Voxel-wise Optimization of Pseudo Voigt Profile (VOPVP) for Z-spectra fitting in chemical exchange saturation transfer (CEST) MRI
Original Article

Voxel-wise Optimization of Pseudo Voigt Profile (VOPVP) for Z-spectra fitting in chemical exchange saturation transfer (CEST) MRI

Lihong Zhang, Yingcheng Zhao, Yanrong Chen, Chongxue Bie, Yuhua Liang, Xiaowei He, Xiaolei Song

School of Information Science and Technology, Northwest University, Xi’an 710127, China

Correspondence to: Xiaolei Song. School of Information Science and Technology, Northwest University, Xi’an 710127, China. Email: xlsong8@163.com.

Background: Chemical exchange saturation transfer (CEST) MRI is a promising approach for detecting biochemical alterations in cancers and neurological diseases, but the quantification can be challenging. Among numerous quantification methods, Lorentzian difference (LD) is relatively simple and widely used, which employs Lorentzian line-shape as a reference to describe the direct saturation (DS) of water and takes account of difference against experimental CEST spectra data. However, LD often overestimates CEST and nuclear overhauser enhancement (NOE) effects. Specifically, for fast-exchanging CEST species require higher saturation power (B1_sat) or in the presence of strong magnetization transfer (MT) contrast, Z-spectrum appears more like a Gaussian line-shape rather than a Lorentzian line-shape.

Methods: To improve the conventional LD analysis, the present study developed and validated a novel fitting algorithm through a linear combination of Gaussian and Lorentzian function as the reference spectra, namely, Voxel-wise Optimization of Pseudo Voigt Profile (VOPVP). The experimental Z-spectra were pre-fitted with Gaussian and Lorentzian method independently, in order to determine Lorentzian proportionality coefficient (a). To further compensate for the line-shape changes under different B1_sat’s, a B1-dependent adjustment was applied to the experimental Z-spectra (Z_exp) according to the prior knowledge learned from 5-pool Bloch equation-based simulations at a range of B1_sat’s. Then, the obtained Z-spectra (Z_B1adj) was fitted by the previously defined VOPVP function. Considering the asymmetric component of MT, the positive- and negative-side of Z-spectra were fitted separately, while the middle part (−0.6 to 0.6 ppm, consisted primarily of DS) was fitted using Lorentzian function. Finally, the difference between Z_VOPVP and Z_exp was defined as the CEST and NOE contrast. To validate our VOPVP method, an extensive simulation of CEST Z-spectra was performed using 5-pool model and 6-pool model with greater MT component.

Results: In comparison with LD approach, VOPVP exhibited lower sum of squares due to error (SSE) and higher goodness of fit (R-square) for the experimental Z-spectra at all B1_sat. Moreover, the results indicated that VOPVP fitting improved the overestimated contributions from amide proton transfer (APT) and NOE through LD at all B1_sat. Despite that the relationship for B1-dependent adjustment was pre-determined using a single 5-pool model, the VOPVP fittings obtained accurate quantification for multiple 6-pool models with a range of T1w’s and T2w’s. The robustness of VOPVP fitting was also proved by simulations using 3T parameters. Furthermore, we assessed VOPVP in vivo in a glioblastoma-bearing mouse. Compared to LD maps, VOPVP quantification maps displayed higher contrast-to-noise ratio between tumor and normal contralateral tissue for APT, glutamate and nuclear overhauser effect (NOE), when B1_sat >1 µT.

Conclusions: As an improvement of LD method, VOPVP fitting can serve as a simple, robust and more accurate approach for quantifying CEST and NOE contrast.

Keywords: Chemical exchange saturation transfer (CEST); Lorentzian fit; amide proton transfer (APT); nuclear overhauser enhancement (NOE); Pseudo Voigt profile


Submitted Jul 16, 2019. Accepted for publication Sep 29, 2019.

doi: 10.21037/qims.2019.10.01


Introduction

Chemical exchange saturation transfer (CEST) is a magnetic resonance imaging (MRI) technique for detecting low-concentration metabolites and molecules with exchangeable protons at specific resonance frequencies, which can be labeled by a saturation pulse allowing signal transfer to water pool for detection (1-3). CEST MRI (1,4) has been applied to detect exogenous or endogenous amine (5), amide (6), creatine (7), glucose (8,9), glutamate (10), glycogen (11) and glycosaminoglycan (12). Additionally, CEST technique can probe the micro-environment of tissue, including temperature (13) and pH (14,15). These unique capabilities of CEST MRI make it a promising target for in vivo imaging applications such as the diagnosis of stroke (16-20) as well as detection and grading of tumors (9,21-31).

