Diffusion Weighted Imaging In MS

  1. Diffusion Tensor Imaging of post mortem Multiple Sclerosis Brain
    NeuroImage 2007 Apr 1;35(2):467-77

  2. Diffusion-Tensor Magnetic Resonance Imaging detects Normal-Appearing White Matter damage unrelated to short-term disease activity in patients at the earliest clinical stage of Multiple Sclerosis
    Arch Neurol 2005 May;62(5):803-8

  3. Diffusion-weighted MR of the brain: methodology and clinical application
    Radiol Med (Torino) 2005 Mar;109(3):155-97

  4. White Matter T1 relaxation time Histograms and Cerebral Atrophy in Multiple Sclerosis
    J Neurol Sci 2002 May 15;197(1-2):45-50

  5. MR-based technology for in vivo detection, characterization, and quantification of pathology of Relapsing/Remitting Multiple Sclerosis
    J Rehabil Res Dev 2002 Mar-Apr;39(2):243-59

  6. Overview of Diffusion-weighted Magnetic Resonance studies in Multiple Sclerosis
    J Neurol Sci 2001 May 1;186 Suppl 1:S37-43

  7. Investigation of MS Normal-Appearing Brain using Diffusion Tensor MRI with clinical correlations
    Neurology 2001 Apr 10;56(7):926-33

  8. Diffusion tensor imaging: Concepts and applications
    J Magn Reson Imaging 2001 Apr;13(4):534-546

  9. Diffusion Tensor Magnetic Resonance Imaging in Multiple Sclerosis
    Neurology 2001 Feb 13;56(3):304-311

  10. Magnetization Transfer and Diffusion Tensor MR imaging of Basal Ganglia in Multiple Sclerosis
    J Neurol Sci 2001 Jan 15;183(1):69-72

  11. The PathoGenesis of lesions and Normal-Appearing White Matter changes in Multiple Sclerosis
    Brain 2000 Aug;123(Pt 8):1667-1676

  12. A quantitative study of water diffusion in Multiple Sclerosis lesions and Normal-Appearing White Matter using echo-planar imaging
    Arch Neurol 2000 Jul;57(7):1017-1021

  13. Whole-Brain Diffusion MR Histograms differ between MS subtypes
    Neurology 2000 Apr 11;54(7):1421-7

  14. Diffusion imaging of the Spinal Cord in vivo: Estimation of the principal diffusivities and application to Multiple Sclerosis
    Magn Reson Med 2000 Jan;43(1):133-8

  15. Diffusion imaging of the Spinal Cord in vivo: estimation of the principal diffusivities and application to Multiple Sclerosis
    Magn Reson Med 2000 Jan;43(1):133-8

  16. Diffusion tensor imaging of lesions and Normal-Appearing White Matter in Multiple Sclerosis
    Neurology 1999 May 12;52(8):1626-32

  1. Diffusion time dependence of the apparent Diffusion Tensor in healthy human Brain and White Matter Disease
    Magn Reson Med 2001 Jun;45(6):1126-1129

  2. Mean diffusivity and Fractional Anisotropy Histograms of MS
    AJNR Am J NeuroRadiol 2001 May;22(5):952-8

  3. Weekly Diffusion-weighted imaging of NAWM in MS
    Neurology 2000 Sep 26;55(6):882-4

  4. A quantitative study of water Diffusion in Multiple Sclerosis lesions and Normal-Appearing White Matter using Echo-Planar imaging
    Arch Neurol 2000 Jul;57(7):1017-21

  5. DeMyelinating plaques in R/R and S/P Multiple Sclerosis: assessment with Diffusion MR imaging
    AJNR Am J NeuroRadiol 2000 May;21(5):862-8

  6. Multiple Sclerosis: comparison of trace Apparent Diffusion Coefficients with MR enhancement pattern of lesions
    AJNR Am J NeuroRadiol 2000 May;21(5):869-74

  7. Pathologic damage in MS assessed by Diffusion-weighted and Magnetization Transfer MRI
    Neurology 2000 Mar 14;54(5):1139-44

  8. Water Diffusion is elevated in widespread regions of Normal-Appearing White Matter in Multiple Sclerosis and correlates with Diffusion in focal lesions
    Mult Scler 2001 Apr;7(2):83-9

  9. Quantitative Diffusion weighted MRI, Cerebral atrophy, and disability in Multiple Sclerosis
    J Neurol NeuroSurg Psychiatry 2001 Mar;70(3):318-22

