Setup and characterisation according to NEMA NU 4 of the phenoPET scanner, a PET system dedicated for plant sciences

Objective. The phenoPET system is a plant dedicated positron emission tomography (PET) scanner consisting of fully digital photo multipliers with lutetium–yttrium oxyorthosilicate crystals and located inside a custom climate chamber. Here, we present the setup of phenoPET, its data processing and image reconstruction together with its performance. Approach. The performance characterization follows the national electrical manufacturers association (NEMA) standard for small animal PET systems with a number of adoptions due to the vertical oriented bore of a PET for plant sciences. In addition temperature stability and spatial resolution with a hot rod phantom are addressed. Main results. The spatial resolution for a 22Na point source at a radial distance of 5 mm to the center of the field-of-view (FOV) is 1.45 mm, 0.82 mm and 1.88 mm with filtered back projection in radial, tangential and axial direction, respectively. A hot rod phantom with 18F gives a spatial resolution of up to 1.6 mm. The peak noise-equivalent count rates are 550 kcps @ 35.08 MBq, 308 kcps @ 33 MBq and 45 kcps @ 40.60 MBq for the mouse, rat and monkey size scatter phantoms, respectively. The scatter fractions for these phantoms are 12.63%, 22.64% and 55.90%. We observe a peak sensitivity of up to 3.6% and a total sensitivity of up to S A,tot = 2.17%. For the NEMA image quality phantom we observe a uniformity of %STD = 4.22% with ordinary Poisson maximum likelihood expectation-maximization with 52 iterations. Here, recovery coefficients of 0.12, 0.64, 0.89, 0.93 and 0.91 for 1 mm, 2 mm, 3 mm, 4 mm and 5 mm rods are obtained and spill-over ratios of 0.08 and 0.14 for the water-filled and air-filled inserts, respectively. Significance. The phenoPET and its laboratory are now in routine operation for the administration of [11C]CO2 and non-invasive measurement of transport and allocation of 11C-labelled photoassimilates in plants.


Introduction
Positron emission tomography (PET) is widely used in clinical and pre-clinical studies for non-invasive imaging of tracer transport and allocation.A less known area of application is in the field of plant sciences.For example, the exposure of 11 C labeled CO 2 (short: [ 11 C]CO 2 ) to a plant's leaf allows the labeling of photo-assimilates, the products of photosynthesis, and the in vivo measurement of their transport and allocation.Subsequently, PET allows 3D and temporally resolved measurements of the shoot and especially non-invasive measurements of the root system as well as below ground fruits and organs (Jahnke et al 2009, Metzner et al 2022).
The distribution of radioactive tracers can be obtained from a destructive harvest of a plant (e.g.Pb by Hevesy (1923) or 11 C by Ruben et al (1939), Waller et al (2020)).The first in vivo measurements were then conducted with collimated detectors (Moorby et al 1963, Magnuson et al 1982, Jahnke et al 1989).The next technological step was the introduction of position sensitive detector arrays to obtain 2D-projections of the activity distribution (Kiyomiya et al 2001, Kiser et al 2008, Weisenberger et al 2009).In the recent years plant dedicated PET system have been developed (Beer et al 2010, Wang et al 2014, Chang et al 2018, Kurita et al 2019).In addition, measurements of plants were performed at clinical (e.g.These isotopes are transported by one of the two long distance transport system of a plant.The phloem transports photo-assimilates from source leaves to different sinks like growing leaves, roots or fruits.Xylem is the second transport system and transports water and nutrients from the root system to the rest of the plant.Magnetic Resonance Imaging (MRI) can be used for non-invasive measurements of the water flow in xylem and phloem, while the latter is a greater challenge due to much lower velocities (Windt et al 2006).In addition, PET images can be coregistered with MRI images as well as x-ray computer tomography (CT) to obtain structural information of the plant (Jahnke et al 2009, Garbout et al 2012).
The application of radio tracers like [ 11 C]CO 2 in plant sciences provides a number of challenges and opportunities.While most other PET scanners have a horizontal bore, a vertical bore allows the measurement of plants in their natural orientation.To provide controlled conditions it is desirable to place the PET system inside a climate chamber.While the short half life of 11 C of approximately 20 min allows repetitive labeling for the investigation of short term processes it also hinders the investigation of longer processes and requires onsite tracer production.The application of [ 11 C]CO 2 requires a controlled atmosphere around a single leaf or a complete shoot.We mount transparent labeling chambers, called cuvettes, to provide the light required for photosynthesis and ensure a high level of air-tightness to contain the radioactivity without damaging the plant.The closed system allows the circulation of the [ 11 C]CO 2 .Measurement wise, thin structures of plants can lead to escaping positrons.The escaping positrons do not only reduce the measured activity at the original location, they can also annihilate on other parts of the plant, leading to false positive tracer signals at these locations.For thin structures and transport pathways close to the surface, a major part of the positrons are affected.(Alexoff et al 2011), for example, reported a loss of 64 ± 4.4% of positrons for 11 C from a tabacco leaf.The systematic underestimation of the tracer allocated in a leaf remains nevertheless proportional to the actual activity (Partelová et al 2016) and allows the analysis of flow velocities (Converse et al 2015).Escaping positrons are still a matter of current research (Partelová et al 2016, Galieni et al 2021).A possible non-invasive correction method has been demonstrated with MRI/PET systems (Scheins et al 2017).In below ground measurements escaping positrons are less critical as the growth medium usually stops them close to the plant.Despite these challenges, plants have been investigated using PET systems for over a decade.
After several years of experience with our first generation system PlanTIS (field-of-view (FOV) diameter 70 mm and height 108 mm, total sensitivity S A,tot = 0.24%, (Streun et al 2007, Beer et al 2010, Michel 2011)) we developed phenoPET (for phenotyping PET) as a successor with a larger FOV and a higher sensitivity.In addition phenoPET incorporates the possibility for transmission scans of individual plants to correct the effects of attenuation and scattering.PlanTIS did not provided the possibility to measure attenuation maps as required for quantification.This enables us to measure larger shoots with attached leaf cuvettes as well as larger pots for roots and below ground fruits.The latter allows the measurement of plants without detrimental effects due to limited space (Poorter et al 2012).A long term goal is the complete, high-resolution recording of tracer-uptake and distribution in the plant.This requires a high dynamic range with highest possible sensitivity for simultaneous measurement of shoot and root system.PhenoPET is used to determine the transport velocity and allocation of photo-assimilates (Bühler et al 2018) of plants and their response to treatments.
In the following, we will give an overview on the setup, data processing and image reconstruction of phenoPET.Afterwards we present the current performance of phenoPET according to the national electrical manufacturers association (NEMA) NU-4 standard for small animal PET systems (Belcari et al 2008).

