Positron emission tomography has become one of the most common and useful imaging modalities for detection and treatment monitoring of human diseases because of its high diagnostic efficacy and accuracy (Saha, 2016). Additionally, this imaging technique is used in preclinical studies on rodents and nonhuman primates for research on drug development linked to, e.g., cardiology or neurology (Ametamey et al., 2008). Given the non-invasive in vivo nature of this technique, its use has been extrapolated to plant science. Whereas preclinical studies on animals and clinical trials on human subjects are governed by ethics limiting the number of individuals to be investigated, this is not the case for studies on plants which avoids considerable administration. Although the number of studies on plants is still limited, this functional imaging technique has already shown its applicability to investigate, e.g., the transport of nutrients, phytohormones and photoassimilates (Minchin and Thorpe, 2003; Kiser et al., 2008; Jahnke et al., 2009; Hanik et al., 2010; Hubeau et al., 2018). Moreover, detection of γ-photons emitted by the radioisotopes enables tracking the transport and distribution of the radiotracers in the plant as a function of time. This is a decisive advantage to study dynamic processes like, for instance, CO₂ transport in xylem of tree branches and leaves. Studies that investigated this process with stable ¹³C-carbon (e.g., McGuire et al., 2009; Bloemen et al., 2013a, b; Boellaard et al., 2015) or unstable ¹⁴C-carbon (e.g., Langenfeld-Heyser, 1989) made use of measurement techniques (i.e., isotope-ratio mass spectrometry and autoradiography) that produce discrete temporal results. Although interesting data has been obtained, the results only showed tissue enrichment in a certain treatment at a given point in time after the onset of labeling. A study that applied ¹¹C-carbon in combination with PET to investigate the fate of xylem-transported CO₂ resulted in dynamic data which allowed compartmental modeling to disentangle tracer enrichment in physiological parameters characterizing this process (i.e., CO₂ efflux rate to the atmosphere, assimilation rate by woody tissues and internal CO₂ transport speed) (Mincke et al., 2020). Additionally, the short half-live of the radiotracers (e.g., 2 – 109 min for the most used radioisotopes in plant science – Table 1) in combination with the non-invasive nature of PET enable the same plant to be scanned multiple times without destructive sampling. This feature allows to investigate the plant’s response to environmental changes within the same plant (Kiser et al., 2008). This methodological advantage was also used to investigate photosynthate translocation from strawberry leaves into fruits. First, non-destructive ¹¹C-based imaging was applied to visualize photosynthate transport, and destructive ¹³C-labeling was applied afterwards on the same plant to quantify photosynthate content (Hidaka et al., 2019). Additionally, a study that investigated the effect of girdling on phloem transport dynamics was able to reuse the same young oak trees before and after girdling for up to five measurements in 1 week (De Schepper et al., 2013a). It was found that the position and speed of phloem transport in stems (with a diameter of 1 cm) changed after complete or partial girdling, a result that could only be obtained due to the non-invasive nature of PET. Furthermore, PET is especially suited to decipher phloem functioning. Since this tissue type is pressure-driven (De Schepper et al., 2013b), it is easily disturbed through transport or displacement, complicating its investigation (Pickard and Minchin, 1990; Turgeon and Wolf, 2009). Radiotracers enable visualization of the sugar flow without damaging or perturbing phloem transport. As such, dynamic positron-based imaging has successfully been used to investigate photosynthate translocation to storage organs like, e.g., root crops or fruits (Jahnke et al., 2009; Kawachi et al., 2011; Yamazaki et al., 2015; Hidaka et al., 2019; Kurita et al., 2020), phloem vulnerability to drought (Hubeau et al., 2018), and the effect of electric shock and cold shock on phloem transport (Pickard et al., 1993). Besides studies on phloem functioning, positron-based imaging has also been used to study the transport of jasmonate (i.e., a signal metabolite involved in plant defense) in whole plants (Ferrieri et al., 2005; Thorpe et al., 2007) as well as nitrate transport (Kiyomiya et al., 2001b; Kawachi et al., 2008). An overview on transport of plant metabolites using positron emitting isotopes is given by Kiser et al. (2008); Hubeau and Steppe (2015), Schmidt et al. (2020).

