Betabox: a beta particle imaging system based on a position sensitive avalanche photodiode

The Radiation Monitoring Devices (RMD, Watertown, MA) PSAPD Model P1305-P has a compact design and 4-channel position readout (Shah et al 2002). The PSAPD measures 14 × 14 mm² and has a p-layer thickness of 60 µm, of which 40 µm is depleted when a reverse bias voltage is applied (figure 1(a)). At a room temperature of 21 °C the device was operated with the anodes at a bias voltage of +1750 V, for a gain of approximately 1000 and a leakage current of 1 µA. For isotopes such as ¹⁸F, the positrons eventually produce two 511 keV photons by annihilation. The probability of detecting 511 keV gamma rays through the 60 µm of silicon is less than 0.1%. Gamma ray contribution was therefore ignored in the subsequent counting measurements.

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This work utilizes compact custom built printed circuit boards (PCBs) for the readout electronics, in contrast to earlier work which heavily relied on nuclear instrumentation modules (Fang et al 2010, Vu et al 2011) (figures 1(b) and (c)). In addition to the 4 position outputs encoded from the anodes, the PSAPD has a 5th output from the common cathode that measures the total charge collected. In this new design, the 5 outputs of the PSAPD first pass through high speed field-effect transistor input op-amps configured as transimpedance preamplifiers with a 100 ns RC time constant. This is a significant development over past approaches using charge sensitive preamplifiers (Cremat CR-110, Watertown, MA) as we wanted to optimize count rate performance (Dooraghi et al 2011). The input stage feedback network values were selected so that the resistor would provide the highest conversion gain possible and still allow for a finite parallel capacitance necessary to compensate for the large PSAPD junction capacitance (∼150 pF) and maintain circuit stability. This is followed by a gain stage to provide for volt-level signals, and then shaping amplifiers (shaping time: 500ns) (figure 1(d)). The shaped sum signal then passes to a threshold comparator. The trigger pulse output of the threshold comparator is delayed in order to align with the peak of the position channels. The delayed trigger is fed to four sample and hold (S/H) circuits (53ns acquisition time, 6 µs hold time) that maintain the peak voltage of the position channels. The delayed trigger also initiates an analog to digital conversion of the sampled position channel voltages using a DT9816-A ECON Series simultaneous sampling data acquisition system (Data Translation, Marlboro, MA), which has a maximum sampling rate of 150 kS s⁻¹ (figure 1(e)).

Due to nonlinearity along the edges of the PSAPD, significant pincushion distortion occurs in the image when using the traditional Anger logic (Després et al 2007). A modified Anger-like algorithm was used, which employs the pairs of diagonal channels and has been shown to reduce the pincushion distortion (Zhang et al 2007).

Since this work focuses on only beta particle detection, unless otherwise stated, the PSAPD was covered with two layers of 0.3 µm of aluminum on 3 µm of Mylar film in order to block ambient light, and an additional film of 3 µm of transparent Mylar to serve as a protective layer. The covering to block out light and protect the device from damage is referred to as the passivation layer for the PSAPD.

¹⁸F was produced at UCLA using an RDS-111 cyclotron (Siemens Molecular Imaging, Koxville, TN). A NIST traceable ⁵⁵Fe source (∼5 mm diameter, 1900 Bq), which emits monoenergetic 5.9 keV x-rays, was used to calibrate the energy spectrum. A NIST traceable ²⁰⁴Tl (∼5 mm diameter, 1244 Bq) point source was used to correct for temperature dependent gain differences of the PSAPD, as well as to measure sensitivity. The ²⁰⁴Tl source was selected as it is an electron emitter with similar average and maximum energy (245 and 764 keV, respectively) as ¹⁸F (243keV and 634keV) but with a much longer half-life of 3.8 years.

The use of an inkjet printer to produce radioactive phantoms for quality assurance purposes has been shown to be reliable and inexpensive (van Staden et al 2007). While the density of the paper and the depth of the positron source inside the paper are not an exact match for microfluidic circuits, this method is analogous to the use of lucite or water phantoms to simulate soft tissues for high energy photon or charged particle tracking. These measurements introduce a level of bias, but can be used to understand basic device functionality or the effects of physical processes. Phantoms were designed using desktop drawing software and printed using a PIXMA iP4700 inkjet printer (Canon, Tokyo, Japan) on glossy photographic paper to access spatial resolution, spatial distortion, efficiency, and count rate. To determine printing reliability, the printed radioactive density as a function of total printed area was examined. A total of 32 MBq was diluted in ∼3 mL of ink and the solution was introduced into an empty ink cartridge. A printed area of 25 mm² was sampled for every 425 mm² region and its radioactivity measured in a Model 1480 Wizard 3'' calibrated well-type gamma counter (Perkin Elmer, Waltham, MA). The printed radioactive density was decay corrected to the time of measurement of the injected radioactive concentration. The ratio of decay corrected printed radioactive density (Bq mm⁻²) to initial radioactive concentration (Bq nl^–1) was determined for each data sample and plotted as a function of total printed area (figure 2). The average ratio value was determined to be ∼13 nl mm⁻² with a per cent standard deviation of less than 2%. The ink soaked into the photographic quality paper approximately 7 µm deep, as measured by a microscope (data not shown).

