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Michiel Cottaar

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11 papers

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YNIMG Journal 2022 Journal Article

Estimating axial diffusivity in the NODDI model

Amy FD Howard
Michiel Cottaar
Mark Drakesmith
Qiuyun Fan
Susie Y. Huang
Derek K. Jones
Frederik J. Lange
Jeroen Mollink

To estimate microstructure-related parameters from diffusion MRI data, biophysical models make strong, simplifying assumptions about the underlying tissue. The extent to which many of these assumptions are valid remains an open research question. This study was inspired by the disparity between the estimated intra-axonal axial diffusivity from literature and that typically assumed by the Neurite Orientation Dispersion and Density Imaging (NODDI) model ( d ∥ = 1. 7 μ m 2 /ms ). We first demonstrate how changing the assumed axial diffusivity results in considerably different NODDI parameter estimates. Second, we illustrate the ability to estimate axial diffusivity as a free parameter of the model using high b-value data and an adapted NODDI framework. Using both simulated and in vivo data we investigate the impact of fitting to either real-valued or magnitude data, with Gaussian and Rician noise characteristics respectively, and what happens if we get the noise assumptions wrong in this high b-value and thus low SNR regime. Our results from real-valued human data estimate intra-axonal axial diffusivities of ∼ 2 − 2. 5 μ m 2 /ms, in line with current literature. Crucially, our results demonstrate the importance of accounting for both a rectified noise floor and/or a signal offset to avoid biased parameter estimates when dealing with low SNR data.

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YNIMG Journal 2022 Journal Article

Identifying microstructural changes in diffusion MRI; How to circumvent parameter degeneracy

Hossein Rafipoor
Ying-Qiu Zheng
Ludovica Griffanti
Saad Jbabdi
Michiel Cottaar

Biophysical models that attempt to infer real-world quantities from data usually have many free parameters. This over-parameterisation can result in degeneracies in model inversion and render parameter estimation ill-posed. However, in many applications, we are not interested in quantifying the parameters per se, but rather in identifying changes in parameters between experimental conditions (e.g. patients vs controls). Here we present a Bayesian framework to make inference on changes in the parameters of biophysical models even when model inversion is degenerate, which we refer to as Bayesian EstimatioN of CHange (BENCH). We infer the parameter changes in two steps; First, we train models that can estimate the pattern of change in the measurements given any hypothetical direction of change in the parameters using simulations. Next, for any pair of real data sets, we use these pre-trained models to estimate the probability that an observed difference in the data can be explained by each model of change. BENCH is applicable to any type of data and models and particularly useful for biophysical models with parameter degeneracies, where we can assume the change is sparse. In this paper, we apply the approach in the context of microstructural modelling of diffusion MRI data, where the models are usually over-parameterised and not invertible without injecting strong assumptions. Using simulations, we show that in the context of the standard model of white matter our approach is able to identify changes in microstructural parameters from conventional multi-shell diffusion MRI data. We also apply our approach to a subset of subjects from the UK-Biobank Imaging to identify the dominant standard model parameter change in areas of white matter hyperintensities under the assumption that the standard model holds in white matter hyperintensities.

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YNIMG Journal 2021 Journal Article

Modelling white matter in gyral blades as a continuous vector field

Michiel Cottaar
Matteo Bastiani
Nikhil Boddu
Matthew F. Glasser
Suzanne Haber
David C. Van Essen
Stamatios N. Sotiropoulos
Saad Jbabdi

Many brain imaging studies aim to measure structural connectivity with diffusion tractography. However, biases in tractography data, particularly near the boundary between white matter and cortical grey matter can limit the accuracy of such studies. When seeding from the white matter, streamlines tend to travel parallel to the convoluted cortical surface, largely avoiding sulcal fundi and terminating preferentially on gyral crowns. When seeding from the cortical grey matter, streamlines generally run near the cortical surface until reaching deep white matter. These so-called "gyral biases" limit the accuracy and effective resolution of cortical structural connectivity profiles estimated by tractography algorithms, and they do not reflect the expected distributions of axonal densities seen in invasive tracer studies or stains of myelinated fibres. We propose an algorithm that concurrently models fibre density and orientation using a divergence-free vector field within gyral blades to encourage an anatomically-justified streamline density distribution along the cortical white/grey-matter boundary while maintaining alignment with the diffusion MRI estimated fibre orientations. Using in vivo data from the Human Connectome Project, we show that this algorithm reduces tractography biases. We compare the structural connectomes to functional connectomes from resting-state fMRI, showing that our model improves cross-modal agreement. Finally, we find that after parcellation the changes in the structural connectome are very minor with slightly improved interhemispheric connections (i.e, more homotopic connectivity) and slightly worse intrahemispheric connections when compared to tracers.