Nevertheless, the full potential of ¹¹C-PET in plant studies remains largely unexploited. Unlike human or laboratory animal imaging, where the object size is fairly fixed, the size of plant tissues may range from several millimeters to one meter, indicating that the scanner should have a large field of view (FOV) and a high spatial resolution. However, most of the PET studies carried out on plants use either PET systems that were specifically developed for plant imaging (Kume et al., 1997; Uchida et al., 2004; Jahnke et al., 2009; Beer et al., 2010; Wu and Tai, 2011; Weisenberger et al., 2012; Wang et al., 2014) or laboratory animal PET scanners (e.g., Alexoff et al., 2011; Hubeau et al., 2018), which are both characterized by a limited FOV (axial and transverse FOV of ∼ 7 and 10 cm, respectively, for cylindrical detector configurations as depicted in Figure 1, or ∼13 × 20 cm for planar detector configurations). Although these scanning systems benefit from a high spatial resolution (∼1.5 mm and sometimes submillimetre) generally only one or two plant organs (stem, leaves, fruits, or roots) can be visualized (e.g., Jahnke et al., 2009; Hubeau et al., 2018; Hidaka et al., 2019). Additionally, a more comprehensive view of whole-plant carbon allocation patterns can be gained from mature organs in large plants, where a quasi-active carbon sink for carbohydrate storage competes with different plant carbon sinks as growth or respiration (Sala et al., 2012; Hartmann and Trumbore, 2016). These difficulties may be overcome by making use of clinical PET systems, which are developed for human imaging, as these systems have two main advantages. Firstly, these imaging devices allow visualization of larger objects since they are characterized by a transverse and axial field of view (FOV – Figure 1) up to 85 and 26 cm, respectively (Vandenberghe and Marsden, 2015; Vandenberghe et al., 2016). Additionally, clinical PET scanners are equipped with a moving bed on which the plant can be placed, which enables visualization of even larger plants than the volume of the FOV, by acquiring multiple bed positions that can be stitched together into a larger volume. Another advantage of clinical PET systems is that they are nearly exclusively used in combination with structural imaging like computed tomography (CT) or magnetic resonance imaging (MRI). Consequently, the functional information provided by PET can be combined with structural data provided by CT or MRI, but only few plant studies have been reported making use of this multimodal imaging approach (e.g., Jahnke et al., 2009; Garbout et al., 2012). A drawback of clinical PET systems is the lower spatial resolution (∼3 – 5 mm - Vandenberghe and Marsden, 2015) compared to the laboratory animal PET scanners (España et al., 2014; Fine et al., 2014). A poor spatial resolution implies that small plant tissues cannot be distinguished from each other on the resulting PET images, e.g., phloem from xylem in small branches or different parts of a fruits’ pericarp or seeds. However, a good resolution is not always mandatory which is the case when long-distance transport of the radiotracer (in the order of 10 cm) is intended, e.g., transport of photosynthates from leaf to fruit or phytohormone transport. Additionally, the FOV of clinical PET systems have a horizontal axis while in some cases where large plants are studied, it might be appropriate to have a vertical orientation of the PET scanner. An overview of the above-mentioned specifications of laboratory animal and clinical PET imaging systems is given in Table 2 along with those for an ideal plant-PET system. Additionally, environmental parameters within the PET room that are of relevance for plant science, are listed. Note that temperature and relative humidity within a PET room are tightly controlled by air-conditioning. Lighting providing photosynthetically active radiation (PAR) is not present inside a PET room but the FOV is generally spacious enough to include LEDs beside the plant material.

Despite the intensive occupancy of clinical PET systems, we believe that studies making use of these functional imaging devices will make an important contribution to reveal complex in vivo interactions in plants, like the link between xylem and phloem tissue. For example, dynamic PET imaging in combination with compartmental modeling could potentially be applied to investigate phloem vulnerability to drought by repeatedly labeling a tree that is gradually experiencing more drought stress. The same combination of dynamic PET and modeling can be employed to investigate whether xylem embolism repair relies on photosynthates that originate from phloem, storage or local production related to woody tissue photosynthesis. Furthermore, improving our understanding of the mechanisms that drive phloem transport will undoubtedly lead to new approaches for manipulating photoassimilate allocation patterns in crops and fruits.