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Even after the implementation of the modified Anger logic, the PSAPD exhibits increasing distortion further from the center of the device due to the four corner anode design and the logic used for producing the images (Zhang et al 2007). This pattern is expected to be distinct for each device, but constant, given the same operating parameters. To correct for this remaining distortion, nonlinearity maps are generated from measurements for each device.

To generate the nonlinearity correction maps, we performed the following steps:

• (1)  
  Create a known dot pattern printed phantom
• (2)  
  Align and image the known pattern on Betabox
• (3)  
  Correlate control points on the image with their known x and y coordinate locations
• (4)  
  Interpolate between known control points to estimate the correction for the entire image space

The interpolation method selected is Laplace interpolation (Press et al 2007) which is a more general form of bilinear interpolation that is easily applied to unevenly spaced control points (Sukumar 2003). The end results are x and y correction look up tables that give the corrected x and y coordinates x_cor and y_cor in terms of the distorted locations x_dis and y_dis:

$$\begin{equation} x_{{\rm cor}} = F_x ( {x_{{\rm dis}} ,y_{{\rm dis}} } ) \end{equation} \tag{ 1 }$$

$$\begin{equation} y_{{\rm cor}} = F_y ( {x_{{\rm dis}} ,y_{{\rm dis}} } ) \end{equation} \tag{ 2 }$$

These nonlinearity correction look up tables are then applied to the result of the positioning algorithm before creating a 2D histogram to display the image. Figure 3 shows the result of imaging an array of ∼0.3 mm printed dots (pitch 1.55 mm) containing ¹⁸F using the modified Anger positioning logic with and without distortion correction applied. The pixel size was set to 62 × 62 µm². The pixel size was selected in order to have adequate sampling points to access spatial resolution.

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The microfluidic chip used in this study was made from a low cost polymer, polydimethylsiloxane (PDMS) (Duffy et al 1998). PDMS is a soft semi-porous material that allows the exchange of gases, but is impermeable to liquids. This makes PDMS microfluidic chips ideal for biological applications such as cell incubation. Figure 4 shows a schematic and image of our current PDMS chip design. Each chip contains five microchannels. Each microchannel consists of an inlet port for cell loading and reagent delivery via pipette, a bubble depletion region to minimize trapped air that can prevent flow within the microchannel, four cell capture chambers connected serially, and an outlet. Each cell capture chamber is 1 mm in width, 0.5 mm in height and 0.25 mm in depth, with a 0.8 mm separation between chambers. Each microchannel is separated from its neighbor by 2.0 mm, an adequate distance to avoid spillover effects between channels during measurements with ¹⁸F. Connections leading to chambers and between chambers have a cross section of 40 × 250 µm². The bottom layer of the chip, which is in contact with the passivated PSAPD, is 50 µm and is also made of PDMS. Further details on the design and fabrication of these chips will be published elsewhere.

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Figure 5 shows the measured ⁵⁵Fe energy histogram plotted alongside that of ¹⁸F. The ⁵⁵Fe x-ray energy resolution was measured to be 2.4 keV full width half maximum (FWHM). ¹⁸F emits positrons in a continuous energy spectrum with an average energy of 243 keV. The detection layer of the PSAPD is approximately 60 µm thick. This thin layer is insufficient to completely stop the ¹⁸F positrons as they traverse through the detector. Instead they deposit a fraction of their kinetic energy. For ¹⁸F positrons, the average energy deposited in the PSAPD was measured to be 58 keV when the source was placed directly on top of the unpassivated PSAPD. Figure 5 shows that a low energy threshold of 4 keV could be used to discriminate against most of the low energy noise from the PSAPD as shot noise due to the capacitance produced from the surface area of the device (Kim et al 2011) and readout electronics. All subsequent measurements in this work were performed with an energy threshold of 4 keV.