Setup
The phenoPET system has a vertically oriented FOV with a radius of 90 mm and a height of 202 mm and is observed by 36 detector modules which are organized in twelve sectors (figure 1(a)), resulting in a distinct arrangement of crystal matricies (figure 1(b)).Opposing sectors have a distance of 255 mm.Each module consists of an 2 × 2 array of digital photon counters (DPCs) (Type: DPC3200-22-44 (Philips Digital Photon Counting 2015), called tile, figure 2(a)).Each tile consists of an array of 8 × 8 digital silicon photomultipliers (SiPMs).The readout is realized on die level, which are arrays of 2 × 2 SiPMs.An event on a die delivers the time stamp of the first trigger and the energy deposition on each SiPM in number of triggered cells.The DPCs are operated with trigger scheme 2 and validation pattern 0x00: OR within 40 ns (see (Zwaans 2012, Philips Digital Photon Counting 2016) for detailed description).The integration time is 85 ns long.Each tile is attached to a matrix of 16 × 16 lutetium-yttrium oxyorthosilicate (LYSO) crystals (figure 2(b)), Crystal Photonics, Inc., Sanford, Florida 32773).These crystals have a dimension of 1.85 mm × 1.85 mm × 10 mm and transparent and intransparent coupling allows the separation between the four crystals above each SiPM (Streun 2014).This results in 96 crystal rings with 384 crystals per ring.The mechanical mount and the readout for the three modules on top of each other is provided by twelve sector boards.Each of those is connected over an high definition multimedia interface (HDMI) cable to the concentrator board (CCB).Those cables are used to distribute the clock signal and allow a data transfer of up to 50 MB s −1 for each module.The DPCs operate fully digital and provide data in packages covering 327.68 μs.The CCB gathers those packages and groups the packages of the same time into frames, which are written to disc over USB 3 connection with a transfer rate of up to 375 MB s −1 .In case the modules provide more data then the bandwidth of the USB 3 allows to transfer, the CCB starts a controlled dropping of frames.This increases the dynamic range by a factor of up to four.For higher data rates, the transfer between the modules and the CCB becomes the bottle neck.This results in dropping of  packages by each module in combination with a change of the data format, which ensures the transfer of all events within the 327.68 μs packages.Due to technical reasons these data are not yet written to disc and thus limit our dynamic range.
Photon events are potentially scattered over multiple dies.The so-called clustering (Streun 2014) combines all events on a tile within 5 ns to a photon candidate.The position of the event is assumed on the die with the highest energy deposition and calculated by Anger logic, i.e. the mean of the four SiPM positions weighted by their energy depositions (Streun 2014).This position is assigned to one crystal by the floodmap of the tile.The resulting single has the time stamp of the first triggered die and the sum of all triggered cells as energy deposition.The position of the 511 keV peak for each crystal is identified in the energy spectra of singles and used for a linear calibration.Those energy calibration factors and the floodmaps are precomputed from a dedicated calibration measurement (35 min rotating rod source, A = 1.6 MBq).The coincidence sorting is done using a multiwindow coincidence sorter with a takeAll Good handling of multiple coincidences (compare (Strydhorst and Buvat 2016)).The coincidence window is 2.5 ns with an energy window of 348-652 keV.The coincidence timing resolution for a centered rod source is 0.631 ns after the correction of skews (timing differences between detectors (Streun et al 2016b(Streun et al , 2017))).The time of flight (TOF) leads to the coincidence window to safely get all coincidences inside the FOV (compare (Hinz 2021)).We observe a mean energy resolution of 16.6% at 511 keV (FWHM, see (Hinz 2021)).Random coincidences are obtained from delayed coincidence sorting with a 20 ns delay.
A chiller outside of the climate chamber with a set point of 3.5 °C provides liquid cooling to the modules.Furthermore, the housing is flushed by dry air to prevent condensation inside of phenoPET (figure 1(a)).The temperature and humidity are monitored by a Raspberry Pi, that can shut down the system in case of condensation or overheating.The system is surrounded by extruded polystyrene (XPS) for isolation and protected by a white plastic hull.Transmission measurements are performed with a 68 Ge rod source (Type LS-30: length 300 mm, diameter 8.5 mm) fixed to a rotation system which is mounted beneath of phenoPET.The source is rotated at a radius of 95 mm close to the border of the plant port, which has a radius of 100 mm.Here, the mechanical protection inside of the XPS is provided by a 1 mm thick aluminum shell.A more detailed description of the setup, operation and data processing are provided in Hinz (2021).
The phenoPET system is mounted on a custom lifting table (FL Mechanik GmbH and Co.KG, Alsdorf, Germany), which allows an adjustment of the axial position along a plant (figure 3).An acquisition computer is placed on the lifting table to receive the data from the USB 3 with a minimum cable length and store them over 10 Gbit ethernet on a 200 TB redundant array of independent disks system outside of the climate chamber.The climate chamber is developed by the Institute of Bio-and Geosciences: Plant Sciences (IBG-2) to control and monitor the environmental conditions with temperatures of 10 °C-30 °C and variable air humidity, wind force and light intensity.Two climate chambers of the same type are setup at our plant-dedicated MRI-facility.This allows plant growth and coregistration with PET and MRI under similar conditions.
In our current plant research [ 11 C]CO 2 is used, which is produced onsite by a cyclotron for plant research (CYPRES).The tracer application (also refereed to as labeling) is done with gas tight cuvettes.Different types of cuvettes allow the labeling of the complete shoot or of a single leaf.An upgraded version of the gas exchange system of PlanTIS creates the gas mixture for the cuvette and adds [ 11 C]CO 2 for the labeling (Chlubek 2013).This system monitors the gas exchange inside the cuvette.After labeling the cuvette is flushed and the remaining [ 11 C]CO 2 is directed onto an absorber.

Image reconstruction and projection data
Two image reconstruction frameworks were implemented for the phenoPET data.Besides the standard image reconstruction based on ordinary poisson maximum likelihood expectation-maximization (OP-MLEM), a filtered back projection was used to fulfill the requirements of the NEMA NU 4 protocol (Belcari et al 2008).In the following, both reconstruction pipelines are described.

Transmission reconstruction
The reconstruction of quantitative images of roots in a pot requires the correction of scatter and attenuation by the growth medium (e.g.soil, hydroponics).Here, individual attenuation maps for each measurement are important as the attenuation depends on the soil type with different dependencies on the water content of the soil, which changes over the day (Lee et al 2013, Hinz 2021).
Attenuation maps are obtained from a transmission scan with a rotating 68 Ge rod source (15 min at 25 MBq).The image reconstruction applies maximum likelihood for transmission reconstruction (MLTR) (Fessler 1995, Nuyts et al 1998) with 15 iterations and four scatter iteration.Small dead time effects whenever the source is close to a die, are compensated by acquiring blank scans at similar activities (2 h at 25 MBq).A maximum likelihood estimation is used to calculate expectation values for true coincidences each line-ofresponse (LOR) B i as gA, with the global scaling factor A, factors for the two crystals ò a and a factor for each set of symmetric LORs g i .This approach is similar to a component-based normalization (Hogg et al 2001).Scattered coincidences for each scatter iteration are estimated with a Monte Carlo simulation (Scheins et al 2021).The scatter simulation simulates 3 × 10 10 coincidence pairs with an enhanced effective number by multiplexing (Scheins et al 2021).

