
==== Front
Sci Rep
Sci Rep
Scientific Reports
2045-2322
Nature Publishing Group UK London

39256482
71695
10.1038/s41598-024-71695-7
Article
Ortho-positronium lifetime for soft-tissue classification
Avachat Ashish V. ashish.avachat@pitt.edu

1
Mahmoud Kholod H. 3
Leja Anthony G. 3
Xu Jiajie J. 45
Anastasio Mark A. 2
Sivaguru Mayandi 6
Di Fulvio Angela difulvio@illinois.edu

3
1 https://ror.org/01an3r305 grid.21925.3d 0000 0004 1936 9000 Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, USA
2 https://ror.org/047426m28 grid.35403.31 0000 0004 1936 9991 Department of Bioengineering, University of Illinois Urbana-Champaign, Champaign, USA
3 https://ror.org/047426m28 grid.35403.31 0000 0004 1936 9991 Department of Nuclear, Plasma, and Radiological Engineering, University of Illinois Urbana-Champaign, Champaign, USA
4 https://ror.org/047426m28 grid.35403.31 0000 0004 1936 9991 Department of Clinical Medicine, University of Illinois Urbana-Champaign, Champaign, USA
5 https://ror.org/047426m28 grid.35403.31 0000 0004 1936 9991 Animal Care Program, University of Illinois Urbana-Champaign, Champaign, USA
6 https://ror.org/047426m28 grid.35403.31 0000 0004 1936 9991 Cytometry and Microscopy to Omics Facility, Roy J Carver Biotechnology Center, University of Illinois Urbana-Champaign, Champaign, USA
10 9 2024
10 9 2024
2024
14 2115515 5 2024
30 8 2024
© The Author(s) 2024
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
The objective of this work is to showcase the ortho-positronium lifetime as a probe for soft-tissue characterization. We employed positron annihilation lifetime spectroscopy to experimentally measure the three components of the positron annihilation lifetime—para-positronium (p-Ps), positron, and ortho-positronium (o-Ps)—for three types of porcine, non-fixated soft tissues ex vivo: adipose, hepatic, and muscle. Then, we benchmarked our measurements with X-ray phase-contrast imaging, which is the current state-of-the-art for soft-tissue analysis. We found that the o-Ps lifetime in adipose tissues (2.54 ± 0.12 ns) was approximately 20% longer than in hepatic (2.04 ± 0.09 ns) and muscle (2.03 ± 0.12 ns) tissues. In addition, the separation between the measurements for adipose tissue and the other tissues was better from o-Ps lifetime measurement than from X-ray phase-contrast imaging. This experimental study proved that the o-Ps lifetime is a viable non-invasive probe for characterizing and classifying the different soft tissues. Specifically, o-Ps lifetime as a soft-tissue characterization probe had a strong sensitivity to the lipid content that can be potentially implemented in commercial positron emission tomography scanners that feature list-mode data acquisition.

Keywords

Positronium annihilation lifetime spectroscopy
PALS
Soft tissue analysis
X-ray phase-contrast imaging
Subject terms

