called Linear Multi-scale Modeling (LMM) for diffusion MRI data that enables detailed microstructural tissue characterization by separating orientation distributions of restricted and hindered diffusion water compartments over a range of length scales. We demonstrate the ability of LMM to estimate volume fractions, compartment sizes and orientation distributions utilizing both simulations as well as empirical data from one healthy subject and one tumor patient acquired using a human 3T MRI scanner equipped with a 300mT/m gradient system. Possible applications of our modeling framework include characterization of diffusion microstructural signatures of pathological vs. healthy tissue.


Diffusion MRI methods enable noninvasive investigation of tissue microstructure in vivo1. Restriction Spectrum Imaging (RSI)2 is a method that reconstructs the diffusion tissue orientation distribution over a spectrum of length scales. However, by assuming a spectrum of Gaussian diffusion response functions, the RSI model is unable to fully capture the complex diffusion time dependency of the signal within restricted (e.g., intra-cellular) water compartments. Here we introduce a new analysis framework for diffusion MRI data called Linear Multi-scale Modeling (LMM) that extends the RSI approach to represent restricted water compartments with non-Gaussian response functions. LMM can be employed to estimate tissue microstructure parameters, including volume fractions of compartments of variable sizes as well as orientation distribution information of the diffusion media. Using a human 3T MRI scanner equipped with 300mT/m gradients, we demonstrate the ability of the LMM approach to distinguish normal gray and white matter structures in a healthy subject and to characterize the tissue microenvironment surrounding the resection bed of a brain tumor patient.


Simulation. Synthetic MRI data with an SNR of 10 was generated using the Monte Carlo diffusion simulator of Camino3 for diffusion within impermeable, regular packed cylinders with a range of diameters (2.5-20µm) and intra-axonal volume fractions (0.1-0.9).

Data acquisition. With approval from the institutional review board, a healthy volunteer and a patient with a resected left frontal anaplastic oligodendroglioma were scanned on a dedicated high-gradient 3T MRI scanner (MAGNETOM CONNECTOM, Siemens Healthcare) with a maximum gradient strength of 300mT/m and maximum slew rate of 200T/m/s4. Sagittal 2mm isotropic resolution diffusion-weighted spin echo EPI images were acquired using simultaneous multislice (SMS) imaging4 and zoomed/parallel imaging5 for high-resolution whole-brain coverage. The following parameters were used: δ/Δ=8/19, 8/30, 6/50 ms, 4-5 diffusion gradient increments linearly spaced from 55-293mT/m per Δ, TE/TR=77/4400ms, GRAPPA acceleration factor R=2, and SMS MB factor=2. Diffusion gradients were applied in 64 to 128 non-collinear directions with interspersed b=0 images every 16 directions. The maximum b-value at the longest diffusion time was 10,350 s/mm2. Total acquisition time was 90 min.

Data analysis. Following preprocessing to correct for gradient nonlinearity, motion and eddy currents6, spherical harmonics expansion of order 6/8 with Laplace-Beltrami regularization7 was used to interpolate the diffusion signal on each q-shell (regularization parameter λ set to 0.006). The linear multi-scale forward model of different sized restricted and hindered diffusion compartments was obtained by concatenating two spectra of response functions (Fig. 1): 1) a non-Gaussian diffusion response function8 for water restricted inside cylindrical structures and 2) a Gaussian diffusion response function2 for hindered water and free water diffusion. For a more compact and efficient linear implementation we parameterized the orientation distribution of the hindered and restricted compartments with a set of order 4 and 6 spherical harmonics, respectively. To obtain the orientation distribution functions and corresponding volume fractions, the multi-scale deconvolution inverse problem was solved by standard least-squares estimation with Tikhonov regularization.


Analysis of our simulation data yielded a fiber orientation distribution spectrum consistent with the simulated axon diameters and volume fractions (Fig. 2). For empirical data, the brain maps comprising the signal from all restricted, hindered, and free compartments showed a high fraction of restricted water within the densely packed white matter and free water nearly exclusively originating from the ventricles (Fig. 3). Voxel-wise estimated volume fractions of the different sized water compartments were clearly distinguishable between different anatomical structures within the brain (Fig. 4). In the brain tumor patient, the area surrounding the tumor resection showed distinct areas of restricted and hindered water with a different signature compared to normal gray and white matter (Fig. 4). For each length scale, the fiber orientation distribution was obtained, allowing for scale-specific tractography (Fig. 5).


When combined with cutting-edge acquisition techniques, the LMM framework offers a powerful analysis method to separate orientation distributions of restricted and hindered diffusion water compartments over a range of length scales, thereby allowing more detailed characterization of tissue microstructure. The estimation of restricted and hindered volume fractions and compartment sizes may provide insight into the distinct microstructural features of healthy and diseased tissue, while orientation distribution information at different length scales could give additional information about structural connectivity in the brain and provide a roadmap for surgical planning. Future work will focus on optimization of the acquisition protocol and refinement of the reconstruction methods.


LMM provides detailed characterization of tissue microstructure and orientation distribution that may enable the development of distinct diffusion microstructural signatures of pathology compared to healthy tissue.


Research reported in this publication was supported by the National Institutes of Health under NIBIB award number R00EB015445, P41EB015896, U01MH093765 (Human Connectome Project), 1U01CA154601, K23CA169021-01.


[1] Yablonskiy DA et al. NMR Biomed 23: 661-81 (2010). [2] White NS et al. Hum. Brain Mapp. 34: 327-346 (2013). [3] Cook PA et al. ISMRM 14: 2759 (2006). [4] Setsompop K et al. NI 80: 220-233 (2013). [5] Eichner C et al. MRM 71: 1518-1525 (2014). [6] Fan Q. et al. Brain Connect 4: 718-726 (2014). [7] Descoteaux M et al. MRM 58: 497-510 (2007). [8] van Gelderen P et al. Journal of magnetic resonance 103: 255-260 (1994)


Fig.1: The diffusion-weighted signal equals the sum of each water compartment’s orientation distribution convoluted with its corresponding response function f. We distinguish (1) restricted (e.g., intracellular) compartments described by 5 non-Gaussian diffusion response functions, (2)hindered (e.g., extracellular) compartments described by 5 Gaussian diffusion response functions, (3)a free Gaussian diffusion compartment.

Fig.2: Volume fraction estimates for a voxel of tightly packed (A) 6μm impermeable cylinders and (B) 12μm showing consistently higher signal originating from the corresponding length scales.

Fig.3: Volume fraction brain maps comprising (A) all restricted length scales, (B) all hindered length scales and (C) the free diffusion compartment.

Fig.4: Representative volume fraction estimates for voxels within (A) gray matter and (B) white matter. (C) Volume fraction estimates for tissue surrounding the tumor resection area showing a different distribution to that of white matter and gray matter.

Fig.5: Orientation distribution for two exemplary length scales: (A) 2nd restricted length scale and (B) 3rd hindered length scale. Allowing for scale specific tractography for example of the 1st restricted length scale (C).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)