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Some new angles on the magic angle: what MSK radiologists know and don’t know about this phenomenon

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Abstract

Purpose

Magic angle effects (MAE) are well-recognized in musculoskeletal (MSK) MRI. With short TE acquisitions, the signal intensity of tendons, ligaments, and menisci depend on their orientation relative to the main magnetic field (B0). An interactive resident physics teaching module simulating MR imaging of a tendon forced us to identify and correct several misconceptions we had about MAE. We suspected these misconceptions were shared by other MSK radiologists.

Materials and methods

We surveyed members of the Society of Academic Bone Radiologists (SABR) regarding which pulse sequences, acquisition parameters, tissues and angles relative to B0 were most likely to produce MAE.

Results

Survey respondents knew that MAE strongly depend on TE and commonly appear on T1W, FSE and PD sequences, but were less aware that MAE may also appear on T2W, STIR and DWI sequences. They knew of MAE effects in tendons, ligaments and cartilage, but were less aware of those in entheses, peripheral nerves and intervertebral discs. Respondents underestimated the wide angular range (full-width at half-maximum ≈ 40∘) over which significant MAE can be seen with short TE.

Conclusions

Collagen-containing tissues with parallel molecular alignment exhibit increased signal intensity when oriented at 55∘ relative to B0. Experienced MSK radiologists were found to underestimate the combinations of image parameters, pulse sequences, tissues and collagen orientations in which significant MAE may be seen. Our survey results highlight the need for ongoing MR physics education for practicing radiologists.

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Author information

Authors and Affiliations

  1. Department of Radiology, University of Washington, Seattle, WA, USA

    Michael L. Richardson & Todd L. Richards

  2. Department of Radiology, M. D. Anderson Cancer Center, Houston, TX, USA

    Behrang Amini

Authors
  1. Michael L. Richardson
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  2. Behrang Amini
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  3. Todd L. Richards
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Corresponding author

Correspondence to Michael L. Richardson.

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Conflict of interests

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Additional information

This research was presented as an electronic poster at the annual Meeting of the Society of Skeletal Radiology, March 2018.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Appendix A

Appendix A

Our simulator was created using Project Jupyter Jupyter [21, 22] and the code is available online (http://uwmsk.org/jupyter/).

A.1 Calibration of magic angle effect simulator

We calibrated our model using measurements from experimental tendon data for conventional spin-echo (CSE), fast spin-echo (FSE) and gradient echo (GRE) sequences published by Li and Mirowitz [4]. To calibrate our model we performed two sequential curve fits for each pulse sequence (CSE, FSE and GRE), using non-linear least-squares regression. These non-linear curve fits were performed using the scipy.optimize.curve_fit algorithm from the Scientific Python (SciPy) library [23, 24]. In the first regression for each pulse sequence, we fitted Eq. 1 to the tendon signal intensity data as a function of orientation angle. The least-squares coefficients (S1, S0 and α) from these initial fits were then applied to Eq. 3, and a second non-linear regression was performed to estimate β, the exponential decay constant for MAE signal intensity as a function of TE. This second regression was performed for each pulse sequence.

Once intensity has been calculated for each portion of the tendon, our simulator automatically enhances the contrast of the MAE in the tendon to improve its conspicuity. The highest intensity area of the MAE is automatically scaled to white, and the lowest intensity portion of the tendon is automatically scaled to black, with a linear ramp of gray scale values between those intensity values.

A.2 Validation of magic angle simulator

Non-linear least-squares procedure resulted in close fits of our model to the experimental tendon data from Li and Mirowitz (Figs. 7, 8, 9, and 10).

Fig. 7
figure 7

Non-linear least-squares fits of Eq. 3 to the Li and Mirowitz tendon data [25] for gradient echo (GRE) sequences (TE = 9 msec), fast spin-echo (FSE) (TE = 9 msec), and conventional spin-echo (CSE) (TE = 10 msec), where T2 = 1.5 msec. Least-squares coefficients for these fits for GRE: α = 0.159, S1 = 88.4, and S0 = 348. Least-squares coefficients for these fits for FSE: α = 0.125, S1 = 89.5, and S0 = 427. Least-squares coefficients for these fits for CSE: α = 0.190S1 = 121, and S0 = 514

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Fig. 8
figure 8

Non-linear least-squares fit of the Li and Mirowitz tendon data [25] for conventional spin-echo (CSE) where T2 = 1.5 msec. Least-squares fit for β, the exponential decay constant was 0.0766

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Fig. 9
figure 9

Non-linear least-squares fit of the Li and Mirowitz tendon data [25] for fast spin-echo (FSE) where T2 = 1.5 msec. Least-squares fit for β, the exponential decay constant was 0.0504

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Fig. 10
figure 10

Non-linear least-squares fit of the Li and Mirowitz tendon data [25] for gradient echo (GRE) where T2 = 1.5 msec. Least-squares fit for β, the exponential decay constant was 0.141

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Richardson, M.L., Amini, B. & Richards, T.L. Some new angles on the magic angle: what MSK radiologists know and don’t know about this phenomenon. Skeletal Radiol 47, 1673–1681 (2018). https://doi.org/10.1007/s00256-018-3011-8

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  • DOI: https://doi.org/10.1007/s00256-018-3011-8

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