A theoretical framework for retrospective $T_2^{\ast }$ correction to the arterial input function in quantitative myocardial perfusion MRI

Purpose: To develop and evaluate a flexible, Bloch-equation based framework for retrospective $T_2^{\ast }$ correction to the arterial input function (AIF) obtained with quantitative cardiac perfusion pulse sequences.

Methods: Our framework initially calculates the gadolinium concentration [Gd] based on T₁ measurements alone. Next, $T_2^{\ast }$ is estimated from this initial calculation of [Gd] while assuming fast water exchange and using the literature native T₂ and static magnetic field variation (ΔB₀ ) values. Finally, the [Gd] is recalculated after performing $T_2^{\ast }$ correction to the Bloch equation signal model. Using this approach, we performed $T_2^{\ast }$ correction to historical phantom and in vivo, dual-imaging perfusion data sets from 3 different patient groups obtained using different pulse sequences and imaging parameters. Images were processed to quantify both the AIF and resting myocardial blood flow (MBF). We also performed a sensitivity analysis of our $T_2^{\ast }$ correction to ±20% variations in native T₂ and ΔB₀ .

Results: Compared with the ground truth [Gd] of phantom, the normalized root-means-square-error (NRMSE) in measured [Gd] was 5.1%, 1.3%, and 0.6% for uncorrected, our corrected, and Kellman's corrected, respectively. For in vivo data, both the peak AIF (7.0 ± 3.0 mM vs. 8.6 ± 7.1 mM, 7.2 ± 0.9 mM vs. 8.6 ± 1.7 mM, 7.7 ± 1.8 mM vs. 10.3 ± 5.1 mM, P < .001) and resting MBF (1.3 ± 0.1 mL/g/min vs. 1.1 ± 0.1 mL/g/min, 1.3 ± 0.1 mL/g/min vs. 1.1 ± 0.1 mL/g/min, 1.2 ± 0.1 mL/g/min vs. 0.9 ± 0.1 mL/g/min, P < .001) values were significantly different between uncorrected and corrected for all 3 patient groups. Both the peak AIF and resting MBF values varied by <5% over the said variations in native T₂ and ΔB₀ .

Conclusion: Our theoretical framework enables retrospective $T_2^{\ast }$ correction to the AIF obtained with dual-imaging, cardiac perfusion pulse sequences.