CEST MRI often involves a series of images with saturation pulse sweeping over a range of frequency offsets, with the signal changes along the extracted offset, also termed as Z-spectra (32). The most commonly used CEST quantification method, namely, MT ratio asymmetry (MTRasym) analysis (33), takes the difference between two CEST images at opposite frequency offsets (+/−∆ω) as

where Ssat(−∆ω) and Ssat(∆ω) are signals with saturated RF irradiation, which applied at the reference frequency and labeled proton frequency; S0 is the reference signal without RF irradiation. MTRasym is simple and easy to be calculated, which has been shown to correlate with tumor grade in case of amide proton transfer (APT) (34-36). However, MTRasym is susceptible to several types of contamination, including B0 inhomogeneity (37), direct saturation (DS) and semisolid macromolecular magnetization transfer (MT). Moreover, it is incapable to separate nuclear overhauser effect (NOE) at resonance frequencies up field of water based on CEST contrast.

To further improve CEST specificity and its signal quantification, Z-spectra fitting has been employed to distinguish the contributions from multiple origins (38). Theoretically, the enhancement of CEST through Z-spectra is dependent on the pool size, exchange rate and relaxation time (25,34), as demonstrated by Bloch-McConnell equations. However, the complex Bloch fitting strongly relies on the initialization and boundaries of fitting parameters (39). According to the shape of Z-spectra, other quantification methods have been proposed, including multiple-pool Lorentzian fitting (7,24,38-40) and Lorentzian difference (LD) analysis (18,40-42). Multiple-pool Lorentzian fits each ‘dip’ in Z-spectra using a Lorentzian shape, in which the reference signals can be obtained by setting the fitted amplitude of the target CEST or NOE pools to zero. However, multiple-pool Lorentzian fitting requires the Z-spectra to be collected at a sufficient sampling frequency, and thus such method is time consuming. In addition, it has different fitting parameters, and is sensitive to the signal-to-noise ratio of Z-spectra. Besides, the LD method is a simplified method that employs a single Lorentzian line as a reference to describe the DS and takes account of difference against experimental data for quantifying CEST and NOE signal. LD can be an easy and robust quantification method, especially at low B1_sat (≤1 µT at 9.4 Tesla) (40), which has been initially validated in patients with stroke (18,40-42). However, LD analysis possesses the disadvantage of overestimating contributions from CEST and NOE effects (40). In particular, for fast-exchanging species that require higher B1_sat, or for tissue with a strong MT contrast, the Z-spectra exhibit non-Lorentzian line-shape (40) making the results of LD analysis invalid. More importantly, the Z-spectrum appears more like a Gaussian line-shape, rather than a Lorentzian line-shape, when B1_sat is higher or in the presence of strong MT contrast (20,43).

During NMR spectroscopy analysis, Voigt spectra line profile is often defined by the convolution of Lorentzian and Gaussian terms (44-46). As an excellent approximation to Voigt profile, Pseudo Voigt profile is best defined as the weighted sum of Gaussian and Lorentzian (47). In this study, a Voxel-wise Optimization Pseudo Voigt Profile (VOPVP) fitting algorithm was developed to improve the reliability of in vivo CEST MRI quantification. To further compensate for the different levels of MT and DS, a B1_sat-dependent optimization was adopted into the VOPVP fitting based on the 5-pool Bloch simulations under different B1_sat. To evaluate the performance of VOPVP fitting, an extensive Bloch-simulations was performed using previously published parameters (i.e., 5-pool model and 6-pool model with greater MT contributions) at various B1_sat. The conventional LD and an analytical standard were also assessed and compared. Finally, an initial validation for in vivo application was carried out using a brain tumor-bearing mouse.


Methods

Theoretical concepts

The detailed flow of our VOPVP method is illustrated in Figure 1. The proposed fitted function, or termed as Pseudo Voigt profile (47), was expressed by a weighted sum of Gaussian (G) and Lorentzian (L):

Figure 1 Flow chart of data processing steps of Voxel-wise Optimization Pseudo Voigt Profile (VOPVP) fitting approach.

where α and 1–α denote the proportionality coefficients of Lorentzian and Gaussian functions, respectively. The model function of Gaussian fitting can be described by

where ω1 is the frequency offset from the water resonance, while ω is the frequency offset of the CEST peak for the proton pool.

