High-Resolution Positronium Lifetime Tomography at Clinical Activity Levels on the PennPET Explorer

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Abstract

The objective of this study is to demonstrate high-resolution positronium lifetime tomography using a 3-dimensional phantom with multiple radioisotopes at activity levels relevant to human imaging. Methods: A cylinder phantom was constructed with a 6-mm thick polycarbonate slab inserted at its center. The phantom was filled with radioactive solutions and scanned in the PennPET Explorer scanner, a long–axial-field-of-view scanner with high sensitivity. Four scans were conducted with 3 different radioisotopes at varying activity levels: ⁸²Rb (240 MBq), ⁶⁸Ga (110 MBq), and ⁴⁴Sc (7.4 and 40.7 MBq). The average positron lifetime images were reconstructed with correction for random events. Radial and axial resolutions were measured from lifetime profiles across a hole on the slab and through the slab, respectively. Results: The polycarbonate slab was resolvable in all reconstructed positron lifetime images and showed a lifetime longer than that in water. The lifetime images from ⁸²Rb and ⁶⁸Ga were noisy because of their low prompt γ yields and high random fractions, whereas noise was substantially reduced in the ⁴⁴Sc images. The average lifetime estimates were consistent across the 4 scans. The estimated radial and axial resolutions were 3.7 ± 1.8 mm and 3.9 ± 0.4 mm, respectively. Conclusion: This study successfully demonstrated the feasibility of high-resolution positronium lifetime tomography using ⁸²Rb, ⁶⁸Ga, and ⁴⁴Sc on the PennPET Explorer.

Positronium is abundantly formed during clinical PET scans. The lifetime of ortho-positronium (o-Ps) can be affected by tissue microstructure and the concentration of specific molecules, including O₂ (1–3). The potential of using o-Ps lifetime as a novel biomarker for studying human diseases and identifying hypoxic regions has stimulated growing interest in positronium lifetime imaging using existing time-of-flight (TOF) PET scanners (4).

A recent human study (5) using the J-PET scanner and ⁶⁸Ga-DOTA-SP reported a shorter o-Ps and average lifetime in human brain glioblastoma than in normal brain tissue. An earlier study (6) using ex vivo tissue samples and ²²Na sources found a longer o-Ps lifetime in human adipose tissue than in cardiac myxoma tissue. Experiments using point sources and uniform phantoms have also been performed using other clinical scanners, such as the Siemens Quadra (7), a long–axial-field-of-view (FOV) whole-body scanner, and VRAIN (8), a dedicated brain scanner. However, these studies use TOF information to approximate the location of positron annihilation, which limits the spatial resolution of the lifetime images to a few centimeters.

To obtain positronium lifetime images with a high spatial resolution comparable to standard PET activity images, model-based lifetime image reconstruction methods have been developed (9–12). We refer to this emerging imaging technique as positronium lifetime tomography (PLT) because the reconstruction methods are conceptually similar to those used in PET. These techniques have been successfully applied to simulation and small phantom scans at low activity levels (13). Significant challenges remain for future clinical application of PLT. The main challenge is the high random fraction at clinical activity levels, caused by triple coincidence detection within a wide coincidence window for prompt γ rays.

In this paper, we demonstrate high-resolution PLT on the PennPET Explorer scanner (14,15) at activity levels comparable to those used in clinical PET imaging. A novel 3-dimensional phantom is designed to provide lifetime contrast and showcase the spatial resolution of PLT. The phantom was measured using 3 isotopes including ⁸²Rb, ⁶⁸Ga, and ⁴⁴Sc. The first 2 are clinically available radioisotopes that provide prompt γ rays, which are essential for PLT. However, they are not ideal because of their low prompt γ yields (1.2% for ⁶⁸Ga, 13% for ⁸²Rb) and the short half-life of ⁸²Rb (1.25 min), which limit triple coincidence counts. In contrast, ⁴⁴Sc outperforms both radioisotopes with its 94% prompt γ yield and 4-h half-life. Additionally, ⁴⁴Sc shares similar chemical properties with ⁶⁸Ga, and its labeled compounds (16), ⁴⁴Sc-DOTATOC and ⁴⁴Sc-PSMA-617, have been used in human imaging for neuroendocrine (17) and prostate (18) cancers, respectively. To our knowledge, this study represents the first demonstration of high-resolution PLT imaging using a 3-dimensional phantom and the first application of ⁴⁴Sc as a radioisotope for PLT.

