Evaluating the use of a continuous approximation for model-based quantification of pulsed chemical exchange saturation transfer (CEST)

Abstract

Many potential clinical applications of chemical exchange saturation transfer (CEST) have been studied in recent years. However, due to various limitations such as specific absorption rate guidelines and scanner hardware constraints, most of the proposed applications have yet to be translated into routine diagnostic tools. Currently, pulsed CEST which uses multiple short pulses to perform the saturation is the only viable irradiation scheme for clinical translation. However, performing quantitative model-based analysis on pulsed CEST is time consuming because it is necessary to account for the time dependent amplitude of the saturation pulses. As a result, pulsed CEST is generally treated as continuous CEST by finding its equivalent average field or power. Nevertheless, theoretical analysis and simulations reveal that the resulting magnetization is different when the different irradiation schemes are applied. In this study, the quantification of important model parameters such as the amine proton exchange rate from a pulsed CEST experiment using quantitative model-based analyses were examined. Two model-based approaches were considered - discretized and continuous approximation to the time dependent RF irradiation pulses. The results showed that the discretized method was able to fit the experimental data substantially better than its continuous counterpart, but the smaller fitted error of the former did not translate to significantly better fit for the important model parameters. For quantification of the endogenous CEST effect, such as in amide proton transfer imaging, a model-based approach using the average power equivalent saturation can thus be used in place of the discretized approximation.

Graphical abstract

Fig. 1

Simulated z-spectra using continuous approximation (AF and AP) and discretization method. The light green circles highlight the major differences in the off resonance excitation between different methods. The right inlet plot shows a single Gaussian pulse with its equivalent AF and AP.

Fig. 2

The minimal number of discretization, N, required to achieve normalized RMS error to be less than 0.1% when compared with the benchmark magnetization (1024 segments) for different set of pulsed parameters at 4.7 T. This four dimensional relationship (FA (x), T_pd (y), DC (z) and N (color)) can be read by following the grid lines along each axis: there will always be 6 ‘balls’ along the z direction which represent DC values from 30% to 80%.

Fig. 3

(a) Measured z-spectra of different creatine concentration phantoms at pH 6.5. (b) Measured spectra of 125 mM creatine phantoms with different pH values. The asymmetry analysis spectra are plotted underneath the z-spectra in each plot. (c) CESTR image and (d) its corresponding error bar plot.

Fig. 4

(a) Measured data of phantom with 125 mM creatine concentration at pH 6.0 and continuous (AP) and discretized model fitted spectrum. The residuals are plotted below the fitted spectra (dotted lines). (b) Normalized sum of square error plot of continuous (AP) and discretized model fitting for phantoms with different pH values and concentrations.

Fig. 5

Fitted values of water center frequency, ω_w, using (a) discretized and (b) AP continuous model-based analysis, (c) is the B₀ map generated using WASSR.

Fig. 6

Fitted values of amide proton exchange rate, C_labile, using (a) discretized and (b) AP continuous model-based analysis. The error plot of fitted C_labile using different methods is shown in (c). The P values displayed above the bars are the results of the two-tail t-tests (P < 0.05).

Fig. 7

The other sets of pulsed parameters which should produce equivalent quantitative fitting results (white circles) for the important model parameters investigated when AP approximation is used. Black circles represent the sets of pulsed parameters that had sum of square and CESTR difference bigger than the benchmark (the one used in this study).