Swarm Intelligence Robotics

†These authors contributed equally to this work.

Abstract

Swarm robotics utilises decentralised self-organising systems to form complex collective behaviours built from the bottom-up using individuals that have lim- ited capabilities. Previous work has shown that simple occlusion-based strategies can be effective in using swarm robotics for the task of transporting objects to a goal position. However, this strategy requires a clear line-of-sight between the object and the goal. In this paper, we extend this strategy by allowing robots to form sub-goals; enabling any member of the swarm to establish a wider range of visibility of the goal, ultimately forming a chain of sub-goals between the object and the goal position. We do so while preserving the fully decentralised and communication-free nature of the original strategy, while main- taining performance in object-free scenarios. In five sets of simulated experiments, we demonstrate the generalisability of our proposed strategy. Our finite-state machine allows a sufficiently large swarm to transport objects around obstacles that block the goal. The method is robust to varying starting positions and can handle both concave and convex shapes.

Keywords: Swarm robotics, cooperative object transport, cooperation without communication, occlusion, obstacles, self-organisation.

Ntroduction

In swarm robotics, multiple small robots collectively execute a task. These robots are designed to be simple and inexpensive to construct; thereby possessing limited sensing and communication abilities. One task that such robots are applied to is collaborative object manipulation, with a frequently studied example being the box-pushing task (Bayindir, 2016). This task calls for robots to move boxes, located in some environment

Arxiv:2605.13006V1 [Cs.Ro] 13 May 2026

or arena, to a specific target or goal location. The boxes are typically such that they cannot be moved by just a single robot, but require multiple robots to push the object by applying force in the same direction.

Autonomous multi-robot systems capable of cooperative object transportation have the potential to be extremely beneficial in a wide variety of applications, such as waste retrieval and de-mining (Tuci, Alkilabi, & Akanyeti, 2018), or operations carried out in situations impractical or challenging for humans, such as space or in deep-sea environments (Farivarnejad, Lafmejani, & Berman, 2021; Huntsberger, Rodriguez, & Schenker, 2012; Parker & Zhang, 2006; Woern, Szymanski, & Seyfried, 2006). Cen- tralised multi-robot systems have proven effective in warehouses and distribution centres when performing storage tasks in highly controlled environments (Roodber- gen & Vis, 2009), with potential users perceiving the usefulness of swarm robots in facilitating efficient storage, sorting or inventory checking abilities (Carrillo-Zapata et al., 2020). Further studies examine using multiple aerial robots to move heavy objects using cables (Bernard, Kondak, Maza, & Ollero, 2011; Michael, Fink, & Kumar, 2011), while cooperative transportation in micro-scale applications, such as molecular deliv- ery to targeted cells, minimally invasive surgery, and tissue engineering (Hu, Ishii, & Ohta, 2011; Rahman, Cheng, Wang, & Ohta, 2017; Shahrokhi & Becker, 2016), are also gaining traction.

As seen in the next section, a wide variety of approaches have been taken to try and solve the task of object transportation with swarm robots. One novel strat- egy proposed by Chen et al. (2013; 2015) utilises occlusion to organise the swarm of robots to complete the task of transporting an object, by instructing the robots to push the object whenever it occludes the direct line-of-sight towards the goal. The use of multiple identical robots, each equipped with relatively limited task-solving ability and knowledge about the environment, through their interactions exhibit a behaviour that is complex enough to solve the object transportation task. While this fully decentralised, communication-free, and scalable approach works well in simple environments, Chen et al. (2015) note that this strategy is not effective in complex environments where an obstacle may impede the ability to perceive the goal from posi- tions immediately surrounding the object. While Chen et al. (2015) suggest a method where the robots rely on a human-controlled mobile goal, in this paper we propose an adaptation to this occlusion-based strategy that enables the robots to transport objects around obstacles fully autonomously by adding a behaviour that allows the robots to decide to turn into sub-goals themselves. Our adaptation maintains the fully decentralised, communication-free, vision-based nature of their original strategy.

The paper is organised as follows. In Section 2 we discuss related works in the field of object transportation with swarm robotics. Section 3 describes the problem statement, introduces our occlusion-based state machine for the object transportation task, and establishes the conditions used in our simulation experiments. The follow- ing five sections each present a different set of experiments. In Section 4 we compare this proposed state machine against the original occlusion-based strategy (Chen et al., 2015) in an environment where no obstacles are present. Section 5 presents a set of experiments performed in environments where at least one obstacle blocks the line of sight between the object and the goal. Section 6 studies the robustness of our pro- posed strategy when using differently shaped objects in environments both with and without obstacles. In Section 7, we examine the effect of the robots’ starting position on their ability to efficiently complete the object transportation task by comparing three different robot position initialisation methods. In Section 8, we compare our strategy to a similar method, but where the sub-goal robot is teleoperated (Chen et al., 2015). This reference strategy departs from our assumption that the environment is not known beforehand, but acts as a heuristic for a more idealised scenario with which we can analyse the nuances of our method in unknown environments. Section 9 concludes the paper and makes proposals for future works.

Related Works

A wide range of object manipulation strategies using a swarm of robots have been studied. Tuci et al. (2018) categorise these strategies into three broad groups; pushing- only, caging, and grasping strategies. As the name suggests, the first strategy involves the miniature robots simply pushing the object with their bodies to induce its move- ment on a path towards the goal (Chen et al., 2013, 2015; Neumann, Chin, & Kitts, 2014; Sugie, Inagaki, Ono, Aisu, & Unemi, 1995; Y. Wang & de Silva, 2006). The caging strategy moves the box using a similar method but distributes the robots along the entire object’s circumference (Brown & Jennings, 1995; Sudsang & Ponce, 2000; Z. Wang, Hirata, & Kosuge, 2003). This allows for more controlled and precise manip- ulations of the object’s orientation and trajectory, as its motion is controlled from all sides. Finally, the grasping strategy; rather than simply pushing against the side of an object, the robots bind themselves to the side of an object, often using an arm, grasping point or interlocking mechanism, which allows them to push and pull the object. Motivated by the way ants depend on individual-level rules to make decisions when transporting objects within a multi-agent system, the grasping strategy has been widely studied (Berman, Lindsey, Sakar, Kumar, & Pratt, 2011; Gelblum, Pinkoviezky, Fonio, Gov, & Feinerman, 2016; Guo et al., 2017; Wilson et al., 2014). This group of manipulation strategies may also include robots that lift the object (Jurt, Milner, Sooriyabandara, & Hauert, 2022) or are attached to the object by means of cables, such as with aerial robots (Michael et al., 2011). We also note some works that incor- porate a mix of the aforementioned strategies, such as by Ebel and Eberhard (2021) where a dynamic algorithm distributes the robots around the side of the object in either a caging or pushing strategy dependent on the number of robots available, how- ever, these more complex methods also often have higher computational demands to decide the optimal strategy than simply using one method.

There is also a wide range of techniques used to control and organise the swarm of miniature robots. These make use of methods ranging from finite-state machine (FSM) (Chen et al., 2015; Kube & Zhang, 1997), decision trees (Ligot, Kuckling, Bozhinoski, & Birattari, 2020) and, more recently, neural network-based methods that utilise evo- lutionary computing (Alkilabi, Narayan, & Tuci, 2017; Groß & Dorigo, 2009) or deep reinforcement learning (Zhang, Xiong, Ma, & Wang, 2020) for synthesising the neural network robot controller. Within these control methods lies a range of implementa- tions with varying presuppositions, robot capabilities, and levels of autonomy. Kube and Zhang (1997) were one of the first to propose a cooperative box manipulation task using a FSM relying purely on perceptual cues. More centralised state machines have also been proposed. A leader-follower strategy includes multiple robots push- ing a box while following the trajectory of an (often human-controlled) ‘leader’ robot towards the goal (Brown & Jennings, 1995; Kosuge & Oosumi, 1996; Rauniyar, Upreti, Mishra, & Sethuramalingam, 2021; Takeda, Hirata, Wang, & Kosuge, 2002; Z. Wang & Schwager, 2016). Habibi, Xie, Jellins, and McLurkin (2016) designed a system where a path from the box to the goal is formulated by a number of ‘mapping’ robots that are not responsible for transporting the object. In some studies, the entire environ- ment is visible to one camera (Sugie et al., 1995) or robot (Y. Wang & de Silva, 2006) that contributes to the centralised coordination of a global strategy over the multiple pushing robots. Neumann et al. (2014) achieved this via an external server, that sends commands to every robot.

Despite a myriad of object manipulation and robot swarm control methods, the task of object transportation using a swarm of miniature robots faces several obstacles that limit the robustness and feasibility of the above-mentioned methods in real- world applications or uncontrolled, unknown or dynamic environments. Many previous studies rely on presuppositions around some, or all, of the following (Farivarnejad & Berman, 2022; Jurt et al., 2022; Tuci et al., 2018): • Predefined robot paths.

• Explicit robot-to-robot or controller-to-robot communication abilities. • Global knowledge about an environment and/or robot position(s). • A static or controlled environment.

• A lack of obstacles between the object and the goal. • The initial positioning of the robots relative to the object or the goal. • The shape, size or grasping points of the object.

Furthermore, strategies may not be robust to a fault in some element of the system. For instance, a failure of the camera or coordination server in a system reliant on global knowledge is much harder to absorb than the breakdown of a single robot in a system of twenty decentralised robots.

While certain presuppositions and requirements seem to be an inescapable feature of many multi-robot object transportation strategies, in this study, we examine the issue of complex environments where objects are present that may block the straight- line path between the object and the goal. Existing strategies able to overcome this challenge often make use of a leader-follower approach (Rauniyar et al., 2021), wherein the leader traces a path around the obstacles. However, this comes with the assumption that the leader possesses knowledge of the global environment, or that the leader is human-controlled. Using knowledge of only the local environment has proved limiting; obstacles may occlude the vision of the simple swarm robots and hinder their ability to perceive enough of the environment to effectively execute the task at hand. While occlusion typically presents an obstacle to the object manipulation task, some works Kube and Zhang (1997) and Kube and Bonabeau (2000) use a light source positioned above the goal to indicate to their simple (camera-equipped) robots the goal’s position, allowing them to reposition themselves accordingly.

