The existence of biexponential signal decay in magnetic resonance diffusion‐weighted imaging appears to be independent of compartmentalization

Schwarcz, Attila; Bogner, Péter; Méric, P.; Correze, Jean Loup; Berente, Zoltán; Pál, József; Gallyas, Ferenc; Dóczi, Tamás; Gillet, Brigitte; Beloeil, Jean Claude

doi:10.1002/mrm.10702

Cited by 74 publications

(66 citation statements)

References 36 publications

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“…Furthermore, the average relative signal changes [ Ϫ9 for gradient scheme "b" using Eqs. [9]- [14]. These average values are certainly negligible compared to the detected signal change in the range of 0.2% to 2% (see below).…”

Section: Resultsmentioning

confidence: 90%

Transient signal changes in diffusion‐weighted stimulated echoes during neuronal stimulation at 3T

Goerke¹,

Möller²

2007

Magnetic Resonance Imaging

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Purpose: To develop a sensitive method for detecting minute transient signal changes that can arise due to variations in the extravascular apparent self-diffusion coefficient, D, during neuronal activation. Materials and Methods:A three-pulse sequence that reads out a moderately diffusion-weighted (DW) primary echo (PRE) and a heavily DW stimulated echo (STE) was employed to investigate whether small transient signal changes in extravascular D occur in response to a visual stimulus. Contributions to signal changes caused by subtle differences in the transient variations of the apparent transverse relaxation constant, T 2 , between the PRE and STE were also quantified. Results:On z-maps obtained from the STE, more voxels showed significant stimulus-related signal changes compared to maps of the PRE. The average maximum signal change of the STE was larger than that of the PRE. The observed increase in the relative signal change was independent of the strength of the diffusion weighting. Conclusion:The STE is more sensitive to neuronal activity than the PRE. The discrepancy between the two echoes does not arise from transient changes in D, but from subtle differences in stimulus-related variations of T 2 between the two echoes. THE BLOOD OXYGEN LEVEL-DEPENDENT (BOLD) effect detects activation only indirectly by the vascular response; therefore, the search for alternative functional magnetic resonance imaging (fMRI) methods to probe neuronal activity more directly is an area of ongoing research. It was recently hypothesized that the apparent water self-diffusion coefficient, D, decreases in the primary visual cortex during visual stimulation (1). It is assumed that cellular microstructure and morphology change as a result of neuronal activity, which can potentially be probed using diffusion-weighted (DW) fMRI. Swelling of neurons or astrocytes and associated morphological changes of the macromolecular matrix in brain tissue and the spinal cord have been intensively investigated with the use of intrinsic optical signals (2-7). Microstructural changes have been observed under various pathological conditions, including stroke, ischemia, and osmotic challenge. Furthermore, it has been demonstrated that electrically induced neuronal activity causes cellular swelling accompanied by structural changes in the macromolecular matrix.Water motion in biological tissue is affected by interaction with cell membranes and macromolecules. The non-monoexponential signal decay in DW MRI (DWI) strongly suggests that water self-diffusion is a sensitive probe for assessing structure and morphology on the cellular level. Initially, non-exponential behavior was assumed to reflect diffusion in the intra-and extracellular compartments. However, it has been shown that the two-compartment model oversimplifies the more complex interaction between water and the microanatomical environment in biological tissue (8 -10). It was also demonstrated that structural and morphological changes induced by pathological conditions known to cause cellular swe...

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Section: Resultsmentioning

confidence: 90%

Transient signal changes in diffusion‐weighted stimulated echoes during neuronal stimulation at 3T

Goerke¹,

Möller²

2007

Magnetic Resonance Imaging

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“…Equation [1] suggests the presence of two compartments in the brain tissue; however, any attempt to identify them histologically has failed (1,(3)(4)(5)(6). This supports another interpretation of biexponential diffusion as a manifestation of microscopic restrictions in biological tissue (7)(8)(9).…”

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confidence: 76%

“…Equation [5] was fitted to data by analytical minimization (nonlinear regression) of the weighted sum…”

Section: Data Processingmentioning

confidence: 99%

Is the “biexponential diffusion” biexponential?

