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At least 19 recordsLinked to original sources
PubMed2006

Diffusion anisotropy and diffusivity of white matter tracts within the temporal stem in Alzheimer disease: evaluation of the "tract of interest" by diffusion tensor tractography.

PURPOSE: Our aim was to determine whether diffusion anisotropy and diffusivity of white matter tracts of the temporal stem in patients with Alzheimer (AD) can be evaluated independently by using diffusion tensor tractography. MATERIALS AND METHODS: Subjects included 15 patients with AD (11 women and 4 men; mean age, 74 years) and 15 age-matched control subjects (11 women and 4 men; mean age, 72 years). Diffusion tensor images were acquired by using echo-planar imaging. We drew tractographies of the uncinate fasciculus, inferior occipitofrontal fasciculus, and Meyer's loop, with diffusion tensor analysis software. We measured diffusion anisotropy, diffusivity, and the number of voxels along the "tracts of interest" and used the Student t test to compare results between patients with AD and controls. RESULTS: Values of diffusion anisotropy of the bilateral uncinate fasciculus and left inferior occipitofrontal fasciculus were significantly lower for patients with AD than for controls. Also, values of diffusivity in the bilateral uncinate fasciculus were significantly greater for patients with AD than for controls. There was no significant difference in diffusion anisotropy or diffusivity along Meyer's loop between the 2 groups. There was no significant difference in the number of voxels included in all constructed tracts between patients with AD and controls. CONCLUSION: White matter tracts of the temporal stem can be evaluated independently by using diffusion tensor tractography, which appears to be a promising technique for determining changes in white matter in degenerative diseases.

Aged↗
PubMed1998

Analysis of fluorophore diffusion by continuous distributions of diffusion coefficients: application to photobleaching measurements of multicomponent and anomalous diffusion.

Fluorescence recovery after photobleaching (FRAP) is widely used to measure fluorophore diffusion in artificial solutions and cellular compartments. Two new strategies to analyze FRAP data were investigated theoretically and applied to complex systems with anomalous diffusion or multiple diffusing species: 1) continuous distributions of diffusion coefficients, alpha(D), and 2) time-dependent diffusion coefficients, D(t). A regression procedure utilizing the maximum entropy method was developed to resolve alpha(D) from fluorescence recovery curves, F(t). The recovery of multi-component alpha(D) from simulated F(t) with random noise was demonstrated and limitations of the method were defined. Single narrow Gaussian alpha(D) were recovered for FRAP measurements of thin films of fluorescein and size-fractionated FITC-dextrans and Ficolls, and multi-component alpha(D) were recovered for defined fluorophore mixtures. Single Gaussian alpha(D) were also recovered for solute diffusion in viscous media containing high dextran concentrations. To identify anomalous diffusion from FRAP data, a theory was developed to compute F(t) and alpha(D) for anomalous diffusion models defined by arbitrary nonlinear mean-squared displacement versus time relations. Several characteristic alpha(D) profiles for anomalous diffusion were found, including broad alpha(D) for subdiffusion, and alpha(D) with negative amplitudes for superdiffusion. A method to deduce apparent D(t) from F(t) was also developed and shown to provide useful complementary information to alpha(D). alpha(D) and D(t) were determined from photobleaching measurements of systems with apparent anomalous subdiffusion (nonuniform solution layer) and superdiffusion (moving fluid layer). The results establish a practical strategy to characterize complex diffusive phenomena from photobleaching recovery measurements.

Biophysical Phenomena↗
PubMed2003

Diffusion-weighted MR imaging with apparent diffusion coefficient and apparent diffusion tensor maps in cervical spondylotic myelopathy.

