Analysis of model-based and model-free CEST effect quantification methods for different medical applications

Journal Pre-proofs Analysis of Model-Based and Model-Free CEST Effect Quantification Methods for Different Medical Applications Lee Sze Foo, Wun-She Yap, Yan Chai Hum, Hanani Abdul Manan, Yee Kai Tee PII: DOI: Reference:

S1090-7807(19)30287-3 https://doi.org/10.1016/j.jmr.2019.106648 YJMRE 106648

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Journal of Magnetic Resonance

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23 June 2019 11 November 2019 12 November 2019

Please cite this article as: L. Sze Foo, W-S. Yap, Y. Chai Hum, H. Abdul Manan, Y. Kai Tee, Analysis of ModelBased and Model-Free CEST Effect Quantification Methods for Different Medical Applications, Journal of Magnetic Resonance (2019), doi: https://doi.org/10.1016/j.jmr.2019.106648

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Analysis of Model-Based and Model-Free CEST Effect Quantification Methods for Different Medical Applications Lee Sze Foo, B.S, a, Wun-She Yap, PhD, b, Yan Chai Hum, PhD, a, Hanani Abdul Manan, PhD, c, Yee Kai Tee, DPhil, a*. a Department

b

of Mechatronics and Biomedical Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Malaysia.

Department of Electrical and Electronic Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Malaysia. c

Department of Radiology, Universiti Kebangsaan Malaysia Medical Centre, Malaysia.

Running Title: Analysis of model-based and model-free CEST quantification methods Word Count: 5229 *Correspondence

to:

Yee Kai Tee

Universiti Tunku Abdul Rahman Jalan Sungai Long, Bandar Sungai Long Cheras 43000, Kajang, Selangor, Malaysia.

Phone: + 60390860288 Fax: + 60390198868 Email: [email protected]

ABSTRACT Chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI) holds great potential to provide new metabolic information for clinical applications such as tumor, stroke and Parkinson’s Disease diagnosis. Many active research and developments have been conducted to translate this emerging MRI technique for routine clinical applications. In general, there are two CEST quantification techniques: (i) model-free and (ii) model-based techniques. The reliability of these quantification techniques depends heavily on the experimental conditions and quality of the collected data. Errors such as noise may lead to misleading quantification results and thus inaccurate diagnosis when CEST imaging becomes a standard or routine imaging scan in the future. This paper investigates the accuracy and robustness of these quantification techniques under different signal-to-noise (SNR) levels and magnetic field strengths. The quantified CEST effect before and after adding random Gaussian White Noise using model-free and model-based quantification techniques were compared. It was found that the model-free technique consistently yielded larger average percentage error across all tested parameters compared to its modelbased counterpart, and that the model-based technique could withstand SNR of about 3 times lower than the model-free technique. When applied on noisy brain tumor, ischemic stroke, and Parkinson’s Disease clinical data, the model-free technique failed to produce significant differences between normal and abnormal tissue whereas the model-based technique consistently generated significant differences. Although the model-free technique was less accurate and robust, its simplicity and thus speed would still make it a good approximate when the SNR was high (> 50) or when the CEST effect was large and well-defined. For more accurate CEST quantification, model-based techniques should be considered. When SNR was low (< 50) and the CEST effect was small such as those acquired from clinical field strength scanners, which are generally 3T and below, model-based techniques should be considered over model-free counterpart to maintain an average percentage error of less than 44% even under very noisy condition as tested in this work. Keywords CEST; APT; MRI; Brain Tumor; Ischemic Stroke; Parkinson’s Disease.

1. INTRODUCTION Chemical exchange saturation transfer (CEST) is a magnetic resonance imaging (MRI) technique in which selective saturation is performed on exogenous or endogenous compounds containing either exchangeable protons or molecules. Through the chemical exchange of saturated protons from the compound to the bulk water, the CEST effect can be detected indirectly through the water saturation signal [1]. This allows for the indirect detection of previously otherwise undetectable lowly-concentrated labile protons. By evaluating the changes in the properties of these labile protons at their resonance frequencies, CEST MRI has been found useful and can provide new metabolic information for various medical applications, such as those related to brain tumor [2–9], stroke [10–16], and Parkinson’s Disease (PD) [17–19] imaging. In a recent high field clinical brain tumor imaging study, CEST imaging was shown to have the potential of identifying chemoradiotherapy responders and non-responders immediately after the treatment [20]. It was found that CEST imaging was at least 4 weeks faster than the standard clinical evaluation according to standard response assessment in neuro-oncology, highlighting the promising potential of CEST imaging as an early response tool in clinical tumor imaging. Other studies have also shown CEST imaging to be pH-sensitive [21], allowing for improved identification of ischemic penumbra in acute stroke patients [10,12] when compared to the current standard medical practice – identification of mismatch between diffusion-weighted imaging (DWI) and perfusion-weighted imaging (PWI). Many studies have shown that the mismatch between DWI and PWI is not an accurate measure to estimate the final ischemic injury due to the presence of oligemia in large portions of the mismatch [22]. In PD related studies, CEST imaging of the substantia nigra has been shown to not only be able to distinguish between PD patients and healthy individuals but also provide distinction between early and late-stage PD patients [17,19]. This suggests that CEST MRI may be used as an imaging marker for early PD detection, which remains a significant clinical challenge. In short, CEST MRI has the potential to complement or even provide new crucial information to the existing clinical imaging techniques, particularly in brain tumor, stroke, and PD related medical applications. As such, there have been many studies over the years on translating CEST MRI for routine clinical use. This includes developing a more accurate and reliable CEST quantification technique which can generally be classified into two categories, namely model-free and modelbased techniques. One of the earliest and most common quantification techniques used for CEST MRI is CEST ratio (CESTR) – a form of model-free asymmetry analysis where the difference between the zspectrum in the negative and positive frequency offsets are calculated. This metric inherently assumes that non-CEST contributions are symmetric around water resonance. However, this is not true since the z-spectra of tissue in vivo are actually intrinsically asymmetric due to the presence of many exchangeable protons in the positive frequency offsets such as amide [23,24], amine [25,26] and glucose [27,28], and negative frequency offsets such as intramolecular and intermolecular nuclear Overhauser enhancement (NOE) effects [29–32]. CESTR is also dependent on magnetic field strength [33,34] and other experimental parameters [35,36] such as