  10. Analysis of Normal-Appearing White Matter in Multiple Sclerosis: comparison of Diffusion Tensor MR imaging and Magnetization Transfer imaging
    AJNR Am J NeuroRadiol 2001 Nov-Dec;22(10):1893-900

  11. Intra-voxel and inter-voxel Coherence in Multiple Sclerosis assessed using Diffusion Tensor MRI
    J Neurol 2002 Jul;249(7):875-83

  12. A normal distribution for Tensor-valued random variables: applications to Diffusion Tensor MRI
    IEEE Trans Med Imaging 2003 Jul;22(7):785-94







#1

Diffusion Time Dependence Of The Apparent Diffusion Tensor In Healthy Human Brain And White Matter Disease

Clark CA, Hedehus M, Moseley ME
Magn Reson Med 2001 Jun;45(6):1126-1129
Lucas MRSI Center, Stanford, California
PMID# 11378893
Abstract

The Diffusion time dependence of the Brain water Diffusion Tensor provides information regarding Diffusion restriction and hindrance.

But has received little attention, primarily due to limitations in gradient amplitude available on clinical MRI systems, required to achieve short Diffusion times.

Using new, more powerful gradient hardware, the Diffusion time dependence of Diffusion Tensor-derived metrics were studied in human Brain in the range 8-80 ms, which encompasses the shortest Diffusion times studied to date.

There was no evidence for a change in Mean Diffusivity, Fractional Anisotropy, or in the EigenValues with Diffusion time in healthy human Brain.

The findings are consistent with a model of unrestricted, but hindered water Diffusion with semipermeable membranes, likely originating from the ExtraCellular Space in which the average ExtraCellular separation is less than 7 microns.

Similar findings in two Multiple Sclerosis plaques indicated that the size of the water Diffusion Space in the lesion did not exceed this dimension.

Copyright 2001 Wiley-Liss, Inc.



#2

Mean Diffusivity And Fractional Anisotropy Histograms Of Multiple Sclerosis

Cercignani M, Inglese M, Pagani E, Comi G, Filippi M
AJNR Am J NeuroRadiol 2001 May;22(5):952-8
Scientific Institute, Ospedale San Raffaele, NeuroImaging Research Unit, and Clinical Trials Unit; and Univ Milan, Dept of NeuroScience, Milan, Italy
PMID# 11337342; UI# 21234674
Abstract

Background And Purpose
Compared with conventional T2-weighted MR imaging, Diffusion Tensor MR imaging provides quantitative indices with increased specificity to the most destructive aspects of Multiple Sclerosis.

In this study, we obtained Brain Mean Diffusivity (D) and Fractional Anisotropy Histograms of patients with Multiple Sclerosis to compare them with those of healthy volunteers.

And to investigate the correlation between Diffusion Tensor MR imaging Histogram-derived measures and the level of Disability and quantities derived from conventional MR imaging.

Methods
Dual-Echo and Diffusion Tensor MR images were obtained from 78 patients with Relapsing/Remitting, Secondary/Progressive, or Primary/Progressive Multiple Sclerosis and from 20 healthy control volunteers.

After obtaining Mean Diffusivity D and Fractional Anisotropy images and image coregistration, and Fractional Anisotropy Histograms were created. From each Histogram, the following measures were derived:

  1. Average and Fractional Anisotropy
  2. Histogram peak heights
  3. Histogram peak locations

Results
All the Mean Diffusivity D and Fractional Anisotropy Histogram-derived measures were different between patients and controls at a significance level of P <.001.

No differences were found in any of the considered quantities among the three Multiple Sclerosis phenotypes.

In patients with Relapsing/Remitting Multiple Sclerosis, disability was correlated with Histogram average (r = 0.4, P =.01) and peak height (r = -0.4, P =.01).

In patients with Secondary/Progressive Multiple Sclerosis, disability was correlated with Fractional Anisotropy Histogram peak position (r = -0.6, P =.01).

Significant correlations were also found between T2 Lesion Load and various Diffusion Tensor MR quantities.

Conclusion
This study shows that Brain and Fractional Anisotropy Histograms are different for patients with Multiple Sclerosis compared with control volunteers.

This study also shows that quantities derived from Diffusion Tensor MR imaging are correlated with Disability in patients with Relapsing/Remitting Multiple Sclerosis and Secondary/Progressive Multiple Sclerosis.

Suggesting that they might serve as additional measures of outcome when monitoring Multiple Sclerosis evolution in these patients.