The model function of Lorentzian fitting can be given by

where ω1 is the frequency offset from the water resonance, whereas A, ω and σ are the amplitude, frequency offset and linewidth of the CEST peak for the proton pool, respectively.

Thompson et al. (45) have proposed the following expression for the pseudo-Voigt approximation for the convolution of both Gaussian and Lorentzian functions, as presented by the full width at half maximum (FWHM) values of Gaussian and Lorentzian:

where

where and are the FWHM of Gaussian and Lorentzian, respectively.

VOPVP fitting

Figure 1 shows the flow chart of the proposed VOPVP fitting algorithm. Firstly, for the raw Z-spectra data, WASSR was performed to correct B0 inhomogeneity. The obtained Z-spectra is labeled as Z_exp. Gaussian and Lorentzian model pre-fitting was performed for Z_exp in order to achieve the Lorentzian proportionality coefficient (a), based on the FWHM of Gaussian and Lorentzian derived from Eqs. [5] and [6], respectively. Subsequently, the area values of Z_loren under Z_exp between 4 and 6 ppm and between −4 and −6 ppm are named as L_pos and L_neg, respectively.

To further compensate for the line-shape changes under different B1_sat’s, a B1-dependent adjustment was applied to the experimental Z-spectra (Z_exp) according to the prior knowledge learned from 5-pool Bloch equation-based simulations at a range of B1_sat’s. Simulated Z-spectra (Z5-pool) of brain tissue with B0 =9.4 T were obtained through 5-pool Bloch equation-based simulations (48), for a range of B1_sat (0.5, 1, 1.5, 2, 2.5 and 3 µT). Accurate reference spectra describing DS and MT were determined using a 2-pool model (water and semisolid), with the residual with Z5-pool for CEST quantification. The Lorentzian fitting was also performed. The residual areas with regarding to Z5-pool, were calculated for Lorentzian fitting [u_pos (4 to 6 ppm) and u_neg (−4 to −6 ppm)], and also for the 2-pool model [v_pos (4 to 6 ppm) and v_neg (−4 to −6 ppm)]. Then, for each B1_sat, the two ratios of ∆ω and −∆ω were calculated as follows: (A) Ratio (∆ω) =v_pos / u_pos. (B) Ratio (–∆ω)=v_neg / u_neg. Figure 2 plotted Ratio (∆ω) and Ratio (–∆ω) as a function of B1_sat. As seen, when B1_sat <1 µT, ratio values are close to 1, indicating accurate quantification of LD. However, when B1_sat ≥1 µT LD become inaccurate with ratio >1. For both Ratio (∆ω) and Ratio (–∆ω), a linear relationship with B1_sat can be determined, providing the prior knowledge of fitting errors. Here, before starting VOPVP optimization, a B1-dependent adjustment was applied to Z_exp, resulting in Z_B1adj=Z_exp (1+Ratio × L × |∆ω|/3). By multiplying Z_exp with the Ratio values at the applied B1_sat, the adjusted spectra (Z_B1adj) can compensate for the difference between LD and accurate quantification.

Figure 2 Relationship between (A) Ratio (∆ω), (B) Ratio (–∆ω), and B1_sat.

Then, with the initial value of VOPVP fitting defined by Eqs. [2-4], the fitting to Z_B1adj was divided into three parts. Part I, VOPVP function was used to fit the Z_B1adj between 0 and 6 ppm. Part II, VOPVP function was used to fit the Z_B1adj between −6 and 0 ppm. Part III, Lorentzian was employed to fit the Z_B1adj between −0.4 and 0.4 ppm. The final fitting results integrated the fitted data from part I (0.6 to 6 ppm), part II (−6 to −0.6 ppm) and part III (−0.4 to 0.4 ppm). Then, Spline interpolation was used to assess the final fitting data, namely, Z_VOPVP_final. For all Voxels, the difference between Z_VOPVP_final and Z_exp was calculated to obtain the amplitude of maps at ∆ω. DS effects in weak range at both sides of 0 ppm with the line-shape similar to Lorentzian were fitted into the part III. The Z-spectra was far from 0 ppm and might contain MT components, which made Pseudo Voigt Profile an ideal fitting method. Moreover, there was no exchangeable proton within 0.6 ppm, according to the exchangeable proton chemical shifts for various diamagnetic agents (49) ranging from 0 to 7 ppm. Therefore, only the accuracy of fitting within ±6 ppm was considered.

