Diffusion broadening of the point spread function in steady-state MRI
Abstract
Purpose: To demonstrate how diffusion blurs the longitudinal magnetization in steady-state gradient-echo imaging, quantify resolution dependence on flip angle and repetition time, and the effects on relaxometry at microscopic resolution. Methods: Diffusion was incorporated into the Bloch-Torrey equation in k space to determine how the point spread function (PSF) of T1-weighted spoiled gradient-echo images varies with flip angle. Theoretical predictions were validated numerically and extended to b-SSFP. Results: Diffusion acts as a low-pass filter whose width depends on the diffusion rate (D), repetition time (TR), T1 and flip angle (α). The blurring length spans from √(D · TR/2) at large α to √(D T1) as α→ 0, equaling √(D T1/2) at the Ernst angle. Consequently, multi-angle acquisitions have mismatched resolution (PSF widths of 39 μm at α= 10∘ versus 11 μm at α= 80∘ for TR = 50 ms). For the flip-angle pair optimizing variable-flip-angle T1 mapping, the effective resolutions differ by a factor of 2.4. In simulated DESPOT1 maps the R1 of a 30 μm feature is reduced to 1.80 s−1 (true value 2.00 s−1). In b-SSFP, blurring depends on T1, T2, and α but is independent of TR, with a minimum of √(D T2). Conclusion: The PSF of a steady-state sequence depends on the flip angle and T1. Combining images acquired at different flip angles implicitly assumes identical spatial resolution, but that is not valid at microscopic scales, affecting the accuracy of quantitative relaxometry. The theory identifies a new limitation on the ultimate resolution of MRI set by diffusion.
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BibTeX
@misc{dhakal2026diffusion,
title = {{Diffusion broadening of the point spread function in steady-state MRI}},
author = {Bibek Dhakal and John C. Gore},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02132},
eprint = {2610.02132},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02132},
}
RIS
TY - UNPB
TI - Diffusion broadening of the point spread function in steady-state MRI
AU - Bibek Dhakal
AU - John C. Gore
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02132
UR - https://arxiv.org/abs/2610.02132
AB - Purpose: To demonstrate how diffusion blurs the longitudinal magnetization in steady-state gradient-echo imaging, quantify resolution dependence on flip angle and repetition time, and the effects on relaxometry at microscopic resolution. Methods: Diffusion was incorporated into the Bloch-Torrey equation in k space to determine how the point spread function (PSF) of T_1-weighted spoiled gradient-echo images varies with flip angle. Theoretical predictions were validated numerically and extended to b-SSFP. Results: Diffusion acts as a low-pass filter whose width depends on the diffusion rate (D), repetition time (TR), T_1 and flip angle (α). The blurring length spans from √(D · TR/2) at large α to √(D T_1) as α→ 0, equaling √(D T_1/2) at the Ernst angle. Consequently, multi-angle acquisitions have mismatched resolution (PSF widths of 39 μm at α= 10^∘ versus 11 μm at α= 80^∘ for TR = 50 ms). For the flip-angle pair optimizing variable-flip-angle T_1 mapping, the effective resolutions differ by a factor of 2.4. In simulated DESPOT1 maps the R_1 of a 30 μm feature is reduced to 1.80 s^−1 (true value 2.00 s^−1). In b-SSFP, blurring depends on T_1, T_2, and α but is independent of TR, with a minimum of √(D T_2). Conclusion: The PSF of a steady-state sequence depends on the flip angle and T_1. Combining images acquired at different flip angles implicitly assumes identical spatial resolution, but that is not valid at microscopic scales, affecting the accuracy of quantitative relaxometry. The theory identifies a new limitation on the ultimate resolution of MRI set by diffusion.
ER -