3-Dimensional magnetic resonance imaging of the freely moving human eye

On the Determination of Lagrange Multipliers for a Weighted LASSO Problem Using Geometric and Convex Analysis Techniques

Compressed Sensing (CS) encompasses a broad array of theoretical and applied techniques for recovering signals, given partial knowledge of their coefficients, cf. Candés (C. R. Acad. Sci. Paris, Ser. I 346, 589-592 (2008)), Candés et al. (IEEE Trans. Inf. Theo (2006)), Donoho (IEEE Trans. Inf. Theo. 52(4), (2006)), Donoho et al. (IEEE Trans. Inf. Theo. 52(1), (2006)). Its applications span various fields, including mathematics, physics, engineering, and several medical sciences, cf. Adcock and Hansen (Compressive Imaging: Structure, Sampling, Learning, p. 2021), Berk et al. (2019 13th International conference on Sampling Theory and Applications (SampTA) pp. 1-5. IEEE (2019)), Brady et al. (Opt. Express 17(15), 13040-13049 (2009)), Chan (Terahertz imaging with compressive sensing. Rice University, USA (2010)), Correa et al. (2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) pp. 7789-7793 (2014, May) IEEE), Gao et al. (Nature 516(7529), 74-77 (2014)), Liu and Kang (Opt. Express 18(21), 22010-22019 (2010)), McEwen and Wiaux (Mon. Notices Royal Astron. Soc. 413(2), 1318-1332 (2011)), Marim et al. (Opt. Lett. 35(6), 871-873 (2010)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)), Yu and Wang (Phys. Med. Biol. 54(9), 2791 (2009)). Motivated by our interest in the mathematics behind Magnetic Resonance Imaging (MRI) and CS, we employ convex analysis techniques to analytically determine equivalents of Lagrange multipliers for optimization problems with inequality constraints, specifically a weighted LASSO with voxel-wise weighting. We investigate this problem under assumptions on the fidelity term A x - b 2 2 , either concerning the sign of its gradient or orthogonality-like conditions of its matrix. To be more precise, we either require the sign of each coordinate of 2 ( A x - b ) T A to be fixed within a rectangular neighborhood of the origin, with the side lengths of the rectangle dependent on the constraints, or we assume A T A to be diagonal. The objective of this work is to explore the relationship between Lagrange multipliers and the constraints of a weighted variant of LASSO, specifically in the mentioned cases where this relationship can be computed explicitly. As they scale the regularization terms of the weighted LASSO, Lagrange multipliers serve as tuning parameters for the weighted LASSO, prompting the question of their potential effective use as tuning parameters in applications like MR image reconstruction and denoising. This work represents an initial step in this direction.

Hi-Fi fMRI: High-resolution, fast-sampled and sub-second whole-brain functional MRI at 3T in humans

Functional magnetic resonance imaging (fMRI) is a methodological cornerstone of neuroscience. Most studies measure blood-oxygen-level-dependent (BOLD) signal using echo-planar imaging (EPI), Cartesian sampling, and image reconstruction with a one-to-one correspondence between the number of acquired volumes and reconstructed images. However, EPI schemes are subject to trade-offs between spatial and temporal resolutions. We overcome these limitations by measuring BOLD with a gradient recalled echo (GRE) with 3D radial-spiral phyllotaxis trajectory at a high sampling rate (28.24ms) on standard 3T field-strength. The framework enables the reconstruction of 3D signal time courses with whole-brain coverage at simultaneously higher spatial (1mm ³ ) and temporal (up to 250ms) resolutions, as compared to optimized EPI schemes. Additionally, artifacts are corrected before image reconstruction; the desired temporal resolution is chosen after scanning and without assumptions on the shape of the hemodynamic response. By showing activation in the calcarine sulcus of 20 participants performing an ON-OFF visual paradigm, we demonstrate the reliability of our method for cognitive neuroscience research.