The basic requirement for conducting plant-PET experiments is access to both radioisotopes and a PET scanner. If not yet the case, contact should be established with key staff of a PET center, i.e., a medical imaging expert (e.g., typically the head of the preclinical imaging lab or clinical PET center) and a radiochemist, at least, if the PET center is accommodated with a cyclotron to produce the required radiotracer. PET centers are growing in large numbers worldwide and can be found in academic institutes as well as in smaller and larger hospitals. Smaller hospitals usually do not have a cyclotron, generally have a single PET scanner (typically combined with CT) and purchase their PET radiopharmaceuticals from commercial vendors that have a cyclotron facility. Larger hospitals and academic institutes have PET centers that can accommodate one or more cyclotrons, a radiochemistry laboratory and often several (multimodal) PET scanners, including laboratory animal (e.g., Alexoff et al., 2011; Hubeau et al., 2019b), clinical (e.g., Garbout et al., 2012; Karve et al., 2015), or self-designed imaging systems (e.g., Uchida et al., 2004; Jahnke et al., 2009; Weisenberger et al., 2012; Kurita et al., 2020). In these larger centers the integral multidisciplinary workflow (Figure 2) can be followed. As indicated earlier, the most frequently used PET isotopes in plant science are characterized by a short half-life (2.03, 9.96, 20.39 min for ¹⁵O, ¹³N and ¹¹C, respectively - Table 1) making it necessary for them to be produced on site. An exception is the longer-lived ¹⁸F (half-life 109.74 min), which can be purchased from an isotope supplier, e.g., Curium (France & United States), NTP (South Africa), Isotope-Rosatom (Russia), and ANSTO (Australia). Purchasing radiotracers is regulated and can, for example, only be done via a hospital’s radiopharmacy. There are more than 700 cyclotrons available worldwide of which many are dedicated to the production of PET isotopes (IAEA, 2012). Most of the recent cyclotron facilities are primarily constructed for the production of ¹⁸F in the form of the well-defined radiotracer ¹⁸FDG (2-[¹⁸F]-fluoro-2-deoxy-D-glucose) for cancer detection. Additionally, a sizeable fraction of these facilities has active research programmes for the creation of other ¹⁸F-labeled compounds and ¹¹C-labeled compounds (IAEA, 2012). Hence, there is a high probability that one of the nearest cyclotron departments is able to produce ¹¹C and potentially ¹¹CO₂, subject to some changes (see “Production and Formulation of Radiotracers”). Assuming that the PET center is interested in a mutual cooperation and a cyclotron facility is able to deliver the required tracer, proof of concept experiments may be organized to investigate the feasibility of the proposed plant-PET idea.

Other important points of discussion are related to the provisioning of dedicated lighting and space. Because of the strict regulations regarding radiation exposure, PET centers are heavily shielded to minimize radiation exposure to workers (Saha, 2016). This usually implies that the rooms do not have windows and thus have a limited availability of sunlight. By consequence, it is advised to provide (timed) lighting supplying PAR to maintain regular plant functioning when performing plant-PET imaging. Additionally, depending on the size of plant species that will be investigated, it might be necessary to discuss the availability of sufficient space to (safely) store plants before and after scanning. Lastly, due to the seasonal dependence of plant material, it is advised to plan experiments well in advance (∼2 months, although depending on the number of scans) as these medical imaging devices are generally well occupied.

Performing experiments with PET tracers involves exposure to ionizing radiation which could lead to harmful effects. To measure the amount of and exposure to ionizing radiation, several units are used. As indicated earlier, radioactive decay of a PET isotope occurs by the emission of a positron from its nucleus. Since this is a dynamic process, the amount of radioactivity of this type of radiotracers (as well as others used in e.g., SPECT) is quantified by the number of nuclei that decay per unit time. The standard international unit of radioactivity is Becquerel (Bq). One Bq corresponds with one disintegration per second. Curie (Ci) is the original unit of radioactivity and corresponds with the amount of radiation that is produced by one gram of radium (²²⁶Ra). This is an enormous unit as it equals 37 GBq compared to clinical used activities for PET imaging, which are in the range of 37 – 740 MBq (1-20 mCi). Regardless the amount of activity used, radiation exposure should be reduced or preferably avoided at all time, which forms the basis of radiation protection. This can be realized by using protective measures, personally and set-up wise.