RF irradiation power and saturation time. Despite having these limitations, CESTR continues to be widely used for various applications [37–39] due to its computational simplicity and thus speed. Multi-pool model fitting is an alternative model-based CEST quantification technique where zspectra are generated based on the modified Bloch equations for chemical exchange and fitted to the experimental data [12,13,40,41]. The z-spectra are generated by solving the modified Bloch equations, taking into account each proton pool as well as the underlying physical parameters that describe the CEST exchange system, such as concentration, relaxation times, and exchange rates of the pools. By describing the various effects observed in vivo with a separate pool, a pure and more accurate CEST effect can be quantified from the data. However, this quantification technique suffers from longer processing time because it is computationally more demanding. Both of the mentioned model-free and model-based quantification techniques are widely used in CEST imaging experiments. However, the reliability of these quantification methods depends heavily on the quality of the experimental data [35,42] which is affected by the spatiotemporal resolution as well as other factors during image acquisition such as measurement noise. Currently, CEST imaging is being actively studied for clinical translation. The errors due to noise may affect the assessment of CEST effect in tissues, producing inaccurate results or misleading CEST images. Furthermore, if CEST imaging is implemented for routine clinical use in the future, these errors may even pose the risk of misdiagnoses which may lead to wrong or delay treatment decisions that may be detrimental to the patient, such as under- or overestimation of the size of a tumor in cancer patients and penumbra in ischemic stroke patients, or inaccurate diagnosis of the stage of a PD patient. Recently, there are suggestions [15,43] to use CEST imaging for graded regional CEST signal changes, relying on each pixel information for diagnosis or treatment, further highlighting the importance to identify whether the observed changes in the pixels are due to the underlying physiological changes or experimental noise when model-free or model-based quantification technique is used. In this work, the robustness and reliability of the mentioned model-based and model-free CEST quantification methods for the brain tumor, stroke, and PD imaging under different signal-to-noise ratios (SNR) are studied. The findings should contribute positively to the clinical translation of CEST imaging for the mentioned applications in determining which quantification method is more suitable under different experimental conditions.

2. THEORY 2.1 Model-Free Quantification Technique – CESTR CESTR is a form of model-free asymmetry analysis define as: CESTR(Δ𝜔) =

𝑀( ―Δω) ― 𝑀(Δω) 𝑀0

,

(1)

where 𝑀(𝛥𝜔) and 𝑀( ―𝛥𝜔) are the measured intensity at the resonance frequency of the labile protons and its mirror frequency about the water resonance respectively. 𝑀0 refers to the unsaturated signal. Amide proton transfer (APT) MRI, a specific form of CEST MRI, measures CESTR at 3.5 ppm, CESTR(3.5ppm), which links to amide protons of endogenous mobile proteins and peptides in tissues. APT is one of the most widely studied proton exchanges and it has shown very promising results in clinical applications related to brain tumor [44,45], ischemic stroke assessment [12,13,16], and PD [17–19]. As a result, this study focused on CESTR(3.5ppm) for the CEST quantification technique analysis. 2.2 Model-Based Quantification Technique – Multi-Pool Model Fitting 2.2.1 Modified Bloch Equations In multi-pool model fitting, the CEST effect of the pools are modelled with the Bloch equations modified for chemical exchange [46,47]. The modified Bloch equations for a three-pool exchange model are given by: 𝑑𝑀𝑎𝑥

