Home

Search

Collections

Journals

About

Contact us

My IOPscience

Thermal regulation for APDs in a 1mm3 resolution clinical PET camera: design, simulation and experimental verification

This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 Phys. Med. Biol. 59 3951 (http://iopscience.iop.org/0031-9155/59/14/3951) View the table of contents for this issue, or go to the journal homepage for more

Download details: IP Address: 129.101.79.200 This content was downloaded on 13/02/2015 at 12:13

Please note that terms and conditions apply.

Institute of Physics and Engineering in Medicine Phys. Med. Biol. 59 (2014) 3951–3967

Physics in Medicine and Biology

doi:10.1088/0031-9155/59/14/3951

Thermal regulation for APDs in a 1 mm3 resolution clinical PET camera: design, simulation and experimental verification Jinjian Zhai 1,2 , Arne Vandenbroucke 3 and Craig S Levin 3,4,5,6 1

Department of Mechanical Engineering, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA 2 Department of Computer Science, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA 3 Department of Radiology, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA 4 Department of Physics, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA 5 Department of Electrical Engineering, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA 6 Department of Bioengineering, Stanford University, 300 Pasteur Drive, Stanford, CA 94305, USA E-mail: [email protected] Received 29 January 2014, revised 1 May 2014 Accepted for publication 29 May 2014 Published 27 June 2014 Abstract

We are developing a 1 mm3 resolution positron emission tomography camera dedicated to breast imaging. The camera collects high energy photons emitted from radioactively labeled agents introduced in the patients in order to detect molecular signatures of breast cancer. The camera comprises many layers of lutetium yttrium oxyorthosilicate (LYSO) scintillation crystals coupled to position sensitive avalanche photodiodes (PSAPDs). The main objectives of the studies presented in this paper are to investigate the temperature profile of the layers of LYSO–PSAPD detectors (a.k.a. ‘fins’) residing in the camera and to use these results to present the design of the thermal regulation system for the front end of the camera. The study was performed using both experimental methods and simulation. We investigated a design with a heat-dissipating fin. Three fin configurations are tested: fin with Al windows (FwW), fin without R Al windows (FwoW) and fin with alumina windows (FwAW). A Fluent simulation was conducted to study the experimentally inaccessible temperature of the PSAPDs. For the best configuration (FwW), the temperature difference from the center to a point near the edge is 1.0 K when 1.5 A current was 0031-9155/14/143951+17$33.00

© 2014 Institute of Physics and Engineering in Medicine Printed in the UK & the USA 3951

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

applied to the Peltier elements. Those of FwoW and FwAW are 2.6 K and 1.7 K, respectively. We conclude that the design of a heat-dissipating fin configuration with ‘aluminum windows’ (FwW) that borders the scintillation crystal arrays of 16 adjacent detector modules has better heat dissipation capabilities than the design without ‘aluminum windows’ (FwoW) and the design with ‘alumina windows’ (FwAW), respectively. Keywords: temperature, PET, high resolution, Peltier, finite volume method, semiconductor photodetectors, LYSO-PSAPD (Some figures may appear in colour only in the online journal)

1. Introduction Modern positron emission tomography (PET) cameras increasingly make use of solid-state photodetectors such as avalanche photodiodes and solid-state photomultipliers. It is well established that the gain of these devices is strongly temperature dependent. A drifting gain may cause a degraded energy resolution and/or a degraded timing resolution. In this paper we present a method to provide cooling for tightly packed solid-state phototdetectors. We used finite element simulations as a verification of our design as well as experimental measurements. Although the results presented in this paper are focused on the design of a high resolution camera under development in our lab, we believe that the methodology is of interest to the scientific community, especially those groups developing imaging systems based on semiconductor-based photodetectors. Section 1 of the paper discusses the camera under development, its cooling requirement, as well as a brief discussion of thermal regulation methods used in literature. In section 2 we discuss our experimental and simulation methodology. Section 3 presents the results of both the experiment and simulation, and finally we provide a discussion in section 4. 1.1. Configuration of the PET Camera

The 1 mm3 resolution PET system under development in our lab is configured as a dual panel camera. Each panel comprises layers of lutetium yttrium oxyorthosilicate (LYSO) crystals coupled to PSAPDs in a novel arrangement (Lau et al 2009, 2008, Levin 2012, Zhang et al 2007, Reynolds et al 2011). Annihilation radiation enters the layers edge-on as shown by the arrows in figure 1. The crystals generate optical photons upon absorption of 511 keV photons originating from positron annihilation in a patient’s body. The PSAPD collects the scintillation light and converts it to electric charge. The design is shown in the three panels of figure 1. A detector module is depicted in panel A. It comprises a pair of 8 × 8 arrays of 1 mm3 LYSO crystals each coupled to a PSAPD. The PSAPDs are mounted on a Kapton flex circuit covered with Espanex L series liquid crystal polymer (Nippon Steel and Sumitomo Metal ). An alumina (Al2 O3 ) frame is used to prevent high voltage (HV) breakdown and to provide rigidity. 16 of these modules are arranged in columns as indicated in panel B of figure 1. The modules are attached to an aluminum fin (panel A of figure 1) using miniature screws. The fin depicted measures 167.1 mm × 37.6 mm × 0.5 mm. The horizontal pitch of the modules in the lower left picture is 405 mil (or 10.29 mm). 72 detector fins will be stacked to form an imaging head as shown in panel C of figure 1. The vertical pitch of fins is 1.3 mm. The full camera will comprise two such imaging heads. 3952

