Multi Agent Robot System

Abstract

Communication is an effective mechanism for coordinating the behaviors of multiple agents, broad- ening their views of the environment, and to support their collaborations. In the field of multi-agent deep reinforcement learning (MADRL), agents can improve the overall learning performance and achieve their objectives by communication. Agents can communicate various types of messages, either to all agents or to specific agent groups, or conditioned on specific constraints. With the grow- ing body of research work in MADRL with communication (Comm-MADRL), there is a lack of a systematic and structural approach to distinguish and classify existing Comm-MADRL approaches.

In this paper, we survey recent works in the Comm-MADRL field and consider various aspects of communication that can play a role in designing and developing multi-agent reinforcement learn- approaches can be analyzed, developed, and compared. By projecting existing works into the multi- dimensional space, we discover interesting trends. We also propose some novel directions for de- signing future Comm-MADRL systems through exploring possible combinations of the dimensions.

Keywords Multi-Agent Reinforcement Learning · Deep Reinforcement Learning · Communication · Survey

Ntroduction

Many real-world scenarios, such as autonomous driving , sensor networks , robotics and game-playing [4, 5], reinforcement learning (MARL) techniques to learn the behavior of individual agents, which can be cooperative, competitive, or a mixture of them. As agents are often distributed in the environment where they only have access to their local observations rather than the complete state of the environment, partial observability becomes an essential assumption in MARL [6, 7, 8]. Moreover, MARL suffers from the non-stationary issue , since each agent faces a dynamic environment that can be influenced by the changing and adapting policies of other agents. Communication has been viewed as a vital means to tackle the problems of partial observability and non-stationary in MARL. Agents can communicate individual information, e.g., observations, intentions, experiences, or derived features, to have a broader view of the environment, which in turn allows them to make well-informed decisions [9, 10].

Due to the recent success of deep learning and its application to reinforcement learning , multi-agent deep reinforcement learning (MADRL) has witnessed great achievements in recent years, where agents can process high- dimensional data and have generalization ability in large state and action spaces [7, 8]. We notice that a large number

Arxiv:2203.08975V2 [Cs.Ma] 18 Oct 2024

of research works focus on learning tasks with communication, which aim at learning to solve domain-specific tasks, such as navigation, traffic, and video games, by communicating and sharing information. To the best of our knowledge, there is a lack of survey literature that can cover recent works on learning tasks with communication in multi-agent deep reinforcement learning (Comm-MADRL). Early surveys consider the role of communication in MARL but as- sume it to be predefined rather than a subject of learning [13, 14, 15]. Most Comm-MADRL surveys cover only a small number of research works without proposing a fine-grained classification system to compare and analyze them.1 In cooperative scenarios, Hernandez-Leal et al. use learning communication to denote the area of learning com- munication protocols to promote the cooperation of agents.2 The only survey that we found classifying some early works in Comm-MADRL is from Gronauer and Diepold , which is based on distinguishing whether messages are received by all agents, a set of agents, or a network of agents. However, other aspects of Comm-MADRL, such as the type of messages and training paradigms, which are essential for communication and can help characterize existing communication protocols, are ignored. As a result, the reviewed papers in recent surveys regarding learning tasks with communication are rather limited and the proposed categorizations are too narrow to distinguish existing works in Comm-MADRL. On the other hand, there is a closely related research area, emergent language/communication, which also considers learning communication through various reinforcement learning techniques . Different from Comm-MADRL, the primary goal of emergent language studies is to learn a symbolic language.3 However, a subset of emergent language research works pursues an additional goal to leverage learnable symbolic language to enhance task-level performance. Notably, these research works have not been encompassed within existing Comm-MADRL surveys but included in our survey, referred to learning tasks with emergent language. In summary, our survey overlaps in scope with surveys of emergent language (i.e., in learning tasks with emergent language), but our survey focuses on different primary goals (i.e., achieving domain-specific tasks rather than learning a symbolic language). We further clarify the differences between learning tasks with communication and emergent language in Section 2.2.