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Due to the ∼1000 fold gain of the PSAPD (Shah et al 2002) and the relatively large amount of energy deposited by beta particles such as ¹⁸F positrons, an energy threshold could be set to exclude most of the background noise. Figure 6 shows the background energy spectrum acquired in the entire device over a period of 72 h at a room temperature of 21 °C (see supplementary figure 1 for further illustration, available from stacks.iop.org/PMB/58/3739/mmedia). The background count rate of the PSAPD was measured to be 1.4 cph mm⁻². As mammalian cells prefer an environmental temperature of 37 °C, operation of the PSAPD at 37 °C may be optimal for biological experiments. Consequently, the background rate at 37 °C was also investigated and found to modestly increase to 1.9 cph mm⁻². The majority of the increase in counts originates just above the 4 keV threshold and can be removed with a modest increase in threshold. Since the PSAPD gain decreases with increasing temperature (Spanoudaki et al 2008), prior to the background measurement at this elevated temperature, the high voltage was increased to +1775 V. This voltage was selected by closely matching the measured ²⁰⁴Tl energy spectrum at 37 °C with the energy spectrum measured at 21 °C and + 1750 V, thereby correcting gain effects due to temperature (see supplementary figure 2, available from stacks.iop.org/PMB/58/3739/mmedia). The expected background rate due only to cosmic ray events on the PSAPD was estimated to be approximately 0.6 cph mm⁻² (Knoll 2000). Further study is necessary to determine the relative contributions of cosmic rays, terrestrial environmental radiation and electronic noise to the PSAPD background count rate.

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A phantom line source was used to examine the position dependence of the spatial resolution of the PSAPD. The line source was approximately 110 µm wide and was placed over the protective Mylar film. Figure 7(a) shows an image acquired at 21 °C with the line source centrally positioned, as well as 1.6 mm, 3.3 mm and 4.4 mm away from center. The inset shows the central horizontal profile. A plot of the measured FWHM as a function of offset distance is shown in figure 7(b). Within 3 mm of the image center, the line profile resolution is better than 500 µm FWHM. Toward the edge of the PSAPD, 5 mm from the center, the line profile resolution degrades significantly to ∼1 mm FWHM. Measurements conducted at 37 °C demonstrate similar behavior. The intrinsic spatial resolution of the PSAPD has been reported to be 300 µm FWHM at the image center when measured with a high intensity light source (Shah et al 2002), in agreement with these measurements.

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Current microfluidic system designs being developed for Betabox applications use a PDMS substrate layer onto which cells are incubated, and this layer affects the measured spatial resolution. Using layers of thin low density polyethylene (LDPE) film, the spatial resolution was evaluated as a function of substrate thickness. The LDPE film was placed between the line source and the sacrificial Mylar film. Each layer of LDPE film had a thickness of 15.7 µm with a density of 0.92 g cm⁻³, which is similar to the density of PDMS (0.96 g cm⁻³). The line source was positioned at the center of the device over varying layers of LDPE. A plot of the FWHM as a function of LDPE thickness is shown in figure 7(c). At the image center, the line profile FWHM was measured to be 400 µm when the source was placed directly on top of the passivated detector. As the source to detector distance was increased by adding layers of LDPE material, the line profile FWHM degraded by approximately 180 µm for every 100 µm of LDPE.

The source to detector distance degrades not only the spatial resolution of the PSAPD for beta particle detection, but also the sensitivity. Larger source to detector distances and higher density materials will attenuate the beta particles more as they traverse through. The absolute efficiency of the PSAPD detector was measured using the ²⁰⁴Tl source. The source to detector distance was again varied by using layers of LDPE film. Figure 8(a) shows the absolute efficiency as a function of LDPE film thickness. If the source was placed in direct contact with the PSAPD top surface, the absolute sensitivity, including the geometrical factor, would approach 50%. Given that positrons are emitted randomly and have an equal probability to be emitted toward or away from the detector, these results indicate that if a charged particle traverses the depletion layer of the detector, its detection would be almost certain.

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An important parameter of any imaging system is the uniformity of response over the field of view (FOV) of the camera. Therefore, the sensitivity was measured as a function of position on the PSAPD FOV. An array of 4 × 4 ¹⁸F-ink sources was printed on photographic paper (diameter ∼0.5 mm, pitch 3.1 mm). Figure 8(b) shows the PSAPD image of the 4 × 4 printed sources after applying the spatial distortion correction. The radioactivity of each individual FDG-ink source was measured using a Model 1480 Wizard 3'' calibrated well-type gamma counter (Perkin Elmer, Waltham, MA). The average absolute sensitivity measured for all the sources was 46% ± 1% (figure 8(c)). Excluding the 50% geometric efficiency of the detector, the intrinsic efficiency of Betabox is 92% ± 2%. This indicates that for this specific application, the Betabox performance is approaching the physical limits.