PURPOSE: To evaluate diffusion-weighted magnetic resonance (MR) imaging in patients with cervical spondylosis and/or myelopathy. MATERIALS AND METHODS: A multishot echo-planar imaging sequence with calculation of apparent diffusion coefficient (ADC) and apparent diffusion tensor (ADT) was applied in 36 patients with symptomatic cervical spondylosis. Diffusion-weighted images read by two neuroradiologists were compared with T2-weighted fast spin-echo images read independently by three neuroradiologists with regard to clinical status (n = 36). MR findings in a selected subgroup of 20 patients whose clinical status was confirmed by electrophysiologic examination also were compared. Sensitivity, specificity, positive predictive value, and negative predictive value of both T2-weighted imaging and diffusion-weighted imaging (ADC and ADT) were calculated and compared. RESULTS: Patients with myelopathy had abnormal ADC (17 of 21) and ADT (15 of 19) maps with increased ADC and ADT values and decreased anisotropy. For the detection of myelopathy, diffusion-weighted ADC maps had a sensitivity of 80% (17 of 21), while T2-weighted images had a sensitivity of 61% (13 of 21). The negative predictive value was 63% (seven of 11) and 60% (12 of 20) for ADC maps and T2-weighted images, respectively. Conversely, the specificity of diffusion-weighted images (53%; seven of 13) was lower than that of T2-weighted images (92%; 12 of 13). In patients with myelopathy confirmed at electrophysiologic examination, the sensitivity of diffusion-weighted images increased to 92% (12 of 13) and the negative predictive value increased to 75% (three of four), while T2-weighted images had a 53% (seven of 13) sensitivity and a 50% (six of 12) negative predictive value. CONCLUSION: Diffusion weighting improved the sensitivity of imaging in cervical spondylotic myelopathy.

Adult↗
PubMed2001

Utilizing the diffusion-to-noise ratio to optimize magnetic resonance diffusion tensor acquisition strategies for improving measurements of diffusion anisotropy.

It is well known that quantitative anisotropy measurements derived from the diffusion tensor are extremely sensitive to noise contamination. The level of noise in the diffusion tensor imaging (DTI) experiment is usually measured from some estimate of the signal-to-noise ratio (SNR) in the component diffusion-weighted (DW) images. This measure is, however, highly dependent on experimental parameters, such as the diffusion attenuation b-value and the diffusion coefficient of the subject. Conversely, the diffusion-to-noise ratio (DNR), defined as the SNR of the calculated diffusion tensor trace map, provides a reliable estimate of noise contamination, which is largely independent of such parameters. In this work it is demonstrated how reliable anisotropy measurements can be obtained using an image acquisition strategy that optimizes the DNR of the DTI experiment. This acquisition scheme is shown to provide noise-independent measurements of typical diffusion anisotropy values found in the human brain.

Anisotropy↗
PubMed2002

Diffuse axonal injury: detection of changes in anisotropy of water diffusion by diffusion-weighted imaging.

Myelinated axons of white matter demonstrate prominent directional differences in water diffusion. We performed diffusion-weighted imaging on ten patients with head injury to explore the feasibility of using water diffusion anisotropy for quantitating diffuse axonal injury. We showed significant decrease in diffusion anisotropy indices in areas with or without signal abnormality on T2 and T2*-weighted images. We conclude that the water diffusion anisotropy index a potentially useful, sensitive and quantitative way of diagnosing and assessing patients with diffuse axonal injury.

Adult↗
PubMed2006

Understanding diffusion MR imaging techniques: from scalar diffusion-weighted imaging to diffusion tensor imaging and beyond.

The complex structural organization of the white matter of the brain can be depicted in vivo in great detail with advanced diffusion magnetic resonance (MR) imaging schemes. Diffusion MR imaging techniques are increasingly varied, from the simplest and most commonly used technique-the mapping of apparent diffusion coefficient values-to the more complex, such as diffusion tensor imaging, q-ball imaging, diffusion spectrum imaging, and tractography. The type of structural information obtained differs according to the technique used. To fully understand how diffusion MR imaging works, it is helpful to be familiar with the physical principles of water diffusion in the brain and the conceptual basis of each imaging technique. Knowledge of the technique-specific requirements with regard to hardware and acquisition time, as well as the advantages, limitations, and potential interpretation pitfalls of each technique, is especially useful.

Body Water↗
PubMed2005

Lambert diffusion in porous media in the Knudsen regime: equivalence of self-diffusion and transport diffusion.

We study molecular diffusion in nanopores with different types of roughness under the exclusion of mutual molecular collisions, i.e., in the so-called Knudsen regime. We show that the diffusion problem can be mapped onto Levy walks and discuss the roughness dependence of the diffusion coefficients D(s) and D(t) of self- and transport diffusion, respectively. While diffusion is normal in d=3, diffusion is anomalous in d=2 with D(s) approximately ln t and D(t) approximately ln L, where t and L are time and system size, respectively. Both diffusion coefficients decrease significantly when the roughness is enhanced, in remarkable disagreement with earlier findings.

Journal Article↗
PubMed2003

Generalized diffusion tensor imaging and analytical relationships between diffusion tensor imaging and high angular resolution diffusion imaging.

