Modeling Diffusion in the Brain White & Gray Matter
Ileana Jelescu1
1Lausanne University Hospital, Switzerland

Synopsis

In this lecture, we will (i) clarify the distinction between signal representations and biophysical tissue models and provide an overview of relevant model features in white and gray matter, respectively, (ii) review the challenges and most recent developments in model parameter estimation, and (iii) discuss the potential for clinical translation of biophysical models.

Signal representations vs biophysical models

Signal representations are convenient ways of describing the signal as a function of diffusion weighting, without making any assumption about the underlying medium in which diffusion is taking place, i.e. the tissue. The most widespread signal representation is the cumulant expansion (Basser et al., 1994; Jensen et al., 2005), meaning an expansion of the logarithm of the signal in polynomials up to a given order in b. Diffusion tensor imaging (DTI) is an expansion up to the first order in b, and diffusion kurtosis imaging (DKI) up to the second order in b. The metrics obtained from signal representations are sensitive markers of tissue change with development, aging and/or pathology. However, they are not specific and thus do not allow a depiction of the underlying microstructure.
In order to gain specificity to microstructure features, a modeling step needs to be introduced. Biophysical models assume a given simplified geometry – a “sketch” – of the underlying tissue. The first implication of this is that there is no single biophysical model of microstructure, but multiple biophysical models, each developed to describe the microstructure of a specific type of tissue. The bedrock of biophysical models of diffusion is water compartmentalization, which implies that “tissue compartments” can be characterized individually in terms of geometry, relative size and diffusion properties (Beaulieu and Allen, 1994). The main open challenges of modeling are the appropriateness of the selected model to describe the tissue and the biological validity of their underlying assumptions, as well as the ill-posed nature of the fitting procedure involved in parameter estimation.
In this lecture, we focus on brain white and gray matter models, which have drawn most research efforts and attention so far (Alexander et al., 2010; Assaf et al., 2004; Fieremans et al., 2011; Jelescu et al., 2021; Jespersen et al., 2007; Novikov et al., 2018b; Olesen et al., 2022; Palombo et al., 2020; Zhang et al., 2012). Reviews on this topic include (Jelescu et al., 2020; Jelescu and Budde, 2017; Novikov et al., 2019, 2018a).
We will describe the relevant building blocks for white and gray matter respectively, and how the diffusion time and diffusion weighting regime impact the features that should be parametrized.

Building blocks of brain microstructure models

Tissue models consist in expressing the diffusion signal behavior in a given (simplified) geometry, and then fitting this analytical signal equation to the diffusion data, to extract the relevant parameters of the assumed geometry. Numerical models are also gaining increasing attention.
On the front of parameter estimation, most models rely on non-linear fitting, which is computationally expensive and strongly affected by noise and local minima (Harms et al., 2017; Jelescu et al., 2016). Different approaches such as Bayesian optimization (Reisert et al., 2017) and deep learning (de Almeida Martins et al., 2021) are good alternatives, at least to provide a measure of uncertainty and to speed up the estimation, respectively.
The limitations of parameter estimation related to the amount of information contained in the data vs model complexity remain regardless of the chosen optimization procedure. Indeed, the main challenge for fit accuracy and precision is related to model degeneracy, which refers to the existence of multiple sets of model parameters values that all explain the measured signal equally well (Jelescu et al., 2016; Novikov et al., 2018b). It is mostly due to the incapacity of the acquired dMRI data to support the model complexity, that is the number of free parameters to be estimated from the data. In some cases, multi-modal approaches such as combined diffusion-relaxation acquisitions (Lampinen et al., 2020) or generalized gradient waveform techniques (Lampinen et al., 2017; Reymbaut et al., 2020) can increase the amount of information in the measured data and remove the degeneracy for some models.

Clinical translation

The final goal of diffusion modeling in the brain is certainly its successful translation to clinical studies and its added value in terms of characterizing physiological and pathological processes in the human brain on a routine basis, informing on progression and response to treatment, and perhaps even inspiring new therapeutic strategies. While the measurement of the apparent diffusion coefficient has revolutionized the fast diagnosis of stroke, microstructure models proposed since 1997 (Stanisz et al., 1997) have so far failed to reach that “game-changer” level. We identify potential hurdles to clinical translation as: (i) complex and time-consuming acquisition protocols, (ii) perpetual questioning and reconsideration of biophysical models for a given tissue, which is a natural process for research, but understandably not very reassuring for clinicians and (iii) limited or inefficient communication between model developers and clinicians. We finally propose leads to overcome each of these hurdles.

Acknowledgements

I would like to thank the entire Diffusion Microstructure community for pushing the field forward.

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Proc. Intl. Soc. Mag. Reson. Med. 30 (2022)