A Machine-Learning Approach to Measuring Tumor Ph Using MRI

A Machine-Learning Approach to Measuring Tumor pH Using MRI

Item Type text; Electronic Thesis

Authors DeGrandchamp, Joseph B.; Cárdenas-Rodríguez, Julio

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/624957

A MACHINE-LEARNING APPROACH TO MEASURING TUMOR pH USING MRI

Author: Joseph B. DeGrandchamp Project Advisor: Dr. Julio Cárdenas-Rodríguez

A Thesis Submitted to the Department of Chemistry and Biochemistry and the Honors College in Partial Fulfillment of the Bachelors of Science degree with Honors in Chemistry.

Department of Chemistry & Biochemistry University of Arizona Spring 2017

Approved by:

Dr. Julio Cárdenas-Rodríguez Faculty Thesis Advisor

Date A Machine-Learning Approach to Measuring Tumor pH using MRI

J. DeGrandchamp*,1,2, J. Cárdenas-Rodríguez*,1

1. Department of Medical Imaging, University of Arizona, Tucson, AZ.

2. Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ.

*To whom correspondence should be addressed. E-mail: [email protected], [email protected]

ABSTRACT

Tumor pH can become an important consideration in diagnosis and choosing an effective therapy. Measuring pH currently requires invasive procedures or has problems with sensitivity. Previous methods for the measurement of pH by MRI are dependent on knowing the concentration of contrast agents or are useful at a limited pH range. Determining the concentration of a contrast agent in vivo is a very difficult task. We propose to use machine learning to decouple the estimation of pH from requiring knowledge of contrast agent concentration. This approach makes it possible to use new contrast agents and extends the ranges of pH than can be studied. In addition, this technique uses the entirety of the data instead of fitting parameters in order to make pH predictions. We evaluated the performance of this new method to measure pH by repurposing a clinically approved X-ray contrast agent, ioxilan, as an MRI agent. The pH was successfully measured in vitro with a small margin of error (RMSE = 0.0515), and the method was able to produce reliable parametric maps of pH for acquired image sets. We will extend this new method to measure pH in mouse models of cancer.

1 Introduction

Clinicians are constantly in search of better tools to diagnose cancer and aid in its treatment.

Cancerous tissues typically exhibit lower extracellular pH than their surroundings due to their altered metabolic activity. Knowledge of the exact level of pH adjustment in tumors could aid clinicians in numerous ways. Acidic tumor pH is correlated with higher incidence of metastasis, and thus with higher mortality.1 Furthermore, the effectiveness of many chemotherapies has shown a dependence on pH.2 Doxorubicin for example is weakly basic, and its uptake into acidic tissues is decreased.2 Clinicians could therefore use tumor pH in choosing the most effective treatment from the multitudes of therapies available. However, we currently do not have a general method to measure the pH of tumors in vivo in a non-invasive manner.

One method for measuring tumor pH consists of inserting a physical probe into the tissue.3

This can be useful during surgery where the extracellular pH can be key in differentiating healthy tissue from cancerous tissue.3 However in the case of surgery, the tissue is already exposed and readily accessible. Measuring pH in this manner prior to surgery or in cases where surgery is not required becomes a very invasive process. Non-invasive methods have been developed to address this issue. pH measurement using MRI has seen some success using

Chemical exchange saturation transfer (CEST).4,5 CEST MRI is a method that is dependent on the exchange of protons between a contrast agent and bulk water. A CEST spectra is constructed by applying a saturation pulse at different frequencies relative to water (Figure 1). The shape of this CEST is a function of the experimental parameters used in its collection, the exchange rate of the protons under study, the number of protons, and their concentration.4,5 Depending on the agent used, the exchange rate could be either acid or base catalyzed. In ioxilan, the observed signal is from a group of amides with an offset ~4.2 ppm (Figure 1), the proton exchange of

2 which is base catalyzed. Faster exchange rates result in increased peak amplitude and width. This pH dependency makes CEST MRI a suitable method to measure pH in vivo. However, this methods still suffers from low sensitivity, variance, and requires knowledge of contrast agent concentration.4,5 Determining concentration is a difficult, time-consuming, and often inviable process.6 By using machine learning, the pH and concentration dependencies can be decoupled.

Figure 1. The (A) structure of ioxilan and (B) corresponding CEST spectra (normalized and corrected for B0 inhomogeneity) for a range of 9 concentrations at pH 7.02. Here, the y-axis is displayed as the signal (MZ) divided by the initial signal (M0). It is often interpreted as a percentage of the water signal, where 1 would be 100%. Bulk water appears as a broad peak at 0 ppm (B). The amide groups (circled in (A)) appear as a single peak at ~4.2 ppm (B) due to their chemical similarity. As ioxilan concentration increases, the amplitude of the 4.2 ppm peak increases as well (B).