Whereas nowadays radioactive tracers are inherently linked to clinical practice, their first application to study biological processes made use of plants and was described by de Hevesy (1923). He played a key role in the development of radiotracers, which has indirectly led to the development of nuclear medicine and PET imaging. As indicated earlier, the production of radiotracers for PET imaging starts with a cyclotron, where a charged particle (usually a hydrogen ion, e.g., H⁺) is accelerated to a high velocity to bombard a target atom, eventually creating an unstable nucleus that decays by positron emission. Depending on the target atom a certain radionuclide can be produced (Table 1). The most widely used positron-emitting nuclide in plant science is carbon-11 (¹¹C, half-life of 20.39 min), which is usually administered as gaseous ¹¹CO₂ to study long-distance transport of photosynthates (Minchin and Thorpe, 2003; Karve et al., 2015; Hubeau et al., 2018) or can also be administered in an aqueous solution to study xylem-transported CO₂ (Bloemen et al., 2015; Mincke et al., 2018, 2020; Hubeau et al., 2019b). ¹¹CO₂ is generally produced in two different ways depending on the target material, i.e., N₂/O₂ (Karve et al., 2015) or N₂/H₂ (Hubeau et al., 2018). In the former case, the nuclear reaction results immediately in the formation of ¹¹CO₂, however, with the undesired by-product ¹¹CO. Yet, CO can be oxidized to CO₂ by passing the target gas over hot copper oxide (Ferrieri and Wolf, 1983; Saha, 2016). Application of N₂/H₂ results in the formation of ¹¹CH₄ which subsequently needs to be oxidized via a cobalt oxide column to yield ¹¹CO₂ (Landais and Finn, 1989). This last step involves heating to 500 °C, requiring the use of a tube furnace that might not be a part of the standard equipment in a cyclotron unit. Other, albeit less frequently used, methods to produce ¹¹CO₂ are described by Ferrieri and Wolf (1983). Guidance information on operation and maintenance together with methodologies and relevant analyses regarding cyclotron production of the radionuclides listed in Table 1 is presented by IAEA (2012), which can be downloaded for free from the IAEA website along other complementary information regarding the development and production of radioisotopes and generators.

After its production, ¹¹CO₂ can either be channeled immediately to the plant labeling chamber when a direct connection is made from the cyclotron target or be trapped in a portable medium to be transported to the PET scanner. In the former case, ¹¹CO₂ can be concentrated through selective adsorption onto a molecular sieve (Ferrieri et al., 2005; Babst et al., 2013). Once the tracer is concentrated, it can be desorbed from the module to be directed to the experimental labeling chamber using a controlled air flow (Ferrieri et al., 2005). When ¹¹CO₂ requires transport to the nearby PET facility it can, depending on the research objective, either be trapped in a NaOH solution to be applied as a gas (e.g., Hubeau et al., 2018), or bubbled through a slightly acidic buffer (e.g., Tris, phosphate or citric acid) to obtain an aqueous ¹¹CO₂ solution (e.g., Mincke et al., 2018). In both cases, the liquid tracer solution can be transported in a shielded syringe carrier. The dissolved ¹¹CO₂ can be released from the NaOH solution by injection into an excess acidic solution (e.g., H₂SO₄), which can subsequently be directed towards the plant tissue by bubbling air into the solution. Safe transport of gaseous ¹¹CO₂ trapped in a miniature molecular sieve of a portable handheld delivery system (Kim et al., 2014) or a stainless steel trap immersed in liquid nitrogen or liquid argon (Ishioka et al., 1999; Hidaka et al., 2019) are described. With regard to the formulation of a ¹¹CO₂-enriched buffered solution that has to be exposed to the xylem (regardless the radioisotope), the buffer’s pH is allowed to deviate slightly from the pH of xylem sap of the species under study. Specifically, once the tracer is taken up, equilibrium reactions will occur, creating the right pH inside the tissue (Butler, 1991). Hence, the pH of an ¹¹CO₂-enriched aqueous solution can be slightly more acidic than the xylem sap to favor the ¹¹C-label being dissolved as CO₂ (aq.) over bicarbonate.