LD fitting

In addition, Lorentzian difference (LD) fitting (40,50) was carried out during the simulation. In this method, Lorentzian fitting was performed to evaluate the values of Z-spectra (−10 to −6.25 ppm, −1.7 to 1.7 ppm and 6.25 to 10 ppm at 9.4T), while spline interpolation was used to complete the entire fitting process. The fitted spectra were adopted as reference signals, representing the DS and semi-solid MT effects. The residual spectra of CEST (40) were formed by subtracting the measured Z-spectra from the fitted spectra.

For in vivo experiments, the offsets greater than ±6 ppm were not collected due to the restriction of scanning time. To improve LD performance, a compensate strategy similar to previous research (18) was employed, where the acquired Z-spectra were normalized by Ssat (−6 ppm) of the lower B1-sat, and then fitted by Lorentzian fitting.

Simulation

To assess the performance of the proposed VOPVP method, Bloch equation-based simulations were carried out using both 5-pool exchange model (free water, amide, amine, MT and NOE at −3.5 ppm) (51) and 6-pool model (free water, amide, amine, MT, NOE at −3.5 ppm and NOE at −1.6 ppm) (40). Simulation parameters for rodent brain tissue at 9.4 Tesla are listed in Table 1. Specifically, the 6-pool model contained more MT and NOE components but less amides and amines in comparison with 5-pool model (40,48). To further evaluate the robustness of our method, simulations were performed at six different B1_sat levels, i.e., 0.5, 1, 1.5, 2, 2.5 and 3 µT.

Table 1
Table 1 Parameters for the Bloch equation-based simulations (9.4T)
Full table

To assess the robustness of our VOPVP method, we further performed simulation for a range of T1w (0.5 to 2.5 s) and T2w (25 to 125 ms), all using the same ratio values. To prove the feasibility at clinical field strengths, the ratios were calculated (Figure S1) using the parameters at 3T for rodent brain tissue (Table S1). Then the VOPVP fittings were performed and compared, using either ratios calculated from 3T, or those from 9.4T.

Figure S1 Relationship between (A) Ratio (∆ω), (B) Ratio (–∆ω), and B1_sat at 3 T.
Table S1
Table S1 Parameters for the Bloch Equation-Based simulations at 3T (5-pool) (48)
Full table

In vivo experiment

Animal experiments were performed in accordance with the guidelines of Johns Hopkins University Animal Care and Use Committee guidelines. Balb/c NOD/SCID mouse were xenografted intracranially with 100,000 human glioblastoma cells to striatum of the brain (52,53) with MR imaging performed 6-week post-injection. In vivo MRI experiments were conducted on an 11.7T horizontal bore scanner (Bruker Biospec, Germany) using a transmit-receiver volume coil (23 mm diameter). CEST MRI images were acquired using a continuous wave pre-saturation pulse (Tsat =2,500 ms), followed by a rapid acquisition with relaxation enhancement (RARE) readout (RARE factor =12). B0 inhomogeneity was then corrected using WASSR (54). The Z-spectra were acquired from −6 to 6 ppm with an interval of 0.25 ppm at three B1_sat of 0.8, 1.2 and 2.4 µT. The other parameters were as follows: TR/TE =5,500 ms/11 ms, slice thickness =1 mm, FOV =17×14 mm2 and matrix size =96×64.

Evaluation criteria

The obtained data were evaluated by four parameters: (I) the sum of squares due to error (SSE), (II) coefficient of (R-square) determination (39), (III) simple analytic solution to the apparent exchanged-dependent relaxation (AREX) (20,23,51,55,56), and (IV) contrast-to-noise ratio (CNR) for in vivo experiments (39). The AREX was further defined as follows:

To evaluate the accuracy of CEST quantification methods in numerical simulations, we used (20,40,55,57) as a gold standard, which is independent of non-specific tissue parameters such as T1w, DS and semi-solid MT effects:

where fs is solute concentration, ksw is solute-water exchange rate, R2s is solute transverse relaxation and ω1 is irradiation power. In comparison with (∆ω), AREX, the inverse metric of the Z-spectra fitted by LD and VOPVP, was defined as below (40,55):

where fc is semi-solid MT pool size ratio.