Biomedical engineering
Characterization and analytical techniques
http://dx.doi.org/10.13039/100005187 U.S. Nuclear Regulatory Commission 31310018K0002 Di Fulvio Angela issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Positron Annihilation Lifetime Spectroscopy (PALS) is a well-established, non-destructive analysis technique, widely used in the realm of material science since the seventies1,2. PALS employs positrons and their meta-stable products as probes for material characterization. In a material to be characterized, the positrons recombine with the electrons of this host material and annihilate by emitting two back-to-back 511-keV photons. Before this annihilation, a positron can alternatively interact with an electron by forming a bound exotic state called positronium (Ps). Such Ps can appear in two forms: para-positronium (p-Ps, with antiparallel spin) or ortho-positronium (o-Ps, with parallel spin). Typically, a p-Ps annihilates by emitting two back-to-back 511-keV photons and an o-Ps annihilates through a three-quantum process3, emitting three photons with a total energy of 1022 keV. O-Ps annihilation can also yield higher odd multiplets with a much lower probability4; one-quantum annihilation of free o-Ps is instead prohibited. The mean lifetime of o-Ps in a vacuum is approximately 142 ns5, but it decreases to hundreds of picoseconds to a few nanoseconds in matter6,7 because the positron of the bound pair can also annihilate with an electron of opposite spin of the surrounding medium. This process of o-Ps annihilation with a lattice electron, which results in 2-γ emission, is referred to as the o-Ps pick-off. As a result, o-Ps in matter can either annihilate emitting two 511-keV gamma rays after pick-off or through the three-quantum intrinsic decay process. The likelihood of each of these processes occurring depends on the material properties of the host—primarily, the electron density and the average radius of micro-structural voids within the material. The distribution of void radii quantifies the distribution of the sizes of empty spaces or defects within the structure of the host material3. The lifetime of the o-Ps and, hence, the ratio between 3γ and 2γ emissions in a given material are proportional to the average void radius of the material2,3.

For instance, in materials with high electron density and small average void radius, o-Ps is more likely to annihilate via the two-quantum process rather than the three-quantum process. This phenomenon results in a shorter mean lifetime of o-Ps in materials with high electron density and a small average void radius. On the other hand, in materials with low electron density and large average void radius, the o-Ps can get trapped in the voids and is more likely to undergo the three-quantum process rather than annihilate via 2γ emission. Such conditions comprising low electron density and large average void radius result in a longer mean lifetime of o-Ps than in materials with high electron density and small average void radius (Fig. 1a illustrates the transport physics for a positron from a 22Na isotope. A comprehensive review of Ps interactions with matter can be found elsewhere4).Figure 1 (a) Illustration of the physics of positronium transport. 22Na undergoes β+ decay (positron and neutrino emissions) and turns into an excited 22Ne∗, which in turn decays by emitting a prompt-γ (1274.6 keV gamma emission). Hereafter, the emitted positron is referred to as free positron (FP). FP can either directly annihilate by 2γ emission or can form a positronium (Ps); Ps can take a form of a para-positronium (p-Ps) or an ortho-positronium (o-Ps); p-Ps directly annihilates by 2γ emission; and o-Ps can either annihilate by 2γ emission (pick-off annihilation) or 3γ emission. (b) Histological photomicrographs of example soft tissues. Hematoxylin and eosin (H &E) stained histological photomicrographs for adipose, hepatic, and muscle tissues. Scale bars represent 100 μm.

Under a nonrelativistic approximation, the lifetime of the positron in the bound pair (τPS) decreases with the electron density (Ne) of the medium: τPS=1/πro2cNe, with ro being the classic electron radius (2.80×10-13 cm) and c being the speed of light2. The measurement of o-Ps lifetime (τo-Ps) and the 3γ annihilation fraction (f3γ)—i.e., the ratio of the 3γ annihilation events and the total number of annihilation events—can be used to characterize the density and average size of empty spaces in the medium. Equation (1) applies to porous materials and shows that the o-Ps lifetime in the medium (τo-Ps-medium) increases with the 3γ annihilation fraction3,8:1 τo-Ps-medium=f3γ--43Po-Ps370τo-Ps-vacuumPo-Ps.

In Eq. (1), Po-Ps is the probability of o-Ps formation in the material, τo-Ps-vacuum is the o-Ps lifetime in vacuum, and the constant 370 is the computed ratio of cross sections of 2γ annihilation and 3γ annihilation (σ2γ/σ3γ≈370) for particles in free relative motion, as calculated by Ore and Powell using the time-dependent perturbation theory5. The o-Ps lifetime is also directly related to the average void radius, R (Eq. (2)3,8), as:2 τo-Ps-medium=1λb1-RR-Δ+12πsin2πRR+Δ-1.