Ordinary poisson maximum likelihood expectation-maximization
The image reconstruction for phenoPET is done with the PET Reconstruction software toolkit (PRESTO) (Scheins and Herzog 2008, Scheins et al 2011, 2015) and applies OP-MLEM.The system response matrix is given by the volume-of-intersection (VOI) by using tubes-of-response (TORs) between pairs of crystals with a maximum ring difference of 80 rings (Scheins et al 2011).A subsequent scaling ensures a comparability with lengths-of-intersection between the voxels and the LORs.The resulting images have Cartesian voxels with a size of 0.9 mm × 0.9 mm × 1 mm.The required corrections for quantitative image reconstruction are presented in (Hinz 2021) and here only a brief summary is provided.Random coincidences are passed to variance reduction after the integration for a frame has been performed (Casey andHoffman 1986, Badawi et al 1999).The component-based normalization is fitted with maximum likelihood (Hogg et al 2001).The factorisation model is restricted to the sensitivity of each crystal and geometric sensitivities using the symmetries of the system.For normalization a rotating 68 Ge rod source (2.88 MBq) is measured for 82.5 h and the expectation values are obtained from numerical integration along each LOR through the analytically calculated activity distribution of a full rotation.
The dead time correction is calculated for each module combination and separated into three components (Bai et al 2002).First, the frame dropping is corrected by the ratio of expected frames over the number of frames with valid data from each pair of modules.Second, the dead time for the measurement of singles on each module is corrected.Third, a minor remaining dead time in the coincidences is corrected with a global factor.The latter two parts apply non-paralyzable dead time models (Knoll 2010), which remain in the linear domain for the complete dynamic range.For the maximum of 100 MBq centered in the FOV correction factors of about 0.25, 0.9 and 0.97 are observed for the frame dropping, the dead time on each module and the minor global dead time, respectively.
The attenuation correction uses the attenuation map reconstructed with MLTR (section 3.1.1).Emission images are reconstructed with 15 iterations and one scatter iteration.The scatter correction is obtained from a Monte Carlo simulation (Scheins et al 2021) with the attenuation map reconstructed with MLTR.The simulation for each frame contains 1.2 × 10 9 coincidence pairs with an enhanced effective number by multiplexing (Scheins et al 2021).For an optional speedup, we can perform scatter simulation only for each fourth frame and estimate the scatter distribution for the skipped frames by linear interpolation.

Implementation of filtered back projection for phenoPET
For the analysis of the spatial resolution of phenoPET according to NEMA NU 4 standard (Belcari et al 2008) 3D filtered back projection is realised with software for tomographic image reconstruction (STIR 5.0.2) (Thielemans 2022).The filling of the sinograms incorporates a virtual detector close to the FOV of phenoPET, as introduced for PRESTO (Scheins et al 2011).The cylinder surface with a radius of 90 mm is divided into 192 rings and each ring is divided into 758 virtual crystals.For each accepted coincidence the LOR between the two real crystals is used to project the event onto a pair of crystals of the virtual scanner.The ring difference and the LOR of the virtual crystals is used to fill the coincidences into sinograms with 384 views and a tangential bin size of 0.5 mm.The reconstructed images have a voxel size of 0.25 mm × 0.25 mm × 0.5 mm.This reconstruction with filtered back projection (FBP) does not apply any corrections.

Filling of sinograms with SSRB
Beside the reconstruction with FBP, the NEMA protocol requires the analysis of sinograms filled with singleslice-rebinning (SSRB) (Daube-Witherspoon and Muehllehner 1987).SSRB assigns all oblique LORs into the sinograms of the crystal rings.The assignment is done by calculating the mean axial position z s between the two crystals with z k and z l as Therefore, phenoPET is divided into 100 sinograms with slightly different axial dimensions (figure 4).Each physical crystal ring defines one axial position, while the axial boundaries are defined by the mean of axial center of mass of adjacent rings (figure 4(a)).In the axial gaps between the modules two rings are introduced with their axial center of mass placed at 1/3 and 2/3 of the gap (figure 4(b)).For the SSRB two possibilities are applied.In the first case, a LOR is assigned to the sinogram with the shortest distance to the mean of the axial coordinates of its crystals center of mass.In the second case, LORs with an odd ring difference (e.g. between neighboring rings like LOR 1, figure 4(a)) are assigned to the two rings closes to the mean axial position with a weight of 0.5 to keep the number of events constant.This is referred to as division of events with odd ring differences.

Characterization according to NEMA
In the following section the analysis procedures according to the NEMA NU 4-2008 standard for small animal PET scanner (Belcari et al 2008) will be presented.We stick to the thresholds and especially variable names introduced by NEMA.

Spatial resolution
The spatial resolution is measured with a 22 Na point source embedded in an acrylic cube with 10 mm edge length.For the NEMA NU 4 protocol, this cube needs to be placed at fixed radial and axial positions.For the radial positioning the source is moved on the rail (figure A1).The reconstructed images are rotated to align the radial and tangential direction with the x-axis and y-axis, respectively.According to NEMA the response function in one of these directions includes all one dimensional profiles parallel to this direction in a tube with 6 mm width.These tubes are positioned through the voxel with the highest value.The peak of a response function is determined by a parabolic fit to the highest pixel and its direct neighbors.Afterwards the full width at half maximum (FWHM) and full width at tenth maximum (FWTM) are calculated by linear interpolating between the two pixels around the half and tenth maximum on each side.
As we do not have a positioning system, we validate the radial positions for radii below 30 mm with OP-MLEM.Here, we apply a system response matrix with cubic voxels with a side length of 0.3 mm.The lower radial FOV and the maximum ring difference of 20 are necessary, to keep the memory consumption handy.The position is obtained from the parabolic fit to the response functions as presented for the analysis with FBP.
The spatial resolution during a realistic measurement is investigated with a hot rod phantom (radius 37 mm, height 64 mm).The fillable rods with diameters of 1.0 mm, 1.2 mm, 1.4 mm, 1.6 mm, 1.8 mm and 2.0 mm are separated by their diameter.A system matrix with smaller voxels of 0.45 mm in the x-y plane is applied with 52 iterations and one scatter iteration.These results are also presented in Hinz (2021).

Scatter fraction, count losses and random coincidence measurements
The investigation of the count rate behavior for a small animal PET system is done with three similar cylinder phantoms, which are based on the dimensions of a mouse, a rat and a monkey.For plant sciences, these phantoms provide representative performance values for root imaging with different pot sizes.
The three phantoms are made of polyethylene (figure 5) and have a bore of 3.2 mm for a line source, which has to be 10 mm shorter than the phantom and placed symmetrically to the axial center.The line source is realized by a flexible tube that is longer than the phantom and filled with 60 MBq to 100 MBq of 18 F diluted in water.An emission scan of 20 h is done and a few days later, when all 18 F has decayed, a 12 h background measurement of the 176 Lu.
The placement of the phantoms needs to be adjusted for phenoPET, as no bed is available.The scatter phantoms are placed on polyvinyl chloride (PVC) socket (figure 5) similar to pots for root imaging (more details: figure A2).A slit allows the tube to leave the phantom and the closing of the tube with a clamp.
The prompt and random coincidences in frames of 150 s are filled into sinograms.This results in at least 5 × 10 6 prompts, which is ten times larger than required by NEMA.SSRB is applied for filling the sinograms with the division of coincidences for odd ring differences (section 3.1.4).The first step is the calculation of the prompt, random, true, scattered and background count rate R p,i,j , R r,i,j , R t,i,j , R s,i,j , R B,i in each axial slice i of a time frame j, respectively.According to NEMA, all bins with a radial distance larger then 8 mm plus the radius of the phantom are set to zero.The profile in each view (figure 6(a)) is then shifted to align the bin with the maximum value with the center of the sinogram (figure 6(b)).Afterwards a radial profile is obtained by summing up all views (figure 6(c)).The sum of the radial profile divided by the frame duration t acq,j is R p,i,j .R r,i,j is obtained by summing the random sinogram after applying the tangential cut and dividing this sum by the duration.The same procedure is applied to obtain R B,i from the background measurement.The profile of each sinogram is further analyzed to obtain R t,i,j and R s,i,j .Therefore, the pixel  intensities C L,i,j and C R,i,j are calculated by linear interpolation between the two bins close to -7 mm and +7 mm away from the center of the profile.The sum of random and scattered C s+r,i,j in a profile is then given by the area between C L,i,j and C R,i,j and the x-axis.In addition all bins outside the 14 mm wide strip are added to C s+r,i,j (figure 6(c)).This leads to The resulting count rates are used to calculate the noise-equivalent count rate (NECR) R NEC,i,j as The reported curves show the count rates for each frame j, after summing up all slices i.For phenoPET we only consider slices within the height of the phantom.We obtain the peak R NEC,j and peak R t,j as well as the mean activity concentration at these positions.The mean activity for a frame is given by with the start of a frame t j compared to the measurement of the activity inside the phantom A 0 and the half life of 18 F t 1/2 .The activity concentration is than given by = A V AC 7 ave j ave j , ,

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with the volume V of the complete phantom.In addition, the scatter fraction SF is calculated as and we report the SF j for the frame which has a single count rate five times larger than the background measurement.

