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: We incorporated diffusion in 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 $\sqrt{D \cdot TR/2}$ at large $α$ to $\sqrt{DT1}$ as the $α\rightarrow 0$, equaling $\sqrt{DT1/2}$ at the Ernst angle. Consequently, multi-angle acquisitions have mismatched resolution (PSF widths of 38 $μ$m at $α= 10^\circ$ versus 11 $μ$m at 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 of a 30 $μ$m feature is reduced to be 1.80 s$^{-1}$ (true value 2.00 s$^{-1}$). In b-SSFP blurring depends on by T1, T2, and $α$ but is independent of TR, with minimum of $\sqrt{DT2}$. 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.