#3

Weekly Diffusion-Weighted Imaging Of Normal-Appearing White Matter In MS

Rocca MA, Cercignani M, Iannucci G, Comi G, Filippi M
Neurology 2000 Sep 26;55(6):882-4
Scientific Institute, Ospedale San Raffaele, NeuroImaging Research Unit; and Univ of Milan, Dept of NeuroScience, Milan, Italy
PMID# 10994017; UI# 20451195
Abstract

To elucidate the dynamics and the nature of Normal-Appearing White Matter (NAWM) changes preceding new Lesion formation in MS, the authors obtained weekly Diffusion-weighted images for 12 weeks from 6 patients.

NAWM areas subsequently involved by enhancement had a significant increase in mean Diffusivity values starting 6 weeks before the appearance of enhancement (p values ranging between < 0.0001 and 0.04).

This suggests that focal Edema and DeMyelination play a part in the NAWM changes preceding new lesion formation in MS.



#4

A Quantitative Study Of Water Diffusion In Multiple Sclerosis Lesions And Normal-Appearing White Matter Using Echo-Planar Imaging

Filippi M, Iannucci G, Cercignani M, Assunta Rocca M, Pratesi A, Comi G
Arch Neurol 2000 Jul;57(7):1017-21
Scientific Institute, Ospedale San Raffaele, NeuroImaging Research Unit, Dept of NeuroScience, Via Olgettina, 60, 20132 Milan, Italy
PMID# 10891984, UI# 20351956
Abstract

Objectives
We used an optimized Echo-Planar pulse sequence for IsoTropically weighted Diffusion imaging to:

  1. Measure Mean Diffusivity (D) in lesions and Normal-Appearing White Matter (NAWM) in the entire Brain from patients with mildly disabling Relapsing/Remitting Multiple Sclerosis (MS)

  2. Compare the D of NAWM from patients with that of White Matter from normal controls

  3. Evaluate whether lesions classified on the basis of their appearance on enhanced T1-weighted scans have different D

  4. Investigate the relationship between Diffusion changes in lesions and NAWM

Methods
Dual-Echo and Diffusion-weighted scans were obtained from 35 patients with Relapsing/Remitting MS and 24 sex- and age-matched normal controls.

Postcontrast T1-weighted images were also obtained from the patients. After creating D maps and image coregistration, D values were measured for MS lesions larger than 5 mm and for 22 NAWM areas from each subject.

Results
All NAWM areas studied had significantly higher D in patients than in controls. A total of 173 lesions were identified on the Dual-Echo scans from patients.

The average D for these lesions was significantly higher than that of NAWM. Twenty-two lesions were enhancing and 60 were classified as T1-HypoIntense.

No significant difference in D values was found between enhancing and nonenhancing lesions, while the average D of T1-HypoIntense lesions was significantly higher than the average D of T1-IsoIntense lesions.

There was no significant correlation between the average D in lesions and NAWM.

Conclusions
This study shows that Diffusion-weighted imaging is able to identify MS lesions with severe tissue disruption.

It also shows that widespread increased Diffusion can be measured in the NAWM from patients with MS, and suggests that such changes are, at least partially, independent of larger abnormalities.



#5

DeMyelinating Plaques In R/R And S/P Multiple Sclerosis: Assessment With Diffusion MR Imaging

Scanderbeg AC, Tomaiuolo F, Sabatini U, Nocentini U, Grasso MG, Caltagirone C
AJNR Am J NeuroRadiol 2000 May;21(5):862-8
Dept of Radiology, S. Lucia, Rome, Italy
PMID# 10815661; UI# 20273083
Abstract

Background
Conventional MR imaging does not provide specific information that can be reliably associated with the pathologic substrate and clinical status of patients with Multiple Sclerosis (MS).

    Our goals were:
  1. To determine whether the Orientationally averaged water Diffusion coefficient (<D>) can be used to distinguish between Plaques of different severity in these patients

  2. To assess possible correlations between <D> values and disease duration, Expanded Disability Status Scale (EDSS) score, and signal intensity on T1-weighted MR images.

Methods
Twenty patients (10 with Relapsing/Remitting MS and 10 with Secondary/Progressive MS) and 11 healthy volunteers underwent a combined conventional and Diffusion-weighted MR study of the Brain.

<D>, a parameter that is proportional to the trace of the Diffusion Tensor, was computed by averaging the Apparent Diffusion Coefficients measured in the x, y, and z directions.

<D> measurements were obtained for selected areas of White Matter Plaques. Differences in <D> among the three groups were tested using analysis of variance.

