Biomedical subjects

Peter J Basser

Publications and source records attributed to Peter J Basser.

At least 19 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

Anomalous small angle x-ray scattering determination of ion distribution around a polyelectrolyte biopolymer in salt solution.

The distribution of counterions in solutions of high molecular mass hyaluronic acid, in near-physiological conditions where mono- and divalent ions are simultaneously present, is studied by small angle neutron scattering and anomalous small angle x-ray scattering. The solutions contain either sodium or rubidium chloride together with varying concentrations of calcium or strontium chloride. The effects of monovalent-divalent ion exchange dominate the amplitude and the form of the counterion cloud. In the absence of divalent ions, the shape of the anomalous scattering signal from the monovalent ions is consistent with the distribution calculated from the Poisson-Boltzmann equation, as found by other workers. In mixtures of monovalent and divalent ions, however, as the divalent ion concentration increases, both the diameter and the amplitude of the monovalent ion cloud decrease. The divalent counterions always occupy the immediate neighborhood of the charged polyanion. Above a given concentration their anomalous scattering signal saturates. Even in a large excess of divalent ions, ion exchange is incomplete.

Chemistry, Physical↗

PubMed2006

Observation of anomalous diffusion in excised tissue by characterizing the diffusion-time dependence of the MR signal.

This report introduces a novel method to characterize the diffusion-time dependence of the diffusion-weighted magnetic resonance (MR) signal in biological tissues. The approach utilizes the theory of diffusion in disordered media where two parameters, the random walk dimension and the spectral dimension, describe the evolution of the average propagators obtained from q-space MR experiments. These parameters were estimated, using several schemes, on diffusion MR spectroscopy data obtained from human red blood cell ghosts and nervous tissue autopsy samples. The experiments demonstrated that water diffusion in human tissue is anomalous, where the mean-square displacements vary slower than linearly with diffusion time. These observations are consistent with a fractal microstructure for human tissues. Differences observed between healthy human nervous tissue and glioblastoma samples suggest that the proposed methodology may provide a novel, clinically useful form of diffusion MR contrast.

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

Analytically exact correction scheme for signal extraction from noisy magnitude MR signals.

An analytically exact method is proposed to extract the signal intensity and the noise variance simultaneously from noisy magnitude MR signals. This method relies on a fixed point formula of signal-to-noise ratio (SNR) and a correction factor. The correction factor, which is a function of SNR, establishes a fundamental link between the variance of the magnitude MR signal and the variance of the underlying Gaussian noise in the two quadrature channels. A more general but very similar method is developed for parallel signal acquisitions with multiple receiver coils. In the context of MR imaging, the proposed method can be carried out on a pixel-by-pixel basis if the mean and the standard deviation of the magnitude signal are available.

Algorithms↗

PubMed2006

Investigation of anomalous estimates of tensor-derived quantities in diffusion tensor imaging.

The diffusion tensor is typically assumed to be positive definite. However, noise in the measurements may cause the eigenvalues of the tensor estimate to be negative, thereby violating this assumption. Negative eigenvalues in diffusion tensor imaging (DTI) data occur predominately in regions of high anisotropy and may cause the fractional anisotropy (FA) to exceed unity. Two constrained least squares methods for eliminating negative eigenvalues are explored. These methods, the constrained linear least squares method (CLLS) and the constrained nonlinear least squares method (CNLS), are compared with other commonly used algebraic constrained methods. The CLLS tensor estimator can be shown to be equivalent to the linear least squares (LLS) tensor estimator when the LLS tensor estimate is positive definite. Similarly, the CNLS tensor estimator can be shown to be equivalent to the nonlinear least squares (NLS) tensor estimator when the NLS tensor estimate is positive definite. The constrained least squares methods for eliminating negative eigenvalues are evaluated with both simulations and in vivo human brain DTI data. Simulation results show that the CNLS method is, in terms of mean squared error for estimating trace and FA, the most effective method for correcting negative eigenvalues.

Anisotropy↗

PubMed2005

A model for diffusion in white matter in the brain.

Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging is a powerful noninvasive method to characterize neuronal tissue in the human brain in vivo. As a first step toward understanding the relationship between the measured macroscopic apparent diffusion tensor and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the apparent diffusion tensor and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for diffusion tensor imaging and for the possible in situ estimation of microstructural parameters from diffusion-weighted MR data are discussed in the context of this modeling framework.

Algorithms↗

PubMed2005

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.

Algorithms↗

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

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

Modeling diffusion in white matter in the brain: a composite porous medium.

We model diffusion in white matter fascicles as a problem of diffusion in an array of identical thick-walled cylindrical tubes immersed in an outer medium and arranged periodically in a regular lattice. The diffusing molecules have different diffusion coefficients and concentrations (or densities) within the tubes' inner core, membrane, myelin sheath, and within the outer medium. For an impermeable myelin sheath, diffusing molecules within the inner core are completely restricted, while molecules in the outer medium are hindered due to the tortuosity of the array of impenetrable tubes.

Animals↗

PubMed2004

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.

Animals↗

PubMed2004

"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 approximately 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 approximately 1000 s mm(-2)). Finally, we demonstrate a strategy for ameliorating the rectified noise artifact in data collected at higher b values.

Anisotropy↗

PubMed2004

Scaling laws for myelinated axons derived from an electrotonic core-conductor model.