In Eq. (2), λb is the spin-averaged positronium annihilation rate (λb≈1/4λS=2 ns-1) and Δ is an experimentally measured parameter3. This theory shows that the positron lifetime directly decreases with an increase in electron density, but o-Ps lifetime (τo-Ps-medium) increases with an increase in the average void size in the medium (Eq. (2)). Importantly, τo-Ps-medium and, hence, the average void size can be estimated by measuring the fraction of 3γ-decay events (Eq. (1)). The potential use of o-Ps lifetime to characterize some biological tissues has been recently explored, wherein the viability of using Ps and o-Ps lifetimes to analyze tissue properties, such as oxygen concentration and tissue porosity, was reported9–12. The presence of voids, air pockets, and defects results in a higher probability for the o-Ps to be trapped inside them, which in turn results in longer mean o-Ps-lifetime and a higher f3γ, than the void-absent conditions. The measurement of the mean o-Ps-lifetime provides an indication of the average size of the voids. In the biology domain, f3γ also decreases with the density of free radicals, which have unpaired electrons that easily undergo pick-off9. Using these mechanisms, some promising results have been previously reported in terms of discriminating between healthy and tumor tissues10,12–18, but a generalized characterization framework for discriminating different types of soft tissues has not yet been reported.

In this paper, we report the measured Ps lifetimes in porcine, non-fixated soft tissue samples: adipose, hepatic, and muscle (see Fig. 1b for histological photomicrographs of example soft tissues). These experimental measurements agreed with the previously discussed analytical relationships. To establish PALS as a probe for soft tissue analysis and to benchmark the sensitivity of the PALS to the subtle changes in the soft tissues, we compared its performance with the X-ray phase-contrast computed tomography (XPC-CT), which is the current state-of-the-art in non-invasive soft tissue analysis19.

Experimental results and discussion

We measured the PALS spectra for three types of porcine, non-fixated, soft tissues ex vivo: adipose, hepatic, and muscle. These spectra, the objects of our analysis, consisted of the distribution of the differences in detection times between the 1.27 MeV prompt-γ from 22Na decay chain and the positron products—two- and three-quantum annihilation gamma rays.

Analysis of the positron annihilation lifetime spectra

We resolved five components of lifetimes from the PALS spectra (Fig. 2a). Each of these components characterizes one specific process of the positron interactions20. (Two of these five components were fixed during the analysis of the PALS spectra and are not discussed in this section, but are detailed in “Methods” section: one corresponding to the 5.10-μm-thick titanium foils that encapsulated the 22Na source, 248 ps21, and another corresponding to the 2.5-μm-thick Mylar foils that were wrapped around the tissue samples, 382 ps24). From the fastest to the slowest, the first component corresponds to p-Ps decay (τ1, I1), the second to the annihilation of free positrons (τ2, I2), and the third to o-Ps self-decay (τ3, I3)20. The PALS spectrum, f(t), can be modeled as a convolution of the exponential decay functions corresponding to each process and the detector time resolution function (Eq. (3)), as follows:3 f(t)=∑i=13Iiτie-tτi∗e-t22σ22πσ2=∑i=13Ii2τieσ2-2τit2τi2erfcσ2-τit2στi.

In Eq. (3), τi and Ii are the lifetime and intensity of the i-th component, and σ represents the time resolution of the detection system (198.3 ± 0.8 ps20). This excellent time resolution was achieved through the optimization of the experimental PALS setup and timing algorithms described in our previous work20. Two of the decay constants of the overall Ps-lifetime—the ones that correspond to the p-Ps decay (τ1) and to the free-positron (FP) annihilation (τ2)—were comparable in the three types of tissues (Fig. 2b). On the other hand, the o-Ps lifetime (τ3) component of the PALS spectrum showed a significant difference (about 20%) for the adipose tissue compared to that of hepatic and muscle tissues (Fig. 2b; the mean o-Ps lifetimes w/mean intensities for the adipose, hepatic, and muscle tissues with five repeats for each tissue type: 2.54 ± 0.12 ns w/18.60 ± 2.90%, 2.04 ± 0.09 ns w/12.92 ± 2.36%, 2.03 ± 0.12 ns w/14.47 ± 2.89%, respectively). Here, the uncertainties in the o-Ps lifetimes were calculated as the sampled uncertainties of five samples of the same tissue type utilizing the confidence interval method22.