Results
<D> was significantly higher (1.445 +/- 0.129 x 10(-3) mm2/s) in Secondary/Progressive lesions than in Relapsing/Remitting lesions (0.951 +/- 0.08), and both values were higher than <D> in normal White Matter (0.732 +/- 0.02).

There was a significant negative correlation between <D> and the degree of HypoIntensity on T1-weighted images, and a positive correlation between <D> and both EDSS score and disease duration.

Conclusions
Our findings suggest that <D> is useful for distinguishing MS Lesions of different severities, which are associated with different degrees of clinical Disability.



#6

Multiple Sclerosis: Comparison Of Trace Apparent Diffusion Coefficients With MR Enhancement Pattern Of Lesions

Roychowdhury S, Maldjian JA, Grossman RI
AJNR Am J NeuroRadiol 2000 May;21(5):869-74
Hospital of the Univ of Pennsylvania, Dept of Radiology, Philadelphia, Pennsylvania 19104, USA
PMID# 10815662; UI# 20273084
Abstract

Background And Purpose
Diffusion-weighted MR imaging and the trace Apparent Diffusion Coefficient (ADC) provide important structural information about tissues.

The purpose of this study was to investigate the relationship between trace ADC values and the enhancement pattern of Multiple Sclerosis (MS) Lesions.

Methods
Ninety-six lesions, identified in 24 patients with MS, were characterized by their enhancement pattern on contrast-enhanced T1-weighted MR images.

    There were:
  • 57 NonEnhancing Lesions (NELs)
  • 28 Homogeneously Enhancing Lesions (HELs)
  • 11 Ring-Enhancing Lesions (RELs)

The trace ADC means for each type of lesion and for Normal-Appearing White Matter (NAWM) were calculated and compared using Student's t-test.

Results
The mean trace ADC values for HELs (mean, 7.7 x 1(-10) m2s (-1); SD, 1.4 x 10(-10) m2s (-1)) were less than those for RELs (mean, 1.2 x 10(-9) m2s (-1); SD, 3.5 x 10(-10)m2s (-1)) and NELs (mean, 1.3 x 10(-9) m2(s-1); SD, 2.6 x 10(-10) m2(s-1)).

There was a significant difference between the mean trace ADC values of HELs and RELs as well as between those for HELs and NELs.

There was also a significant difference in the mean trace ADC values between all lesion types and NAWM (mean, 6.9 x 10(-10) m2s (-1); SD, 5.0 x 10(-11) m2s (-1)).

Conclusion
We found a predictable relationship between mean trace ADC and the pattern of enhancement in MS Lesions, corresponding to reported HistoPathologic differences in Myelination between lesion types and Magnetization Transfer Ratios.



#7

Pathologic Damage In MS Assessed By Diffusion-Weighted And Magnetization Transfer MRI

Cercignani M, Iannucci G, Rocca MA, Comi G, Horsfield MA, Filippi M
Neurology 2000 Mar 14;54(5):1139-44
Scientific Institute, Ospedale San Raffaele, Univ of Milan, Dept of NeuroScience, Milan, Italy
PMID# 10720288; UI# 20183230
Abstract

Objective
To compare Diffusion characteristics of MS lesions, Normal-Appearing White Matter (NAWM) from patients, and normal White Matter from control subjects.

And to investigate the correlations between the Magnetization Transfer Ratio (MTR) and a directionally averaged tissue water Diffusion Coefficient (D) in patients.

Background
MS and other pathologic processes that modify tissue integrity can result in abnormal Diffusion of water molecules detectable by Diffusion-Weighted Imaging (DWI).

Methods
Conventional Dual-Echo and DWI scans were obtained from 35 patients with Relapsing/Remitting MS and 24 healthy control subjects.

MT scans were also obtained from the patients. After coregistration of all scans, MTR and D values from MS lesions and NAWM in different regions were marked using the Dual-Echo scans as a reference.

D values from the same Brain regions in control subjects were acquired. Histograms of MTR and D were also produced.

Results
Patients with MS had significantly higher D values in all the areas studied.

Moreover, Histogram metrics (peak height, peak site, and average D) from patients were substantially different from those of control subjects.

In patients, average lesion D and MTR were markedly different from those in the NAWM.

There was an inverse correlation between average lesion MTR and D inside lesions, whereas no correlation was found for average MTR and D taken from the Histograms.