Results

Simulations

Figure 3 displays the simulated Z-spectra, VOPVP fitting and LD fitting of B1_sat at 0.5, 1, 1.5, 2, 2.5 and 3 µT, apart from the difference between VOPVP and the simulated data. For the simulated data through 5-pool model, the difference spectra generated by VOPVP and Lorentzian fitting could reveal the peaks arising from amide proton at 3.5 ppm, amine protons at 2 ppm and NOE at −3.5 ppm (NOE at −1.6 ppm for 6-pool only). However, LD overestimated the amide, amine CEST signals when B1_sat =1, 1.5 and 2 µT, while underestimated NOE when B1_sat =2.5 and 3 µT. In contrast, for all the saturation powers, our VOPVP method could provide a closer fitting to the non-specific parts of Z-spectra (−6 to −5 ppm, −1.5 to 1.5 ppm and 4 to 6 ppm), as quantitatively indicated by both SSE and R-square (Table 2). As aforementioned, the 6-pool model may contain more MT and NOE components but less amides and amines than the 5-pool model. Our results showed the SSE of 6-pool increased by up to 100% from 5-pool model (Table 2) (B1_sat =3 µT) is not only NOE at −1.6 ppm but also the 6-pool model containing more MT components.

Figure 3 Comparison of VOPVP fitting and LD fitting using simulating Z-spectra, for B1_sat of 0.5, 1, 1.5, 2, 2.5 and 3 µT, respectively. (A) The 5-pool Bloch-simulation; (B) the 6-pool Bloch-simulation.
Table 2
Table 2 Comparison of fitting quality of LD and VOPVP in simulation
Full table

In addition, the AREX metrics derived from VOPVP fitting and LD fitting were further compared with analytical standard (Figure 4 and Table 3). For the 6-pool model, LD overestimated all the CEST and NOE signals. For the 5-pool model, LD overestimated amides and NOE (3.5 ppm) at B1_sat ≤2 µT (1, 1.5 and 2 µT), while underestimated APT and NOE (3.5 ppm) at 3 µT. For both the 5-pool and the 6-pool models, the derived AREXVOPVP spectra were significantly closer to the standard spectra, especially at B1_sat ≥1 µT (1, 1.5, 2, 2.5 and 3 µT). Table 3 lists the ratios of the peak intensities of the AREXLD and AREXVOPVP metrics to those of . Notably, for the 5-pool model, AREXVOPVP at amide frequency (3.5 ppm) and NOE (−3.5 ppm) were relatively close to at all B1_sat. While for the 6-pool model with a greater MT contribution, AREXVOPVP could estimate more accurately at lower B1_sat (≤2 µT), but still underestimated the APT at 2.5 and 3 µT; Nevertheless, for all cases, AREXVOPVP outperformed AREXLD with regard to all peaks (i.e., APT, amine and NOE).

Figure 4 Quantification of the fitted Z-spectra using AREX (AREXLD and AREXVOPVP), and comparison with the analytical spectra, for B1_sat of 0.5, 1, 1.5, 2, 2.5 and 3 µT, respectively. (A) The 5-pool Bloch-simulation; (B) the 6-pool Bloch-simulation.
Table 3
Table 3 Comparison of quantified peaks using LD and VOPVP with the analytical as a gold standard (40)
Full table

The fitted linear function at 3T (Figure S1) suggested a slightly different slope and shift compared with those calculated at 9.4T (Figure 2). As seen, AREXVOPVP values were closer to the analytical solution than AREXLD values, for both B1_sat =1 µT and B1_sat =2 µT (Figure 5). As seen, the two kinds of VOPVP fitting curves are almost identical, which both resulted in accurate quantification (AREXVOPVP) compared with the analytical standard) (Figure S2, Table S2).

