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Bias Field Correction and Intensity Normalisation for Quantitative Analysis of Apparent Fibre Density


Abstract and Figures

Apparent Fibre Density (AFD) is a measure derived from un-normalised fibre orientation distributions. To make AFD quantitative across subjects, images need to be intensity normalised and bias field corrected. Here we present a fast and robust approach to simultaneous bias field correction and intensity normalisation by exploiting tissue compartment maps derived from multi-tissue constrained spherical deconvolution. We performed simulations to show that the method can accurately recover a ground truth bias field, while also demonstrating qualitative results on in vivo data.
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Bias Field Correction and Intensity Normalisation for Quantitative Analysis of
Apparent Fibre Density
David Raffelt , Thijs Dhollander , J-Donald Tournier , Rami Tabbara , Robert E Smith , Eric Pierre , and Alan
Florey Institute of Neuroscience, Melbourne, Australia, Centre for the Developing Brain, Division of Imaging Sciences and Biomedical
Engineering, Kings College London, London, United Kingdom
Apparent Fibre Density (AFD) is a measure derived from un-normalised fibre orientation distributions. To make AFD quantitative
across subjects, images need to be intensity normalised and bias field corrected. Here we present a fast and robust approach to
simultaneous bias field correction and intensity normalisation by exploiting tissue compartment maps derived from multi-tissue
constrained spherical deconvolution. We performed simulations to show that the method can accurately recover a ground truth
bias field, while also demonstrating qualitative results on in vivo data.
A new method for bias field correction and intensity normalisation to enable quantitative comparison of apparent fibre density.
Apparent Fibre Density (AFD) is a Fibre Orientation Distribution-derived measure developed to enable fibre-specific quantitative
analysis using HARDI data . While most DWI models derive quantitative measures by normalising the DW signal to the b=0 signal
within each voxel, issues arise when all compartments within the voxel (and their T2s) are not modelled appropriately (i.e. CSF, GM,
extra-axonal space, myelin) . In contrast, previous AFD studies have relied on global intensity normalisation (based on the median
CSF or WM b=0s/mm value), following bias field correction (with the field estimated from the b=0s/mm image). This approach is not
ideal since: 1) intensity normalisation using the median CSF or WM b=0s/mm value may be biased when pathology is extensive or
influences the selection of exemplar voxels for intensity normalisation; 2) the similar T2w values for GM and WM make histogram-
based bias field estimation difficult.
Here we propose a fast and robust method for simultaneous intensity normalisation and bias field correction of DWI data by
exploiting information derived from multi-tissue constrained spherical deconvolution (mtCSD) .
All brain voxels contain either GM, WM or CSF (or some mixture thereof); ideally, therefore, the tissue compartment maps from
mtCSD should sum to 1. In practice, variations in T2 will mean that the compartment weights do not generally sum to 1. While a unit
sum constraint could be imposed on the output of mtCSD, in practice the method operates without any form of voxel-wise
normalisation to ensure linearity of the estimated volume fractions with respect to the measured DW signal. Consequently, the
output tissue compartment maps are also affected by intensity variations due to the bias field (Fig. 1a-c). Furthermore, because the
response functions used in the mtCSD are estimated from a subset of voxels in each tissue class , the magnitude of the response
functions may not be appropriate for the whole brain, leading to tissue-specific hyper- or hypo-intensities in the summed image
(GM+GM+CSF) (Fig. 1d).
We estimate a bias field and a global scale factor per tissue type by minimising the cost function, :
where the bias field is modelled by polynomial basis functions at voxel with weights . is the value of the
compartment density map for tissue , is the number of tissue compartments, and is used to account for global differences in
magnitude between tissue types due to miscalibrated response function magnitudes.
To minimise , we iterate between performing a least squares solve for a vector containing the global scale factors (given the
current estimate of ), and a least squares solve for (given the current estimate of ), normalising the bias field to average 1 in
all brain mask voxels. Optimisation is stopped at convergence (~5 iterations).
To evaluate the proposed method, we applied 10 different “ground truth” bias fields to a bias-field-free diffusion MRI phantom . The
ground truth fields were obtained from 10 different subjects from the human connectome project (HCP) . We then performed
mtCSD using GM, WM and CSF response functions that were randomly scaled by a factor (range 0.8-1.2) to simulate miscalibration of
the response functions. We performed two experiments: 1) estimation of the bias field (i.e. no intensity normalisation by ) 2)
Estimating the bias field and intensity normalisation. Results were evaluated by computing the error at each voxel as the absolute
difference between the estimated field and the ground truth, expressed as percentage of the ground truth.
