The Experts below are selected from a list of 21189 Experts worldwide ranked by ideXlab platform
D D Sokoloff - One of the best experts on this subject based on the ideXlab platform.
-
evolution of magnetic helicity and energy spectra of solar active regions
The Astrophysical Journal, 2016Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We adopt an isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA. 11158 and NOAA. 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/ 3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA. 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field.
-
magnetic helicity and energy spectra of a solar active region
The Astrophysical Journal, 2014Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time the magnetic helicity and energy spectra of the solar active region NOAA 11158 during 2011 February 11-15 at 20° southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field. The sign of the magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ≈ 0.4 Mm–1, corresponding to a scale of 2π/k ≈ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k –11/3 power law at large wavenumbers, which implies a k –5/3 spectrum for the modulus of the current helicity. A k –5/3 spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm–1, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artifacts at small scales.
-
magnetic helicity and energy spectra of a solar active region
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field. The sign of magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ~ 0.4 Mm^{-1}, corresponding to a scale of 2pi/k ~ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k^{-11/3} power law at large wavenumbers, which implies a k^{-5/3} spectrum for the modulus of the current helicity. A k^{-5/3} spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm^{-1}, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artefacts at small scales.
Axel Brandenburg - One of the best experts on this subject based on the ideXlab platform.
-
evolution of magnetic helicity and energy spectra of solar active regions
The Astrophysical Journal, 2016Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We adopt an isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA. 11158 and NOAA. 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/ 3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA. 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field.
-
magnetic helicity and energy spectra of a solar active region
The Astrophysical Journal, 2014Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time the magnetic helicity and energy spectra of the solar active region NOAA 11158 during 2011 February 11-15 at 20° southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field. The sign of the magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ≈ 0.4 Mm–1, corresponding to a scale of 2π/k ≈ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k –11/3 power law at large wavenumbers, which implies a k –5/3 spectrum for the modulus of the current helicity. A k –5/3 spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm–1, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artifacts at small scales.
-
magnetic helicity and energy spectra of a solar active region
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field. The sign of magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ~ 0.4 Mm^{-1}, corresponding to a scale of 2pi/k ~ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k^{-11/3} power law at large wavenumbers, which implies a k^{-5/3} spectrum for the modulus of the current helicity. A k^{-5/3} spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm^{-1}, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artefacts at small scales.
Hongqi Zhang - One of the best experts on this subject based on the ideXlab platform.
-
evolution of magnetic helicity and energy spectra of solar active regions
The Astrophysical Journal, 2016Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We adopt an isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field to estimate the magnetic energy and helicity spectra as well as current helicity spectra of two individual active regions (NOAA. 11158 and NOAA. 11515) and the change of the spectral indices during their development as well as during the solar cycle. The departure of the spectral indices of magnetic energy and current helicity from 5/ 3 are analyzed, and it is found that it is lower than the spectral index of the magnetic energy spectrum. Furthermore, the fractional magnetic helicity tends to increase when the scale of the energy-carrying magnetic structures increases. The magnetic helicity of NOAA. 11515 violates the expected hemispheric sign rule, which is interpreted as an effect of enhanced field strengths at scales larger than 30-60Mm with opposite signs of helicity. This is consistent with the general cycle dependence, which shows that around the solar maximum the magnetic energy and helicity spectra are steeper, emphasizing the large-scale field.
-
magnetic helicity and energy spectra of a solar active region
The Astrophysical Journal, 2014Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time the magnetic helicity and energy spectra of the solar active region NOAA 11158 during 2011 February 11-15 at 20° southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field. The sign of the magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ≈ 0.4 Mm–1, corresponding to a scale of 2π/k ≈ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k –11/3 power law at large wavenumbers, which implies a k –5/3 spectrum for the modulus of the current helicity. A k –5/3 spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm–1, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artifacts at small scales.