Kiselev

Il’yasov

2007

Magnetic Resonance in Med

123

160

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Diffusion-weighted signal from the brain, S, deviates from monoexponential dependence on the b-factor. This property is often referred to as biexponential diffusion, since the corresponding model fits data well. The aim of this study is to examine the necessity of using the biexponential model in homogeneous voxels under isotropic diffusion weighting up to b = 2.5 ms/µm 2 . The model is compared to the cumulant expansion of ln S in a power series in b, which takes its origin in fundamental properties of the diffusion-weighted signal, but diverges at large b. Numerous studies [ (1-3) and following papers] indicate that the diffusion-weighted signal from a single voxel can be described as a weighted sum of two exponential functions,where b is the b-value, w 1 and w 2 are the weights, and D 1 and D 2 are the corresponding diffusion coefficients. Equation [1] suggests the presence of two compartments in the brain tissue; however, any attempt to identify them histologically has failed (1,3-6). This supports another interpretation of biexponential diffusion as a manifestation of microscopic restrictions in biological tissue (7-9).In this paper, we scrutinize the description of diffusion in the brain. The aim is to determine whether the biexponential model, Eq. [1], is required by experimental data on a statistically significant level. The good quality of fitting of Eq.[1] to data is not sufficient to prove the relevance of this function. It can be superfluous in the presence of another model with a smaller number of adjustable parameters describing experimental data equally well. METHODS TheoryAs a framework for the present analysis, we use a modelindependent description of the magnitude of the isotropically weighted signal as a power series in b:Medical Physics, Department of Diagnostic Radiology, University Hospital Freiburg, Freiburg, Germany. For the biexponential function, Eq.[1], the convergence radius is determined by the complex-valued solution to the equation S biexp = 0:This value should be compared with the interval of experimental b-factors. If the condition b < b c fulfils, then the series in Eq. [2] can be terminated to a couple of low-order terms. The higher-order terms give a small contribution that cannot be determined from noisy experimental data. This means that the information content of the model, Eq. [1], may be reduced to a smaller number of parameters, which are the first coefficients in Eq. [2]. If so, the model is superfluous and a good accuracy of fitting does not prove its validity.In the opposite case of large b-factors, b > b c , the model represents a specific function that cannot be reduced to a polynomial. In this case, a good quality of fitting gives more credit to the underlying model.The aim of this study can now be formulated as to find out which of the above cases holds for the brain tissue for b-factors up to b = 2.5 ms/µm 2 . MR MeasurementsAll measurements were performed on a 3-T whole-body clinical scanner (Magnetom Trio, Siemens Medical Systems, Erlangen, Germany). The scann...

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“…7,15,17 The decrease in ADC mainly results from increased cellularity, but some tumors show other changes, such as ‰uid viscosity and cell permeability, as well. [23][24][25][26][27][28][29][30] In this respect, biexponential signal analysis will provide more precise information about tissue character. Thus, we performed DWI with high b-values up to 3500 s/mm 2 and examined the character of biexponential signal attenuation using Equation [3], in which fast and slow components are postulated.…”

Section: Magnetic Resonance In Medical Sciencesmentioning

confidence: 99%

“…However, the estimated ratios of f 1 :f 2 (9:1¿7:3) are clearly diŠerent from the actual component fractions (1:9¿3:7) determined with other physical methods. After Niendorf'sˆndings, many researchers have investigated this discrepancy and indicated in‰uence from permeability or restriction of cell membrane [23][24][25] and diŠerence of relaxation time of intra-and extracellular space 26,27 as well as other factors. [28][29][30] However, the detailed cause of biexponential signal attenuation remains unclear.…”

Section: Introductionmentioning

confidence: 99%

Biexponential Signal Attenuation Analysis of Diffusion-weighted Imaging of Breast

et al. 2010

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Purpose: In vivo, the attenuation of diŠusion-weighted imaging (DWI) signal at high bvalues is sometimes nonlinear when plotted with semilogarithmic function and isˆt well by a biexponential function. Previous reports have indicated that the fast and slow component fractions of the apparent diŠusion coe‹cient (ADC) can be derived by biexponentialˆtting and that these fractions correspond to the actual diŠusion components in the extra-and intracellular space. In this study, we investigated the clinical utility of DWI for the breast by performing DWI using multiple b-factors on healthy volunteers and clinical subjects, analyzing the signal byˆtting it with a biexponential equation, and comparing theˆtting parameters of breast lesions.Patients and Methods: We investigated 8 healthy women as normal cases and 80 female patients with a total of 100 breast tumors (42 benign, 58 malignant tumors) as clinical cases. We performed DWI using 12 b-values for the healthy cases and 6 b-values for the clinical cases, up to a maximum b-value of 3500 s/mm 2 .Results: Decay of DWI signal of normal mammary glands, most cysts, and someˆbro-adenomas showed a monoexponential relationship, and conversely, that of intraductal papilloma (IDP) and malignant tumors was wellˆtted by a biexponential function. Comparison of parameters derived from biexponentialˆtting demonstrated no signiˆcant difference between benign and malignant lesions. For malignant tumor subtype, the fast component fraction of noninvasive ductal carcinoma was statistically greater than that of invasive ductal carcinoma.Conclusions: Although the parameters from biexponentialˆtting may re‰ect the character of tumor cellularity, because pathological diagnosis was performed with an emphasis on cell conˆguration or shape rather than cellularity, it was di‹cult to distinguish malignant from benign tumors, including many IDPs, or to distinguish tissue types using DWI signal attenuation alone.

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The existence of biexponential signal decay in magnetic resonance diffusion‐weighted imaging appears to be independent of compartmentalization

Cited by 74 publications

References 36 publications

Transient signal changes in diffusion‐weighted stimulated echoes during neuronal stimulation at 3T

Transient signal changes in diffusion‐weighted stimulated echoes during neuronal stimulation at 3T

Is the “biexponential diffusion” biexponential?

Biexponential Signal Attenuation Analysis of Diffusion-weighted Imaging of Breast

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