The differences between the major in vivo ions potassium, chloride and sodium were examined at 21.1 T using triple quantum (TQ) MR signals in a rat head. A novel detection of TQ signals was performed at triple frequency, relative to a single quantum (SQ) signal, without traditional filtration using a time proportional phase increment (TPPI) method1. The results obtained in vivo in a rat head were compared with model systems to support the findings. The TQ data give insights on intracellular and extracellular ion binding. The process of creating TQ signals was assessed and visualized using angular dependence of corresponding spherical tensors2.The MR experiments were performed on a 21.1 T magnet using Bruker MRI Avance III console (PV 5.1). The TQ signals were detected by the TQTPPI pulse sequence 90º(α) - t - 90º(α+β) - 90º(0). The phase "α" and time delay "t" were incremented simultaneously by 45º and step ~ 0.2 ms, respectively. The phase “β” was alternated for each scan (±90º) and the results were added before incrementing phase and time delay to suppress the double quantum (DQ) signal. The in vivo experiments were performed using 6 male Fisher 344 rats (~ 200 g). The total MR signals of potassium (41.8 MHz), chlorine (87.8 MHz) and sodium (237.1 MHz) from the rat head were detected. The difference in ion binding was also tested using 5% agarose samples containing 154 mM KCl, NaCl or both ions at the same time. The visualization of the TQ signals was performed using Mathematica 10.2. All animal experiments were conducted according to the protocols approved by The Florida State University ACUC.

The 100% binding of ions yields a TQ signal of ~ 60% of the corresponding SQ signal. This is close to a theoretically expected value for the intensity of the satellite transitions for spin system with S=3/2. Thus, the TQ signal is a useful reference for evaluating the level of ion binding. The large difference in ratio between areas of the TQ/SQ signals in vivo for potassium (41 %) and sodium (20 %) observed earlier1 is not due to the intracellular location of potassium. The comparable difference in TQ/SQ was also observed in agarose samples for potassium (38.5 %) and sodium (27 %). Thus, potassium is more efficiently bound in vivo relative to sodium. A stronger binding of potassium is also demonstrated in the case where both potassium and sodium are present at the same time. Here, the potassium binding remains the same (38.5 %) in the presence of sodium while binding of sodium in the presence of potassium was decreased from 27 ± 0.4 % to 24 ± 0.1 %. The analysis of the in vivo data suggests that the efficiency of intracellular and extracellular binding can be similar. Chloride in vivo had the lowest TQ/SQ ratio of ~16 %, while it has the strongest binding in an agarose sample where all chloride ions were bound (TQ/SQ ~59 %).

For nuclei having spin = 3/2 (as potassium, chlorine and sodium) in the presence of ion binding (or quadrupolar interactions), a vector model of the nuclear magnetization rotation by RF pulses is no longer useful. The angular behavior of MR magnetization in this case can be presented (Fig. 1) by spherical harmonics representing the corresponding irreducible tensors. It is important that at the middle of the pulse sequence, the magnetizations (Y33, Y31) have a sum of all its components equal to zero. Thus, at these moments the magnetization is not observable. The symmetrical process of the magnetization transfer Y11->Y31->Y33->Y31->Y11 through the invisible states can be accomplished only in the presence of non-averaged quadrupole interactions O22 at the beginning and the end of the pulse sequence.

The results support the model that in normal cells the intracellular and extracellular ion binding are comparable. TQ signals demonstrate a strong and competitive binding of potassium relative to sodium. In vivo chlorine gives the lowest TQ signals relative to potassium and sodium. TQTPPI approach has a unique potential for intact detection of intracellular ion concentration. Visualization of the TQ magnetization using spherical harmonics represents an explicit way to analyze the multiple features and applications of the TQ signals.