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Figure 1. The 1 mm3 resolution PET breast imaging system. Panel A shows an LYSO– PSAPD module. Panel B shows an aluminum fin with windows that supports 16 adjacent modules. Panel C depicts an imaging head. The head comprises stacks of the aluminum fins loaded with modules as well as data acquisition (DAQ) boards. A penny is shown in panel B to indicate the scale.

Because many detectors are tightly packed in the imaging head, the only plausible thermal regulation option is to conduct heat to the edge of the imaging head, where thermoelectric coolers (Peltier elements) as well as heat sinks can be positioned. Three fin structures to draw heat from the detectors to the edges were investigated: one using an aluminum fin with windows (FwW), another one using an aluminum fin without windows (FwoW), and the last using an aluminum fin with alumina windows (FwAW). These fins are depicted in panel (a), (b) and (c) of figure 2. Due to the high bias voltage of PSAPDs (in this project −1750 V) and their compact configuration, the grounded fin introduces a potential risk of electrical shorts. We needed to ensure that the assembly of fin and modules could withstand this HV. In order to reduce the risk of HV breakdown, a 10 mil (25.4 μm) thick thermoplastic layer—Polyether ether R ketone (PEEK) (Hammoud et al 1992), was cut to the shape of FwW using LaserCAMM and sandwiched between the fin and the modules. PEEK is a high-temperature thermoplastic insulating material which is stable even when heated up. PEEK polymers are characterized for ac and dc dielectric breakdown in air at temperatures down to 185 K and have a dielectric strength of 4.37 kV mil−1 (under 60 Hz ac) or 7.93 kV mil−1 (under dc) at 185 K in air (Hammoud et al 1992). In addition, it ensures a minimal separation of 20 mils between the fin at 0 V and the top of the PSAPD surface, potentially at −1750 V. According to Paschen’s Law, the breakdown voltage of an air gap of 20 mils is 2750 V, at 1 atm pressure (Paschen 1889, Hourdakis et al 2006). The PEEK layer prevents any direct HV path from the edge of the PSAPD to the fin. Figure 2 also shows a cross section of the entire stack. The aluminum fin is shown as the top layer and is isolated by a PEEK layer from the PSAPDs embedded in an Al2 O3 frame, comprising two layers of Al2 O3 . The risk of electrical shorts is absent in the FwoW and FwAW configurations, hence these do not need a PEEK layer. 3953

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

FwW (a)

FwoW (b)

FwAW (c) Figure 2. Top and side views of aluminum fins and modules. Panel (a) shows the FwW

configuration, which includes the aluminum window structures and the Polyether ether ketone (PEEK). The FwoW configuration in panel (b) does not have any windows or a PEEK layer. Panel (c) displays the FwAW configuration, which has alumina windows (light gray in the side view) but no PEEK layer. The vertical dimensions have been stretched in these drawings to facilitate labeling of the stack up.

Studies (Spanoudaki et al 2010) showed that the introduction of aluminum structures interspersed between the scintillation crystals causes only minimal photon sensitivity reduction and minimal additional Compton scatter. The aluminum fins are cooled from their sides using aluminum sidewalls which are cooled using thermoelectric (Peltier) elements out of field of view. Previous studies (Vandenbroucke et al 2010, Madsen et al 2006) showed that shielding is required to reduce annihilation photon background. Therefore, a layer of tungsten shielding was added between the aluminum sidewalls and the Peltier cooler. The hot sides of the Peltier elements are cooled using liquid-tube-embedded heat sinks as shown in figure 3.