Sensitivity
The sensitivity according to NEMA is given as the fraction of detected decays from a known source.The same source as used for the spatial resolution is placed at 100 axial positions, which are defined by the sinograms filled with SSRB (section 3.1.4).The source is centered in the transaxial plane with OP-MLEM reconstructions with the same system response matrix used for the confirmation of source placement for the spatial resolution (section 3.2.1).The lifting table is used to position the source in the center of each crystal ring based on the construction plans.In addition, the source is positioned in center of the dummy rings.At each position an emission measurement and a dedicated background measurement of 1 min are acquired.
The point source is placed on two different mounts.The first mount is a socket made of PVC (figure 7(a)).This can be considered as a source close to the surface of the soil in a pot and we will refer to it as surface setup.In the second case, the source is placed on a small plastic rod with a thin shell, which represents the measurement of a stem (figure 7(b)).We will refer to this as stem setup.The prompt and random coincidences are filled into sinograms (section 3.1.4).
The calculation of the sensitivity selects the sinogram with the highest entry.In a selected sinogram a mask is created.In each view only bins in a 20 mm wide strip around the bin with the highest bin value are considered.The same mask is also applied to the background measurement.The count rates for the emission and the background measurement, R i and R B,i , are obtained by summing all remaining bins and division by the actual measurement duration.The sensitivity S i for position i in cps kBq −1 and the absolute sensitivity S A,i in % are given by with the activity of the source during the measurement A source = 101 kBq and the branching ratio of 22 Na of 0.9060.The NEMA NU 4 standard requires the calculation of the sensitivity for each position of the source in only a single slice.A number of reconstructed images show, that the source can be shifted by about 0.5 mm.This results in a spread of events into neighboring rings.Therefore, we also calculate the sensitivity including the directly neighboring rings, the two neighboring rings in each direction and also including all rings.In each considered sinogram the same radial conditions are applied.
From these sensitivities the mean sensitivity for a mouse SM tot , for a rat SR tot and the complete system S A,tot are calculated as Here, N denotes the number of summands contributing to each individual sum.
In addition we perform the analysis of the stem measurement with the division of events on LORs with odd ring differences for a larger energy window of 250 keV to 750 keV.This is another common energy window and should allow for a comparison with other system.

Image quality, accuracy of attenuation, and scatter correction
The image quality is investigated using a cylindrical phantom made of polymethyl-methacrylat (PMMA).Its main features are a uniform region (figure 8 The phantom is filled with about 70 MBq 18 F and placed in the axial center of the FOV on a thin PMMA cylinder shell (figure A3).An emission measurement of ten half lives is acquired and followed by a subsequent transmission scan of 15 min with a rotating 68 Ge rod source (A ≈ 25 MBq).Afterwards a blank measurement of 120 min is acquired to account for dynamic sensitivities whenever the rod source is close to the modules during the transmission reconstruction.
A 20 min frame is reconstructed with a initial activity of 3.7 MBq.For the uniformity a 10 mm long region of interest (ROI) with a diameter of 22.5 mm is analyzed.The mean activity concentration Mean AC and its standard deviation STD AC are obtained as well as the relative standard deviation %STD and the minimum and maximum activity concentration.
The recovery coefficients RC are obtained for each of the five rods.Here, an average slice is computed from the slices covering the central 10 mm of the rods.For each pixel in the average slice also the relative standard deviation is calculated.For each rod the pixel with the highest average activity concentration is selected and the

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The last aspect is the accuracy of corrections, especially attenuation correction and scatter correction.Here, a ROI is placed in each of the two cold regions with a height of 7.5 mm and a diameter of 4 mm.The mean (Mean cold ) and standard deviation (STD cold ) are obtained to calculate the spill-over ratios SOR for the waterfilled and the air-filled insert similar to (16) as and adapting (17) for the %STD SOR .

Temperature dependency
The temperature dependency of the count rates of the SiPMs is investigated with a 22 Na point source.A measurement is conducted over several hours with a day and night cycle set to the operation boundries of the climate chamber (10 °C at night and 30 °C over day).An additional measurement is done at the current standard day time temperature of 22 °C.For the analysis the mean count rate of prompt coincidences is obtained as soon as a temperature equilibrium is reached.The FOV allows all coincidences from the seven opposing sectors.As measure for the temperature dependency the relative difference to 22 °C are studied.

Plant measurement
A group of four maize plants was grown in Speyer 2.1 (Landwirtschaftliche Untersuchungs-und Forschungsanstalt Speyer, D-67346 Speyer, Germany) soil in pots (diameter: 90 mm and height 200 mm) for 21 d for the validation of the measurement protocols with phenoPET in 2021.Here, we report measurements of one plant, that was measured on two subsequent days as the complete measurement is part of a dedicated project (Schultes et al 2019(Schultes et al , 2020)).As other plants were measured in the morning, the cuvette covering the complete shoot was mounted 2.1 h and 1.5 h before the measurement on the two days (figure 9).Between the two measurements the plant was kept in the climate chamber.
The chamber was operated with a 22 °C/16 °C (12/10) day/night cycle and an air humidity of 60%.The LED-panels provided 315 μmol m −2 s −1 of photosynthetically active radiation.Linear ramps of 1 h are used as sunset and sunrise.The labeling of the complete shoot was done with about 100 MBq of [ 11 C]CO 2 for 6 min.The transmission measurements were conducted right before the emission scan with an increased duration of 60 min as the rod source decayed to 0.68 MBq and a 82.5 h blank scan at 2.88 MBq with an older reconstruction schema (Hinz 2021), which required knowledge on the imaged object.
The emission scans are reconstructed including attenuation correction and one scatter iteration with a frame length of 5 min.

Spatial resolution
The results for the FWHM and FWTM according to NEMA are presented in figure 10 for the center and at 1/4 of the axial FOV.In general the FWHM and FWTM increase for larger radii.The largest exception are the radial FWHM at 75 mm at both axial positions (figures 10(a), (b)).The observed decrease at least partly results from artifacts visible in the reconstructed images.Those result from the gaps between the modules and crystals and degrade the response functions.This is especially visible for the axial resolution at 50 mm and 75 mm.
In the reconstruction of the hot rod phantom the 1.6 mm rods can be visually distinguished for a single slice (figure 11(a)).The profiles support this separation and indicate a sufficient statistics as they do not change, when averaging over three slices (figure 11(b)).
In addition to the FBP which is required for NEMA, point sources are often additionally reconstructed with an iterative method (Liang et al 2020, Khateri et al 2022).This originates from the well known degradation of the spatial resolution by FBP for systems with gaps in the detector ring (Hallen et al 2020).It has to be noted that a spatial resolution obtained from an iterative reconstruction strongly depends on the number of iterations (Gong et al 2016).We calculated the resolutions for the reconstruction with OP-MLEM (appendix C).

