Carlo Pierpaoli

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.

Color Schemes to Represent the Orientation of Anisotropic Tissues From Diffusion Tensor Data: Application to White Matter Fiber Tract Mapping in the Human Brain

This paper investigates the use of color to represent the directional information contained in the diffusion tensor. Ideally, one wants to take into account both the properties of human color vision and of the given display hardware to produce a representation in which differences in the orientation of anisotropic structures are proportional to the perceived differences in color. It is argued here that such a goal cannot be achieved in general and therefore, empirical or heuristic schemes, which avoid some of the common artifacts of previously proposed approaches, are implemented. Directionally encoded color (DEC) maps of the human brain obtained using these schemes clearly show the main association, projection, and commissural white matter pathways. In the brainstem, motor and sensory pathways are easily identified and can be differentiated from the transverse pontine fibers and the cerebellar peduncles. DEC maps obtained from diffusion tensor imaging data provide a simple and effective way to visualize fiber direction, useful for investigating the structural anatomy of different organs. Magn Reson Med 42:526‐540, 1999. r 1999 Wiley-Liss, Inc.

RESTORE: robust estimation of tensors by outlier rejection.

Signal variability in diffusion weighted imaging (DWI) is influenced by both thermal noise and spatially and temporally varying artifacts such as subject motion and cardiac pulsation. In this paper, the effects of DWI artifacts on estimated tensor values, such as trace and fractional anisotropy, are analyzed using Monte Carlo simulations. A novel approach for robust diffusion tensor estimation, called RESTORE (for robust estimation of tensors by outlier rejection), is proposed. This method uses iteratively reweighted least‐squares regression to identify potential outliers and subsequently exclude them. Results from both simulated and clinical diffusion data sets indicate that the RESTORE method improves tensor estimation compared to the commonly used linear and nonlinear least‐squares tensor fitting methods and a recently proposed method based on the Geman–McClure M‐estimator. The RESTORE method could potentially remove the need for cardiac gating in DWI acquisitions and should be applicable to other MR imaging techniques that use univariate or multivariate regression to fit MRI data to a model. Magn Reson Med 53:1088–1095, 2005. Published 2005 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.

Anatomical accuracy of brain connections derived from diffusion MRI tractography is inherently limited

Significance Diffusion-weighted MRI (DWI) tractography is widely used to map structural connections of the human brain in vivo and has been adopted by large-scale initiatives such as the human connectome project. Our results indicate that, even with high-quality data, DWI tractography alone is unlikely to provide an anatomically accurate map of the brain connectome. It is crucial to complement tractography results with a combination of histological or neurophysiological methods to map structural connectivity accurately. Our findings, however, do not diminish the importance of diffusion MRI as a noninvasive tool that offers important quantitative measures related to brain tissue microstructure and white matter architecture. Tractography based on diffusion-weighted MRI (DWI) is widely used for mapping the structural connections of the human brain. Its accuracy is known to be limited by technical factors affecting in vivo data acquisition, such as noise, artifacts, and data undersampling resulting from scan time constraints. It generally is assumed that improvements in data quality and implementation of sophisticated tractography methods will lead to increasingly accurate maps of human anatomical connections. However, assessing the anatomical accuracy of DWI tractography is difficult because of the lack of independent knowledge of the true anatomical connections in humans. Here we investigate the future prospects of DWI-based connectional imaging by applying advanced tractography methods to an ex vivo DWI dataset of the macaque brain. The results of different tractography methods were compared with maps of known axonal projections from previous tracer studies in the macaque. Despite the exceptional quality of the DWI data, none of the methods demonstrated high anatomical accuracy. The methods that showed the highest sensitivity showed the lowest specificity, and vice versa. Additionally, anatomical accuracy was highly dependent upon parameters of the tractography algorithm, with different optimal values for mapping different pathways. These results suggest that there is an inherent limitation in determining long-range anatomical projections based on voxel-averaged estimates of local fiber orientation obtained from DWI data that is unlikely to be overcome by improvements in data acquisition and analysis alone.