1.2. APD cooling methods

The 1 cm × 1 cm PSAPDs in our system produce about 1 to 2 mW of power when the PSAPDs are fully biased. It is well known that PSAPDs are sensitive to temperature variation (Spanoudaki et al 2008, Vandenbroucke et al 2012). In particular, the gain of PSAPDs varies with temperature. A lower operating temperature increases the mean free path of electron hole pairs created and hence enhances avalanche gain (Ma et al , Despr´es et al 2006, Solovov et al 2003). This is also observed by a decreased leakage current for decreasing temperatures. An unstable PSAPD temperature may impair system performance parameters such as energy and time resolution, as well as the crystal segmentation ability (Vandenbroucke et al 2012, Kim et al 2011). In order to facilitate calibration and feedback methods we prefer a uniform temperature across the imaging head. Our goal therefore is to control the overall temperature as well as the temperature variation on multiple PSAPD modules. 3954

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Figure 3. Illustration of the cooling as located in the ‘Heat Sink’ portion of figure 1. Aluminum fins, aluminum and tungsten sidewalls (for shielding), Peltier elements (embedded between the tungsten sidewall and the heat sink) and the heat sink can be seen from left to right.

In general three types of APD cooling approaches have been used in the past. (1) Chilled dry air. This method is for example used for uniform cooling of PSAPDs in a MR-compatible PET system to cool the detectors to −10 ◦ C (Wu et al 2010, Catana et al 2008). (2) Dry nitrogen gas is used to keep the temperature below −60 ± 1 ◦ C in a PSAPD-based camera detecting 140 keV Gamma Ray in tiny crystals of 0.4 × 0.4 × 4 mm3 CsI(Tl) (Despr´es et al 2007a). A temperature of −20◦ C was used in PSAPD-CsI:Tl scintillator setup using the same cooling method (Kim et al 2009). (3) Peltier elements (thermoelectric coolers) are most commonly used. These were for example used to control the temperature of an APD-based PET scanner for small animal imaging (Lecomte et al 1994). A more complicated cooling system consisting of copper fingers, Peltier elements and a liquid circulation heat sink were used in an avalanche photodiode based gamma camera (Despr´es et al 2007b) and for a 4 × 8 LYSO–APD detector in a small animal PET imaging system (MADPET-II) at 25 ◦ C (Spanoudaki et al 2008). Other systems operated in vacuum also used a water-cooled heat sink and Peltier elements to cool the APD photosensor down to −30 ◦ C (Okusawa et al 2000, 2001). Because of their high sensitivity, good reliability, fast controlling, small volume, and precise adjustment Peltier elements will be used to thermally regulate PSAPDs in our project. We plan to cool the hot side by a liquid circulated heat sink. We used both simulation and experimental methods to research the possible ways to cool PSAPDs. Although the focus of this paper is to study thermal issues associated with our particular system configuration, we expect that the general methodology will be useful to those PET system developers employing novel semiconductor photodetectors such as APDs and silicon photomultipliers in a densely-packed arrangement. While it is true that the DAQ-backend as indicated in panel C of figure 1 also generates heat which needs to be dissipated, the primary focus of this paper is on the performance of the PSAPD cooling. The requirements in terms of stability are less stringent on the backend, where temperature uniformity is less important. We anticipate to dissipate the heat produced by the readout electronics using a copper strip connected to a liquid coolant pipe, as explained in Lau et al (2008). The HV supply electronics are cooled using a method described in Lau et al (2012). 3955

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Figure 4. Fin loaded with LYSO–PSAPD modules in the experimental box. The positions of the six thermocouples (TC) are indicated on the fin. The labels ‘A’ and ‘B’ correspond to the edge ‘A-B’ in figure 5. Two CPU coolers are visible as well.

2. Experimental and simulation methodology 2.1. Experimental methodology

We machined fins using annealed high-strength aluminum alloy (Al-7075). Fins of various designs were manufactured on the computer numerical controlled machine at Stanford University. Subsequently, 16 LYSO–PSAPD modules were attached to the fin using miniature screws. All three types of fin assemblies (FwW, FwoW and FwAW) were loaded with 16 dual LYSO–PSAPD modules which were biased to −1650 V (for FwW and FwoW) and −1725 V (for FwAW). In order to measure the temperature along the fin, thermocouples (TCs) were added at six equidistant points as shown in figure 4. The entire fin, loaded with modules, was embedded in thermal insulation to create an adiabatic system with conrolled input. Temperatures were logged every 4 min until equilibrium was reached. As shown in figure 4, two copper plates underneath the fans were connected to both sides of the fin to transfer heat. Each copper plate was cooled by a Peltier element which was cooled in turn by a CPU cooler. At room temperature (25 ◦ C) and relative humidity of 45%, the dew point of water vapor is 12.3 ◦ C. The entire setup was placed in a sealed dry box lowers the relative humidity of the experimental environment and avoids vapor condensation. The relative humidity was kept around 15%, at which the dew point is −3.44 ◦ C, a temperature which is out of the range of our cooling setup. By keeping temperature well above the dew point, the risk of condensation is significantly reduced. In order to investigate experimental uncertainties, TC errors were determined by measuring the same temperature 30 times each 3 min apart using K-type TCs. A standard deviation of σ = 0.13 K was obtained. The absolute error is estimated to be T = 0.5 K over different measured objects. The experiment with FwAW was performed with a different set of modules from those in the FwW and FwoW measurements. The HV of the modules in the FwAW setup was adjusted until the PSAPD power consumption was equal to the FwW and FwoW at room temperature. Because of process variations, the bias for modules attached to FwAW is larger than those for FwW and FwoW. 3956

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Figure 5. Top-view of the meshing into finite volumes for the leftmost PSAPD (in blue).

