Peter J. Basser

MR DIFFUSION TENSOR SPECTROSCOPY AND IMAGING

This paper describes a new NMR imaging modality--MR diffusion tensor imaging. It consists of estimating an effective diffusion tensor, Deff, within a voxel, and then displaying useful quantities derived from it. We show how the phenomenon of anisotropic diffusion of water (or metabolites) in anisotropic tissues, measured noninvasively by these NMR methods, is exploited to determine fiber tract orientation and mean particle displacements. Once Deff is estimated from a series of NMR pulsed-gradient, spin-echo experiments, a tissues three orthotropic axes can be determined. They coincide with the eigenvectors of Deff, while the effective diffusivities along these orthotropic directions are the eigenvalues of Deff. Diffusion ellipsoids, constructed in each voxel from Deff, depict both these orthotropic axes and the mean diffusion distances in these directions. Moreover, the three scalar invariants of Deff, which are independent of the tissues orientation in the laboratory frame of reference, reveal useful information about molecular mobility reflective of local microstructure and anatomy. Inherently tensors (like Deff) describing transport processes in anisotropic media contain new information within a macroscopic voxel that scalars (such as the apparent diffusivity, proton density, T1, and T2) do not.

In Vivo Fiber Tractography Using DT-MRI Data

Fiber tract trajectories in coherently organized brain white matter pathways were computed from in vivo diffusion tensor magnetic resonance imaging (DT‐MRI) data. First, a continuous diffusion tensor field is constructed from this discrete, noisy, measured DT‐MRI data. Then a Frenet equation, describing the evolution of a fiber tract, was solved. This approach was validated using synthesized, noisy DT‐MRI data. Corpus callosum and pyramidal tract trajectories were constructed and found to be consistent with known anatomy. The methods reliability, however, degrades where the distribution of fiber tract directions is nonuniform. Moreover, background noise in diffusion‐weighted MRIs can cause a computed trajectory to hop from tract to tract. Still, this method can provide quantitative information with which to visualize and study connectivity and continuity of neural pathways in the central and peripheral nervous systems in vivo, and holds promise for elucidating architectural features in other fibrous tissues and ordered media. Magn Reson Med 44:625–632, 2000. Published 2000 Wiley‐Liss, Inc.

Water diffusion changes in Wallerian degeneration and their dependence on white matter architecture.

This study investigates water diffusion changes in Wallerian degeneration. We measured indices derived from the diffusion tensor (DT) and T2-weighted signal intensities in the descending motor pathways of patients with small chronic lacunar infarcts of the posterior limb of the internal capsule on one side. We compared these measurements in the healthy and lesioned sides at different levels in the brainstem caudal to the primary lesion. We found that secondary white matter degeneration is revealed by a large reduction in diffusion anisotropy only in regions where fibers are arranged in isolated bundles of parallel fibers, such as in the cerebral peduncle. In regions where the degenerated pathway crosses other tracts, such as in the rostral pons, paradoxically there is almost no change in diffusion anisotropy, but a significant change in the measured orientation of fibers. The trace of the diffusion tensor is moderately increased in all affected regions. This allows one to differentiate secondary and primary fiber loss where the increase in trace is considerably higher. We show that DT-MRI is more sensitive than T2-weighted MRI in detecting Wallerian degeneration. Significant diffusion abnormalities are observed over the entire trajectory of the affected pathway in each patient. This finding suggests that mapping degenerated pathways noninvasively with DT-MRI is feasible. However, the interpretation of water diffusion data is complex and requires a priori information about anatomy and architecture of the pathway under investigation. In particular, our study shows that in regions where fibers cross, existing DT-MRI-based fiber tractography algorithms may lead to erroneous conclusion about brain connectivity.

Daily repetitive transcranial magnetic stimulation (rtms) improves mood in depression

Converging evidence points to hypofunction of the left prefrontal cortex in depression. Repetitive transcranial magnetic stimulation (rTMS) activates neurons near the surface of the brain. We questioned whether daily left prefrontal rTMS might improve mood in depressed subjects and report a pilot study of such treatment in six highly medication-resistant depressed inpatients. Depression scores significantly improved for the group as a whole (Hamilton Depression Scores decreased from 23.8 ± 4.2 (s.d.) at baseline to 17.5 ± 8.4 after treatment; t = 3.03, 5DF, p = 0.02, two-tailed paired t-test). Two subjects showed robust mood improvement which occurred progressively over the course of several weeks. In one subject, depression symptoms completely remitted for the first time in 3 years. Daily left prefrontal rTMS appears to be safe, well tolerated and may alleviate depression.

Axcaliber: A method for measuring axon diameter distribution from diffusion MRI

The diameter of a myelinated nerve axon is directly proportional to its conduction velocity, so the axon diameter distribution helps determine the channel capacity of nervous transmission along fascicles in the central (CNS) and peripheral nervous systems (PNS). Previously, this histological information could only be obtained using invasive tissue biopsies. Here we propose a new NMR‐based approach that employs a model of water diffusion within “restricted” cylindrical axons to estimate their diameter distribution within a nerve bundle. This approach can be combined with MRI to furnish an estimate of the axon diameter distribution within each voxel. This method is validated by comparing the diameter distributions measured using the NMR and histological techniques on sciatic and optic nerve tissue specimens. The axon diameter distribution measured in each voxel of porcine spinal cord using MRI and using histological methods were similar. Applications are expected in longitudinal studies designed to follow nerve growth in normal and abnormal development, as well as in diagnosing disorders and diseases affecting specific populations of axons in the CNS and PNS. Magn Reson Med 59:1347–1354, 2008.