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YNIMG Journal 2020 Journal Article

Improved fibre dispersion estimation using b-tensor encoding

Michiel Cottaar
Filip Szczepankiewicz
Matteo Bastiani
Moises Hernandez-Fernandez
Stamatios N. Sotiropoulos
Markus Nilsson
Saad Jbabdi

Measuring fibre dispersion in white matter with diffusion magnetic resonance imaging (MRI) is limited by an inherent degeneracy between fibre dispersion and microscopic diffusion anisotropy (i. e. , the diffusion anisotropy expected for a single fibre orientation). This means that estimates of fibre dispersion rely on strong assumptions, such as constant microscopic anisotropy throughout the white matter or specific biophysical models. Here we present a simple approach for resolving this degeneracy using measurements that combine linear (conventional) and spherical tensor diffusion encoding. To test the accuracy of the fibre dispersion when our microstructural model is only an approximation of the true tissue structure, we simulate multi-compartment data and fit this with a single-compartment model. For such overly simplistic tissue assumptions, we show that the bias in fibre dispersion is greatly reduced (~5x) for single-shell linear and spherical tensor encoding data compared with single-shell or multi-shell conventional data. In in-vivo data we find a consistent estimate of fibre dispersion as we reduce the b-value from 3 to 1. 5 m s / μ m 2, increase the repetition time, increase the echo time, or increase the diffusion time. We conclude that the addition of spherical tensor encoded data to conventional linear tensor encoding data greatly reduces the sensitivity of the estimated fibre dispersion to the model assumptions of the tissue microstructure.

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YNIMG Journal 2020 Journal Article

Use of multi-flip angle measurements to account for transmit inhomogeneity and non-Gaussian diffusion in DW-SSFP

Benjamin C. Tendler
Sean Foxley
Moises Hernandez-Fernandez
Michiel Cottaar
Connor Scott
Olaf Ansorge
Karla L. Miller
Saad Jbabdi

Diffusion-weighted steady-state free precession (DW-SSFP) is an SNR-efficient diffusion imaging method. The improved SNR and resolution available at ultra-high field has motivated its use at 7T. However, these data tend to have severe B1 inhomogeneity, leading not only to spatially varying SNR, but also to spatially varying diffusivity estimates, confounding comparisons both between and within datasets. This study proposes the acquisition of DW-SSFP data at two-flip angles in combination with explicit modelling of non-Gaussian diffusion to address B1 inhomogeneity at 7T. Data were acquired from five fixed whole human post-mortem brains with a pair of flip angles that jointly optimize the diffusion contrast-to-noise (CNR) across the brain. We compared one- and two-flip angle DW-SSFP data using a tensor model that incorporates the full DW-SSFP Buxton signal, in addition to tractography performed over the cingulum bundle and pre-frontal cortex using a ball & sticks model. The two-flip angle DW-SSFP data produced angular uncertainty and tractography estimates close to the CNR optimal regions in the single-flip angle datasets. The two-flip angle tensor estimates were subsequently fitted using a modified DW-SSFP signal model that incorporates a gamma distribution of diffusivities. This allowed us to generate tensor maps at a single effective b-value yielding more consistent SNR across tissue, in addition to eliminating the B1 dependence on diffusion coefficients and orientation maps. Our proposed approach will allow the use of DW-SSFP at 7T to derive diffusivity estimates that have greater interpretability, both within a single dataset and between experiments.