Figure 5 AREXLD, AREXVOPVP and calculated for APT from simulated Z-spectra with variation of T1w and T2w, with the B1_sat of (A) 1 µT, (B) 2 µT.
Figure S2 Quantitative assessment of simulation Z-spectra using ratios calculated from 3T. (A) Comparison of LD fitting and VOPVP fitting, which simulating Z-spectra using ratios calculated from 3T, for B1_sat of 0.5, 1 and 1.5 µT. (B) Comparison of LD fitting and VOPVP fitting, which simulating Z-spectra using ratios calculated from 9.4 T, for B1_sat of 0.5, 1 and 1.5 µT. (C) Quantification of the fitted Z-spectra using AREX (AREXLD and AREXVOPVP, which using ratios calculated from 3 T, and comparison with the analytical spectra at 3 T, for B1_sat of 0.5, 1 and 1.5 µT. (D) Quantification of the fitted Z-spectra using AREX (AREXLD and AREXVOPVP, which using ratios calculated from 9.4 T, and comparison with the analytical spectra at 3 T, for B1_sat of 0.5, 1 and 1.5 µT. LD, Lorentzian difference; VOPVP, Voxel-wise Optimization of Pseudo Voigt Profile; AREX, apparent exchanged-dependent relaxation.
Table S2
Table S2 Comparison of quantified peaks using LD and VOPVP, which using ratios calculated from 3T and 9.4T, with the analytical as a gold standard at 3 T (40) (5-pool)
Full table

Tumor mouse

Further, VOPVP fitting was applied to quantify the contributions of APT, glutamate, amine and NOE effects in a mouse bearing glioblastoma. The T2w image (Figure 6A) indicated the anatomy, with a tumor ROI and the contralateral control one marked. To visualize the quantified spectra for all voxels, the offset-cut images were plotted with the residual spectra of LD fitting and VOPVP (Figure 6B,C). Transverse coordinates between 56 and 66 are the location of the tumor. Notably, the offset-cut values of VOPVP fitting were significantly higher at 3.5 ppm and 2 ppm in tumor than those in normal contralateral tissue. In contrast, the offset-cut values of LD fitting were significantly higher for Amide 3.5 ppm, Glu-CEST 3 ppm, Guanidinium-Amine 2 ppm and lower for NOE between −2 and −5 ppm in the tumor than those in normal contralateral tissue. The differences between VOPVP fitting and LD fitting for tumor ROI and normal contralateral ROI at three B1_sat level (0.8, 1.2 and 2.4 µT) are presented in Figure 6D,E. Moreover, the dips centered at −3.5, 2 and 3.5 ppm could be clearly observed on the Z-spectra at relatively low B1_sat, which corresponded to aliphatic NOE, guanidine amine and amide, respectively. Another dip around −1.6 ppm was observed in normal tissues, but not in tumors with low B1_sat, which were consistent with previous reports (58,59). Theoretically, a dip at 3 ppm from Glu-CEST should be visible at high B1_sat (10). However, it was not obviously shown on the Z-spectra due to the broadened dips. The residual of both VOPVP and LD fitting for the ROIs of tumor and normal contralateral tissue appeared at 3.5 ppm (amide), downfield from water and 2–5 ppm (NOE) up field from water. Overall, the fitting curves of VOPVP for the two ROIs were closer to the experimental measurements compared to those obtained by LD. Besides, the overestimation of LD fitting becomes obvious with the increasing B1_sat, which was also observed in a recent CEST study of simulations at 9.4T (40). The peaks appeared at 2 ppm could be clearly observed on the MTRasym map (Figure 6F) at all B1_sat, which were consistent with the conclusion drawn from the fitted residual spectra.

Figure 6 Quantitative assessment of in vivo tumor-bearing mouse brain. (A) The T2w image, marked with a tumor ROI and the contralateral control for spectral analysis. (B) The offset-cut map using residual spectra of LD fitting for B1_sat =1.2 µT, which locations are indicated by dash line in (A) of T2w image. (C) The offset-cut map using residual spectra of VOPVP for B1_sat =1.2 µT, which locations are indicated by dash line in (A) of T2w image. (D) Comparison of VOPVP fitting and LD fitting for tumor region. (E) Comparison of VOPVP fitting and LD fitting for the normal contralateral region. (F) MTRasym analysis both for the tumor region and the normal contralateral region. VOPVP, Voxel-wise Optimization of Pseudo Voigt Profile; LD, Lorentzian difference; MTRasym, magnetization transfer ratio asymmetry.