Composite hindered and restricted model of diffusion (CHARMED) MR imaging of the human brain

High b value diffusion-weighted images sampled at high angular resolution were analyzed using a composite hindered and restricted model of diffusion (CHARMED). Measurements and simulations of diffusion in white matter using CHARMED provide an unbiased estimate of fiber orientation with consistently smaller angular uncertainty than when calculated using a DTI model or with a dual tensor model for any given signal-to-noise level. Images based on the population fraction of the restricted compartment provide a new contrast mechanism that enhances white matter like DTI. Nevertheless, it is assumed that these images might be more sensitive than DTI to white matter disorders. We also provide here an experimental design and analysis framework to implement CHARMED MRI that is feasible on human clinical scanners.

“Squashing peanuts and smashing pumpkins”: How noise distorts diffusion-weighted MR data†‡

New diffusion‐weighted imaging (DWI) methods, including high‐b, q‐space, and high angular resolution MRI methods, attempt to extract information about non‐Gaussian diffusion in tissue that is not provided by low‐b‐value (b ≈ 1000 s mm−2) diffusion or diffusion tensor magnetic resonance imaging (DT‐MRI). Additionally, DWI data with higher spatial resolution are being acquired to resolve fine anatomic structures, such as white matter fasciculi. Increasing diffusion‐weighting or decreasing voxel size can reduce the signal‐to‐noise ratio so that some DWI signals are close to the background noise level. Here we report several new artifacts that can be explained by considering how background noise affects the peanut‐shaped angular apparent diffusion coefficient (ADC) profile. These include an orientationally dependent deviation from Gaussian behavior of the ADC profile, an underestimation of indices of diffusion anisotropy, and a correlation between estimates of mean diffusivity and diffusion anisotropy. We also discuss how noise can cause increased gray/white matter DWI contrast at higher b values and an apparent elevation of diffusion anisotropy in acute ischemia. Importantly, all of these artifacts are negligible in the b‐value range typically used in DT‐MRI of brain (b ≈ 1000 s mm−2). Finally, we demonstrate a strategy for ameliorating the rectified noise artifact in data collected at higher b values. Magn Reson Med 52:979–993, 2004. Published 2004 Wiley‐Liss, Inc.

Comprehensive Approach for Correction of Motion and Distortion in Diffusion-Weighted MRI

Patient motion and image distortion induced by eddy currents cause artifacts in maps of diffusion parameters computed from diffusion‐weighted (DW) images. A novel and comprehensive approach to correct for spatial misalignment of DW imaging (DWI) volumes acquired with different strengths and orientations of the diffusion sensitizing gradients is presented. This approach uses a mutual information‐based registration technique and a spatial transformation model containing parameters that correct for eddy current‐induced image distortion and rigid body motion in three dimensions. All parameters are optimized simultaneously for an accurate and fast solution to the registration problem. The images can also be registered to a normalized template with a single interpolation step without additional computational cost. Following registration, the signal amplitude of each DWI volume is corrected to account for size variations of the object produced by the distortion correction, and the b‐matrices are properly recalculated to account for any rotation applied during registration. Both qualitative and quantitative results show that this approach produces a significant improvement of diffusion tensor imaging (DTI) data acquired in the human brain. Magn Reson Med 51:103–114, 2004. Published 2003 Wiley‐Liss, Inc.

New modeling and experimental framework to characterize hindered and restricted water diffusion in brain white matter

To characterize anisotropic water diffusion in brain white matter, a theoretical framework is proposed that combines hindered and restricted models of water diffusion (CHARMED) and an experimental methodology that embodies features of diffusion tensor and q‐space MRI. This model contains a hindered extra‐axonal compartment, whose diffusion properties are characterized by an effective diffusion tensor, and an intra‐axonal compartment, whose diffusion properties are characterized by a restricted model of diffusion within cylinders. The hindered model primarily explains the Gaussian signal attenuation observed at low b values; the restricted non‐Gaussian model does so at high b. Both high and low b data obtained along different directions are required to estimate various microstructural parameters of the composite model, such as the nerve fiber orientation(s), the T2‐weighted extra‐ and intra‐axonal volume fractions, and principal diffusivities. The proposed model provides a description of restricted diffusion in 3D given by a 3D probability distribution (average propagator), which is obtained by 3D Fourier transformation of the estimated signal attenuation profile. The new model is tested using synthetic phantoms and validated on excised spinal cord tissue. This framework shows promise in determining the orientations of two or more fiber compartments more precisely and accurately than with diffusion tensor imaging. Magn Reson Med 52:965–978, 2004. Published 2004 Wiley‐Liss, Inc.

A model of the stimulation of a nerve fiber by electromagnetic induction

A model is presented to explain the physics of nerve stimulations by electromagnetic induction. Maxwells equations predict the induced electric field distribution that is produced when a capacitor is discharged through a stimulating coil. A nonlinear Hodgkin-Huxley cable model describes the response of the nerve fiber to this induced electric field. Once the coils position, orientation, and shape are given and the resistance, capacitance, and initial voltage of the stimulating circuit are specified, this model predicts the resulting transmembrane potential of the fiber as a function of distance and time. It is shown that the nerve fiber is stimulated by the gradient of the component of the induced electric field that is parallel to the fiber, which hyperpolarizes or depolarizes the membrane and may stimulate an action potential. The model predicts complicated dynamics such as action potential annihilation and dispersion.<<ETX>>