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Article ; Online: Diffusional kurtosis time dependence and the water exchange rate for the multi-compartment Kärger model.

Jensen, Jens H

2023 Volume 91, Issue 3, Page(s) 1122–1135

Abstract: Purpose: To demonstrate an analytic formula giving the time dependence of the diffusional kurtosis for the Kärger model (KM) with an arbitrary number of exchanging compartments and its application in estimating the mean KM water exchange rate.: Theory ...

Abstract	Purpose: To demonstrate an analytic formula giving the time dependence of the diffusional kurtosis for the Kärger model (KM) with an arbitrary number of exchanging compartments and its application in estimating the mean KM water exchange rate. Theory and methods: The general formula for the kurtosis is derived from a power series solution for the multi-compartment KM. A lower bound on the exchange rate is established from the observation that the kurtosis is always a logarithmically convex function of time. Both the kurtosis time dependence and the lower bound are illustrated with numerical calculations. The lower bound is also applied to previously published data for the time dependence of the kurtosis in both brain and tumors. Results: The kurtosis for the multi-compartment KM is given by a sum in which each term is associated with an eigenvector of the exchange rate matrix. The lower bound is determined from the most negative value for the logarithmic derivative of the kurtosis with respect to time. In the cerebral cortex, the lower bound is found to vary from 15 to 76 s Conclusion: The time dependence of the kurtosis for the multi-compartment KM has a simple analytic solution that allows a lower bound for the mean KM water exchange rate to be determined directly from experiment. This may be useful in tissues with complex microstructure that is difficult to model explicitly.
MeSH term(s)	Humans ; Water/metabolism ; Brain/diagnostic imaging ; Brain/metabolism ; Diffusion Magnetic Resonance Imaging/methods ; Diffusion Tensor Imaging/methods ; Neoplasms/metabolism
Chemical Substances	Water (059QF0KO0R)
Language	English
Publishing date	2023-11-13
Publishing country	United States
Document type	Journal Article
ZDB-ID	605774-3
ISSN	1522-2594 ; 0740-3194
ISSN (online)	1522-2594
ISSN	0740-3194
DOI	10.1002/mrm.29926
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Article ; Online: Impact of intra-axonal kurtosis on fiber orientation density functions estimated with fiber ball imaging.

Jensen, Jens H

Magnetic resonance in medicine

2022 Volume 88, Issue 3, Page(s) 1347–1354

Abstract: Purpose: To determine the impact of an intra-axonal kurtosis on estimates of the fiber orientation density function (fODF) obtained with fiber ball imaging (FBI).: Theory and methods: Standard FBI assumes Gaussian diffusion within individual axons ... ...

Abstract	Purpose: To determine the impact of an intra-axonal kurtosis on estimates of the fiber orientation density function (fODF) obtained with fiber ball imaging (FBI). Theory and methods: Standard FBI assumes Gaussian diffusion within individual axons and estimates the fODF by applying an inverse generalized Funk transform to diffusion MRI data for b-values of 4000 s/mm Results: The first order approximation indicates the estimated fODF is altered by a few percent for an intra-axonal kurtosis of 0.4 in comparison to predictions of standard FBI. If one neglects the intra-axonal kurtosis, the angular resolution of the point spread function for the fODF is changed by <1°, whereas the axonal water fraction is overestimated by ∼ 5%. The gamma distribution model shows that the first order approximation is accurate to within a few percent. Conclusion: The intra-axonal kurtosis has a small impact on fODFs estimated with FBI.
MeSH term(s)	Axons ; Brain ; Diffusion Magnetic Resonance Imaging/methods ; Normal Distribution ; Water ; White Matter
Chemical Substances	Water (059QF0KO0R)
Language	English
Publishing date	2022-04-18
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Extramural
ZDB-ID	605774-3
ISSN	1522-2594 ; 0740-3194
ISSN (online)	1522-2594
ISSN	0740-3194
DOI	10.1002/mrm.29270
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Article ; Online: Advanced DWI Methods for the Assessment of Ischemic Stroke.

Jensen, Jens H

AJR. American journal of roentgenology

2018 Volume 210, Issue 4, Page(s) 728–730

Abstract: Objective: This commentary discusses recent preclinical research on the potential feasibility and benefits of applying advanced DWI methods for the assessment of acute stroke.: Conclusion: A DWI parameter known as kurtosis shows promise in helping to ...