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YNIMG Journal 2019 Journal Article

Automated quality control for within and between studies diffusion MRI data using a non-parametric framework for movement and distortion correction

Matteo Bastiani
Michiel Cottaar
Sean P. Fitzgibbon
Sana Suri
Fidel Alfaro-Almagro
Stamatios N. Sotiropoulos
Saad Jbabdi
Jesper L.R. Andersson

Diffusion MRI data can be affected by hardware and subject-related artefacts that can adversely affect downstream analyses. Therefore, automated quality control (QC) is of great importance, especially in large population studies where visual QC is not practical. In this work, we introduce an automated diffusion MRI QC framework for single subject and group studies. The QC is based on a comprehensive, non-parametric approach for movement and distortion correction: FSL EDDY, which allows us to extract a rich set of QC metrics that are both sensitive and specific to different types of artefacts. Two different tools are presented: QUAD (QUality Assessment for DMRI), for single subject QC and SQUAD (Study-wise QUality Assessment for DMRI), which is designed to enable group QC and facilitate cross-studies harmonisation efforts.

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YNIMG Journal 2019 Journal Article

Joint modelling of diffusion MRI and microscopy

Amy FD. Howard
Jeroen Mollink
Michiel Kleinnijenhuis
Menuka Pallebage-Gamarallage
Matteo Bastiani
Michiel Cottaar
Karla L. Miller
Saad Jbabdi

The combination of diffusion MRI (dMRI) with microscopy provides unique opportunities to study microstructural features of tissue, particularly when acquired in the same sample. Microscopy is frequently used to validate dMRI microstructure models, addressing the indirect nature of dMRI signals. Typically, these modalities are analysed separately, and microscopy is taken as a gold standard against which dMRI-derived parameters are validated. Here we propose an alternative approach in which we combine dMRI and microscopy data obtained from the same tissue sample to drive a single, joint model. This simultaneous analysis allows us to take advantage of the breadth of information provided by complementary data acquired from different modalities. By applying this framework to a spherical-deconvolution analysis, we are able to overcome a known degeneracy between fibre dispersion and radial diffusion. Spherical-deconvolution based approaches typically estimate a global fibre response function to determine the fibre orientation distribution in each voxel. However, the assumption of a ‘brain-wide’ fibre response function may be challenged if the diffusion characteristics of white matter vary across the brain. Using a generative joint dMRI-histology model, we demonstrate that the fibre response function is dependent on local anatomy, and that current spherical-deconvolution based models may be overestimating dispersion and underestimating the number of distinct fibre populations per voxel.

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YNIMG Journal 2018 Journal Article

A gyral coordinate system predictive of fibre orientations

Michiel Cottaar
Matteo Bastiani
Charles Chen
Krikor Dikranian
David Van Essen
Timothy E. Behrens
Stamatios N. Sotiropoulos
Saad Jbabdi

When axonal fibres approach or leave the cortex, their trajectories tend to closely follow the cortical convolutions. To quantify this tendency, we propose a three-dimensional coordinate system based on the gyral geometry. For every voxel in the brain, we define a “radial” axis orthogonal to nearby surfaces, a “sulcal” axis along the sulcal depth gradient that preferentially points from deep white matter to the gyral crown, and a “gyral” axis aligned with the long axis of the gyrus. When compared with high-resolution, in-vivo diffusion MRI data from the Human Connectome Project, we find that in superficial white matter the apparent diffusion coefficient (at b = 1000) along the sulcal axis is on average 16% larger than along the gyral axis and twice as large as along the radial axis. This is reflected in the vast majority of observed fibre orientations lying close to the tangential plane (median angular offset < 7°), with the dominant fibre orientation typically aligning with the sulcal axis. In cortical grey matter, fibre orientations transition to a predominantly radial orientation. We quantify the width and location of this transition and find strong reproducibility in test-retest data, but also a clear dependence on the resolution of the diffusion data. The ratio of radial to tangential diffusion is fairly constant throughout most of the cortex, except for a decrease of the diffusivitiy ratio in the sulcal fundi and the primary somatosensory cortex (Brodmann area 3) and an increase in the primary motor cortex (Brodmann area 4). Although only constrained by cortical folds, the proposed gyral coordinate system provides a simple and intuitive representation of white and grey matter fibre orientations near the cortex, and may be useful for future studies of white matter development and organisation.