A new method for mapping diffusivity profiles in tissue is presented. The Bloch-Torrey equation is modified to include a diffusion term with an arbitrary rank Cartesian tensor. This equation is solved to give the expression for the generalized Stejskal-Tanner formula quantifying diffusive attenuation in complicated geometries. This makes it possible to calculate the components of higher-rank tensors without using the computationally-difficult spherical harmonic transform. General theoretical relations between the diffusion tensor (DT) components measured by traditional (rank-2) DT imaging (DTI) and 3D distribution of diffusivities, as measured by high angular resolution diffusion imaging (HARDI) methods, are derived. Also, the spherical tensor components from HARDI are related to the rank-2 DT. The relationships between higher- and lower-rank Cartesian DTs are also presented. The inadequacy of the traditional rank-2 tensor model is demonstrated with simulations, and the method is applied to excised rat brain data collected in a spin-echo HARDI experiment.

Animals↗
PubMed1998

[Brain water diffusion coefficients and diffusion anisotropy in non-demented patients with diffuse leuko-araiosis].

PURPOSE: To investigate changes in both water diffusion coefficients and diffusion anisotropy in white matter of non-demented patients with leuko-araiosis using diffusion-weighted MRI. METHODS: Diffusion mapping was performed on 8 non-demented patients with leuko-araiosis, 6 patients with chronic cerebral infarction and 6 healthy volunteers, using a spin-echo sequence with motion probing gradient applied sequentially at two gradient strength settings in three orthogonal directions. The apparent diffusion coefficients (ADC) were calculated from 4 regions of interest located within the frontal and parietal subcortical white matter. The index of diffusion anisotropy (IDA) was calculated from the ADC in three orthogonal directions. (IDA = ADCmax-min/ADCmean x 100). RESULTS: Significantly larger ADC were found within the frontal and parietal subcortical white matter in the non-demented patients with leuko-araiosis (mean = 1.51 +/- 0.36 x 10(-3) mm2/s) and the were also significantly larger in patients with cerebral infarction (mean = 2.12 +/- 0.46 x 10(-3) mm2/s) than in the control group (mean = 1.01 +/- 0.33 x 10(-3) mm2/s). But no significant differences were found in the IDA between the non-demented patients with leuko-araiosis (mean = 43.1 +/- 29.2) and the control group (mean = 46.5 +/- 32.5). CONCLUSION: An increase in extracellular space caused by the loss of axonal fibers and myelin is probably the cause of the higher ADC in periventricular hyperintensity lesions. However, the remaining nerve fibers maintain the anisotropy in the lesions in non-demented patients with leuko-araiosis.

Aged↗
PubMed2006

Retrospective measurement of the diffusion tensor eigenvalues from diffusion anisotropy and mean diffusivity in DTI.

A simple theoretical framework to compute the eigenvalues of a cylindrically symmetric prolate diffusion tensor (D) from one of the rotationally-invariant diffusion anisotropy indices and average diffusivity is presented and validated. Cylindrical or axial symmetry assumes a prolate ellipsoid shape (lambdaparallel=lambda1>lambdaperpendicular=(lambda2+lambda3)/2; lambda2=lambda3). A prolate ellipsoid with such symmetry is largely satisfied in a number of white matter (WM) structures, such as the spinal cord, corpus callosum, internal capsule, and corticospinal tract. The theoretical model presented is validated using in vivo DTI measurements of rat spinal cord and human brain, where eigenvalues were calculated from both the set of diffusion coefficients and a tensor analysis. This method was used to retrospectively analyze literature data that reported tensor-derived average diffusivity, anisotropy, and eigenvalues, and similar eigenvalue measurements were obtained. The method provides a means to retrospectively reanalyze literature data that do not report eigenvalues. Other potential applications of this method are also discussed.

Adult↗
PubMed1999

Measurement of the apparent diffusion coefficient in diffuse renal disease by diffusion-weighted echo-planar MR imaging.

The purpose of this study was to determine the relationship between the apparent diffusion coefficient (ADC) and diffuse renal disease by diffusion-weighted echolanar magnetic resonance (MR) imaging (EPI). Thirty-four patients were examined with diffusion-weighted EPI. The average ADC values were 2.55 x 10(-3) mm2/sec for the cortex and 2.84 x 10(-3) mm2/sec for the medulla in the normal kidneys. The ADC values in both the cortex and medulla in chronic renal failure (CRF) kidneys and in acute renal failure (ARF) kidneys were significantly lower than those of the normal kidneys. In renal artery stenosis kidneys, the ADC values in the cortex were significantly lower than those of the normal and the contralateral kidneys. In the cortex, ADC values were above 1.8 x 10(-3) mm2/sec in all 32 normal kidneys, ranging from 1.6 to 2.0 x 10(-3) mm2/sec in all 8 ARF kidneys, and below 1.5 x 10(-3) mm2/sec in 14 of 15 CRF kidneys. In the medulla, there was considerable overlap in the ADC values of the normal and diseased kidneys. There was a linear correlation between ADC value and sCr level in the cortex (r = 0.75) and a weak linear correlation in the medulla (r = 0.60). Our results show that diffusion-weighted MR imaging may be useful to identify renal dysfunction.

