Quantitative Bayesian model-based analysis of amide proton transfer MRI

Abstract

Amide Proton Transfer (APT) reports on contrast derived from the exchange of protons between amide groups and water. Commonly, APT contrast is quantified by asymmetry analysis, providing an ensemble contrast of both amide proton concentration and exchange rate. An alternative is to sample the off-resonant spectrum and fit an exchange model, permitting the APT effect to be quantified, correcting automatically for confounding effects of spillover, field inhomogeneity, and magnetization transfer. Additionally, it should permit amide concentration and exchange rate to be independently quantified. Here, a Bayesian method is applied to this problem allowing pertinent prior information to be specified. A three-pool model was used incorporating water protons, amide protons, and magnetization transfer effect. The method is demonstrated in simulations, creatine phantoms with varying pH and in vivo (n = 7). The Bayesian model-based approach was able to quantify the APT effect accurately (root-mean-square error < 2%) even when subject to confounding field variation and magnetization transfer effect, unlike traditional asymmetry analysis. The in vivo results gave approximate APT concentration (relative to water) and exchange rate values of 3 × 10(-3) and 15 s(-1) . A degree of correlation was observed between these parameter making the latter difficult to quantify with absolute accuracy, suggesting that more optimal sampling strategies might be required.

Keywords: amide proton transfer; chemical exchange saturation transfer; magnetization transfer.

Figure 1

RMSE and mean error for PTR and PTR* (%) over the 100 instances within the experiments of the simulation study. The coloured bars show RMSE, with the superimposed grey bars give the mean error (a measure of the bias in the estimates over the 100 noisy instances). PTR errors were substantially increased by inclusion of MT effects and shifts in the water center frequency.

Figure 2

RMSE and mean error for k_APT,w and rM₀^APT over the 100 instances within the experiments of the simulation study. The coloured bars show RMSE, with the superimposed grey bars give the mean error (a measure of the bias in the estimates over the 100 noisy instances). Errors were largely insensitive to the inclusion of MT effects and shifts in the water center frequency. Underestimation of k_APT,w for some experiments was compensated for by overestimation of rM₀^APT and vice versa.

Figure 3

Example z-spectra from the phantom study for all three creatine concentrations at a pH of 6.4 (top) and all pH values at a creatine concentration of 125 mM (bottom).

Figure 4

a) Equilibrium magnetization image from the in vitro study labeled with the creatine concentration and pH in each sample, b) and c) estimated rM₀^APT and k_APT,w from the model-based analysis method, d) estimated k_APT,w when the rM₀^APT was fixed using literature values e) mean estimated rM₀^APT vs. pH, f) mean estimated k_APT,w vs. pH within each sample from the in vitro study, g) mean estimated k_APT,w vs. pH when the rM₀^APT was fixed using literature values.

Figure 5

a) PTR and b) PTR* images from the in vitro study.

Figure 6

Water resonant frequency offset images from the in vitro study estimated using a) model fitting the z-spectrum, b) WASSR data and maximum asymmetry method, c) multiple echo time data.

Figure 7

Images from the healthy subject data: a) PTR calculated from the data, b) PTR* using the parameters from the model fit to calculate the spectrum, c), d) and e) rM₀^APT, k_APT,w and rM₀^MT from the model fitting respectively, f) water resonant frequency offset from the model fitting, g) water center frequency offset as calculated for the WASSR data using the asymmetry method of (9).

Figure 8

Results from the simulation study. RMSE for estimating rM₀^APT and k_APT,w, when data were simulated with the ‘true’ values shown, for the four different sampling strategies. Superimposed on the bars is the absolute value of the mean error in the parameter estimate indicating the bias in the results toward under or over estimation. Both the RMSE and bias was reduced by placing more samples around the amide resonance and use of multiple B₁ levels.