= ― 𝑘2𝑎𝑀𝑎𝑥 + 𝐶𝑏𝑀𝑏𝑥 + 𝐶𝑐𝑀𝑐𝑥 ― (𝜔𝑎 ― 𝜔)𝑀𝑎𝑦

𝑑𝑡

𝑑𝑀𝑏𝑥 𝑑𝑡 𝑑𝑀𝑐𝑥 𝑑𝑡 𝑑𝑀𝑎𝑦 𝑑𝑡

= 𝐶𝑎𝑏𝑀𝑎𝑥 ― 𝑘2𝑏𝑀𝑏𝑥 ― (𝜔𝑏 ― 𝜔)𝑀𝑏𝑦 = 𝐶𝑎𝑐𝑀𝑎𝑥 ― 𝑘2𝑐𝑀𝑐𝑥 ― (𝜔𝑐 ― 𝜔) 𝑀𝑐𝑦

= (𝜔𝑎 ― 𝜔)𝑀𝑎𝑥 ― 𝑘2𝑎𝑀𝑎𝑦 + 𝐶𝑏𝑀𝑏𝑦 + 𝐶𝑐𝑀𝑐𝑦 ― 𝜔1𝑀𝑎𝑧

𝑑𝑀𝑏𝑦 𝑑𝑡 𝑑𝑀𝑐𝑦

= (𝜔𝑏 ― 𝜔)𝑀𝑏𝑥 + 𝐶𝑎𝑏𝑀𝑎𝑦 ― 𝑘2𝑏𝑀𝑏𝑦 ― 𝜔1𝑀𝑏𝑧

= (𝜔𝑐 ― 𝜔)𝑀𝑐𝑥 + 𝐶𝑎𝑐𝑀𝑎𝑦 ― 𝑘2𝑐𝑀𝑐𝑦 ― 𝜔1𝑀𝑐𝑧 𝑑𝑡 𝑑𝑀𝑎𝑧 𝑀𝑎0 = + 𝜔1𝑀𝑎𝑦 ― 𝑘1𝑎𝑀𝑎𝑧 + 𝐶𝑏𝑀𝑏𝑧 + 𝐶𝑐𝑀𝑐𝑧 𝑑𝑡 𝑇1𝑎 𝑑𝑀𝑏𝑧 𝑀𝑏0 = + 𝜔1𝑀𝑏𝑦 + 𝐶𝑎𝑏𝑀𝑎𝑧 ― 𝑘1𝑏𝑀𝑏𝑧 𝑑𝑡 𝑇1𝑏 𝑑𝑀𝑐𝑧 𝑀𝑐0 = + 𝜔1𝑀𝑐𝑦 + 𝐶𝑎𝑐𝑀𝑎𝑧 ― 𝑘1𝑐𝑀𝑐𝑧 𝑑𝑡 𝑇1𝑐

where, 𝑘1𝑖 =

1 + 𝐶𝑖 𝑇1𝑖

,

(2)

1 + 𝐶𝑖 , 𝑇2𝑖 𝑀𝑗0 𝐶𝑖 = 𝑖 𝐶𝑗 𝑀0

𝑘2𝑖 =

and 𝑇1𝑖 and 𝑇2𝑖 are the longitudinal and transverse relaxation times of pool i respectively, 𝜔 is the frequency of radio frequency (RF) saturation pulse, 𝜔𝑖 is the resonance frequency of pool i, 𝜔1 is the power of the RF saturation pulse, 𝑀𝑖0 is the proton concentration, and 𝐶𝑖 is the exchange rate of pool i. Here, i and j denotes the i-th and j-th pool respectively (i, j = a, b, and c for the case of the three-pool exchange system). 2.2.2 Solving the Modified Bloch Equations The set of linear differential equations in Equation (2) can be combined into a more general vector equations then solved analytically [48]: 𝑑𝑴(𝑡) = 𝑨𝑴(𝑡0) , 𝑑𝑡

(3)

where 𝑴(𝑡) = (𝑀𝑎𝑥

𝑀𝑏𝑥

𝑀𝑐𝑥

𝑀𝑎𝑦 𝑀𝑏𝑦 𝑀𝑐𝑦 𝑀𝑎𝑧

𝑀𝑏𝑧

𝑀𝑐𝑧

𝑇

1) .

and 𝑨 is a square matrix defined as:

𝑨=

(

― 𝑘2𝑎 𝐶𝑎𝑏 𝐶𝑎𝑐 (𝜔𝑎 ― 𝜔) 0 0

𝐶𝑏 ― 𝑘2𝑏 0 0 (𝜔𝑏 ― 𝜔) 0

𝐶𝑐 0 ― 𝑘2𝑐 0 0 (𝜔𝑐 ― 𝜔)

―(𝜔𝑎 ― 𝜔) 0 0 ― 𝑘2𝑎 𝐶𝑎𝑏 𝐶𝑎𝑐

0 ―(𝜔𝑏 ― 𝜔) 0 𝐶𝑏 ― 𝑘2𝑏 0

0 0 ―(𝜔𝑐 ― 𝜔) 𝐶𝑐 0 ― 𝑘2𝑐

0 0 0 ― 𝜔1 0 0

0 0 0 0 ― 𝜔1 0

0 0 0 0 0 ― 𝜔1

0

0

0

𝜔1

0

0

― 𝑘1𝑎

𝐶𝑏

𝐶𝑐

0

0

0

0

𝜔1

0

𝐶𝑎𝑏

― 𝑘1𝑏

0

0

0

0

0

0

𝜔1

𝐶𝑎𝑐

0

― 𝑘1𝑐

0

0

0

0

0

0

0

0

0

0 0 0 0 0 0 𝑀𝑎0

)

𝑇1𝑎 𝑀𝑏0 𝑇1𝑏 𝑀𝑐0 𝑇1𝑐 0

.