MATERIALS AND METHODS

PennPET Explorer

The PennPET Explorer scanner (14) (Fig. 1A) operates in a 6-ring configuration with an axial FOV of 142 cm and a TOF resolution of 250 ps. Each 3.86 × 3.86 × 19 mm³ lutetium–yttrium–oxyorthosilicate scintillation crystal is 1:1 coupled to a pixel of a 64-channel digital silicon photomultiplier. The measured radial, tangential, and axial resolutions at a 1-cm radial offset for PET imaging are 3.8 ± 0.1 mm, 3.8 ± 0.1 mm, and 4.2 ± 0.3 mm, respectively. The system acquires data in single mode. For PLT, the energy window was extended from the default 439–613 keV to 429–1,533 keV.

FIGURE 1.

(A) PennPET EXPLORER PET/CT scanner. (B) Cylinder phantom. (C) 6-mm-thick polycarbonate insert. (D) Schematic illustration of phantom with dimension and orientation.

Positron Lifetime Phantom

A 3-dimensional phantom was designed to provide lifetime contrast (Fig. 1B). A 6-mm-thick polycarbonate slab, which has a longer o-Ps lifetime than water (19,20), was inserted vertically inside a polypropylene cylinder with an inner diameter of 45 mm and a height of 190 mm. The cylinder was filled with a radioactive solution containing ⁸²Rb, ⁶⁸Ga, or ⁴⁴Sc during each imaging experiment. Because of the positron range effect, a significant number of positron annihilations occurred in the slab, providing lifetime measurements of the polycarbonate slab. To introduce additional lifetime patterns, 4 holes of varying diameters were drilled into the slab. The 2 bottom holes, measuring 20 and 10 mm in diameter, were submerged during the experiments (Figs. 1B and 1C). The phantom was scanned with the slab positioned in the transverse (x–y) plane of the scanner.

The characteristics of the 3 radioisotopes are listed in Table 1. ⁸²Rb and ⁶⁸Ga were produced using the in-house generators at the University of Pennsylvania. ⁴⁴Sc was produced as a mixture of ^44m/44Sc via the ⁴⁷Ti(p,α) reaction through the proton irradiation of enriched TiO₂ targets. Irradiated targets were dissolved through a solid-phase fusion digestion, and the radioactive scandium was separated from the target material using ion chromatography. Purified ^44m/44Sc was shipped to the University of Pennsylvania in a hydrochloric acid solution. Four scans were performed, including 2 scans with ⁴⁴Sc at activity levels of 40.7 and 7.4 MBq. The scan times and injected activities are presented in Table 2.

TABLE 1.

Decay Information of Three Isotopes

Parameter	82Rb	68Ga	44Sc
Half-life	1.25 min	68 min	4.04 h
Prompt γ energy (keV)	777	1077	1157
Fraction of β+ + γ	13.0%	1.2%	94.3%

TABLE 2.

Scan Settings and Measured Counts^*

Isotope	82Rb	68Ga	44Sc	44Sc
Prompt γ energy window (keV)	700–855	1,020–1,215	1,035–1,325	1,035–1,325
Injected activity (MBq)	240	110	40.7	7.4
Scan time (min)	5	270	20	100
Trues (M)	28.4	51.5	302.9	274.6
Randoms (M)	94.4	232.7	168.2	35.1
R/T ratio	3.3	4.5	0.56	0.13
NEC (M)	6.6	9.3	60.1	244.5

^*Number of trues and randoms are estimated by prompt and delayed time windows. M = million.