Conclusions
DWI detects severe tissue disruption inside lesions and subtle widespread abnormalities in NAWM in patients with Relapsing/Remitting MS. MT and DWI may provide information about different aspects of Brain pathology in MS.



#8

Water Diffusion Is Elevated In Widespread Regions Of Normal-Appearing White Matter In Multiple Sclerosis And Correlates With Diffusion In Focal Lesions

Werring DJ, Clark CA, Droogan AG, Barker GJ, Miller DH, Thompson AJ
Mult Scler 2001 Apr;7(2):83-9
Institute of Neurology, NMR Research Unit, Queen Square, London WC1N 3BG, UK
PMID# 11424636; UI# 21318354
Abstract

Pathological changes in the Normal-Appearing White Matter in Multiple Sclerosis are well recognized, but their relationship to pathology in Focal lesions is not well understood.

Magnetic Resonance Diffusion Imaging is sensitive to abnormalities in the integrity, size and geometry of water spaces in Brain tissue.

This study investigated the anatomical distribution of Normal-Appearing White Matter Diffusion abnormalities and their relationship to Diffusion in Focal lesions in Multiple Sclerosis (MS).

The average Apparent Diffusion Coefficient (ADCav) was measured by Three-Axis EchoPlanar Diffusion Imaging in Normal-Appearing White Matter regions.

And lesions throughout the Brain in 40 patients, and in White Matter in 14 matched controls.

The correlation between the ADCav in Normal-Appearing White Matter and Lesions was determined. In controls and patients, Diffusion was highest in the Corpus Callosum.

Patients had a higher mean ADCav than controls in widespread regions including the Corpus Callosum, Cerebellar, Temporal and Occipital Normal-Appearing White Matter.

Mean Normal-Appearing White Matter ADCav correlated strongly with mean lesion ADCav (r = 0.67, P < 0.001).

This study demonstrates that water Diffusion is elevated in widespread areas of Normal-Appearing White Matter in MS, and is correlated with Diffusion in Lesions.

These findings suggest that the PathoGenetic mechanisms causing tissue damage in lesions and Normal-Appearing White Matter are at least partly linked.



#9

Diffusion Weighted Magnetic Resonance Imaging, Cerebral Atrophy, And Disability In Multiple Sclerosis

Wilson M, Morgan PS, Lin X, Turner BP, Blumhardt LD
J Neurol NeuroSurg Psychiatry 2001 Mar;70(3):318-22
Queen's Medical Centre, Univ Hospital, Faculty of Medicine, Division of Clinical Neurology, Nottingham NG7 2UH, UK
PMID# 11181852; UI# 21103986
Abstract

Objectives
To investigate the relations between quantitative Diffusion Coefficient MRI Histograms, clinical variables, and Brain Atrophy.

Methods
Twenty two patients with Clinically Definite Multiple Sclerosis and 11 healthy volunteers were studied.

Histograms of Apparent Diffusion Coefficient (ADC) from a volume of interest that included multiple slices encompassing the Lateral Ventricles were processed from Diffusion weighted MRI.

In addition, total lesion load was measured on T2 weighted Dual Echo images, and Cerebral volume from 3D Magnetization prepared Rapid Acquisition Gradient Echo scans.

All patients underwent Neurological assessment, including disability on the Expanded Disability Status Scale (EDSS).

Results
Histograms from the patient group showed a reduced peak height and a "right shift" compared with healthy controls.

Peak height of the Diffusion Histogram correlated with both EDSS (r=-0.54, p=0.0101) and disease duration (r=-0.52, p=0.0140), but not with age.

Brain Volume correlated with peak height of the ADC Histogram (r=0.55, p=0.0129), but not with disability. Total Lesion Load also correlated moderately with EDSS (r=0.46, p=0.03).

Conclusions
This study shows for the first time that quantitative MRI measures of Diffusion correlate with clinical variables (disability, disease duration) and Brain Atrophy in Multiple Sclerosis.

Cerebral Atrophy and fixed Neurological deficit may be attributed to Axonal Loss, which would be expected to have a significant effect on ADC.

Extension of this method to more patients and longitudinal studies will further elucidate its sensitivity, reproducibility, and potential role in clinical practice and treatment trials.



#10

Analysis Of Normal-Appearing White Matter In Multiple Sclerosis: Comparison Of Diffusion Tensor MR Imaging And Magnetization Transfer Imaging

Guo AC, Jewells VL, Provenzale JM
AJNR Am J NeuroRadiol 2001 Nov-Dec;22(10):1893-900
Duke University Medical Center, Department of Radiology, Durham 27710, NC, USA
PMID# 11733323
Abstract

Background And Purpose
Our purpose was to compare Diffusion Tensor MR and Magnetization Transfer imaging in assessing Normal-Appearing White Matter (NAWM) regions in Multiple Sclerosis (MS).