CEST MRI is currently used to measure pH in vivo using two approaches: 1) Estimate the concentration of a contrast agent and the tissue pH using advanced non-linear curve fitting methods using the Bloch-McConnell equations (Bloch fitting method).5 2) Estimate the pH using an empirical calibration curve based on the ratio of two CEST signals of exchangeable protons in the same molecule and at the same pH (ratiometric method).4 The Bloch fitting method requires substantial expertise, taking more than 45 minutes to analyze a single CEST experiment, and it is sensitive to noise. The ratiometric method does not require substantial fitting, but it only works

3 at pH values less than 7.0 and requires agents with two exchangeable protons discernable by

CEST.4,6

We propose an entirely new approach to measure pH using CEST MRI. Instead of doing

Bloch fitting or creating an empirical calibration curve, we create a model between the observed

CEST spectra at multiple pHs and concentrations using machine learning. Machine learning refers to a variety of computational techniques which are grouped based on their use of training data to create useful models as in Figure 2. Machine learning has seen use in diagnosis of disease and is useful for modeling phenomena where the model is not well understood.7 In this study, we used the machine learning technique known as partial least-squares (PLS) regression.8 PLS regression uses many of the same principles as principal component analysis, but prioritizes prediction instead of data reconstruction. Herein, PLS regression was used to find a model for pH measurement in vitro using a repurposed X-ray contrast agent, ioxilan, at a range of concentrations and pH. This model for ioxilan will in the future be used for pH measurement in vivo by injecting this agent.

Figure 2. A simple flowchart representation of a machine learning workflow

4 Methods

Sample Preparation

Solutions of ioxilan at 8 different pHs and 9 different concentrations were prepared from a clinical stock formulation (Oxilan® 350 mgI/mL, Guerbet LLC). The pH was adjusted using hydrochloric acid and sodium hydroxide. The pH values used were 6.02, 6.25, 6.60, 6.76, 7.02,

7.19, 7.40, and 8.00, and each pH sample was diluted to achieve the following concentrations:

166, 133, 106, 85, 68, 54, 44, 35, and 28 mM. In total, there were 72 samples. Samples were stored and imaged in 200 µL Eppendorf tubes.

Image Acquisition

To acquire images, samples were separated by pH (sets of 9) and inserted into a cradle containing 2% (w/v) agar gel. The gel was kept at 37.0±0.2 °C during scans using a thermostatic heating system equipped with a temperature probe. CEST acquisitions were performed for each pH set. The CEST MRI protocol consisted of CEST-Fast imaging with steady-state precession

(FISP) MR images using 3 µT saturation powers and a saturation time of 5 s.9 The FISP protocol utilized a 35.7461 ms repetition time (TR); 12.6781 ms echo time (TE); 10 µs bp32 excitation pulses; 60° excitation angle; 1 mm slice thickness; 4.0 x 4.0 cm field of view (FOV); 0.0997 mm2 plane resolution; 128 x 128 resolution matrix; centric encoding order; unbalanced “FID” mode; and 500 ms scan time. The protocol was run with acquisitions of 4 and 101 CEST excitation frequencies ranging from -50 to -47 ppm and -8 to 15 ppm respectively.

Data Analysis

Image analysis was conducted in MATLAB® 2016b (Mathworks, Natick, MA). Analysis consisted of first selecting regions of interest (ROIs) for each sample in each set. Average CEST signals of all voxels in the ROIs were then extracted from the image sets. The first four

5 saturation frequencies (which allow the system to reach steady state) were discarded. Spectra were corrected for B0 inhomogeneity by setting the minimum signal to 0 ppm and then normalized to the first value (at -8 ppm). Spectra were then centered and denoised using a

Lorentzian fitting with the following function:

∗/ (1) , , , 1 /

In Eq. 1, x is a vector of offsets (in ppm), A is the peak amplitude, W is the full peak width at

10 its base, and x0 is offset of the peak’s center. The ioxilan spectra were assumed to be a sum of three of these functions (pools) with a water peak, hydroxyl peak, and amine peak present. A non-linear least-squared curve-fitting algorithm was utilized to estimate A, W, and x0 for each

2 peak in all 72 spectra (all r > 0.98) . The x0 values were then shifted so that the center of the water peak was identically 0 ppm. Spectra were then rebuilt by inserting the estimated parameters back into the Lorentzian fit, producing centered, “clean” spectra in which offsets are aligned between samples.

Figure 3. A simple flowchart representation of the data analysis workflow

6 Lastly, pH prediction was done using a Partial Least-Squares (PLS) regression algorithm with leave-one-out cross-validation.8 A model was found by the algorithm using all 72 spectra and their associated, measured pH as training data. A vector of coefficients was produced that, when applied to a CEST spectrum of the same length as the training data, can be used to predict pH. pH prediction was validated by predicting the pH for each spectra using the model and comparing the prediction to the measured pH. Models can be built with PLS regression using different numbers of components with a maximum equal to the number of observations minus one (71 here).9 The number of components was optimized by determining the best model performance indicated by the minimum root mean square error (RMSE) using each possible number of components (from 2 to 71). Parametric maps of pH and concentration were then made for each image set by applying the PLS model from the average data to the centered CEST spectra of each voxel in the ROIs. The mapping performance was optimized in the same manner to find the most suitable number of components to use.