Scatter fraction, count losses and random coincidence measurements
The count rates for the mouse, rat and monkey sized scatter phantoms are given in figure 12.The peak values for the three phantoms are given in table 1.
In general the count rates are limited by the band width of the USB 3, which results in the controlled dropping of frames (section 2).This causes a saturation of the single count rate.Therefore, also the number of trues and scattered coincidences is fixed.With increasing activity the density of the singles increases and thus the number of randoms.This also leads to an increase of prompts coincidences.The frame dropping discards up to 75% of the frames.The individual modules show count rate loses due to dead time well below 10% at the maximum measurable activity (section 2).
The integration over 150 s averages small fluctuations of the data transfer.For example, the monkey size phantom has a data rate of 374.12 ± 0.49 MB s −1 while the frame dropping is required.The maximum activity  without frame dropping A frame dropping increases slightly for larger phantoms.For the monkey size phantom a larger increase is visible, as the activity is not fully contained inside in the FOV.For the A t,peak the larger step is between the mouse and rat phantom because the shorter mouse phantom does not reach the upper and lower detector ring.

Sensitivity
The sensitivity profiles for the two setups of the 22 Na cube (surface and stem) and the different filling of LORs with odd ring differences are shown in figure 13.In table 2 the mean sensitivities are presented.
The sensitivity profiles for the surface measurement (figures 13(a) and (c)) are discontinuous for the analysis of only one sinogram for each position, as suggested by NEMA.The profiles for the stem setup (figures 13(b) and (d)) are much smoother.Therefore, these differences arise from the additional scattering in the socket used for the surface measurements (figure 7(a)).These profiles for the surface setup are not symmetric to z = 0 mm.This is especially visible for the steps observed at the gaps of 4.3 mm between the modules (figure 13(a)).Additional  steps are visible at the center of each module (figure 13(c)), where the crystals have a gap of 1.3 mm.The discontinuities and the size of the steps are reduced, when the neighboring sinograms are included into the calculation of the sensitivity.Here, the direct neighbors show the largest improvement.In all profiles now a third step becomes visible at one and three quarters of the module.These steps can not be correlated to a gap between the crystals.Besides the misplacement due to scatter the additional rings compensate for a small misplacement of the source.Reconstructions with OP-MLEM show deviations in the range of 0.5 mm to the intended position.This is 27% of a crystal.The origin of these misplacements is not yet understood.
The peak sensitivities as well as the mean sensitivities in table 2 depend on the mount for the source as well as on the number of sinograms considered for the calculation.The division of LORs with odd ring differences reduces all sensitivities by around 0.2% for N R = 1 compared to the case without division.These reductions are only about 0.02% as soon as neighboring rings are included.A comparison of the sensitivities SM A,tot , SR A,tot and S A,tot for the two setups shows, that the differences increase for larger N R and decrease for a larger number of S i contributing to a mean sensitivity.
In table 2 also the results for the larger energy window 248 keV to 752 keV are given.Those values show an absolute increase of at least 1% for the absolute sensitivities.The corresponding curves are given in appendix D.
We observed peak sensitivities of 1.6% and 1.9% for the surface and stem setup, respectively.Those values increase to 2.7% and 3.6%, when including all rings into the calculation of the sensitivity instead of a single sinogram.This behavior for larger N R is similar to the mean sensitivities.

Image quality, accuracy of attenuation and scatter correction
The averaged slice of the five rods and a slice through the cold region are shown in figure 14 for 15 and 52 iterations.The quantitative results for the uniformity test, the recovery coefficient test and the accuracy of the corrections are presented in tables 3, 4 and 5, respectively.
The activity concentration in the uniform region has a larger %STD and covers a wider range for 52 iterations compared to 15 iterations.The mean does only change by 1.1% and is quite stable.A deviation of about 5% to the activity concentration provided by a dose calibrator (Curiementor 2, PTW-Freiburg, Germany) is observed, which is the required precision.The mean attenuation coefficients in the uniform region is 11% Table 2. Mean sensitivities for mouse, rat and the total system.Clear differences are visible for the stem and surface scenario.The increase of the number of rings (N R ) contributing to the sensitivity from one to three provides the largest sensitivity increase.This also reduces the differences between the different handling of LORs with odd ring differences.below the expectation for water.Nevertheless, the attenuation corrections for each LOR through the phantom match the expected values as further voxels contribute.This results in a bias on the scatter correction.
The position of the ROI for the analysis of the 1 mm rod is chosen to be applied for both images (figures 14(a), (b)).For this rod the additional iterations improve the RC but increase its %STD.For the 2 mm and 3 mm rod the RC is improved and the %STD decreases or keeps similar.In all three cases the absolute STD increases.For these three rods the same pixel is selected for both numbers of iteration.The two other rods show smaller changes and here adjacent pixels are selected for the different numbers of iteration.Interestingly, for the 4 mm and 5 mm rod pixels at the edge of the hot region are selected, while for the other three rods the central pixel has the highest amplitude (figures 14(a), (b)).These results illustrate the decrease of the partial-volume effect for a higher spatial resolution (Cherry et al 2012).
The additional iterations also decrease the SOR for the air-filled and water-filled cylinders but increase their %STD.The larger SOR for the air-filled are caused by the bias in the attenuation maps, as the blurred walls of the insert result in a too high attenuation inside it.While the improvement SOR improve for more iteration, the STD increase (figures 14(c), (d)).For the air-filled cylinder higher values are visible at the left border of the ROI, which contribute to a higher %STD and keep the STD similar.For the water-filled cylinder the absolute STD decreases.

Temperature dependency
The operation of the climate chamber at 22 °C results in a mean temperature on the tiles of 10.8 ± .6 °C (for details see (Hinz 2021), Chapter 8.1).
The relative differences of the coincidence count rates at 10 °C and 30 °C chamber temperature compared to 22 °C are shown in figure 15.While cooling to 10 °C causes only a neglectable average increase of 1%, 30 °C (8 K higher temperature) causes an average decrease of 7%.The liquid cooling and isolation of phenoPET reduce the temperature increase to 3 K on the tiles.This results in an increase of the readout events by about 4.7% on a tile due to the increased dark count rate, which doubles every 7.5 K (Philips Digital Photon Counting 2015).
The observed differences between individual modules result from a slightly different thermal coupling of each module to the cooling system.The ring structure of the cooling system also introduces a dependency of the absolute temperatures on the position of the modules in the ring, compare figure 1(a).
For our current experiments, the climate chamber is operated at 22 °C and 16 °C at day and night time, respectively.This results in count rate differences well below 2% which can be neglected.This is especially true for transmission scans or other phantom measurements which are often performed over night.
For the operation of the climate chamber we observed, that the ramping of the temperatures is 0.5 h and 0.25 h slower for the warm-up and cooling-down, receptively.The equilibrium temperatures of the tiles for the warm-up is reached even 4.5 h later.This in combination with the large 7% reduction of the prompt count rate requires a careful planing of potential experiments with complex or extreme temperature changes.
Our current experiments are conducted during the day with a constant temperature.While measurements at 22 °C are established, measurements at different constant climate chamber temperatures should be possible by adjusting the temperature of the chiller to obtain the same temperatures on the tiles.Minor adjustments can be achieved by correcting the bias voltage to the temperature.