The formal solution to Equation (3) is written as: 𝑴(𝑡) = 𝑒𝑨 ∙ 𝑡𝑴(𝑡0).

(4)

where 𝑴(𝑡0) is the matrix of initial magnetizations of the pool; 𝑴(𝑡0) is [0 0 0 0 0 0 1 1 1 1] for the 3-pool example as shown in Equation (2). In this study, the exponential term in Equation (4) is calculated using the MATLAB built-in function “expm”.

Solving this set of linear differential equations for a range of saturation pulse frequencies yields the magnetization as a function of saturation frequencies, i.e. the z-spectrum. In multi-pool model fitting, this theoretically obtained z-spectrum is fitted to experimental data to quantify the pure CEST effect. 3. METHODS AND MATERIAL The study was split into two parts. Part 1 was to determine the accuracy of the model-free (CESTR) and model-based (multi-pool model fitting) quantification techniques by using simulated CEST data. The second part focused on demonstrating the reliability of both quantification techniques when used for brain tumor, stroke, and PD imaging. For both parts, the comparison of the accuracy and reliability between CESTR and multi-pool model fitting was done by determining the CESTR(3.5ppm) value of noisy CEST data before and after performing multi-pool model fitting. For simplicity, “CESTRpure” was referred to as the CESTR(3.5ppm) analysis without performing data fitting, basically directly using Equation (1) to find CESTR(3.5ppm) from the noisy zspectrum; “CESTRfitted” referred to the CESTR(3.5ppm) analysis after performing multi-pool model fitting, i.e. fitting the modified Bloch equations to the noisy z-spectrum then using the fitted parameters to re-generate the clean z-spectrum before calculating CESTR(3.5ppm) using the Equation (1).

3.1 Accuracy of the CEST Quantification Techniques using Simulated Data The modified Bloch equations were used to generate simulated z-spectra at 3T, 4.7T, 7T, and 9.4T field strengths. The parameters used are shown in Table 1 and were taken from literature with slight adjustments for field strength [33,49]. A saturation time, 𝑇sat of 5 s was used. The saturation was performed from -6 ppm to 6 ppm with 0.1 ppm increments (121 data points). A continuous saturation RF pulse of power 0.5 µT was used. For multi-pool fitting of the simulated data, the z-spectra were fitted from -6 ppm to 6 ppm at increments of 0.1 ppm using the MATLAB built-in function “lsqcurvefit”. There were a total of 15, 20, 25, and 30 parameters to be fitted for the 3T, 4.7T, 7T, and 9.4T field strength models respectively. These parameters were the longitudinal (T1s) and transverse (T2s) relaxations, the amplitude of the RF pulse, proton concentrations (Ms0), exchange rates (Cs), and resonance frequency of the pools (𝜔𝑠). However, the z-spectra were not sensitive to certain parameters, namely the longitudinal and transverse relaxations of the labile pools with the exception of the transverse relaxation of MT pool [40]. Labile pool resonance frequencies could usually be determined relatively accurately prior to the CEST experiment. As a result, only a total of 9, 11, 13, and 15 parameters were fitted for the simulated data at 3T, 4.7T, 7T, and 9.4T respectively. The initial fitting parameters were set by increasing the simulation parameters in Table 1 by 5%; the lower and upper limits were set as 20% below and above the simulation parameters respectively.

Gaussian white noise with a mean of zero and standard deviation of 0.1%, 0.5%, 1%, 2%, 4%, and 6% of the unsaturated signal were added to the simulated z-spectra to mimic the real CEST data that were considered to be good to moderate and very noisy. The Gaussian noises added were equivalent to CEST data of having SNR = 1000, 200, 100, 50, 25 and 16.7. For each set of simulated CEST data, 100 sets of random Gaussian noises were added for each SNR. From the noisy simulated data, the average percentage error of CESTR(3.5ppm) using CESTRpure and CESTRfitted were calculated; the ground truth was the original simulated z-spectra without noise. The coefficient of variation was also calculated (standard deviation divided by mean) to quantify the variation in CESTR(3.5ppm) of each set of noisy CEST data calculated using CESTRpure and CESTRfitted; the better quantification method should have a smaller coefficient of variation value.