Line AB is meshed using exponential intervals. The edge ‘A-B’ corresponds to the ‘A’ and ‘B’ labels in figure 4.

2.2. Simulation methodology

We simulated the heat transfer process using a partial differential equation with source term q:  2  ∂u ∂ u ∂ 2u ∂ 2u (1) + 2 + 2 + q, = αk ∂t ∂x2 ∂y ∂z where u is the temperature and αk is the thermal diffusivity of the material, which is related to thermal conductivity k, density ρ and specific heat c p of the material: κ αk = . (2) ρc p To solve equations (1) and (2) numerically, a finite volume methodology was used. The simulation steps include geometric modeling, meshing and calculation. Three geometric models FwW, FwoW and FwAW were made using 3D Computer Aided Design R R (CAD) software—(Solidworks ) and were meshed in Gambit . The total volumetric meshing consisted of up to 127,182 T-grid tetrahedrons wrapping the nodes of interest. The meshing of PSAPDs in the left most module in the fin is illustrated in figure 5. The A side corresponds to the edge of the aluminum fin, which required finer meshing than the frame at B side to improve performance of the finite volume simulation. Several tests of different meshing sizes were made to balance between the quality (non-singularity) of the results and the required computational time. The finest linear meshing interval in the model was 0.1 mm. Next, these meshed volumes were used as the finite volumes in a computational fluid R , which is based on finite volume methods dynamics using the software package Fluent (Versteeg and Malalasekra 2007). Different initial and boundary conditions (BCs) were set to simulate various experimental conditions. Five BCs were implemented corresponding to the temperatures associated with the five different Peltier currents (PCs) in each implementation. Temperature curves and heat fluxes were generated for analysis. 3. Results 3.1. Experimental results

The cooling experiments with modules were performed on a fin with windows/PEEK (FwW), fin without windows/PEEK (FwoW) and fin with alumina windows (FwAW) as shown in figure 2. The results are presented in figure 6. A temperature gradient is observed along each fin. The thermal gradient increases with increasing PC. The left–right asymmetry in the figure is caused by different thermal barriers at the interface between the fin and copper plates. The thermal gradient is largest for FwoW, smaller for FwAW, and smallest for FwW. A temperature gradient was calculated by subtracting the TC reading at the edge of the fin from the TC reading in the middle and are shown in table 1. Large left(TC3-TC1)–right(TC43957

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

FwW (a)

FwoW (b)

FwAW (c) Figure 6. Experimental measurements of the temperature of FwW (a), FwoW (b) and

FwAW (c) with 16 modules and Peltier cooling (PC = Peltier current). 6 data points on each curve correspond to the six locations (1–6) labeled in figure 4. The left–right asymmetry is caused by different thermal barriers between the fin and the copper plates. Table 1. Experimentally measured temperature differences between first and third as

well as between fourth and sixth thermocouples (TCs) in K and IPSAPD (μA) under high voltage bias for FwW, FwoW and FwAW for five different PCs. Peltier current (A)

0

0.5

0.75

1.0

1.25

1.5

FwW (Bias: −1650 V) IPSAPD (μA) TC3-TC1( K) TC4-TC6( K) IPSAPD (μA) TC3-TC1( K) TC4-TC6( K)

11.2 9.8 9.0 8.4 0.5 0.7 0.9 –a – 0.2 0.4 0.5 FwoW (Bias: −1650 V) 12 9.3 8.3 7.4 – 0.7 1.1 1.4 – 1.3 1.8 2.2

IPSAPD (μA) TC3-TC1( K) TC4-TC6( K)

FwAW (Bias: −1725 V) 11.2 10.1 9.7 9.3 – 0.7 1.1 1.3 – 0.5 1 1.2

a

Temperature difference is negligible when PC is zero. 3958

7.5 1.0 0.7

6.7 1.2 0.8

6.8 1.6 2.7

7.1 1.9 3.2

9 1.6 1.4

8.7 1.7 1.6

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Figure 7. Measured PSAPD power consumptions of FwW, FwoW and FwAW with 16

modules as a function of PC.