-
magnetic helicity and energy spectra of a solar active region
arXiv: Solar and Stellar Astrophysics, 2013Co-Authors: Hongqi Zhang, Axel Brandenburg, D D SokoloffAbstract:We compute for the first time magnetic helicity and energy spectra of the solar active region NOAA 11158 during 11-15 February 2011 at 20^o southern heliographic latitude using observational photospheric vector magnetograms. We adopt the isotropic representation of the Fourier-transformed two-point Correlation Tensor of the magnetic field. The sign of magnetic helicity turns out to be predominantly positive at all wavenumbers. This sign is consistent with what is theoretically expected for the southern hemisphere. The magnetic helicity normalized to its theoretical maximum value, here referred to as relative helicity, is around 4% and strongest at intermediate wavenumbers of k ~ 0.4 Mm^{-1}, corresponding to a scale of 2pi/k ~ 16 Mm. The same sign and a similar value are also found for the relative current helicity evaluated in real space based on the vertical components of magnetic field and current density. The modulus of the magnetic helicity spectrum shows a k^{-11/3} power law at large wavenumbers, which implies a k^{-5/3} spectrum for the modulus of the current helicity. A k^{-5/3} spectrum is also obtained for the magnetic energy. The energy spectra evaluated separately from the horizontal and vertical fields agree for wavenumbers below 3 Mm^{-1}, corresponding to scales above 2 Mm. This gives some justification to our assumption of isotropy and places limits resulting from possible instrumental artefacts at small scales.
Noam Shemesh - One of the best experts on this subject based on the ideXlab platform.
-
evidence for microscopic kurtosis in neural tissue revealed by Correlation Tensor mri
Magnetic Resonance in Medicine, 2021Co-Authors: Rafael Neto Henriques, Sune Norhoj Jespersen, Noam ShemeshAbstract:Purpose The impact of microscopic diffusional kurtosis (µK), arising from restricted diffusion and/or structural disorder, remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, Correlation Tensor imaging (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori multi-gaussian component (MGC) or other microstructural assumptions. Here, we investigated µK in in vivo rat brains and assessed its impact on state-of-the-art methods ignoring µK. Theory and methods CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of the improved CTI protocol was assessed via simulations. In vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of µK, anisotropic kurtosis, and isotropic kurtosis. Results The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust µK estimation, alongside Kaniso and Kiso metrics. Our CTI experiments revealed positive µK both in white and gray matter of the rat brain in vivo; µK is the dominant kurtosis source in healthy gray matter tissue. The non-negligible µK substantially were found to bias prior MGC analyses of Kiso and Kaniso . Conclusions Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. µK is non-negligible in vivo in healthy white and gray matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future dMRI research.
-
evidence for microscopic kurtosis in neural tissue revealed by Correlation Tensor mri
arXiv: Biological Physics, 2021Co-Authors: Rafael Neto Henriques, Sune Norhoj Jespersen, Noam ShemeshAbstract:Purpose: The impact of microscopic diffusional kurtosis ($\mu K$) - arising from restricted diffusion and/or structural disorder - remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, Correlation Tensor MRI (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori assumptions. Here, we aimed to investigate $\mu K$ in in vivo rat brains and assess its impact on state-of-the-art methods ignoring $\mu K$. Methods: CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of CTI estimates from the improved protocol is assessed in simulations. The in vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of $\mu K$, anisotropic kurtosis, and isotropic kurtosis. Results: The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust $\mu K$ estimation, alongside Kaniso and Kiso metrics. Our CTI experiments revealed positive $\mu K$ both in white and grey matter of the rat brain in vivo; $\mu K$ is the dominant kurtosis source in healthy grey matter tissue. The non-negligible $\mu K$ substantially biases prior state-of-the-art analyses of Kiso and Kaniso. Conclusion: Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. $\mu K$ is non-negligible in vivo in healthy white and grey matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future experiments.