An interesting comparison with previous work by Moskal et al. is worthy of noting here: the difference between the o-Ps lifetimes of adipose and the cardiac myxoma for humans was found to be about 30%18. Although our counterpart of this difference was about 20% and not an exact match with that presented in Moskal et al.18 study, the trend of o-Ps lifetime of adipose tissue being higher than that of a myocyte-based tissue agreed with each other in these two studies. This disparity between the exact values of the said differences can be associated to (1) the two studies have two different species (humans tissues for Moskal et al.18 and porcine tissues for ours); and (2) the myocyte-based tissue counterparts of the two studies were of different types (anomalous cardiac muscle tissues for Moskal et al.18 and healthy skeletal muscle tissues for ours). However, a more comprehensive study involving o-Ps lifetime measurements of different species and biophysical analysis of positronium interaction is required to confidently draw inferences on such cross-species correlations and on explicitly describing the possible underlying mechanisms for the different o-Ps lifetimes. (One of such possible underlying mechanisms is the oxygen concentration15,23).Figure 2 Results of PALS analysis and its benchmarking with XPC-CT. (a) The five components Ps-lifetime—p-Ps, fixed component for titanium (Ti) foil encapsulation of the source (248 ps21), fixed component for Mylar foil that was used to wrap the tissue samples (382 ps24), free-positron (FP), and o-Ps lifetimes—can be decomposed from the measured PALS spectrum (example PALS spectrum and its decomposed components for adipose tissues in a). (b) The comparison of three non-fixed components of the PALS spectrum for the three soft tissue types with 5 repeats for each type (n = 5) showed that o-Ps was the most sensitive out of the three components for discerning the subtle changes between the different types of soft-tissue. Single standard-deviation error bars are added to the plot. (c) Comparison of PALS as a method for soft-tissue analysis with the current state-of-the-art, XPC-CT. PALS probe measurement—o-Ps lifetime—showed less variations across the samples than the mean voxel value measurement through XPC-CT. The adipose tissue was significantly more discernible from the hepatic and the muscle tissues using mean o-Ps lifetime compared to using mean voxel values in XPC-CT. (For the box-and-whiskers plot in (c), the PALS measurements and XPC-CT mean voxel values were normalized to their respective maximums for presentation purposes.)

PALS analysis for soft-tissue discrimination and its benchmarking with the current state-of-the-art

We found that the adipose tissues can easily be discriminated from the other two tissues by thresholding the mean o-Ps lifetime (Fig. 2c). The difference between the mean o-Ps lifetime for hepatic and muscle tissues was subtle, yet discernible (Fig. 2b,c). Based on the previously discussed positronium transport physics, the significant difference in mean o-Ps lifetimes in adipose tissues and in hepatic and muscle tissues can be attributed primarily to the different structural porosity.

