Synopsis
Diffusing spins probe length scales on the order of 2–10 µm during
typical diffusion weighted MRI experiments, and their trajectories are
therefore shaped by the tissue structure on this scale. The exciting prospect is
that diffusion MRI can provide detailed quantitative information of microstructural
properties, surpassing the nominal image resolution by orders of magnitude. Achieving
this goal depends on biophysical modelling and subsequent validation. The purpose
of this lecture is to give the
audience an understanding of the principles underlying the quantification of
microstructural tissue features from diffusion MRI, as well as the potential
and the pitfalls.Highlights
-extraction of microstructural features from
diffusion MRI relies mainly on biophysical modelling
-biophysical modelling and mathematical
representations are two different things
-biophysical models must be validated
-accessible microstructural features include aspects
of fiber orientation distributions, compartment shape and dimensions,
permeabilities, tortuosity of the extracellular space, volume fractions and
intrinsic diffusivities.
Target audience
Scientists and clinicians interested in modelling and measuring tissue microstructure
Purpose
The
purpose of this lecture is to give
the audience an understanding of the principles underlying the quantification
of microstructural tissue features from diffusion MRI. These principles most
often involve biophysical modelling of tissue and subsequent validation. I will
critically review some current models, their assumptions, and the state of
validation.
Methods
Diffusing spins probe length scales on
the order of 2 to 10 µm during the typical diffusion weighted MRI experiments,
and their trajectories are therefore highly shaped by the tissue structure on
this scale. This sensitivity is reflected in the diffusion signal, which
basically measures statistics of spin trajectories. The exciting prospect of
this is, of course, that with the right approach, diffusion MRI can provide
detailed quantitative information of microstructural properties of tissue,
surpassing the nominal image resolution by orders of magnitude. Achieving this
goal is highly dependent on adequate biophysical modelling and subsequent
validation. Biophysical modelling involves applying the principles of physics
to identify the relevant features of tissue structure, aiming to reduce the
vast complexity of real tissue microstructure to a few tractable degrees of
freedom. Such modelling depends on having a clear picture of tissue microstructure.
Subsequent validation, for example using histology, is crucial, as model
fitting quality is an insufficient indicator of model appropriateness. These
considerations are particularly acute in diffusion MRI, where a plethora of models
claiming to measure axonal diameter distributions, dispersion, neurite density,
intra-and extracellular diffusivities etc., have been put forward.
On the experimental side, most
approaches are still based on the classical Stejskal-Tanner (1) pulse sequence, its stimulated echo
counterpart (2), or variations thereof. Combined with
biophysical modelling, this sequence has been proposed to be sensitive to
compartment dimensions such as surface to volume fraction(3), axon diameters(4-6), neurite
dispersion and density (7-10), neurite
beading(11), and membrane permeability (12-14). Ideally,
such measurements sample the Fourier transform of the average propagator (15), describing the distribution of spin
translational displacements. Microstructural features are subsequently
estimated from the best fit of the predicted signal to the observed data. Hence,
modelling amounts to studying the form of the diffusion propagator and its
relation to tissue microstructure. Often, the diffusion propagator has been
obtained using known exact solutions of the diffusion equation as building
blocks, such as cylinders and spheres, taken to represent neurites (axons and
dendrites) and cell bodies respectively. In contrast, the seminal result by
Mitra et al. (3) demonstrating the short time
diffusivity to depend on the surface to volume ratio does not depend on a
particular geometry, but rather is a more fundamental result of having pores or
compartments with reflecting walls. Recently, significant progress has been
made to by the use of so-called effective medium theory(16,17), which
again does not rely on a particular geometric view of tissue structure, but
describes it as a disordered medium from the point of view of the diffusing
spins. This approach identifies properties such as membrane permeability and
disorder class (e.g. statistics of fiber packing) as relevant degrees of
freedom obtainable by diffusion MRI.
