Temporal stability of adaptive 3D radial MRI using multidimensional golden means

Abstract

Breast tumor diagnosis requires both high spatial resolution to obtain information about tumor morphology and high temporal resolution to probe the kinetics of contrast uptake. Adaptive sampling of k-space allows images in dynamic contrast-enhanced (DCE)-magnetic resonance imaging (MRI) to be reconstructed at various spatial or temporal resolutions from the same dataset. However, conventional radial approaches have limited flexibility that restricts image reconstruction to predetermined resolutions. Golden-angle radial k-space sampling achieves flexibility in-plane with samples that are incremented by the golden angle, which fills two-dimensional (2D) k-space with radial spokes that have a relatively uniform angular distribution for any time interval. We extend this method to threedimensional (3D) radial sampling, or 3D-Projection Reconstruction (3D-PR) using multidimensional golden means, which are derived from modified Fibonacci sequences by an eigenvalue approach. (1) and patients with hereditary breast cancer (HBC) have an 85% lifetime risk of contracting the disease (2). Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a highly sensitive technique for detecting breast cancers (3-5), but specificity is somewhat lower (6). Diagnosis of breast lesions using DCE-MRI could potentially be made more accurate using images that have high spatial resolution to characterize lesion morphology, and high temporal resolution to probe the contrast kinetics of a lesion. However, there is an intrinsic trade-off between temporal and spatial resolution in MRI, and there is currently little agreement on an optimal balance of temporal and spatial resolution.Adaptive sampling of k-space data, first proposed by Song et al. (7), achieves both high spatial or high temporal resolution images from the same dataset by frequently sampling the central part of k-space that gives useful information regarding image contrast. Originally used for the purposes of time-resolved angiography, projection reconstruction-time-resolved imaging of contrast kinetics (PR-TRICKS) (8), is an example of a trajectory that samples 3D k-space in an adaptive manner. PR-TRICKS sampling allows both high temporal resolution (fast) images to be reconstructed from blocks of central k-space data, or high spatial resolution images to be obtained by including data from the periphery of k-space. Ramsay et al. (9) have applied PR-TRICKS imaging to breast DCE-MRI in an adaptive manner to reconstruct images at discrete temporal/spatial resolutions. Although fast images from PR-TRICKS contain useful image contrast, they are corrupted by aliasing artifacts that arise from undersampling. The temporal instability of these streaking artifacts over successive fast images can reduce the accuracy of physiological parameters derived from pharmacokinetic modelling of enhancement curves. Minimizing these undersampling artifacts is important to improving the diagnostic quality of high-temporal-resolution images.It has been shown that if the streaking artifacts are p...

Carotid Intraplaque Hemorrhage Imaging with Quantitative Vessel Wall T1 Mapping: Technical Development and Initial Experience

“…A 3D golden angle order is proposed to achieve a uniform distribution of spokes that are used for reconstruction at a certain inversion time (Fig 1b). For spokes acquired at the same inversion time in adjacent IRTRs (eg, S 1, S 1′ in Fig 1a), the azimuthal angle increment (Δβ) and the polar angle increment (Δα) are defined, as follows: $$\mathrm{normal\Delta }\mathrm{normal\beta }\left(S1,S{1}^{\prime }\right)=\mathrm{normalacos}\left(\left\{{\varphi }_1\right\}\right),\mathrm{normal\Delta }\mathrm{normal\alpha }\left(S1,S{1}^{\prime }\right)=2{\pi }^{\ast }\left\{{\varphi }_2\right\},$$where ϕ 1 and ϕ 2 are the two-dimensional (2D) golden angle means (14), and the “∙” operator means to extract the fraction parts. For adjacent spokes in an IRTR (eg, S 1, S 2 in Fig 1a), the angle increments are defined as follows: $$\mathrm{normal\Delta }\mathrm{normal\beta }\left(S1,S2\right)=\mathrm{normalacos}\left(\left\{\mathrm{M}{\varphi }_1\right\}\right),\mathrm{normal\Delta }\mathrm{normal\alpha }\left(S1,S2\right)=2{\pi }^{\ast }\left\{M{\varphi }_2\right\},$$where M is the total number of IRTRs.…”

Four‐dimensional MRI using three‐dimensional radial sampling with respiratory self‐gating to characterize temporal phase‐resolved respiratory motion in the abdomen

“…In an attempt to preserve the sampling pattern stability required for arbitrary retrospective data sorting, the 3D radial k -space is filled using the 2D golden means ordering (26), a generalization of the original golden-angle ordering for 2D radial imaging (27). The polar and azimuthal angles are calculated using the following equations: $${\theta }_m={\cos }^{-1}false(\mathrm{italicmod}false(m{\phi }_1,1false)false),m=1,2,\dots$$ $${\varphi }_m=2\pi \mathrm{italicmod}false(m{\phi }_2,1false),m=1,2,\dots$$ where φ 1 = 0.4656 and φ 2 =0.6823 are the 2D golden means, θ is the polar angle, ϕ is the azimuthal angle, and m is the radial line index.…”

Feasibility of high temporal resolution breast DCE‐MRI using compressed sensing theory

“…20 Because of their mutual importance, consistent efforts have been aimed at accomplishing both high temporal and spatial resolution DCE-MRI. [21][22][23][24][25][26][27] A recently developed mathematical theory of signal processing and data acquisition, compressed sensing ͑CS͒ theory, [28][29][30][31] provides a novel way to accomplish this goal. The breakthrough in the CS theory is its ability to allow images to be faithfully recovered from what appear to be highly incomplete data sets, where one of the central tenets of signal processing and data acquisition, the Nyquist sampling theory, has been violated.…”