Design of an Anthropomorphic Respiratory Phantom for PET Imaging

Purpose: Respiratory motion during positron emission tomography (PET) can be a major detriment to image quality in oncological imaging, causing loss of quantiﬁcation accuracy and false negative ﬁndings. The impact of motion on lesion quantiﬁcation and detectability can be assessed using anthropomorphic phantoms with realistic anatomy representation and motion modeling. In this work we design and build such a phantom, with careful consideration of system requirements and detailed force analysis. Methods: We start from a previously-developed anatomically accurate shell of a human torso and add elastic lungs with a highly controllable actuation mechanism which replicates the physics of breathing. The space outside the lungs is ﬁlled with a radioactive water solution. To maintain anatomical accuracy in the torso and realistic gamma ray attenuation, all motion mechanisms and actuators are positioned outside of the phantom compartment. The actuation mechanism can produce a plethora of custom respiratory waveforms with breathing rates up to 25 breaths per minute and tidal volumes up to 1200mL. Results: Several tests were performed to validate the performance of the phantom assembly, in which the phantom was ﬁlled with water and given respiratory waveforms to execute. All parts demonstrated nominal performance. Force requirements were not exceeded and no leaks were detected, although continued use of the phantom is required to evaluate wear. The respiratory motion was determined to be within a reasonable realistic range. Conclusions: The full mechanical design is described in this paper, as well as a software application with graphical user interface which was developed to plan and visualize respiratory patterns. Both are available open source and linked in this paper. The developed phantom will facilitate future work in evaluating the impact of respiratory motion on lesion quantiﬁcation and detectability.


I. Introduction
Positron emission tomography (PET) imaging is widely used in oncology for tumor detection, monitoring, and quantification. A leading factor that can adversely affect the quality of thoracic PET images is respiratory motion during the scans 1 . One of the main negative effects is the reduction of contrast for small lesions (e.g. cancer metastases) 2 , which worsens lesion detectability and introduces bias in the measured standardized uptake values (SUVs).
For larger lesions, respiratory motion may introduce bias in radiomic features that quantify their shape and texture 3 4 5 . In normal respiration, the amplitude of diaphragm movement is on the order of 1.5-2cm 6 , while deep inspiration may result in 7-13cm diaphragm displacement 7 . For clinical PET scanners with spatial resolution around 0.4-0.5cm full-width at half-maximum (FWHM), motion of this magnitude can lead to effective usable resolution closer to 1cm 8 9 . Thus, motion needs to be taken into account in the process of cancer diagnosis and staging 10 . as well as during image-guided radiotherapy 11 .
Since it is impossible to know the ground truth with real subjects, the impact of motion on PET image quantification is typically assessed using geometrically simple phantoms that simulate motion with a precisely-known trajectory, such as the QUASAR Phantom (Modus QA, Ontario, Canada). On the other hand, with continuous advances in PET scanner sensitivity and resolution 12 , as well as development of novel image quantification paradigms 13 , it becomes of interest to evaluate the effects of respiratory motion under more anatomically realistic conditions. Several anthropomorphic phantoms have been developed in the past, each of which solves a subset of the problems associated with modeling respiratory motion.
These phantoms are compared in Table 1. While Wilhelm 14 has the most realistic overall motion of any existing device, it lacks any bone structure, which greatly affects the realism of the phantom as gamma ray attenuation and scatter by bones can significantly affect the image quality and quantification. Conversely, Alderson 15 has bones as well as respiratory and cardiac motion; however its anatomy is simplified. It also does not support the addition of lesions, which are key in any studies investigating the effect of motion on image quantification.
The goal of this work was to create an anatomically accurate phantom with realistic modeling of respiratory motion. We build upon an existing phantom previously developed and tested by Kadrmas et al. 16 17 , henceforth referred to as "Probe-IQ" (Image Quality Probe). To the best of our knowledge, Probe-IQ to this day has the highest level of anatom-ical realism in the field. While highly realistic in PET and, to a lesser extent, computed tomography (CT) scans, the phantom has previously been completely static and not used to study motion effects. The motion-enabled phantom described in this paper uses the shell and rib-cage of the original Probe-IQ phantom, but adds custom-built elastic lungs with trachea, and an electronically-controlled actuation mechanism to create realistic respiratory motion. The lungs expand and contract during the respiration.
The Probe-IQ phantom enhanced with respiratory motion aims to achieve the following: Anatomical Accuracy • Builds off the static anatomical accuracy of Probe-IQ and has realistic lung motion.
• Avoids any unrealistic parts like connecting rods or metal components in the torso.
• All materials carefully selected with reference to mass attenuation coefficients 18 that resemble human tissue.