Plant measurement
Two frames from each of the two measurements are presented in figure 16.The time difference between the two days is a 1.5 min delay of the labeling on the second day.The comparison of the early and later frame on each day, reveals a later arrival of the tracer in the root system on the second day.Furthermore, the two hot regions labeled with α) and ψ) in the images indicate growing root tips.Beside the earlier arrival on the first day (figure 16(a)), also larger activity concentrations and prompt count rates are observed compared to the second day (figure 16(b)).The maximum activity in the FOV show the similar behavior with 6.6 MBq and 3.9 MBq on the first and second day, respectively.The CO 2 -uptake on the second day was higher −118 ppm compared to −88 ppm on the first day.This results in a higher uptake on the second day from a gas mixture with an about 5% larger activity concentration.The larger fractions of delayed coincidences on the second day is partly caused by the higher activity in the shoot, which is outside the FOV.
The later arrival and the lower amount of tracer inside the root system might results from the adoption of the plant to the later mounting of the cuvette on the second day, 95 min instead of 126 min before the start of the measurement.There are also other biological factors that might play a role, e.g. a change of the root-shoot allocation ratio.A detailed analysis is beyond the scope of this work as it requires additional replicates for a statistically sufficient analysis.
In the images also the partial volume effect becomes visible, as along some of the roots the activity concentration seems to increase and decrease.Especially for thin lateral roots (around η) gaps in the activity distribution are visible.The lower activity on the second day increases the effect.

Discussion
In the following comparison we focus on three other PET systems, which were characterized according to NEMA NU 4. At first, our first generation system PlanTIS (Michel 2011) to illustrate the achieved improvements, second, the Hyperion IIDPET/MRI (Hallen et al 2018) as this is based on the same SiPM as phenoPET but with a different geometry and data processing and third the PET/CT System Discoverist 180 (D180) (Liang et al 2020).The latter one is a commercial scanner, that includes initial results for the measurement of a leaf in the characterization and therefore allows a comparison of phenoPET to a state-of-theart scanner.These systems have distances between opposing modules of 124 mm, 209.6 mm and 213 mm and axial FOV of 108 mm, 96.9 mm and 100 mm for PlanTIS, Hyperion and D180, respectively.
For spatial resolution and sensitivity we also report available results for other plant dedicated systems.

Spatial resolution
In comparison to PlanTIS, phenoPET shows a smaller FWHM and FWTM.An exception is the radial direction at a distance of 10 mm at the axial center.Here, phenoPET has a resolution of 1.97 mm and PlanTIS of 1.90 mm (Michel 2011).
At the 5 mm position in the axial center, radial spatial resolutions with FBP of 1.45 mm, 2.32 mm, 1.7 mm and 2.56 mm are obtained for phenoPET, PlanTIS (Michel 2011), Hyperion (Hallen et al 2018) and D180 (Liang et al 2020), respectively.
The spatial resolutions with the hot rod phantom are quite similar for PlanTIS and phenoPET.A resolution between 1.6 mm and 2.4 mm is obtained from a Derenzo phantom filled with 11 C for PlanTIS (Beer et al 2010).The fundamental limits on the spatial resolution (Moses 2011) indicate that these similar results can be explained by the smaller diameter of PlanTIS, while in phenoPET the crystals are slightly smaller.Therefore, phenoPET with 11 C can be expected to achieve a spatial resolution of at least 1.8 mm compared of 1.6 mm with 18 F due to the higher positron range (section 4.1).The Hyperion system achieves a spatial resolution better than 1 mm with a hot rod phantom and optimized settings (Schug et al 2016, Hallen et al 2018).Here, the Hyperion system strongly profits from its smaller crystals with 0.93 mm edge length.
The PETIS system reports a spatial resolution of up to 1.6 mm with a 22 Na point source in the focal plain (Uchida et al 2004).The OpenPET system achieves a spatial resolution of 1.6 mm with a hot rod phantom (Yamaya et al 2011).At Washington University a spatial resolution 1.25 mm is achieved with a hot rod phantom (Wang et al 2014).Therefore, we achieve a comparable spatial resolution with respect to other plant dedicated systems, while et al Wang achieves a better resolution.
A comparison of the results from the 22 Na cube and the hot rod phantoms illustrates how misleading the FBP based evaluation can be.The Hyperion system shows a significant better resolution for a hot rod phantom with an iterative reconstruction than with FBP.Hallen et al (2018) point out, that the disadvantages arise from scanners with a non-cylindrical geometry like Hyperion and phenoPET.(Liang et al 2020) state that most vendors no longer provide FBP.Here, also the shift from FBP to an iterative reconstruction provided a large improvement.A comparison of iterative algorithms can only be done for a specific set of parameters because the resolution depends on the number of iterations (Gong et al 2016).There are suggestions to perform a quantitative analysis of hot rod phantoms.Hallen et al (2020) propose a comparison of the peak-to-valley ratio.Another alternative might be the measurement of spheres and fitting of their profile to obtain the resolution (Hofheinz et al 2010).Both approaches would allow measurements without the necessity of establishing FBP.On the other hand, the selection of the parameters like the number of iterations and their adequate documentation would become of greater importance.

Scatter fraction, count losses and random coincidence measurements
For the count rate performance we restrict the comparison to the NECR and the SF of the three phantoms.In general, the D180 has the highest A NEC,peak with about 97 MBq (Liang et al 2020).This is double the value of the Hyperion (46 MBq) and three times the results for phenoPET (30)(31)(32)(33)(34)(35).In the comparison between PlanTIS and phenoPET we could improve the A NEC,peak for the rat phantom by about 33%.
For the mouse size phantom an R NEC,peak of 550 kcps, 20.2 kcps, 407 kcps and 713 kcps are obtained with phenoPET, PlanTIS (Michel 2011), Hyperion (Hallen et al 2018) and D180 (Liang et al 2020), respectively.Here, PlanTIS shows the worst results, which mainly results from the incomplete detector ring.The Hyperion uses a killAll policy for multiple coincidences, which discards all non-unique coincidences, i.e. more than two singles in the coincidence timing window.This policy was discarded for phenoPET due to the reduced efficiency to identify true coincidences (Hinz 2021).A similar reduced efficiency can be expected for Hyperion causing a reduction of the R NEC,peak .
For the rat sized phantom an R NEC,peak of 308 kcps, 7 kcps and 207 kcps are reported for phenoPET, PlanTIS (Michel 2011) and D180 (Liang et al 2020), respectively.Here, phenoPET achieves the highest count rates.For the monkey size phantom, this changes as phenoPET obtains 45 kcps and D180 47 kcps.
The scatter fractions of phenoPET are always larger than for the other system, except for the rat size phantom (table 6).PlanTIS has the lowest SF for the mouse phantom, as there is no hull covering the detector modules.Nevertheless the SF is larger for the rat sized phantom.For the monkey phantom the D180 has a significant smaller SF than the 55.9% of phenoPET.
These results lead to two main conclusions for phenoPET: First, the mechanical protection of the plant port should be optimized to reduce scattering and second, the dynamic performance could be further improved by enhancing the data transfer rate.Here, a new data acquisition (DAQ) system is under development which will replace the USB 3 by a custom protocol over a 10 Gbit link.This will allow the detection of all events for four times larger activities and therefore can be expected to significantly improve the count rate performance of phenoPET.

