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P J Basser

Publications and source records attributed to P J Basser.

At least 19 recordsLinked to original sources
PubMed1998

Mechanical properties of the collagen network in human articular cartilage as measured by osmotic stress technique.

We have used an isotropic osmotic stress technique to assess the swelling pressures of human articular cartilage over a wide range of hydrations in order to determine from these measurements, for the first time, the tensile stress in the collagen network, Pc, as a function of hydration. Osmotic stress was applied by means of calibrated solutions of polyethylene glycol. Calculations of osmotic stress were based on the balance, at equilibrium, between the applied stress, the collagen stress, and the proteoglycan osmotic pressure, piPG, acting within the extrafibrillar matrix compartment. Pc vs hydration was determined for several normal human samples, both native and trypsin-treated, and for cartilage from one osteoarthritic (OA) joint. We found that for normal cartilage the collagen network does not become "limp" until the volume of cartilage has decreased by 20-25% of its initial value and that its contribution to the balance of forces in cartilage therefore must be taken into account over a much wider range of hydrations than was previously thought. For normal cartilage, the Pc vs hydration curves exhibit a steep increase with increasing hydration; trypsin treatment does not change their slope, showing that PG concentration does not influence the inherent stiffness of the collagen network. By contrast, the curves for OA specimens are considerably shallower and displaced to higher hydrations. Our findings thus highlight the role of the stiffness of the collagen network in limiting hydration in normal cartilage and ensuring a high PG concentration in the matrix, which is essential for effective load-bearing and is lost in OA.

Cartilage, Articular↗
PubMed1998

A simplified method to measure the diffusion tensor from seven MR images.

Analytical expressions of the diffusion tensor of water, D, and of scalar invariants derived from it, are given in terms of the intensities of seven diffusion-weighted images (DWIs). These formulas simplify the post-processing steps required in diffusion tensor imaging, including estimating D in each voxel (from the set of b-matrices and their corresponding DWIs), and then computing its eigenvalues, eigenvectors, and scalar invariants. In a study conducted using artifact-free DWIs with high diffusion weighting (bmax approximately 900 s/mm2, maps of Trace(D) and the Relative and Lattice Anisotropy indices calculated analytically and by multivariate linear regression showed excellent agreement in brain parenchyma of a healthy living cat. However, the quality of the analytically computed maps degraded markedly as diffusion weighting was reduced. Although diffusion tensor MRI with seven DWIs may be useful for clinical applications where rapid scanning and data processing are required, it does not provide estimates of the uncertainty of the measured imaging parameters, rendering it susceptible to noise and systematic artifacts. Therefore, care should be taken when using this technique in radiological applications.

Animals↗
PubMed1998

Anisotropically weighted MRI.

The intensity of an isotropically weighted MR image is proportional to a rotationally invariant measure of bulk diffusion, Trace(D) (where D is the effective diffusion tensor). Such images can be acquired from as few as two diffusion-weighted images (DWIs). Analogously, the intensity of an anisotropically weighted MR image is proportional to a rotationally invariant measure of diffusion anisotropy derived from D, such as the variance of the principal diffusivities of D. By using linear algebra, we show that to produce an anisotropically weighted MR image requires acquiring at least seven DWIs, which is also the minimum number of DWIs sufficient to estimate the entire diffusion tensor, as well as the T2-weighted amplitude image, A(b = 0), in each voxel. A general mathematical framework for constructing isotropically weighted and anisotropically weighted MR images is also provided.

Anisotropy↗
PubMed1997

The b matrix in diffusion tensor echo-planar imaging.

In diffusion tensor imaging (DTI) an effective diffusion tensor in each voxel is measured by using a set of diffusion-weighted images (DWIs) in which diffusion gradients are applied in a multiplicity of oblique directions. However, to estimate the diffusion tensor accurately, one must account for the effects of all imaging and diffusion gradient pulses on each signal echo, which are embodied in the b matrix. For DTI to be practical clinically, one must also acquire DWIs rapidly and free of motion artifacts, which is now possible with diffusion-weighted echo-planar imaging (DW-EPI). An analytical expression for the b matrix of a general DW-EPI pulse sequence is presented and then validated experimentally by measuring the diffusion tensor in an isotropic phantom whose diffusivity is already known. The b matrix is written in a convenient tabular form as a sum of individual pair-wise contributions arising from gradient pulses applied along parallel and perpendicular directions. While the contributions from readout and phase-encode gradient pulse trains are predicted to have a negligible effect on the echo, the contributions from other imaging and diffusion gradient pulses applied in both parallel and orthogonal directions are shown to be significant in our sequence. In general, one must understand and account for the multiplicity of interactions between gradient pulses and the echo signal to ensure that diffusion tensor imaging is quantitative.