-
Correlation Tensor magnetic resonance imaging
NeuroImage, 2020Co-Authors: Rafael Neto Henriques, Sune Norhoj Jespersen, Noam ShemeshAbstract:Abstract Diffusional Kurtosis Magnetic Resonance Imaging (DKI) quantifies the extent of non-Gaussian water diffusion, which has been shown to be a sensitive biomarker for microstructure in health and disease. However, DKI is not specific to any microstructural property per se since kurtosis may emerge from several different sources. Q-space trajectory encoding schemes have been proposed for decoupling kurtosis arising from the variance of mean diffusivities (isotropic kurtosis) from kurtosis driven by microscopic anisotropy (anisotropic kurtosis). Still, these methods assume that the system is comprised of multiple Gaussian diffusion components with vanishing intra-compartmental kurtosis (associated with restricted diffusion). Here, we develop a more general framework for resolving the underlying kurtosis sources without relying on the multiple Gaussian diffusion approximation. We introduce Correlation Tensor MRI (CTI) – an approach harnessing the versatility of double diffusion encoding (DDE) and its sensitivity to displacement Correlation Tensors capable of explicitly decoupling isotropic and anisotropic kurtosis components from intra-compartmental kurtosis effects arising from restricted (and time-dependent) diffusion. Additionally, we show that, by subtracting these isotropic and anisotropic kurtosis components from the total diffusional kurtosis, CTI provides an index that is potentially sensitive to intra-compartmental kurtosis. The theoretical foundations of CTI, as well as the first proof-of-concept CTI experiments in ex vivo mouse brains at ultrahigh field of 16.4 T, are presented. We find that anisotropic and isotropic kurtosis can decouple microscopic anisotropy from substantial partial volume effects between tissue and free water. Our intra-compartmental kurtosis index exhibited positive values in both white and grey matter tissues. Simulations in different synthetic microenvironments show, however, that our current CTI protocol for estimating intra-compartmental kurtosis is limited by higher order terms that were not taken into account in this study. CTI measurements were then extended to in vivo settings and used to map heathy rat brains at 9.4 T. These in vivo CTI results were found to be consistent with our ex vivo findings. Although future studies are still required to assess and mitigate the higher order effects on the intra-compartmental kurtosis index, our results show that CTI's more general estimates of anisotropic and isotropic kurtosis contributions are already ripe for future in vivo studies, which can have significant impact our understanding of the mechanisms underlying diffusion metrics extracted in health and disease.
Sune Norhoj Jespersen - One of the best experts on this subject based on the ideXlab platform.
-
evidence for microscopic kurtosis in neural tissue revealed by Correlation Tensor mri
Magnetic Resonance in Medicine, 2021Co-Authors: Rafael Neto Henriques, Sune Norhoj Jespersen, Noam ShemeshAbstract:Purpose The impact of microscopic diffusional kurtosis (µK), arising from restricted diffusion and/or structural disorder, remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, Correlation Tensor imaging (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori multi-gaussian component (MGC) or other microstructural assumptions. Here, we investigated µK in in vivo rat brains and assessed its impact on state-of-the-art methods ignoring µK. Theory and methods CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of the improved CTI protocol was assessed via simulations. In vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of µK, anisotropic kurtosis, and isotropic kurtosis. Results The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust µK estimation, alongside Kaniso and Kiso metrics. Our CTI experiments revealed positive µK both in white and gray matter of the rat brain in vivo; µK is the dominant kurtosis source in healthy gray matter tissue. The non-negligible µK substantially were found to bias prior MGC analyses of Kiso and Kaniso . Conclusions Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. µK is non-negligible in vivo in healthy white and gray matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future dMRI research.
-
evidence for microscopic kurtosis in neural tissue revealed by Correlation Tensor mri
arXiv: Biological Physics, 2021Co-Authors: Rafael Neto Henriques, Sune Norhoj Jespersen, Noam ShemeshAbstract:Purpose: The impact of microscopic diffusional kurtosis ($\mu K$) - arising from restricted diffusion and/or structural disorder - remains a controversial issue in contemporary diffusion MRI (dMRI). Recently, Correlation Tensor MRI (CTI) was introduced to disentangle the sources contributing to diffusional kurtosis, without relying on a-priori assumptions. Here, we aimed to investigate $\mu K$ in in vivo rat brains and assess its impact on state-of-the-art methods ignoring $\mu K$. Methods: CTI harnesses double diffusion encoding (DDE) experiments, which were here improved for speed and minimal bias using four different sets of acquisition parameters. The robustness of CTI estimates from the improved protocol is assessed in simulations. The in vivo CTI acquisitions were performed in healthy rat brains using a 9.4T pre-clinical scanner equipped with a cryogenic coil, and targeted the estimation of $\mu K$, anisotropic kurtosis, and isotropic kurtosis. Results: The improved CTI acquisition scheme substantially reduces scan time and importantly, also minimizes higher-order-term biases, thus enabling robust $\mu K$ estimation, alongside Kaniso and Kiso metrics. Our CTI experiments revealed positive $\mu K$ both in white and grey matter of the rat brain in vivo; $\mu K$ is the dominant kurtosis source in healthy grey matter tissue. The non-negligible $\mu K$ substantially biases prior state-of-the-art analyses of Kiso and Kaniso. Conclusion: Correlation Tensor MRI offers a more accurate and robust characterization of kurtosis sources than its predecessors. $\mu K$ is non-negligible in vivo in healthy white and grey matter tissues and could be an important biomarker for future studies. Our findings thus have both theoretical and practical implications for future experiments.