Triple Coincidence Identification

Each singles event in the data stream was characterized by its time, energy, and crystal identification. The 511-keV photons were identified using an energy window of 430–630 keV. For prompt γ events in the ⁸²Rb and ⁶⁸Ga scans, energy windows were optimized by maximizing the noise equivalent count (NEC), as they have a low prompt γ fraction. The NEC is defined as

$$\mathrm{NEC}=\frac{T^2}{T+R},$$ Eq. 1

where T is the number of true events and R is the number of random events. For ⁴⁴Sc, we used the prompt γ rays at the photopeak. The prompt γ-energy windows for the 3 radioisotopes are listed in Table 2.

Triple coincidences were identified using a software-based method. We used 1 prompt window and 4 delayed windows as previously proposed (9) to estimate the prompt and 3 types (I–III) of random triple coincidences. Type I randoms are formed by a pair of 511-keV photons from the same annihilation with an unrelated prompt γ; type II randoms are formed by a 511-keV photon and a prompt γ from the same decay with an unrelated 511-keV photon; type III randoms are formed by photons from 3 different decays.

The lifetime measurement of each event is obtained as

$$\tau ={\widehat{t}}_{511}-{\widehat{t}}_{\mathrm{PG}},$$ Eq. 2

where ${\widehat{t}}_{511}$ and ${\widehat{t}}_{\mathrm{PG}}$ are the estimated emission times of the 511-keV photons and the prompt γ, respectively. These times were derived by subtracting the photon travel time from the detection time. The travel time of a photon was estimated using the distance between the most likely annihilation point along the line of response and its detected location in the detector ring. For the delayed events, the same travel-time correction is applied, with the offset of each delayed window removed from the calculated time measurements. Lifetime events within [T₁,T₂] are selected for reconstruction. To reduce image noise caused by the randoms while preserving the average lifetime from the untruncated lifetime spectrum, the upper limit T₂ was set to 10 ns and the lower limit T₁ was set to −0.06 ns. The coincidence window width for 511-keV photon pairs was set to 1.5 ns, which is narrower than the default timing window of 4.5 ns because the small phantom was placed at the center of the scanner FOV.

Reconstruction of Average Lifetime Images

On the basis of the findings from the previous human study (5), which showed that the average lifetime provided a higher contrast-to-noise ratio between brain glioma and normal tissue than the o-Ps lifetime, we focus on reconstruction of average lifetime images using the SIMPLE (statistical image reconstruction of positron lifetime via time-weighting) method (13). The average lifetime image m is defined as the expected lifetime of events originated from each voxel. The SIMPLE method first estimates an activity-weighted lifetime image and then calculates the average lifetime image by dividing the activity-weighted lifetime image by the activity image. The previous work (13) did not fully address the correction of all 3 types of random events. Here, we present a complete derivation of the SIMPLE method.

Since 511-keV photon pairs in type I randoms are in true coincidence and can be mapped into a valid image, we reconstruct a combined activity image

$$\mathit{x}\prime =\mathit{q}\odot \mathit{x}+{\mathit{x}}^{\mathrm{r}},$$ Eq. 3

where x is the true activity image, the operator ⊙ denotes element-wise multiplication, each element of q is the probability of detecting a prompt γ originated from a voxel, and ${\mathit{x}}^{\mathrm{r}}$ is the type I random image. Type I randoms are included in the reconstructed image to avoid bias in reconstructing low-count PET data (21). ${\mathit{x}}^{\mathrm{r}}$ is not modulated by the prompt γ efficiency because every coincident 511-keV pair have the equal probability to be paired with a random prompt γ to form a type I random event. Type II and type III randoms can only be modeled in the projection domain because they involve unrelated 511-keV photons. As the core of the SIMPLE method, a combined activity-weighted lifetime image, representing the expected total time delay in a voxel, is given by

$$\mathit{w}\prime =\mathit{m}\odot \mathit{q}\odot \mathit{x}+m^{\mathrm{r}}{\mathit{x}}^{\mathrm{r}},$$ Eq. 4

where m is the average lifetime image, $m^{\mathrm{r}}$ = 0.5 × (T₁ + T₂), reflecting the uniform lifetime distribution of type I randoms.