More recently, Chen et al. (2013, 2015) proposed a novel transport strategy that utilises occlusion to determine whether a robot should push the object from its cur- rent position. Their approach is summarised as follows. The robots, the object and the goal each have distinctly different colours, and the robots, equipped with simple RGB cameras and no means to communicate with one another, all seek out and approach the object. Once at the object, they determine whether the goal is unoccluded from their position. If it is, they do not push the box from this direction (as they would push it further from the goal) and they thus opt to move around the box until the goal becomes occluded. If the goal is occluded from a robot, the robot pushes the box (towards the goal, as they are pushing the side of the object that is opposite to the goal). Chen et al. (2015) offers a mathematical proof that if the pushing robots dynamically reallocate themselves along the occluded edge of the object, the direc- tion of the object’s movement will eventually cause it to reach the goal. The success of this strategy is reliant on the object being the only item that occludes the goal from the robots, necessitating an obstacle-free path between the object and the goal.

This limits the applicability of the occlusion-based strategy to environments where no, or few, obstacles are present. While noting that a single human-controlled robot with the same colour as the goal could somewhat mitigate this issue by acting as a mobile goal, Chen et al. (2015) recognise the limitation of requiring an obstacle-free path. Regardless, their occlusion-based approach demonstrates an effective method of object manipulation using simple and low-cost swarm robots without a need for global knowledge or explicit communication between the robots.

A similar work to the occlusion-based strategy proposed by Chen et al. is (Alki- labi, Narayan, Lu, & Tuci, 2018). Here, the authors develop a neural network-based controller, synthesised through evolutionary computation techniques. They note that most of the best-performing strategies in their experiments exploited the occlusion of the target position by the object to determine when the robots should push the object; this strategy, developed through artificial evolution, is very similar to the explicitly- coded behaviours by Chen et al. (2015). Furthermore, Alkilabi et al. analysed the relationship between the mass and length of the objects on the task completion rate.

The shorter objects are more challenging for large groups of robots due to the smaller occluded region and limited surface area upon which the robots can apply pushing force. The robots often push into each other, rather than into the object, significantly reducing the total force applied to the object. Alkilabi et al. conclude that while the cylindrical shape of the robots used is a limiting factor in occlusion-based swarm transportation strategies when the surface area of the object is small, this same round shape allows the robots to move horizontally across the sides of the object.

One proposal to overcome the challenge of finding a path to the goal using only local knowledge is made by Nouyan, Campo, and Dorigo (2008). Their method for determining a path from the object to the goal when obstacles are present entails robots forming (tightly connected) chains from the object to a position where the goal is unoccluded. Once a robot finds another robot that is part of a chain, it follows the chain until its end and either joins the chain or ends the trial if it finds an object near the (end of the) chain. Nouyan, Gross, Bonani, Mondada, and Dorigo (2009) extend this strategy for the object transportation task by adding behaviours that allow the robots to grasp onto the object and pull it towards the nearest member of a chain of robots connecting the prey (the object) to the nest (the goal). In both of these works, the robots indicate to each other their current state and behaviour by using different colours generated by RGB LEDs positioned around the circumference of the robots.

Sugawara, Kazama, and Watanabe (2004) and Campo et al. (2010) implemented path selection through the use of artificial pheromones emitted by each robot, acting as a simple messaging system, in response to which each robot decides whether to join, leave, or maintain a chain of robots.

Ethodology

This study extends upon the work of Chen et al. (2013, 2015), complementing their occlusion-based FSM with additional behaviours, inspired by the proposals of Nouyan et al. (2008, 2009), that enable the robots to form stationary sub-goals along the path between the object and the goal. We construct a similar setup as by Chen et al. (2015) using simple simulated swarm robots equipped with cameras and infrared sensors and without any means of communication, pheromones, or access to any global knowledge or coordination system. Using merely visual perceptual cues, the swarm robots and their state machine are tested across multiple environments, each with different configurations of environment layouts, number of robots, and object shapes.

In the remainder of this section, we will describe the robot behaviour (Section 3.1), simulation implementation (Section 3.2), robot design (Section 3.3), environments (Section 3.4) and shapes of the object (Section 3.5) in detail. The end of this section outlines the experimental setup of this work.

The problem statement is as follows. The task consists of a bounded environment containing an object, a goal and a swarm of miniature robots that must push the object to the goal position. The environment may contain obstacles, such as walls, that block the direct path or line-of-sight between the object and the goal, but where a path between the two is still possible such that the object can fit in-between or around the walls regardless of the orientation of the object.

Following Chen et al. (2015), we assume that the robots can distinguish the object, goal and robots in the environment by observing their colour. The dimensions of the object are such that it is large enough to completely occlude the robots’ perception of the goal, should the object be in-between the robot and the goal. Unlike Chen et al., we do not assume that the goal can only be occluded to the viewpoint of any robot by the target object. We depart from this assumption in this study as our methodology aims to navigate complex environments where obstacles are present, while Chen et al. presented their results in obstacle-free environments. We do, however, maintain the assumption that other robots cannot block another robot’s view of the goal (and object). A further departure from the methodology by Chen et al. is that we do not statically assign a (sub-)goal robot; our FSM dynamically determines which robots should become a goal, and when they should do so, while Chen et al. perform an experiment where one robot is set to be a goal and it’s movement is controlled by a human. We maintain no control over the individual robots; their movement and behaviours are entirely controlled by the FSM.

Occlusion-Based State Machine

The behaviour of each robot is modulated by a FSM. We implement two versions of this FSM, the first replicates that of Chen et al. (2015). This FSM serves as a baseline with which to compare our proposed FSM as we wish to ensure no performance is lost in obstacle-free settings as a result of our proposed changes. The proposed FSM augments the baseline FSM with additional behaviours that enable the robots to form sub-goal goal positions; allowing the multi-robot swarm to transport objects around obstacles present in the environment. In Figure 1, the behaviours of both FSMs are shown, where each of the states and transitions illustrated by black lines and arrows represent the behaviours of the baseline FSM, while the blue items indicate the additions made to the baseline FSM in the proposed FSM. Specifically, the state S5 represents our proposed addition to the FSM. A description of each state in Figure 1, and their respective state transition conditions, follows below: • S1: Search For Object. In our implementation, the robot performs a random walk by varying the heading angle between −α and α according to a random walk process. The value of α is set to 0.2 radians to introduce dynamic and less pre- dictable movement during navigation. We opt for this approach as the random walk behaviour in Chen et al. (2015) is not described. Transitions: - S1 →S2: If both the object and a (sub-)goal are unoccluded.

- S1 →S5: If all previously unoccluded (sub-)goal(s) become occluded. If the object and a (sub-)goal were simultaneously unoccluded at any point in the past, the robot will not be allowed to change to the S5 state until it has seen the goal and object with an angle greater than 90° between them.1 1This angle is calculated from the dot product of the vectors that point from the robot’s position to the observed (sub-)goal, and from the robot to the object. This angle is explained in more detail in Section A Fig. 1: Finite-state machine (FSM) diagram of the proposed occlusion-based coop- erative object transportation strategy. Black-coloured items indicate behaviours replicated from (Chen et al., 2015), and demonstrate the behaviour of the baseline FSM. The blue-coloured items indicate our proposed alterations. Both the blue- and black-coloured items apply to the proposed FSM.

• S2: Approach Object. The object is unoccluded and the robot moves towards it. The robot’s trajectory towards the goal is controlled by the relative angle of the object to the robot, observed via the robot’s cameras. Transitions: - S2 →S1: If the object becomes occluded to the robot, or the robot has spent over 1 minute in this state without reaching the object.

- S2 →S3: If arrived at the object, there is no unoccluded goal and there is a free space on the object’s edge to push it from.2 The robot determines if it is near the object by using its RGB camera and IR sensors.

- S2 →S4: If arrived at the object, and either a goal is unoccluded or there is no free space to push from. • S3: Push Object. The robot pushes the object perpendicular to the object’s surface via the robot’s point of contact with the object. Transitions: - S3 →S1: If the object becomes occluded, or the robot has been in this state for over 1 minute.

- S3 →S4: If a goal is unoccluded or there is no free position from which to push the object. • S4: Move Around Object. To find a suitable position to push the object from (at which no other robots are impeding the robot’s path and the goal is occluded), the 2The determination of whether or not there is a free space to push from is explained in Section A.

robot moves around the object’s perimeter. This is implemented via left- and right- wall following, with the direction of the wall following determined by the relative position of the goal and is such that the robot should not move in front of the object’s path as other robots push it towards the goal. If the goal is occluded, the robot performs right-wall following around the object’s perimeter. Transitions: - S4 →S1: If the object becomes occluded, or the robot has been in this state for over 1 minute.

- S4 →S3: If all goals are occluded and there is a free position from which to push the object. • S5: Be a Goal. The robot acts as a sub-goal on the path towards the final goal.

To identify itself as a goal to the other pusher robots, it turns the same colour as the goal. When leaving this state, the robot’s colour returns to blue. Transitions: - S5 →S1: If a goal is unoccluded, or the object is nearby.

Figure 2 shows a time-lapse of the simulation using the proposed FSM, where 20 robots are tasked with transporting a red circular object to the green goal. The robots turn into a sub-goal when a goal/sub-goal is occluded from its cameras. Once a chain between the goal and object is created, the other robots can push the object towards the sub-goals until the goal is reached.

Fig. 2: Time lapse of the simulation using the proposed FSM. Initially, some robots turn into sub-goals, which are later used as sub-goals by the other robots when pushing the object.