Sensitivity
We previously reported a peak sensitivity of 6% and 9.5% for the energy window of 350-650 keV and 250-750 keV, respectively (Streun et al 2021).This measurement used a different source and a minimum of scattering material to mount the source.The trigger mode for the DPCs was set to 4 instead of 2 (see (Philips Digital Photon Counting 2016) for details).The most important differences are the missing radial and axial acceptance cutoffs applied during the NEMA analysis.
For PlanTIS SM A,tot = 0.29% and SR A,tot = S A,tot = 0.24% are reported, when including all sinograms in the calculation of each sensitivity value (Michel 2011).The sensitivity for phenoPET are between a factor of 7-12 larger.Here, the reduced material in the stem setup leads to larger improvements of the sensitivity.Beside the setup of the source, the improvements result from the full detector rings and longer FOV of phenoPET.
The Hyperion and D180 report peak sensitivities of 4% (Hallen et al 2018).In addition, Hyperion reports total sensitivities of SM A,tot = 2.5% and SR A,tot = S A,tot = 1.9% (Hallen et al 2018), while D180 reports SR A,tot = S A,tot = 2.25% (Liang et al 2020).These results are obtained with energy windows of 250-625 keV and 350-650 keV, respectively.The Hyperion includes all sinograms with an axial distance below 10 mm.For the surface setup, we observe lower sensitivities for N R = 3 but can improve SM A,tot and SR A,tot when adding all rings.For the stem setup, we obtain larger sensitivities as soon as N R > 3.Even larger sensitivities could by achieved by applying the larger energy window of 250-750 keV.We expect a decrease of the sensitivity from the larger distance between the modules of phenoPET.The longer FOV leads to an improvement, as indicated by the slightly larger SR A,tot and the lower S A,tot for the surface setup.Further differences might result from the different readout settings.The fill-factor which is the fraction of cylinder surface covered with crystal fronts is quite similar for phenoPET (0.76) and Hyperion (0.73) and should not have an influence (see Hallen et al (2018) for calculation).The Hyperion system benefits from its 12 mm long crystals.
The total sensitivity S A,tot of the D180 is always larger than the S A,tot of phenoPET, regardless of the setup or the N R .The description of the data analysis for the D180, does not explicitly mention the number of sinograms considered for the calculation of the sensitivity of each position of the 22 Na source.There are numerous possibilities to interpret the analysis procedure suggested by the NEMA standard (Hallen et al 2020).Our own results also show the strong dependency of the obtained sensitivity on the measurement and the subsequent data analysis.
The three plant dedicated system unfortunately do not report sensitivities with a common method.The PETIS system reports a sensitivity of 107 cps/(kBq/ml) ≈0.08% for a 18 F filled plane source (V ≈ 139 ml) (Uchida et al 2004).For OpenPET the sensitivity (400-600 keV) in the center of the FOV is between 6.6% and 8.0% depending on the distance between the two rings (Yamaya et al 2011).The maximum sensitivities with a 68 Ge point source (350-650 keV) for the scanner at Washington University depends on radial position 1.3%, 1.4% and 3% at 5 mm towards its smaller half rings, the center of the FOV and at 5 mm towards its larger half ring (Wang et al 2014).As we discussed above, the setup and data analysis have a significant influence on a result and therefore an explicit comparison of these sensitivities is not meaningful.

Image quality
Our phenoPET shows an improved uniformity in %STD of at least a factor of two compared to the 8.6% of PlanTIS.Here, PlanTIS suffers from the missing scatter and attenuation corrections.With 52 iterations we are close to the result of the Hyperion system (3.7%).The better uniformity for a lower number of iterations, i.e. 2.5% for 15 iterations results from the lower spatial resolution and thus lower recovery coefficients (table 4).
The recovery coefficients of the three other systems are summarized in table 7. PlanTIS only shows a better RC for the 1 mm and 2 mm rods compared to 15 iterations with phenoPET.For all other cases phenoPET shows an improved performance with larger RC and smaller %STD.The Hyperion system shows a better performance for the 1 mm and 2 mm rods and compatible results for the other three rods.The D180 shows an improved performance for the 1 mm and 2 mm rods compared to phenoPET.For the 4 mm and 5 mm rods phenoPET shows the better performance.The performance for the 3 mm rod depends on the number of iterations used for phenoPET.Those values show the reduction of the partial-volume-effect by a better spatial resolution, that results from the higher number of iterations.It has to be noted, that the voxel size of 0.9 mm for phenoPET also leads to a degradation of the effective spatial resolution and therefore influences the RC.
The limited recovery coefficient has also an impact on the analysis of plant measurements.For roots, which can have diameters well below 1 mm, the ROIs need to be created sufficiently large to include the complete activity, which is distributed into the growth medium.In addition the analysis should be based on the total activity in a ROI and not the mean activity concentration.The range of the positrons in the growth medium is limited and also calls for sufficiently large ROIs.This changes for measurements of the shoot.Here, positrons leave the plant and do not annihilate in the adjacent air, which underestimates the qualitative values for the concentration in the shoot.
The spill-over ratios for PlanTIS (Michel 2011), Hyperion (Hallen et al 2018) and D180 (Liang et al 2020) are 0.15 ± 15.44%, 0.05 ± 14% and 0.11 ± 7.9% for the water-filled cylinder and 0.25 ± 13.31%, 0.06 ± 14% and 0.12 ± 6.76% for the air-filled cylinder, respectively.The SOR for PlanTIS are compatible to the results of phenoPET for 15 iterations.For 52 iterations phenoPET shows better SOR but the %STD are quite similar.The Hyperion system shows the lowest SOR and the D180 shows the lowest %STD.The D180 gives better SOR compared to 15 iterations, while phenoPET has a better SOR for the water-filled and a compatible SOR for the air-filled cylinder, when using 52 iterations.Further improvements might be achieved by optimizing the transmission measurement for small objects instead of relying on the setup for plants, which we grow in pots with at least 62 mm diameter.The good performance of scatter and attenuation correction in the uniform region (%STD = 4.12%), further underlines a possible improvement by enhancing the attenuation map.

Conclusion
We have presented an overview on our new phenoPET system and its data processing and image reconstruction.In addition, we provided insights in our PET laboratory for plant sciences.We achieve a significant improvement for the sensitivity and dynamic range compared to our first generation system PlanTIS.The performance according to the NEMA NU 4 standard is compatible with the state-of-the-art Hyperion IIDPET/ MRI and the PET/CT Discoverist 180 and therefore with similar state-of-the-art systems.A main difference to these systems is the larger axial FOV and the required isolation to reduce the influence of the climate chamber onto the SiPMs.The phenoPET system achieves a spatial resolution of up to 1.45 mm, 0.82 mm and 1.88 mm with FBP in the radial, tangential and axial direction, respectively, and up to 1.6 mm with a hot rod phantom.In addition phenoPET has a peak sensitivity of 3.5% and an average sensitivity of 2.17%.The peak NECR are 550 kcps @ 35.08 MBq, 308 kcps @ 33 MBq and 45 kcps @ 40.60 MBq for the mouse, rat and monkey size scatter phantoms, respectively.The maximum measurable activity is around 100 MBq in the center of the FOV.
Table 7. Recovery coefficient of PlanTIS Michel (2011), Hyperion Hallen et al (2018) and D180 Liang et al (2020).In Hallen et al (2018) the STD are only provided as a graph and thus are not given here.For phenoPET the number of iterations for OP-MLEM are given in brackets.An upgrade for phenoPET is under development.A reduction of the internal scatter is planed by replacing the mechanical protection.Furthermore, an upgrade of the electronics is under development to enhance the USB 3 by a 10 Gbit connection via fibre optics, which is expected to improve the performance for higher count rates.The offline analysis of the raw data from the DPCs provides us with a number of possibilities for further testing and optimization.For the routine operation with 300 GB to 1000 GB of raw data per measurement, this mainly requires a careful handling of the available disc space.
The focus of our current work is the application of phenoPET in plant sciences.Up to four measurements of 2.5 h can be conducted per day and reconstructed into 30 frames with 5 min duration.The plants can thereby kept under controlled conditions.A remaining challenge is the low throughput of individual plants.This could be improved by alternating measurements of several plants as presented by Bühler et al (2018).Further improvements to their model family are under development as well as the establishing of protocols for further plant species.