The forward projections of the combined activity $\mathit{x}\prime$ and the activity-weighted lifetime image $\mathit{w}\prime$ are given by

$$\overline{\mathit{y}}=\mathit{H}\mathit{x}\prime +\mathit{r},\mathrm{\hspace{1em}}\mathrm{ }\overline{\mathit{z}}=\mathit{H}\mathit{w}\prime +\mathbf{\rho },$$ Eq. 5

where H is the standard TOF system matrix for activity reconstruction, r is the expected counts of type II and III randoms, and ρ is the corresponding lifetime-weighted factor of r. We estimated r using the delayed windows that we previously developed (9). ρ was set to ${\overline{\tau }}_{\mathrm{r}}\mathit{r}$, where ${\overline{\tau }}_{\mathrm{r}}$ denotes the average lifetime of all type II and III randoms in the delayed windows. Since $\overline{\mathit{y}}$ is the expectation of the projection data formed by the 511-keV coincidence photons in the triple coincidence events including trues and type I randoms, an estimate of $\mathit{x}\prime ,\mathrm{ }\widehat{\mathit{x}\prime },$ can be reconstructed from the 511-keV photon pairs in the triple coincidence data using the standard maximum-likelihood expectation-maximization (MLEM) algorithm. Similarly, ${\mathit{x}}^{\mathrm{r}}$ can be reconstructed from the type I randoms in the delayed window by the standard MLEM algorithm. To estimate $\mathit{w}\prime$, we note that $\overline{\mathit{z}}$ is the expectation of the projection data z constructed by summing the lifetime measurements in each TOF projection bin:

$$z_i=\sum _{k\in K_i}{\mathrm{\tau }}_k,$$ Eq. 6

where $K_i$ denotes the set of list-mode indices k corresponding to events detected in TOF projection bin i, so an estimate of $\mathit{w}\prime ,\mathrm{ }\widehat{\mathit{w}\prime },$ can be obtained by minimizing the Kullback–Leibler (KL) distance (22) between the data vector z and the forward projection $\overline{\mathit{z}}$:

$$\widehat{\mathit{w}\prime }=\underset{\mathit{w}\prime }{\mathrm{argmin}} \mathrm{KL}\left(\mathit{z},\mathit{H}\mathit{w}\prime +\mathbf{\rho }\right).$$ Eq. 7

The KL distance between 2 vectors a and b with nonnegative entries is defined as $\mathrm{KL}\left(\mathit{a},\mathit{b}\right)={\sum }_i\mathrm{KL}(a_i,b_i)$, where KL(a_i, b_i) = $a_i\mathrm{ }\log \left(\frac{a_i}{b_i}\right)$ + b_i − a_i for a_i, b_i > 0, KL(a_i, 0) = +∞, and KL(0, b_i) = b_i. Using the optimization transfer principle, $\widehat{\mathit{w}\prime }$ can be iteratively estimated by a weighted list-mode MLEM (23) update equation:

$${\widehat{w\prime }}_j^{n+1}=\frac{{\widehat{w\prime }}_j^n}{\sum _{i=1}^M{H}_{ij}}\sum _k\frac{H_{ij}{\mathrm{\tau }}_k}{\sum _{l=1}^N{H}_{il}{\widehat{w\prime }}_l^n+{\mathrm{\rho }}_i},$$ Eq. 8

where each event is weighted by its time measurement ${\mathrm{\tau }}_k$. Although the PennPET Explorer activity images are routinely reconstructed with the TOF list-mode ordered-subset expectation maximization algorithm (25 subsets and 5 iterations) with spheric image basis functions to avoid over-convergence (24), we use 2 × 2 × 2 mm³ cubic voxels for reconstructing $\widehat{\mathit{w}\prime }$, $\widehat{\mathit{x}\prime }$, and $\widehat{{\mathit{x}}^r}$with 2 subsets and 2–8 iterations in this study. Corrections for scatters, attenuation, and normalization were not performed. This omission should not significantly alter the results because of the small size of the phantom.