Breathing Control
• Able to achieve a wide range of breathing rates and tidal volumes (i.e. air displaced between inhalation and exhalation). Namely, at least up to 25 breaths per minute at 1L tidal volume; typical relaxed breathing is 500mL at 15-20 breaths per minute 19 .
• Has highly controllable, repeatable, consistent breathing motion to generate high quality data, but also can include occasional disrupted breaths or inconsistencies, as would happen in a real patient.
In addition, safety is a concern, as the phantom is filled with about 15L of radioactive solution (300 to 1000MBq of radioactivity per scan) for PET acquisitions. The design must avoid leaks, and minimize the possibility of large spills. Easy fill-ability of the phantom is also desirable to reduce radiation exposure to users and to increase usability.

II. Materials and Methods
The respiratory motion-enabled Probe-IQ phantom involves three main components: 1) elastic lungs, 2) an actuation method, and 3) a control system (electronics and software).
The overall structure can be seen in Fig. 1 and all design files and code can be accessed in the Open Source Section at the end of this paper. The lungs are located inside the rib cage of the existing Probe-IQ phantom (A), and surrounded by a radioactive water solution creating the warm, non-specific background typically present in oncologic PET images. The lungs are connected to the atmosphere by a breathing tube (trachea) (F), which can be sealed at the neck. The actuating mechanism is positioned below the phantom (B, C, D), where the pelvis of a human would be located. It is outside the field of view of the PET scanner so as not to create image artefacts. The phantom operates by piston-actuated passive breathing, as explained below and seen in figure 2.
Achieving respiratory motion with the lungs is possible through a variety of mechanisms, which fall into two main classes.
First, the lungs can be directly inflated using air pumps or compressors. This is the most obvious approach, but involves a number of complicating factors. The lung volume cannot simply increase inside a sealed, rigid torso filled with an incompressible fluid. An overflow tube or expanding section of the torso would be required. The former would create the risk of leakage, while the latter would require a powerful compressor. Furthermore, control is much more difficult with a pneumatic system and would require a great increase in complexity.
The second, and preferred method is to instead modulate the volume or pressure of the whole phantom in a manner analogous to actual respiratory breathing. Since the phantom is sealed, rigid, and entirely filled with water, except for the air-filled lungs, changing its volume by ∆V induces an equal volume change of ∆V in the lungs. Instead of compressing the air in a sealed set of lungs, the pressure requirement of the actuating mechanism can be dramatically decreased by opening the lungs to the atmosphere once the phantom has been filled and sealed. Contrary to intuition, the lungs will not collapse under the pressure of the water since the water volume is constant and cannot expand to fill the vacant space created if the lungs were to collapse. In effect, a relative negative pressure is created in the liquid anterior to the lungs, just as human breathing relies on negative intrapleural pressure. Now, when the volume of the torso is changed, that volume of air is simply exhaled to or inhaled from the atmosphere (figure 2). To prepare the phantom for imaging, the following steps are taken:

II. MATERIALS AND METHODS
1. The lungs, organs, and bones are positioned inside the thorax.
2. The lungs are inflated to their maximum capacity via a Schrader valve and a manual pump and sealed ( figure 3).
3. The piston is moved to its most retracted position (i.e. the phantom is at maximum volume), and the base plate is attached.
4. The torso is completely filled with radioactive water solution using the ports in the neck, without leaving air pockets. A valve in the base plate, at the highest point in the torso, is used to release the displaced air ( figure 3).
5. The torso is sealed, and the lungs opened to the atmosphere.
Since the torso is rigid and sealed, its volume cannot change, so the lungs remain inflated.
At this point, the lung volume can be fine-tuned by opening the water-filling port and/or base purge valve while pumping air into the lungs through the Schrader valve using a manual pump. Thus, any small changes or issues can be rectified. With the phantom set up, the user can define a wide variety of respiratory patterns, rates, and volumes using a graphical user interface. The piston then moves along the defined trajectory for the duration of a scan, causing the lungs to expand and contract due to the changes in pressure. The piston motion can also be coupled directly to the lungs using thin cables, which are not visible in the PET scan. The next three sections explain the lungs, breathing mechanism, and software in more detail.

