Fernando Calamante

Direct estimation of the fiber orientation density function from diffusion-weighted MRI data using spherical deconvolution

Diffusion-weighted magnetic resonance imaging can provide information related to the arrangement of white matter fibers. The diffusion tensor is the model most commonly used to derive the orientation of the fibers within a voxel. However, this model has been shown to fail in regions containing several fiber populations with distinct orientations. A number of alternative models have been suggested, such as multiple tensor fitting, q-space, and Q-ball imaging. However, each of these has inherent limitations. In this study, we propose a novel method for estimating the fiber orientation distribution directly from high angular resolution diffusion-weighted MR data without the need for prior assumptions regarding the number of fiber populations present. We assume that all white matter fiber bundles in the brain share identical diffusion characteristics, thus implicitly assigning any differences in diffusion anisotropy to partial volume effects. The diffusion-weighted signal attenuation measured over the surface of a sphere can then be expressed as the convolution over the sphere of a response function (the diffusion-weighted attenuation profile for a typical fiber bundle) with the fiber orientation density function (ODF). The fiber ODF (the distribution of fiber orientations within the voxel) can therefore be obtained using spherical deconvolution. The properties of the technique are demonstrated using simulations and on data acquired from a volunteer using a standard 1.5-T clinical scanner. The technique can recover the fiber ODF in regions of multiple fiber crossing and holds promise for applications such as tractography.

Robust determination of the fibre orientation distribution in diffusion MRI: Non-negativity constrained super-resolved spherical deconvolution

Diffusion-weighted (DW) MR images contain information about the orientation of brain white matter fibres that potentially can be used to study human brain connectivity in vivo using tractography techniques. Currently, the diffusion tensor model is widely used to extract fibre directions from DW-MRI data, but fails in regions containing multiple fibre orientations. The spherical deconvolution technique has recently been proposed to address this limitation. It provides an estimate of the fibre orientation distribution (FOD) by assuming the DW signal measured from any fibre bundle is adequately described by a single response function. However, the deconvolution is ill-conditioned and susceptible to noise contamination. This tends to introduce artefactual negative regions in the FOD, which are clearly physically impossible. In this study, the introduction of a constraint on such negative regions is proposed to improve the conditioning of the spherical deconvolution. This approach is shown to provide FOD estimates that are robust to noise whilst preserving angular resolution. The approach also permits the use of super-resolution, whereby more FOD parameters are estimated than were actually measured, improving the angular resolution of the results. The method provides much better defined fibre orientation estimates, and allows orientations to be resolved that are separated by smaller angles than previously possible. This should allow tractography algorithms to be designed that are able to track reliably through crossing fibre regions.

Measuring Cerebral Blood Flow Using Magnetic Resonance Imaging Techniques

Magnetic resonance imaging techniques measuring CBF have developed rapidly in the last decade, resulting in a wide range of available methods. The most successful approaches are based either on dynamic tracking of a bolus of a paramagnetic contrast agent (dynamic susceptibility contrast) or on arterial spin labeling. This review discusses their principles, possible pitfalls, and potential for absolute quantification and outlines clinical and neuroscientific applications.

MRtrix: Diffusion tractography in crossing fiber regions

In recent years, diffusion‐weighted magnetic resonance imaging has attracted considerable attention due to its unique potential to delineate the white matter pathways of the brain. However, methodologies currently available and in common use among neuroscientists and clinicians are typically based on the diffusion tensor model, which has comprehensively been shown to be inadequate to characterize diffusion in brain white matter. This is due to the fact that it is only capable of resolving a single fiber orientation per voxel, causing incorrect fiber orientations, and hence pathways, to be estimated through these voxels. Given that the proportion of affected voxels has been recently estimated at 90%, this is a serious limitation. Furthermore, most implementations use simple “deterministic” streamlines tracking algorithms, which have now been superseded by “probabilistic” approaches. In this study, we present a robust set of tools to perform tractography, using fiber orientations estimated using the validated constrained spherical deconvolution method, coupled with a probabilistic streamlines tracking algorithm. This methodology is shown to provide superior delineations of a number of known white matter tracts, in a manner robust to crossing fiber effects. These tools have been compiled into a software package, called MRtrix, which has been made freely available for use by the scientific community.

Delay and dispersion effects in dynamic susceptibility contrast MRI: Simulations using singular value decomposition

Dynamic susceptibility contrast (DSC) MRI is now increasingly used for measuring perfusion in many different applications. The quantification of DSC data requires the measurement of the arterial input function (AIF) and the deconvolution of the tissue concentration time curve. One of the most accepted deconvolution methods is the use of singular value decomposition (SVD). Simulations were performed to evaluate the effects on DSC quantification of the presence of delay and dispersion in the estimated AIF. Both delay and dispersion were found to introduce significant underestimation of cerebral blood flow (CBF) and overestimation of mean transit time (MTT). While the error introduced by the delay can be corrected by using the information of the arrival time of the bolus, the correction for the dispersion is less straightforward and requires a model for the vasculature. Magn Reson Med 44:466–473, 2000.

Resolving crossing fibres using constrained spherical deconvolution: validation using diffusion-weighted imaging phantom data.

