1 Introduction

PAC(Perturbed Angular Correlation)[1,2,3] is a powerful method to determine the physical and chemical information surrounding the target nuclei and it has been used to quantify the local electro-magnetic environment in crystals and to identify the decay mode in nuclear physics by utilizing the cascade gamma-rays emitted from specific radioactive nuclei.

On the other hand, specific radioisotopes (RI) has been utilized in the area of medical diagnosis and therapy after the invention of PET (Positron Emission Tomography)[4, 5] and SPECT (Single Photon Emission Computed Tomography) [6] devices in the field of nuclear medicine. Those devices have a clear advantage in detecting the molecule position with extremely low concentration and now be widely utilized for diagnosing and detecting diseases, such as cancer and Alzheimer diseases. However, PET and SPECT are currently used for detecting only the position of RI labeled molecules.

Several researches of PAC have been conducted for biological samples and summarized in the paper [7]. Recently, it has been proposed to use PAC method within the framework of nuclear medicine which combines the imaging[8, 9] of RI labeled molecules and the extraction of local chemical environment surrounding the molecule, such as pH information or chemical structure[10]. The simultaneous acquisition of position and surrounding environment information could provide more accurate diagnosis with pH, chemical forms and internalization etc. In this study, we have utilized \(^{111}\)In radioisotope since it is a clinically used SPECT tracer and also a powerful PAC nuclide. In the work[10], it is characterized that the angular distribution of cascade photons from liquid InCl\(_3\) solution are changed with the surrounding pH value.

In nuclear medicine, metal RIs, such as \(^{111}\)In, \(^{64}\)Cu, \(^{225}\)Ac, are often chelated and bound with chelators, such as DTPA and DOTA for combining them with antibodies, nano-particles and molecules to deliver the target cancer tissues. It is known that the condition of pH in normal human is supposed to be approximately 7, however pH can be more acidic around 4-6 in lysosome, where the drug is delivered and released after the internalization. In this point of view, it is important to understand the behaviors of cascade gamma-ray emission from PAC nuclide chelated with DOTA. We have examined the emission of cascade gamma-rays from \(^{111}\)In chelated with DOTA in different pH condition.

2 Materials and methods

2.1 Gamma-ray detector system

To capture the cascade gamma-rays from \(^{111}\)In radioisotope, a ring-shape gamma-ray detectors array was designed and constructed. The ring consists of eight detector modules and one detector module is composed of 8 \(\times \) 8 HR-GAGG [11] scintillation crystals (2.5 \(\times \) 2.5 \(\times \) 4 mm) array coupled to 8 \(\times \) 8 silicon photomultiplier (SiPMs Hamamatsu MPPC S13361-3050) array. The charge signals were processed by custom signal processing boards using dynamic time-over-threshold method [12] to convert the pulse height to digital pulse (TOT time-over-threshold) with energy information and timing information. TOT signals were captured and processed by FPGA (field-programable-gate-array) based custom TDC[13] (Time to digital converter) with the accuracy of 1 ns for making the list-mode event data with energy, timing and position of detected gamma-rays. The time resolution of total system is approximately 10 ns. In the measurement, the prepared samples are located at the center of the ring-shape detectors with a diameter of 87.4 mm and measured for 180 mins. Figure 1 shows the whole structure of angular correlation measurement system.

Fig. 1
figure 1

Developed measurement system of angular correlation and signal processing system

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Fig. 2
figure 2

The structure and chemical formula of Psyche-DOTA (top and lower left) is shown. Metal RIs are chelated to DOTA structure (lower right) for the delivery of diagnostic and therapeutic drug

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2.2 Preparation of DOTA-chelated samples

Cupid-Psyche system[14] is an established diagnostic system utilizing the strong non-covalent interaction between Biotin and Streptavidin. Psyche-DOTA is aimed for nuclear medicine to capture metal RIs, such as \(^{111}\)In, \(^{64}\)Cu, \(^{225}\)Ac, combined with Cupid for the targeting drug delivery. Figure 2 shows the chemical formula and structure of Psyche-DOTA molecule. Psyche-DOTA was provided by Prof. Kanai’s group at the University of Tokyo. The purity of Psyche-DOTA is 98.5 \(\%\), which is measure by LC-MS (Liquid Chromatography Mass Spectrometry). The radiochemical yield (RCY) is approximately 86 \(\%\) confirmed with TLC. Psyche-DOTA chelated \(^{111}\)In is prepared by mixing \(^{111}\)InCl\(_3\) solution (Nihon Medi-Physics) and Psyche-DOTA with a molar concentration of 1:1000 and heated at 80°C for 15 min. The measured pH value of the original Psyche-DOTA chelated \(^{111}\)In was 3.0. The pH value of prepared samples is measured with a pH meter (HORIBA Laqua F-72M). Five samples with pH value of 3.0, 4.7, 5.9, 11.6 and 12.1 were prepared by adding NaOH solution to the original one. The volume of samples is approximately 30 \(\mu \)L which is a negligible size in the angle measurement. Table 1 shows the activity of \(^{111}\)In used in different pH samples.

