This lecture presents the key concepts behind modelling diffusion MRI signal. Specifically, it focuses on various techniques that go beyond the standard diffusion tensor model, and aim to provide biomarkers which can be related to tissue microstructure.
Following this lecture, the audience will understand:
This lecture will cover the following topics:
Diffusion MRI and tissue microstructure
In diffusion MRI, the acquired signal depends on the displacement of the water molecules inside the tissue on the order of tens of milliseconds. The distance travelled during this time is on the scale of microns and, fortunately, is similar to cellular sizes in biological tissue. The molecular displacement is affected by the presence of cellular membranes and their properties, which makes the acquired signal sensitive to the tissue microstructure. Thus, the diffusion MRI signal depends on tissue features such as cellular size, shape, density, orientation, membrane permeability, etc. By analysing the measurements acquired with different experimental parameters, it is possible to infer some of these properties.
Standard diffusion models and their limitations
The standard techniques for analysing diffusion MRI images are the estimation of apparent diffusion coefficient 1 (ADC) and diffusion tensor imaging 2 (DTI). The estimation of ADC assumes that the tissue is isotropic at the voxel level and the measured signal can be explained by one diffusion coefficient. ADC is mainly used in body MRI, and especially in cancer imaging. DTI extends the ADC model to account for anisotropic diffusion and has many applications in brain imaging. Both models make the assumption that the diffusion coefficients do not depend on the timing parameters of the sequences or the strength of the diffusion weighting, which is not the case in restricted diffusion in biological tissue. Moreover, the DTI model assumes one principal diffusion direction in neural tissue, and cannot distinguish between more complex fibre configurations which are present in the brain, such as crossing, bending, fanning, etc. To address these limitations, various techniques have been developed in the literature in order to extract more specific information regarding tissue structure. The rest of the lecture covers some of the main modelling technique used in diffusion MRI which can be loosely regarded as signal models, which aim to capture the features of the measured signal and indirectly infer tissue related properties, and biophysical models, which aim to explicitly relate various microstructural features to the measured signal.
Signal models
Signal modelling approaches aim to explain the measured diffusion signal acquired with various sequence parameters. Their strengths include the generic representation that is not specific to a particular kind of tissue. Usually such models are described using function bases, that often leads to efficient parameter estimation. The model parameters do not directly relate to specific microstructural features but usually combine to reflect interesting features of the dispersion pattern that users can subsequently relate to microstructural properties in specific applications. In this lecture we cover the general q-space formalism and estimation of the diffusion propagator 3, models that capture the deviation of the signal from the Gaussian regime with increasing diffusion weighting, such as diffusion kurtosis imaging 4 (DKI) or stretched exponential 5, as well as techniques that are able to characterise areas of crossing fibres, such as spherical deconvolution 6.
Biophysical models
Biophysical and multi-compartment modelling approaches aim to relate various microscopic tissue properties to the dMRI signal. Thus, fitting the model to the measured data results in parameters that reflect tissue features, such as cellular density, cell size, shape, fibre orientation, etc. In this lecture we present the general idea of creating geometrical models to represent various components of the tissue and their relation to the diffusion signal. We discuss the parameters that can be estimated from such approaches, including intracellular volume fraction, axon diameter index in white matter, cell radius for tumour tissue, etc. Then, we show various examples from the literature of multi-compartment geometrical model that have been used for brain imaging, such as CHARMED 7, AxCaliber 8, ActiveAx 9, NODDI 10, Spherical Mean Technique (SMT) 11, Restriction Spectrum Imaging 12 (RSI) etc. as well as for cancer imaging, such as VERDICT 13, RSI 14, etc. Finally, we discuss the strengths and the pitfalls of different techniques, which are essential when interpreting the estimated parameter values.
Current trends
Finally, we present the most recent developments in terms of modelling diffusion signal, including more sophisticated models of extracellular space and membrane permeability, as well as advances in combining numerical simulations and machine learning to improve parameter estimation. We also briefly mention the recent developments in terms of using more advanced acquisitions, however this topic will be thoroughly covered in a different lecture.
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