Diffusion-weighted imaging can potentially be used to infer the connectivity of the human brain in vivo using fibre-tracking techniques, and is therefore of great interest to neuroscientists and clinicians. A key requirement for fibre tracking is the accurate estimation of white matter fibre orientations within each imaging voxel. The diffusion tensor model, which is widely used for this purpose, has been shown to be inadequate in crossing fibre regions. A number of approaches have recently been proposed to address this issue, based on high angular resolution diffusion-weighted imaging (HARDI) data. In this study, an experimental model of crossing fibres, consisting of water-filled plastic capillaries, is used to thoroughly assess three such techniques: constrained spherical deconvolution (CSD), super-resolved CSD (super-CSD) and Q-ball imaging (QBI). HARDI data were acquired over a range of crossing angles and b-values, from which fibre orientations were computed using each technique. All techniques were capable of resolving the two fibre populations down to a crossing angle of 45 degrees , and down to 30 degrees for super-CSD. A bias was observed in the fibre orientations estimated by QBI for crossing angles other than 90 degrees, consistent with previous simulation results. Finally, for a 45 degrees crossing, the minimum b-value required to resolve the fibre orientations was 4000 s/mm(2) for QBI, 2000 s/mm(2) for CSD, and 1000 s/mm(2) for super-CSD. The quality of estimation of fibre orientations may profoundly affect fibre tracking attempts, and the results presented provide important additional information regarding performance characteristics of well-known methods.

Quantification of Perfusion Using Bolus Tracking Magnetic Resonance Imaging in Stroke Assumptions, Limitations, and Potential Implications for Clinical Use

Background— MR techniques have been very powerful in providing indicators of tissue perfusion, particularly in studies of cerebral ischemia. There is considerable interest in performing absolute perfusion measurements, with the aim of improving the characterization of tissue “at risk” of stroke. However, some important caveats relating to absolute measurements need to be taken into account. The purpose of this article is to discuss some of the issues involved and the potential implications for absolute cerebral blood flow measurements in clinical use. Summary of Comment— In bolus tracking MRI, deconvolution of the concentration-time course can in theory provide accurate quantification. However, there are several important assumptions in the tracer kinetic model used, some of which may be invalid in cerebral ischemia. These can introduce significant errors in perfusion quantification. Conclusions— Although we believe that bolus tracking MRI is a powerful technique for the evaluation of perfusion in cerebral ischemia, interpretation of perfusion maps requires caution; this is particularly true when absolute quantification is attempted. Work is currently under way in a number of centers to address these problems, and with appropriate modeling they may be overcome in the future. In the interim, we believe that it is necessary for users of bolus tracking perfusion data to be aware of the current technical limitations if they are to avoid misinterpretation or overinterpretation of their findings.

Track-density imaging (TDI): Super-resolution white matter imaging using whole-brain track-density mapping

Neuroimaging advances have given rise to major progress in neurosciences and neurology, as ever more subtle and specific imaging methods reveal new aspects of the brain. One major limitation of current methods is the spatial scale of the information available. We present an approach to gain spatial resolution using post-processing methods based on diffusion MRI fiber-tracking, to reveal structures beyond the resolution of the acquired imaging voxel; we term such a method as super-resolution track-density imaging (TDI). A major unmet challenge in imaging is the identification of abnormalities in white matter as a cause of illness; super-resolution TDI is shown to produce high-quality white matter images, with high spatial resolution and outstanding anatomical contrast. A unique property of these maps is demonstrated: their spatial resolution and signal-to-noise ratio can be tailored depending on the chosen image resolution and total number of fiber-tracks generated. Super-resolution TDI should greatly enhance the study of white matter in disorders of the brain and mind.

White matter fiber tractography: why we need to move beyond DTI.

OBJECT Diffusion-based MRI tractography is an imaging tool increasingly used in neurosurgical procedures to generate 3D maps of white matter pathways as an aid to identifying safe margins of resection. The majority of white matter fiber tractography software packages currently available to clinicians rely on a fundamentally flawed framework to generate fiber orientations from diffusion-weighted data, namely diffusion tensor imaging (DTI). This work provides the first extensive and systematic exploration of the practical limitations of DTI-based tractography and investigates whether the higher-order tractography model constrained spherical deconvolution provides a reasonable solution to these problems within a clinically feasible timeframe. METHODS Comparison of tractography methodologies in visualizing the corticospinal tracts was made using the diffusion-weighted data sets from 45 healthy controls and 10 patients undergoing presurgical imaging assessment. Tensor-based and constrained spherical deconvolution-based tractography methodologies were applied to both patients and controls. RESULTS Diffusion tensor imaging-based tractography methods (using both deterministic and probabilistic tractography algorithms) substantially underestimated the extent of tracks connecting to the sensorimotor cortex in all participants in the control group. In contrast, the constrained spherical deconvolution tractography method consistently produced the biologically expected fan-shaped configuration of tracks. In the clinical cases, in which tractography was performed to visualize the corticospinal pathways in patients with concomitant risk of neurological deficit following neurosurgical resection, the constrained spherical deconvolution-based and tensor-based tractography methodologies indicated very different apparent safe margins of resection; the constrained spherical deconvolution-based method identified corticospinal tracts extending to the entire sensorimotor cortex, while the tensor-based method only identified a narrow subset of tracts extending medially to the vertex. CONCLUSIONS This comprehensive study shows that the most widely used clinical tractography method (diffusion tensor imaging-based tractography) results in systematically unreliable and clinically misleading information. The higher-order tractography model, using the same diffusion-weighted data, clearly demonstrates fiber tracts more accurately, providing improved estimates of safety margins that may be useful in neurosurgical procedures. We therefore need to move beyond the diffusion tensor framework if we are to begin to provide neurosurgeons with biologically reliable tractography information.

A Rigorous Framework for Diffusion Tensor Calculus

In biological tissue, all eigenvalues of the diffusion tensor are assumed to be positive. Calculations in diffusion tensor MRI generally do not take into account this positive definiteness property of the tensor. Here, the space of positive definite tensors is used to construct a framework for diffusion tensor analysis. The method defines a distance function between a pair of tensors and the associated shortest path (geodesic) joining them. From this distance a method for computing tensor means, a new measure of anisotropy, and a method for tensor interpolation are derived. The method is illustrated using simulated and in vivo data. Magn Reson Med 53:221–225, 2005.