A macroscopic cable equation, which describes the passive linear ("electrotonic") response of a myelinated axon, was previously derived from a segmented cable equation using Keller's two-space homogenization method [Basser, PJ, Med. and Biol. Comput., 1993, Vol. 31, pp. S87-S92]. Here we use the space and length constants of this averaged cable equation to predict classical scaling laws that govern relationships among the inner and outer diameters of the axon's myelin sheath and the distance separating adjacent nodes of Ranvier. These laws are derived by maximizing the characteristic speed of an electrical disturbance along the axon, i.e., the ratio of the characteristic length and the characteristic time constants of the macroscopic cable, subject to the constraint that the nodal width is constant. Using this result, it is also possible to show that all myelinated axons are equally fault tolerant. No free parameters were used in this analysis; all variables and physical constants used in these calculations were taken from published experimental data.

Action Potentials↗

PubMed2004

Adsorption of divalent cations on DNA.

The distribution of divalent ions in semidilute solutions of high-molecular-mass DNA containing both sodium chloride and strontium chloride in near-physiological conditions is studied by small-angle x-ray scattering and by small-angle neutron scattering. Both small-angle neutron scattering and small-angle x-ray scattering reveal a continuous increase in the scattering intensity at low q with increasing divalent ion concentration, while at high q the scattering curves converge. The best fit to the data is found for a configuration in which DNA strands of cross-sectional radius 10 angstroms are surrounded by a counterion sheath of outer radius approximately 13.8 angstroms, independent of the strontium chloride concentration. When the strontium chloride is replaced by calcium chloride, similar results are obtained, but the thickness of the sheath increases when the divalent salt concentration decreases. These results correspond in both cases to partial localization of the counterions within a layer that is thinner than the effective Debye screening length.

Adsorption↗

PubMed2003

Parametric and non-parametric statistical analysis of DT-MRI data.

In this work parametric and non-parametric statistical methods are proposed to analyze Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. A Multivariate Normal Distribution is proposed as a parametric statistical model of diffusion tensor data when magnitude MR images contain no artifacts other than Johnson noise. We test this model using Monte Carlo (MC) simulations of DT-MRI experiments. The non-parametric approach proposed here is an implementation of bootstrap methodology that we call the DT-MRI bootstrap. It is used to estimate an empirical probability distribution of experimental DT-MRI data, and to perform hypothesis tests on them. The DT-MRI bootstrap is also used to obtain various statistics of DT-MRI parameters within a single voxel, and within a region of interest (ROI); we also use the bootstrap to study the intrinsic variability of these parameters in the ROI, independent of background noise. We evaluate the DT-MRI bootstrap using MC simulations and apply it to DT-MRI data acquired on human brain in vivo, and on a phantom with uniform diffusion properties.

Artifacts↗

PubMed2003

The electric field induced in the brain by magnetic stimulation: a 3-D finite-element analysis of the effect of tissue heterogeneity and anisotropy.

We investigate the effect of tissue heterogeneity and anisotropy on the electric field and current density distribution induced in the brain during magnetic stimulation. Validation of the finite-element (FE) calculations in a homogeneous isotropic sphere showed that the magnitude of the total electric field can be calculated to within an error of approximately 5% in the region of interest, even in the presence of a significant surface charge contribution. We used a high conductivity inclusion within a sphere of lower conductivity to simulate a lesion due to an infarct. Its effect is to increase the electric field induced in the surrounding low conductivity region. This boost is greatest in the vicinity of interfaces that lie perpendicular to the current flow. For physiological values of the conductivity distribution, it can reach a factor of 1.6 and extend many millimeters from the interface. We also show that anisotropy can significantly alter the electric field and current density distributions. Either heterogeneity or anisotropy can introduce a radial electric field component, not present in a homogeneous isotropic conductor. Heterogeneity and anisotropy are predicted to significantly affect the distribution of the electric field induced in the brain. It is, therefore, expected that anatomically faithful FE models of individual brains which incorporate conductivity tensor data derived from diffusion tensor measurements, will provide a better understanding of the location of possible stimulation sites in the brain.

Anisotropy↗

PubMed2003

A normal distribution for tensor-valued random variables: applications to diffusion tensor MRI.

Diffusion tensor magnetic resonance imaging (DT-MRI) provides a statistical estimate of a symmetric, second-order diffusion tensor of water, D, in each voxel within an imaging volume. We propose a new normal distribution, p(D) alpha exp(-1/2 D: A: D), which describes the variability of D in an ideal DT-MRI experiment. The scalar invariant, D : A : D, is the contraction of a positive definite symmetric, fourth-order precision tensor, A, and D. A correspondence is established between D: A: D and the elastic strain energy density function in continuum mechanics--specifically between D and the second-order infinitesimal strain tensor, and between A and the fourth-order tensor of elastic coefficients. We show that A can be further classified according to different classical elastic symmetries (i.e., isotropy, transverse isotropy, orthotropy, planar symmetry, and anisotropy). When A is an isotropic fourth-order tensor, we derive an explicit analytic expression for p(D), and for the distribution of the three eigenvalues of D, p(gamma1, gamma2, gamma3), which are confirmed by Monte Carlo simulations. We show how A can be estimated from either real or synthetic DT-MRI data for any given experimental design. Here we propose a new criterion for an optimal experimental design: that A be an isotropic fourth-order tensor. This condition ensures that the statistical properties of D (and quantities derived from it) are rotationally invariant. We also investigate the degree of isotropy of several DT-MRI experimental designs. Finally, we show that the univariate and multivariate distributions are special cases of the more general tensor-variate normal distribution, and suggest how to generalize p(D) to treat normal random tensor variables that are of third- (or higher) order. We expect that this new distribution, p(D), should be useful in feature extraction; in developing a hypothesis testing framework for segmenting and classifying noisy, discrete tensor data; and in designing experiments to measure tensor quantities.

Algorithms↗