II.A. Lungs
The lung shapes were derived from a CT scan of an adult male lung and simplified using mesh editing software (Blender Foundation, Amsterdam) to reduce the cardiac notch and make the right and left lungs more symmetrical ( figure 4). This was done primarily for ease   The lungs were manufactured from Chlorosil-35 (Ottobock, Germany), a two-part, silicone-based elastomer with Shore A hardness 35. Following high temperature vulcanization, this material is durable, long-lasting, and thermostable, yet flexible to allow contraction and expansion. The material was previously tested in another phantom 14 . The lung manufacturing process was as follows: 1. A negative mold was 3D-printed out of polylactic acid (PLA) in two halves due to size constraints in 3D-printing.
2. Dental plaster was poured into the negative mold using a hole at the base.
3. Once the plaster dried, it was extracted from the mold and put in a polyvinyl alcohol (PVA) bag. This bag prevents the Chlorosil catalyst from reacting with the plaster.
4. The Chlorosil was rolled onto the positive dental plaster mold of the lungs and placed in an evacuated plastic bag to obtain a uniform shape and thickness.
5. The mold with the rolled Chlorosil was placed in an oven at 200°C for 12 hours to cure the Chlorosil.
Last edited December 19, 2020 6. A thin piece of stiffer plastic with a mounting point for a cable was placed in a silicone pocket at the base of each lung.
7. The mold was removed from inside the Chlorosil-35 lungs through the breathing hole to which the trachea will be attached; this is possible because the material is highly flexible.

II.B. Breathing Mechanism
To modulate the volume, both a rubber "diaphragm" membrane stretched across the entire phantom base and a piston mechanism were considered. After preliminary testing, the diaphragm mechanism was found to be unreliable, so the piston mechanism was chosen.
This consists of a large cylinder attached directly to the base plate of the phantom. A piston is driven back and forth in the cylinder using a linear actuator to create the volume change.
The actuator works against the piston friction, water viscosity/inertia, and elastic forces in the lungs.
The mechanism consists of three major components: the piston and cylinder (figure 6), the base and mounting plates, and the linear actuator. Each is described below, before outlining their cumulative capabilities. The assembled mechanism is shown in figure 8.

II.B.1. Piston and cylinder
A key consideration in the piston and cylinder design was dimensional tolerance and stability.
To ensure a good seal, specific dimensions with low tolerances had to be chosen, according to the Parker O-ring Handbook for dynamic sealing. To achieve and maintain the tight tolerances (eg. ±0.1mm over a 14cm diameter) while avoiding attenuation and scatter from metallic components, both the piston and cylinder were manufactured from Delrin acetal plastic. Delrin is known to be dimensionally stable and machinable. It has a low water absorption of 0.25% (according to McMaster-Carr), which allows it to keep its shape when in contact with water. Furthermore, Delrin has a low friction coefficient of 0.2, which reduces piston-cylinder friction and greatly decreases the required actuator load 20 . Beyond material choice, the cylinder was designed with thick, 27-mm walls to avoid any warping. A 3.8mm long chamfer at the mouth of the cylinder ensures easy insertion of the piston without scratching any of the surfaces important for the seal.
Two opposing factors played a role in determining the inner diameter of the cylinder.
The larger the diameter, the smaller the piston displacement has to be for a given volume change, and thus the lower the speed requirement on the linear actuator. However, a larger piston is harder to machine within tolerance and to fit onto the base plate. A diameter of 14cm was chosen as a compromise. At this diameter, the piston displacement for a given volume change is approximately equal to the axial lung extension for a given tidal volume 7 .
For example, a piston movement of 3cm leads to a volume change of 500ml, which is a typical relaxed adult tidal volume. According to Wade et al. 7 , the lungs should very roughly extend on average 1.5cm for 500ml tidal volume, though this varies widely between individuals.
Ultimately, with the chosen dimensions, the change in the torso's (and thus also lungs') volume, ∆V , is given by: where D and ∆x are given in Fig. 2. The system's stroke is 8cm, so tidal volumes of up to 1232ml are possible, which constitute realistic deep breaths.
The piston has 2 O-ring grooves which ensure alignment inside the cylinder and provide a watertight dynamic seal (Fig. 7). The actuator-side groove is 6% (0.  does not break down easily under influence of radiation. X-and circular-profile rings were tested, but no major difference in performance was detected. The cylinder's inner surface was honed to 8-16µin RA roughness. An O-ring groove was milled into one end of the cylinder (part A in Fig. 7), with the mounting screws located radially inside the groove to avoid leaks through the screw holes. As the second plate is further away from the scanner's gantry, and supported fully by  Last edited December 19, 2020

II.B.3. Linear Actuator
The actuator type and model were selected based on the criteria outlined in Table 2, as well as cost. We set out to achieve a 1000ml tidal volume at 25 breaths per minute. While the piston was designed to provide up to 1232ml tidal volume, and the 90mm actuator stroke supports the full range of piston motion, the actuator must be fast enough to reach 25 breaths per minute at this amplitude.