In order to experimentally corroborate these observations of mean o-Ps lifetimes, we compared our o-Ps lifetime measurements with the current state-of-the-art in soft tissue analysis19,25–28: X-ray phase-contrast computed tomography (XPC-CT). The analysis of 3D image data from XPC-CT informed us about the relative contrast that is currently achievable and can be used for discriminating the selected soft tissues. The benchmarking with XPC-CT showed that the mean o-Ps lifetime followed a similar trend as the mean voxel value from XPC-CT (Fig. 2c). The mean XPC-CT voxel values for soft tissue samples depend mainly on their mass densities and effective atomic number (zeff). XPC-CT results showed that the X-ray attenuation coefficients of the analyzed muscle and hepatic tissues are comparable, on the other hand, the adipose tissues exhibit a lower attenuation coefficient, owing to its lower density and zeff, as expected. Similarly, o-Ps lifetime is longer in adipose tissues than in hepatic and muscle tissues. However, the relative difference between the signal from adipose tissues and that from the other tissues is notably higher in PALS than XPC-CT. This result indicates that relatively fewer o-Ps collisions—that result in “pick-off”—occur in adipose tissues than in hepatic and muscle tissues. This effect is likely due to the porous structure of adipocytes filled with low density lipids. In addition, we found that the inter-sample variations in the mean o-Ps lifetimes for the selected soft tissues was significantly lower than that of mean voxel value (Fig. 2c). Combined, the findings from this comparison—one, the higher difference between the mean o-Ps lifetime of adipose tissue and that of hepatic and muscle tissues and, two, the lower inter-sample variations—show that it is easier to identify a threshold to discriminate adipose tissues from the hepatic and muscle tissues by employing PALS analysis than the current state-of-the-art, XPC-CT.

It should be noted that our XPC-CT imaging system employed an extended propagation distance for enhancing the phase effects in a laboratory setting. Although such propagation-based XPC-CT is widely used for soft-tissue analysis as a virtual histology tool19,25–28, it is only one of the forms of acquiring phase-contrast. One of the other forms of acquiring phase-contrast is by employing grating-interferometry. The effect of larger average void radii, which our propagation-based XPC-CT system was unable to resolve, might be captured using grating-based XPC-CT, because such system will provide an image that maps X-ray scattering29,30. A comparison between mean o-Ps lifetime with mean voxel values for diffraction or scattering images from grating-based XPC-CT for soft tissue analysis will be a valuable next step.

Conclusion

We analyzed three types of porcine, non-fixated soft tissues—adipose, hepatic, and muscle—using positron annihilation lifetime spectroscopy (PALS). The PALS spectra included contributions from three annihilation lifetimes: p-Ps, free-positron, and o-Ps. We found that the o-Ps lifetime in adipose tissue was, on average, 20% longer than in hepatic and muscle tissues. Although it is known that mean o-Ps lifetime increases with porosity in inorganic materials; in biological tissues, mean o-Ps lifetime is the convolution of several phenomena, such as oxygen and free radical concentration, in addition to the average void radius. The oxygen partial pressure was alike in all the measured samples, and no free radicals were induced in the tissues. Therefore, the significantly higher response of adipose tissue—in terms of o-Ps lifetime, when compared to hepatic and muscle tissue—can likely be ascribed to a higher average void radius, which was not resolved by the benchmarking XPC-CT imaging. Given the recent surge in positronium imaging within the health sciences domain13,15,31–33 the impact of this result in this domain is that mean o-Ps lifetime can be used as a non-invasive probe for detecting and quantifying lipid content in soft tissues or organs.

Methods

We acquired porcine tissue samples of adipose, hepatic, and muscle types from the Meat Science Laboratory of the University of Illinois Urbana-Champaign (five samples of each type from five castrated males; 24 weeks old, PIC 800 sires x PIC Camborough dams). Each tissue sample was analyzed, consecutively, by PALS and XPC-CT in a non-fixated state.

PALS: measurements and analysis

Figure 3 Methods for PALS analysis and its benchmarking with XPC-CT. (a) The PALS measurement setup: two scintillation detectors with tissue samples in the middle irradiated by the 22Na source. (b) 22Na source was placed between two tissue samples that were kept cooled by a Peltier-cell based system. The tissue samples were wrapped with Mylar foils of 2.5 μm thickness to avoid these tissue samples from touching the 22Na source. (c) An example tomographic slice of XPC-CT images. The blue, green, and red boxes represent a 2D slice of the 3D regions-of-interest corresponding to the adipose, hepatic, and muscle tissues, respectively, in the given example XPC-CT slice. (d) Sample fast pulse acquired by the organic scintillation detector, (1) its attenuated version by a factor F, (2) the original pulse delayed by Δ ns and inverted, and the (3) bipolar pulse obtained by subtracting (2) from the original pulse. The zero-crossing point corresponds to the pulse time stamp. (e) Energy spectrum and its average energy for 70 kVp X-ray beam from the liquid-metal-jet-based X-ray source used by XPC-CT system.