TC6) asymmetries are observed. The maximum temperature difference in the FwW is 1.2 K, in the FwoW 3.2 K and in FwAW 1.7 K. FwW has the lowest PSAPD leakage current at 1.5 A PC, indicating the lowest PSAPD temperature. The difference between FwW and FwoW can be explained by a large heat capacity in the FwW due to the larger volume of aluminum metal. The errors for temperature and current are ±0.1 K and ±0.1 μA, respectively. IPSAPD of FwAW is higher because of the higher bias (−1725 V). Figure 7 shows the PSAPD power consumption versus PC. A decrease in power consumption is observed with increasing PC. However, the power consumption at 1.5 A PC for FwoW is higher than at 1.25 A, indicating that we reached the limitation of the cooling method. The cross-over of the current profiles between 0.0 and 0.5 A is due to the influence of the uncontrolled room temperature under small PC.

3.2. Simulation results

Both steady state and transient simulations were performed to analyze the heat transfer. Figure 8 shows the simulated temperature as well as the experimental counterparts (taken from figure 6) along the FwW, FwoW and FwAW for varying cooling power. Because of symmetry, only one half of each configuration was simulated. A good agreement between experiment and simulation is observed, showing that we are able to accurately model the experimental setup. However, the results seem to be more accurate in the cases of (a) FwW and (c) FwAW, where larger volume of the conductive materials are used. An agreement between simulation and experimental results for FwoW under high PC is harder to reach because of the divergence of the temperature measured at the two ends of the fin. The error bars show the spread in experimental data between left and right measurements. Temperature gradient simulations are summarized in the top rows of table 2. The temperature difference from middle to the edge, as shown in the table, is larger than the maximum temperature gradient in the experiment as the latter is associated with the differences between the first and third TCs and the former reflect differences between the center and the edge of the fin. The table also lists the gradients between corresponding TC positions in 3959

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

FwW (a)

FwoW (b)

FwAW (c) Figure 8. Comparison of simulated (curves) and experimental fin temperature profile data (green squares with black edges, and a 1σ error bar) of temperature along the X-axis (defined by the coordinate system in panel B of figure 1) of the FwW (a), FwoW (b) and FwAW (c). The horizontal bars are 1-σ above and below the data points. The blue dots connected by the dashed line correspond to measured data on each half of the full fin (see figure 6 ). Table 2. Simulated temperature difference between the edge and the middle (top rows)

as well as the differences between TC positions (bottom rows), expressed in K, for FwW, FwoW and FwAW for five boundary conditions (BCs). The BCs correspond to the boundary temperatures of FwW, FwoW and FwAW under Peltier current (PC) 0.5 A–1.5 A, respectively. Fin Type\BC

1

2

3

FwW FwoW FwAW

4

0.88 1.24 1.53 1.71 2.18 3.31 4.09 5.20 1.67 2.28 2.47 3.06 Values Comparable to TC3-TC1 and TC4-TC6 FwW 0.45 0.63 0.78 0.87 FwoW 1.02 1.53 2.26 2.37 FwAW 0.82 1.11 1.21 1.49

3960

5 1.91 5.39 3.30 0.97 2.48 1.61

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

FwW (a)

FwoW (b)

FwAW (c)

Picture of FwAW (d)

Figure 9. Simulated overall fin temperature profile in two dimensions over the right half of FwW (a), FwoW (b) and FwAW (c), under the same heating power and BCs. Panel (d) shows a picture of the fin, the alumina windows and the modules which are used in experiments to help interpret the results from the simulated model of FwAW (c). The relative locations of the fin to the modules in FwW (a) and FwoW (b) are similar to those in FwAW (c). The red box in panel (a) shows the position of the PSAPDs in the X–Y plane. The extension visible on the lower right edge in panel (b) is the aluminum fin extending beyond the modules. The temperature of the modules is visible in this panel due to the absence of any window piece (as opposed to FwW and FwAW).

figure 4. As also observed in the experimental data, the temperature gradient of FwW is the smallest among the three configurations, followed by the gradient of the FwAW. The simulated data allows a comparison between the temperature profiles of the three studied cases as shown in figure 9, where profiles are drawn corresponding to the experimental cases at 1.5 A PC for half of the fin. The observed temperature profile is most uniform for FwW, followed by the profile for FwAW, the FwoW configuration is least uniform. The aluminum fin in the FwoW configuration extends beyond the rightmost module as can be seen from panel (b) in the figure. The simulated temperature of the PSAPDs themselves are shown in figure 10 in case of FwW. These temperatures are higher than the surface temperature of the LYSO because the PSAPD is the heat source underneath the LYSO (see figure 2), and LYSO is an excellent thermal insulator. A gradient of 1.5 K is observed across all eight PSAPDs, yet only small variations are observed within one PSAPD. The simulated temperature profile of the PSAPDs are shown in figure 11. The range of temperatures across Y and Z are shown for each position X. The profiles for the FwoW in panel (b) and the FwAW in panel (c) show that the temperature is unevenly distributed across PSAPDs. The figure shows superiority of the FwW for PSAPD cooling because there is no 3961

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Figure 10. Simulated PSAPD temperature profile for the FwW configuration under 1.5 A Peltier current. The position of the PSAPDs in the X–Y plane of the fin is shown as the red box in panel (a) of figure 9.