By using Equation 1 and noticing that a single breath involves both extension and
retraction of the actuator, we find an expression for speed,ẋ, in mm/s as a function of breathing rate, ν, and amplitude, V , in breaths per minute and ml: Hence, to fulfil the design objective, a linear speed of at least 54mm/s is required (assuming the actuator accelerates instantly, which is a reasonable assumption: the chosen actuator has a max acceleration of 1667mm/s 2 ).
With some simplification, the required force is approximately the sum of the piston friction (F f ), the water inertia (F i ), and the elastic stretching of the lungs (F e ): To calculate the inertial force, assume the actuator accelerates to the 54mm/s velocity within 0.5cm. This corresponds to an acceleration of a = (0.054m/s) 2

2·0.005m
= 0.292m/s 2 . While most of the water in the phantom does not move much during the acceleration, at least the water that was in the piston will be accelerated, in addition to some water in the rest of the phantom. Suppose, then, that the total volume of water being accelerated is twice the maximum tidal volume -i.e. 2000ml -which is 2kg. Then This is negligible compared to the frictional force. Even if we took the whole 15kg of water to be accelerating, it would still only constitute about 4N . This can therefore be ignored.
Similarly, the static pressure on the piston can be ignored because the lungs in the water are at atmospheric pressure, and the piston sits at almost the same height as the lungs. Thus, the water pressure on the front of the piston and the air pressure on the back effectively cancel out.
The pressure required to stretch the lungs is more difficult to derive. To simplify the problem, let us assume that the lungs are cylindrical, and use the thin-wall approximation to find the hoop stress in one lung. This, however, also assumes that Hooke's Law holds for rubber-like elastomers. Merrit and Weinhaus 21 found that this is not the case, and that after an initial linear section, the required pressure to increase the radius sharply falls off. Thus, Hooke's Law provides a rough, very conservative estimate. Let , r, t be the cylindrical lung's length, radius, and wall thickness respectively, and 0 = 200mm, r 0 = 52mm, and t 0 = 2mm be the initial values. These give the expected initial volume of 1700ml, as well as an initial material volume of V mat 0 ≈ 2πr 0 t 0 ( 0 + r 0 ) = 21000mm 3 . Using the incompressibility of , so the wall thickness relates to the length and radius by: Now using hoop stress, r∆P t = σ H , and Hooke's Law, σ H = H E = t 0 −t t 0 E, we obtain an expression for the required pressure differential applied by the piston: Combining Equations 5 and 6: ∆P = 21000 r 2 ( + r) 1 − 21000 rt 0 ( + r) E Last edited December 19, 2020 This pressure is exerted evenly across the piston surface, so using F = P A we find F e : F e = (0.14) 2 π 4 21000 r 2 ( + r) 1 − 21000 rt 0 ( + r) E to be mounted as seen in Fig. 8.
According to the manufacturer specifications, the actuator position is accurate to within 0.03mm per cm of movement 23 , which translates to a volumetric error of up to 0.3ml per 100ml volume change, using Equation 1. In addition, the 1.8°/step stepper motor combined with the 5mm-lead ball screw mechanism, as well as 2000-count encoder feedback facilitate exact velocity and acceleration control.
The force analysis was verified during testing by running the actuator at 40% force, where it stalled, and then at 60%, where it ran smoothly. This implies the required force is around 50% of the actuator's force capability, which, given the chosen safety factor of 2, means the required force corresponds closely to the derived value.

II.C. Software and Electrical Design
The Tolomatic ERD15 actuator is driven by a stepper motor with encoder feedback, which is in turn powered by a 120W, 48V power supply, and controlled by stepper driver hardware from Tolomatic. The goal in this control system is to create realistic, consistent, repeatable lung motion with flexibility in breathing rate and amplitude, as well as the ability to include breathing inconsistencies for added realism. Two distinct control methods were created for the phantom and are described below. The first is simple and fast to set up while the second provides more realism, so each is useful in different applications.
First, a free Windows application (described below) can be used to communicate with the stepper driver over USB to configure the actuator. This option is explored in-depth below. The second option is analog position control. Here, a 0-10V analog signal can be input to the driver, which moves to the corresponding position. Control through ethernet and Modbus RTU over RS-485 are also possible, but neither was investigated in this work.