The use of ¹¹C is not limited to CO₂ as it can also be built into other traces like methyl jasmonate, auxin or salicylic acid (Thorpe et al., 2007; Agtuca et al., 2014). Other positron-emitting isotopes applied in plant studies are fluorine-18 (¹⁸F), nitrogen-13 (¹³N) and oxygen-15 (¹⁵O), which can be incorporated into biologically active molecules like ¹⁸FDG, ¹³NO3- and H₂¹⁵O, respectively. Therefore, the use of these radiolabelled molecules includes, but is not limited to, investigating sugar transport (e.g., Fatangare and Svatoš, 2016), nitrate uptake via roots (e.g., Siddiqi et al., 1989; Liang et al., 2011), and water transport (e.g., Mori et al., 2000; Kiyomiya et al., 2001a), respectively. Application of ¹⁸F-fluorine is described as a proxy for tracing water transport (e.g., Ishioka et al., 1999). ¹³N has also been applied as gaseous ¹³N₂ to study nitrogen fixation of rhizobium root nodules (Ishii et al., 2009; Kasel et al., 2010; Yin et al., 2019) and as ammonium (¹³NH₄) to study the effect of nitrogen deficiency, phytohormones and lighting treatments on its uptake and translocation in rice plants (Kiyomiya et al., 2001b). A nice tabular overview of positron-based plant experiments carried out to date, including the topics listed above as well as uptake and translocation of heavy metals, is provided by Schmidt et al. (2020). The above-mentioned radiotracers, together with their involved pathways, form only a fraction of the potential molecules that can be studied in plants using PET imaging. By making use of organic (radio)chemistry, radionuclides can be incorporated in many other dedicated molecules. However, due to the short half-life, the isotope needs to be labeled to the required molecule by a radiochemist in a short time frame requiring simple and efficient chemical conversion and purification methods (Figure 2). After labeling, the radiotracer is ready to be exposed to the plant material and PET imaging can start.

The aim of plant-PET is to quantitatively determine the dynamic flow of a radioactively labeled compound inside the plant. The measured data after PET scanning represent the total activity along lines of known location, i.e., LORs (Figure 4). To obtain a final image, the mathematical problem consists of reconstructing the spatial distribution of radioactivity in the plant, at specific time points from these LORs. These measurements are generally noisy because limited amounts of radioactivity will be used in practice and constraints on acquisition time due to the isotope’s half-life. For emission tomography, there are two categories of reconstruction algorithms, namely, analytical and iterative methods. The reconstruction algorithm that is used will have important effects on the noise properties of the final image. Note that regardless of the reconstruction algorithm, exponential decay of the radiotracer is corrected. However, due to the noisy nature of the acquired emission data, it is desirable to use a reconstruction approach that takes into account the statistical nature of the noise. Since the emission and detection of photons are Poisson processes, iterative methods that model Poisson statistics have become the standard for PET reconstructions (Vandenberghe et al., 2016). Analytical methods, such as the filtered back projection (FBP) algorithm, are computationally very efficient. However, they do not take into account counting statistics, and consequently the use of these analytical methods has been completely replaced by iterative reconstruction methods. Here, the maximum-likelihood expectation maximization (MLEM) is the foundational algorithm (Lange and Carson, 1984) and it has been shown that it provides images with better noise properties compared to analytical methods (Shepp et al., 1984). However, MLEM is computationally expensive and requires many iterations to reach a suitable image. To reduce computational cost, block-iterative algorithms such as the ordered-subsets expectation maximization (OSEM) algorithm (Hudson and Larkin, 1994; Hutton et al., 1997) and the Row-Action Maximum Likelihood Algorithm (RAMLA) (Browne and De Pierru, 1996; Teymurazyan et al., 2013) have been introduced and can be regarded as modified versions of MLEM and OSEM, respectively (Tarantola et al., 2003). Still, in each of these reconstruction methods the target remains maximization of a likelihood function. In both OSEM and RAMLA, the measured data is divided into subsets that are sequentially used to accelerate the reconstruction process compared to MLEM. The number of subsets provides a good estimate of the acceleration factor that can be obtained (Hudson and Larkin, 1994; Hutton et al., 1997). The effect of reconstruction algorithms MLEM and OSEM as well as the effect of a varying number of OSEM subsets on plant-PET data was tested for a study visualizing phloem transport in Arabidopsis (Figure 5A). In this study the rosette of an Arabidopsis plant was labeled with one pulse of ¹¹CO₂ while the inflorescence was positioned in the FOV. Data was acquired for 120 min but to reduce the computational cost of the reconstruction only one time frame of 5 min was selected towards the end of the scanning period, i.e., when the activity inside the FOV was maximal (inserted PET image of Figure 5A). Comparison of the different reconstruction algorithms was based on the convergence of the sum of all voxel values of the reconstructed time frame in function of the number of iterations per subset (Figure 5B). It can be assumed that with convergence of the total voxel value, more iterations will not lead to a better-quality image; on the contrary, the noise present can be amplified with further iterations. Application of MLEM and OSEM using 4 subsets (i.e., OSEM 4) led to a similar convergence of the total voxel value. The total voxel value was slightly lower when OSEM 4 was applied instead of MLEM, because each subset contained only one fourth of the acquired data. The main difference between both algorithms is the reconstruction time needed per iteration as OSEM 4 was roughly four times faster compared to MLEM (0.145 vs. 0.5 s per iteration – Table 5). Further increase of the number of subsets is accompanied with faster reconstruction speeds (Table 5) but at a cost of image quality (Figure 5B) since less data is used in each subset. An indication of image quality can be provided by calculating the signal-to-noise ratio (SNR), which was determined by dividing the average voxel value by the standard deviation in an ROI that closely fits part of the plant tissue (indicated by arrow on insert Figure 5A). As can be observed in Table 5, the SNR decreases with a higher number of subsets and one should be careful not to select too many subsets, because then each individual subset contains less tomographic and statistical information, potentially resulting in a loss of image quality.