Adolescent↗
PubMed1998

Normal brain in human newborns: apparent diffusion coefficient and diffusion anisotropy measured by using diffusion tensor MR imaging.

PURPOSE: To establish quantitative standards for the directionally averaged water apparent diffusion coefficient (D) and quantitative diffusion anisotropy (A sigma) of normal brains in newborns by using diffusion tensor magnetic resonance (MR) imaging. MATERIALS AND METHODS: Diffusion tensor MR imaging was performed during the first 36 hours of life in 22 newborns (gestational age range, 31-41 weeks). Values of D and A sigma were measured in regions of interest chosen in the cortical gray matter, centrum semiovale, caudate nuclei, lentiform nuclei, thalami, internal capsules, and cerebellar hemispheres. RESULTS: The D values in the gray and white matter in newborns are considerably higher than those in adults. There is a striking correlation between gestational age and D, with D decreasing as gestational age increases. The A sigma values in the white matter in newborns are lower than those in adults. Values of A sigma show statistically significant correlations with gestational age only in the white matter of the centrum semiovale, in which A sigma values increase sharply near term. CONCLUSION: The D values primarily reflect overall brain water content. The A sigma values are more sensitive to tissue microstructure (e.g., white matter packing and myelination). The D and A sigma images reveal information and not apparent on T1- and T2-weighted images.

Adult↗
PubMed1992

Diffuse Mallory bodies in the liver, diffuse Lewy bodies in the brain and diffuse fat replacement (lipomatous pseudohypertrophy) of the pancreas in a patient with juvenile Parkinson's disease.

A 38-year-old male patient with the juvenile variant of Parkinson's disease, in whom onset had occurred at the age of 24 yr, was autopsied. There were no clear symptoms of pancreatic or hepatic insufficiency during the entire clinical course. The only notable features were a slightly delayed decrease of the blood glucose level in an oral glucose tolerance test, slightly elevated levels of serum alkaline phosphatase and serum lactate dehydrogenase, and episodic loose stools. Autopsy revealed uniform enlargement of the pancreas due to massive fat replacement (lipomatous pseudohypertrophy): the exocrine glandular elements showed marked atrophy and loss, while the islets of Langerhans were preserved. The liver exhibited a histology closely mimicking alcoholic hepatitis associated with the diffuse presence of Mallory bodies (MBs), possibly indicative of a disturbance of protein metabolism. The nervous system showed the diffuse presence of Lewy bodies (LBs) in the cerebrum in addition to the ordinary lesions of Parkinson's disease. Although the etiopathogenesis of none of these three lesions has been well elucidated, common epitopes of MBs and LBs have recently been demonstrated. Therefore, the present case study suggests that a specific underlying toxic agent may cause diffuse LBs in the brain on the one hand, and diffuse MBs in the liver and lipomatous pseudohypertrophy of the pancreas on the other.

Adult↗
PubMed1975

Diffusing capacity, specific diffusing capacity and interpretation of diffusion defects.

Six pathophysiologic mechanisms of a reduced single breath CO diffusing capacity are discussed and the usefulness of relating carbon monoxide (CO) uptake to the functioning alveolar volume (DL/VA, specific diffusing capacity) is illustrated for several pulmonary diseases. In patients with emphysema and pulmonary emboli (pulmonary vascular occlusive disease), reduced CO uptake is associated with significantly reduced DL/VA and is compatible with reduction of pulmonary capillary bed. In patients with pulmonary alveolar proteinosis, improvement in CO uptake and DL/VA follows lung lavage and suggests that lung units partially filled with proteinaceous material are responsible for hypoxemia, reduced CO uptake and reduced DL/VA. In most cases of radiation fibrosis, sarcoidosis and miscellaneous interstitial fibrosis, reduced CO uptake is associated with a normal DL/VA and suggests that loss of alveolar units, both capillaries and alveoli, has occurred. New regression equations for DL and DL/VA are established for children and adults. DL/VA is linearly related to height and independent of age and sex, while different predictive equations must be used for DL for the 5 through 17 and 18 through 76 age groups. The new regression equations for DL show better correlation in adults we studied over 50 years of age than previous regression equations which use a constant reduction of 2 to 3 ml CO per minute per mm of mercury for each 10 years of adult aging.

