Design and Validation of Diffusion MRI Models of White Matter

Abstract

Diffusion MRI is arguably the method of choice for characterizing white matter microstructure in vivo. Over the typical duration of diffusion encoding, the displacement of water molecules is conveniently on a length scale similar to that of the underlying cellular structures. Moreover, water molecules in white matter are largely compartmentalized which enables biologically-inspired compartmental diffusion models to characterize and quantify the true biological microstructure. A plethora of white matter models have been proposed. However, overparameterization and mathematical fitting complications encourage the introduction of simplifying assumptions that vary between different approaches. These choices impact the quantitative estimation of model parameters with potential detriments to their biological accuracy and promised specificity. First, we review biophysical white matter models in use and recapitulate their underlying assumptions and realms of applicability. Second, we present up-to-date efforts to validate parameters estimated from biophysical models. Simulations and dedicated phantoms are useful in assessing the performance of models when the ground truth is known. However, the biggest challenge remains the validation of the “biological accuracy” of estimated parameters. Complementary techniques such as microscopy of fixed tissue specimens have facilitated direct comparisons of estimates of white matter fiber orientation and densities. However, validation of compartmental diffusivities remains challenging, and complementary MRI-based techniques such as alternative diffusion encodings, compartment-specific contrast agents and metabolites have been used to validate diffusion models. Finally, white matter injury and disease pose additional challenges to modeling, which are also discussed. This review aims to provide an overview of the current state of models and their validation and to stimulate further research in the field to solve the remaining open questions and converge towards consensus.

Diffusional kurtosis imaging and white matter microstructure modeling in a clinical study of major depressive disorder

“…Though smaller values of D e∥ were seen with Method 2 in Region II, the large estimation error warns against relating this to underlying pathology. The accuracy of diffusivities in this study is also questionable in view of recent evidence that suggested D a ≥ D e∥ and D a ≈ 1.9‐2.2 μm 2 /ms . Though D a by Method 2 was close to the expected range, the observed D a ≤ D e∥ trend possibly indicates that our estimation might have fallen into the wrong branch or some spurious local minima due to the low maximum b ‐value and SNR.…”

“…To date, many such models have been proposed and used in clinical and experimental studies . However, it is emphasized that so far no definite consensus has been reached on how to parameterize the complex brain microstructure . Besides, works by Jelescu et al, Novikov et al, and Reisert et al demonstrated that typical DKI acquisition with a maximum b ‐value of 2000‐3000 s/mm 2 is not sufficient to determine all of the parameters, even for a simple two‐compartment model.…”

Measuring intra‐axonal T2 in white matter with direction‐averaged diffusion MRI

“…In microstructural models for white matter based on dMRI data, differences in the intra‐axonal and extra‐axonal T 2 values have typically been ignored . This is understandable, considering that the daunting task of linking brain microstructure to dMRI data necessitates simplifying assumptions to obtain a tractable mathematical description capable of yielding useful predictions.…”

Histologically derived fiber response functions for diffusion MRI vary across white matter fibers—An ex vivo validation study in the squirrel monkey brain

“…Other algorithms, and possibly multi‐channel fluorescence microscopy data, will be required to identify the biophysical changes that account for the observed spatial variation of response functions in the brain. In principle, knowledge of the relevant biophysical parameters would allow calculation of the local response function—see Reference for a review of the challenges and recent progress in diffusion MRI modeling.…”