Simulation Implementation

We present the capabilities of our modifications to the occlusion-based transport strat- egy using a set of experiments in a simulated environment.3 The experiments are implemented using the Atta simulator version 0.4.0. Atta (Queiroz, 2020) is an open- infrared sensor was implemented using ray casting in conjunction with the Box2D physics engine. The cameras were rendered using OpenGL in a 3D environment. We focused on algorithm validation, thus simplifying the rendering process by exclud- ing shadows and textures while still obtaining meaningful sensor data, as shown in Figure 3.

Fig. 3: Simulation performed in Atta with simplified rendering. In this instance, 30 robots are moving the triangular object in the 2-Corners environment. Note how 3 of the 30 robots are forming sub-goals (green) that lead the (blue) robots to push the (red) object on a path around the walls and towards the (green) final goal.

Robot

Within the simulated experiments, we implement a simple differential wheeled minia- ture robot. The robot’s body consists of a blue-coloured cylinder with a diameter of 8.0 cm and a height of 6.0 cm. Each robot has a mass of 300 g. Its wheels are tucked under the bottom of the robot, are 6.0 cm apart, are both 2.0 cm in diameter, and possess a maximum speed of 0.5 m/s. The robots are not fitted with any means of explicit communication. A schematic of the robot is shown in Figure 4.

The robot possesses two types of sensors with which to observe its environment; four directional RGB cameras and eight infrared proximity sensors. The cameras are positioned at a point just above the centre of the top surface of the robot (9.0 cm above 3The source code for the simulation experiments is open-source and can be found on our research repository in https://github.com/brenocq/object-transportation.

the ground), and each has a field of view of 90°. This configuration of the cameras enables the simulated robot to gain a 360° view of its surroundings, allowing the state machine to perform in optimal conditions uninhibited by sensor limitations without having to pause to rotate on the spot to observe its entire surroundings.4 Each camera captures an image with a resolution of 64×64 pixels, at a rate of 30 frames per second.

The eight infrared proximity sensors operate at a rate of 100 measurements per second and are distributed equidistantly around the circumference of the robot, as shown in Figure 4, at a height of 3.0 cm from the ground. Finally, the robots in our simulation are able to change colour. While physical robots would likely implement this ability through the use of RGB lights, for the sake of simplicity, the colour of the simulated robot’s cylindrical body itself can change between a pure blue and a pure green.

Fig. 4: A top-down view schematic of the robots used in the simulation experiments indicating its dimensions and the positioning of the two differential-drive wheels, four RGB cameras, and eight infrared proximity sensors. In the simulations, the body of the robot is a bright blue, with the ability to change colour into a bright green.

Environments

We create four different environments upon which to conduct our object transportation experiments. All four environments are 3 × 3 m in size and are bounded on each side by a 20 cm tall wall. The floor of the environment is a light grey colour, while the walls are black. Each environment contains a green, cylinder-shaped goal and a red object that are both initialised at the predefined positions illustrated in Figure 5 at the start of every trial.

The first environment, the Reference environment (Figure 5, top left), contains an environment with no obstacles. The object and the goal are placed at opposite corners of the environment, with no obstacles obstructing the line-of-sight between the object and goal. Next, the Corner environment (Figure 5, top right) contains one obstacle; a wall which the robots must manoeuvre the object around in order to reach the goal.

There is only one possible path for the object to reach the goal, however, the goal is completely occluded from the object’s starting position. This environment serves to 4As would be the case with just one (forward-facing) camera.

illustrate how well our proposed FSM operates in a setting where the goal is occluded from the starting position of the object; the robots must devise a path around the wall. Similarly, the 2-Corners environment (Figure 5, bottom left) environment places the object and goal at opposite corners, with the additional challenge of having two walls which the robots must navigate the object around. This environment presents a more challenging version of the Corner environment, as the robots must navigate the object via a longer path around two separate walls. The primary difficulty in this environment is the length of the path that the sub-goal robots have to form to connect the path from the object to the goal. The rendering of the 2-Corners environment within a simulated experiment can also be seen in Figure 3, where three (green) robots are forming a chain of sub-goals. Finally, the Middle environment (Figure 5, bottom right) contains just one wall that blocks the line-of-sight between the goal and the starting position of the object, however, in this environment, there are two possible paths around the sides of the obstacle. This presents a unique challenge for the proposed robot FSM, which includes no explicit decision mechanism for deciding which path (if there are multiple available) is best.

Fig. 5: Maps of the four environments used in the simulated experiments. The envi- ronments are all square-shaped with bounding walls. All environments, except for the Reference environment, have walls (shown in black) that block the line-of-sight path between the goal position (indicated by the green circle) and the initial position of the object. The red square indicates this initial position, however, in our experiments, the object may instead be any of the other six object shapes described in the text. To demonstrate their proportions relative to both each other and the goal, the shapes of the objects are shown on the right side of the image. Units: cm.

Object Shapes

The objective of the robots is to move the (red) object to the position of the (green) goal. The objects have a base that can either be square, rectangular, circular, trian- gular, plus-, L- or H-shaped (see Figure 5). The physical characteristics of each of the object shapes used in our experiments are provided in Table 1. The objects are all 20 cm tall and have a mass of 5 kg, which is heavy enough such that a single robot can- not move the object alone; multiple robots (at least two) are needed for the object to move at all. The goal position is always indicated by a green circular object, with a diameter of 40 cm and a height of 20 cm.

The circular object presents the theoretically ideal case as the resulting force of the robots upon the object points directly towards the goal, however, the curved perimeter of the object increases the probability that the robots collide with one another while the object is moving. The elongated rectangle object is a challenging shape for the occlusion-based transport strategy, as the resultant force can easily cause the rectangle to rotate, rather than move directly towards the goal, depending upon which positions along the object’s perimeter the robots are pushing from. The triangular object is asymmetric, which causes the resultant force vector applied to the object to rarely pass through the object’s centroid. This increases the likelihood that the object rotates on the spot before achieving translational motion, which requires multiple robots pushing from the same side. The square object presents a balance of the qualities and challenges of the other four objects; it is symmetrical around its centroid and has similar dimensions to the circle object, while also having corners that would induce torque when the robots push along certain positions of the object’s perimeter.

The plus (or cross) shaped object poses a different challenge for the occlusion-based strategy as, unlike the other shapes, it is a concave-shaped object. This shape consists of two identical rectangle objects, with a length of 40 cm and a width of 10 cm, adjoined at their centres at a 90° angle to form a plus (or ‘cross’). This means the plus- shaped object has more sides which the robots can push from, and which may incur more directions of motion (or rotation) than the convex objects. The same is true for the L- and H-shaped objects, which are also concave-shaped, have the same maximum dimensions as the plus shape, and have the same thickness across their ‘arms’.

Kg

Table 1: Characteristics of the objects used in the experiments.

Experimental Setup

With the different environments and object shapes described above, we divide our simulated experiments into five sets. The first set of experiments takes place in the ref- erence environment. In this environment, the baseline FSM is expected to complete the object transportation task as there are no obstacles present. This set of experiments serves to demonstrate that there is no change in performance in this setting as a result of our proposed additions of the sub-goal behaviour to the robots’ FSM. The setup of this experiment is nearly identical to that of Chen et al. (2015); there are no obstacles present within the boundaries of the environment, although there is a slight difference in the positioning of the robots at the start of a trial, which will be explained below.

In the second set of experiments, we apply the proposed FSM to environments where there are obstacles present that block the line-of-sight path between the object and the goal. While current vision-based communication-free decentralised object trans- portation methods are unable to do so, in this set of experiments we demonstrate the potential of our proposed transportation strategy to complete the transportation task in environments with obstacles. In the third set of experiments, we demonstrate the robustness of our proposed FSM to different object shapes. This set of experiments shows that the successful performance of our proposed FSM is not conditioned on the specific shape of the object being transported, and that it is still able to complete the object transportation task if the shape is round, oblong, triangular, or concave. In the fourth set of experiments, we investigate the effect the initial positioning of the robots has on the task completion rate. More specifically, we compare three different robot position initialisation methods that are used at the start of each trial: all robots are placed near the goal, all robots are placed near the object, and all robots are placed randomly anywhere in the environment.

In the final experiment, we benchmark our proposed method against a strategy that uses a simulated teleoperated goal robot. In this benchmark strategy, one robot is assigned to act as a green sub-goal, and is driven along a predefined path between the object’s starting position and the goal while maintaining a constant distance of 0.5 m away from the object. The path is calculated using Dijkstra’s algorithm, with the condition that the path must always be at least the width and depth of the object (whichever is larger) away from the environment’s walls. All other robots are controlled using the baseline FSM (and thus can not form additional subgoals). The assumptions made in this STR strategy mark a significant departure from those used in our proposed method; the teleoperation assumes that the environment’s layout is known beforehand, while our method does not require this knowledge. Thus, the simulated teleoperation strategy serves as a heuristic for the ‘ideal’ problem scenario.

This method is inspired by a very similar experiment carried out by Chen et al., wherein they use the same method except for that the statically-assigned goal robot in their work is controlled by a human, while in this work the robot is self-controlled.

We opt to use this method as it ensures that the distance between the mobile sub-goal robot and the object remains constant, and such that the path the robot takes towards the final goal is as efficient as possible at each timestep throughout the experiment.

Within each set of experiments, we utilise various configurations of the task. As described above, we may utilise different environments, object shapes and FSMs to control the robots, but we observe the impact of having different numbers of robots present in the environment on the robots’ task performance. The possible configura- tions of these parameters for each of the five sets of experiments are summarised in Table 2. For each possible combination of the four parameters shown in this table (that is, one value per column), we run 50 trials. Thus, for the experiments in an obstacle- free environment, we use 500 trials as we have two possible FSMs and five possible values for the number of robots present in the environment. Using the same reason- ing, we use 750 trials for the experiments using environments with obstacles (three possible environments, five numbers of robots), 1400 for the experiments using differ- ent shapes (four environments, seven different object shapes), 600 for the initialisation

Random

Table 2: Summary of the configuration of each set of experiments. Rows: the experi- ments. Columns: experiment parameters. strategy experiments (four environments, three initialisation methods), and 400 trials for the teleoperation comparison (four environments, two robot FSMs).5 Unless otherwise specified, the robots’ initial positions on each trial are generated randomly by a uniform distribution over the surface of the environment, but such that their positions do not overlap with the obstacle, goal, walls or another robot.6 The object is also initialised with a randomised orientation on the starting position indicated by the red square in Figure 5. Each trial ends once one of the following

Conditions Are Met:

1. When the distance between the centroids of the object and the goal falls below a distance threshold, the trial is considered successful. 2. A time limit of 20 minutes is reached, and the trial is considered unsuccessful.