Furthermore, the proposed VOPVP method was evaluated by comparing with LD fitting and MTRasym (3.5 ppm) (Figure 7). Figure 7 shows the fitted amplitude maps using MTRasym at 3.5 ppm, LD fitting and VOPVP fitting in a mouse tumor model. The images were fitted voxel-wise to Eq. [2] by using the nonlinear fitting function (lsqcurvefit) in MATLAB. In line with previous findings on the APT imaging of glioma (4,60-62), a remarkably higher APT effect was found in tumors fitted by VOPVP. For NOE (VOPVP fitting), our results demonstrated the intensity of tumor was increased at higher B1_sat (1.2 and 2.4 µT) compared to normal tissue, but decreased at lower B1_sat (0.8 µT). Moreover, VOPVP fitting revealed a pronounced positive contrast in the tumor analyzed by Glu-CEST map. Whilst, the NOE (LD fitting) in tumor was lower than that in normal tissue at B1_sat = 0.8 µT, which were consistent with previous findings (63). Additionally, MTRasym (3.5 ppm) indicated that the signal intensity of tumor location was significantly higher than that of normal contralateral tissue location, which was in accordance with the results of previous studies (4,63,64).

Figure 7 Comparison of fitted amplitudes maps using VOPVP fitting, Voxel-wise LD fitting and MTRasym (3.5 ppm) in a representative mouse brain, for B1_sat of (A) 0.8 µT, (B) 1.2 µT and (C) 2.4 µT. VOPVP, Voxel-wise Optimization of Pseudo Voigt Profile; LD, Lorentzian difference; MTRasym, magnetization transfer ratio asymmetry.

Table 4 describes the quality of each CEST map. For APT and Glu-CEST, VOPVP method exhibited higher CNR than LD method and MTRasym (3.5 ppm), when B1_sat >1 µT.

Table 4
Table 4 Comparison of CNR between MTRasym (3.5 ppm), LD fitting and VOPVP fitting in tumor mouse brain at 11.7T
Full table

Discussion

In this study, we propose a novel CEST quantification method, namely VOPVP, by fitting Z-spectra with a linear combination of Gaussian- and Lorentzian-line shapes as the reference spectra and taking the difference among experimental data for CEST quantification. To improve the conventional LD and enhance its robustness for various occasions (e.g., larger B1_sat and greater MT), we not only modified the fitting function from Lorentzian to Pseudo Voigt Profile (PVP), but also integrated a B1-dependent optimization for better compensation of the altered DS (spillover effect) and MT under different B1_sat. The main purposes of Z-spectra fitting in Lorentzian and VOPVP are to generate a reference spectrum without CEST and NOE, and to best simulate the confounding MT and DS. The semisolid MT effect is asymmetric around the water peak, which induces signal decline over a wide frequency range. It has been reported that a baseline term against the Lorentzian analysis can minimize the impact of global MT effect and noise arising from motion (40,50). A previous study has renormalized CEST Z-spectra by averaging the signal intensity of both end of Z-spectra of at relatively lower B1_sat (18) before performing LD fitting. Similarly, in our VOPVP method, a compensate ratio factor was applied to the experimental Z-spectra data, according to the acquisition B1_sat. The relationship between the ratio and B1_sat was established in advance through an offline step using the 5-pool Bloch simulation (Figures 1,2). Both simulation and in vivo mouse revealed that VOPVP displayed a better approximation to the referenced part of Z-spectra in comparison with LD analysis. Despite that VOPVP outperformed the conventional LD when the acquisition B1_sat is larger for fast-exchangeable species or when the tissue imposes a greater MT contribution, this method does not work well with larger B1_sat and greater MT component, especially not appropriate for amines and NOE (−1.6 ppm) that are closer to water (Table 3).

In the proposed approach we applied a B1-dependent adjustment to the measured Z-spectra, before starting of the optimization of pseudo voigt profile. The equation for adjustment was obtained offline, through simulations using a previously-published 5-pool model for brain tissue at 9.4T. Accurate reference spectra describing DS and MT were determined using a 2-pool model (water and semisolid), while Lorentzian fitting was also performed. The inaccuracy of LD fitting was further defined by the ratio of two residual areas, corresponding to the Lorentzian fitting spectrum and the accurate reference spectrum. As seen in Figure 2, when B1-sat <1 µT, the ratio is close to 1, indicating accurate quantification of LD. But, for larger B1-sat, LD inaccurately quantified CEST signal with ratio >1. We also figured the linear relationships between ratios and B1-sat. This prior knowledge of inaccuracy of LD at different B1_sat, was then employed in the online optimization step, to produce an adjusted Z-spectra better representing the DS and MT contributions under applied B1_sat. In another word, our quantification approach employed the prior knowledge of LD mismatch at different B1_sat to constrain the optimization algorithm (Levenberg-Marquardt algorithm here), leading to more accurate quantification. Despite that the adjustment uses Ratios that calculated from a 5-pool model of brain tissue, the followed VOPVP optimization will make it work for a range of tissue parameters (T1w and T2w), as shown in Figures 3,4,5. The Ratios is also applicable for different filed strengths, as validated by the 3T simulations (Figures S1,S2, Table S1). This constrained optimization method, through learning from the off-line simulations, could also applied to other fitting methods for CEST MRI in future.