3.2 Reliability of the CEST Quantification Techniques for Medical Applications CEST data from published literature on brain tumor [50], stroke [51], and PD [18] CEST imaging were extracted. From each literature, a set of clinical patient CEST data – z-spectra of abnormal and normal healthy tissue, were extracted using WebPlotDigitizer [52]. For Ref. [50], region of interest (ROI) averaged tumor core and contralateral normal appearing white matter (CNAWM) z-spectra extracted from Fig. 2(c); for Ref. [51], averaged stroke lesion and CNAWM z-spectra of four stroke patients were extracted from Fig. 3(d); for Ref. [18], averaged z-spectra of advanced stage PD patients and normal control groups were extracted from Figure 2(A). All the extracted CEST data were those obtained using 3T which is the typical clinical field strength scanner available in most of the hospitals. To each set of extracted data, random Gaussian white noise corresponding to SNR = 50 with respect to the unsaturated signal were added to generate 100 noisy datasets. From the noisy zspectra of abnormal and normal tissue, CESTR(3.5ppm) of both z-spectra were calculated using CESTRpure and CESTRfitted. For multi-pool model fitting in CESTRfitted, the noisy data were fitted using the built-in function “lsqcurvefit”. The saturation schemes and saturation power B1 used were those as described in the original references from which the in vivo data were extracted, that is, a continuous wave RF saturation of 4 µT power and 500 ms duration for the brain tumor data [50]; continuous wave RF saturation of 2 µT power and 500 ms duration for the stroke patient data [51]; four pseudocontinuous wave RF saturation pulses with saturation duration of 200 ms, inter-pulse delay of 10 ms, and power of 2 µT for the PD data [18]. In the case of the pulsed RF schemed used in Parkinson’s disease data modelling, the transverse magnetizations of the pools were set to zero at the end of each inter-pulse delay to simulate the use of a crusher gradient. The fitting limits and initial fitting parameters used can be found in Table S4 and S5 in Supplementary Material. A two-tailed paired t-test at 5% significance level was then performed on the noisy CESTR(3.5ppm) results of the abnormal and normal tissue z-spectra to test for significant

difference between the two tissue regions. The CESTR(3.5ppm) values quantified using CESTRpure and CESTRfitted were also plotted to evaluate the noisy CEST images qualitatively.

4. RESULTS 4.1 Accuracy of the CEST Quantification Techniques using Simulated Data Fig. 1 shows the fitting of a simulated 3T field strength z-spectrum with SNR = 1000 and 16.7 after adding the Gaussian white noise at 3T. The asymmetric spectrum of CESTR at different saturation frequencies using CESTRpure and CESTRfitted are also shown in the figures. From the figure, it can be seen that CESTR without model fitting was clearly noisier than after the model fitting when the SNR was low. The average percentage errors of CESTR(3.5ppm) of 3T, 4.7T, 7T, and 9.4T field strength cases with different SNR values using CESTRpure and CESTRfitted are shown in Table 2. In general, the average percentage error for CESTRpure decreased as field strength increased. Comparing between CESTRpure and CESTRfitted, the average percentage error of CESTRfitted was much lower than that of CESTRpure for all the tested SNR values and field strengths, indicating CESTRfitted was more accurate than CESTRpure. In general, CESTRpure yielded more than 8% average percentage error when SNR < 200 for all tested field strengths. For very noisy cases such as SNR = 16.7, CESTRpure even yielded average percentage errors of more than 140%. On the other hand, CESTRfitted never exceeded 44% across all the tested parameters. These results suggests that CESTRpure was more susceptible to error under low SNR conditions when compared to CESTRfitted. The CESTR(3.5ppm) values quantified using CESTRpure and CESTRfitted were plotted as images as shown in Fig. 2; each pixel represents the CESTR(3.5ppm) value of noisy simulated 3T field strength z-spectra obtained using CESTRpure or CESTRfitted. It was obvious that CESTRpure was not as robust as CESTRfitted for all the experiments, as the former started to lose its resemblance to the original clean image (no noise) when SNR < 100 whereas the quantified CEST effect using CESTRfitted was still very much like its clean image. Based on the calculated CV and average percentage error, CESTRfitted was able to tolerate noise with SNR about 3 times smaller: CESTRpure started to lose its resemblance to the clean image with CV of 0.550 and average percentage error of 46.83% when SNR = 50; the CV and average percentage of CESTRfitted was around these figures at 0.583 and 43.54% respectively when SNR = 16.7, indicating CESTRfitted was about 3 times (~ 50/16.7) more robust to noise.

4.2 Reliability of the CEST Quantification Techniques for Different Medical Applications Fig. 3Fig. 3 shows the extracted CEST images and the z-spectra of abnormal and normal tissue from the published literature. Below each pair of CEST image and z-spectra are the respective CESTR(3.5ppm) values quantified from the z-spectra with Gaussian noise added (SNR = 50)

using CESTRpure and CESTRfitted. From the results, it could be observed that CESTRpure failed to produce proper qualitative contrast between the abnormal and normal tissues for all tested medical applications under the presence of noise as the two halves (abnormal and normal tissue) could not be distinguished from one another. The paired t-test from CESTRpure also showed no significant difference between the two tissues at 5% significant level, as shown by the P value in the middle row of Fig. 3. In contrast, CESTRfitted showed a significant difference between the two halves for all tested medical applications. Visually, the abnormal and normal halves obtained using CESTRfitted were also distinct from one another. For brain tumor imaging, CESTRfitted indicated CESTR(3.5ppm) of abnormal tissue was higher than that of normal tissue while the reversed was true for stroke and PD imaging. This was consistent with the respective extracted CEST brain images shown in the figure and as reported in the literature [18,50,51].