The distance thresholds are dependent upon the shape used in that specific trial. We define the threshold as the maximum possible distance between the centroids of the two shapes while they are still colliding, plus a small margin of 5 cm. The precise thresholds for each of the object shapes are described below: - Square: The sum of half of the diagonal length of the square object and the radius of the goal, plus 5 cm.

- Rectangle: The sum of half of the rectangle’s diagonal length and the radius of the goal, plus 5 cm. - Circle: The sum of the object’s radius and the goal’s radius, plus 5 cm.

- Triangle: The sum of half of the triangle’s longest side length and the goal’s radius, plus 5 cm. - Plus, L and H : The same ending condition as the square object, as these shapes have the same maximum length and width as the square object.

Finally, when analysing the results of the trials, three metrics are used. First, the completion rate indicates the percentage of the 50 trials using that configuration of parameters wherein the object transportation task was completed. Second, the task completion duration measures the amount of time, in seconds, taken for the robots to complete the task. Finally, we record the path efficiency of successful trials. The path 5Note that we do not re-run a set of 50 trials if a certain combination of configurations is shared between the sets of experiments. For example, the same results for the trials of the Corner environment with 20 proposed FSM robots, the square object and random initialisation are used in all but the first set of experiments, as that configuration is used within each of those sets.

6This is a slight deviation from the methodology of Chen et al. (2015), as they initialise their robots within a smaller region in-between the object and the goal, while our initialisation spreads the robots out over the entire environment.

(1)

where d is the length of the path travelled by the object’s centroid throughout one trial, and dmin is the length of the shortest possible path of the centroid between the object’s initial position and the radius around the goal defined by the distance thresholds above. dmin differs per environment layout and is also dependent on the object’s shape.7 Both d and dmin are defined purely by the translational motion of the object’s centroid, and do not incorporate the amount of rotation experienced by the object throughout the trial. The optimal path is therefore also independent of the number, or positions, of waypoints indicated by the robot sub-goals. The paths of the object in each trial across all five experiments in this paper are presented in the supplementary material. For the latter two metrics, we only present the results of the successful trials. In the following five sections, we describe the results of each set of experiments outlined in Table 2.

Experiments In The Obstacle-Free Environment

The first experiments concern the baseline and proposed FSMs when applied to the Reference environment, where no obstacles are present. For both FSMS, the task completion rate is 100%, regardless of the number of robots used. The task completion times and path efficiencies for each configuration of the number of robots are also shown in Figure 6. We observe that the time taken to complete the task is consistent between the baseline and the proposed FSM. Furthermore, the path efficiency of the object is not affected by which FSM is used. From the results of this set of experiments, we conclude that our proposed changes to the baseline FSM do not result in a loss of performance in environments the baseline FSM was designed for: environments where no obstacles are present that occlude the line-of-sight between the object’s position and the goal.

Reference Environment

Fig. 6: Task completion duration (a) and path efficiency (b) results of the simulated trials in the obstacle-free Reference environment. 7The waypoints of the shortest possible path account for the object being rotated against the corners of the walls, as this path defines the shortest path that the centroid has to travel to reach the goal. The optimal path differs per shape as the centroids of narrower objects can trace closer to the corners of the walls in the environments, and because the shapes have different distance thresholds for the task completion criteria.

Authors:

Peder EZ Larson 1, 2,* , Jenna ML Bernard1, James A Bankson 3, Nikolaj Bøgh 4, Robert A Bok1, Albert P. Chen 5, Charles H Cunningham 6,7, Jeremy Gordon1, Jan-Bernd Hövener 8, Christoffer Laustsen 4, Dirk Mayer 9,10, Mary A McLean11 12, Franz Schilling13, James Slater1, Jean-Luc Vanderheyden5, 14, Cornelius von Morze 15, Daniel B Vigneron1, 2, Duan Xu1, 2, and the HP 13C

94143, Usa.

Denmark. 5 GE Healthcare, Menlo Park, California, USA. 6 Physical Sciences, Sunnybrook Research Institute, Toronto, Ontario, Canada.

8 Section Biomedical Imaging, Molecular Imaging North Competence Center (MOIN CC), Medicine, Baltimore, MD, USA. Cambridge, United Kingdom.

14Jlvmi Consulting Llc, Dousman, Wi, Usa

#See Acknowledgements for a list of all HP 13C MRI Consensus Group Members This work was supported by the ISMRM Hyperpolarized Media MR Study Group, the ISMRM Hyperpolarization Methods & Equipment Study Group, and the Hyperpolarized MRI Technology Resource Center (NIH/NIBIB grant P41EB013598).

Abstract

MRI with hyperpolarized (HP) 13C agents, also known as HP 13C MRI, can measure processes such as localized metabolism that is altered in numerous cancers, liver, heart, kidney diseases, and more. It has been translated into human studies during the past 10 years, with recent rapid growth in studies largely based on increasing availability of hyperpolarized agent preparation methods suitable for use in humans. This paper aims to capture the current successful practices for HP MRI human studies with [1-13C]pyruvate - by far the most commonly used agent, which sits at a key metabolic junction in glycolysis. The paper is divided into four major topic areas: (1) HP 13C-pyruvate preparation, (2) MRI system setup and calibrations, (3) data acquisition and image reconstruction, and (4) data analysis and quantification. In each area, we identified the key components for a successful study, summarized both published studies and current practices, and discuss evidence gaps, strengths, and limitations. This paper is the output of the “HP 13C MRI Consensus Group” as well as the ISMRM Hyperpolarized Media MR and Hyperpolarized Methods & Equipment study groups. It further aims to provide a comprehensive reference for future consensus building as the field continues to advance human studies with this metabolic imaging modality.

Keywords: Hyperpolarized MRI, metabolic imaging, carbon-13, pyruvate, dissolution dynamic

Introduction

MRI with hyperpolarized 13C agents, also known as hyperpolarized (HP) 13C MRI, has shown great potential as a novel imaging modality, particularly for its ability to probe metabolic processes in real time. The first human studies with HP [1-13C]pyruvate were performed in 2011 in prostate cancer patients (1).

Since then, there have been over 60 papers published with imaging results of human subjects from 13 different sites, with applications including prostate cancer, brain tumors, breast cancer, kidney cancer, pancreatic cancer, metastatic disease, liver disease, ischemic heart disease, diabetes and cardiomyopathies. The vast majority of these studies used [1-13C]pyruvate (1–63), where [2-13C]pyruvate (64) and 13C-urea (56) have been demonstrated too.

As clinical HP 13C MRI advances, there is a growing need to build consensus for best practices, which are critical for comparing data across sites, performing multi-site trials,deploying methods to new sites, partnering with vendors, and potentially for obtaining broader regulatory approvals.

In March 2022, we initiated an effort to build consensus within the HP 13C MRI community with this opportunity in mind, and it was greeted with strong enthusiasm. The “HP 13C MRI Consensus Group”, containing over 55 members from 27 sites, identified the area of greatest need and opportunity for consensus building to be HP [1-13C]pyruvate human

●

Pyruvate is the most mature and widely used HP agent and has the most significant translational evidence emphasizing the potential clinical impact.

●

Clinical trials, particularly multi-site trials, have the strongest need for consensus methods to ensure that data can be combined across sites. This work is a Position Paper for which the goal is to describe current successful practices and study methods for HP [1-13C]pyruvate human studies along with justification to support those practices. This is divided into four major topic areas: (1) HP 13C-pyruvate preparation, (2) MRI system setup and calibrations, (3) data acquisition and image reconstruction, and (4) data analysis and quantification (Fig. 1). The current successful practices and study methods include a literature review of published peer-reviewed journal papers showing human HP [1-13C]pyruvate study data, up to September 2022 (1–63), as well as new unpublished information from surveys of HP 13C study sites. Based on this information, we also highlight the evidence gaps, strengths, and limitations of current practices which are summarized at the end of each section.

Figure 1: Illustration of the HP 13C MRI human study process, including the 4 major areas covered in this paper: Hyperpolarized 13C-pyruvate preparation, MRI system setup and calibration, Acquisition and Reconstruction, and Data Analysis and Quantification.

Figure 2: Anatomical targets of HP [1-13C]pyruvate MRI human studies published up to September 2022.

Hyperpolarized 13C-Pyruvate Preparation

This section covers the processes for creating the HP agent, 13C pyruvate, and will include many aspects and considerations that are needed to safely and effectively prepare doses for metabolic imaging studies in human subjects. These include material, personnel, equipment and facility, fluid path preparation, quality control, and release.

It is helpful to understand that the specifications of a dose of 13C pyruvate suitable for in vivo MR HP metabolic imaging were shaped in part by early preclinical studies performed by GE HealthCare summarized in Ref. (65). In short, the safety of the two novel drug components, 13C pyruvate and the electron paramagnetic agent (EPA) AH111501, were demonstrated in those studies. The more precise formulation of the dose suitable for human use was then determined from clinical studies (66) that included two Phase 1 clinical trials in young and elderly healthy volunteers without hyperpolarization of the 13C nuclei and another Phase 1/2a dose escalation and imaging feasibility study with HP 13C pyruvate in 31 prostate cancer patients at the With the exception of the first HP 13C imaging clinical trial, which utilized a prototype device in a cleanroom (1), all HP 13C studies performed in humans to date have utilized the SPINlab polarizer (manufactured by GE HealthCare). Consequently all doses of the HP 13C pyruvate delivered by SPINlab have been produced using the “SPINlab Pharmacy Kit” that serves as the container-closure system for the various drug components (13C pyruvic acid and EPA mixture, dissolution medium, and neutralization and dilution medium) during sample polarization, dissolution and quality control (QC) processes. Thus many aspects of the HP sample preparation considerations discussed below are related to the SPINlab instrument and the consumables designed to be used with it (67).