Table 1 Activity used in different pH samples
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2.3 Data analysis

The coincidence events are extracted from the list-mode data within the coincidence time window (-100 ns to 600 ns, Tw= 700 ns) of 171 keV and 245 keV events. It is assumed the location of sources is (x, y, z) = (0,0,0). The angle \(\theta \) between the cascade gamma-ray with the energy of 171 keV and 245 keV is calculated by taking the arc-cosine of inner product of two vectors derived from detected positions. For eliminating the effect of geometry in the angular correlation, the measured data within time window was divided and calibrated by the random coincidence data outside the coincidence time window (-900 ns to -200 ns). This method is also previously used in the reference[10]. The non-uniformity of detection efficiency caused by the geometry can be calibrated by using the random data which is expected to be isotropic. In addition to the standard coincidence time window setup, for examining the effect of integration time, the anisotropy with different time window (Tw = 100 ns, 150 ns, 200 ns, 400 ns and 700 ns) is also calculated. The data with the angle from 50° to 170° is used with the bin size of 4 °. The data with the angle less than 50°  is not used because of the expected optical cross-talk in the detector itself. The measured data plot was fitted with the function of \( y = a + b P_2 (cos\theta ) \) . The value of \(\frac{b}{a}\) is used as an anisotropy factor. The fitting was conducted with the function of "fitnlm" in MATLAB and one sigma standard error was used as the error bar.

3 Results

Figure 3 shows the coincidence time histogram between 171 keV and 245 keV cascade gamma-rays. 85 ns intermediate decay time is clearly observed in the figure. The data between -100 ns and 600 ns is used for the calculation of angular correlation and it is calibrated by the random coincidence data between -900 ns and -200 ns.

Fig. 3
figure 3

Coincidence timing histogram between 171 keV and 245 keV. The data from -100 ns to 600 ns is regarded as coincidence and that from -900 ns to -200 ns as random coincidence

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Figure 4 shows the TOT based energy spectrum of \(^{111}\)In measurement. 171 keV and 245 keV peaks are clearly observed and used for the coincidence detection for angular calculation.

Fig. 4
figure 4

Energy histogram of Psyche-DOTA-\(^{111}\)In sample. The energy information is estimated by TOT based method and 171 keV and 245 keV are identified

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Figure 5 shows the angular distribution of Psyche-DOTA chelated \(^{111}\)In in five different pH conditions (pH 3 (Original), pH 4.7, pH 5.9, pH 11.6 and pH 12.1) and the fitting curves. The value of \(\frac{b}{a}\) is extracted as an anisotropy factor from the fitting data. The measured anisotropy and its fitting standard error in different pH conditions are summarized in Table 2.

Fig. 5
figure 5

Measured angular correlation from Psyche-DOTA chelated \(^{111}\)In in different pH conditions and thier fitting curves

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Table 2 Anisotropy and its standard error in different pH samples
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Figure 6 shows the measured anisotropy \(\frac{b}{a}\) plot of emitted cascade gamma-ray from Psyche-DOTA chelated \(^{111}\)In in different pH conditions. A significant transition of anisotropy was observed between 5.9 and 11.6, which is supposed to be caused by the chemical structure change of DOTA surrounding \(^{111}\)In.

Fig. 6
figure 6

The measured anisotropy depending on the different pH value in Psyche-DOTA chelated \(^{111}\)In

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Figure 7 shows the measured anisotropy depending on the different time window (Tw = 100 ns, 150 ns, 200 ns, 400 ns and 700 ns). The data with Tw from 150 ns to 700 ns indicates the same tendency with transition from pH 5.9 to 11.6. In addition to the transition, the shift of anisotropy is observed from Tw=150 ns to Tw=400 ns, which is indicating that the perturbation mostly happens in the time range from 0 ns to 300 ns.

Fig. 7
figure 7

The measured anisotropy depending on the different integration time window Tw= 100 ns (-100 ns to 0ns), 150 ns (-100 ns to 50 ns), 200 ns (-100 ns to 100 ns), 400 ns (-100 ns to 300 ns) and 700 ns (-100 ns to 600 ns)

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4 Conclusion and discussion

We have measured the angular correlation emitted from Psyche-DOTA chelated \(^{111}\)In using originally developed ring-shape gamma-ray detector system with different pH conditions. The significant transition in the anisotropy was observed between pH 5.9 and 11.6 from -0.08 to -0.06 with Tw=700 ns. The similar transition is observed in the time window from Tw=150 ns to Tw=700 ns and it is estimated that the perturbation mostly happens in the time range from 0 ns to 300 ns. Psyche-DOTA captures \(^{111}\)In with four nitrogen atom fingers and carboxy groups. It is estimated the pH condition affects the bounding structure of \(^{111}\)In and the change was detected through PAC caused by different electric field gradient. However, further study is necessary to determine the actual structure change by analyzing time differential response and conducting simulation. The observed transition could be used for the detection of pH change surrounding the Psyche-DOTA-\(^{111}\)In drug, such as internalization to lysosome, cancer cell etc. The further investigation is necessary to compensate the data between pH 5.9 and 11.6 to identify the real transition point combined with quantum chemical calculation. In-vivo experiment will follow after confirming the results of in-vitro experiment combining imaging. By clarifying the behaviors of angular correlation in liquid state, which is common in-vivo environment, further researches utilizing different modalities and stimuli, such as ultrasound [15] and magnetic field[16, 17], will be also of interest in the future medical application study of PAC.