5. DISCUSSION This study compared the accuracy and reliability of model-based and model-free CEST effect quantification techniques under different SNRs and magnetic field strengths. From the simulation experiment results, the average percentage error decreased as field strength increased when using CESTRpure. This was because the CEST effects became bigger and more defined when the field strength of the scanner increased [34], leading to higher tolerance of noise. Comparing between CESTRpure and CESTRfitted, the average percentage errors of CEST effect quantified using CESTRpure were found to be consistently larger than CESTRfitted for all tested parameters. In Fig. 2, the effects of noise on the CEST image produced using CESTRpure became evident as for low SNR (< 50), the CEST image no longer resembled the original clean image. When applied on noisy z-spectra (SNR = 50) of abnormal and normal tissue extracted from published clinical studies, CESTRpure failed to provide significant contrast between the two tissues whereas CESTRfitted was able to consistently distinguish between the two quantitatively and qualitatively as shown in Fig. 3. CESTRfitted of brain tumour showed that the CESTR(3.5ppm) of abnormal tissue is higher than that of normal tissue. In a recent tumour study [53], the increase in APT CEST effect was attributed to ~66% change in protein concentration and ~34% change in pH level. In this work, an increase in amide proton concentration and change in exchange rate were also observed in the abnormal tissue (please refer to Supplementary Material for the fitted parameters). However, since only single B1 power was used in the in vivo data, the effects of amide proton concentration and exchange rate might not be separated effectively [54]. Thus it was difficult to quantify the proportion of the two parameters contributing to the increase in the APT CEST effect. As the magnetic field strength of the scanner increases, the CEST effect becomes bigger. However clinical scanners are normally 3T and below, in such cases the CEST effect is not big and thus the rest of the discussion will mainly focus on the implication of this work for clinical translation of CEST imaging. In the simulation, a 5 s continuous saturation was used to saturate the amide protons to be close to its fully steady state at 3T in order to have a bigger CEST effect. This saturation time is less practical at clinical 3T scanners due to specific absorption rate and

hardware limitations. Although the hypothetical saturation time is used to ensure the saturation effect is bigger at 3T, CESTRpure still performs badly compared to CESTRfitted as shown in Table 2. CESTRpure, particularly at 3.5ppm, has been showing promising results in various clinical studies such as those involving brain tumor [4], stroke [55], and PD diagnosis [18]. However, as the results of this study suggest, if CESTRpure is used under high levels of noise in future clinical applications that are pre-dominantly 3T and below, it may not be able to provide a proper distinction between normal and abnormal tissue. This is because the CEST effect is small and not well-defined under low magnetic field strength scanner, improper experimental setup can lead to diminishing of the tiny CEST signal. The consequence is that it may lead to false estimation of tumor and ischemic penumbra sizes, or improper diagnoses of PD patients. In addition, recent literature reports the potential of using CEST imaging for the determination of graded regional tissue pH changes [15] and regional differences in glycosaminoglycan content to examine the biochemical changes in articular cartilage which may be associated with early stages of cartilage degeneration [43]. It is important to ensure that the results obtained for these applications are caused by the disease or treatment applied, and not due to experimental factors such as poor shimming, leading to low SNR CEST data and subsequently signal variation as shown in Fig. 2. For CESTRfitted in 3T, MT and NOE were modelled as together as one pool to account for the asymmetry in the in vivo environment in 3T field strength [13,16,54,56]. However, it has been suggested in other studies that MT effects are better modelled with superLorentzian lineshape instead. Nevertheless, the use of MT+NOE as a single pool modelled the in vivo z-spectra well for the purposes of this comparison study. Since MT and NOE were modelled together in contrast to being modelled separately at 4.7T and above, in the simulation study, the MT+NOE concentration value of 15% Mw0 at 3T was different from the concentration values used for 4.7T and above (referring to Table 1). Ref. [54], which similarly modelled the two pools together at -2.41ppm, was referenced for the MT+NOE concentration for 3T instead; we have checked with one of the authors in Ref. [54], there is a typo in the reported MT+NOE concentrations, the values should be relative concentrations instead of absolute concentrations. There are several important factors to consider in a CEST experiment that may influence the performance of either CEST effect quantification methods. Firstly, the CEST image SNR is highly dependent on the acquisition scheme and acceleration method used. Typically, for proper analysis, volume data are needed, which are in general more time consuming to acquire than single-slice or two-dimensional (2D) acquisition. In order to achieve practical clinical standards, fast data acquisition is desirable as scan time is often constrained by patient comfort and criticality of the diseases. As such, some studies propose the use of multi-slice image acquisition techniques. For example, a recent study shows the development of an ultrafast CEST segmented spatiotemporally encoded sequence (SeSPEN) which drastically shortens the image scan time to less than a second [57] (about 600 ms for 20 slices). However, the main drawback of this image acquisition technique is that the SNR is significantly lower than the more conventional techniques such as echo planar imaging (EPI), and is therefore more prone to error caused by noise. The use of CESTRpure in conjunction with such multi-slice CEST imaging schemes in potential future clinical applications would complicate data analysis as it will be difficult to assess the change of CEST signal is due to the underlying disease or the acquisition technique. Other alternative acquisition schemes include accelerated three-dimensional (3D) acquisition schemes such as

