Year: 2026
Type: preprint
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 $T_1$-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 $\sqrt{D \cdot \mathrm{TR}/2}$ at large $α$ to $\sqrt{D T_1}$ as $α\rightarrow 0$, equaling $\sqrt{D T_1/2}$ at the Ernst angle. Consequently, multi-angle acquisitions have mismatched resolution (PSF widths of 39 $μ$m at $α= 10^\circ$ versus 11 $μ$m at $α= 80^\circ$ 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 $μ$m 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 $\sqrt{D T_2}$. 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.
Source: arXiv (Cornell University)
Authors: Dhakal, Bibek, Gore, John C.
Institutions: Vanderbilt University, Vanderbilt University Medical Center
Language: English
Subfield: Radiology, Nuclear Medicine and Imaging
Field: Medicine
Domain: Health Sciences
Open Access status: green
OpenAlex ID: W7219155413