Synopsis

Keywords: Spectroscopy, Non-Proton, 31P, phosphorus, pH

³¹P MRSI enables non-invasive mapping of pH value and magnesium content in vivo, and is conventionally done by calibration equations, like the modified Henderson-Hasselbalch equation, relating ³¹P chemical shifts to physiological parameters. The reliability of this approach might be hampered when applied to diseased tissue, like cancer, where the chemical conditions are altered. Recently, we proposed a chemical shift dictionary for ³¹P MRSI to potentially enable a condition-independent estimation of pH value and magnesium content. In this study, the applicability of this approach to in vivo data is tested, and its potential for further research identified.

Introduction

³¹P MRSI enables non-invasive imaging of pH values and magnesium ion content in living tissues^1-3, employing the chemical shift changes of inorganic phosphate (P_i) and Adenosine-5’-Triphosphate (ATP). The chemical shifts are related to biochemical parameters via calibration equations, like the Henderson-Hasselbalch equation (HHE) in the case of pH⁴. However, therein required constants, e.g. pK_A, are typically only characterized under physiological conditions. This poses a particular challenge in pathological conditions, e.g. in tumor tissue, where chemical conditions might change manifold, hence potentially hampering reliability of the employed equations. Recently, we proposed a dictionary-based approach potentially enabling the estimation of pH and magnesium ion concentration under varying chemical conditions, i.e. ionic strength, which might provide a valuable alternative to characterize the tissue’s microenvironment⁵. The purpose of this study was to test the applicability of this dictionary-based approach for in vivo ³¹P MRSI data, and to identify its potential value for biomedical research.

Methods

The implemented dictionary is based on the chemical shifts of $$$\gamma$$$- and $$$\beta$$$-ATP obtained from ³¹P FID measurements at 9.4T (Bruker) in 114 model solutions prepared with different (pH, R = [Mg²⁺] /[ATP^4-], Ion) conditions. The quantity Ion acts as a surrogate for the true ionic strength scaled with an arbitrary factor. To extend the dictionary, the chemical shifts were interpolated using a multidimensional model function based on the Hill equation, yielding a final number of 426,951 entries. The dictionary search algorithm assigns output values for (pH, R, and Ion) for a given chemical shift combination based on combined probability density functions for the interpolation model, as described in detail in⁵. The algorithm was applied to in vivo 3D ³¹P MRSI datasets measured at 7T (Magnetom 7T, Siemens), comprising data from lower leg muscles of 3 healthy volunteers³, and data from brain tissue of 3 patients with glioblastoma². For a description of the ³¹P MRSI data acquisition and quantification, the reader is referred to^1-3. Locally quantified chemical shifts of $$$\gamma$$$- and $$$\beta$$$-ATP were fed into the dictionary algorithm to yield voxelwise output triples (pH_Dict, R_Dict, Ion_Dict), resulting in three different 3D maps for each volunteer and patient. For comparison, conventional maps for pH and the free magnesium ion concentration [Mg²⁺_free] were calculated with the modified HHE with constants from⁴ for pH, and the approach by Golding and Golding⁶ for magnesium. Regions-of-interest (ROIs) covering three different muscle groups (muscle data), and ROIs covering the whole tumor and white matter (brain data), were defined on morphological images.

Results

All in vivo datasets showed regional variations in the combination of the quantified chemical shifts of $$$\gamma$$$- and $$$\beta$$$-ATP. Applied to the in vivo datasets, the dictionary algorithm successfully assigned output values (pH_Dict, R_Dict, Ion_Dict) in 98% (muscle) and 90% (brain) of all tissue voxels, showing that the dictionary space well covers the chemical shift combinations observed in vivo. Representative 3D maps of the output triples (pH_Dict, R_Dict, Ion_Dict) in the lower leg muscles of one healthy volunteer (Figure 1) and in the brain of one patient with glioblastoma (Figure 2) are shown in comparison to the conventionally calculated pH and [Mg²⁺_free] maps. The ROI analyses are presented for all volunteers and patients (Figures 3 and 4), comparing the median values between dictionary and conventional maps. The dictionary maps resemble the morphological features of the conventional maps, but have different absolute output values. In the magnesium maps, the trends of high and low values are the same for both maps (R_Dict and Mg_conv), whereas a stronger variation is observed in the pH_Dict maps, which is in accordance with a reversed variation in the Ion_Dict map. For the leg muscle datasets, the maps and the ROI analysis yielded the same patterns and trends for all volunteers. For the glioblastoma data, the trends in the pH_Dict and Ion_Dict maps differ between patients.

Discussion

While for the muscle data the results are comparable between all volunteers (only muscle tissue being present), the situation is more complex in the brain, where brain parenchyma, muscle tissue (voxel bleed) and tumors with varying biochemistry may interfere, yielding a larger variation in chemical shift combinations. The stronger fluctuations in the dictionary maps of the patients (Figure 4) could be explained by strong differences in the ionic strength, which might be expected for heterogeneous glioma tissue. The resemblance of the Ion_Dict map with the pH_conv map in the muscle datasets might be a hint towards a change in the pK_A value in some tissue areas, leading to higher pH_conv values calculated via the HHE, as pK_A changes with ionic strength. However, the current version of the dictionary is so far not sensitive enough to ionic strength (coarse spacing of Ion entries), which needs to be refined in future work.

Conclusion

The proposed dictionary algorithm successfully assigns plausible biochemical parameters to in vivo ³¹P MRSI data, and might provide an alternative to the conventional approaches to obtain pH values and magnesium ion content in the future. The lack of necessity to calibrate physical quantities, e.g. pK_A, makes the application to tissues with a priori unknown chemical microenvironment like tumors particularly interesting. Using this approach, novel knowledge about the tumor microenvironment could be obtained in the future.

Acknowledgements

No acknowledgement found.