Practically, image reconstruction methods are generally included in the software that comes with the PET system. Hereby, MLEM and OSEM are currently incorporated in many PET systems and it is advised to use these reconstruction algorithms over FBP to obtain high-quality (dynamic) images. RAMLA is implemented on some commercial PET systems and, when available, could lead to faster convergence than OSEM (Saha, 2016).

Iterative methods have the theoretical potential to produce unbiased estimates of the tracer distribution within an object and thus to provide absolute quantification. Two criteria characterize the reliability of absolute quantification: accuracy and precision (Frey et al., 2012; Vanhove et al., 2015). Iterative methods can substantially improve both criteria because they include an appropriate statistical model to describe the measured data, resulting in better noise properties and thus improved precision, and they allow to accurately model image degrading effects such as photon attenuation, scattered and random coincidences (Figure 4), resulting in a more accurate representation of the tracer distribution when a sufficient number of iterations are used (Vandeghinste et al., 2014). When absolute quantification is required, it is important to perform a cross-calibration between the PET camera and the dose calibrator required to measure the amount of radioactivity used during the plant-PET experiments. Cross-calibration is a direct, relative calibration between the institution’s own dose calibrator and PET camera. In short, the procedure is as follows: a syringe has to be filled with a radioactive solution with an activity (in Bq) that is close to the injected activity applied during the plant-PET experiments. This syringe should be measured in the institution’s dose calibrator. The solution should then be introduced into a calibration phantom (mostly a cylindrical phantom) with an exact known volume (in mL) filled with water, resulting in a solution with known activity concentration in Bq/mL. After acquiring a PET scan of the calibration phantom, the acquired data have to be reconstructed using the same reconstruction parameters that will be used during the plant experiment. A region-of-interest has to be drawn on the reconstructed images of the calibration phantom in order to determine the average volumetric concentration of activity within the phantom as measured by the PET scanner. Conversion factors can then be directly derived so that the measurements from dose calibrator and PET camera can be synchronized (Boellaard et al., 2010, 2015). Karve et al. (2015) described the impact of some image degrading effects using a phantom when imaging sorghum and found that scatter correction had little effect (<1%) on the stem and shoot, whereas attenuation of the γ-photons (due to energy loss to the irradiated tissue) led to an error of 30% in the stem and 55% in the root. It is thus especially important to investigate the impact of these effects when comparing plant tissues of different sizes as well as larger tissues (e.g., stems) given the half-value layer of 29 cm for wood (Table 3). When CT data is acquired in addition to PET images, it is generally used to correct the latter for photon attenuation. CT data can additionally be used to facilitate image analysis (see “Image Processing and Quantification”).

