Bessel Fourier Orientation Reconstruction: An Analytical EAP Reconstruction Using Multiple Shell Acquisitions in Diffusion MRI

Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu-Chien; Alexander, Andrew L.

doi:10.1007/978-3-642-23629-7_27

Cited by 7 publications

(7 citation statements)

References 13 publications

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“…The acquisition time for whole-brain coverage with these approaches is on the order of 15 minutes to more than an hour. Recently analytic model solutions for estimating the propagator based upon q -space measurements have been proposed including diffusion propagator imaging (DPI) (Descoteaux et al, 2011), spherical polar Fourier expansion (SPF) (Assemlal et al, 2009), and Bessel Fourier orientation reconstruction (BFOR) (Hosseinbor et al, 2011). These analytic models may enable sparser sampling schemes of q -space to be used.…”

Section: Diffusion Mrimentioning

confidence: 99%

Characterization of Cerebral White Matter Properties Using Quantitative Magnetic Resonance Imaging Stains

Alexander

Samsonov²,

Adluru³

et al. 2011

Brain Connectivity

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406

380

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The image contrast in magnetic resonance imaging (MRI) is highly sensitive to several mechanisms that are modulated by the properties of the tissue environment. The degree and type of contrast weighting may be viewed as image filters that accentuate specific tissue properties. Maps of quantitative measures of these mechanisms, akin to microstructural/environmental-specific tissue stains, may be generated to characterize the MRI and physiological properties of biological tissues. In this paper, three quantitative MRI (qMRI) methods for characterizing white matter microstructural properties are reviewed. All of these measures measure complementary aspects of how water interacts with the tissue environment. Diffusion MRI including diffusion tensor imaging characterizes the diffusion of water in the tissues and is sensitive to the microstructural density, spacing and orientational organization of tissue membranes including myelin. Magnetization transfer imaging characterizes the amount and degree of magnetization exchange between free water and macromolecules like proteins found in the myelin bilayers. Relaxometery measures the MRI relaxation constants T1 and T2, which in white matter has a component associated with the water trapped in the myelin bilayers. The conduction of signals between distant brain regions occurs primarily through myelinated white matter tracts, thus these methods are potential indicators of pathology and structural connectivity in the brain. This paper provides an overview of the qMRI stain mechanisms, acquisition and analysis strategies, and applications for these qMRI stains.

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Section: Diffusion Mrimentioning

confidence: 99%

Characterization of Cerebral White Matter Properties Using Quantitative Magnetic Resonance Imaging Stains

Alexander

Samsonov²,

Adluru³

et al. 2011

Brain Connectivity

Self Cite

406

380

View full text Add to dashboard Cite

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“…Therefore, the development of a robust analytical model of the signal that could be used to describe data acquired over the entire three-dimensional q -space would be highly useful. To this end, several models have been introduced in recent years to represent the three-dimensional q -space signal (Özarslan et al, 2006b, 2009c; Assemlal et al, 2009; Ozcan, 2010; Cheng et al, 2010; Descoteaux et al, 2011; Hosseinbor et al, 2011; Assemlal et al, 2011; Yeh et al, 2011; Ye et al, 2012). …”

Section: Introductionmentioning

confidence: 99%

Mean apparent propagator (MAP) MRI: A novel diffusion imaging method for mapping tissue microstructure

et al. 2013

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Diffusion-weighted magnetic resonance (MR) signals reflect information about underlying tissue microstructure and cytoarchitecture. We propose a quantitative, efficient, and robust mathematical and physical framework for representing diffusion-weighted MR imaging (MRI) data obtained in “q-space,” and the corresponding “mean apparent propagator (MAP)” describing molecular displacements in “r-space.” We also define and map novel quantitative descriptors of diffusion that can be computed robustly using this MAP-MRI framework. We describe efficient analytical representation of the three-dimensional q-space MR signal in a series expansion of basis functions that accurately describes diffusion in many complex geometries. The lowest order term in this expansion contains a diffusion tensor that characterizes the Gaussian displacement distribution, equivalent to diffusion tensor MRI (DTI). Inclusion of higher order terms enables the reconstruction of the true average propagator whose projection onto the unit “displacement” sphere provides an orientational distribution function (ODF) that contains only the orientational dependence of the diffusion process. The representation characterizes novel features of diffusion anisotropy and the non-Gaussian character of the three-dimensional diffusion process. Other important measures this representation provides include the return-to-the-origin probability (RTOP), and its variants for diffusion in one- and two-dimensions—the return-to-the-plane probability (RTPP), and the return-to-the-axis probability (RTAP), respectively. These zero net displacement probabilities measure the mean compartment (pore) volume and cross-sectional area in distributions of isolated pores irrespective of the pore shape. MAP-MRI represents a new comprehensive framework to model the three-dimensional q-space signal and transform it into diffusion propagators. Experiments on an excised marmoset brain specimen demonstrate that MAP-MRI provides several novel, quantifiable parameters that capture previously obscured intrinsic features of nervous tissue microstructure. This should prove helpful for investigating the functional organization of normal and pathologic nervous tissue.

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“…In this paper, we present Bessel Fourier Orientation Reconstruction (BFOR) (Hosseinbor et al, 2011). Rather than assuming the signal satisfies Laplace’s equation, we reformulate the problem into a Cauchy problem and assume E ( q ) satisfies the heat equation.…”

Section: Introductionmentioning

confidence: 99%

Bessel Fourier Orientation Reconstruction (BFOR): An analytical diffusion propagator reconstruction for hybrid diffusion imaging and computation of q-space indices

Hosseinbor

Chung

et al. 2013

NeuroImage

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The ensemble average propagator (EAP) describes the 3D average diffusion process of water molecules, capturing both its radial and angular contents. The EAP can thus provide richer information about complex tissue microstructure properties than the orientation distribution function (ODF), an angular feature of the EAP. Recently, several analytical EAP reconstruction schemes for multiple q-shell acquisitions have been proposed, such as diffusion propagator imaging (DPI) and spherical polar Fourier imaging (SPFI). In this study, a new analytical EAP reconstruction method is proposed, called Bessel Fourier orientation reconstruction (BFOR), whose solution is based on heat equation estimation of the diffusion signal for each shell acquisition, and is validated on both synthetic and real datasets. A significant portion of the paper is dedicated to comparing BFOR, SPFI, and DPI using hybrid, non-Cartesian sampling for multiple b-value acquisitions. Ways to mitigate the effects of Gibbs ringing on EAP reconstruction are also explored. In addition to analytical EAP reconstruction, the aforementioned modeling bases can be used to obtain rotationally invariant q-space indices of potential clinical value, an avenue which has not yet been thoroughly explored. Three such measures are computed: zero-displacement probability (Po), mean squared displacement (MSD), and generalized fractional anisotropy (GFA).

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Bessel Fourier Orientation Reconstruction: An Analytical EAP Reconstruction Using Multiple Shell Acquisitions in Diffusion MRI

Cited by 7 publications

References 13 publications

Characterization of Cerebral White Matter Properties Using Quantitative Magnetic Resonance Imaging Stains

Characterization of Cerebral White Matter Properties Using Quantitative Magnetic Resonance Imaging Stains

Mean apparent propagator (MAP) MRI: A novel diffusion imaging method for mapping tissue microstructure

Bessel Fourier Orientation Reconstruction (BFOR): An analytical diffusion propagator reconstruction for hybrid diffusion imaging and computation of q-space indices

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