FwW (a)

FwoW (b)

FwAW (c) Figure 11. The simulated PSAPD temperature along the X-axis of fin with windows (FwW) (a), fin without windows (FwoW) (b) and fin with alumina windows (FwAW) (c). The broad band of the temperature shows the PSAPD temperature along the Y-axis of the fin. The coordinate system is defined in panel B of figure 1.

3962

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

(a)

(b)

Figure 12. Simulated temperatures along half of the X-axis of FwW (a) and FwoW (b)

for −1650 V bias and −1750 V (full) PSAPD bias with 0.5 A current applied to the Peltier elements.

temperature gradient along the Y-axis of the fin when the position on the X-axis is fixed. Both FwoW and FwAW show a temperature gradient across the PSAPDs. FwW does not have a temperature gradient because the aluminum windows are more conductive than air (FwoW) and the alumina windows (FwAW). The previously mentioned results were obtained at a bias of −1650 or −1725 V, which is not the expected operating voltage. Therefore, we estimated the total cooling power needed by implementing a full bias simulation for the FwW and FwoW configurations. The parameters of the full biased simulation were obtained from a power measurement where −1750 V bias was used on single modules. Temperature profiles shown in figure 12 show a 0.5 and 0.25 K temperature rise from −1650 V bias to −1750 V bias for FwW and FwoW, respectively with 0.5 A PC. The maximum outward heat flux through the side of fin, which is defined as ‘cooling power’ in this paper, is 0.15 W per half FwoW, 0.08 W per half FwW and 0.26 W per half FwAW. Thus, the cooling power is 2.4 W(FwoW), 1.3 W(FwW) or 4.1 W(FwAW) for one cartridge, consisting of eight fin layers, and 21.6 W(FwoW), 11.5 W(FwW) or 37.0 W(FwAW) for one panel consisting of nine cartridges. Another practical issue in clinical PET systems is the time it takes to reach equilibrium when switching the HV on. To assess this issue, transient thermal studies were simulated in which the temperature of the PET panel was initialized to an equilibrium of about 300 K. Then 1700 V HV was applied and a cooling power of 1.5 A PC was added. The maximal PSAPD temperature was calculated for each step until the infinite steady state was reached. Results in figure 13 show that after 12 min the PSAPDs of FwoW achieve 74% of the total temperature drop (from about 300 K to the equilibrium at t = ∞), while those of FwW reach 85% of the total temperature drop, showing the superiority of FwW. The equilibrium time is acceptable in preparation of a clinical scan and can be accelerated by additional cooling power. In order to study the influence of the PEEK layer on the cooling, a simulation was run where PEEK was replaced by aluminum. Additionally, we also wanted to investigate the influence of replacing the alumina in the LSO-PSAPD modules by AlN, which has superior thermal conductivity. The simulation developed within this framework allows comparison of the temperature profiles of PSAPDs before expensive and time consuming manufacturing and experimental procedures are implemented. The thermal conductivity of the materials under study is shown in table 3. The three configurations are shown in figure 14. All simulations assumed full bias (−1750 V). 3963

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Figure 13. Simulated transient maximum temperature of PSAPDs on FwoW and FwW after switching to −1700 V PSAPD bias (cooled by Peltier with 1.5 A current). The dashed horizontal lines show the temperature after thermal equilibrium is established.

(a)

(b )

(c)

Figure 14. An end on view of the FwW configuration (a) and two other hypothetical

configurations studied: (b) replacing PEEK in (a) by aluminum and (c) replacing alumina in (b) by aluminum nitride. Table 3. Comparison of the thermal conductivity of various materials used in our design.

Material

Value (W/(m · K))

Al2 O3 Al PEEK AlN

27.5 237 0.25 140–185

Figure 15 shows that the temperature of the configuration with AlN layer, which is shown in panel (c) of figure 14, is the lowest of all studied configurations. The temperature difference in the middle of the PSAPD between curve 1 and curve 3 is 0.17 K as shown in panel (b) in figure 15. The 0.17 K drop of maximum temperature is about 15% of the gradient between center and edge of the FwW of all three curves, which is a significant decrease in percentage of PSAPD temperature profile. The temperature gradient is also 10% smaller in curve 3 (green curve) compared to curve 1 (red curve). The results show a superior performance when using thermal conductors such as AlN and Al. However, the performance degradation (higher temperature) when using a PEEK layer and Al2 O3 frames is acceptable from studies of the effect of temperature on PSAPD performance (Lau et al 2012). 3964

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

(a)

(b)

Figure 15. Simulated temperature profiles of fins (a) and PSAPDs (b) along half of the

X-axis of FwW for the configuration of figure 2 (curve 1), for the case of replacing PEEK by an aluminum layer (curve 2) and for the case of replacing Al2 O3 by AlN layer (curve 3) at full bias.