II.C.1. USB Interface
The actuator manufacturer provides a software interface called Tolomatic Motion Interface (TMI) to communicate with its stepper controllers over USB. While the software is primarily used to configure the driver by setting acceleration, deceleration, maximum velocity, error states and more, it can also be used to directly control the actuator's movement. In 'Indexing Mode' up to 16 moves can be defined, each with a certain acceleration, deceleration, velocity, and goal position. Any of these moves can then be chosen and combined in any order to form a repeating series of up to 16 moves. Taking the simplest example, one may define just 2 moves, one to 45mm, and one to 1mm, and cycle between these two positions indefinitely.
By combining more positions, however, and altering their accelerations and decelerations, a wide variety of breathing patterns can be achieved, including realistic respiratory cycles.
The problem with this method is that visualizing what the respiratory cycle will look like based on a series of linear position, velocity, and acceleration values is difficult. A graphical user interface (GUI) was therefore developed in Python to allow motion planning Last edited December 19, 2020 and visualization of the lung volume as a function of time (figure 9). Figure 9: Screenshot of motion planning application. The green curve is the desired respiratory cycle, while the red is the pattern carried out by the phantom based on the GUI inputs.
In the application, the user can define the breathing rate, amplitude, and base lung volume. We used published models 24 to identify a physiologically representative equation for a respiratory curve (Equation 9, x = amplitude, t = time), which can be scaled and shifted to match the desired, user-defined breathing parameters. This curve is plotted in green in figure 9.
x = e −1.71668t 0.0106 + 2.3313t + 0.535t 2 + 3.9594t 3 2.3062 + 0.3517t − 0.6487t 2 + 0.1177t 3 The user can then define up to 4 moves with position, velocity, acceleration, and deceleration, and place them in any order. The corresponding motion profile is generated through iterative kinematic simulation of the actuator, and plotted in real time, in red in Fig. 10, as the parameters are changed. With the red actuator plot overlaid onto the green desired plot, the optimal set of motion parameters can be determined. It is also possible to save configurations in automatically-formatted JSON files to be loaded later.
This control method is simple because the respiratory cycle is visualized, input into user-friendly software, and relayed to the actuator directly over USB. While a variety of motions can be achieved in this manner, it is nonetheless limited by the discrete nature of a set of individual moves. To overcome this problem, at the cost of simplicity, analog control can be used.

II.C.2. Analog Position Control
The second method controls the ERD15 actuator using a 0-10V analog signal. The voltage range is mapped onto the positional range of the actuator so that a given voltage causes the actuator to move to that position. The move occurs with predefined acceleration, deceleration, and maximum velocity, which can be configured using the Tolomatic Motion Interface software, but is non-blocking; i.e. a new position command can be given before the current position has been reached, and the actuator will immediately move towards the new position.
In this way, arbitrary continuous waveforms can be realized by the actuator, if they do not exceed the configured acceleration and velocity values.  For the actuator to respond to the analog input voltage, analog control must be enabled through a digital input. The digital I/O operates on 28V logic (18-28V is considered high) with respect to the digital common pin (COM). Thus, digital COM is tied to the power supply ground, and a voltage divider is used to provide the 24V needed to enable motion.
Last edited December 19, 2020 An N-channel MOSFET whose gate voltage is set by the Raspberry Pi switches the enable input between 0 and 24V. The MOSFET gate is pulled down to ground through a 1MΩ resistor and attached to the Pi through a 100Ω resistor to prevent parasitic ringing. The voltage divider uses 100kΩ resistors so the maximum current draw is 0.24mA, which does not affect the operation of the actuator.
With this setup, arbitrary waveforms can be saved as CSV files on the Raspberry Pi. A Python program converts the volumetric data to actuator positional curves using the piston geometry, and then to voltages using the voltage-position mapping. The voltages are sent via I2C to the DAC, where they are converted to analog voltages and input into the actuator, thus generating the desired lung motion.