We also demonstrate the proposed method on an in vivo dataset, using tissue maps obtained from mtCSD of a single HCP subject,
and visually compare the result to a commonly used approach .
1 1 2 1 1 1
1 2
2,3 4
2 2
F(w,s) = |1 − dx
As shown by Fig 2, for all 10 simulations the median error for all voxels in the brain mask was substantially reduced when modelling
the bias field from the summed tissue compartment image. When also estimating tissue normalisation scale factors to account for
the effect of miscalibration in response function magnitudes, the error in the estimated field was further reduced. Fig. 3
demonstrates that in real in vivo data, the proposed method produces a map of summed tissue densities that is more homogeneous
(and hence more biologically realistic) than the N4-based approach .
Discussion and Conclusion
We have demonstrated a fast a robust method for simultaneously correcting the bias field and performing global intensity
normalisation of mtCSD compartment maps. The corrected tissue maps may be subsequently used for direct quantitative analysis
(e.g. fixel-based analysis ) or connectivity studies .
No acknowledgement found.
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4 11
Figure 1. Example multi-tissue CSD results from HCP data showing a bias field present in the a) GM b) WM c) CSF tissue
compartments. d) The sum of all tissue compartments, demonstrating a reduced intensity of WM compared to GM and CSF. This is a
consequence of the estimated WM response not being representative in magnitude of all WM.
Figure 2. Simulations demonstrating the error between the estimated bias field and the ground truth. Each box plot contains the
error from all voxels within a brain mask. Shown in red is the error before bias field correction (i.e. an identity bias field). The green
box plots demonstrate that the bias field cannot be accurately estimated if the tissue compartments are not normalised to account
for possible mis-calibrations. The error is substantially reduced when estimating the field from the intensity normalised tissue
compartments (blue plots).
Figure 3. Example of the proposed method applied to an in vivo dataset. a) Summed (GM + WM +CSF) tissue compartment map
before bias field correction or tissue normalisation. b) Bias field estimated by the proposed method. c) Summed tissue compartment
map resulting from the proposed method. d) Summed tissue compartment map after correction by a field estimated from the b=0
images only with N4. Differences between c and d can be observed most prominently in the frontal lobe.
Proc. Intl. Soc. Mag. Reson. Med. 25 (2017)
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To overcome the fact that the fibre orientation distribution (FOD) from constrained spherical deconvolution (CSD) assumes a single-fibre white matter (WM) response function—and is thus inappropriate and distorted in voxels containing grey matter (GM) or cerebrospinal fluid (CSF)—multi-shell multi-tissue CSD (MSMT-CSD) was proposed. MSMT-CSD can resolve WM, GM and CSF signal contributions, but requires multi-shell data. Very recently, we proposed a novel method that can achieve the same results using just single-shell data. We refer to this method as "single-shell 3-tissue CSD" (SS3T-CSD). Both MSMT-CSD and SS3T-CSD require WM, GM and CSF response functions. These can be obtained from manually selected exemplary voxels of the tissue classes, or via the procedure described initially in the MSMT-CSD paper, which relies on a highly accurately co-registered T1 image. We propose an unsupervised procedure that does not depend on a T1 image, nor registration, and works for both single-shell and multi-shell data.