Finally, the lifetime image is estimated as

$$\widehat{\mathit{m}}=\frac{\widehat{\mathit{w}\prime }-m^{\mathrm{r}}\widehat{{\mathit{x}}^{\mathrm{r}}}}{\widehat{\mathit{x}\prime }-\widehat{{\mathit{x}}^{\mathrm{r}}}}-\widehat{\mathrm{\mu }},$$ Eq. 9

where $\widehat{\mathrm{\mu }}$ is the system offset in the measured time, which is caused by the detector time-walk due to the energy difference between 511-keV photons and prompt γ rays. This offset was estimated by fitting the whole spectrum of the scan (13).

CT-Guided Postreconstruction Filtering

To suppress noise in the lifetime images, especially those obtained using ⁸²Rb and ⁶⁸Ga, the intermediate images ($\widehat{\mathit{x}\prime }$, $\widehat{\mathit{w}\prime }$, and $\widehat{{\mathit{x}}^r}$) were smoothed using a CT-guided nonlocal means filter, which was implemented using the kernel method (25). A kernel matrix was constructed using the gaussian radial kernel with its (j,l)th element given by

$$K_{jl}=\left\{\begin{array}{ll}\frac{1}{\sum _{k\in {\mathcal{N}}_j}\exp \left(-\frac{{\Vert {\mathit{f}}_k-{\mathit{f}}_j\Vert }^2}{2{\mathrm{\sigma }}^2}\right)}\exp \left(-\frac{{\Vert {\mathit{f}}_l-{\mathit{f}}_j\Vert }^2}{2{\mathrm{\sigma }}^2}\right),& l\in {\mathcal{N}}_j\\ \hfill 0,& \text{otherwise}\end{array}\right.,$$ Eq. 10

where f_j is the feature vector of the jth voxel and ${\mathcal{N}}_j$ is a neighborhood of voxel j. The feature vector of each voxel was formed by vectorizing the 3 × 3 × 3 patch centered at the given voxel in the coregistered CT image, which had been normalized by its SD first. The kernel parameter σ was set to 1. The neighborhood ${\mathcal{N}}_j$ was selected to contain 48 voxels with the smallest value of ${\Vert {\mathit{f}}_l-{\mathit{f}}_j\Vert }^2$ within the 7 × 7 × 7 neighborhood of each voxel. The filtered lifetime image is then obtained by

$$\widehat{{\mathit{m}}^f}=\frac{\mathit{K}\left(\widehat{\mathit{w}\prime }-m^{\mathrm{r}}\widehat{{\mathit{x}}^{\mathrm{r}}}\right)}{\mathit{K}\left(\widehat{\mathit{x}\prime }-\widehat{{\mathit{x}}^{\mathrm{r}}}\right)}-\widehat{\mathrm{\mu }}.$$ Eq. 11

Quantitative Evaluation

Regions of interest (ROIs) were manually drawn inside the water and slab, and the mean positron lifetime in each region was evaluated. The slab ROI was transaxially drawn to align with portion of the slab submerged in water but with a 2-mm margin on the boundary; axially the ROI was at the center of the slab with a thickness of 2 mm to exclude boundary voxels. The water ROI is a phantom-sized cylinder, excluding the region within 5 mm of the central slice. To reduce bias introduced while taking ratio between noisy images in Equation 9, the mean lifetime in a ROI was calculated using the ROI means of $\widehat{\mathit{w}\prime }$, $\widehat{\mathit{x}\prime }$, and $\widehat{{\mathbf{x}}^{\mathrm{r}}}$, as follows:

$${\widehat{m}}_{\mathrm{ROI}}=\frac{{\widehat{w\prime }}_{\mathrm{ROI}}-m^{\mathrm{r}}{\widehat{x^{\mathrm{r}}}}_{\mathrm{ROI}}}{{\widehat{x\prime }}_{\mathrm{ROI}}-{\widehat{x^{\mathrm{r}}}}_{\mathrm{ROI}}}-\widehat{\mathrm{\mu }}.$$ Eq. 12