We extracted the p-Ps, free positron (FP), and o-Ps lifetime components from the PALS spectra for porcine, non-fixated adipose, hepatic, and muscle tissues. The PALS spectra were acquired by using a 22Na source and by recording the distribution of the differences in detection times between the 1.27 MeV prompt decay gamma ray and the positron products—annihilation and decay gamma rays. The positron emitting 22Na source used for the presented measurements was a POSN series positron source from Eckert & Ziegler, POSN-2235, with initial activity of 10-μCi on February 1st 2023; and the presented measurements were completed between June 20th and 23rd 2023. In this PSON-22 22Na source, the positron emitting active diameter of 9.53 mm is encapsulated between two titanium foils (5.10 μm thickness), which is then supported by two 250 μm thick titanium disks (19.10 mm outer diameter and 9.53 mm inner diameter) sealed by electron beam welding to form a brim for the source. In the experimental setup for PALS measurement (Fig. 3a,b), this source was placed between two samples of a given tissue type (one type at a time: adipose, hepatic, and muscle) with five repeats of each type to capture inter-sample statistical variations. By such sandwiching of the positron emitter with two samples, we maximized the tissue interaction and reduced the overall data acquisition time. Each tissue sample was wrapped with a 2.5 μm-thick Mylar foils to avoid the tissue samples from directly touching the 22Na source. This assembly of source and two tissue samples was secured using a 3D-printed holder made of acrylonitrile butadiene styrene (ABS, Fig. 3a). The o-Ps lifetime for the holder material was measured before and after each tissue type for consistency (mean o-Ps lifetime: 1.63 ns). But, during the PALS measurements for the tissues samples, the probability of positrons reaching the holder was expected to be negligible because of the high thickness (5 mm) of the tissue samples that completely covered the active area of the 22Na source, axially, and because of about 4.8 mm radial width of the titanium brim of the source that can stop majority of radially emitted positrons.

The 22Na emits a positron, and the daughter nucleus de-excites in about 3 ps by emitting a 1.27 MeV gamma ray. Therefore, the emission of the 1.27 MeV was considered as a timestamp for the β+ decay (positron emission time). During the irradiation, the approximate 1 ×1 ×0.5 cm3 tissue samples were kept at approximately 9∘C by employing an environment cooling system based on Peltier coolers, dry-ice, and forced convection (Fig. 3a,b). The temperature of the sample was measured using a Fluke-62 MAX Infrared Thermometer. Two fast EJ-220 plastic organic scintillators of 5.08 cm length and 5.08 cm in diameter coupled to 9214B ETEL photomultiplier vacuum tubes (PMT) were used to detect gamma rays in coincidence. We selected EJ-220 because of its fast light response; previously, we reported a time resolution of 183 ± 0.8 ps with this measurement system20. We used a high-voltage power supply (DT5533EN, CAEN Technologies) to power the PMTs. The detected pulses were directly digitized by a 14-bit 500 MSps digitizer (DT5730, CAEN Technologies) and transferred to a workstation as full waveforms in binary format using the acquisition software CoMPASS36.