Image reconstruction is demanding in terms of computational power and time, especially when the stored LORs have to be reconstructed into different time frames to monitor a dynamic process, which is called dynamic or 4D PET. Here, series of PET images are obtained per e.g., 2–10 min of the acquisition time, depending on the sensitivity of the PET scanner and the amount of radioactivity added. However, it is also advised to reconstruct a static image that is the mean/sum of the all the individual time frames. This static 3D image has a higher SNR than the individual time frames (Turkheimer et al., 2014) and it is particularly useful for visual assessment of the entire dynamic process in one 3D image. This is demonstrated in Figure 6, where the static image is shown in the upper left corner along with some dynamic time frames of 20 min. To this end, a Populus tremula L. branch was exposed to gaseous ¹¹CO₂. The static image shows ¹¹C-tracer accumulation in the complete branch segment inside the FOV in contrast to the dynamic images, where only part of the branch segment is visible due to dynamic nature of the process. Aside from the higher SNR, the reconstruction time of such a static image is generally much shorter than the dynamic reconstruction time.

After image reconstruction, while applying the necessary corrections (if needed), 3D or 4D images are obtained, which can be analyzed using image analysis software. Commonly used software includes OsiriX (Rosset et al., 2004 – commercial), Horos [¹ GNU Lesser General Public License, Version 3.0 (LGPL 3.0) – open-source] and AMIDE (Loening and Gambhir, 2003 – open-source). These software packages allow to reduce noise by smoothing or blurring the images, which can be executed on both static and dynamic reconstructed images. A common approach is the application of a gaussian filter, whereby a gaussian curve is applied to calculate the intensity of each voxel by using a fixed number of voxels around it. However, reducing noise will also result in poorer spatial resolution. Finding the ideal trade-off between noise and spatial resolution is usually performed on the static image when a dynamic process needs to be quantified. Subsequently, the static 3D image can be used to draw regions of interest (ROIs) onto the plant tissue under study (Figure 7A). In Figure 7A, xylem-transported ¹¹CO₂ in a young branch segment of Populus tremula is imaged and the goal was to visualize and quantify its dynamic transport. In this example, four consecutive ROIs are drawn (colored ROIs 1 – 4) on the static 3D image because it depicts the branch more clearly than each separate image that makes up dynamic 4D image (see “Image Reconstruction”). Image analysis software allows to upload multiple datasets in one study so that the dynamically reconstructed 4D PET data can be uploaded as well. All image analysis software includes the possibility to calculate the measured activity in each ROI for any of the 4D PET images over time. This data can be plotted directly as time-activity curves (TACs – one for each ROI) which can be used for further quantification. An example of measured TACs (circles) for each of the four colored ROIs (Figure 7A) is shown in Figure 7B. TACs can for example be used to retrieve physiological properties of the plant like phloem transport speed (based on the time of first tracer arrival, e.g., Karve et al., 2015), uptake and distribution of plant nutrients like NO₃ (e.g., Kawachi et al., 2008; Liang et al., 2011), NH₄ (e.g., Kiyomiya et al., 2001b), or Fe (e.g., Tsukamoto et al., 2009), photoassimilate translocation to storage organs (e.g., Kikuchi et al., 2008; Hidaka et al., 2019), xylem-transported CO₂ (Hubeau et al., 2019b), as well as changes in whole-plant carbon allocation (e.g., Karve et al., 2015).