4. Discussion and conclusion The PSAPD cooling for a dedicated breast PET camera was developed in this work. Dense packing of PSAPD modules enforces a thermal regulation design comprising heat conduction to the sides, where thermoelectric elements are positioned. In this paper we focused on studying the temperature gradient across one fin to understand the heat dissipation efficacy of the different fin structure designs. Any gradients produced among fins when multiple fins are stacked on top of each other will be studied in future work. Three different fin configurations were analyzed (see figure 2), one is heat dissipation by a fin with windows/PEEK (FwW), one by a fin without windows/PEEK (FwoW) and the last by a fin with alumina windows (FwAW). We examined the design for one layer of detector modules experimentally (figure 6) and predicted the temperature profile of PSAPDs under different boundary conditions in simulations (figure 9). Due to the complex nature of the problem, an analytical solution was impossible to achieve. Instead, asymptotic solutions were calculated and compared with the temperature gradient measured from experiments, which agrees well with our simulations (e.g. see figure 8). The simulation predicts the temperature profile of PSAPDs and verifies the design of aluminum fin/PEEK structure for the thermal regulation system. We conclude that the design of the FwW housing with 16 adjacent detector modules has best heat dissipation performance. We measured a temperature difference between our thermocouple positions of 0.97 K in simulation and 1.0 K in experiment (figure 8). The total cooling power is 0.15 W per side of FwoW, 0.08 W per side of FwW and 0.26 W per side of FwAW when the PSAPDs are fully biased (figure 9). Due to the proximity of Al near high voltage surfaces (figure 2), we found that the FwW configuration is more susceptible to high voltage breakdown and so it was not selected as the final configuration. Finally, we tested the influence of using a thermally and electrically insulating PEEK layer in the design as well as the potential use of AlN instead of Al2 O3 (figure 14). We observe a small performance degradation when using PEEK and a 10% increase when using alumina instead of AlN. Although these results are specific to our particular PET camera design, the thermal regulation design considerations, the methods for studying the thermal gradient, and 3965

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

the results are useful for other system designs employing a densely-packed arrangement of semiconductor-based detectors. In order to fully benefit from the implementation of thermoelectric elements in the camera, a feedback control loop is desired. We intend to include small thermistors in each individual fin and read these out using a Kapton flex circuit. In addition, the direct relation between temperature and PSAPD leakage current allows one to determine temperature variations by observing leakage currents. We believe that the leakage current in combination with the thermistor readout will yield enough information to implement an adequate feedback loop. Acknowledgments This work was supported by United States National Institute of Health (NIH) grants NIH-NCI R01 CA119056, NIH-NCI R01 CA119056-S1 (ARRA), Fellowship of China Scholarship Council and United States Department of Defense grant DOD BC094158. The simulation was performed on software in the Computer Lab of Mechanical Engineering Department of Stanford University. We are thankful for the help of F Lau, V Spanoudaki and D Innes from the Molecular Imaging Instrumentation Laboratory (MIIL), and R Farrell from Radiation R ), Inc. during the experiment. Monitoring Devices (RMD References Catana C, Procissi D, Wu Y, Judenhofer M, Qi J, Pichler B, Jacobs R and Cherry S 2008 Simultaneous in vivo positron emission tomography and magnetic resonance imaging Proc. Natl. Acad. Sci. USA 105 3705–10 Despr´es P, Barber W, Funk T, McClish M, Shah K and Hasegawa B 2006 Investigation of a continuous crystal PSAPD-based gamma camera IEEE Trans. Nucl. Sci. 53 1643–9 Despr´es P, Barber W, Funk T, McClish M, Shah K and Hasegawa B 2007a Modeling and correction of spatial distortion in position-sensitive avalanche photodiodes IEEE Trans. Nucl. Sci. 54 23–9 Despr´es P, Funk T, Shah K and Hasegawa B 2007b Monte Carlo simulations of compact gamma cameras based on avalanche photodiodes Phys. Med. Biol. 52 3057–74 Hammoud A, Baumann E, Overton E, Myers I, Suthar J, Khachen W and Laghari J 1992 High temperature dielectric properties of Apical, Kapton, Peek, Teflon A F, and Upilex polymers NASA Technical Memorandum p 8 (http://catalogue.nla.gov.au/Record/4050298) Hourdakis E, Simonds B J and Zimmerman N M 2006 Submicron gap capacitor for measurement of breakdown voltage in air Rev. Sci. Instrum. 77 4702–8 Kim S, McClish M, Alhassen F, Seo Y, Shah K S and Gould R G 2011 Temperature dependent operation of PSAPD-based compact gamma camera for SPECT imaging IEEE Trans. Nucl. Sci. 58 2169–74 Kim S, Shah K, McClish M, Seo Y and Gould R 2009 Phantom experiments on a compact gamma camera based on a position-sensitive avalanche photodiode J. Nucl. Med. 50 1534 (Suppl. 2) Lau F W Y, Fang C, Reynolds P D, Olcott P D, Vandenbroucke A, Olutade F, Horowitz M A and Levin C 2008 1 mm3 resolution breast-dedicated PET system Conf. Record of IEEE NSS-MIC pp 5619–22 Lau F W Y, Vandenbroucke A, Reynolds P D, Olcott P D, Horowitz M A and Levin C S 2010 Analog signal multiplexing for PSAPD-based PET detectors: simulation and experimental validation Phys. Med. Biol. 55 7149–74 Lau F W Y, Yeom J Y, Vandenbroucke A, Innes D and Levin C S 2012 A cost-effective modular programmable HV distribution system for photodetectors Conf. Record of IEEE NSSMIC pp 3504–6 Lecomte R, Cadorette J, Richard P, Rodrigue S and Rouleau D 1994 Design and engineering aspects of a high resolution positron tomography for small animal imaging IEEE Trans. Nucl. Sci. 41 1446–52 Levin C S 2012 Promising new photon detection concepts for high-resolution clinical and preclinical PET J. Nucl. Med. 53 167–70 Ma Q, Nathan A and Murthy R 1999 Ito/A-Si:H Schottky photodiode with low leakage current and high stability MRS Proceedings 558 231 3966