Abstract	Objective: This commentary discusses recent preclinical research on the potential feasibility and benefits of applying advanced DWI methods for the assessment of acute stroke. Conclusion: A DWI parameter known as kurtosis shows promise in helping to identify tissue that is likely salvageable at reperfusion.
MeSH term(s)	Animals ; Brain Ischemia ; Diffusion Magnetic Resonance Imaging ; Hemodynamics ; Magnetic Resonance Imaging ; Rodentia ; Stroke
Language	English
Publishing date	2018-02-15
Publishing country	United States
Document type	Journal Article ; Comment
ZDB-ID	82076-3
ISSN	1546-3141 ; 0361-803X ; 0092-5381
ISSN (online)	1546-3141
ISSN	0361-803X ; 0092-5381
DOI	10.2214/AJR.17.19223
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Article ; Online: High fidelity fiber orientation density functions from fiber ball imaging.

Moss, Hunter G / Jensen, Jens H

NMR in biomedicine

2021 Volume 35, Issue 1, Page(s) e4613

Abstract: The fiber orientation density function (fODF) in white matter is a primary physical quantity that can be estimated with diffusion MRI. It has often been employed for fiber tracking and microstructural modeling. Requirements for the construction of high ... ...

Abstract	The fiber orientation density function (fODF) in white matter is a primary physical quantity that can be estimated with diffusion MRI. It has often been employed for fiber tracking and microstructural modeling. Requirements for the construction of high fidelity fODFs, in the sense of having good angular resolution, adequate data to avoid sampling errors, and minimal noise artifacts, are described for fODFs calculated with fiber ball imaging. A criterion is formulated for the number of diffusion encoding directions needed to achieve a given angular resolution. The advantages of using large b-values (≥6000 s/mm
MeSH term(s)	Anisotropy ; Diffusion Magnetic Resonance Imaging/methods ; Humans ; Nerve Fibers ; White Matter/diagnostic imaging
Language	English
Publishing date	2021-09-12
Publishing country	England
Document type	Journal Article ; Research Support, N.I.H., Extramural
ZDB-ID	1000976-0
ISSN	1099-1492 ; 0952-3480
ISSN (online)	1099-1492
ISSN	0952-3480
DOI	10.1002/nbm.4613
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Article ; Online: Quantitative microglia morphological features correlate with diffusion MRI in 2-month-old 3xTg-AD mice.

Falangola, Maria Fatima / Dhiman, Siddhartha / Voltin, Joshua / Jensen, Jens H

Magnetic resonance imaging

2023 Volume 103, Page(s) 8–17

Abstract: Microglia (MØ) morphologies are closely related to their functional state and have a central role in the maintenance of brain homeostasis. It is well known that inflammation contributes to neurodegeneration at later stages of Alzheimer's Disease, but it ... ...

Abstract	Microglia (MØ) morphologies are closely related to their functional state and have a central role in the maintenance of brain homeostasis. It is well known that inflammation contributes to neurodegeneration at later stages of Alzheimer's Disease, but it is not clear which role MØ-mediated inflammation may play earlier in the disease pathogenesis. We have previously reported that diffusion MRI (dMRI) is able to detect early myelin abnormalities present in 2-month-old 3xTg-AD (TG) mice; since MØ actively participate in regulating myelination, the goal of this study was to assess quantitatively MØ morphological characteristics and its association with dMRI metrics patterns in 2-month-old 3xTg-AD mice. Our results show that, even at this young age (2-month-old), TG mice have statistically significantly more MØ cells, which are overall smaller and more complex, compared with age-matched normal control mice (NC). Our results also confirm that myelin basic protein is reduced in TG mice, particularly in fimbria (Fi) and cortex. Additionally, MØ morphological characteristics, in both groups, correlate with several dMRI metrics, depending on the brain region examined. For example, the increase in MØ number correlated with higher radial diffusivity (r = 0.59, p = 0.008), lower fractional anisotropy (FA) (r = -0.47, p = 0.03), and lower kurtosis fractional anisotropy (KFA) (r = -0.55, p = 0.01) in the CC. Furthermore, smaller MØ cells correlate with higher axial diffusivity) in the HV (r = 0.49, p = 0.03) and Sub (r = 0.57, p = 0.01). Our findings demonstrate, for the first time, that MØ proliferation/activation are a common and widespread feature in 2-month-old 3xTg-AD mice and suggest that dMRI measures are sensitive to these MØ alterations, which are associated in this model with myelin dysfunction and microstructural integrity abnormalities.
MeSH term(s)	Mice ; Animals ; Diffusion Tensor Imaging/methods ; Microglia/pathology ; Diffusion Magnetic Resonance Imaging/methods ; Brain/diagnostic imaging ; Brain/pathology ; Alzheimer Disease/diagnostic imaging ; Alzheimer Disease/pathology ; White Matter/pathology ; Mice, Transgenic
Language	English
Publishing date	2023-06-29
Publishing country	Netherlands
Document type	Journal Article ; Research Support, N.I.H., Extramural
ZDB-ID	604885-7
ISSN	1873-5894 ; 0730-725X
ISSN (online)	1873-5894
ISSN	0730-725X
DOI	10.1016/j.mri.2023.06.017
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Article ; Online: Optimized rectification of fiber orientation density function with background threshold.

