Introduction
In living species, extracellular pH (pH
e) is an important physiological parameter that is tightly regulated by intrinsic buffer systems. Locally, deviations from the systemic pH are often caused by pathologies, such as cancer, inflammation, infection, ischemia, renal failure or pulmonary disease [
1‐
3]. Since pH
e can play a critical role in disease progression [
4] and can influence therapeutic success [
5], many efforts have been undertaken to develop a quantitative non-invasive pH imaging technique [
3,
4,
6]. However, there is no clinical routine method available for spatial quantification of pH
e, rendering it still an important target in biomedical imaging.
Magnetic resonance-based pH imaging methods offer high spatial resolution without limitations on the penetration depth and without involving ionizing radiation. In addition, conventional
1H MRI offers high anatomical soft tissue contrast that can be overlaid on top of pH images. MRI-based pH
e imaging techniques that have been applied in vivo require the use of exogenous molecules and rely either on their pH-dependent chemical exchange saturation transfer (CEST) or on their pH dependence of chemical shifts [
1]. Utilizing endogenous molecules, the intracellular pH (pH
i) can be measured by pH
i-dependent proton exchange from amide groups of intracellular proteins [
4].
Magnetic resonance-based detection of biochemical and physicochemical quantities by exogenous molecules was revolutionized by dissolution dynamic nuclear polarization (DNP) which lifts nuclear spin polarization to a so-called hyperpolarized state leading to a sensitivity gain of more than four orders of magnitude [
7]. Hyperpolarized [1-
13C]pyruvic acid is currently being used in clinical studies to examine its use for metabolic imaging of cancer, as well as in the brain and the heart [
8‐
10]. Several pH-sensitive molecules have been hyperpolarized and been used for in vitro pH mapping including
13C,
15N,
31P,
89Y and
129Xe spin-1/2 nuclei [
11]. Only two of those have so far been applied for pH imaging in vivo: hyperpolarized
13C-labelled bicarbonate [
3,
12] and hyperpolarized [1,5-
13C
2]zymonic acid (ZA) [
13] as well as its deuterated variant [1,5-
13C
2,3,6,6,6-D
4]zymonic acid (ZA
d) [
14].
With hyperpolarized bicarbonate, pH
e is being determined by the signal intensity ratio of the CO
2 and HCO
3− peaks, while the pH
e determination with ZA works via spectral analysis of the peak position, i.e. the chemical shifts. Chemical shift-based pH
e detection offers the unique advantage compared to intensity-based pH detection that multiple pH
e compartments within one imaging voxel can be resolved if their spectral peaks are separable, e.g. for resolving different pH
e compartments in the kidney [
13]. For intensity-based pH
e detection, on the other hand, multiple pH compartments within one imaging voxel result in one signal intensity ratio, allowing only the determination of an average voxel pH. The concept of chemical shift-based detection of quantitative physiological measures using hyperpolarized magnetic resonance sensors has, besides for detection of pH
e, also been used to quantify zinc [
15], calcium/magnesium/iron ions [
16], temperature [
17], or ligand-receptor interactions [
18].
Quantification of these measurements with hyperpolarized NMR sensors is done via analysis of the peak positions of the respective molecular sensors. Typically, the NMR spectra and all respective peaks are fitted via an optimization procedure giving the peak positions and amplitudes. However, such line-fitting procedures are error-prone in cases of low signal-to-noise ratio (SNR) and peak overlap, e.g. for multiple pH
e compartments within the kidneys [
13]. In recent years, deep learning has shown its potential for magnetic resonance spectroscopy (MRS) and magnetic resonance spectroscopic imaging (MRSI) data in several applications to improve analysis of noisy data with interfering signals [
19,
20]. Among these, artificial neural networks (ANN) demonstrated their value for spectroscopy analysis in medicine by classifying lung cancer tissue based on
1H MRS [
21] or denoising of brain
1H MRS [
22]. Furthermore, it was shown that convolutional neural networks (CNN) and multilayer perceptrons (MLP) can be trained to classify specific chemical compounds in various spectroscopy data sets [
23,
24]. Nevertheless, we hypothesize that there is an advantage in applying a CNN for spectral analysis, as this class of network is invariant under frequency shifts of the entire spectrum which can be caused by B
0 inhomogeneities.
We also hypothesize that transfer learning with real mice kidney data could improve the performance for our deep learning model. Transfer learning and domain adaptation have been used to adapt the model trained by one data distribution to the target data domain [
25,
26], especially when the target domain data is limited [
27]. Our target domain data,
13C-labelled zymonic acid kidney spectra, are by definition of the animal study and experimental efforts limited in size. Only one or two PRESS spectra or one CSI data set, still containing only a few single voxel spectra from kidneys, can be obtained from a single imaging experiment.
In this work, we investigate whether deep learning can improve the prediction of multiple pHe compartments from magnetic resonance data using hyperpolarized ZA. For this task, we evaluate the performance of a CNN compared to a MLP as well as to conventional line fitting on both a single type of data (synthetic) and real data adaptation (a mix of real and synthetic data). For deep learning evaluation, both real data using line fitting as a gold-standard for evaluation of pHe compartments as well as synthetic data with known pHe compartments are used.
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