Each pulse, detected upon gamma-ray interaction in the scintillator, was associated with a time stamp. Accurate pulse timing is crucial to reconstruct the PALS spectrum successfully20. Therefore, we developed and optimized a constant fraction discrimination (CFD) algorithm to accurately find each pulse onset time37. Digital CFD provides accurate timing and is superior to other timing algorithms (e.g., analog CFD or leading edge) in terms of time resolution when used for processing the organic scintillation pulses38. Pulses were digitized at a 500 MSps sampling frequency using the DT5730 digitizer. We interpolated these digitized voltage values, one every 2 ns, to densely sample the rising edge, which typically lasts less than 10 ns. Each pulse can be modeled as the convolution between the sampled voltage values and a terminated sinc function (tsinc)39. This model is detector-invariant and satisfies the Nyquist condition20,40. The tsinc function is a sinc function modulated by a Gaussian function and is needed for time-finite, non-periodic signals. Equation (4) is the k-th linearly interpolated sample obtained after dividing the measurement sampling time into N intervals inside a window of width L, where, gs(j) is the j-th sampling value of the input waveform:4 G(j,k)=∑i=0L-1gsj-itsinci+kN+gsj+1+itsinci+1-kN.

After pulse interpolation, the time stamp was determined by the CFD algorithm:5 CFDl=F×gsl-gsl-Δ,

where, gs(l) is l-th sample of the interpolated pulse, with l=j×N+k, CFD(l) is a bipolar pulse with the zero-crossing point being the time stamp, the attenuation factor F (0-1) and time shift Δ are two data processing parameters that depend on the scintillator type. The pulse timing was obtained as the pulse zero-crossing time after subtracting the original pulse inverted and delayed by Δ nanoseconds from an attenuated version of the original pulse (Fig. 3d). For our experimental setup, the optimum values for F and Δ are 0.4 ns and 4 ns, respectively20.

The annihilation and self-decay of the Ps in the tissue samples resulted in the emission of two or three gamma rays. The emission of two gamma rays in coincidence (the prompt 1.27 MeV followed by a lower energy gamma ray) was detected by the scintillator pair by applying a coincidence time gate of 200 ns, after determining the pulse detection times. The PALS spectra were created by histogramming the time interval between the arrival times of the 1.27 MeV decay gamma ray and of lower-energy annihilation or decay gamma rays. Each sample was measured for 180 min, obtaining approximately 130,000 time-coincidence counts contributing to the PALS distribution in each run. The inherent low energy resolution of organic scintillation detectors does not allow us to discriminate 511 keV from lower energy gamma rays from 3γ self-decay, but their use in this study was mainly motivated by their fast response. As a result, the discrimination of the positron lifetime components was merely based on the cumulative PALS spectra. PALS spectra are well described by the linear combination of different components: the fast decay of p-Ps, the slow decay of FP, and the delayed self-decay of o-Ps (Eq. (3)). We used the software LT1041 to decompose five components: p-Ps component, fixed component for the titanium (Ti) foil encapsulation of the 22Na source (248 ps21), fixed component for the Mylar foils that were used for wrapping the tissue samples (382 ps24), FP component, and o-Ps component for a given tissue sample. LT10 is one of the most popular software for positron lifetime spectra analysis, which was developed by Kansy and Giebel42,43. It relies on the deconvolution of the experimental data into the model’s exponential functions followed by a nonlinear fitting procedure to find the model’s parameters that best fit the measured PALS distribution43. The user can either select one of the predefined LT10 models to fit the data or implement a custom one. We used the model described in Eq. (3) to fit our data, with τ1, τ2, τ3, I1, I2, and I3 as parameters with a lower bound to zero. The time resolution of our measurement system is also needed in the PALS model (σ) and was previously determined experimentally to be 198.3 ± 0.8 ps20; therefore, σ is a constant in the LT10 model. Further details on the LT10 software can be found elsewhere41,42. The analysis using LT10 also provided the fitting uncertainties associated with the derived p-Ps, FP, and o-Ps lifetimes in each tissue sample. The error bars in Fig. 2b account for the propagation of the 1-standard-deviation uncertainties associated with the fitted parameters of the lifetime distribution measured on multiple samples from the same tissue batch. We calibrated this PALS measurement and analysis procedure by employing a Certified Reference Material (CRM)—polycarbonate (National Metrology Institute of Japan NMIJ CRM 5602-a)—and a previously characterized quartz sample20.