Background noise was quantified by the SD of voxels inside the water region. The mean positron lifetime versus background noise curve was then plotted by varying the iteration number.

The axial and radial resolution of the lifetime image was quantified from an axial and a radial profile, respectively, as follows. The axial profile was extracted across the slab using a 30 mm × 24 mm × 22 mm cuboid (x, y, z, respectively, in scanner coordinate), which encompassed both the slab and the surrounding water but excluded the holes. The 1-dimensional axial profile was then obtained by averaging the voxel values within the cuboid for each x–y plane. The radial profile was taken vertically through the center of the 20-mm hole in the central slice of the slab. To reduce noise, each data point was obtained by averaging 3 voxels in the horizontal (x) direction. The profiles were then fitted to a convolution model between the true lifetime profile and a gaussian resolution kernel:

$$\widehat{\mathrm{\sigma }},{\widehat{m}}_{\mathrm{BG}},{\widehat{m}}_{\mathrm{ROI}}=\underset{\mathrm{\sigma },m_{\mathrm{BG}},m_{\mathrm{ROI}}}{\min } {\Vert f\left(z\right)-r\left(z|\tau \right)*g\left(z|\mathrm{\sigma }\right)\Vert }_2^2,$$ Eq. 13

where f(z) is the measured profile, $r\left(z|\tau \right)$ represents the true lifetime profile modeled as

$$r\left(z|\tau \right)=\mathrm{rect}\left(\frac{z}{a}\right)\times \left(m_{\mathrm{ROI}}-m_{\mathrm{BG}}\right)+m_{\mathrm{BG}},$$ Eq. 14

with a as the feature width, $m_{\mathrm{BG}}$ as the background lifetime, and $m_{\mathrm{ROI}}$as the lifetime of the contrasted region, which corresponded to the water and slab, respectively, in the axial profile and vice versa in the radial profile. σ is the SD of the gaussian resolution kernel, $g\left(z|\mathrm{\sigma }\right)$. To reduce the influence of image noise, we used the 7.4-MBq ⁴⁴Sc scan. The fitting was performed using the lsqcurvefit function in MATLAB. The estimate SD of the gaussian kernel was then converted to full width at half maximum using $2.355\widehat{\mathrm{\sigma }}.$ The uncertainty of the estimate was determined on the basis of the fitting residual.

RESULTS

The numbers of collected events, along with the NEC and randoms-to-trues (R/T) ratios, are summarized in Table 2. The sensitivity gain of ⁴⁴Sc over ⁶⁸Ga is 79-fold, matching well with the difference in their prompt γ yields. The sensitivity gain of ⁴⁴Sc over ⁸²Rb is slightly lower than the prompt γ yield ratio, likely due to ⁸²Rb’s lower prompt γ energy, which results in higher detection efficiency. The R/T ratios of ⁴⁴Sc scans are much lower than those of ⁸²Rb and ⁶⁸Ga scans. This is primarily because the activity of ⁴⁴Sc is lower, and ⁶⁸Ga and ⁸²Rb scans are more affected by additional randoms from ¹⁷⁶Lu emissions due to their low prompt γ yields.

