Comparison of z-spectrum interpolation methods for brain tumor CEST magnetic resonance imaging

Abstract

Chemical Exchange Saturation Transfer (CEST) magnetic resonance imaging (MRI) is a technique for characterizing brain tumors at the molecular level. A critical aspect of CEST MRI involves generating a z-spectrum, which captures frequency-dependent signal intensity changes that arise from proton exchange between water and various metabolites. However, z-spectra are often acquired with sparse sampling due to time constraints, especially in clinical setting, requiring sufficient interpolation methods.

Aim: To evaluate second-order polynomial, Gaussian, Lorentzian, and pseudo-Voigt functions as interpolation models for a z-spectrum in CEST MRI. The goal is to assess each function's goodness of fit (GOF) to the reference z-spectrum acquired from raw chicken egg white. Additionally, we evaluate how well each interpolation model quantifies the asymmetry introduced into the z-spectrum by the saturation transfer (ST) effects.

Methods: Two chicken eggs were imaged using a 3 tesla MAGNETOM Vida whole-body MRI scanner (Siemens Healthineers AG, Forchheim, Germany) with a 64-channel head coil. Data processing for the reference z-spectrum involves normalization and external magnetic field correction. Since symmetrical functions are used in interpolation, opposing sides of the spectrum are mirrored with respect to the minimum of the spectrum, resulting in two symmetrical data point groups. Each function is interpolated to the data point groups using least square approximation (LSA). The GOF is evaluated using R² and the sum of squares due to error (SSE). For the asymmetry quantification, a magnetization transfer difference (MTD) value is defined and calculated. A total of three reference spectra are analyzed. Mean values for GOF parameters are calculated from the three reference spectra.

Results: All fitting functions performed adequately in terms of MTD and GOF parameters. The pseudo-Voigt function showed highest GOF in the first data point group, while polynomial showed highest GOF in the second data point group. The Gaussian function showed the highest asymmetry.

Conclusions: The methodology presented in this thesis provides a robust and straightforward approach for generating amide proton transfer-weighted (APTw) images using MTD maps. Due to its robustness in fitting and adequate MTD, the polynomial can be considered the best option for CEST contrast generation. While the approach presented in this thesis can be generalized to a variety of CEST MRI contrasts, a more sensitive differentiation of APT effects specifically might be observed by fitting functions to specific regions of interest in the z-spectrum. The thesis also sparks interest to investigate Gaussian and pseudo-Voigt functions as surrogate functions to the Lorentzian function in multi-pool fitting methods, with the hypothesis that pseudo-Voigt may offer increased sensitivity in multi-pool analysis compared to the Lorentzian.