General Considerations

While more than 860 patients or healthy subjects having been injected with HP 13C pyruvate as of January 2022 without reports of any serious adverse events (68), HP 13C pyruvate injection remains an investigational MR contrast agent and can only be administered by those with Investigational New Drug (IND) exemption from the Food and Drug Administration (FDA) in the USA, a Clinical Trial Application (CTA) in Canada, approval from National Research Ethics Committee Services in the UK, or approval from the relevant local regulatory body. Thus, methods and processes involved to produce a dose should have patient safety as the first priority. Since utilizing dissolution dynamic nuclear polarization (dissolution-DNP) for human use is still a relatively new development, there are no existing published regulatory guidelines specifically for this method.

There are two major production styles that determine how various sites approach the agent preparation. In the US, the most common approach is to rely on a sterilizing filter (“Terminal Sterilization”) to ensure sterility of the final product, akin to PET tracer production, where a starting molecule with a radioisotope is processed using various other ingredients to make the final, desired and injectable contrast agent within a necessarily short amount of time (69). For these sites, sterilization of the components and accessories upstream of this filter are not required, although many of them were manufactured and tested following Good Manufacturing Practice (GMP) or Good Laboratory Practice (GLP) requirements. The filling process is usually performed under an ISO 5 laminar flow hood, but a clean room or an isolator is not required.

This approach is typically accompanied by testing the integrity of the sterilizing filter prior to release of the dose for injection. Typically, post release endotoxin and sterility tests are performed using an aliquot reserved from each released dose.

In the UK and EU, the most common approach is to more-closely follow sterile pharmaceutical compounding guidelines (70), where all components and ingredients are required to be sterile or manufactured under GMP guidelines and are assembled and filled within a clean room environment or an isolator system (“Sterile Preparation”). Typically a batch of Pharmacy Kits for HP 13C pyruvate injection are prepared together. The sterility of the final dose is also ensured by batch validation testing, in addition to the sterility of the ingredients and the sterile compounding process. The endotoxin and sterility testing are performed for the process validation but are not performed for each injected dose.

Some institutions fill and assemble the Pharmacy Kit required for a specific study on the same day or the day prior to polarization, dissolution, and patient administration, but others have also demonstrated the feasibility of preparing a batch of kits, keeping them in a -20ºC freezer and using them over a period of a few months.

Beyond the obvious requirements that the process and the facility has to ultimately produce a dose that is safe to inject into a human, regulatory authorities will also focus on the question “Are you in control of your processes?”. To be in control of your process requires an in-depth and broad understanding of all processes involved in pre, post, and during the production process.

Personnel

It is typical and may be required to have licensed personnel involved in the production process depending on local regulations.Typically a pharmacist, radiopharmacist or other similarly qualified person (QP), in charge of the facility where the Pharmacy Kit filling and preparation is taking place, is responsible for the overall process and the release of the injectable dose.

Qualified cleanroom technicians are often involved in the Pharmacy Kit filling under the supervision of the pharmacist or QP. As is required for pharmaceutical compounding or PET tracer production, training requirements and training records for all personnel need to be maintained and available for audit by the FDA or equivalent.

Equipment And Facility

The facility and all equipment need to have standard operating procedures (SOPs) that describe how equipment is used, maintained, and calibrated to comply with relevant legislation. Currently, almost all the filling of the Pharmacy Kit takes place within a compounding laminar flow hood or isolator (typically ISO 5). At some sites, the filling is conducted within a cleanroom, while at others, it is conducted in a dedicated non-cleanroom space, reflecting differences in cleanroom approach and specifications between regulators worldwide (71). Some equipment or facilities, such as the compounding hood or cleanroom, may require external certified laboratories for testing.

Material Handling

Material handling guidelines (69,70) require SOPs detailing a system to track all of the materials involved in the HP production process for a particular patient dose, similar to current good manufacturing practice (cGMP) requirements for material handling for drug compounding. This includes acceptance standards, storage conditions, amount used in the patient dose for each ingredient and materials used in the assembly of the fluid path and Pharmacy Kit. Currently some users choose to open and inspect and sometimes modify the Pharmacy Kits upon arrival, but some users keep them in the sealed packaging until they are required for dose preparation.

Pharmacy Kit Filling And Assembling

As required by an IND or its equivalent, the preparation of the doses of HP 13C agent are detailed in the Chemistry, Manufacturing, and Control (CMC) section of an applicable regulatory submission; an example of this has been made available (72). It describes the processes of filling the Pharmacy Kit with the different components that make up the final drug product, and of assembling the final kit for either storage or immediate use in the polarizer. Special attention should be given to the laser welding process in order to satisfy installation qualification (IQ) and operational qualification (OQ). Typically, the final developed process is validated by process qualification (PQ) runs, during which 3 or more Pharmacy Kits are filled and used and the final HP 13C products are tested for endotoxin and sterility and to confirm that they meet the dose specifications for injections (usually including pyruvate concentration, residual EPA concentration, pH, liquid state polarization level and dose temperature). The data from 3 consecutive PQ runs are submitted as part of the IND submission (or its equivalent), and are often also reviewed by the Institutional Review Board (IRB) where the studies are conducted.

Quality Control And Dose Release

The quality control (QC) and dose release can be separated into two aspects: one is the QC and release of the filled Pharmacy Kit, and second is the QC and release of the HP 13C agent for injection, after polarization and dissolution. For institutions filling a batch of kits and storing them to use over a period of time, typically the batch can be released based on initial validation, environmental monitoring data from the day of kit production, and if filters are used during preparation of any of the components, filter integrity testing. But in some cases one or more kits are used for validation before the batch of kits are released for future use. For institutions that fill only the kits required for specific studies shortly before the experiment, the filled kits often do not go through separate release tests before they are used.

The quality control of the HP 13C pyruvate solution post dissolution is primarily performed to ensure that the agent meets the dose specifications (Table 1) before it is administered to the subject. These specifications target both safety (pH, residual EPA, temperature) and efficacy (pyruvate concentration, polarization, volume). Typically, the pyruvate concentration, residual EPA concentration, pH, dose temperature, dose volume, and liquid state polarization are measured by the QC accessory associated with the SPINlab polarizer. Some users perform a secondary measurement for one of the parameters, such as pH, using a different instrument or pH paper. For sites that do not go through a separate release testing process for batch filled kits, the integrity of the sterilization assurance filter, a part of the Pharmacy Kit, is typically tested as a part of the dose release. It is also common for these users to preserve an aliquot of the final HP 13C pyruvate solution for post-release endotoxin and sterility testing. This testing cannot be completed fast enough to test an individual dose prior to injection, but this is why other processes such as PQ runs and validation testing are done to minimize the chance a subject could be injected with a contaminated dose.

The Final Dose Release And Injection

should be done under the supervision of a licensed professional, based on local regulations.

Some Key Challenges

Many of the challenges associated with HP 13C pyruvate preparation can be attributed to the conditions required for the dissolution-DNP method of high magnetic field (~3-7 T) and very low temperature (~1 K) during polarization, with pressurized and superheated water necessary for the rapid dissolution event. These extreme conditions are quite challenging for the design of the container-closure and fluid path system. In particular, the cryogenic temperature in the polarizer requires special attention to any moisture or ambient (moist) air introduced into that portion of the fluid path, which can form an ice block at ~1 K. This ice can lead to flow restriction during the dissolution event and reduce the strength of the laser welded bond between the cryovial and its cap. This can ultimately produce failures in the dissolution step, including variations in final pyruvate concentration and pH that may fail to meet QC release criteria as well as fluid path ruptures that provide no available dose and result in polarizer down-time.

The polarization of the HP 13C pyruvate sample decays quickly over the span of a few minutes after dissolution, and thus the process of dissolution, QC for release, and injection should be completed as fast as possible to preserve the high polarization level achieved. Any delays in the preparation process, such as transportation time or equipment malfunction, can significantly reduce the final polarization and result in lower quality imaging data.

Current Practices

A summary of data collected from all sites performing clinical trials with HP 13C-pyruvate is shown in Fig. 3 and Table 1, including the specification of the final dose and how the quality control and release of the final dose are performed. There is a split in the Production Style, described in the General Considerations section above, with 8/13 sites using Sterile Preparation versus 5/13 using Terminal Sterilization. While many of the dose specifications show notable differences in acceptable ranges, all of these variations listed in tables have been successfully and safely been used to perform HP 13C pyruvate studies in humans. Their differences depend on the institutions’ preferences, resources and their particular regulatory situation. There is high similarity in pyruvate ranges, temperature ranges, EPA limits, and volume limits. There is modest variability in pH ranges and large variability in the endotoxin test limit. There is a 3-fold difference in acceptable polarization levels, which are measured to ensure a futile dose is not injected since the polarization is directly proportional to SNR. This reflects the decision by several sites to believe that useful data can be still be obtained with suboptimal polarizations.

Figure 3: Hyperpolarized agent preparation methods reported by sites currently performing HP

In House

Table 1: HP 13C-pyruvate preparation parameters, methods, and dose specifications used for quality control testing and release as well as validation. These were obtained from a survey of all sites performing clinical trials with HP [1-13C]pyruvate. The parameters used for product release are noted in bold text, otherwise these parameters are measured for batch validation or other QC measurements. The endotoxin and sterility testing are performed during process validation of the batch and/or post-injection, and largely depends on the agent production approach.

Summary

The overall safety record of HP 13C-pyruvate has been very strong, and the SPINlab hyperpolarizer has proven to provide high polarizations at human sized doses while meeting numerous QC and release criteria. A weakness remains the failure modes of the SPINlab Phamacy Kits (e.g. ice blocks, path ruptures), which are placed under extreme requirements particularly during dissolution. The preparation process still requires a high degree of expertise.

