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Anomalous diffusion MRI model parameters vary in the human corpus callosum sub-regions with age

Qianqian Yang¹ and Viktor Vegh²
¹School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia, ²Centre for Advanced Imaging, University of Queensland, Brisbane, Australia

Synopsis

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 process, and infer information from the different anomalous diffusion equation parameters. Here, we show how parameters of three established anomalous diffusion equations change with age, in a microstructurally complex tissue, the human corpus callosum.

Introduction

Diffusion MRI (dMRI) allows measurements of diffusion in tissue. Various classical mathematical models have been developed to link voxel-level measurements (mm scale) with changes at the microscale. For example, variations in axon radius¹, and neurite orientation and density² have been inferred from dMRI data and associated mathematical models. Whilst these methods have been derived based on the classical diffusion process, models capturing the anomalous nature of diffusion in tissue have been proposed as well.
Traditionally, the diffusion signal was assumed to decay mono-exponentially with b-value. However, studies have shown the diffusion signal as a function of b-value to deviate from mono-exponential decay³. The existing various anomalous diffusion models were developed in view of the hindered and restricted nature of diffusion in biological tissue^4-10. Anomalous diffusion models are able to better fit the dMRI signal than the mono-exponential model, and potentially provide a link to tissue microstructure variations through anomalous diffusion model parameters^11-15. Here, we provide the first evaluation of how parameters of three different anomalous diffusion models vary in the human corpus callosum as a function of age.

Methods

Anomalous diffusion models
Here we limited the study to the fixed diffusion time regime for dMRI data. We considered three different anomalous diffusion models, namely the super-diffusion (a.k.a. stretched exponential model³), sub-diffusion^16,17 and continuous time random walk¹³ (CTRW) models:
$$SUP: S/S_0 = \exp\left(-(bD)^\alpha\right),~~~ 0<\alpha\leq1, $$
$$SUB: S/S_0 = E_\beta(-bD), ~~~ 0<\beta\leq 1, $$
$$CTRW: S/S_0 = E_\beta(-(bD)^\alpha), ~~~ 0<\alpha,\beta\leq 1.$$
where S0 is the signal at b = 0, and parameters α and β are not interchangeably interpretable across the different models, and the Mittag-Leffler function is given as $$$ E_{\beta}(z)=\sum^\infty_{k=0}\frac{z^k}{\Gamma(1+\beta k)}$$$ where $$$\Gamma$$$ is the Gamma function and $$$E_1(z) = \exp(z)$$$.
Diffusion-weighted MRI data
The study was approved by the human ethics committee of the University of Queensland. We recruited 30 healthy participants aged 19 to 67 (42$$$\pm$$$13.5) with mostly 2-3 year age gaps and a maximum of a 7 year age gap (37-44), and half of the participants were female. The dMRI data was collected using a 7T Siemens Magnetom research MRI scanner with the following acquisition parameters: TE = 73 ms, isotropic resolution of 1.6 mm³, fixed Δ = 31.9 ms and δ = 21.6 ms. By varying the gradient strength, multiple b-values were acquired (b = 0, b = 500, b = 1500, b = 2500, and b = 3500 s/mm²). With increasing b-value increasing number of diffusion directions were acquired to maintain SNR (total of 126 acquisitions including six b = 0 datasets; directions at each b-value were chosen based on the electrostatic model^18,19). dMRI data were corrected for motion and eddy currents using MRtrix3, and trace-weighted images were computed at each b-value (i.e. geometric mean across directions, see Figure 1).
Analysis
In each human brain the corpus callosum was segmented manually near the mid-sagittal plane using MIPAV. The template described by Witelson²⁰ was then used to manually sub-segment the corpus callosum into seven sub-regions (1 – rostrum, 2 – genu, 3 – rostral body, 4 – anterior midbody, 5 – posterior midbody, 6 – isthmus, 7- splenium). Each anomalous diffusion model was fitted to the multiple b-value dMRI data in a voxel-by-voxel manner using MATLAB's lsqcurvefit (note: D was estimated first using b-value $$$\leq$$$1,500 s/mm² data, after which $$$\alpha_{sup}$$$, $$$\beta_{sub}$$$ and ($$$\alpha_{ctrw}, \beta_{ctrw}$$$) were fitted using all of the data with fixed D). Using the binary masks created in MIPAV, parameter values for each sub-region were extracted and averaged for that sub-region. The MATLAB functions fitlm and predict were used to perform linear regression of the mean parameter values vs age for each sub-region and to find the 95% confidence interval of the parameter values.