The polycarbonate samples were 15×15×1.5 mm3 in size, and the quartz samples were 10×10×1 mm3 each. We measured the o-Ps lifetime to be 2.07 ± 0.05 ns and 1.38 ± 0.05 ns for polycarbonate and quartz, respectively. These results agreed, within two standard deviations, with the one provided by the vendor for the polycarbonate CRM (2.10 ± 0.05 ns44) and with the previous measurement for quartz (1.34 ± 0.05 ns20), respectively.

X-ray phase-contrast imaging: measurements and analysis

The X-ray phase-contrast imaging of the selected non-fixated soft tissues was performed using the propagation-based X-ray phase-contrast CT (XPC-CT) system of the Computational X-ray Imaging Science Laboratory at the Beckman Institute of the University of Illinois Urbana-Champaign45. This XPC-CT system included: a liquid-metal-jet-based X-ray source (MetalJet D2, Excillum) operated at 70 kVp, 130 W power, and about 14 μm focal spot size; a CsI(Tl) scintillator-based X-ray imager with a pixel pitch of 13 μm, active area of about 542 mm2, and 2 × 2 binning (4k × 4k X-Ray GSENSE SCMOS, Photonic Science); and an object manipulation system to rotate the imaging samples. A propagation distance (object-to-detector distance) of approximately 2.15 m was utilized to enhance the phase effects. This propagation distance, paired with the source-to-object distance of approximately 1.85 m, resulted in a magnification of 2.16 and Fresnel number of approximately 2.82 for an average X-ray energy of 19.17 keV for the 70 kVp X-ray energy spectrum of our liquid-metal-jet-based X-ray source (Fig. 3e). A set of 720 projections was acquired to fully scan the imaging object (0∘  to 360∘) with an exposure time of about 2.4 s per projection. Paganin’s phase-retrieval toolbox, ANKAPhase, was used to recover the phase map for each projection46. An in-house implementation of the Feldkamp, Davis, and Kress (FDK) algorithm was used to reconstruct the tomographic volume from the phase-contrast enhanced projections47. For XPC-CT scanning, a PMMA rod and the three soft tissue samples were stacked together, with each wrapped in an ultra-thin Mylar sheets. (PMMA rod was added to the assembly for being able to quantify and normalize the mean voxel values between air- and water-equivalent attenuation.) This assembly was taped together tightly such that the field-of-view (FOV= 25 mm) had the following sequence (top to bottom in Fig. 3c): PMMA rod, muscle sample, adipose sample, and hepatic sample. The mean voxel values for each sample (5 samples of each tissue type) were calculated by randomly inserting 3D regions-of-interest (1003 voxels) with ten repeats (Fig. 3c).

Histology: measurements

One of each soft tissue types were fixed under pressure and vacuum with 10% formalin after PALS measurement and XPC-CT imaging. Then fixed samples were embedded in paraffin, and ten slices of 8–10 micron thickness were cut using a microtome from each block sample (1 cm3). Two sections were extracted from each slice. Out of the ten slides for each type of sample, five were stained using Mason’s Trichrome and the remaining five using hematoxylin and eosin. Microscopy was performed using a Hamamatsu Nanozoomer using a 20 × 0.75 NA Olympus objective.

Acknowledgements

This work was funded in-part by the Nuclear Regulatory Commission, United States award number 31310018K0002. We thank Karen Doty for preparing the tissue samples for the histology analysis and Ming Fang for his help to setup the PALS experiment and use the LT10 software. We also thank Anna Dilger and Bailey Harsh of Meat Science Laboratory for helping in acquiring the tissue samples.

Author contributions

A. Avachat and A. Di Fulvio conceived the experiment(s); A. Avachat, A. Leja, K. Mahmoud, J. Xu, M. Sivaguru and A. Di Fulvio conducted the experiment(s) and processed the data, A. Avachat, A. Leja, K. Mahmoud, and A. Di Fulvio wrote the manuscript; A. Avachat, and A. Di Fulvio analyzed the results. All authors reviewed the manuscript.

Data availability

The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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