Therefore, there is a significant need to improve the reliability, robustness, and ease of operation for generating HP 13C-pyruvate doses for human studies. Furthermore, there is a divide between manufacturing and sterile compounding style preparation as well as other site-specific practices, resulting in variations in SOPs and justification required to relevant regulatory bodies. There have also been no comparisons between these approaches. It is also unclear what release criteria and QC parameters are truly required to ensure patient safety.

However, all of the reported methods are acceptable and approved by the appropriate regulatory authorities, and have led to the rapid expansion of successful human studies in recent years.

Mri System Setup And Calibrations

This section covers the MRI system setup, including the imaging system, RF coils, phantoms, and prescan calibration methods.

Imaging System

The main prerequisite for a given MRI scanner to be capable of supporting studies with HP 13C is its “broadband” capability to transmit and receive radiofrequency (RF) signal at the frequency of 13C, which is around 4 times lower than 1H. This does not come as a default on clinical MR devices. The transmit power of the broadband amplifier should also be sufficient to support the intended flip angle and RF pulse shape with the employed transmission RF coil(s) for 13C. Most studies to date use relatively low flip angles (< 90 degrees) for HP 13C in order to preserve polarization for time-resolved imaging. The capability to receive 13C signal on multiple channels is also desirable to increase SNR, as discussed further in the “RF coils” section.

The choice of magnetic field strength is primarily dependent on the metabolites’ frequency separation due to chemical shift dispersion and 1H imaging. High field strengths do not enhance hyperpolarized 13C signal as they do for 1H because the signal strength in a HP experiment relies on manipulating the population of quantum energy states outside of the MRI scanner.

However, the injected HP 13C-pyruvate and its metabolic products have greater frequency separation at higher fields, and it may thus be easier to separate and quantify these resonances at higher fields. This comes at the cost of a reduction in the achievable T2* and often reduced T1. As the initial polarization is independent of the imaging field strength it has been proposed that the increased T2* at 1.5T can potentially be exploited to increase SNR by adapting the acquisition bandwidth or reduce off-resonance imaging effects in cases when the decay of the transverse magnetization is dominated by T2* (73). In practice, 3T has been used in all published human 13C-pyruvate studies surveyed (Supporting Table S1), and comprises the majority of scanners currently in use for human studies (Table 3). A field strength of 3T is well-suited for 1H MRI anatomical reference and correlative imaging.

Stronger and more rapidly slewing magnetic field gradients support more rapid spatial encoding, particularly for metabolite-specific single-shot imaging using echo-planar imaging (EPI) or spiral imaging (See “Acquisition and Reconstruction”). Although the spatial resolution acquired for HP 13C imaging is typically much coarser than for 1H MRI, the factor of ~4 in gyromagnetic ratio leads to the same reduction factor in performance of the gradient system, so 13C experiments are potentially more limited by gradient hardware performance. To date, all human studies have used the commercially-available integrated gradient systems provided in clinical MRI scanners.

Optimization of scanner design has understandably focused on minimization of artifacts in 1H MRI, where devices such as room lights, the gradient amplifiers, and the motors driving the patient bed are checked to ensure that they do not produce RF interference at the 1H frequency, but artifacts may arise at other frequencies. Eddy current compensation is also not always appropriately adjusted for nuclei at other frequencies (74). In order to optimize for 13C, many sites have performed checks on phantoms for RF interference, gradient artifacts, and eddy currents (74), including the use of post-hoc gradient impulse response function characterisation and correction, and some vendors have fixed these issues as well.

Rf Coils

For HP 13C imaging studies in humans, RF coils for both 1H and 13C nuclei are needed, with 1H MRI providing an anatomical reference for registration and optional additional multiparametric MRI readouts. At the Larmor frequency of 13C nuclei, the relative contributions from coil noise compared to sample noise increase compared to 1H (73,75), although sample noise still is likely the dominant contributor for human-sized coils at 32.1MHz - the resonance frequency of 13C nuclei at 3T.

The key requirement for human 13C-pyruvate RF coils are that the coil geometry and sensitive volume must cover the volume of interest in the subject. Table 2 and Figure 4 shows coil configurations that have been used and optimized for applications in different anatomic regions.

Volume resonators are most commonly used for transmit, as they surround the subject to

Provide B1 Transmit Across The Fov (B1

+). While 1H relies on a large birdcage (“body”) coil built into the scanner, 13C transmit coils must be placed inside the bore. This takes up valuable space within the magnet, and also has led to the use of designs with relatively inhomogeneous

B1

+. Many human studies have used Helmholz pair resonators for transmit, including the “clamshell coil”, which has a notably inhomogeneous B1

+ Profile But Has Been Used Because Of

relatively easy integration into the scanner bore. B1

+ Variation Results In Variations In The Flip

angles that control the use of the hyperpolarized magnetization and creates errors in common HP metrics (9,76). The exception are head coils, where birdcage designs with highly

Homogeneous B1

+ can be placed around the head while easily fitting inside the bore. As with 1H MRI, higher SNR can typically be achieved by smaller receive coil elements, such as surface coils or phased arrays, and the majority of 13C receive coils used have layouts similar to 1H phased arrays.

RF coil quality control is important to ensure proper functioning of the coils to provide consistent imaging quality, especially with limited natural abundance 13C signal in vivo. It typically involves 1) a physical integrity check of the coil cables and connectors and 2) phantom SNR tests to check the coil’s performance and to monitor it over time (see Phantoms below). An useful reference for RF coil quality control is outlined in the MRI accreditation program of the American College of Radiology (77) and can be adapted for 13C coils.

Notably, configurations for brain and prostate studies used dual-tuned 1H/13C coil designs, which greatly simplify workflow and registration of 1H and 13C images, as no switching of coils is needed.

(1)

Table 2: RF coil configurations reported for human HP [1-13C]pyruvate studies.

Tx = Transmit

coil, RX = receive coil. The commonly used “clamshell” TX coil is a Helmholz pair design. For 1H RF configurations, all used the Body coil for TX unless otherwise noted, and “repositioned” indicates the 13C coil was removed for 1H imaging. One representative reference is listed for each configuration. The RF coil configurations reported in the reviewed papers are shown in Supporting Table S1.

Figure 4: Examples of RF coil configurations used for human HP [1-13C]pyruvate brain studies. (A,B) 13C Clamshell TX (Helmholz pair) and 2× 4-channel paddle RX arrays. (C) 13C Birdcage volume TX and 32-channel RX array (RX array slides into TX coil). (D) 13C Birdcage volume TX and 24-channel RX array, combined with a 1H 8-channel RX array. Image reproduced with permission from Ref (16).

Phantoms

Since hyperpolarized magnetization is non-renewable, phantoms containing 13C nuclei are important to: 1) test the multi-nuclear capabilities of the imaging system, including all parts of the signal excitation and receive chain; 2) perform calibration measurements before a scan with hyperpolarized nuclei; and 3) perform necessary pre-scan adjustments (see “Prescan Calibration” section). The phantoms currently in use are listed in Table 3. Their composition must provide sufficient 13C signal, with additional considerations of conductivity, stability, chemical shift(s) present, potential for dynamic imaging, and cost. The phantom geometries are typically either compact, in order to be used alongside the subject during a HP scan, or large enough to mimic the inner volume of a RF coil for system testing.

One popular compact design contains enriched 13C-urea at high concentration, typically 8 M, which provides a single resonance, placed inside a small container ~1 mL. The most common recipe mixes 13C-urea in a 90% water/10% glycerol solution, with glycerol used to increase the urea solubility and doping with a Gd-based contrast agent to shorten T1 which increases the potential SNR per unit time. For example, when Dotarem is added at a 3:1000 volume ratio the 13C-urea T1 is around 500 ms and T2 is around 100 ms. However, when testing pulse sequences influenced by T1 and T2, doping should be used carefully. This phantom is suitable for frequency calibration, transmit gain calibration, sequence testing, and as a fiducial marker when placed next to a patient. However, enriched 13C-urea has a relatively high cost compared to natural abundance compounds.

For larger volumes (>100 ml), the phantoms most often used contain undiluted ethylene glycol, glycerol, or dimethyl silicone. These compounds have sufficiently high carbon concentrations to provide sufficient 13C signal even with the 1.1% natural abundance of 13C. These larger phantoms matching the inner volume of an RF coil are useful for coil testing, including transmit

+) And Receive (B1

-) coil profile mapping, as well as to mimic acquisitions using in vivo FOV requirements. In this case, size and conductivity should match the expected subject size in order to mimic coil loading and get a realistic estimation of B1+. Large-volume natural abundance urea phantoms have also been used by some sites, but suffer from higher conductivity compared to biological tissues. Typically, it is easier to increase the conductivity and hence coil loading of the non-conductive phantom by adding NaCl to match physiological loading (16,78).

Dynamic phantoms that aim to mimic metabolite kinetics have also been developed (79–81), and have the potential to more closely mimic the HP experiment, but so far these are not widely used.

Prescan Calibration

Prior to performing an MRI acquisition, the so-called prescan procedure is used to set the shim parameters to maximize B0 homogeneity over the field of view (FOV) or a specific region of interest (ROI), the scanner center frequency (CF), the RF transmit gain, and the receiver gain.

While this calibration procedure is usually automated for 1H, the lack of sufficient natural abundance 13C signal prevents use of automated methods. (Although natural abundance 13C lipid signal has been detected, there are so far no reports on using this signal for prescan.) Table 3 shows current practices across sites.

Maximizing B0 homogeneity is independent of the nucleus and is therefore performed prior to 13C imaging using the 1H water signal and existing shimming tools, such as by a standard automated process (“Auto Shimming”) or using high order shimming routines. Similarly, the 13C CF can be calculated from the 1H CF using a predetermined scaling factor that depends on the target chemical shift (82). Another common approach used is to have a small, high-concentration 13C phantom, e.g. 8M 13C-urea, integrated in the RF coil or placed next to the scan subject (1). The reference frequency can also be based on real-time measurements after the HP injection but prior to imaging (83). Both the CF and B0 shimming are critical when using spectrally-selective RF pulses, as inmetabolite-specific imaging methods, where the desired excitation bandwidths are typically very narrow and frequency offsets can lead to a failure mode that is only apparent after injection.

