Extracting Quantitative Measures from EAP: A Small Clinical Study Using BFOR

Hosseinbor, A. Pasha; Chung, Moo K.; Wu, Yu‐Chien; Fleming, John O.; Field, Aaron S.; Alexander, Andrew L.

doi:10.1007/978-3-642-33418-4_35

Cited by 7 publications

(12 citation statements)

References 18 publications

(34 reference statements)

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“…This pitfall is usually circumvented by defining scalar measures directly related to the characteristics of diffusion acting as biomarkers candidates (such as diffusivity, anisotropy, intracellular vs. extra-cellular water movement, etcetera). Some late examples are the probability of zero displacement (or return-to-origin probability, RTOP), the mean-squared displacement (MSD), the qspace inverse variance (QIV), or the return-to-plane and return-to-axis probabilities (RTPP, RTAP) (Hosseinbor et al, 2012;Wu et al, 2008;Ning et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Microstructure Diffusion Scalar Measures from Reduced MRI Acquisitions

Aja‐Fernández¹,

Luis‐García²,

Afzali³

et al. 2019

Preprint

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In diffusion MRI, the Ensemble Average diffusion Propagator (EAP) provides relevant microstructural information and meaningful descriptive maps of the white matter previously obscured by traditional techniques like the Diffusion Tensor. The direct estimation of the EAP, however, requires a dense sampling of the Cartesian q-space. Due to the huge amount of samples needed for an accurate reconstruction, more efficient alternative techniques have been proposed in the last decade. Even so, all of them imply acquiring a large number of diffusion gradients with different b-values. In order to use the EAP in practical studies, scalar measures must be directly derived, being the most common the return-to-origin probability (RTOP) and the return-to-plane and return-to-axis probabilities (RTPP, RTAP).In this work, we propose the so-called "Apparent Measures Using Reduced Acquisitions" (AMURA) to drastically reduce the number of samples needed for the estimation of diffusion properties. AMURA avoids the calculation of the whole EAP by assuming the diffusion anisotropy is roughly independent from the radial direction. With such an assumption, and as opposed to common multi-shell procedures based on iterative optimization, we achieve closed-form expressions for the measures using information from one single shell. This way, the new methodology remains compatible with standard acquisition protocols commonly used for HARDI (based on just one b-value). We report extensive results showing the potential of AMURA to reveal microstructural properties of the tissues compared to state of the art EAP estimators, and is well above that of Diffusion Tensor techniques. At the same time, the closed forms provided for RTOP, RTPP, and RTAP-like magnitudes make AMURA both computationally efficient and robust.

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Section: Introductionmentioning

confidence: 99%

Microstructure Diffusion Scalar Measures from Reduced MRI Acquisitions

Aja‐Fernández¹,

Luis‐García²,

Afzali³

et al. 2019

Preprint

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“…The second-order moment tensor of E ( q ) is defined as R q ≜ ∫ ℛ 2 qq T E ( q ) d q which is a 3 × 3 positive-semidefinite matrix. In the proposed method, R q is estimated as

R_{q} = 2 π^{\frac{3}{2}} \sum_{n = 0}^{N} w_{n} {∣ D_{n} ∣}^{- \frac{1}{2}} (\frac{1}{2} D_{n}^{- 1} + {\overset{q}{true}}_{n} {\overset{q}{true}}_{n}^{T}) .

As an analogy to the mean-squared-displacement (MSD), we define the q-space mean-squared-displacement (QMSD) as

QMSD ≜ \int_{ℝ^{2}} {false‖ bold-italicq false‖}^{2} E false(bold-italicq false) d bold-italicq = trace false(R_{q} false) .

The reciprocal of QMSD was referred to as the q-space inverse variance (QIV) in [41], [42]. For Gaussian propagators, R g equals to the inverse of the covariance R of P ( r ).…”

Section: A Second Order Momentmentioning

confidence: 99%

“…The reciprocal of QMSD was referred to as the q-space inverse variance (QIV) in [41], [42]. For Gaussian propagators, R g equals to the inverse of the covariance R of P ( r ).…”

Section: A Second Order Momentmentioning

confidence: 99%

Estimating Diffusion Propagator and Its Moments Using Directional Radial Basis Functions

Ning

Westin

Rathi

2015

IEEE Trans. Med. Imaging

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The ensemble average diffusion propagator (EAP) obtained from diffusion MRI (dMRI) data captures important structural properties of the underlying tissue. As such, it is imperative to derive an accurate estimate of the EAP from the acquired diffusion data. In this work, we propose a novel method for estimating the EAP by representing the diffusion signal as a linear combination of directional radial basis functions scattered in q-space. In particular, we focus on a special case of anisotropic Gaussian basis functions and derive analytical expressions for the diffusion orientation distribution function (ODF), the return-to-origin probability (RTOP), and mean-squared-displacement (MSD). A significant advantage of the proposed method is that the second and the fourth order moment tensors of the EAP can be computed explicitly. This allows for computing several novel scalar indices (from the moment tensors) such as mean-fourth-order-displacement (MFD) and generalized kurtosis (GK) – which is a generalization of the mean kurtosis measure used in diffusion kurtosis imaging. Additionally, we also propose novel scalar indices computed from the signal in q-space, called the q-space mean-squared-displacement (QMSD) and the q-space mean-fourth-order-displacement (QMFD), which are sensitive to short diffusion time scales. We validate our method extensively on data obtained from a physical phantom with known crossing angle as well as on in-vivo human brain data. Our experiments demonstrate the robustness of our method for different combinations of b-values and number of gradient directions.

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“…The QIV is a more robust measure of diffusivity than the MSD, especially when high b -values are concerned, and exhibits white matter/gray matter contrast unlike the MSD (Hosseinbor et al, 2012). The QIV is defined mathematically as QIV = [ ∫q 2 E (q) d 3 q] −1 .…”

Section: Theorymentioning

confidence: 99%

A 4D hyperspherical interpretation of q-space

Hosseinbor

Chung

et al. 2015

Medical Image Analysis

Self Cite

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Abstract3D q-space can be viewed as the surface of a 4D hypersphere. In this paper, we seek to develop a 4D hyperspherical interpretation of q-space by projecting it onto a hypersphere and subsequently modeling the q-space signal via 4D hyperspherical harmonics (HSH). Using this orthonormal basis, we analytically derive several quantitative indices and numerically estimate the diffusion ODF. Importantly, we derive the integral transform describing the relationship between the diffusion signal and propagator on a hypersphere. We also show that the HSH basis expends less fitting parameters than other well-established methods to achieve comparable signal and better ODF reconstructions. All in all, this work provides a new way of looking at q-space.

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Extracting Quantitative Measures from EAP: A Small Clinical Study Using BFOR

Cited by 7 publications

References 18 publications

Microstructure Diffusion Scalar Measures from Reduced MRI Acquisitions

Microstructure Diffusion Scalar Measures from Reduced MRI Acquisitions

Estimating Diffusion Propagator and Its Moments Using Directional Radial Basis Functions

A 4D hyperspherical interpretation of q-space

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