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Keywords: data collection ; diffusion magnetic resonance imaging ; phantoms ; imaging ; connectomics ; evaluation ; simulations Reference EPFL-ARTICLE-217746doi:10.3339/fninf.2016.00004View record in Web of Science Record created on 2016-04-01, modified on 2016-08-09
Constrained spherical deconvolution (CSD) has become one of the most widely used methods to extract white matter (WM) fibre orientation information from diffusion-weighted MRI (DW-MRI) data, overcoming the crossing fibre limitations inherent in the diffusion tensor model. It is routinely used to obtain high quality fibre orientation distribution function (fODF) estimates and fibre tractograms and is increasingly used to obtain apparent fibre density (AFD) measures. Unfortunately, CSD typically only supports data acquired on a single shell in q-space. With multi-shell data becoming more and more prevalent, there is a growing need for CSD to fully support such data. Furthermore, CSD can only provide high quality fODF estimates in voxels containing WM only. In voxels containing other tissue types such as grey matter (GM) and cerebrospinal fluid (CSF), the WM response function may no longer be appropriate and spherical deconvolution produces unreliable, noisy fODF estimates. The aim of this study is to incorporate support for multi-shell data into the CSD approach as well as to exploit the unique b-value dependencies of the different tissue types to estimate a multi-tissue ODF. The resulting approach is dubbed multi-shell, multi-tissue CSD (MSMT-CSD) and is compared to the state-of-the-art single-shell, single-tissue CSD (SSST-CSD) approach. Using both simulations and real data, we show that MSMT-CSD can produce reliable WM/GM/CSF volume fraction maps, directly from the DW data, whereas SSST-CSD has a tendency to overestimate the WM volume in voxels containing GM and/or CSF. In addition, compared to SSST-CSD, MSMT-CSD can substantially increase the precision of the fODF fibre orientations and reduce the presence ofspurious fODF peaks in voxels containing GM and/or CSF. Both effects translate into more reliable AFD measures and tractography results with MSMT-CSD compared to SSST-CSD.
A variant of the popular nonparametric nonuniform intensity normalization (N3) algorithm is proposed for bias field correction. Given the superb performance of N3 and its public availability, it has been the subject of several evaluation studies. These studies have demonstrated the importance of certain parameters associated with the B -spline least-squares fitting. We propose the substitution of a recently developed fast and robust B-spline approximation routine and a modified hierarchical optimization scheme for improved bias field correction over the original N3 algorithm. Similar to the N3 algorithm, we also make the source code, testing, and technical documentation of our contribution, which we denote as ??N4ITK,?? available to the public through the Insight Toolkit of the National Institutes of Health. Performance assessment is demonstrated using simulated data from the publicly available Brainweb database, hyperpolarized <sup>3</sup>He lung image data, and 9.4T postmortem hippocampus data.
The Human Connectome Project (HCP) is an ambitious 5-year effort to characterize brain connectivity and function and their variability in healthy adults. This review summarizes the data acquisition plans being implemented by a consortium of HCP investigators who will study a population of 1200 subjects (twins and their non-twin siblings) using multiple imaging modalities along with extensive behavioral and genetic data. The imaging modalities will include diffusion imaging (dMRI), resting-state fMRI (R-fMRI), task-evoked fMRI (T-fMRI), T1- and T2-weighted MRI for structural and myelin mapping, plus combined magnetoencephalography and electroencephalography (MEG/EEG). Given the importance of obtaining the best possible data quality, we discuss the efforts underway during the first two years of the grant (Phase I) to refine and optimize many aspects of HCP data acquisition, including a new 7T scanner, a customized 3T scanner, and improved MR pulse sequences.
This article proposes a new measure called Apparent Fibre Density (AFD) for the analysis of high angular resolution diffusion-weighted images using higher-order information provided by fibre orientation distributions (FODs) computed using spherical deconvolution. AFD has the potential to provide specific information regarding differences between populations by identifying not only the location, but also the orientations along which differences exist. In this work, analytical and numerical Monte-Carlo simulations are used to support the use of the FOD amplitude as a quantitative measure (i.e. AFD) for population and longitudinal analysis. To perform robust voxel-based analysis of AFD, we present and evaluate a novel method to modulate the FOD to account for changes in fibre bundle cross-sectional area that occur during spatial normalisation. We then describe a novel approach for statistical analysis of AFD that uses cluster-based inference of differences extended throughout space and orientation. Finally, we demonstrate the capability of the proposed method by performing voxel-based AFD comparisons between a group of Motor Neurone Disease patients and healthy control subjects. A significant decrease in AFD was detected along voxels and orientations corresponding to both the corticospinal tract and corpus callosal fibres that connect the primary motor cortices. In addition to corroborating previous findings in MND, this study demonstrates the clear advantage of using this type of analysis by identifying differences along single fibre bundles in regions containing multiple fibre populations.
CSF contamination contributes to apparent microstructural alterations in mild cognitive impairment
  • R Berlot
  • C Metzler-Baddeley
  • D K Jones
  • O' Sullivan
Berlot R, Metzler-Baddeley C, Jones DK, O'Sullivan MJ. CSF contamination contributes to apparent microstructural alterations in mild cognitive impairment. Neuroimage 2014;92:27-35.
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