The calibration of the RF transmit power is typically performed on a small, high-concentration 13C phantom placed near the region of interest during the scan or on a large 13C phantom of similar size and coil loading as the subject, prior to the subject scan. Reference power is often done by sweeping the power in a pulse-acquire sequence (53,62), or the Bloch-Siegert method (52,84). When using a small phantom, the location of the phantom, B1

+ Inhomogeneity As Well

as any shielding effects, e.g., when the phantom is integrated into a coil (1), may degrade the accuracy. Other methods include real-time Bloch-Siegert method measurements after the HP injection (83), and using the stronger natural abundance 23Na signal that is close enough to the 13C resonance frequency to be detected by 13C coils (82).

The receiver gain is predetermined, either systematically based on independent phantom measurements and assuming the dose and polarization of the HP compound is known prior to injection, or based on past HP imaging studies.

Power [Kw]

Phantom(s) - during study Phantom(s) - before study 13C Frequency

8

13C-bicarbonate doped with dimethyl silicone, various

Power [Kw]

Phantom(s) - during study Phantom(s) - before study 13C Frequency

Maximum Values

Table 3: Summary of the imaging systems, phantoms, and prescan procedures used at sites currently performing HP 13C-pyruvate human studies. These were obtained from a survey of all sites performing clinical trials with HP [1-13C]pyruvate. *Previously performed studies with a Siemens 3T Tim Trio. The imaging systems, phantoms, and prescan procedures reported in the reviewed papers are shown in Supporting Table S1.

Summary

Commercially available 3T MRI systems are by far the most commonly used for human HP 13C-pyruvate studies, although a systematic investigation of the impact of B0 has only recently been investigated (73). The multi-nuclear RF transmit and receive chain has proven sufficient for current acquisition strategies, although many sites have observed artifacts due to RF interference, gradient interference, and residual eddy currents when operating at the 13C frequency. A variety of 13C RF coils, tailored for numerous anatomical targets, have been successfully demonstrated, with the main limitation that most transmit coils take up a lot of additional space inside the bore and provide relatively inhomogeneous B1

+ Profiles. The

phantoms used have converged into generally 2 categories - small phantoms containing 13C-enriched compounds that can be used during the study and human-sized phantoms containing compounds with high carbon concentrations but without 13C enrichment that are used to test and calibrate the coils. There are no standardized compositions or geometry, and dynamic phantoms that recapitulate in vivo kinetics would be desirable but are still an emerging area. Prescan calibration procedures were not well defined in most publications, so we surveyed individual sites to determine current practices. Calibration procedures for the B0 field (13C CF and shimming) for most sites take advantage of 1H signal and methods, while methods

For Calibration Of B1

+ is more variable across sites, likely a reflection of remaining challenges in how to perform this calibration. Standardization of both phantoms and calibration procedures would synergistically improve the robustness and reproducibility of HP 13C studies.

Acquisition And Reconstruction

Data acquisition strategies in human HP [1-13C]pyruvate MRI studies must account for multiple chemical shifts, efficiently utilize the non-renewable HP magnetization, and acquire data quickly relative to metabolism and relaxation decay processes. These studies require spectral encoding to separate metabolites, necessitating pulse sequences that efficiently encode up to 5D data (3 spatial + 1 spectral + 1 temporal dimension). RF pulses must efficiently sample without immediately saturating the non-renewable HP magnetization, and sequences must acquire data quickly and be robust to both experimental and physiologic variation (e.g. B1

+ Inhomogeneity,

variation in perfusion) to ensure reproducibility and minimize scan-to-scan variability. This section covers current successful practices for data acquisition in human [1-13C]pyruvate studies, and accompanying 1H imaging, from different anatomic regions, including scan parameters and image reconstruction.

Acquisition And Reconstruction Methods

The acquisition methods used in human [1-13C]pyruvate studies can be classified into 3 categories: 1) MR spectroscopy or MR spectroscopic imaging (“MRS/I”), 2) chemical shift encoding methods, and 3) metabolite-specific imaging (Fig. 5).

Mrs/I Methods Specifically

resolve a spectrum that can be analyzed to extract expected as well as unexpected resonances, making this approach very robust. It was used in many initial studies (1).

Chemical Shift

encoding methods, most commonly the Iterative Decomposition of water and fat with Echo Asymmetry and Least-squares estimation (IDEAL) method, use imaging sequences acquired with multiple TEs and rely on a model-based separation of expected chemical shifts (85).

Metabolite-specific imaging methods use specialized RF pulses that are spatially and spectrally selective to excite individual metabolites which are then typically imaged with fast k-space trajectories such as echo planar imaging (EPI) or spirals (86).

Their Application To Different

organ systems is described below. The image reconstruction methods used in human [1-13C]pyruvate studies have typically been conventional methods (e.g. FFT, non-uniform FFT, or equivalent). The incorporation of accelerated imaging and advanced reconstruction methods including parallel imaging (4,57,87) and compressed sensing (7) has also been applied in human studies for improved spatial resolution, temporal resolution and coverage, but have the potential for additional artifacts as well as SNR losses due to ill-conditioning of the reconstruction (e.g. g-factor).

The Majority Of

published studies do not use accelerated imaging indicating the resolution and coverage achievable without acceleration is currently adequate for successful data collection. Performing coil combination, even with fully sampled data has also been shown to have specific challenges for HP human images: using naive sum-of-squares methods suffer from high noise amplification in the relatively low SNR regime of HP [1-13C]pyruvate (compared to 1H), motivating several HP 13C-specific methods that include data-driven coil sensitivity estimation which have shown obvious improvements over sum-of-squares (11).

More recently denoising techniques have been applied as post-processing of human HP data(41,42,44). The techniques applied are based on spatial-temporal singular value decomposition for unsupervised estimation of signal and noise components. They have shown improvements in apparent SNR in the brain and liver, while care must be taken to choose parameters such as the rank threshold to avoid oversmoothing and overfitting to the estimated signal components.

Prostate Studies

Prostate cancer was the first human application of HP [1-13C]pyruvate (1), and data was acquired with MRS/I methods: 1D dynamic MRS, single-slice 2D dynamic echo-planar spectroscopic imaging (EPSI), and single time point 3D EPSI. Advances in imaging strategies led to the development and application of new acquisition schemes, including undersampled 3D EPSI with compressed-sensing (7), model-based chemical shift encoding methods that use a priori information (47,59), and metabolite-specific EPI (10), all of which can provide volumetric whole-organ coverage and dynamic acquisitions.

The pyruvate bolus arrival in the prostate can vary by ± 10 s between patients, necessitating dynamic imaging to reliably and consistently capture the pyruvate bolus (18). For this reason, all currently ongoing studies acquire dynamic data. While MRS/I, chemical shift encoding, and metabolite-specific imaging can all achieve dynamic imaging, chemical shift encoding and metabolite-specific imaging provide greater dynamic and volumetric coverage (85). For scan prescriptions, the FOV is designed to provide full prostate coverage and typically to match the orientation of the anatomic imaging used for registration. Flip angles used in current studies are constant through time, as quantification with a variable-through-time flip scheme is highly sensitive to bolus timing (8) and errors in the RF transmit (B1 +) field (76).

Heart Studies

Data acquisition methods for 13C imaging in the heart must be designed to meet the demands of significant cardiac motion and blood flow. To cope with the periodic cardiac motion, most human heart studies to date used gating to the diastolic window, the longest cardiac cycle interval, which has reduced motion (2,22,28,30,35,36,38,45,52). The duration of the diastolic window limits the available data sampling time, making cardiac acquisitions the most time-constrained of the HP 13C MRI applications. The most common acquisition approach is metabolite-specific imaging with spiral k-space trajectories (2). Their single-shot imaging capability makes these methods particularly robust to motion effects. Furthermore, spiral k-space trajectories provide rapid k-space coverage and relatively benign flow and motion artifacts. The majority of studies have used 2D multi-slice acquisitions, but 3D encoding has also been used successfully (35).

Brain Studies

For HP 13C MRI of the human brain, the majority of studies have also used 2D (slice selective) acquisitions (10–12,14,16,28,33,40,41,44,51,53,60), with a trend toward volumetric coverage using 2D multi-slice metabolite-specific imaging. 3D metabolite-specific imaging of the whole brain, with phase encoding of the slice direction (34,57), has been shown to provide similar SNR efficiency (88) compared with multislice imaging. A number of studies have employed MRS/I (5,6,29,31–33,50,55) resulting in a spectrum from each voxel, which has the advantage of not requiring a priori information about which peaks to encode. This was important in early brain studies when it was not known which peaks would be detectable. Chemical shift encoding, using a set of images with different echo times and an iterative reconstruction of the individual resonances (i.e. the IDEAL approach (85)), has also been used (12,49,54), with the drawback that coverage in the slice direction was limited due to the time required to acquire multiple echo time images.

Abdomen And Breast Studies

The fundamental approaches to data acquisition and reconstruction in the abdomen and breast are largely similar to the aforementioned applications, but demand attention to particular challenges associated with these anatomic regions, especially relating to respiratory motion.

Although it has been shown that a basic 2D MRSI approach based on phase encoding and FID readout can be successfully applied for HP 13C imaging in breast (15) and kidney (13), major advantages in terms of spatiotemporal resolution and coverage have been realized using tailored approaches based on metabolite-specific imaging (43,62) and chemical shift encoding (43), which have facilitated multi-slice or 3D dynamic acquisitions over large FOVs in the abdomen (4,37,46).