Gleaning Multicomponent T-1 and T-2 Information From Steady-State Imaging Data

The driven‐equilibrium single‐pulse observation of T1 (DESPOT1) and T2 (DESPOT2) are rapid, accurate, and precise methods for voxelwise determination of the longitudinal and transverse relaxation times. A limitation of the methods, however, is the inherent assumption of single‐component relaxation. In a variety of biological tissues, in particular human white matter (WM) and gray matter (GM), the relaxation has been shown to be more completely characterized by a summation of two or more relaxation components, or species, each believed to be associated with unique microanatomical domains or water pools. Unfortunately, characterization of these components on a voxelwise, whole‐brain basis has traditionally been hindered by impractical acquisition times. In this work we extend the conventional DESPOT1 and DESPOT2 approaches to include multicomponent relaxation analysis. Following numerical analysis of the new technique, renamed multicomponent driven equilibrium single pulse observation of T1/T2 (mcDESPOT), whole‐brain multicomponent T1 and T2 quantification is demonstrated in vivo with clinically realistic times of between 16 and 30 min. Results obtained from four healthy individuals and two primary progressive multiple sclerosis (MS) patients demonstrate the future potential of the approach for identifying and assessing tissue changes associated with several neurodegenerative conditions, in particular those associated with WM. Magn Reson Med 60:1372–1387, 2008.

Age Effects on Diffusion Tensor Magnetic Resonance Imaging Tractography Measures of Frontal Cortex Connections in Schizophrenia

Diffusion tensor magnetic resonance imaging (DT‐MRI) has previously been used to investigate white matter tracts in schizophrenia, with inconsistent results. The aim of the study was to use a novel method for tract‐specific measurements of fronto‐temporal fasciculi in early‐onset schizophrenia. We hypothesized that by making tract‐specific measurements, clear diffusion abnormalities would be revealed in specific fasciculi in schizophrenia. Measurements of diffusion anisotropy and mean diffusivity were localized within fronto‐temporal fasciculi by forming 3‐D reconstructions of the cingulum, uncinate, superior longitudinal, and inferior fronto‐occipital fasciculi using diffusion tensor tractography. We were limited in our ability to test our hypothesis by the important and surprising finding that age affected DT‐MRI‐based measures in schizophrenia patients in a different way from comparison subjects, most notably in the left superior longitudinal fasciculus. The youngest schizophrenia patients that we studied had lower diffusion anisotropy than age‐matched comparison subjects, but this difference diminished with increasing age. The main conclusion of this study was that direct comparisons of absolute DT‐MRI‐based measures between individuals with schizophrenia and comparison subjects may be problematic and misleading because of underlying age‐related differences in brain maturation between groups. Hum Brain Mapp, 2005.

Visualizing and characterizing white matter fiber structure and architecture in the human pyramidal tract using diffusion tensor MRI.

We used diffusion tensor imaging to assess diffusion anisotropy in the pyramidal tract in ten young, and ten elderly subjects (five males and five females in each group). The purpose of this study was to define normative values for anisotropy at different anatomic levels of the brainstem as well as to assess differences due to age, gender, and laterality. In all subjects, anisotropy was highest in the cerebral peduncle, lowest in the caudal pons, and intermediate in the medulla. In the pons and medulla the regional variability was high, with significant differences in anisotropy even between contiguous slices. Multifactorial ANOVA (performed using the average value of anisotropy within each region of interest) revealed that elderly subjects had significantly lower values than young subjects in the cerebral peduncle, with no differences in the pons and medulla. No significant differences in anisotropy due to gender and side were found. The differences in anisotropy at different levels of the brainstem reflect differences in the local architecture of white matter fibers. Anisotropy is high in the cerebral peduncle because fibers have a highly ordered arrangement, while in the pons and medulla, anisotropy is lower because the local fiber architecture is less coherent due to the presence of other fibers and nuclei. The biologic meaning of the intergroup differences in anisotropy is discussed in light of the structure and architecture of the tissue under investigation. We also consider potential sources of artifacts, such as noise and motion, partial volume contamination, anatomic mismatching, and the use of inappropriate statistical tests. We conclude that the age-related decrease in anisotropy in the cerebral peduncle is not artifactual but rather reflects subtle structural changes of the aging white matter. Our study however shows that caution must be exercised in interpreting diffusion anisotropy data.

Confidence Mapping in Diffusion Tensor Magnetic Resonance Imaging Tractography Using a Bootstrap Approach

The bootstrap technique is an extremely powerful nonparametric statistical procedure for determining the uncertainty in a given statistic. However, its use in diffusion tensor MRI tractography remains virtually unexplored. This work shows how the bootstrap can be used to assign confidence to results obtained with deterministic tracking algorithms. By invoking the concept of a “tract‐propagator,” it also underlines the important effect of local fiber architecture or architectural milieu on tracking reproducibility. Finally, the practical advantages and limitations of the technique are discussed. Not only does the bootstrap allow any deterministic tractography algorithm to be used in a probabilistic fashion, but also its model‐free inclusion of all sources of variability (including those that cannot be modeled) means that it provides the most realistic approach to probabilistic tractography. Magn Reson Med 53:1143–1149, 2005. Published 2005 Wiley‐Liss, Inc.