fast spin-echo imaging [58], gradient- and spin—echo (GRASE) [59], and MR fingerprinting based 3D imaging [60]. These acquisition methods are able to achieve higher SNR compared to EPI. However, the acquisition times are slower compared to ultrafast multi-slice SeSPEN, ranging from 4 to 10 mins for whole brain scans. Besides the imaging acquisition method, the offset sampling schedule also plays an important factor. A high frequency spectral resolution can enable more reliable CEST quantification for both CESTRpure and CESTRfitted, and repeated acquisition at ±3.5 ppm and averaging is also possible to reduce the effects of noise. However, the drawback is that these sampling schedules may be more time consuming to acquire. To address this, an Optimized Sampling Schedule (OSS) may be implemented where only frequency offsets that are highly sensitive to the variations of CEST pool of interest are repeatedly sampled as opposed to sweeping across the saturated frequency offsets with a fixed interval. This may help to reduce acquisition time while maximizing useful information present in the collected data [41]. In this study, CESTR was used because of its widespread use. However, aside from CESTR, there have also been developments of other quantification methods. Relaxation-compensated metric, for example, is a model-free quantification technique where the difference of the inverse metrics of the label and reference scan are divided by the longitudinal relaxation for spillover, magnetization transfer (MT), and relaxation correction [3,61]. The relaxation-compensated metric is in fact a form of quantification equivalent to that of CESTR with correction for spillover, MT, and relaxation. Although our study focuses on CESTR, other CESTR-derived techniques or simple model-free CEST quantification techniques such as this are also believed to be compromised in the same way when there is a presence of large noise such as the results shown in Fig. 2 and Fig. 3. Similarly, there are also other model-based quantification techniques such as multiLorentzian fitting. Instead of modelling the CEST process of the system through the parameters of all the proton pools as with multi-pool model fitting, multi-Lorentzian fitting models the shape of the z-spectrum of the system using Lorentzian curves. It is expected that the results from this study is also applicable to multi-Lorentzian fitting as in it should be more robust against noise when compared to simple model-free techniques such as CESTR. If the parameters of interest are the amplitude and linewidth of labile pool, or CESTfitted, multi-Lorentzian fitting would appear to be a more suitable choice compared to multi-pool model fitting due to its simplicity thus speed. When the collected data are more favorable for multi-pool model fitting such as multi-B1 data and relaxation maps are acquired to increase the information available in the data, multi-pool model fitting should be considered to relate whether the observed changes in the CEST signal are due to the underlying physiological changes. Previous studies have also implemented denoising techniques on the acquired CEST data to reduce the effects of noise. These denoising techniques include interpolation based smoothing algorithms such as smoothing splines [62], or more sophisticated denoising approaches such as Fourier time domain and principal component analyses. Although these denoising techniques may be much less time consuming than multi-pool model fitting, simple smoothing algorithms are not able to model or describe the CEST processes thus the use should be limited to high SNR CEST data only (see Supplementary Material). However, it is probable that more advanced

smoothing algorithms may lead to similar results to CESTRfitted with proper fine tuning of the smoothing parameters. The experiments done throughout this study focused on CEST effect at 3.5 ppm linked to amide protons of endogenous mobile proteins and peptides in tissues. This saturation effect is commonly used for CEST imaging in the medical applications focused in this study. There are also other saturation effects that have been shown to be potential biomarkers for these medical applications. For example, creatine at 2ppm and NOE at -1.6ppm has been showed to be potential biomarkers for brain tumor [2] and ischemic stroke [63] diagnosis respectively. Although our study focuses on CEST quantification techniques at 3.5 ppm, the findings should be extendable to other saturation effects if only simple model-free quantification techniques such as CESTR are used. Overall, although the speed of CESTR is desirable, it is important to take into consideration the quality of the collected data when deciding which CEST quantification technique to use. In less time critical clinical applications such as cancer diagnosis and treatment monitoring, model-based quantification techniques such as CESTRfitted should always be considered to get a more accurate quantification of the CEST effect under investigation when the CEST effect is not well-defined and big. This is usually the case when the magnetic field strength of the scanner is 3T and below. CESTRfitted should also precede CESTRpure when SNR is low either due to improper experimental setup such as poor shimming, incorporated patients with constant minor movement, or ultrafast multi-slice CEST imaging scheme which sacrifices SNR for multiple slice acquisition [57].