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YNIMG Journal 2018 Journal Article

Disambiguating brain functional connectivity

Eugene P. Duff
Tamar Makin
Michiel Cottaar
Stephen M. Smith
Mark W. Woolrich

Functional connectivity (FC) analyses of correlations of neural activity are used extensively in neuroimaging and electrophysiology to gain insights into neural interactions. However, analyses assessing changes in correlation fail to distinguish effects produced by sources as different as changes in neural signal amplitudes or noise levels. This ambiguity substantially diminishes the value of FC for inferring system properties and clinical states. Network modelling approaches may avoid ambiguities, but require specific assumptions. We present an enhancement to FC analysis with improved specificity of inferences, minimal assumptions and no reduction in flexibility. The Additive Signal Change (ASC) approach characterizes FC changes into certain prevalent classes of signal change that involve the input of additional signal to existing activity. With FMRI data, the approach reveals a rich diversity of signal changes underlying measured changes in FC, suggesting that it could clarify our current understanding of FC changes in many contexts. The ASC method can also be used to disambiguate other measures of dependency, such as regression and coherence, providing a flexible tool for the analysis of neural data.

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YNIMG Journal 2017 Journal Article

Evaluating fibre orientation dispersion in white matter: Comparison of diffusion MRI, histology and polarized light imaging

Jeroen Mollink
Michiel Kleinnijenhuis
Anne-Marie van Cappellen van Walsum
Stamatios N. Sotiropoulos
Michiel Cottaar
Christopher Mirfin
Mattias P. Heinrich
Mark Jenkinson

Diffusion MRI is an exquisitely sensitive probe of tissue microstructure, and is currently the only non-invasive measure of the brain's fibre architecture. As this technique becomes more sophisticated and microstructurally informative, there is increasing value in comparing diffusion MRI with microscopic imaging in the same tissue samples. This study compared estimates of fibre orientation dispersion in white matter derived from diffusion MRI to reference measures of dispersion obtained from polarized light imaging and histology. Three post-mortem brain specimens were scanned with diffusion MRI and analyzed with a two-compartment dispersion model. The specimens were then sectioned for microscopy, including polarized light imaging estimates of fibre orientation and histological quantitative estimates of myelin and astrocytes. Dispersion estimates were correlated on region – and voxel-wise levels in the corpus callosum, the centrum semiovale and the corticospinal tract. The region-wise analysis yielded correlation coefficients of r = 0. 79 for the diffusion MRI and histology comparison, while r = 0. 60 was reported for the comparison with polarized light imaging. In the corpus callosum, we observed a pattern of higher dispersion at the midline compared to its lateral aspects. This pattern was present in all modalities and the dispersion profiles from microscopy and diffusion MRI were highly correlated. The astrocytes appeared to have minor contribution to dispersion observed with diffusion MRI. These results demonstrate that fibre orientation dispersion estimates from diffusion MRI represents the tissue architecture well. Dispersion models might be improved by more faithfully incorporating an informed mapping based on microscopy data.

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YNIMG Journal 2017 Journal Article

Improved tractography using asymmetric fibre orientation distributions

Matteo Bastiani
Michiel Cottaar
Krikor Dikranian
Aurobrata Ghosh
Hui Zhang
Daniel C. Alexander
Timothy E. Behrens
Saad Jbabdi

Diffusion MRI allows us to make inferences on the structural organisation of the brain by mapping water diffusion to white matter microstructure. However, such a mapping is generally ill-defined; for instance, diffusion measurements are antipodally symmetric (diffusion along x and –x are equal), whereas the distribution of fibre orientations within a voxel is generally not symmetric. Therefore, different sub-voxel patterns such as crossing, fanning, or sharp bending, cannot be distinguished by fitting a voxel-wise model to the signal. However, asymmetric fibre patterns can potentially be distinguished once spatial information from neighbouring voxels is taken into account. We propose a neighbourhood-constrained spherical deconvolution approach that is capable of inferring asymmetric fibre orientation distributions (A-fods). Importantly, we further design and implement a tractography algorithm that utilises the estimated A-fods, since the commonly used streamline tractography paradigm cannot directly take advantage of the new information. We assess performance using ultra-high resolution histology data where we can compare true orientation distributions against sub-voxel fibre patterns estimated from down-sampled data. Finally, we explore the benefits of A-fods-based tractography using in vivo data by evaluating agreement of tractography predictions with connectivity estimates made using different in-vivo modalities. The proposed approach can reliably estimate complex fibre patterns such as sharp bending and fanning, which voxel-wise approaches cannot estimate. Moreover, histology-based and in-vivo results show that the new framework allows more accurate tractography and reconstruction of maps quantifying (symmetric and asymmetric) fibre complexity.

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