In our survey paper, we review the Comm-MADRL literature by focusing on how communication can be utilized to improve the performance of multi-agent deep reinforcement learning techniques. Specifically, we focus on learn- able communication protocols, which are aligned with recent works that emphasize the development of dynamic and adaptive communication, including learning when, how, and what to communicate with deep reinforcement learning techniques. Through a comprehensive review of recent Comm-MADRL literature, we propose a systematic and struc- tured classification methodology designed to differentiate and categorize various Comm-MADRL approaches. Such we plan to develop a Comm-MADRL system for a domain task at hand. Starting with the questions of when, how, and what to communicate, the system can be characterized from various aspects. Agents need to learn when to com- municate, with whom to communicate, what information to convey, how to integrate received information, and, lastly, what learning objectives can be achieved through communication. We propose 9 dimensions that correspond to unique aspects of Comm-MADRL systems: Controlled Goals, Communication Constraints, Communicatee Type, Commu- nication Policy, Communicated Messages, Message Combination, Inner Integration, Learning Methods, and Training Schemes. These dimensions, which form the skeleton of a Comm-MADRL system, can be used to analyze and gain insights into designed Comm-MADRL approaches thoroughly. By mapping recent Comm-MADRL approaches into this multi-dimensional structure, we not only provide insight into the current state of the art in this field but also The remaining sections of this paper are organized as follows. In Section 2 the preliminaries of multi-agent RL are discussed, together with existing extensions regarding communication and a detailed comparison of recent surveys. In Section 3, we present our proposed dimensions, explaining how we group the recent works in the categories of each dimension. In Section 4, we discuss the trends that we found in the literature, and, driven by the proposed dimensions, 5.

Background

In this section, we first provide the necessary background on multi-agent reinforcement learning. Then, we show how multi-agent reinforcement learning can be extended to consider communication between agents. Finally, we present 1We provide a detailed comparison of recent surveys on MADRL which involves communication in Section 2.3.

2In our survey, we extend the concept of learning communication to general multi-agent tasks and use the term learning tasks with communication to emphasize that the primary goal of recent research, which is centered on solving specific domain tasks through the use of communication.

3In the literature, emergent language and emergent communication are used interchangeably. In our survey, we use emergent and compare recent surveys involving communication, from which we can directly see our motivations to fill the gaps among existing surveys.

Ulti-Agent Reinforcement Learning

Real-world applications often contain more than one agent that operate in the environment. Agents are generally assumed to be autonomous and required to learn their strategies for achieving their goals. A multi-agent environment can be formalized in several ways , depending on whether the environment is fully observable, how agents’ goals are correlated, etc. Among them, the Partially Observable Stochastic Game (POSG) [20, 21] is one of the most flexible

, Where I Is A (Finite) Set Of Agents

indexed as {1, ..., n}, S is a set of environment states, ρ0 is the initial state distribution over state space S, Ai is a set of actions available to agent i, and Oi is a set of observations of agent i. We denote a joint action space as A = ×i∈IAi and a joint observation space of agents as O = ×i∈IOi. Therefore, P : S × A →∆(S) denotes the transition probability from a state s ∈S to a new state s′ ∈S given agents’ joint action⃗a = ⟨a1, ..., an⟩, where⃗a ∈A. With the environment transitioning to the new state s′, the probability of observing a joint observation⃗o = ⟨o1, ..., on⟩(where⃗ o ∈O) given the joint action⃗a is determined according to the observation probability function O : S × A →∆(O).

Each agent then receives an immediate reward according to their own reward functions Ri : S × A × S →R. Similar to the joint action and observation, we could denote⃗r = ⟨r1, ..., rn⟩as a joint reward. If agents’ reward functions happen to be the same, i.e., they have identical goals, then r1 = r2 = ... = rn holds for every time step.

In this setting, the POSG is reduced to a Dec-POMDP . If at every time step the state is uniquely determined from the current set of observations of agents, i.e., s ≡⃗o, the Dec-POMDP is reduced to a Dec-MDP. If each agent knows what the true environment state is, the Dec-MDP is reduced to a Multi-agent MDP. If there is only one single agent in the set of agents, i.e., I = {1}, then the Multi-agent MDP is reduced to an MDP and the Dec-POMDP is reduced to a POMDP. Due to the partial observability, MARL methods often use the observation-action history τi,t = {oi,0, ai,0, oi,1, ..., oi,t} up to time step t for each agent to approximate the environment state. Note that time step t is often omitted for the sake of simplification.

In the multi-agent reinforcement learning setting, agents can learn their policies in either a decentralized or a cen- tralized fashion. In decentralized learning (e.g., decentralized Q-learning [22, 23]), an n-agent MARL problem is decomposed into n decentralized single-agent problems where each agent learns its own policy by considering all other agents as a part of the environment [24, 25]. In such a decentralized setting, the learned policy of each agent is conditioned on its local observation and history. A major problem with decentralized learning is the so-called non-stationarity of the environment, i.e., the fact that each agent learns in an environment where other agents are simultaneously exploring and learning. Centralized learning enables the training of either a single joint policy for all agents or a centralized value function to facilitate the learning of n decentralized policies. While centralized (joint) learning removes or mitigates issues of partial observability and non-stationarity, it faces the challenge of joint action (and observation) spaces that expand exponentially with the number of agents and their actions. For a deeper dive into various training schemes used in MARL, we recommend the comprehensive survey by , which offers valuable insights into the training and execution of policies. Based on whether policies are derived from value functions or directly learned, multi-agent reinforcement learning methods can be categorized into value-based and policy-based methods. Both methods have been largely utilized in Comm-MADRL.