Methods
Diffusion Tensor, Magnetization Transfer, and conventional MR imaging were performed in 12 patients with MS.

Fractional Anisotropy, Apparent Diffusion Coefficients (ADCs), and Magnetization Transfer Ratios (MTRs) were measured in plaques, Normal-Appearing PeriPlaque WM (PWM) regions, and Normal-Appearing WM regions remote from plaques.

Mean Fractional Anisotropy, ADCs, and MTRs were calculated and compared in WM regions.

Results
Fractional Anisotropy was lower in Normal-Appearing PWM regions than in remote WM regions (P < .001) but higher than in plaques (P < .001).

MTRs were lower (not significantly, P =.19) in Normal-Appearing PWM regions than in remote regions. MTRs were higher in Normal-Appearing PWM regions than in Plaques (P < .001).

ADCs were higher in Normal-Appearing PWM regions than in remote regions (P =.008) but lower than in Plaques (P =.001).

Correlation between Fractional Anisotropy and MTRs of individual Lesions was poor (r = 0.18) and between Fractional Anisotropy and ADC, modest (r = -0.39).

Conclusion
In MS, Diffusion Tensor MR imaging can depict differences between WM regions that are not apparent on conventional MR images.

Anisotropy measurements may be more sensitive than those of MTRs in detecting subtle abnormalities in PWM.



#11

Intra-Voxel And Inter-Voxel Coherence In Multiple Sclerosis Assessed Using Diffusion Tensor MRI

Cercignani M, Bozzali M, Iannucci G, Comi G, Filippi M
J Neurol 2002 Jul;249(7):875-83
Scientific Institute and University, Ospedale San Raffaele, NeuroImaging Research Unit, Dept. of NeuroScience, via Olgettina 60, 20132 Milan, Italy
PMID# 12140672; UI# 22135914
Abstract

Previous Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) studies reported Mean Diffusivity (Diffusivity) and Fractional Anisotropy (FA) changes in lesions and Normal-Appearing White Matter (NAWM) of patients with Multiple Sclerosis (MS).

But, neglected the additional information which can be obtained by the analysis of the Inter-Voxel Coherence (C).

The present study is based on a large sample of patients with MS and it is aimed at assessing the potential role of C in the quantification of MS-related tissue damage of T2-visible lesions and NAWM.

We obtained dual-echo, T1-weighted and DT-MRI scans from 78 patients with Relapsing/Remitting (RR), Secondary/Progressive (SP), or Primary/Progressive (PP) MS and from 26 healthy volunteers.

We calculated Diffusivity, FA and C of T2-HyperIntense lesions, T1-IsoIntense lesions, T1-HypoIntense lesions and several areas of the NAWM.

Diffusivity and FA of the majority of NAWM regions studied from MS patients were different from the corresponding quantities of the White Matter from controls.

NAWM C from patients was lower than White Matter C from controls only for the Parietal PeriCallosal Areas.

SPMS patients had higher Corpus Callosum Diffusivity and lower Corpus Callosum FA and C than patients with either RRMS or PPMS.

Average lesion Diffusivity was higher, and average FA and C lower than the corresponding quantities measured in the NAWM.

Average T1-HypoIntense lesion Diffusivity was higher and average FA lower than the corresponding quantities of T1-IsoIntense lesions, whereas average C of these two lesion populations were not different.

SPMS had higher average lesion Diffusivity than both PPMS and RRMS patients.

NAWM Diffusivity and C of the Corpus Callosum were moderately correlated with disability.

This study confirms the role of DT-MRI metrics to identify MS lesions with different amounts of tissue damage and to detect diffuse changes in the NAWM.

It also shows that measuring C enables us to obtain additional information about tissue damage, which is complementary to that given by the analysis of Diffusivity and FA.



#12

A Normal Distribution For Tensor-Valued Random Variables: Applications To Diffusion Tensor MRI

Basser PJ, Pajevic S
IEEE Trans Med Imaging 2003 Jul;22(7):785-94
STBB/LIMB/NICHD, National Institutes of Health, Bldg. 13, Rm. 3W 16, 13 South Drive, Bethesda, MD 20892-5772, USA
PMID# 12906233
Abstract

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.



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