-
Correlation Tensor magnetic resonance imaging
NeuroImage, 2020Co-Authors: Rafael Neto Henriques, Sune Norhoj Jespersen, Noam ShemeshAbstract:Abstract Diffusional Kurtosis Magnetic Resonance Imaging (DKI) quantifies the extent of non-Gaussian water diffusion, which has been shown to be a sensitive biomarker for microstructure in health and disease. However, DKI is not specific to any microstructural property per se since kurtosis may emerge from several different sources. Q-space trajectory encoding schemes have been proposed for decoupling kurtosis arising from the variance of mean diffusivities (isotropic kurtosis) from kurtosis driven by microscopic anisotropy (anisotropic kurtosis). Still, these methods assume that the system is comprised of multiple Gaussian diffusion components with vanishing intra-compartmental kurtosis (associated with restricted diffusion). Here, we develop a more general framework for resolving the underlying kurtosis sources without relying on the multiple Gaussian diffusion approximation. We introduce Correlation Tensor MRI (CTI) – an approach harnessing the versatility of double diffusion encoding (DDE) and its sensitivity to displacement Correlation Tensors capable of explicitly decoupling isotropic and anisotropic kurtosis components from intra-compartmental kurtosis effects arising from restricted (and time-dependent) diffusion. Additionally, we show that, by subtracting these isotropic and anisotropic kurtosis components from the total diffusional kurtosis, CTI provides an index that is potentially sensitive to intra-compartmental kurtosis. The theoretical foundations of CTI, as well as the first proof-of-concept CTI experiments in ex vivo mouse brains at ultrahigh field of 16.4 T, are presented. We find that anisotropic and isotropic kurtosis can decouple microscopic anisotropy from substantial partial volume effects between tissue and free water. Our intra-compartmental kurtosis index exhibited positive values in both white and grey matter tissues. Simulations in different synthetic microenvironments show, however, that our current CTI protocol for estimating intra-compartmental kurtosis is limited by higher order terms that were not taken into account in this study. CTI measurements were then extended to in vivo settings and used to map heathy rat brains at 9.4 T. These in vivo CTI results were found to be consistent with our ex vivo findings. Although future studies are still required to assess and mitigate the higher order effects on the intra-compartmental kurtosis index, our results show that CTI's more general estimates of anisotropic and isotropic kurtosis contributions are already ripe for future in vivo studies, which can have significant impact our understanding of the mechanisms underlying diffusion metrics extracted in health and disease.
-
the displacement Correlation Tensor microstructure ensemble anisotropy and curving fibers
Journal of Magnetic Resonance, 2011Co-Authors: Sune Norhoj Jespersen, Niels BuhlAbstract:Experiments with multiple diffusion wave vectors are known to carry more information than what is available from standard diffusion experiments. Here we consider a special case of this class of pulse sequences, the double wave vector diffusion experiment, and use the cumulant expansion of the signal to introduce the displacement Correlation Tensor. We discuss its physical interpretation and properties, noting in particular that its short time behavior allows determination of the surface to volume ratio of the pore space. We present a general expression for the displacement Correlation Tensor, and provide explicit expressions for a few model geometries. We then show that the scatter matrix characterizing the orientation distribution of an ensemble of cylinders is simply related to the displacement Correlation Tensor. This result is generalized to ensembles of pores with arbitrary shapes allowing a precise formulation of the influence of microstructural and ensemble anisotropy on the double wave vector diffusion signal in the Gaussian phase approximation. Finally, as a new application of the double wave vector diffusion signal, we analyze its behavior in a curving fiber, and suggest that the displacement Correlation Tensor may be used to estimate sub-voxel fiber curvature and deflection angle. The theoretical results are corroborated by computer simulations.