The lower detection limit (LDL), in units of cps mm⁻², was determined by requiring a minimum per pixel signal to noise ratio of 5 as necessitated by the Rose Criterion (Cherry et al 2003). Thus the LDL is given as:

$$\begin{equation} {\rm LDL} = \frac{{5R\sigma _{bg} }}{T} \end{equation} \tag{ 3 }$$

where σ_bg is the standard deviation of the background counts for a specified acquisition time measured in one pixel, T is the acquisition time in seconds, and R is the pixel per area factor.

To measure the LDL, a uniformly printed ¹⁸F-ink flood source was placed directly on top of the passivated PSAPD and allowed to decay over time. The initial radioactivity of the printed plane source was measured using a Model 1480 Wizard 3'' gamma counter (Perkin Elmer, Waltham, MA). Acquisitions of 1 min duration were taken sequentially as the source decayed on the protected PSAPD. An 18.8 mm² region of interest (ROI) was then drawn at the center of each image. The background counts in the ROI measured independently for the same acquisition time were also subtracted. Figure 9 shows the net detected count rate per area as a function of the known radioactivity per area. In the calculation of LDL from equation 3, only statistical fluctuation in background was assumed so that σ_bg is equal to $\sqrt {N_{{\rm bg}} }$ where N_bg is the average number of background counts per pixel for a 60 s acquisition. Given this background rate, LDL was measured to be of 0.2 cps mm⁻² for a 1 min acquisition and 62 × 62 µm pixel size. Taking into account the sensitivity of Betabox and the branching fraction of positron emission for ¹⁸F, the LDL for 1 min measurements was determined to be 0.5 Bq mm⁻². The dotted vertical line represents this calculated LDL.

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In order to measure dead time, an ¹⁸F source was placed on the camera system and allowed to decay (figure 10). A nonparalyzable dead time model was then used to estimate dead time using:

$$\begin{equation} me^{\lambda t} = - n_0 \tau m + n_0 \end{equation} \tag{ 4 }$$

where m is the measured count rate, λ is the decay constant, τ is the dead time, n₀ is the initial true count rate, and t is the elapsed time from initial measurement (Knoll 2000). The dead time from fitting to the model was determined to be 6.5 µs, which is in agreement with the nominal dead time of 6 µs set by the sample and hold circuit parameters.

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Count rate induced image distortion was examined with two hot spots (diameter ∼1.6 mm) of approximately the same radioactivity of ¹⁸F separated by 5 mm. Figure 11(a) shows a sample image at a measured count rate of 102 000 cps. Figure 11(b) shows the resulting image with count rates <1000 cps. The chi square distortion metric was calculated using (Press et al 2007):

$$\begin{equation} \chi ^2 = \sum {\frac{{\left( {\sqrt {\frac{R}{S}}S_i - \sqrt {\frac{S}{R}}R_i } \right)^2 }}{{S_i + R_i }}} \end{equation} \tag{ 5 }$$

where S_i is the number of events in pixel i for the sample high count rate data set, R_i is the number of events in pixel i for the reference low count rate data set, S = ∑S_iand R = ∑R_i. The metric was used to determine the count rate at which distortion became statistically significant (5% probability level). Spatial distortion reached statistical significance at 21 000 cps (figures 11(c) and (d)). With an ¹⁸F source placed directly on the protected PSAPD, this corresponds to 55 kBq after correcting for the isotope branching fraction, system sensitivity and dead time. Since most probe uptake experiments to date (Fang et al 2010, Vu et al 2011) were performed at count rates below 5000 cps, an upper count rate limit of 21 000 cps should not affect practical experiments.

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Four microchannels were filled with progressively lower radioactive concentrations of ¹⁸F in an aqueous solution, while the fifth microchannel was left unfilled. Radioactive concentrations were prepared at ratios of 1.00:0.50:0.33:0.25 with values at start of imaging 5.2, 2.7, 1.7 and 1.3 kBq µL⁻¹ as measured using a Model 1480 Wizard 3'' gamma counter (Perkin Elmer, Waltham, MA) (figures 12(a) and (b). ROIs encompassing a region of 1.0 mm × 0.5 mm were drawn over each cell culture chamber on the acquired image. The ROI values were averaged and plotted as a function of initial ¹⁸F concentration in figure 12(c) to demonstrate the imaging linearity of the Betabox system in conjunction with a microfluidic cell culture chip.

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