The significant respiratory motion encountered in these regions can directly blur 13C images, and has further favored these rapid acquisition strategies. Motion also degrades B0 homogeneity, which can shift frequency-selective excitation profiles and introduce artifacts into rapid imaging readouts. This makes accurate determination of the acquisition center frequency and shimming essential in these regions which often cover large FOVs. (See “Prescan Calibration” section for more information). In some studies, breath-holding was used to minimize motion effects and enforce frame-to-frame data consistency (42). A pragmatic and reasonably effective approach for dealing with respiratory motion during 13C data acquisition is an initial breath-hold (as long as can be tolerated), followed by free-breathing (46,62).

1H Imaging

Collection of 1H imaging data is essential both for prescribing the 13C acquisition and for interpretation of the resulting 13C data. Multi-planar 1H scouts are acquired prior to 13C acquisition to enable graphical prescription of the 13C imaging region. All human HP 13C-pyruvate imaging studies acquire conventional MRI scans (e.g. T1- and T2-weighted volumes) for anatomic reference, aiming to cover at least the full 13C FOV. Acquiring these anatomic scans as close as possible to the time of 13C imaging (immediately before or after) minimizes potential misregistration between the data sets. Depending on the application, other advanced 1H sequences are also acquired (e.g. diffusion-weighted imaging for cancer imaging).

When contrast-enhanced data is acquired, it is done after 13C imaging, as paramagnetic contrast agents will accelerate 13C relaxation.

Reported Study Parameters

Figures 5 and 6, and Supporting Table S2 shows the reported acquisition study parameters for human HP [1-13C]pyruvate studies published as of September 2022. Figure 5 shows a mixture of MRS/I, metabolite-specific imaging, and chemical shift encoding methods have been successfully used, where spectroscopy-based methods have become less prevalent in recent studies. Figure 6 shows the acquisition timing, including the important start time and interval/temporal resolution, is quite variable across studies.

Figure 5: Acquisition methods used in published HP [1-13C]pyruvate human studies published up to September 2022, classified into: MR spectroscopy and spectroscopy imaging (MRS/I); chemical shift encoding methods, such as IDEAL, that use multiple TEs and model-based reconstructions; and metabolite-specific imaging methods that use spectrally-selective excitation to image a single resonance at a time.

Figure 6: Temporal acquisition characteristics reported in HP [1-13C]pyruvate human studies published up to September 2022. (a) Reported referencing of acquisition start times.

(B)

Acquisition start times reported when using dynamic imaging and when timing was reported relative to the end of the injection. (c) Temporal resolutions. “Not Applicable” indicates dynamic imaging was not used.

Summary

Three general categories of acquisition strategies have been used successfully for human HP 13C-pyruvate studies: MRS/I, model-based chemical shift encoding (e.g. IDEAL) methods, and metabolite-specific imaging methods. These have enabled successful studies in the prostate, heart, brain, abdomen, and breast. Recent studies increasingly have used the imaging-based strategies of metabolite-specific imaging and chemical shift encoding which are the fastest methods, although a heads-to–head comparison between techniques has not been performed.

Metabolite-specific imaging is quite popular because of its speed and compatibility with single-shot imaging, but is sensitive to B0 field variations and thus requires careful calibrations. Nearly all studies surveyed acquired data dynamically, allowing measurement of the bolus and metabolite kinetics. The exact timings and associated flip angles vary quite widely across reported studies, with no consensus yet as to how to choose these parameters. Image reconstruction is typically done directly using Fourier Transform methods, and accelerated imaging strategies are uncommon.

Data Analysis And Quantification

This section covers the analysis of data from human HP [1-13C]pyruvate studies, including modeling and metrics, visualization, as well as considerations for how to store data and metadata. Depending on study design, the analysis may need to give quantitative or semi-quantitative output reflecting a biological process or may just reflect a contrast between different regions of interest for quantitative evaluation.

Metrics

Figure 7: HP [1-13C]pyruvate raw data (A) have typically been quantified using four categories of metrics depending on the acquisition. Data acquired as a single time point are often quantified using normalized metabolite images or metabolite ratios (B). Dynamic data can be quantified using normalized metabolite images or metabolite ratios (B), or with metabolite timings such as time-to-peak (TTP) or pharmacokinetic (PK) models (C). The latter two require the data to be time-resolved. [1-13C]alanine and 13C-bicarbonate are analyzed similarly to [1-13C]lactate but omitted here for display.

Metabolite images are commonly used as summary metrics for HP MRI data, often including some form of normalization as well as summed over time as an area under the time curve (AUC) (17). These are analogous to the visual evaluation that is most used for routine clinical work (89,90). In these metabolite images, we expect that the [1-13C]pyruvate AUC signal is predominantly weighted towards perfusion and uptake, while [1-13C]lactate, [1-13C]alanine and 13C-bicarbonate AUCs represent metabolic conversion. The strength of this approach lies in its simplicity and relatively few underlying assumptions. Limitations to the use of single-metabolite images or AUCs include sensitivity to inhomogeneous coil profiles (57,87,91), the acquisition strategy and acquisition parameters, pyruvate polarization and concentration level, and signal relaxation rates (92). Further, the reader must be careful to interpret all the images in conjunction to better understand the underlying biology; for example, increased [1-13C]lactate in the presence of decreased [1-13C]pyruvate delivery can have a very different meaning compared to increased [1-13C]lactate with increased [1-13C]pyruvate delivery.

In an attempt to address variations in coil sensitivity, polarization level, and pyruvate delivery, AUC images are often computed by normalizing to a specified parameter, such as the maximum pyruvate or average lactate signals, or presented as a ratio such as lactate/pyruvate or divided by “total Carbon” - the sum total of HP 13C signal observed across all metabolites. The AUC ratios between metabolites and pyruvate are proportional to the corresponding forward kinetic rates (81,93), but are not directly comparable to rate constants when magnetization loss rates (e.g. relaxation and losses due to signal excitation) differ between studies. Similarly, the ratios between the produced metabolites (e.g. bicarbonate/lactate) can reflect the balance between downstream metabolic pathways (12,55). Care must be taken to consider how AUC images are calculated and normalized before comparing values between studies.

To further quantify the interpretation, pharmacokinetic (PK) modeling approaches were developed to compute the apparent kinetics of pyruvate-to-metabolite exchange (92,94–99). These yield semi-quantitative to quantitative apparent rate constants, given in s-1. Some models require a vascular input function, while others avoid this requirement (95). PK models can explicitly account for acquisition-specific details such as excitation angle and repetition time, and thus may reduce the effects of these details on quantification. An input-less model, provided in the Hyperpolarized-MRI-Toolbox (https://github.com/LarsonLab/hyperpolarized-mri-toolbox) (100) and thus frequently employed for human data, has been shown to fit well and robustly to prostate and brain data (8,20). PK models are quantitative in nature, arguably provide more relevant biological information (8,20), and appear to be reproducible across sites (51). However, rate constants derived from PK models are still apparent rates, and likely do not reflect a single biological characteristic.

Some additional considerations include whether complex or magnitude data is used, as the noise behaviors will impact the analysis differently. Additionally, cut-off thresholds or other criteria may be used to identify and avoid voxels with insufficient SNR before analysis to improve robustness (20,41).

Regardless of the analysis approach, the underlying biology is not always clearly represented by the data; instead, the metrics may be influenced by perfusion, barrier permeability, intercellular shuttles, enzyme activities, co-substrate concentrations, or combinations thereof, depending on the organ and disease of interest (19,43,94,101–103). This may be addressed by incorporating complementary information. As an example, HP 13C pyruvate data is influenced by perfusion, and thus addition of perfusion MRI could be important for interpretation (98,104,105).

All the methods outlined above have been explored in clinical studies, described in Supporting Table 3 and summarized in Figure 8. As of September 2022, approximately 52% of studies involving human subjects report rate constants derived from a PK model with a few different models reported. A nearly equal fraction (51%) of the studies report AUC ratio values.

Approximately 66% of these studies report metabolite-specific images or AUC values. About 40% report SNR values; this metric is particularly frequent in manuscripts that describe technical developments for clinical HP MRI. Approximately 16% of these studies summarize model-free metrics, and 10% report measurements from a single timepoint. Most studies report a combination of quantities.

Figure 8: Reported metrics used for analysis in HP [1-13C]pyruvate human studies published up to September 2022.

Visualization

A wide variety of approaches have been used for visualizing data from human HP 13C-MRI studies. The challenges and practical considerations are: 1) choosing the appropriate metrics to display, 2) how to encode the parameters (e.g. the colormap), and 3) choosing how to provide anatomical context and other multi-parametric data. The choice of visualization also depends on the goal which could be for diagnostic interpretation, but also quality control, reproducibility among readers and publication.

Metrics

The choice of HP 13C metrics is described in detail above. At this stage in HP 13C development where there is no standardized metric, often a combination of metabolite images and ratios or PK model parameters are shown.

Parameter Encoding

The mapping function chosen should provide an adequate, often quantitative, impression of the parameter mapped. There is a consensus in the visualization field that perceptually uniform maps are best suited to visualize continuous parameters, like the greyscale typically used by radiologists as well as other monochrome (black to blue) and color ranges (fire-type, rainbow-type) (106,107). Multi-color heatmaps have been the most frequently employed method for HP 13C data, while greyscale has infrequently been used but it ensures there is no coloring-based bias as well as facilitating later reuse (Fig. 9a). Among the color schemes employed in the clinical HP 13C literature, fire-type scheme seems to be the most common [similar to “Plasma” or “Inferno” in matplotlib.org]. Next most commonly employed is the rainbow-type scheme [similar to “Rainbow” in matplotlib.org].

Anatomical Context

HP MRI faces the challenge that it does not necessarily depict the anatomical features, similar to PET, and thus requires an anatomical reference. Most often, a grayscale anatomical image is overlaid with a HP colormap (Fig. 9c,d). This approach is very intuitive, but can skew perception as the grey-scale anatomical reference may affect the brightness of the HP data (e.g. signal in the skull). This bias does not occur when showing adjacent maps (Fig. 9a, b). Here, anatomical outlines may help to provide reference (Fig. 9b).

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