Adolescent↗
PubMed1998

A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms.

Experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms are reviewed. Effective diffusive permeabilities, the parameter appropriate to the analysis of reaction-diffusion interactions, depend on solute type and biofilm density. Three categories of solute physical chemistry with distinct diffusive properties were distinguished by the present analysis. In order of descending mean relative effective diffusive permeability (De/Daq) these were inorganic anions or cations (0.56), nonpolar solutes with molecular weights of 44 or less (0.43), and organic solutes of molecular weight greater than 44 (0.29). Effective diffusive permeabilities decrease sharply with increasing biomass volume fraction suggesting a serial resistance model of diffusion in biofilms as proposed by Hinson and Kocher (1996). A conceptual model of biofilm structure is proposed in which each cell is surrounded by a restricted permeability envelope. Effective diffusion coefficients, which are appropriate to the analysis of transient penetration of nonreactive solutes, are generally similar to effective diffusive permeabilities in biofilms of similar composition. In three studies that examine diffusion of very large molecular weight solutes (>5000) in biofilms, the average ratio of the relative effective diffusion coefficient of the large solute to the relative effective diffusion coefficient of either sucrose or fluorescein was 0.64, 0.61, and 0.36. It is proposed that large solutes are effectively excluded from microbial cells, that small solutes partition into and diffuse within cells, and that ionic solutes are excluded from cells but exhibit increased diffusive permeability (but decreased effective diffusion coefficients) due to sorption to the biofilm matrix.

Biofilms↗
PubMed1996

Encoding of anisotropic diffusion with tetrahedral gradients: a general mathematical diffusion formalism and experimental results.

A diffusion imaging method with a tetrahedral sampling pattern has been developed for high-sensitivity diffusion analysis. The tetrahedral gradient pattern consists of four different combinations of x, y, and z gradients applied simultaneously at full strength to uniformly measure diffusion in four different directions. Signal-to-noise can be increased by up to a factor of about three using this approach, compared with diffusion measurements made using separately applied x, y, and z gradients. A mathematical formalism is presented describing six fundamental parameters: the directionally averaged diffusion coefficient D and diffusion element anisotropies eta and epsilon which are rotationally invariant, and diffusion ellipsoid orientation angles theta, phi, and omega which are rotationally variant. These six parameters contain all the information in the symmetric diffusion tensor D. Principal diffusion coefficients, reduced anisotropies, and other rotational invariants are further defined. It is shown that measurement of off-diagonal tensor elements is essential to assess anisotropy and orientation, and that the only parameter which can be measured with the orthogonal method is D. In cases of axial diffusion symmetry (e.g., fibers), the four tetrahedral diffusion measurements efficiently enable determination of D, eta, theta, and phi which contain all the diffusion information. From these four parameters, the diffusion parallel and perpendicular to the symmetry axis (D and D) and the axial anisotropy A can be determined. In more general cases, the six fundamental parameters can be determined with two additional diffusion measurements. Tetrahedral diffusion sequences were implemented on a clinical MR system. A muscle phantom demonstrates orientation independence of D, D, D, and A for large changes in orientation angles. Sample background gradients and diffusion gradient imbalances were directly measured and found to be insignificant in most cases.

Animals↗
PubMed2004

ISSLS prize winner: A study of diffusion in human lumbar discs: a serial magnetic resonance imaging study documenting the influence of the endplate on diffusion in normal and degenerate discs.