Apart from taking the difference between a fitting reference spectra and the experimental data, several other quantification methods have been proposed, including apparent exchange-dependent relaxation (AREX) (5), extrapolated semi-solid magnetization transfer reference (EMR) (4,65), multi-pool Bloch-McConnell (BM) fitting (32), three-offset approach (23,66) and the combination of these quantitative methods (20,23,35,51). Superior to MTRasym, all these methods allow the separation of CEST and NOE effect. However, the accuracy and robustness of these methods are varied, and each has its own limitations. For instance, AREX has been applied only to slow- (e.g., APT) (27,38) and intermediate-exchangeable [e.g., creatine (creCEST) (67)] solutes, which is also a fitting approach to quantify fast-exchangeable amine CEST signals (5,27). BM fitting requires prior knowledge of parameters (e.g., T2 and kex of each exchanging proton) and is time consuming compared to LD fitting and AREX (68). EMR approach has the potential to be an important and accurate CEST MRI quantitative technique (4), but it may overestimate the measurements of APT and NOE (4). Three-offset method is a relatively simple quantification approach (23,66). However, the linear assumption underlying the three-offset method may be oversimplified (39,40).

NOEs are depended on the applied B1_sat and filed strength. It has been reported there is no significant difference in the NOE (9.4T, 1 µT) between tumors and normal contralateral tissues (23). Previous findings have shown that the NOE signal at 4.7 Tesla in tumor is lower than that in normal contralateral tissue (63), which are consistent with the results of offset-cuts (Figure 6B,C). APT imaging, a specific form of CEST, can potentially serve as a non-invasive means to characterize abnormal tissues such as tumors (23). Previous reports have shown that the APT-related pool size of the tumor center and rim is significantly larger than that of normal tissue, as opposed to the NOE-related pool size. Moreover, APT can detect malignant tumors (63,64,69), the changes that have been induced by elevated mobile cellular and peptide contents (70). In the present study, it can be seen that the intensity of APT signal is higher in tumor than in normal contralateral tissue, as revealed the offset-cuts (Figure 6B,C) and fitted amplitudes maps (Figure 7) of our proposed VOPVP fitting, which is consistent with the findings of previous literature (4,70).

As an improvement of LD method, our VOPVP fitting may provide a simple, robust and more accurate approach for quantifying CEST and NOE contrast. More in vivo validations and at the clinical field strength will be performed in the future.


Acknowledgments

The authors would like to thank Dr. Chengyan Chu and Dr. Piotr Walczak at Johns Hopkins University for their generous offering of a tumor-bearing mouse.

Funding: This work was supported by the National Natural Science Foundation of China under Grant No.61601364, Xi’an Key Laboratory of Radiomics and Intelligent Perception Grant 201805060ZD11CG44, and by the Postgraduate Independent Innovation Project of Northwest University (China) Grant YZZ17180. In vivo MRI data of the mouse were collected under support of Johns Hopkins Radiology Britestar Award to Dr. Xiaolei Song.


Footnote

Conflicts of Interest: The authors have no conflicts of interest to declare.

Ethical Statement: MR imaging experiment on a tumor-bearing mouse was performed under the approval of the Johns Hopkins University Animal Care and Use Committee (ACUC) with protocol # MO13M251.


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Cite this article as: Zhang L, Zhao Y, Chen Y, Bie C, Liang Y, He X, Song X. Voxel-wise Optimization of Pseudo Voigt Profile (VOPVP) for Z-spectra fitting in chemical exchange saturation transfer (CEST) MRI. Quant Imaging Med Surg 2019;9(10):1714-1730. doi: 10.21037/qims.2019.10.01