The energy spectra of the 3 isotopes are shown in Figure 2A, with the background radiation from ¹⁷⁶Lu subtracted. The photopeak of prompt γ rays is clearly resolved for each isotope. The time histograms of true events are shown in Figure 2B. The curves of ⁸²Rb and ⁶⁸Ga scans are much noisier than that of the ⁴⁴Sc scan because of their lower prompt γ fractions and higher R/T ratios. The system timing offset μ was estimated to be 24, 32, and 39 ps for ⁸²Rb, ⁶⁸Ga, and ⁴⁴Sc scans, respectively. The positive correlation between timing offset and prompt γ energy is expected, as higher photon energies result in faster detector triggering.

FIGURE 2.

Left: energy spectra of ⁸²Rb, ⁶⁸Ga, and ⁴⁴Sc scans with background radiation from ¹⁷⁶Lu subtracted. Thirty second data of each scan are used for plot. Their activities were scaled to 40 MBq. Corresponding contribution from ¹⁷⁶Lu radiation is plotted for comparison. Right: true lifetime spectra of ⁸²Rb, ⁶⁸Ga, and ⁴⁴Sc scans with type I–III randoms subtracted. A.U. = arbitrary unit (normalized by maximum).

The reconstructed activity and average lifetime images are shown in Figure 3. In the activity images, the slab appears dark because of the absence of radioactivity; however, a significant number of positrons entered and annihilated inside the slab because of the positron range effect. The vertical gradient in the x–y activity image of the ⁸²Rb scan arises from imperfect mixing of the radioactivity at the beginning of the scan but does not affect the lifetime estimation. The slab is resolvable and appears bright in the y–z lifetime slices of all 4 scans, demonstrating high spatial resolution of the SIMPLE method. Although image noise is notably high in the ⁸²Rb and ⁶⁸Ga images, it is substantially reduced in the ⁴⁴Sc images. The 20-mm hole is visible in both ⁴⁴Sc scans, with the 7.4-MBq ⁴⁴Sc scan further resolving the 10-mm hole. For all scans, the image noise can be greatly reduced using the CT-guided smoothing, which allows the 20-mm hole to be resolvable in the ⁸²Rb and ⁶⁸Ga scans.

FIGURE 3.

x–y and y–z slices (scanner coordinate) of reconstructed activity and lifetime images with and without CT-guided smoothing. For lifetime reconstruction, 2 subsets and 2 iterations were used for ⁸²Rb and ⁶⁸Ga images, whereas 2 subsets and 4 iterations were used for ⁴⁴Sc images. Activity images were reconstructed from triple coincidences using 8 iterations and 2 subsets.

The mean lifetimes in the water and slab ROIs are plotted against the background SD in Figure 4. In the standard SIMPLE images, the lifetime estimates in water are consistent across all 4 scans, all converging to 0.831 ± 0.007 ns. The slab lifetimes also converge to similar values (0.885 ± 0.009 ns), although the converged images from the ⁶⁸Ga and ⁸²Rb scans are too noisy to visually distinguish the slab. The 2 ⁴⁴Sc scans exhibit different convergence behaviors for the slab lifetime because of their different R/T ratios. The lifetime images obtained using the CT-guided filter achieve similar accuracy while reducing the image noise by approximately 90% across all 4 scans.

FIGURE 4.

Plots of mean lifetime value in water (A) and slab (B) ROIs against background SD by varying iteration number with 2 subsets. Dashed lines represent results of kernel method. Eight iterations are shown for all scans.

The radial and axial lifetime profiles are presented in Figure 5. The fitted lifetime profiles are in good agreement with the measured profiles. The radial and axial full width at half maximum values were determined to be 3.7 ± 1.8 mm and 3.9 ± 0.4 mm, respectively, which are close to the reported scanner resolutions for PET activity images. The estimated radial resolution exhibits higher uncertainty than the axial resolution because there is less averaging for the radial profile. This clearly demonstrates that PLT can achieve the same spatial resolution as standard PET.

FIGURE 5.

Measured and fitted lifetime profiles. Radial profile (A) traverses through 20-mm hole, and axial profile (B) across 6-mm thick slab. Radial and axial full width at half maximum values were determined to be 3.7 ± 1.8 mm and 3.9 ± 0.4 mm, respectively.