Moss, Hunter G / Benitez, Andreana / Jensen, Jens H

Magnetic resonance imaging

2022 Volume 95, Page(s) 80–89

Abstract: Purpose: To describe an optimized fiber orientation density function (fODF) rectification procedure that removes negative values and absorbs all features below a specified threshold into a constant background.: Theory and methods: The fODF for a ... ...

Abstract	Purpose: To describe an optimized fiber orientation density function (fODF) rectification procedure that removes negative values and absorbs all features below a specified threshold into a constant background. Theory and methods: The fODF for a white matter imaging voxel describes the angular density of axons. Because of signal noise and Gibbs ringing, fODFs estimated with diffusion MRI may take on unphysical negative values in some directions and contain spurious peaks. In order to suppress such artifacts, an fODF rectification procedure is proposed that both eliminates all negative values and incorporates all features below a specified threshold, η, into a constant background while at the same time minimizing the mean square deviation from the original, unrectified fODF. Calculating this fODF is straightforward, and the directions and shapes of peaks not absorbed into the background are preserved. The rectification method is illustrated for an analytic fODF model and for experimental diffusion MRI data obtained in healthy human brain, with the original fODFs being obtained from fiber ball imaging. Results: Examples of optimal rectified fODFs are given for three choices of the background threshold referred to as minimal rectification (η = 0), average-level rectification (η ≈ 0.08), and fractional-anisotropy-axonal-based rectification (η ≈ 0.1). As η is increased, artifacts and other small features are more strongly suppressed, but the major fODF peaks are largely unaffected for the range of η values illustrated by these three alternatives. Conclusion: Artifactual features of fODFs estimated with diffusion MRI can be effectively suppressed by applying the proposed optimized rectification procedure. Since it minimizes fODF distortion in the mean square sense, it may be useful in the study of how fODF fine structure is affected by aging and disease.
MeSH term(s)	Humans ; Image Processing, Computer-Assisted/methods ; Diffusion Magnetic Resonance Imaging/methods ; White Matter/diagnostic imaging ; Brain/diagnostic imaging ; Anisotropy
Language	English
Publishing date	2022-11-08
Publishing country	Netherlands
Document type	Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't
ZDB-ID	604885-7
ISSN	1873-5894 ; 0730-725X
ISSN (online)	1873-5894
ISSN	0730-725X
DOI	10.1016/j.mri.2022.11.001
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Article ; Online: Optimized rectification of fiber orientation density function.

Moss, Hunter G / Jensen, Jens H

Magnetic resonance in medicine

2020 Volume 85, Issue 1, Page(s) 444–455

Abstract: Purpose: To demonstrate an optimized rectification strategy for fiber orientation density functions (fODFs).: Theory and methods: In white matter, fODFs can be estimated with diffusion MRI. However, because of signal noise, imaging artifacts and ... ...

Abstract	Purpose: To demonstrate an optimized rectification strategy for fiber orientation density functions (fODFs). Theory and methods: In white matter, fODFs can be estimated with diffusion MRI. However, because of signal noise, imaging artifacts and other factors, experimentally determined fODFs may take on unphysical negative values in some directions. Here, we show how to rectify such fODFs to eliminate all negative values while minimizing the mean square difference between the original and rectified fODFs. The method is demonstrated for a mathematical model and for fODFs estimated from experimental human data using both constrained spherical deconvolution and fiber ball imaging. Comparison with an alternative nonoptimized rectification approach is also provided. Results: For the mathematical model, it is found that the optimized rectification procedure removes negative fODF values while at the same time reducing the mean square error. Relative to the alternative rectification approach, the optimized fODFs are substantially more accurate. For the experimental data, the optimized fODFs have a lower average fractional anisotropy axonal and often fewer small peaks than the original, unrectified fODFs. The calculation of optimized fODFs is straightforward where the main step is the finding of the root to an equation in one variable, as may be efficiently accomplished with the bisection method. Conclusion: Unphysical negative fODF values can be easily eliminated in a manner that minimizes the mean square difference between the original and rectified fODFs. Optimized fODF rectification may be useful in applications for which negative values are problematic.
MeSH term(s)	Anisotropy ; Axons ; Brain/diagnostic imaging ; Diffusion Magnetic Resonance Imaging ; Humans ; Image Processing, Computer-Assisted ; White Matter/diagnostic imaging
Language	English
Publishing date	2020-07-25
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Extramural
ZDB-ID	605774-3
ISSN	1522-2594 ; 0740-3194
ISSN (online)	1522-2594
ISSN	0740-3194
DOI	10.1002/mrm.28406
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Article ; Online: Stejskal's formula for multiple-pulsed diffusion MRI.

