Studies of anomalous diffusion in the human brain using fractional order calculus

Zhou, Xiaohong Joe; Gao, Qing; Abdullah, Osama; Magin, Richard L.

doi:10.1002/mrm.22285

Cited by 170 publications

(193 citation statements)

References 25 publications

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“…The signal-to-noise ratios in the temporal lobe for b of 5000 sec/mm 2 images in biexponential and stretched exponential models and b of 2500 sec/ mm 2 images in the DKI model were calculated to be 12-15 and 19-25, respectively. When compared with some other studies (18,20,21), the signal-tonoise ratios in these diffusion models of our study are reliable even with the highest b values.…”

Section: Advances In Knowledgesupporting

confidence: 81%

“…According to previous studies (11,18,19), the selections for distributions of b values and numbers of signals acquired in our study are tradeoffs between acquisition times and signal-to-noise ratios in the models. The signal-to-noise ratios in the temporal lobe for b of 5000 sec/mm 2 images in biexponential and stretched exponential models and b of 2500 sec/ mm 2 images in the DKI model were calculated to be 12-15 and 19-25, respectively.…”

Section: Advances In Knowledgementioning

confidence: 99%

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Grading of Gliomas by Using Monoexponential, Biexponential, and Stretched Exponential Diffusion-weighted MR Imaging and Diffusion Kurtosis MR Imaging

Bai¹,

Lin²,

Hui³

et al. 2016

Radiology

187

162

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).q RSNA, 2015 Purpose:To quantitatively compare the potential of various diffusion parameters obtained from monoexponential, biexponential, and stretched exponential diffusion-weighted imaging models and diffusion kurtosis imaging in the grading of gliomas. Materials andMethods:This study was approved by the local ethics committee, and written informed consent was obtained from all subjects. Both diffusion-weighted imaging and diffusion kurtosis imaging were performed in 69 patients with pathologically proven gliomas by using a 3-T magnetic resonance (MR) imaging unit. An isotropic apparent diffusion coefficient (ADC), true ADC, pseudo-ADC, and perfusion fraction were calculated from diffusionweighted images by using a biexponential model. A water molecular diffusion heterogeneity index and distributed diffusion coefficient were calculated from diffusion-weighted images by using a stretched exponential model. Mean diffusivity, fractional anisotropy, and mean kurtosis were calculated from diffusion kurtosis images. All values were compared between high-grade and low-grade gliomas by using a Mann-Whitney U test. Receiver operating characteristic and Spearman rank correlation analysis were used for statistical evaluations. Results:ADC, true ADC, perfusion fraction, water molecular diffusion heterogeneity index, distributed diffusion coefficient, and mean diffusivity values were significantly lower in high-grade gliomas than in low-grade gliomas (U = 109, 56, 129, 6, 206, and 229, respectively; P , .05). Pseudo-ADC and mean kurtosis values were significantly higher in high-grade gliomas than in low-grade gliomas (U = 98 and 8, respectively; P , .05). Both water molecular diffusion heterogeneity index (area under the receiver operating characteristic curve [AUC] = 0.993) and mean kurtosis (AUC = 0.991) had significantly greater AUC values than ADC (AUC = 0.866), mean diffusivity (AUC = 0.722), and fractional anisotropy (AUC = 0.500) in the differentiation of low-grade and high-grade gliomas (P , .05). Conclusion:Water molecular diffusion heterogeneity index and mean kurtosis values may provide additional information and improve the grading of gliomas compared with conventional diffusion parameters.q RSNA, 2015

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Section: Advances In Knowledgesupporting

confidence: 81%

Section: Advances In Knowledgementioning

confidence: 99%

Grading of Gliomas by Using Monoexponential, Biexponential, and Stretched Exponential Diffusion-weighted MR Imaging and Diffusion Kurtosis MR Imaging

Bai¹,

Lin²,

Hui³

et al. 2016

Radiology

187

162

View full text Add to dashboard Cite

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“…In recent years, several approaches have been proposed to quantify non-Gaussian [31][32][33][34][35] and AD processes in heterogeneous systems [8,13,14,[18][19][20][36][37][38][39][40][41]. In this paper, for the first time, we show and compare anomalous subdiffusive Mα maps together with anomalous pseudo-superdiffusion Mγ and conventional MD maps obtained from the same samples (controlled phantom and excised brain tissues).…”

Section: Resultsmentioning

confidence: 97%

Spatio-temporal anomalous diffusion imaging: results in controlled phantoms and in excised human meningiomas