DISCUSSION

Our phantom study demonstrated that high-resolution PLT is achievable at clinical PET imaging activity levels. As expected, ⁴⁴Sc yielded the best image noise performance. Its high prompt γ efficiency and long lifetime enable the collection of sufficient counts at a lower activity level with fewer randoms. In contrast, ⁶⁸Ga has low prompt γ efficiency, and ⁸²Rb suffers from a very short half-life. We extended the scan time of ⁶⁸Ga to obtain a comparable NEC to the ⁸²Rb scan. However, type I and III randoms in the ⁶⁸Ga and ⁸²Rb scans were significantly elevated because of the ¹⁷⁶Lu background radiation. Another factor contributing to the increase in randoms for ⁶⁸Ga is the electron capture process, which produces prompt γ rays of the same energy. For ⁶⁸Ga, the fraction of β⁺ + γ decay is 1.19% of total decays (Table 1), whereas the fraction of EC + γ is 2.03%, indicating that, independent of the ¹⁷⁶Lu background, 63% of type I randoms arise from electron capture.

These 4 scans span a wide range of activity levels and R/T ratios. Despite these variations, the lifetime estimate in the water background is highly consistent across all scans, validating the effectiveness of the randoms correction method. When the images are compared, the noise level in the lifetime images correlates with the NEC, though it does not follow the relationship of SD ∝ $1/\sqrt{\mathrm{N}\mathrm{EC}}$. This deviation is expected because lifetime estimation is more complex than activity estimation. The findings also highlight the need for a new metric specifically tailored to lifetime image quality, which would aid in optimization of data acquisition parameters in future studies.

The ⁶⁸Ga and ⁸²Rb images suffer from significant noise, requiring early termination of their reconstructions. Developing regularized lifetime reconstruction methods in the future will be necessary to reduce image noise and improve image quality. Such methods are also useful for performing PLT on whole-body PET scanners with a standard axial FOV, which have much lower sensitivity for triple coincidence detection.

Since the phantom size in this study is relatively small, object scatter was not considered. However, scattering inside the detectors is inevitable. To mitigate this, the prompt γ ray energy window was set high enough to avoid detecting a down-scattered prompt γ as 2 separate events—one 511-keV photon and one prompt γ ray. In this setting, a down-scattered prompt γ can only be misidentified as a 511-keV photon, resulting in a random triple coincidence with an unrelated prompt γ, which can be estimated using the delayed window technique. For larger objects and human imaging, development of scatter correction methods will be essential for fully quantitative PLT.

CONCLUSION

We have successfully demonstrated high-resolution PLT using ⁸²Rb, ⁶⁸Ga, and ⁴⁴Sc at activity levels relevant to human imaging on a long axial FOV PET scanner. The phantom images confirm that the SIMPLE method, combined with randoms correction, can reliably reconstruct average lifetime images with consistent accuracy across varying activity levels and R/T ratios.

DISCLOSURE

This study is supported by the U.S. National Institutes of Health under grant R21 EB032101 and R01 CA113941. The production of ⁴⁴Sc was supported through the DOE University Isotope Network under grant DESC0021269. No other potential conflict of interest relevant to this article was reported.

KEY POINTS

QUESTION: Can high-resolution PLT be achieved using ⁸²Rb, ⁶⁸Ga, and ⁴⁴Sc at activity levels relevant to human imaging?

PERTINENT FINDINGS: A cylinder phantom filled with different radioactive solutions was scanned by the PennPET EXPLORER. The spatial resolution of lifetime images was measured to be comparable with the reported system resolution. The accuracy of lifetime estimates is consistent across all scans, and ⁴⁴Sc outperformed the other tracers with significantly reduced noise in the lifetime image.

IMPLICATIONS FOR PATIENT CARE: This study paves the way for high-resolution clinical PLT.