Jensen, Jens H

Magnetic resonance imaging

2015 Volume 33, Issue 9, Page(s) 1182–1186

Abstract: A fundamental theoretical result for diffusion MRI is the formula by Stejskal showing that the diffusion NMR signal is proportional to the Fourier transform of the diffusion displacement probability density function. Here this result is extended to ... ...

Abstract	A fundamental theoretical result for diffusion MRI is the formula by Stejskal showing that the diffusion NMR signal is proportional to the Fourier transform of the diffusion displacement probability density function. Here this result is extended to multiple-pulsed diffusion MRI (MP-dMRI) by using a higher dimensional q-space formalism to express the diffusion-weighted signal for a sequence with N diffusion wave vectors in terms of a Fourier transform of a diffusion displacement probability density function in a 3N-dimensional space. As an illustration of the application of this extended version of Stejskal's formula, it is used to analyze the cumulant expansion of the signal magnitude for MP-dMRI.
MeSH term(s)	Algorithms ; Diffusion Magnetic Resonance Imaging/methods ; Fourier Analysis ; Humans ; Image Interpretation, Computer-Assisted/methods ; Imaging, Three-Dimensional/methods
Language	English
Publishing date	2015-11
Publishing country	Netherlands
Document type	Journal Article
ZDB-ID	604885-7
ISSN	1873-5894 ; 0730-725X
ISSN (online)	1873-5894
ISSN	0730-725X
DOI	10.1016/j.mri.2015.07.001
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Article ; Online: Sufficiency of diffusion tensor in characterizing the diffusion MRI signal to leading order in diffusion weighting.

Jensen, Jens H

NMR in biomedicine

2014 Volume 27, Issue 8, Page(s) 1005–1007

MeSH term(s)	Diffusion Tensor Imaging/methods ; Magnetic Resonance Imaging/methods ; Models, Theoretical ; Signal Processing, Computer-Assisted ; Time Factors
Language	English
Publishing date	2014-08
Publishing country	England
Document type	Letter
ZDB-ID	1000976-0
ISSN	1099-1492 ; 0952-3480
ISSN (online)	1099-1492
ISSN	0952-3480
DOI	10.1002/nbm.3145
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Article ; Online: Characterizing intra-axonal water diffusion with direction-averaged triple diffusion encoding MRI.

Jensen, Jens H / Helpern, Joseph A

NMR in biomedicine

2018 Volume 31, Issue 7, Page(s) e3930

Abstract: For large diffusion weightings, the direction-averaged diffusion MRI (dMRI) signal from white matter is typically dominated by the contribution of water confined to axons. This fact can be exploited to characterize intra-axonal diffusion properties, ... ...

Abstract	For large diffusion weightings, the direction-averaged diffusion MRI (dMRI) signal from white matter is typically dominated by the contribution of water confined to axons. This fact can be exploited to characterize intra-axonal diffusion properties, which may be valuable for interpreting the biophysical meaning of diffusion changes associated with pathology. However, using just the classic Stejskal-Tanner pulse sequence, it has proven challenging to obtain reliable estimates for both the intrinsic intra-axonal diffusivity and the intra-axonal water fraction. Here we propose to apply a modification of the Stejskal-Tanner sequence designed for achieving such estimates. The key feature of the sequence is the addition of a set of extra diffusion encoding gradients that are orthogonal to the direction of the primary gradients, which corresponds to a specific type of triple diffusion encoding (TDE) MRI sequence. Given direction-averaged dMRI data for this TDE sequence, it is shown how the intra-axonal diffusivity and the intra-axonal water fraction can be determined by applying simple, analytic formulae. The method is illustrated with numerical simulations, which suggest that it should be accurate for b-values of about 4000 s/mm
MeSH term(s)	Axons/metabolism ; Computer Simulation ; Diffusion ; Diffusion Magnetic Resonance Imaging ; Numerical Analysis, Computer-Assisted ; Water/metabolism
Chemical Substances	Water (059QF0KO0R)
Language	English
Publishing date	2018-05-04
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't
ZDB-ID	1000976-0
ISSN	1099-1492 ; 0952-3480
ISSN (online)	1099-1492
ISSN	0952-3480
DOI	10.1002/nbm.3930
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