Capuani

Palombo

Gabrielli³

et al. 2013

Magnetic Resonance Imaging

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Recently, we measured two anomalous diffusion (AD) parameters: the spatial and the temporal AD indices, called γ and α, respectively, by using spectroscopic pulse gradient field methods. We showed that γ quantifies pseudo-superdiffusion processes, while α quantifies subdiffusion processes. Here, we propose γ and α maps obtained in a controlled heterogeneous phantom, comprised of packed micro-beads in water and in excised human meningiomas. In few words, α maps represent the multi-scale spatial distribution of the disorder degree in the system, while γ maps are influenced by local internal gradients, thus highlighting the interface between compartments characterized by different magnetic susceptibility. γ maps were already obtained by means of AD stretched exponential imaging and α-type maps have been recently achieved for fixed rat brain with the aim of highlighting the fractal dimension of specific brain regions. However, to our knowledge, the maps representative of the spatial distribution of α and γ obtained on the same controlled sample and in the same excised tissue have never been compared. Moreover, we show here, for the first time, that α maps are representative of the spatial distribution of the disorder degree of the system. In a first phase, γ and α maps of controlled phantom characterized by an ordered and a disordered rearrangement of packed micro-beads of different sizes in water and by different magnetic susceptibility (Δχ) between beads and water were obtained. In a second phase, we investigated excised human meningiomas of different consistency. Results reported here, obtained at 9.4 T, show that α and γ maps are characterized by a different image contrast. Indeed, unlike γ maps, α maps are insensible to (Δχ) and they are sensible to the disorder degree of the microstructural rearrangement. These observations strongly suggest that AD indices α and γ reflect some additional microstructural information which cannot be obtained using conventional diffusion methods based on Gaussian diffusion. Moreover, α and γ maps obtained in excised meningiomas seem to provide more microstructural details above those obtained with conventional DTI analysis, which could be used to improve the classification of meningiomas based on their consistency.

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“…Recognizing the limitation of ADC, several research groups developed a number of more sophisticated diffusion models to extract structural tissue information beyond what ADC can provide (28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38)(39)(40). One such model is known as the fractional order calculus (FROC) model, which yields a new set of parameters to describe the anomalous diffusion process in complex biologic tissues: diffusion coefficient (D), which is measured in square micrometers per millisecond; fractional order derivative in space (b); and a spatial parameter (m), which is measured in micrometers (30,35).…”

Section: Patientsmentioning

confidence: 99%

Differentiation of Low- and High-Grade Pediatric Brain Tumors with Highb-Value Diffusion-weighted MR Imaging and a Fractional Order Calculus Model

Sui¹,

Wang

Liu

et al. 2015

Radiology

Self Cite

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).q RSNA, 2015 Purpose:To demonstrate that a new set of parameters (D, b, and m) from a fractional order calculus (FROC) diffusion model can be used to improve the accuracy of MR imaging for differentiating among low-and high-grade pediatric brain tumors. Materials and Methods:The institutional review board of the performing hospital approved this study, and written informed consent was obtained from the legal guardians of pediatric patients. Multi-b-value diffusion-weighted magnetic resonance (MR) imaging was performed in 67 pediatric patients with brain tumors. Diffusion coefficient D, fractional order parameter b (which correlates with tissue heterogeneity), and a microstructural quantity m were calculated by fitting the multi-b-value diffusion-weighted images to an FROC model. D, b, and m values were measured in solid tumor regions, as well as in normal-appearing gray matter as a control. These values were compared between the lowand high-grade tumor groups by using the Mann-Whitney U test. The performance of FROC parameters for differentiating among patient groups was evaluated with receiver operating characteristic (ROC) analysis. Results:None of the FROC parameters exhibited significant differences in normal-appearing gray matter (P  .24), but all showed a significant difference (P , . Conclusion:The FROC parameters can be used to differentiate between low-and high-grade pediatric brain tumor groups. The combination of FROC parameters or individual parameters may serve as in vivo, noninvasive, and quantitative imaging markers for classifying pediatric brain tumors.q RSNA, 2015

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Studies of anomalous diffusion in the human brain using fractional order calculus

Cited by 170 publications

References 25 publications

Grading of Gliomas by Using Monoexponential, Biexponential, and Stretched Exponential Diffusion-weighted MR Imaging and Diffusion Kurtosis MR Imaging

Grading of Gliomas by Using Monoexponential, Biexponential, and Stretched Exponential Diffusion-weighted MR Imaging and Diffusion Kurtosis MR Imaging

Spatio-temporal anomalous diffusion imaging: results in controlled phantoms and in excised human meningiomas

Differentiation of Low- and High-Grade Pediatric Brain Tumors with Highb-Value Diffusion-weighted MR Imaging and a Fractional Order Calculus Model

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