Fractional diffusion as a probe of microstructural change in a mouse model of Duchenne Muscular Dystrophy

Matt G Hall^{1}, Paola Porcari^{2}, Andrew Blamire^{2}, and Chris A Clark^{1}

*Imaging*

Employing a diffusion-weighted STEAM sequence we acquire images at six diffusion times and four different gradient strengths including an unweighted acquisition per diffusion time (see Table-1 for details). All acquisitions have the same TE/TR (4000/20ms) and gradient pulse duration of 3ms. Samples are positioned such that muscle fibres align with the slice select direction and diffusion encoding gradients are all applied parallel to the phase encode direction. Data are acquired at 7T using a Varian preclinical scanner.

*Histology*

Follow *in vivo * measurements, the gastrocnemius muscle was carefully removed from the left hindlimb of each mouse. The muscle was then mounted on a small mound of Tissue-Tek OCT on a cork disc and frozen using cooled isopentane (2-methylbutane). Cross sections of frozen muscle (8um thick) were stained with laminin alpha-2 chain, rat antibody (1:1000 dilution), fluorescently labelled secondary antibody, goat anti-rat alexa 488 (1:1000 dilution) and DAPI. Five areas on each of the two sections at comparable proximal levels were photographed at 20x magnification and the Feret's diameter of each muscle fibre measured using Fiji (Image-J).

*Modelling*

Diffusion-weighted data were normalised using the unweighted measurement from the appropriate diffusion time and a three parameter Mittag-Leffler function

$$S=S(0)\sum_{k=0}^{\infty}\frac{(-D_{\alpha,\beta}q^\beta \Delta^\alpha)^k}{\Gamma(\alpha k+1)}$$

Where $$$D_{\alpha,\beta}$$$ is the fractional diffusivity, $$$\alpha$$$ is the temporal exponent and $$$\beta$$$ is the temporal exponent, both associated with the underlying diffusion process. Results here concentrate on the $$$\alpha$$$ parameter.

Fits are performed using a Levenberg-Marquardt algorithm. Initial parameters were derived from an approximate, two-parameter Mittag-Leffler model, which is fitted with initial parameters from a linear exponential fit. Fits are performed 100 times in each voxel with random perturbations to initial parameters and the combination chosen that has the smallest sum of squared residuals.

The darkening in the $$$\alpha$$$ maps is present in both Mdx mice and not in either wildtype. Histology of similar regions shows a change in tissue microstructure which supports the idea that the fractional diffusion model used is sensitive to the microstructural changes caused by pathology. This work has a small sample size, but these preliminary results show localised darkened regions which may be associated with disease regions.

This work considers only one parameter of the model and as such there may be further insight to be drawn from considering all three, either singly or in combination. This may lead to increased contrast and improved image-based biomarkers.

There is also scope to optimise the acquisition. The current dataset contains 24 images, which is similar to the number required DTI (for example) but there may be scope to reduce this and reduce acquisition time.

[1] Bushby et al,
*Lancet Neurology* 9 (1) (2010)

[2] Hooijmans et al, *NMR in Biomedicine*, 28 (11) (2015)

[3] Saladin,
*Anatomy and Physiology (3rd ed.)*, Watnik (New York) (2010)

[4] Magin et al, *Microporous and Mesoprous Materials*,
178: 39–43 (2013)

Table-1: Paramters used in diffusion-weighted acquisitions. Data were acquired at several different gradient strengths $$$|\mathbf{G}|$$$ and diffusion times $$$\Delta$$$ in milliseconds. All gradient pulse durations ($$$\delta$$$) were 3ms.

Fig-1: Maps of the fitted $$$\alpha$$$ paramter in wildtype (top row) and Mdx mice (bottom row). The Mdx maps exhibit localised darkening which is not present in the wildtype maps. Circles indicate the feature used in the histograms in Fig-2.

Fig-2: Histograms of fibre size distribution (top) in the central Gastronemius from histology and the $$$\alpha$$$ exponent fitted to diffusion-weighted measurements in an ROI covering the darkened region shown in Fig-1.

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

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