Magnetic resonance-based eye tracking using deep neural networks

Viewing behavior provides a window into many central aspects of human cognition and health, and it is an important variable of interest or confound in many functional magnetic resonance imaging (fMRI) studies. To make eye tracking freely and widely available for MRI research, we developed DeepMReye, a convolutional neural network (CNN) that decodes gaze position from the magnetic resonance signal of the eyeballs. It performs cameraless eye tracking at subimaging temporal resolution in held-out participants with little training data and across a broad range of scanning protocols. Critically, it works even in existing datasets and when the eyes are closed. Decoded eye movements explain network-wide brain activity also in regions not associated with oculomotor function. This work emphasizes the importance of eye tracking for the interpretation of fMRI results and provides an open source software solution that is widely applicable in research and clinical settings.

Ultra-High Field Magnetic Resonance Imaging of the Retrobulbar Optic Nerve, Subarachnoid Space, and Optic Nerve Sheath in Emmetropic and Myopic Eyes

Purpose

We aimed to image the optic nerve, subarachnoid space and optic nerve sheath in emmetropes and myopes ultra-high field (7-Tesla) magnetic resonance imaging (MRI). We targeted the retrobulbar distance of approximately 3 mm behind the eyeball, an area of clinical interest because of optic nerve sheath distensibility and pressure-related enlargement.

Methods

Eleven emmetropes (+0.75 to −0.50D, aged 20–41 years) and 10 myopes (−4.5 to −12D, aged 21–37 years) participated. Cross-sectional area of the optic nerve, subarachnoid space and optic nerve sheath at approximately 3 mm behind the eye were measured from two-dimensional T2-weighted coronal oblique MRI images obtained through the left optic nerve. Axial length of the left eye was measured from T2-weighted axial MRI images. In nine emmetropes and seven myopes, the optic nerve head was imaged with optical coherence tomography to compare retrobulbar and intraocular measures.

Results

Retrobulbar optic nerve, subarachnoid space and optic nerve sheath dimensions differed between myopes and emmetropes. Myopes tended to have smaller optic nerve and subarachnoid space. Longer MRI-derived axial length was associated with smaller optic nerve area (P = 0.03). Bruch's membrane opening area did not predict retrobulbar optic nerve area (P = 0.48).

Conclusions

This study demonstrates the feasibility of using 7-Tesla MRI to measure optic nerve, subarachnoid space, and optic nerve sheath dimensions behind the eye. In healthy adults, the retrobulbar optic nerve and subarachnoid space size are influenced by the degree of myopia.

Translational Relevance

ultra-high field MRI is a practical tool for assessing the morphometry of the optic nerve and surrounding anatomy behind the eye.

Ophthalmic Magnetic Resonance Imaging: Where Are We (Heading To)?

Magnetic resonance imaging of the eye and orbit (MReye) is a cross-domain research field, combining (bio)physics, (bio)engineering, physiology, data sciences and ophthalmology. A growing number of reports document technical innovations of MReye and promote their application in preclinical research and clinical science. Realizing the progress and promises, this review outlines current trends in MReye. Examples of MReye strategies and their clinical relevance are demonstrated. Frontier applications in ocular oncology, refractive surgery, ocular muscle disorders and orbital inflammation are presented and their implications for explorations into ophthalmic diseases are provided. Substantial progress in anatomically detailed, high-spatial resolution MReye of the eye, orbit and optic nerve is demonstrated. Recent developments in MReye of ocular tumors are explored, and its value for personalized eye models derived from machine learning in the treatment planning of uveal melanoma and evaluation of retinoblastoma is highlighted. The potential of MReye for monitoring drug distribution and for improving treatment management and the assessment of individual responses is discussed. To open a window into the eye and into (patho)physiological processes that in the past have been largely inaccessible, advances in MReye at ultrahigh magnetic field strengths are discussed. A concluding section ventures a glance beyond the horizon and explores future directions of MReye across multiple scales, including in vivo electrolyte mapping of sodium and other nuclei. This review underscores the need for the (bio)medical imaging and ophthalmic communities to expand efforts to find solutions to the remaining unsolved problems and technical obstacles of MReye, with the objective to transfer methodological advancements driven by MR physics into genuine clinical value.