6. CONCLUSION In this study, the model-based quantification, CESTRfitted, was found to be more robust against noise when compared to the model-free technique, CESTRpure. Although the model-free technique was less accurate, its simplicity and thus speed would still make it a good approximate when the SNR is high (> 50) or the CEST effect is big and well-defined. When the SNR is low (< 50) or the CEST effect is small, model-based techniques should be considered for more accurate CEST effect quantification and to maintain significant difference and a proper degree of contrast between the normal and abnormal tissues even under very noisy condition as tested in this work.

7. ACKNOWLEDGEMENT YKT was supported by National Cancer Council Malaysia (MAKNA) Cancer Research Award 2018 as well as UTAR Research Fund (project number: IPSR/RMC/UTARRF/2018-C1/T04), and would like to gratefully acknowledge the support of NVIDIA Corporation with the donation of a Quadro P6000 GPU for this research.

8. COMPETING INTERESTS The authors declare that they have no competing interests.

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FIGURE CAPTIONS Fig. 1. Fitted simulated 3T field strength z-spectra with (a) SNR = 1000 and (b) SNR = 16.7. Mw and Mw0 are the magnetization and initial magnetization of bulk water pool respectively. (1.5 column-fitting image)

Fig. 2. Obtained CESTRpure and CESTRfitted values at 3T under different SNRs presented as images. The numbers in bracket below each image are the coefficients of variation of the different CESTR images; higher value represents higher variation across the quantified CEST effect. (Double column-fitting image)

Fig. 3. The extracted z-spectra of abnormal and normal tissue with their respective reported CEST images are shown in the top row. The CESTRpure and CESTRfitted values after adding Gaussian noise (SNR = 50) are presented in the middle and bottom row respectively. The P-values obtained from the significance test quantified using the different methods between the abnormal and normal z-spectra are shown under each APT image. ** indicates no significant difference between the abnormal and normal halves (P > 0.05); †† indicates a significant difference between the two halves (P < 0.05). The data and CEST brain images in the top row were respectively extracted from: brain tumor – Fig. 2(c) and Fig. 2(l) of Ref. [50]; stroke – Fig. 3(d) and Fig. 5(h) of Ref. [51]; PD – Figure 2(A) and Figure 6(A), (C) of Ref. [18]. (Double column-fitting image)

TABLES

Table 1. Parameters used for CEST data simulation taken from literature [33,49].

Chemical Shift (ppm)

Water

Amide

MT*

NOE

Amine

NOE

0

3.5

0

-3.5

2

-1.6

30 Hz

20 Hz

20 Hz

1 kHz

20 Hz

1/250 1.4 s 50 ms 1.8 s 40 ms 2.0 s 38 ms 2.2 s 36 ms

1/25 1.4 s 0.2 ms 1.8 s 20 µs 2.0 s 20 µs 2.2 s 20 µs

1/300 1.8 s 0.4 ms 2.0 s 0.4 ms 2.2 s 0.4 ms

1/500 2.0 s 38 ms 2.2 s 36 ms

3/1000 2.2 s 0.4 ms

Exchange rate Concentration (M0a) 3T /3 Field Strength / No. of pools

4.7T /4 7T /5 9.4T /6

T1 T2 T1 T2 T1 T2 T1 T2

1 1.4 s 100 ms 1.8 s 65 ms 2.0 s 60 ms 2.2 s 36 ms

* For 3 T, MT and NOE are modelled together as a single pool at -2.41 ppm [54] with an exchange rate of 30 Hz and concentration of 15% of M0a.

Table 2. Average percentage errors of CESTR(3.5ppm) using CESTRpure and CESTRfitted. SNR

Quantification Method

Average Percentage Error (%) 3T

4.7T

7T

9.4T

CESTRpure

2.368

0.9515

0.9265

0.7925

CESTRfitted

1.067

0.5382

0.5989

0.5834

200

CESTRpure CESTRfitted

11.81 5.814

4.487 2.779

3.938 2.877

4.082 2.712

100

CESTRpure CESTRfitted

23.29 9.142

9.074 5.107

8.101 5.490

8.414 5.798

50

CESTRpure CESTRfitted

46.83 19.38

19.78 11.14

16.11 9.399

19.04 11.07

25

CESTRpure CESTRfitted

95.66 36.60

42.50 17.42

36.63 17.49

37.75 19.95

16.7

CESTRpure CESTRfitted

141.0 43.54

49.37 22.15

49.27 24.39

52.70 26.68

1000

Graphical abstract

Highlights

-

Model-based and model-free CEST effect quantification methods for different medical applications studied Model-based method was about three time more robust to noise than model-free method Model-free method failed to show significant difference in low SNR brain tumor, stroke, Parkinson’s Disease data Model-based method consistently showed significant differences in the low SNR data

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: