Impact of DOI Capability on Detector Performance: A Comparative Study of DOI and Non-DOI Detectors for High-Resolution and Sensitivity Organ-Specific PET Inserts

Abstract

High-sensitivity organ-specific PET inserts employing long scintillation crystals in combination with small ring diameters require depth-of-interaction (DOI) encoding to ensure uniform spatial resolution across the field of view. In this study, we have developed high-resolution, DOI-capable detectors based on the Hamamatsu C13500 TOF-PET modules, using 1.6×1.6 mm² LSO crystals coupled to 4×4 mm² SiPMs. Detector configurations were designed either for a brain PET/MR insert (26 mm long crystals with a top light guide (TLG) for DOI encoding via light spread) or for a breast PET/MR insert (15 mm long with a TLG; 15 mm long with a stacked dual-layer configuration). Corresponding reference configurations without DOI capability were included to assess the impact of DOI implementation on detector performance. The 26 mm long brain detector configuration with TLG achieved an energy resolution of 12.1% and a coincidence time resolution (CTR) of 684 ps, with a degradation of 148 ps compared to the non-DOI variant. A newly developed DOI parameter calculation method improved DOI resolution from 9.1 ± 1.7 mm to 7.1 ± 1.8 mm. The 15 mm long single layer breast detector configuration with TLG yielded an energy resolution of 10.8%, a CTR of 460 ps, and a DOI resolution of 6.3 ± 1.8 mm. The 15 mm dual layer detector configuration provided comparable performance (11.5% energy resolution, 605 ps CTR) while eliminating the need for DOI calibration. For both the 15 and 26 mm single layer crystal block configurations, introducing a TLG preserved crystal identification and energy resolution. Overall, the DOI-capable designs demonstrated only minor performance trade-offs, supporting the feasibility of both approaches for integration into organ-specific PET/MR inserts.

I. INTRODUCTION

Clinical whole-body positron emission tomography (PET) scanners typically achieve spatial resolutions of 3–4 mm with sensitivities ranging from 14.6 to 18.7 kcps/MBq [1], [2], [3], [4], [5]. Extending the axial field of view from 20–30 cm beyond 1 m, as seen in long axial field of view (LAFOV) PET scanners, highly increases sensitivity, reaching up to 176 kcps/MBq [6], [7]. However, this presents challenges related to cost and implementation complexity. An alternative, cost-effective approach is organ-specific PET systems, particularly for brain [8], [9], [10], [11] and breast [12], [13] imaging applications. Standalone PET scanners for brain imaging can offer an average spatial resolution of up to 1.64 mm and sensitivity of up to 11.8 % in the central field of view [14], while for breast imaging spatial resolution of up to 1.62 mm and sensitivity of up to 3.6 % [15] were reported. Integrating such organ-specific PET systems into magnetic resonance imaging (MRI) scanners as inserts enables the collection of valuable complementary information about the imaged tissue, allowing improved diagnostics, treatment planning and monitoring of patients. However, this integration requires careful engineering to minimize mutual interference and is challenging due to tight space constraints.

Our group previously demonstrated an MRI-compatible [16], compact and high-performance PET module featuring 3 mm silicon photomultipliers (SiPMs) combined with small scintillation crystal dimension of 1.51 mm × 1.51 mm × 10.0 mm designed for high spatial resolution [17]. Building on this work, the present study extends toward realizing PET/MR inserts for brain [18], [19], [20], [21], and breast imaging [16], [22], [23], [24]. The initial 8×8 arrays of 3 mm SiPMs have been replaced with 4×4 arrays of 4 mm SiPMs, reducing channel count and supporting smaller block dimensions of 16 mm. The brain insert features an inner diameter of 32 cm, while the proposed breast insert is designed with an inner diameter of 17.5 cm. To achieve high sensitivity, crystals with lengths of 26 mm and 15 mm are employed for the brain and breast insert, respectively. However, the combination of a small diameter and long crystals increases susceptibility to parallax error, which can be compensated through the use of depth of interaction (DOI) information [25], [26]. Various methods exist for extracting DOI information from detectors, which can be grouped into discrete and continuous DOI encoding schemes. Discrete schemes include phoswich [27], [28] and multiple stacked layers [10], [29]. Continuous schemes include special reflector arrangements [30], [31], prismatoid light guides [32], dual-sided readouts [33], [34], monolithic crystals [35] and employing top light guides (TLG) mounted at the top of the scintillation crystal block [36]. The brain PET insert uses 26 mm long crystals with a TLG for DOI encoding, while for the breast PET insert, 15 mm long crystals either employing a stacked layer design or a TLG approach are considered.

In this study, we evaluated the performance of the detectors for use in the brain and breast inserts with respect to crystal identification, energy resolution, timing resolution, and DOI resolution. To assess the influence of the top lightguide or stacked design on these performance metrics, we compared the results obtained from the DOI-capable block configurations with their respective counterpart without any DOI capabilities. Further, we propose and evaluate an advanced method to obtain the DOI parameter for detector configurations with a top lightguide.

II. Materials and Methods

A. Scintillation Crystal Block and Detector Configurations

Five lutetium oxyorthosilicate (LSO) (Siemens Healthineers, Knoxville, TN, USA) scintillator block configurations, laminated with Enhanced Specular Reflector (ESR) (3M, St. Paul, MN, USA) after all surfaces were lapped with a diamond pad and with different heights, number of layers, and lightguide configurations according to Table 1, were evaluated. The single layer blocks featured 10×10 crystals with a pitch of 1.6 mm.

Table I.

Visualization and specifications of the five scintillator block configurations. The naming scheme of the configurations is compiled from their crystal length (15 mm or 26 mm), the number of crystal layers (1LAY for single-layer, 2LAY for stacked dual-layer design) and presence (wTLG) or absence (woTLG) of a top light guide. Configurations with 26 mm long crystals are intended for the brain PET/MRI insert, while those with 15 mm length are designed for the breast PET/MRI insert.

Detector	26-1LAY-woTLG	15-1LAY-woTLG	26-1LAY-wTLG	15-1LAY-wTLG	15-2LAY-woTLG
Total length (mm)	26	15	26	15	15
Crystal pitch (mm)	1.6	1.6	1.6	1.6	1.6
# of crystals in layer 1 | 2	10 × 10	10 × 10	10 × 10	10 × 10	10 × 10 | 9 × 9
Thickness layer 1 | 2 (mm)	26	15	26	15	9.81 |5.19
Lightguide?	No	No	Yes	Yes	No

To obtain DOI information according to depth-dependent light spread [36], a 16 mm × 16 mm and 380 μm thick epoxy resin (RTV615, Momentive, Waterford, NY, USA) lightguide was positioned on top of both single layer blocks referred to as 15–1LAY-wTLG and 26–1LAY-wTLG.

A second DOI-capable approach was implemented with the dual layer configuration 15–2LAY-woTLG, employing 10×10 9.81 mm long crystals in the bottom layer and 9×9 5.19 mm long crystals in the top layer, both with a pitch of 1.6 mm. The crystal lengths were selected to achieve equal gamma absorption probabilities in the two layers, according to Lambert–Beer’s law, thereby ensuring a comparable number of detected events per layer. Coupling to the 4×4 SiPM array S13546H (Hamamatsu Photonics K.K., Hamamatsu, Japan) with a 4 mm × 4 mm SiPM size and 50 μm pixel size was done via silicone optical grease (BC-630, Saint-Gobain Crystals, Hiram, OH, USA).

B. Detector Front-End Electronics and Readout System

The detector front-end and readout electronics (Figure 1) were based on a modified version of the C13500 TOF-PET modules (Hamamatsu Photonics K.K., Hamamatsu, Japan). This version combines previously implemented features in a compact scalable design suitable for PET inserts, such as the possibility of using small scintillation crystals via light sharing [17] and MRI compatibility enabled by data transmission via optical fibers [16]. In the following, the topology and components are briefly introduced, for more detailed information, refer to [16], [17].

Figure 1.

Schematic of the detector front-end and readout electronics, illustrating the signal chain from the detector block through the data processing board (DPB) and field programmable gate array (FPGA) boards to the event data storage.

Each module included a data processing board (DPB) equipped with four application-specific integrated circuits (ASIC) to derive energy as time-over-threshold (ToT) in ns and timing information with a four-channel time-to-digital converter (TDC). A total of four crystal blocks with 64 SiPM channels (16 per ASIC) could be processed per DPB in this configuration enabling to obtain energies of all 16 individual SiPM channels (later in postprocessing summed for total energy) and a single time stamp per block. Data preprocessing is performed such that once the first SiPM signal exceeds the ToT comparator threshold, all remaining channels within the block are sampled within a fixed time window and assigned to a single event. The corresponding time stamp is defined by the first triggered channel. For more information on energy and time stamp determination refer to [17]. A global high voltage (HV) was supplied via two interconnected connectors, allowing to daisy chain HV power supply for multiple DPBs. The SiPM bias voltage of 59 V was temperature compensated and could be adjusted for each individual SiPM channel. USB-C cables were used for power supply and data transmission to the hub board, for data management and communication. Each hub board could control up to eight DPBs and was connected to the readout electronics via optical fiber to exchange data and provide a clock signal. The readout electronics handled the data stream of a single hub board and were connected via Gigabit Ethernet to a workstation for system control and readout.

C. Experimental Setups and Measurements

All measurements were performed in a climatized dark box with a temperature of 20°C, and SiPM temperature of approximately 26 °C.

1). Panel source for flood map, energy and timing assessment

A pair of opposing detectors of all five block configurations was placed at a distance of 250 mm to a centered ¹⁸F flood source with a size of 16 mm × 16 mm (Figure 2). Activities of 57.5, 64.0, 50.5, 56.9 and 45.3 MBq were used for the measurements with 26–1LAY-wTLG, 26–1LAY-woTLG, 15-LAY-wTLG, 15–1LAY-woTLG and 15–2LAY-woTLG, respectively. In total 10⁸ single events (with a single timestamp and composed of the cluster of up to the 16 SiPM channel signals – likely originating from a single gamma interaction) per block were acquired with this setup to determine flood maps, energy and timing histograms.

Figure 2.

a: Setup with ¹⁸F panel source and front irradiation to determine crystal position profiles, energy and timing histograms; b: Setup with collimated ¹⁸F line source and translational stage for lateral irradiation at different depths to determine DOI profiles.

2). Step-And-Shoot Collimated Line Source for DOI assessment

The two-block configurations with a TLG (26–1LAY-wTLG, 15–1LAY-wTLG) were positioned 75 mm apart for lateral irradiation to obtain DOI profiles at different irradiation depths. An ¹⁸F line source (197.9 / 128.7 MBq for 26–1LAY-wTLG / 15–1LAY-wTLG) was collimated with 22 mm thick tungsten collimators with a 1 mm aperture slit (Figure 2). A translational stage (MTS50/M-Z8, ThorLabs, Newton, NJ, USA) was used to perform measurements at interaction depths of 3, 8, 13, 18, 23 mm / 3, 8, 13 mm from the SiPM array for 26–1LAY-wTLG / 15–1LAY-wTLG, respectively. At each step, 10⁸ single events per detector were acquired, with irradiation from one lateral side, resulting in approximately one-third as many events in the crystals on the far side compared to those on the near side.

D. Data Analysis

Flood maps as 2-D crystal position histograms with a size of 256 × 256 were obtained from the 16 channels of the SiPM array by a centroid calculation. The total event energy was calculated as the sum of a fixed crystal-dependent subset of SiPMs based on the distance of the SiPMs to the respective crystal. To account for inter-crystal scatter (ICS), χ² was determined as

$${\chi }^2={\sum }_{i=1}^N\frac{{(p_i-\overline{p_i})}^2}{{\overline{p_i}}^2}$$ (1)

with N=16 as the number of SiPMs, p_i being the detected intensity for SiPM i and $\overline{p_i}$ the mean detected intensity of SiPM i for all events within 411 – 611 keV. A high χ² value indicates irregular light spread, e.g., due to ICS, thus a crystal individual threshold was applied for ICS rejection (10% of the events in a 511 ± 150 keV energy range). Events triggering at least 11 of the 16 SiPM channels, with an energy of 511 ± 150 keV and within a coincidence window of 10 ns were used for analyses. The influence of the ICS rejection on crystal identification, energy resolution, and timing resolution was evaluated as exemplary for detector configuration 15–2LAY-woTLG.

Crystal identification was based on a common Voronoi approach and was quantitatively assessed by peak-to-valley ratios (PVR) for a selected crystal row and column. Energy calibration was performed crystal-wise by identifying the peak position of the energy histogram (ToT ns) with a Gaussian fit and linear scaling of the values to match the peak to 511 keV. Single crystal energy spectra and distributions of the photopeak position and energy resolution determined by a Gaussian fit with an energy window of 490–650 keV were reported.

The coincidence time resolution (CTR) of a single crystal was obtained by the average full width at half maximum (FWHM) of all timestamp difference distributions of this crystal with all crystals in the opposing detector using an energy window of 511 ± 150 keV. The FWHM was derived from a Gaussian fit of the distribution. For the total block time difference histograms, a crystal-pair-wise time skew correction was applied. Therefore, time difference distributions were calculated for each crystal pair across opposing blocks and fitted with Gaussians to generate a lookup table of mean offsets. These offsets were subtracted from the corresponding event time differences, centering the corrected distributions around zero. To ensure comparability with previous studies [17], [36], [37], [38], [39], [40] and examine the influence of the energy window, CTR was also determined using an energy window of 460 – 560 keV.

Two methods for determining the DOI parameter for 26–1LAY-wTLG and 15–1LAY-wTLG were compared, as depicted in Figure 3. The first method to determine the DOI parameter w was according to [36]

$$w=\frac{p_{\mathit{\text{max}}}}{{\sum }_{i=1}^{16}{p}_i}$$ (2)

where p_i is the intensity of SiPM i and p_max is the highest of these intensities.

Figure 3.

Principle to obtain the depth of interaction of the gamma quanta via depth dependent light spread introduced by the top light guide. Exemplary light intensity distributions across the SiPM array for two distinct irradiation depths at 3 mm and 23 mm are shown. To determine the DOI either the maximum intensity SiPM (purple box) for the first method (DOI value w) or the k=1–3 highest intensities (in this example k=2) SiPMs (red box) for the second method (DOI value w’) are used.

We expanded on this method by including more than only the most intense SiPM and adjusting the weighting, resulting in a modified DOI parameter w′:

$$w\text{'}=\frac{{\left({\sum }_{i=1}^k{p}_{\mathit{\text{max}},i}\right)}^2}{{\sum }_{i=1}^{16}{p}_i}$$ (3)

where p_max,i is the i-th most intense SiPM. The parameter k was empirically optimized for each crystal by iterating over values from 1 to 4, calculating w’ and the corresponding DOI resolution. The crystal-specific k value yielding the best DOI resolution was selected (with all values in a range between 1–3). The use of k SiPM intensities was motivated by the fact that the main light output of a single crystal is often shared among several SiPMs, making the light spread less accurately captured by the single p_max value used in the w method. Introducing the squared sum in the numerator enhances sensitivity to subtle variations in the light pattern compared to the original method [36]. DOI resolution was reported for individual crystals as the mean of the FWHM of the DOI distributions over the irradiation depths and, analogous to the CRT evaluation, reported for energy windows of 511 ±150 keV and 460 – 560 keV.

III. Results

A. Flood Maps and Position Profiles

The flood maps of all block configurations (Figure 4) allowed crystal identification, as confirmed by PVR values of at least 4.3 ± 2.1 (Table 2). The diagonal artifacts towards the corners of the SiPM array (Figure 4f) could be mitigated by rejecting ICS events (Figure 4c) for 15–2LAY-woTLG based on the χ² threshold. The ICS rejection also improved the PVRs in x | y direction from 2.6 ± 1.1 | 3.2 ± 1.2 to 4.3 ± 2.1 | 4.6 ± 2.1. The fraction of events (in a 511 ± 150 keV energy window after the coincidence sorting) that are below the ICS threshold (“χ² survival fraction”) ranged from 83.1% (15–1LAY-wTLG) to 91.3% (26–1LAY-wTLG) (Table 2).

Figure 4.

a-e: Flood maps and position profiles for the five block configurations with and without lightguide, different crystal lengths, single and dual layer. f: Flood map of the dual layer block prior to inter-crystal scatter (ICS) rejection.

Table II.

Detector performance metrics peak-to-valley ratio (PVR), survival fraction after ICS rejection, energy resolution, photo peak position, coincidence time resolution (CTR) and depth of interaction (DOI) resolution for both evaluated methods. All shown values are averaged over all crystals in one block. The evaluated configurations are 26 mm long with and without top light guide (TLG) (26–1LAY-wTLG, 26–1LAY-woTLG) and 15 mm long with and without TLG (15–1LAY-wTLG, 15–1LAY-woTLG), as well as a dual layer configuration without TLG (15–2LAY-woTLG).

	26-1LAY-wTLG	26-1LAY-woTLG	15-1LAY-wTLG	15-1LAY-woTLG	15-2LAY-woTLG bottom layer	15-2LAY-woTLG top layer
PVR (x direction)	7.3 ± 2.7	8.1 ± 2.4	12.0 ± 5.0	12.0 ± 4.9	4.3 ± 2.1
PVR (y direction)	8.3 ± 4.3	9.7 ± 5.1	8.6 ± 4.0	8.5 ± 3.8	4.6 ± 2.1
χ2 survival fraction (%) (511 ± 150 keV)	91.3 ± 0.7	88.4 ± 1.6	83.1 ± 3.8	91.2 ± 1.3	91.1 ± 1.2
Energy resolution (% FWHM)	12.1 ± 1.4	11.2 ± 1.2	10.8 ± 1.9	10.8 ± 2.0	11.5 ± 2.0	9.9 ± 2.1
Photopeak position (ns ToT)	3534 ± 662	3664 ± 694	3383 ± 763	3375 ± 776	3303 ± 914	3784 ± 818
CTR(ps) (511 ± 150 keV)	835 ± 44	788 ± 39	707 ± 38	674 ± 31	769 ± 69	751 ± 48
CTR(ps) (460 – 560 keV)	684 ± 52	536 ± 65	460 ± 9	383 ± 16	605 ± 39	613 ±30
DOI resolution method 1 (mm FWHM) (511 ± 150 keV)	13.4 ± 5.0	none	9.2 ± 2.4	none	9.81 (bottom) | 5.19 (top)
DOI resolution method 2 (mm FWHM) (511 ± 150 keV)	7.1 ± 1.7	none	6.1 ± 1.6	none
DOI resolution method 1 (mm FWHM) (460 – 560 keV)	9.1 ± 1.7	none	8.7 ± 1.8	none
DOI resolution method 2 (mm FWHM) (460 – 560 keV)	7.1 ± 1.8	none	6.3 ± 1.8	none

B. Energy Resolution and Photopeak Position

Energy spectra of the single-layer blocks are shown for the total block (Figure 5a) and selected center and edge crystals (Figure 5b). The distribution of crystal-wise energy resolutions and photopeak positions over the total block are shown in Figure 5c–d with mean values and standard deviation reported in Table 2. The mean energy resolutions were comparable for 15–1LAY-woTLG, 15–1LAY-wTLG and 26–1LAY-woTLG with 10.8 ± 2.0, 10.8 ± 1.9 and 11.2 ± 1.2 %. The mean resolution of 26–1LAY-wTLG was degraded moderately with 12.1 ± 1.4 %. The mean photopeak positions showed moderate deviation, ranging from 3375 ± 776 to 3664 ± 694 ns ToT.

Figure 5.

Single Layer block configurations with different heights and with or without TLG; a: Total block energy histograms; b: Energy histograms of selected center and edge crystals; c-f: Crystal individual energy resolution and photopeak position.

Energy spectra of the bottom and top layer of the 15–2LAY-woTLG block are shown for the total layers (Figure 6a) and selected center and edge crystals (Figure 6b). The distribution of the crystal-wise energy resolutions and photopeak positions for each layer (Figure 6c–d) showed a trend of the top layer performing better with an average energy resolution of 9.9 ± 2.1 % compared to 11.5 ± 2.0 % for the bottom layer. The ICS rejection resulted in an improvement of the energy resolution from 10.9 ± 2.3 | 13.0 ± 2.5 % to 9.9 ± 2.1 | 11.5 ± 2.0 % for the top | bottom layer, respectively.

Figure 6.

Dual layer block configuration 15–2LAY-woTLG; a: Total block energy histograms for top and bottom layer; b: Energy histograms of selected center and corner crystals; c, d: Crystal individual energy resolution and photopeak position for top and bottom l

C. Coincidence Time Resolution

The total block time difference histograms are shown in Figure 7. The increase in length from 15–1LAY-woTLG to 26-1LAY-woTLG degraded the CTR from 674 ± 31 ps to 788 ± 39 ps. The introduction of the TLG for 26–1LAY-wTLG further degraded the CTR to 835 ± 44 ps. Introducing the stacked design 15-2LAY-woTLG resulted in a worse CTR of 751 ± 48 | 769 ± 69 ps top | bottom layer compared to 674 ± 31 ps for 15–1LAY-woTLG. ICS reduction improved the CTR from 801 ± 48 | 821 ± 71 ps to 751 ± 48 | 769 ± 69 ps for top | bottom layer, respectively.

Figure 7.

a: Timing histogram (energy window 460–560 keV) for the five block configurations with and without lightguide, different crystal lengths, single and dual layer. b-g: Distribution of crystal individual CTR.

The use of a narrower energy window resulted in CTR values of 536 ± 65 and 383 ± 16 ps for 26–1LAY-woTLG and 15–1LAY-woTLG respectively. The introduction of the TLG degraded the CTR values to 684 ± 52 and 460 ± 9 ps, respectively. The stacked design 15–2LAY-woTLG yielded a CTR of 613 ± 30 | 605 ± 39 ps for top | bottom layer with the narrow energy window.

D. Depth of Interaction

The DOI profiles for a selected center crystal of the 26–1LAY-wTLG block, obtained using the first DOI method (w, (2)), are shown in Figure 8. The second method (w’, (3)) enhanced the separation of DOI profiles for the distinct irradiation depths (Figure 8), resulting in an improvement in DOI resolution from 6.6 ± 0.8 mm to 5.8 ± 0.3 mm.

Figure 8.

Comparison of DOI profiles and distribution of crystal wise DOI resolution (energy window 460–560 keV) for 15–1LAY-wTLG and 26–1LAY-wTLG using either DOI method 1 (w) or method 2 (w’). DOI profiles for selected center crystals of 26–1LAY-wTLG (a, c) and 15–1LAY-wTLG (b,d) using method w and method w’ respectively. Distribution of crystal wise DOI resolution obtained DOI method w (e,f) and w’ (g,h). The red rectangles indicate the crystals for which the DOI distributions are shown.

Similarly, for the 15–1LAY-wTLG block, the DOI resolution for a selected center crystal improved from 8.6 ± 1.2 mm to 5.1 ± 1.3 mm (Figure 8) for w and w’, respectively.

When averaged over the entire block, the DOI resolution improved from 9.2 ± 2.4 to 6.1 ± 1.6 mm for 15–1LAY-wTLG and from 13.4 ± 5.0 to 7.1 ± 1.7 mm for 26–1LAY-wTLG using w’. A narrower energy window of 460 – 560 keV showed negligible impact on the DOI resolutions, resulting in a DOI resolution of 7.1 ± 1.8 and 6.3 ± 1.8 mm for 26–1LAY-wTLG and 15–1LAY-wTLG respectively.

A more uniform distribution of the DOI resolution across the block was obtained for the shorter block 15–1LAY-wTLG compared to 26–1LAY-wTLG (Figure 8). Employing the w’ method not only improved the overall DOI resolution but also resulted in a more uniform distribution of DOI resolution across the block (Figure 8).

IV. Discussion

In this study, we compared five PET detector block configurations with a length of 15 and 26 mm and either none, a discrete or a continuous DOI encoding scheme intended for use in organ-specific PET/MRI inserts. The 26–1LAY-wTLG configuration with 26 mm long blocks employing a top light guide for continuous DOI is used for a brain PET/MR insert [9], whereas the 15 mm block configurations (15–1LAY-wTLG, 15–2LAY-woTLG) are intended for a breast PET/MR insert both currently under development. Further, we determined the impact of the different DOI encoding schemes on crystal identification, energy resolution and timing resolution. A comparison of these performance metrics with previously reported work employing similar configurations is shown in Table 3.

Table III.

Comparison of performance metrics (ctr, doi and energy resolution) with other publications using comparable configurations with and without doi capabilities.

Publication	CTR (ps)	DOI (mm FWHM)	Energy resolution (% FWHM)	Energy window	Crystal size (mm3)	Crystal material	Crystal surface	Reflector material	DOI method
Pizzichemi et al. [36] & Pizzichemi et al. [37]	307 (no DOI correction)	3	9.9	511 ± 2σ (468 – 554 keV)	1.53 × 1.53 × 15	LYSO	depolished, dry ESR contact	ESR (dry contact)	top lightguide
LaBella et al. [40]	not reported	5.72	20 (no DOI/saturation correction)	not reported	1.4 × 1.4 × 20	LYSO	not reported	BaSO4	top lightguide
Zeng et al. [39] (1.5 mm cuboid)	286	3	11.2	460 – 560 keV	1.5 × 1.5 × 20	LYSO	polished	BaSO4	prismatoid top lightguide
Zeng et al. [39] (1.5 mm tapered)	243	2.4	8.9	460 – 560 keV	1.5 × 1.5 × 20 1.2 × 1.2 toward SiPM	LYSO	polished	BaSO4	prismatoid top lightguide
Schmidt et al. [17]	354	none	14.1	511 ± 2σ (448 – 574 keV)	1.51 × 1.51 × 10	LSO	lapped	laminated with ESR	none
Akamatsu et al. [38]	235	none	12.0	460 – 560 keV	3.1 × 3.1 × 10	LFS	not reported	laminated with reflective foil	none
This study (15-1LAY-wTLG)	460	6.1	10.8	460 – 560 keV	1.51 × 1.51 × 15	LSO	lapped	laminated with ESR	top lightguide
This study (15-1 LAY-woTLG)	383	none	10.8	460 – 560 keV	1.51 × 1.51 × 15	LSO	lapped	laminated with ESR	none
This study (26-1LAY-wTLG)	684	7.1	12.1	460 – 560 keV	1.51 × 1.51 × 26	LSO	lapped	laminated with ESR	top lightguide
This study (26-1LAY-woTLG)	536	none	11.2	460 – 560 keV	1.51 × 1.51 × 26	LSO	lapped	laminated with ESR	none

In terms of crystal identification, the more complex propagation of the scintillation light introduced by the TLG did not compromise the accuracy of visual identification (Figure 4) and maintained high PVR values above 7.3 ± 2.7.

For the single layer 15 mm long crystal block, the TLG had no impact on the energy resolution, measured at 10.8 % for both configurations 15–1LAY-woTLG and 15–1LAY-wTLG.

A comparable energy resolution of 9.9 % was reported by [37] with a similar detector configuration with 1.53 mm × 1.53 mm × 15 mm LYSO:Ce crystals using a 1 mm thick glass TLG.

However, using the TLG for the longer 26 mm blocks resulted in a small degradation of the energy resolution from 11.2 % (26-1LAY-woTLG) to 12.1 % (26–1LAY-wTLG).

In general, crystals with a low cross-section-to-length ratio suffer from light loss and, eventually, degradation of timing and energy resolution [41]. In particular, considering the substantial length of 26 mm for a 1.51 mm × 1.51 mm crystal size, the measured energy resolution is competitive, e.g. compared to the 20 % obtained with a similar configuration with 1.4 mm × 1.4 mm crystals, a 1 mm thick TLG and just 20 mm length [32]. Of note, the authors in [32] improved the energy resolution to 13 % using a DOI-based correction, whereas a similar correction might further improve the energy resolution of block configurations 26–1LAY-wTLG and 15–1LAY-wTLG.

The introduction of a stacked dual layer design for 15–2LAY-woTLG preserved a high energy resolution of 9.9% | 11.5 % (top | bottom layer). The slightly better resolution in the top layer, presumably due to light from the bottom layer propagating upward, thus increasing effective path length to the SiPM, is also reported by [42] using a similar stacked configuration with 6.5 mm | 9.5 mm height and energy resolutions of 19.76 % | 20.52 % (top | bottom layer).

In terms of timing performance, the introduction of the DOI-capable designs for the 15 mm high block configuration led to a modest degradation from an initial CTR of 674 ps to 707 ps due to the TLG and to 751 ps | 769 ps (top | bottom layer) due to the stacked design. Similarly, for the 26 mm block configuration in this study, the introduction of the light guide degraded the CTR by 47 ps. To preserve the comparability between the DOI and non-DOI capable configurations in this study, we did not implement any DOI based corrections. Using a smaller energy window of 460–560 keV, the CTR values for 15–1LAY-woLTG and 15–1LAY-wTLG improved substantially to 383 and 460 ps respectively. This is comparable to other studies using either 1.53 mm × 1.53 mm × 15 mm crystals and a 1 mm TLG, but different electronics [37] or similar electronics with 1.51 mm × 1.51 mm × 10 mm ([17]) or 3.1 mm × 3.1 mm × 10 mm ([39]) crystals. Our CTR values are consistent with the 354 ps reported in [17], while the superior 235 ps in [39] likely reflects the larger crystal cross section of 3.1 mm × 3.1 mm compared to 1.51 mm × 1.51 mm used in this study. The CTR value of 158 ps for the reference configuration (identical but without a TLG) in [37] is attributed to full digitization of the discriminator pulse, enabling more precise timing pick-off. The degradation of 149 ps in CTR for configurations with and without TLG in [37] is comparable to the 77 ps between 15–1LAY-wTLG and 15–1LAY-woTLG. Similarly, the CTR of 26–1LAY-wTLG and 26–1LAY-woTLG improved to 684 and 536 ps, respectively. In a previous study [21], we showed that by implementing a DOI based timing correction combined with an optimization of timing parameters, the CTR could be improved to 586 ps for the 26–1LAY-wTLG configuration, comparable to the 26–1LAY-woTLG configuration. CTR values of 243 and 286 ps have been reported for 1.5 mm × 1.5 mm × 20 mm crystal configurations with a prismatoid lightguide and tapered or cuboid shape, respectively [38]. The differences in timing performance are likely due to variations in crystal lengths, reflector material (ESR vs BaSO4), and different readout electronics (Hamamatsu C13500 TOF-PET vs. TOFPET 2).

In terms of DOI resolution, we obtained 9.2 ± 2.4 mm with block configuration 15–1LAY-wTLG by employing the first method (w) using only the highest intensity SiPM in the numerator (2) to determine the light spread. This approach, initially proposed by Pizzichemi et al [36], yielded a DOI resolution of 3 mm FWHM for scintillation crystals with similar dimensions of 1.53 × 1.53 × 15 mm³ [37]. This discrepancy is most likely attributable to differences in the surface treatment. In [36], de-polishing and dry contact to ESR of the lateral crystal faces were identified as an important factor for DOI resolution. In contrast, the laminated and lapped crystal surfaces in our study are partially smoothed by the optical glue, likely representing an intermediate state between polished and de-polished. Therefore we expect the DOI resolution improvement reported in [36] to be less pronounced in our configuration.

Additionally, in [36], the combination of 1.53 × 1.53 mm² crystals with 3 × 3 mm² SiPMs did not result in any crystal being positioned above multiple SiPMs. In contrast, in our work with the 4 × 4 mm² SiPMs configuration, crystal positioning can span over multiple SiPMs. To account for this overlap, we proposed a different DOI parameter (w’) incorporating more than the single highest intensity value in the numerator (3). This approach improved the DOI resolution for 15–1LAY-wTLG from 9.2 ± 2.4 mm (w) to 6.3 ± 1.8 mm (w’) and resulted in a more homogeneous distribution (Figure 8). Similarly, for the 26–1LAY-wTLG configuration, DOI resolution improved from 9.1 ± 1.7 mm (w) to 7.1 ± 1.8 mm (w’), approaching the 5.72 mm reported for 1.5 mm × 1.5 mm × 20 mm scintillation crystals with a top lightguide in [43], using the method described in [36]. The remaining difference in DOI resolution likely reflects variations in crystal lengths and reflectors (ESR vs BaSO4). A DOI resolution of 3 mm has also been achieved with prismatoid lightguides for controlled lightsharing [38], underlining the advantages of defined lightspread behavior for DOI determination.

A constraint of the continuous DOI approach is the need for dedicated calibration procedures. The collimated step-and-shoot setup employed in this study is labor-intensive, requiring individual calibration for each detector block and is impractical for system-wide or periodic in-situ recalibrations, which may be necessary to account for changes over time. To address this limitation, alternative calibration strategies have been proposed, including the use of intrinsic background radiation from LSO crystals [44], homogeneous side irradiation [33], or collimated phantom irradiation at varying incidence angles [45]. Additionally, the empirically determined values of k can likely be standardized for all detectors with same configurations, as larger values of k coincided with the edges of the SiPMs in the array. In contrast, the stacked dual-layer configuration in this work does not require additional calibration, as discrete DOI information can be directly extracted from the flood maps.

While continuous DOI methods theoretically offer the potential for finer DOI resolution, the results in this study indicate that the 15–1LAY-wTLG configuration (6.1 mm FWHM DOI resolution) yields comparable performance to the 15–2LAY-woTLG configuration with two discrete DOI bins.

In a previous simulation study of the breast PET insert [23], our group demonstrated that a dual-layer configuration substantially mitigates spatial resolution degradation induced by parallax error. While the radial component of the spatial resolution at the transverse edge of the insert was significantly improved from 6.7 mm (no DOI) to 3.3 mm with a dual-layer configuration, a triple-layer configuration yielded a further but more moderate improvement to 2.2 mm.

Given the comparable performance of the 15–1LAY-wTLG and 15–2LAY-woTLG configurations in terms of energy resolution of 10.8 ± 1.9 % and 9.9 ± 2.1|11.5 ± 2.0 % (top | bottom) and only moderate degradation of CTR from 460 ± 9 ps to 605 ± 39 ps, combined with a more robust DOI and no need for calibration, the 15–2LAY-woTLG represents a favorable choice for the breast PET insert.

V. Conclusion

In this study, we evaluated detector configurations intended for use in brain (26–1LAY-wTLG; 26 mm long with a top light guide) and breast PET/MR inserts (15–1LAY-wTLG, 15 mm long with a TLG; 15–2LAY-woTLG, 15 mm long with a stacked layer DOI), alongside respective reference configurations without DOI capability.

The 26–1LAY-wTLG configuration yielded an energy resolution of 12.1 % and CTR of 684 ps, with only a moderate degradation of 144 ps introduced by the TLG. A novel DOI parameter calculation method substantially improved DOI resolution from 9.1 mm (conventional method) to 7.1 mm.

The 15–1LAY-wTLG configuration achieved an energy resolution of 10.8%, a CTR of 460 ps and a DOI resolution of 6.3 mm. The 15–2LAY-woTLG configuration provided comparable performance (11.5% energy resolution, 605 ps CTR) while eliminating the need for DOI calibration.

In both configurations, the introduction of a TLG preserved crystal identification and energy resolution. Overall, both DOI encoding approaches are viable, with the stacked dual-layer design representing a robust and practical solution suited for the breast PET/MR insert.