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Carlo Pierpaoli

Publications and source records attributed to Carlo Pierpaoli.

11 recordsLinked to original sources
PubMed2007

Variance of estimated DTI-derived parameters via first-order perturbation methods.

In typical applications of diffusion tensor imaging (DTI), DT-derived quantities are used to make a diagnostic, therapeutic, or scientific determination. In such cases it is essential to characterize the variability of these tensor-derived quantities. Parametric and empirical methods have been proposed to estimate the variance of the estimated DT, and quantities derived from it. However, the former method cannot be generalized since a parametric distribution cannot be found for all DT-derived quantities. Although powerful empirical methods, such as the bootstrap, are available, they require oversampling of the diffusion-weighted imaging (DWI) data. Statistical perturbation methods represent a hybrid between parametric and empirical approaches, and can overcome the primary limitations of both methods. In this study we used a first-order perturbation method to obtain analytic expressions for the variance of DT-derived quantities, such as the trace, fractional anisotropy (FA), eigenvalues, and eigenvectors, for a given experimental design. We performed Monte Carlo (MC) simulations of DTI experiments to test and validate these formulae, and to determine their range of applicability for different experimental design parameters, including the signal-to-noise ratio (SNR), diffusion gradient sampling scheme, and number of DWI acquisitions. This information should be useful for designing DTI studies and assessing the quality of inferences drawn from them.

Algorithms↗
PubMed2006

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging.

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (<or=5). A new experimental design is, therefore, proposed to properly account for the directional dependence in diffusion weighted signal variance.

Algorithms↗
PubMed2006

Regional distribution of measurement error in diffusion tensor imaging.

The characterization of measurement error is critical in assessing the significance of diffusion tensor imaging (DTI) findings in longitudinal and cohort studies of psychiatric disorders. We studied 20 healthy volunteers, each one scanned twice (average interval between scans of 51 +/- 46.8 days) with a single shot echo planar DTI technique. Intersession variability for fractional anisotropy (FA) and Trace (D) was represented as absolute variation (standard deviation within subjects: SDw), percent coefficient of variation (CV) and intra-class correlation coefficient (ICC). The values from the two sessions were compared for statistical significance with repeated measures analysis of variance or a non-parametric equivalent of a paired t-test. The results showed good reproducibility for both FA and Trace (CVs below 10% and ICCs at or above 0.70 in most regions of interest) and evidence of systematic global changes in Trace between scans. The regional distribution of reproducibility described here has implications for the interpretation of regional findings and for rigorous pre-processing. The regional distribution of reproducibility measures was different for SDw, CV and ICC. Each one of these measures reveals complementary information that needs to be taken into consideration when performing statistical operations on groups of DT images.

Adult↗
PubMed2006

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.

Adult↗
PubMed2005

Estimating intensity variance due to noise in registered images: applications to diffusion tensor MRI.

Image registration techniques which require image interpolation are widely used in neuroimaging research. We show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or approximation kernel chosen. The method is general and could handle various sources of signal variability, such as thermal noise and physiological noise, provided that their effects can be assessed in the original images. Our approach is applied to diffusion tensor (DT) MRI data, assuming only thermal noise as the source of variability in the data. We show that incorrect noise variance estimates in registered diffusion-weighted images can affect DT parameters, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data, such as in relaxometry and functional MRI studies.

Algorithms↗
PubMed2005

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.

Algorithms↗
PubMed2005

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.

Algorithms↗
PubMed2005

PASTA: pointwise assessment of streamline tractography attributes.

Diffusion tensor MRI tractography aims to reconstruct noninvasively the 3D trajectories of white matter fasciculi within the brain, providing neuroscientists and clinicians with a potentially useful tool for mapping brain architecture. While this technique is widely used to visualize white matter pathways, the associated uncertainty in fiber orientation and artifacts have, to date, not been visualized in conjunction with the trajectory data. In this work, the bootstrap method was used to determine the distributions of diffusion indices such as trace and anisotropy, together with the uncertainty in fiber orientation. A novel visualization scheme was developed to encode this information at each point along reconstructed trajectories. By integrating these schemes into a graphical user interface, a new tool which we call PASTA (Pointwise Assessment of Streamline Tractography Attributes) was created to facilitate identification of artifacts in tractography that would otherwise go undetected.

Brain Mapping↗
PubMed2005

Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart.

The time dependence of the apparent diffusion tensor of ex vivo calf heart and tongue was measured for diffusion times (tau(d)) between 32 and 810 ms. The results showed evidence of restricted diffusion in the muscle tissues of both organs. In regions where the myofibers are parallel, the largest eigenvalue (lambda(1)) of the diffusion tensor remained the same for all diffusion times measured, while the other eigenvalues (lambda(2), lambda(3)) decreased by 29-36% between tau(d) = 32 ms and tau(d) = 400 ms. In regions where the fibers cross, the lambda(1) also changed, decreasing by 17% between tau(d) = 32 ms and tau(d) = 400 ms. The restricting compartment size and volume fraction were effectively estimated by fitting the time courses of the eigenvalues to a model consisting of a nonrestricted compartment and a cylindrically restricted compartment. To our knowledge, this study is the first demonstrating diffusion time dependence of measured water diffusion tensor in muscular tissue. With improvement in scanning technology, future studies may permit noninvasive, in vivo detection of changes in muscle myoarchitecture due to disease, treatment, and exercise.

Algorithms↗
PubMed2005

A diffusion tensor magnetic resonance imaging study of frontal cortex connections in very-late-onset schizophrenia-like psychosis.

OBJECTIVE: Onset of psychosis after the age of 60 may be associated with structural abnormalities within cerebral white matter. The authors looked within white-matter tracts, which mediate connectivity of the frontal lobes, in psychotic patients for evidence of loss of fiber integrity consistent with degenerative damage. METHODS: Fourteen patients with very-late-onset schizophrenia-like psychosis and an age-matched control group underwent diffusion tensor magnetic resonance imaging. Tract maps were constructed for each subject from the imaging data, and measurements of fractional anisotropy and mean diffusivity were made within the uncinate, superior longitudinal, and inferior occipito-frontal fasciculi, and the cingulum. RESULTS: There were no significant differences in fractional anisotropy, a measure of the ordering of axons within fiber tracts, nor in mean diffusivity, an orientationally-averaged measure of the bulk diffusivity within each voxel, between patients and control subjects. CONCLUSION: The lack of difference in fractional anisotropy and mean diffusivity measures between patients and controls argues against the presence of structural abnormalities within these tracts and the notion that a focal white-matter abnormality within the tracts investigated underpins the onset of psychosis.

Age of Onset↗