Figure 2 .
Figure 2. Top view on one of the four tiles of a module and its crystal matrix.(a) Setup of a tile (yellow) housing 4 × 4 dies (dark blue), which read out 4 SiPMs (white) each.(b) Matrix of 16 × 16 crystals (red squares) attached to one tile.Arrays of 4 × 4 crystals match the four SiPMs of one die.The combination of transparent coupling and opaque coupling by a 0.183 mm thick foil (cyan) enhances the crystal identification.(a) and (b) adapted from (Hinz 2021).

Figure 1 .
Figure 1.Setup of phenoPET.(a) Inner setup without the hull and removed XPS cap.Adapted from Streun et al (2016a) with additional annotations.(b) Arrangement of crystal matricies attached to the tiles on a sector board.The gaps between tiles and modules are in scale.

Figure 3 .
Figure 3. phenoPET in a climate chamber with open doors.Light-emitting diode (LED)-pannels cover the full ceiling.

Figure 4 .
Figure 4. Sketch for of the axial definition of sinograms with physical (red) and dummy (magenta) rings for filling with (SSRB).Blue vertical lines represent the crystal fronts and horizontal lines mark the axial dimensions.For (a) a gap between two tiles on a module and (b) a gap between two modules.For the example line-of-response (LOR) z s is marked.

Figure 5 .
Figure 5. Setup of scatter phantoms on the example of the rat size phantom with (a) front view on rat phantom located on its PVC socket and (b) top view on phantom and socket.The dimensions of all three phantoms are provided.

Figure 6 .
Figure 6.Illustration of the analysis of an axial slice according to NEMA Nu 4 for a sinogram of the rat size scatter phantom.(a) Original sinogram.(b) Sinogram with maximum aligned to the central bin each view.(c) Summed profile for this sinogram with illustration for R t,i,j , C L,i,j , C R,i,j and C s+r,i,j .

Figure 7 .
Figure 7. Setup of 22 Na point source for measurement of sensitivity.(a) Top view on surface setup and (b) side view on stem setup.

Figure 8 .
Figure 8. Setup of NEMA image quality phantom with (a) axial cross section of phantom, (b) transaxial cross section of cold inserts, (c) transaxial corss section through the fillable rods with their respective diameter stated.For more details see Belcari et al (2008).

Figure 9 .
Figure 9.A 21 d old maize plant mounted inside phenoPET for a measurement of the root system in a soil filled pot after administration of [ 11 C]CO 2 to the shoot.

Figure 10 .
Figure 10.Spatial resolution with 22 Na point source according to NEMA at axial center (a), (c) and 1/4 of axial FOV (b), (d).Top row (a), (b) gives FWHM and bottom row (c), (d) are the FWTM.The values for each point are provided in appendix B.

Figure 11 .
Figure 11.Spatial Resolution with a hot rod phantom filled with 18 F. (a) Single slice of 60 min with 52 iterations.The arrows indicate the location and directions of the profiles displayed in (b).Profiles are within the displayed slice or averaged with the adjacent slices.All corrections except the calibration are taken into account.The rod diameters are given.(a) Is adapted from (Hinz 2021).

Figure 12 .
Figure 12.Count rate performance for the (a) mouse size scatter phantom, (b) rat size scatter phantom and (c) monkey size scatter phantom.Data points are obtained from frames of 150 s.

Figure 13 .
Figure 13.Sensitivity profiles for the surface (a), (c) and stem (b), (d) setup of the source.Top row (a), (b) fills coincidences with odd ring differences into one sinogram and the bottom row (c, d) divides those coincidences, i.e. fills them into the two closest sinograms with a weight of 0.5 to keep the number of events constant.Dots are the physical rings of phenoPET, + represent the dummy rings in the axial gaps and the×are the positions in the centers of the gaps.The black lines show the axial coverage of the modules.

Figure 14 .
Figure 14.Reconstructed slices of the image quality phantom with activity concentrations in MBq ml −1 .Average slice for calculation of RC for (a) 15 and (b) 52 iterations.ROI positions in cold regions for spill-over rations for (c) 15 and (d) 52 iterations.

Figure 15 .
Figure15.Dependency of prompt coincidences on climate chamber temperature as relative differences to 22 °C.The solid lines mark the relative difference for the sum of prompts for the two temperatures of the climate chamber.

Figure 16 .
Figure 16.3D visualizations for two decay corrected frames (5 min) from the measurement of a maize plant (a) labeled at 14:28 and (b) labeled at 14:05 on the subsequent day.The time differences to the labeling are given as well as the prompt (p), delayed coincidences (d) and non-decay-corrected activity inside the FOV A FOV for each frame.The activity is color coded and given in MBq ml −1 .Values above 1.2 MBq ml −1 are also in magenta.The three arrows (length: 50 mm) indicate the directions of the Cartesian coordinate system.

Figure A2 .
Figure A2.Placement of scatter phantom in phenoPET, here rat size phantom.(a) Skew top view on phantom inside of FOV.(b) Phantom on mounting system.The different cylinder allow a variable height.

Figure A3 .
Figure A3.Top view on image quality phantom inside of phenoPET during transmission scan.The mount is a thin cylinder shell made of PMMA.

Figure D1 .
Figure D1.Sensitivity profile for the stem setup.Coincidences with odd ring differences are divided on the two closes rings and an energy window of 250-750 keV is applied.The black lines mark the axial coverage of the modules.

Table 1 .
Peak count rates and corresponding activities and activity concentration (AC) as well as scatter fraction.In addition, the maximum activities without dropping discards are given.

Table 3 .
Report of uniformity test.Activity concentrations inside the ROI are reported in MBq ml −1 .An activity concentration of 0.176 MBq ml −1 is expected.

Table 4 .
Report of recovery coefficient test.

Table 5 .
Report of accuracy of corrections.

Table B1 .
Spatial resolution of phenoPET in center of axial FOV with FBP3D.The bins have a size of 0.25 mm in the transaxial plane and a slice thickness of 0.5 mm.

Table B2 .
Spatial resolution of phenoPET at 1/4 of axial FOV with FBP3D.The bins have a size of 0.25 mm in the transaxial plane and a slice thickness of 0.5 mm.

Table C1 .
Spatial resolution of phenoPET in center of FOV with OP-MLEM.The bins have a size of 0.15 mm.

Table C2 .
Spatial resolution of phenoPET at 1/4 of FOV with OP-MLEM.The bins have a size of 0.15 mm.