Recently, novel pulse sequences using
generalized diffusion gradient waveforms have been developed and applied,
including oscillating gradients (18,19), multiple
diffusion encoding (20-23), and (24-26). Their
motivation lies in practicalities for probing e.g. the short diffusion time
regimes, or their ability to assess novel microstructural facets such as pore
anisotropy (20-22,27-32) or pore
shape (33) in a model independent way. Another
example is the long-narrow gradient approach by Laun et al. (33,34), pores are
imaged directly without the use of modelling. The basic idea is to convert the
diffusion experiment to an imaging experiment with the second pulsed gradient
acting as an imaging gradient, while using the first pulsed gradient to
translate all pores to a common centre of mass frame.
Validation is currently based
primarily on computer simulations and histology. Computer simulations can be
used to verify that one has identified the appropriate degrees of freedom,
given that the input picture of microstructure is correct — this by itself of
course cannot be validated with computer simulations. Histology on the other
hand is used to compare the obtained microstructural features from diffusion
MRI to independent measurements, and is typically based on standard optical
microscopy (including confocal and fluorescence), electron microscopy, and
polarized light imaging. The methods range from qualitative analysis such as
visual comparison, quantitative but indirect approaches such as for example optical
staining density (7),
structure tensor analysis(35-37), Fourier
analysis(38), to quantitive and direct approaches
typically based on stereology (7). In most
cases, the employed histological approach strictly speaking cannot be
considered model validation, but rather correlation of model parameters to
histological parameters. This by itself can be very useful, but the
correlations can be coincidental and a consequence of the diffusion signal
having sensitivity to the given histological feature. Another, perhaps more
powerful, means of validating is based on examining the functional dependency
of diffusion measurements, such as Mitra’s $$$\sqrt{t}$$$ prediction for the
time-dependent diffusion coefficient (3,12,39). Such an
approach is common e.g. in physics, where direct validation is frequently not
possible, but is so far less widespread in diffusion MRI. On the other hand,
maximum likelihood and other measures of fitness quality is not validation, and
have shortcomings even in identifying the correct microstructural model among
candidates that include the known ground truth.
Results
Below is an incomplete list of examples of microstructural features potentially accessible from diffusion MRI
- Axon diameters. This is most often achieved by modelling axons as cylinders and fitting the diffusion signal. The main limitation is diffusion gradient strength (40,41) and possibly subdominance of the diffusion signal from axons at clinically relevant diffusion times (42). Comparison with histology shows a general overestimation of axonal radii.
- Neurite orientation distribution. There is relatively good evidence from histology that diffusion MRI can capture at least basic aspects of the orientation distributions of neurites(36,37,43).
- Neurite beading. Although neurite beading has not been quantified from diffusion-weighted MRI yet, it has been shown to affect the diffusion signal (11)(possibly along with axonal varicosities(17)) and could possibly explain the celebrated decrease in diffusivity observed in stroke.
- Permeability. Measurements of permeability have been reported using modelling to the Stejskal-Tanner pulse sequence, or using the filtered exchange paradigm (44-46). Permeability is difficult to validate independently, except from blood cells, where good agreement has been found with diffusion derived estimates(12).
- Disorder class. Computer simulations verify that the nature of the disorder (disorder class) determines the time dependence of the diffusivity (17). This was validated with phantoms in (42)
- Pore shape. Computer simulations and phantom experiments using Xenon (34,47) have shown good agreement with pore shape imaging. Main limitations for use in biological tissue are the assumption of identical pores shapes and orientations, gradient strength and SNR.
- Microscopic diffusion anisotropy (compartment anisotropy). Validated/evaluated in phantoms (48), in a yeast cell model system (20) and with histology of human brain tumors (49).
Conclusion
The potential
for diffusion MRI to extract and
quantify tissue microstructure noninvasively is exciting. Nevertheless, several
challenges remain, especially concerning the validation of proposed models and
their parameters, which is still quite limited. Hardware limitations,
especially gradient strength, is a severe practical constraint when assessing
small compartment dimensions.
Acknowledgements
The author wishes to acknowledge discussions with colleagues, in particular with Valerij Kiselev and Dmitry Novikov: Some of the content presented here is part of a common work in progress. Financial support from the Danish Ministry of Science, Technology and Innovation’s University Investment Grant (MINDLab), the Lundbeck Foundation R83-A7548 and Simon Fougner Hartmans Familiefond.References
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