STUDY DESIGN: An in vivo serial magnetic resonance imaging study of diffusion characteristics in human lumbar discs over 24 hours in healthy volunteers and patients with low back pain. OBJECTIVES: To document the temporal pattern of diffusion in normal human lumbar discs and to study the influence of the vascularity of bone and the status of endplate on diffusion in the normal and degenerate discs. SUMMARY OF BACKGROUND DATA: Diffusion is the only source of nutrition to the discs, but no firm data are available on pattern of diffusion in humans. More data on this important subject are required to improve our understanding of disc degeneration and to probe research possibilities for preventing the same. METHODS: The diffusion pattern over 24 hours following gadodiamide injection was studied in 150 discs (96 normal and 54 degenerate). Signal intensity values for three regions of interest in bone (i.e., vertebral body, subchondral bone, and endplate zone) and seven in the disc were calculated, and normal percentiles of diffusion were derived for these regions. Enhancement percentage for each time period, peak enhancement percentage for each region, and the time taken to achieve peak enhancement percentage (Tmax) were used to define and compare diffusion characteristics and plot a time-intensity curve to document the 24-hour temporal pattern. The correlation of blood flow of the bone as measured by peak enhancement percentage of vertebral body, the status of the endplate zone as measured by the peak enhancement percentage, and Tmax of the endplate zone were correlated with the diffusion of the disc.Univariate analysis of variance, multiple comparisons, appropriate tests for significance, and stepwise linear regression analysis were used for analysis of the data using SPSS software. RESULTS: In normal discs, a "diffusion march" from the vertebral body to the center of disc was noted with the SImax being observed at 5 min in the vertebral body and subchondral bone, at 2 hours in the endplate zone, and at 6 hours in the nucleus pulposus. A significant difference in mean peak enhancement percentage was observed between that of the body and the discs in those less than 10 years and those above the age of 20 years (P < 0.001). Alterations in endplate zone produced distinct magnetic resonance imaging signs of disturbance in diffusion, which offered a reliable noninvasive method of identifying endplate cartilage damage. Stepwise linear regression analysis showed that the significant variable influencing diffusion to the center of the nucleus pulposus of the total sample was peak enhancement percentage of endplate zone (R2 = 0.216; P < 0.001), that of degenerate discs was peak enhancement percentage of endplate zone (R2 = 0.322; P < 0.001), and that of normal discs (R2 = 0.324; P < 0.001) was age. CONCLUSIONS: Serial postcontrast magnetic resonance imaging studies offer a reliable method of assessing the diffusion of the discs and the functional status of the endplate cartilage. Endplate cartilage damage increases with age and produces considerable changes in diffusion. The present study has described reliable signs by which these damages can be identified in vivo. Aging and degeneration have been shown to be two separate processes by documenting clear-cut differences in diffusion. The present data encourage use of diffusion studies as a noninvasive method to assess the physiologic status of the disc and endplate and to study the effect of drugs, smoking, mechanical loading, exercises, etc. on the physiology of the disc.

Adolescent↗
PubMed2003

Definition of displacement probability and diffusion time in q-space magnetic resonance measurements that use finite-duration diffusion-encoding gradients.

In q-space diffusion NMR, the probability P(r,td) of a molecule having a displacement r in a diffusion time td is obtained under the assumption that the diffusion-encoding gradient g has an infinitesimal duration. However, this assumption may not always hold, particularly in human MRI where the diffusion-encoding gradient duration delta is typically of the same order of magnitude as the time offset Delta between encoding gradients. In this case, finite-delta effects complicate the interpretation of displacement probabilities measured in q-space MRI, and the form by which the signal intensity relates to them. By considering the displacement-specific dephasing, , of a set of spins accumulating a constant displacement vector r in the total time Delta+delta during which diffusion is encoded, the probability recovered by a finite-delta q-space experiment can be interpreted. It is shown theoretically that a data analysis using a modified q-space index q=gammadeltaetag, with gamma the gyromagnetic ratio and eta=square root (Delta-delta/3)/(Delta+delta), recovers the correct displacement probability distribution if diffusion is multi-Gaussian free diffusion. With this analysis, we show that the displacement distribution P(r,texp) is measured at the experimental diffusion-encoding time texp=Delta+delta, and not at the reduced diffusion time tr=Delta-delta/3 as is generally assumed in the NMR and MRI literature. It is also shown that, by defining a probability P(y,Delta) that a time t deltac then eta is not equal to square root (Delta-delta/3)/(Delta+delta) which implies that we can no longer obtain the correct displacement probability from the displacement distribution. In the case that /g/=18 mT/m and Delta-delta=5 ms, the parameter deltac in ms is given by "deltac=0.49a2+0.24" where a is the sphere's radius expressed in microm. Simulation of q-space restricted diffusion MRI experiments indicate that if eta=square root (Delta-delta/3)/(Delta+delta), the recovered displacement probability is always better than the Gaussian approximation, and the measured diffusion coefficient matches the diffusion coefficient at time texp=Delta+delta better than it matches the diffusion coefficient at time tr=Delta-delta/3. These results indicate that q-space MRI measurements of displacement probability distributions are theoretically possible in biological tissues using finite-duration diffusion-encoding gradients provided certain compartment size and diffusion encoding gradient duration constraints are met.

Journal Article↗