Results

Extracted Average CEST Spectra Averaged CEST spectra for the sample ROIs were collected, but as seen in Figure 4A there was a large B0 inhomogeneity effect among the samples as well as a difference in signal baseline. This was corrected to a certain degree before any fitting by setting the minimum signal to 0 ppm (assumed to be water) and normalizing the data to the signal at -8 ppm (Figure 4B). At this level of processing however, the data is still not aligned perfectly. To ensure the PLS method does not mistake B0 inhomogeneity or noise for variability due to pH, the data must be centered further using Lorentzian fitting.

7 (A) (B)

Figure 4 . Raw CEST spectra (A) and corrected CEST spectra (B) for samples of ioxilan at pH 7.02 and varying concentration. CEST spectra were corrected by translating the spectra to make the minimum signal 0 ppm and then normalization to the signal at -8 ppm.

CEST Fitting The fitting of the CEST spectra by Lorentzian functions was successful in all cases as demonstrated in Figure 5A and by the goodness of fit (r2 correlation coefficient of 0.98 or higher for all spectra). The centered CEST spectra (Figure 5B) display the expected increase in the amplitude and width of the amide peak (~4.2 ppm) with increasing concentration.4,5 The spectra also show a drastic change in the peak amplitude and shape with pH. At pH 8.00, the peak is very broad and is not fully resolved from the water peak. In contrast, the peak is completely resolved from water at pH 6.02 and has much smaller amplitude. This difference in both shape and amplitude is useful for measuring the pH.

Figure 5. Observed spectra with an overlay of the Lorentzian-predicted spectra (A) and the final fitted CEST spectra of ioxilan (B). Each plot in (A) demonstrates the goodness of fit of the Lorentzian fitting at 28 mM and at each designated pH, which had an r2>0.98 in all cases including those not shown here. Each plot in (B) shows the spectra of the 9 different concentrations (166, 133, 106, 85, 68, 54, 44, 35, and 28 mM) at the designated pH. The amplitude of the peak at 4.2 ppm increases with concentration.

Validation of Machine Learning Models

Measurement of pH by machine learning was successful using the ROI-averaged CEST spectra (Figure 2). In Figure 2A/B, a perfect model would produce a straight line with no variation but would be suspect of overfitting. The presence of some limited variation inspires confidence in the model’s ability to work with outside data. Increasing the number of components used in the model from 2 (Figure 2A) to 52 (Figure 2B) greatly decreases the variation until a minimum root-mean squared error (RMSE) of 0.0515 is reached at 52

9 10

Figure 7. Voxel-based maps of predicted pH (A-H) and predicted concentration (I-P). The maps are overlaying a single CEST image of a set of ioxilan samples their respective pH. Measured pH values were 6.02 (A/I), 6.25 (B/J), 6.60 (C/K), 6.76 (D/L), 7.02 (E/M), 7.19 (F/N), 7.40 (G/O), and 8.00 (H/P). Measured concentrations were 166, 133, 106, 85, 68, 54, 44, 35, and 28 mM (decreasing from top left to bottom right). These maps were produced by applying a PLS regression model learned from average spectra (Figure 2) with 5 components to the CEST spectrum of each voxel.

Discussion

Tumor pH is important to consider in diagnosis and therapy selection,1,2 but current methods fail to provide sufficient tools for pH determination.3-5 By using machine learning with contrast- agent-enhanced MRI methods, pH measurement becomes viable in a non-invasive manner. pH measurement with the new method demonstrated a higher sensitivity than previous methods without machine learning utilization.4,5 It also continues to perform with good accuracy even at higher pH such as pH 8.00, where other methods typically fail around pH 7.4,5 Lastly, the new method has been demonstrated with a contrast agent (ioxilan) that would have been unsuitable

11 for a ratiometric approach due to producing only a single CEST peak, and this shows new classes of contrast agents can be used.

The method has its drawbacks, but they are within acceptable limits. The data analysis has a large computational cost, as it employs fitting methods that can be quite slow. This makes the construction of the machine learning model slow but it is performed only once. The issue of how many components to use in the PLS regression is also of note. More comprehensive studies will need to be done to determine the ideal number of PLS components and CEST MRI saturation frequencies. It may be beneficial to use a voxel-based training set instead of an average-based set in order to provide more observations. The information provided by the CEST spectra that is related to pH is also all contained in the positive region (>0 ppm), and it may save time or be better for the fitting to change the range of saturation frequencies imaged or used in the analysis.

The most critical step to take next is validation of the method in vivo. A mouse model is being planned that will consist of mice with induced flank tumors. Injections of ioxilan will be conducted at suitable concentrations, and the pH will be measured using the machine learning

CEST MRI method.

Funding Sources

This work is supported by Institutional Research Grant number IRG-16-124-37-IRG from the

American Cancer Society.

REFERENCES

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