Algorithms↗
PubMed1996

Toward a quantitative assessment of diffusion anisotropy.

Indices of diffusion anisotropy calculated from diffusion coefficients acquired in two or three perpendicular directions are rotationally variant. In living monkey brain, these indices severely underestimate the degree of diffusion anisotropy. New indices calculated from the entire diffusion tensor are rotationally invariant (RI). They show that anisotropy is highly variable in different white matter regions depending on the degree of coherence of fiber tract directions. In structures with a regular, parallel fiber arrangement, water diffusivity in the direction parallel to the fibers (Dparallel approximately 1400-1800 x 10(-6) mm2/s) is almost 10 times higher than the average diffusivity in directions perpendicular to them (D + D)/2 [corrected] approximately 150-300 x 10(-6) mm2/s), and is almost three times higher than previously reported. In structures where the fiber pattern is less coherent (e.g., where fiber bundles merge), diffusion anisotropy is significantly reduced. However, RI anisotropy indices are still susceptible to noise contamination. Monte Carlo simulations show that these indices are statistically biased, particularly those requiring sorting of the eigenvalues of the diffusion tensor based on their magnitude. A new intervoxel anisotropy index is proposed that locally averages inner products between diffusion tensors in neighboring voxels. This "lattice" RI index has an acceptably low error variance and is less susceptible to bias than any other RI anisotropy index proposed to date.

Animals↗
PubMed1996

Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI.

Quantitative-diffusion-tensor MRI consists of deriving and displaying parameters that resemble histological or physiological stains, i.e., that characterize intrinsic features of tissue microstructure and microdynamics. Specifically, these parameters are objective, and insensitive to the choice of laboratory coordinate system. Here, these two properties are used to derive intravoxel measures of diffusion isotropy and the degree of diffusion anisotropy, as well as intervoxel measures of structural similarity, and fiber-tract organization from the effective diffusion tensor, D, which is estimated in each voxel. First, D is decomposed into its isotropic and anisotropic parts, [D] I and D - [D] I, respectively (where [D] = Trace(D)/3 is the mean diffusivity, and I is the identity tensor). Then, the tensor (dot) product operator is used to generate a family of new rotationally and translationally invariant quantities. Finally, maps of these quantitative parameters are produced from high-resolution diffusion tensor images (in which D is estimated in each voxel from a series of 2D-FT spin-echo diffusion-weighted images) in living cat brain. Due to the high inherent sensitivity of these parameters to changes in tissue architecture (i.e., macromolecular, cellular, tissue, and organ structure) and in its physiologic state, their potential applications include monitoring structural changes in development, aging, and disease.

Animals↗
PubMed1996

Diffusion tensor MR imaging of the human brain.

PURPOSE: To assess intrinsic properties of water diffusion in normal human brain by using quantitative parameters derived from the diffusion tensor, D, which are insensitive to patient orientation. MATERIALS AND METHODS: Maps of the principal diffusivities of D, of Trace(D), and of diffusion anisotropy indices were calculated in eight healthy adults from 31 multisection, interleaved echo-planar diffusion-weighted images acquired in about 25 minutes. RESULTS: No statistically significant differences in Trace(D) (approximately 2,100 x 10(-6) mm2/sec) were found within normal brain parenchyma, except in the cortex, where Trace(D) was higher. Diffusion anisotropy varied widely among different white matter regions, reflecting differences in fiber-tract architecture. In the corpus callosum and pyramidal tracts, the ratio of parallel to perpendicular diffusivities was approximately threefold higher than previously reported, and diffusion appeared cylindrically symmetric. However, in other white matter regions, particularly in the centrum semiovale, diffusion anisotropy was low, and cylindrical symmetry was not observed. Maps of parameters derived from D were also used to segment tissues based on their diffusion properties. CONCLUSION: A quantitative characterization of water diffusion in anisotropic, heterogeneously oriented tissues is clinically feasible. This should improve the neuroradiologic assessment of a variety of gray and white matter disorders.

Adult↗
PubMed1994

Estimation of the effective self-diffusion tensor from the NMR spin echo.

The diagonal and off-diagonal elements of the effective self-diffusion tensor, Deff, are related to the echo intensity in an NMR spin-echo experiment. This relationship is used to design experiments from which Deff is estimated. This estimate is validated using isotropic and anisotropic media, i.e., water and skeletal muscle. It is shown that significant errors are made in diffusion NMR spectroscopy and imaging of anisotropic skeletal muscle when off-diagonal elements of Deff are ignored, most notably the loss of information needed to determine fiber orientation. Estimation of Deff provides the theoretical basis for a new MRI modality, diffusion tensor imaging, which provides information about tissue microstructure and its physiologic state not contained in scalar quantities such as T1, T2, proton density, or the scalar apparent diffusion constant.

Animals↗
PubMed1994

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 tissue's 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 tissue's 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.

Animals↗
PubMed1994

Focal magnetic stimulation of an axon.

The induced electric field produced by a circular coil during magnetic stimulation of an axon is derived from Maxwell's equations. The foci and virtual cathodal and anodal regions are predicted as a function of coil radius and orientation. Two virtual anode and cathode pairs are predicted, one lying outside the coil's perimeter and predominant in the far field, and one lying within the perimeter of the coil which may stimulate the axon when the coil and nerve are in close proximity. When the coil is positioned tangent to the nerve, an orientation commonly used in clinical magnetic stimulation, the foci of the predominant cathode and anode pair are extremely sensitive to changes in coil placement. In addition, the radius of curvature of the activating function, a measure of the size of the virtual cathode at threshold, is predicted to decrease with decreasing coil diameter and distance to the nerve. These predictions may help explain observed variability in measurements of conduction velocity and latency during magnetic stimulation of peripheral axons.

Axons↗
PubMed1994

A theoretical model for magneto-acoustic imaging of bioelectric currents.

A theoretical model of magneto-acoustic current imaging is derived, based on fundamental equations of continuum mechanics and electromagnetism. In electrically active tissue, the interaction between an applied magnetic field, B, and action currents, J, creates a pressure distribution. In the near field limit, this pressure obeys Poisson's equation, with a source term (delta x J).B. The displacement and pressure fields are calculated for a dipole (q), oriented either parallel or perpendicular to the applied magnetic field (B), at the center of an elastic, conducting sphere (radius a, shear modulus G). Surface displacements are on the order of qB/(4 pi Ga), which is about 1 nm for typical biological parameters. If the applied magnetic field is changing with time, eddy currents induced in the tissue may be larger than the action currents themselves. The frequency of the pressure and displacement arising from these eddy currents, however, is twice the frequency of the applied magnetic field, so it may be possible to eliminate this artifact by filtering or lock-in techniques. Magneto-acoustic and biomagnetic measurements both image delta x J in a similar way, although magneto-acoustic current imaging has the disadvantage that acoustic properties vary among tissues to a greater degree than do magnetic properties.

Acoustics↗
PubMed1993

Cable equation for a myelinated axon derived from its microstructure.

A simplified cable equation that describes the subthreshold behaviour of a myelinated axon is derived from its microstructure. Specifically, a microcontinuum cable model of a composite axon is homogenised, yielding a familiar macrocontinuum cable equation of electrotonus, for which the space and time constants depend on microstructural electrical parameters. Activating functions for magnetic and electrical stimulation can be incorporated into this homogenised cable equation as sources or sinks of transmembrane potential. An integral solution to the forced cable equation is also presented for the subthreshold regime. Errors are introduced when myelin membrane resistance is assumed to be infinite.

Axons↗
PubMed1993

The Donnan model derived from microstructure.

The ideal Donnan potential of an ionized polyelectrolyte medium is shown to be an approximate solution to a system of Poisson-Boltzmann (PB) equations for a periodic array of charged plates in an electrolyte bath. This result, derived using homogenization and scaling methods, demonstrates that the macrocontinuum, thermodynamic Donnan, and statistical mechanical PB models describe the same phenomenon: electrostatic repulsion between fixed-charged groups (albeit at different length scales). The Donnan approximation is accurate at low ionic strength (i.e., where the Debye length is much larger than the separation between charged plates), but is less faithful at physiologic and higher ionic strength. This work also provides a framework for relating theories of electrostatic repulsive interactions formulated at microscopic and macroscopic length scales.

Electrochemistry↗
PubMed1992

Interstitial pressure, volume, and flow during infusion into brain tissue.

A model of infusion-induced swelling in the brain is presented, in which gray and white matter are treated as poroelastic media. The distributions of interstitial pressure, flow, and volume are derived for steady-state and transient infusion protocols. A significant percentage increase in interstitial volume is predicted near the injection site, despite only a modest increase in tissue-averaged fluid content there. The model also can be used to estimate mechanical parameters of brain tissue, such as its hydraulic permeability, shear modulus, and Lamé constant. A solute transport equation that incorporates tissue swelling is also presented. This work suggests that knowing the distribution of swelling induced by infusion is a prerequisite to describing interstitial transport of solutes.

Animals↗
PubMed1992

Relevance of stimulus duration for activation of motor and sensory fibers: implications for the study of H-reflexes and magnetic stimulation.

Electric stimuli with durations of 0.5-1.0 msec are optimal for studies of H-reflexes. It is more difficult to obtain H-reflexes with shorter duration stimuli or with magnetic stimulation. In order to understand this behavior, we studied the excitation thresholds for motor and sensory fibers in the ulnar, median and tibial nerves using both electric and magnetic stimulation. For short duration electrical stimuli (0.1 msec) the threshold for motor fibers is lower than for sensory fibers. For longer duration electric stimuli (1.0 msec) the threshold for sensory fibers is lower. For magnetic stimulation the threshold for motor fibers is much lower than for sensory fibers. Thus, stimulus duration is a critical parameter for sensory fiber excitation, and current magnetic stimulators are not optimal.

Adult↗
PubMed1992

Determining the site of stimulation during magnetic stimulation of a peripheral nerve.

Magnetic stimulation has not been routinely used for studies of peripheral nerve conduction primarily because of uncertainty about the location of the stimulation site. We performed several experiments to locate the site of nerve stimulation. Uniform latency shifts, similar to those that can be obtained during electrical stimulation, were observed when a magnetic coil was moved along the median nerve in the region of the elbow, thereby ensuring that the properties of the nerve and surrounding volume conductor were uniform. By evoking muscle responses both electrically and magnetically and matching their latencies, amplitudes and shapes, the site of stimulation was determined to be 3.0 +/- 0.5 cm from the center of an 8-shaped coil toward the coil handle. When the polarity of the current was reversed by rotating the coil, the latency of the evoked response shifted by 0.65 +/- 0.05 msec, which implies that the site of stimulation was displaced 4.1 +/- 0.5 cm. Additional evidence of cathode- and anode-like behavior during magnetic stimulation comes from observations of preferential activation of motor responses over H-reflexes with stimulation of a distal site, and of preferential activation of H-reflexes over motor responses with stimulation of a proximal site. Analogous behavior is observed with electrical stimulation. These experiments were motivated by, and are qualitatively consistent with, a mathematical model of magnetic stimulation of an axon.

Adult↗
PubMed1992

The activating function for magnetic stimulation derived from a three-dimensional volume conductor model.

A three-dimensional volume conductor model of magnetic stimulation is proposed that relates transmembrane potential of an axon to the induced electric field in a uniform volume conductor. This model validates assumptions used to derive a one-dimensional cable model of magnetic stimulation (Roth & Basser, IEEE Trans. Biomed. Eng., vol. 37, pp. 588-597, 1990) of unmyelinated axons. The three-dimensional volume conductor model reduces to this one-dimensional cable equation forced by the activating function, -delta EzA/delta z.

Axons↗