J Zhai et al

Phys. Med. Biol. 59 (2014) 3951

Madsen M T, Anderson J A, Halama J R, Kleck J, Simpkin D J, Votaw J R, Wendt III R E and Williams L E 2006 AAPM task group 108: PET and PET/CT shielding requirements Med. Phys. 33 4–15 Nippon Steel and Sumitomo Metal 2014, Tokyo, Japan http://www.nssmc.com/en/product/use/elect/ top_ele_steel_homeele/resin/espanex.html Okusawa T, Sasayama Y, Yamasaki M and Yoshida T 2000 Readout of a scintillating fiber array by avalanche photodiodes Nucl. Instrum. Methods Phys. Res. A 440 348–54 Okusawa T, Sasayama Y, Yamasaki M and Yoshida T 2001 Readout of a 3 m long scintillating fiber by an avalanche photodiode Nucl. Instrum. Methods Phys. Res. A 459 440–7 Paschen F 1889 Ueber die zum Funkenubergang in Luft, Wasserstoff und Kohlensaure bei verschiedenen Drucken erforderliche Potentialdifferenz Ann. Phys. Lpz. 273 69–96 Reynolds P D, Olcott P D, Pratx G, Lau F W Y and Levin C S 2011 Convex optimization of coincidence time resolution for a high-resolution PET system IEEE Trans. Med. Imaging 30 391–400 Solovov V N, Neves F, Chepel V, Lopes M I, Marques R F and Policarpo A J P L 2003 Low-temperature performance of a large area avalanche photodiode Nucl. Instrum. Methods Phys. Res. Sect. A 504 53–7 Spanoudaki V C, Lau F W Y, Vandenbroucke A and Levin C S 2010 Physical effects of mechanical design parameters on photon sensitivity and spatial resolution performance of a breast-dedicated PET system Med. Phys. 37 5838–49 Spanoudaki V, McElroy D, Torres-Espallardo I and Ziegler S 2008 Effect of temperature on the performance of proportional APD-based modules for gamma ray detection in positron emission tomography IEEE Trans. Nucl. Sci. 55 469 Vandenbroucke A et al 2012 Influence of temperature and bias voltage on the performance of a high resolution PET detector built with position sensitive avalanche photodiodes J. Instrum. 7 P08 001 Vandenbroucke A, Innes D and Levin C S 2010 Effects of external shielding on the performance of a 1 mm3 resolution breast PET camera Conf. Record of IEEE NSS-MIC pp 3644–8 Versteeg H and Malalasekra W 2007 An Introduction to Computational Fluid Dynamics: The Finite Volume Method Approach (Englewood Cliffs, NJ: Prentice Hall) Wu Y, Yang Y, Bec J and Cherry S R 2010 A DOI-capable MR-compatible PET insert for simultaneous PET/MRI imaging World Molecular Imaging Congress (presentation number 0113, scientific session 12) Zhang J, Olcott P D, Chinn G, Foudray A M K and Levin C S 2007 Study of the performance of a novel 1 × 6 × 8 mm resolution dual-panel PET camera design dedicated to breast cancer imaging using Monte Carlo simulation Med. Phys. 34 689–702

3967