Additionally, dynamic PET measurements can be used as input for mathematical frameworks to retrieve physiological plant parameters that are difficult to measure with other techniques. This can be achieved by means of an input-output framework, as developed by Minchin and co-workers (Minchin and Thorpe, 2003; Minchin, 2007, 2012; Kiser et al., 2008), or by mechanistic compartmental modeling (Bühler et al., 2011, 2014, 2018; Hubeau et al., 2018). Compartmental models have an advantage over input-output models because they restrict model outcomes with physical boundaries, allowing to pose realistic ranges for solute transport characteristics (Bühler et al., 2011; Hubeau and Steppe, 2015). Therefore, compartmental models are of high interest to study long-distance transport in plants for the investigation of functional traits, especially under diverse environmental conditions (Jahnke et al., 2009). This boils down to translating the tracer dynamics (i.e., TACs) by a model that represents the system under study. The model is composed of mass balances (i.e., differential equations) defined by tracer concentrations and kinetic rate constants to describe the exchange between compartments. This method has usually been implemented with the assumption that the system under study does not change during the experiment (Minchin and Thorpe, 2003). The example of xylem-transported ¹¹CO₂ (Figure 7) is described by Mincke et al. (2020) using three compartments which will be simplified in this manuscript to a two-compartment model, purely for demonstration purposes. Each of the ROIs can be regarded as a small branch segment that is divided in two compartments, which are described by two parameters, i.e., xylem CO₂ transport speed v_CO2 (mm min^–1) and exchange fraction a (min^–1) (Figure 8). Sap-dissolved ¹¹CO₂ can move within xylem conduits of each ROI (compartment 1) with transport speed v_CO2 and can move to surrounding chloroplast containing cells (compartment 2) through a to be assimilated and immobilized by woody tissue photosynthesis. The equations describing this model along with extra considerations on the model can be found in Supplementary file 2. This model could equally be applied to study phloem transport within a petiole or a branch after gaseous ¹¹CO₂ exposure (Figure 6) with the two parameters then being phloem transport speed and the unloading fraction.

The goal of fitting a model to dynamic tracer data (i.e., model calibration) is to derive specific parameters that have a physiological meaning, which are difficult to obtain by direct measurement. Specifically, due to the limited spatial resolution of PET (∼ 1 - 3 mm), physiological processes in several tissues are integrated into the measured TACs. In the example of xylem-transported CO₂, these parameters are the xylem CO₂ transport speed v_CO2 and the exchange fraction a that gets photosynthetically incorporated into the tissue. Practically, such physiological parameters can be retrieved by implementation and calibration of plant models using software packages, which include MATLAB (MathWorks, Inc, Natick, MA, United States - commercial), (R Core Team, 2020 - open source) and dedicated plant modeling software PhytoSim (Phyto-IT, Gent, Belgium - commercial). When the proposed model properly describes the system under study (i.e., TACs), model calibration should converge, resulting in the optimal model parameters. These parameters can then be used to simulate the solved differential equations which should fit the measured TACs (continuous lines in Figure 7B). When plant modeling is intended, it is advised to have a profound read on model calibration and simulation (e.g., Sun and Sun, 2015).

It is clear that good and reliable ROI placement is a prerequisite when fitting the resulting TAC data to a model. Therefore, it is of great importance to know which part of the plant is being imaged inside the FOV. Some PET systems are combined with a CT or MRI module which facilitates this process because anatomical images can be obtained aside from the functional PET data. For plant-PET studies, however, simple photographs can generally serve as a good reference instead of CT or MRI data. The importance of good ROI-drawing practices is exemplified in Figure 7C which shows the branch segment that was imaged in Figure 7A. Without this image, it seemed obvious to start drawing ROIs from the point where the highest activity was measured (gray dotted ROIs). However, in these ROIs a petiole originates from the branch and due to the limited spatial resolution of the PET system (∼ 1 – 3 mm), the tracer uptake inside the petiole and branch could not be resolved, resulting in TACs with a higher tracer uptake for these ROIs (gray TACs in Figure 7B). This would inevitably prompt incorrect parameter values upon model calibration. Therefore, it is advisable to select a branch segment without ramifications for ROI analysis.

Aside from studying in vivo dynamics of xylem-transported ¹¹CO₂ (Mincke et al., 2020), compartmental modeling has been applied in plant-PET studies to investigate the vulnerability of phloem characteristics, including the phloem speed to drought (Hubeau et al., 2018) and girdling (De Schepper et al., 2013a), tracer kinetics of plant carbon allocation, including carbon storage and export rate (Fares et al., 1988), and axial and lateral exchanges in transport pathways of plants (e.g., phloem) (Bühler et al., 2011, 2014).