Results

As an example, Figure 2 provides the parameter maps and relative fitting errors obtained for a 19-year-old male participant. Figure 3 shows in the same participant the application of the corpus callosum mask and the seven sub-regions masks to the diffusion coefficient parameter. Figure 4 depicts the trend in the computed mean diffusivity D as a function of age in the entire mid-sagittal section of the corpus callosum, and the seven sub-regions. Figure 5 provides the age-dependent trend in the mean α and β parameters over age, as relevant, for the various models.

Discussion

A significant upward trend with age (p < 0.05) was found for the mean diffusivity D in the rostrum, rostral body and isthmus sub-regions, and the trend was also significant for the entire corpus callosum (Figure 4). There was no significant trend found for the mean $$$\alpha_{sup},~\alpha_{CTRW}$$$, and $$$\beta_{CTRW}$$$, whereas the mean $$$\beta_{sub}$$$ had a significant upward trend in the genu, rostral body and isthmus sub-regions and the entire corpus callosum (Figure 5).

Conclusion

We evaluated how anomalous diffusion model parameters vary as a function of age in the human corpus callosum. We found that sub-diffusion model parameter $$$\beta_{sub}$$$ show significant upward trends in corpus callosum and three sub-regions. No significant trends were found in super-diffusion and CTRW model parameters. Moreover, diffusivity D and $$$\beta_{sub}$$$ show significant trends in different sub-regions, suggesting that D and $$$\beta_{sub}$$$ are sensitive to different age-related tissue microstructural changes in the corpus callosum.

Acknowledgements

Dr Yang is funded by the Australian Research Council Discovery Early Career Researcher Award (DE150101842).

References

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Figures

Figure 1. Trace-weighted diffusion images at multiple b-values for a 19-year-old male participant.

Figure 2: Parameter maps and relative fitting errors presented on a mid-sagittal slice from fitting multi-bvalue diffusion MRI data to three anomalous diffusion models voxel by voxel. row A: super-diffusion model (i.e. stretched exponential model); row B: sub-diffusion model; row C: continuous time random walk (CTRW) model. Note that D map is obtained from fitting the mono-exponential model for b <=1500s/mm^2 and remains fixed. The relative fitting error was calculated by norm(signal values - fitted values)/norm(signal values).

Figure 3. The application of the corpus callosum mask and its seven sub-regions marks to the diffusion coefficient D.

Figure 4. Plots of mean diffusivity D vs age in different sub-regions of corpus callosum and the entire corpus callosum. Red dots are the mean diffusivity D in each ROI for each participant; solid lines represent the linear trend; dashed lines represent the 95% confidence interval. The trends of the mean diffusivity D in sub-regions rostrum, rostral body and isthmus and the entire corpus callosum are statistically significant with p<0.05.

Figure 5. Plots of mean parameter values vs age in different sub-regions of corpus callosum and the entire corpus callosum. Different colors represent different anomalous diffusion models. Solid lines represent the linear trend; dashed lines represent the 95% confidence interval. Pvalues for each trend are also reported. The trends from the sub-diffusion model parameter β are statistically significant with $$$p\leq0.05$$$ in sub-regions genu, rostral body and isthmus and the entire corpus callosum. No significant trends were found in super-diffusion and CTRW model parameters.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)

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