III. Results: Testing and Validation
To validate the efficacy of the piston and lung design, testing of the complete assembly was performed. The primary criteria for evaluation were realism in the trajectory, symmetry between the lungs, consistency of movement, and controllability, as well as validation of the force requirements and mechanical integrity.  After one of the tests that included a total of 40 minutes of almost continuous motion, the phantom was emptied, and the drive mechanism was dismantled and inspected. There were no signs of wear in the mechanism, which would have indicated a problem. The Oring remained very well lubricated, and the cylinder wall behind the O-ring was dry. It is expected that with continued good lubrication and occasional O-ring replacement, the chance of leakage will remain very low. Since the phantom rests on an absorbent sheet throughout operation and is left in isolation until the isotopes have decayed to background levels, individual drops that may get through the piston do not represent a concern, especially as they remain contained within the cylinder. However, the second O-ring can also be installed on the piston to further improve the seal.

IV. Discussion
We have developed and validated the main aspects of the phantom design and usability, including materials, fabrication, couplings, actuation, dynamics, control, and procedures such as filling the phantom. These elements have been shown to work together well to achieve the desired purpose of modeling non-rigid lung motion inside an anthropomorphic phantom. The design objectives of consistent, controllable, symmetric, and realistic motion have been met, though there are a few aspects that can be improved in future work.
In normal respiration, lungs typically expand more axially than in cross-section 7 . In the developed phantom, the lung expansion was more uniform. Thus, artificial lesions attached to inferior lobes of the manufactured lungs will travel a shorter path on average compared to reality (for a similarly-sized person). Two approaches can be taken to increase the axial expansion. First, the lungs could be coupled directly to the piston using an elastic cord.
Making this coupling looser or tighter would produce more or less axial extension, while also keeping the lungs centered in the antero-posterior direction. Alternatively, during the lung fabrication the wall material (Chlorosil) can be strategically rolled thinner in parts that should expand more.
In addition, though the ribs flex to accommodate the lung expansion, the torso shell is rigid, so the lungs are forced to expand dorsally instead of the chest rising as it does in humans. However, by attaching the lungs to the spine so they do not float up when the phantom is placed in a supine position, they can expand upwards during inhalation. In this way, lesions placed on the lungs near the chest retain the expected, anatomically correct IV. DISCUSSION

trajectory.
A limitation of the phantom is that the lungs are filled with air, which makes it impossible to place artificial lesions inside the lungs. Furthermore, the 511keV gamma attenuation coefficient is close to 0 inside the lungs, whereas in reality, it should be around 40% that of soft tissue 17 . We believe that both limitations can be addressed by filling the lungs with light and high-springback foam. If the foam is added inside the lungs in the compressed state, it can hold artificial lesions in place and expand with together with lungs, while also increasing the attenuation coefficient. The same method can be used to fill the space outside the lungs to introduce realistic image heterogeneity through small air bubbles caught in the foam and to facilitate organ placement (liver and heart), as shown previously in the Probe-IQ. The foam can also transmit the lung motion to the other organs, leading to liver motion. Here the foam's effect on lung expansion, and the potential for all the bubbles to escape the foam under the constant motion must be assessed.
The described phantom design, materials and principle of operation can facilitate the construction of similar phantoms elsewhere, and guide the development of a next iteration of phantoms for PET/CT imaging. Once COVID-19 restrictions at our center are eased, CT scans will be performed at different phases of the respiratory cycles to more precisely characterize the motion. Pilot PET scans will also be performed to characterize the effect of lung motion on lesion quantification in a realistic environment. In future work, we will report the results of initial CT and PET scans, and investigate methods to further improve the realism of lung motion.

V. Conclusion
In this work we presented a method and mechanical design to incorporate anatomicallyaccurate, elastic lungs and respiratory motion into an anthropomorphic phantom for PET imaging. The proposed physical principle of operation, materials, couplings and electronics have been validated. A new method to fabricate elastic lung models using 3D-printed molds was established and tested, and a software interface to plan and visualize these breathing patterns was developed, with two separate control schemes. The design can achieve a variety of respiratory wave-forms with up to 25 breaths per minute at 1232ml tidal volume, and is expected to contribute to studies evaluating the effect of respiratory motion on detectability and quantification of cancer lesions.

VI. Open Source
To promote further development of PET and phantom technology, we have opensourced the entire design, including all CAD files, code, engineering drawings, and more, with supporting documentation. This material can be found here: https://github.com/dgblack/robotPhantom.

VII. Acknowledgements
We gratefully acknowledge support by Barber Prosthetics (Vancouver, Canada) in all aspects related to lung manufacturing. The linear actuator for initial testing was provided by Robert de Rot at PQ Systems Ltd (Vancouver, Canada). We also gratefully acknowledge the Engineering Physics Project Lab at the University of British Columbia for financial and expertise support, as well as the BC Cancer Foundation for financial support.