Diffusion MRI has the ability to probe tissue microstructure in detail, due to the effect microstructure has on the motion of water molecules moving due to random thermal motion. After acquiring a series of diffusion weighted images (DWIs), there are numerous post-processing approaches that generate quantitative maps with varying degrees of sensitivity and specificity to microstructural properties. This lecture focuses on microstructural models, i.e., approaches that employ an a priori description of the tissue characterized by specific quantitative parameters that will be estimated from the diffusion MRI signal. It reviews the standard model of diffusion MRI microstructure and its variants, with emphasis on its limitations and recent progress toward reducing these limitations. Understanding these limitations is important for prudent interpretation of results in a clinical context.
Lecture Overview
Inference of the microstructural properties of neuronal tissue from diffusion MRI began before explicit microstructural models were developed. It became clear that while signal representations such as the diffusion tensor were sensitive to microstructural variation, they were not specific. For example, the dominant source of variation in the fractional anisotropy (FA) of the diffusion tensor is fiber geometry, rather than any specific microstructural metric {Hutchinson et al., 2018}. This can lead to paradoxical increases in the FA in cases where microstructural changes would decrease the FA {Douaud et al., 2011}. Modeling offers the possibility of increased specificity over diffusion MR signal representations (e.g., MD and FA obtained from the diffusion tensor), but only if (a) the model assumptions include everything that substantially affects the signal and (b) variations in the parameters of interest substantially affect the signal.
Diffusion MRI microstructural modeling comprises a broad suite of models that are similar but vary as to the constraints and free parameters they include (see, e.g., Jelescu et al., 2017 for a review). Complete relaxation of the constraints generally results in an ill-posed problem, however, particularly in injury and disease, the validity of the constraints used must be well justified. We will explore this issue in the context of existing diffusion MRI models.
In neuronal tissue, the combined dendritic and axon volume fraction is referred to as the neurite density. The microstructural quantities of interest include the intra-neurite, extra-neurite, lesion, and cerebral spinal fluid compartment sizes, and axon diameters. Although they are not structural features, the compartment diffusivities and relaxation times also provide microstructural information. For clinical use, the parameters we measure should have relevant functional correlates. The major assumptions used in diffusion modeling are constraints on the compartment diffusivities (both parallel and perpendicular to the axon orientation), constraints on the compartment T2 relaxation times, constraints on the compartment sizes, assumptions regarding the permeability of neurites, constraints on the form of the orientation distribution function for subvoxel fiber bundle segments, and the assumption that axons are perfect cylinders with diameters that are, or are not, distinguishable from zero.
The use of incorrect model assumptions greatly undermines the usefulness of microstructural parameters. For example, many models constrain the diffusivities of the intra- and extra-neurite space and employ the mean-field tortuosity model for the extra-neurite diffusion, which has been shown to break down for the neurite density expected in healthy tissue {Novikov et al., 2012}. Incorrect diffusivity assumptions result in a coupling between the estimated intra-neurite volume fraction and the true diffusivity {Jelescu et al., 2015; Lampinen et al., 2017}, to the point where, for example, the intra-neurite volume fraction appears significant in pathology such as gliomas, where a significant neurite fraction is not expected {Lampinen et al., 2017}. Relaxing the constraints on the compartment diffusivities results in multiple solutions, making the correct solution unclear {Jelescu et al., 2016}. Progress has been made toward solving this problem by increasing the complexity of the diffusion MRI signal, and hence the number of parameters that can reasonably be estimated. This can be done by using nonlinear b-tensor encoding {Lampinen et al, 2017; Fieremans et al., 2018; Coelho et al., 2019; Reisert et al., 2019, and others} or by varying the diffusion time {Lee et al., 2018; Jespersen et al., 2018}. Given new insight from such acquisitions, it may also be possible to better constrain the diffusivities when analysing existing data {Guerreri et al., 2018}.
Many models assume no T2 variation across tissue compartments, which also leads to biased volume fractions. Recent work has explored using a separate acquisition or diffusion acquisitions with different TEs in order to incorporate compartment T2 in the microstructural model {Bouyagoub et al., 2016; Veraart et al., 2019, Lampinen et al., 2019}.
While early models {Stanisz et al., 1997} incorporated exchange, modern models generally assume no exchange between compartments. However, the permeability of dendrites has been questioned, and it is unclear whether the estimated intra-neurite volume includes dendrites {Lampinen et al., 2017, 2019}.
There is great interest in transferring NMR techniques capable of estimating axon diameters to MRI, however, current hardware capabilities limit the resolution of axon diameter mapping and limit microstructural models that include the axon diameter as a measurable parameter {Nilsson et al., 2017}. Recent gradient strength increases on specialized scanners {Connectom, Siemens, Erlangen} have shown promise in measuring at least an MR-weighted axon diameter distribution {Veraart et al., 2018, Fan et al., 2019}.
In addition to these limitations, standard diffusion MRI does not provide a complete picture of the microstructure, and can be complemented by other contrast mechanisms, for instance myelin-sensitive contrasts such as magnetization transfer or relaxometry {Stikov et al., 2015; de Santis et al., 2016, and others}. Myelin imaging methods include tissue models of their own. Most diffusion imaging protocols yield insignificant signal from myelin water, hence, myelin imaging is required to estimate absolute volume fractions, and to infer functionally relevant parameters such as the g-ratio {Stikov et al., 2015}. Additionally, estimates of myelin content could make diffusion models more accurate, for instance by including myelin content in the tortuosity model.
In summary, the output of microstructural modeling with traditional diffusion MRI acquisition must be interpreted in light of its limitations. Recent sequence advances provide a richer signal from which more microstructural detail may be inferred. Care must be taken in interpreting the output of microstructural models in the context of pathology.
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