Alue-Based

Value-based methods in the multi-agent case borrow considerable ideas from the single-agent case. As one of the most popular value-based algorithms, the decentralized Q-learning learns a local Q-function for each agent. In the cooperative setting where agents share a common reward, the update rule for agent i is as follows:

Where R Is The Shared Reward, And A′

i is the action with the highest Q-value in the next state s′. In partially observable environments, the environment state is not fully observable and is usually replaced by the individual observation or history of each agent. The Q-values for each state-action pair are incrementally updated according to the TD

I Qi(S′, A′

i) −Qi(s, ai), represents the difference between a new estimate (i.e.,

I Qi(S′, A′

i)) and the current estimate (i.e., Qi(s, ai)) based on the Bellman equation . As the state and action space could be too large to be encountered frequently for accurate estimation, function approximation methods, like deep neural networks, have become popular for endowing value or policy models with generalization abilities across both discrete and continuous states and actions . For example, the Deep Q-network (DQN) minimizes the difference between the new estimate calculated from sampled rewards and the current estimate of a parameterized Q-function. In DQN-based methods, the Q-function in Equation 1 is notated as Qi(s, ai; θi), which depends on learnable parameters θi. On the other hand, centralized learning in value-based methods learns a joint Q- function Q(s,⃗a; θ) with parameters θ. However, this approach can be challenging to scale with an increasing number of agents. Value decomposition methods [27, 28, 29, 30] are popular MARL methods that decompose a joint Q- function to enable efficient training. These methods are also widely employed in research works in Comm-MADRL [31, 32, 33]. In partially observable environments, linear value decomposition methods decompose history-based joint

(2)

where the joint Q-function is based on the joint history of all agents and is decomposed into local Q-functions based on individual histories. The weight wi can either be a fixed value [27, 29] or a learnable parameter subject to certain constraints . Advantage functions can also replace the Q-function in the above equation to reduce variance .

Policy-Based

Policy-based methods directly search over the policy space instead of obtaining the policy through value functions implicitly. The policy gradient theorem provides an analytical expression of the gradients for a stochastic policy with learnable parameters in single-agent cases. In the multi-agent case with centralized learning, the policy gradient theorem is expressed as follows: ∇θJ(θ) = E⃗a∼π(·|s),s∼ρπ[∇θ log π(⃗a | s; θ)Qπ(s,⃗a)]

(3)

where J(θ) represents the learning objective, and π(⃗a | s; θ) denotes a stochastic policy parameterized by θ (abbre- viated as π). Additionally, ρπ signifies the state distribution under the policy π, and ∇θJ(θ) represents the expected gradient with respect to all possible actions and states. Due to the computational intractability of the expected gradient, stochastic gradient ascent can be applied to update the parameters θ at every learning step l as follows:

Where Α Is The Learning Rate, And \

∇θJ(θ) is an estimate of the expected gradient based on sampled actions and states. Moreover, the Q-function in Equation 3 can be replaced by average returns over episodes to form REINFORCE algorithms , or by an estimated value function to form actor-critic algorithms [35, 36]. In actor-critic methods, the policy and value function are termed the actor and the critic, respectively. The critic will, therefore, guide the learning of the actor.

Actor-critic methods have undergone various adaptations for multi-agent environments [7, 8, 37, 38]. A typical ex- tension is the multi-agent deep deterministic policy gradient (MADDPG) . In MADDPG, the critic is a centralized Q-function designed to capture global information and coordinate learning signals. Meanwhile, the actors are local policies, ensuring decentralized execution. MADDPG assumes deterministic actors with continuous actions, allowing for the backpropagation of gradients from the value function to the policies. The gradient of each parameterized actor µθi(ai | oi) with learnable parameters θi, abbreviated as µi, is defined as follows:



where D is the experience buffer that contains joint observation-action tuples ⟨⃗o,⃗a,⃗r,⃗o′⟩. Each agent’s Q-function,

Denoted As Qµ

i (⃗o, a1, . . , aN), takes joint observations and actions as inputs, while decentralized actors use local observations as inputs. Contrary to Equation 3, gradients with respect to the current action of agent i (specifically, µi(oi)) are utilized to guide the update of the policy parameter θi. Both MADDPG and its single-agent counterpart, DDPG, have seen widespread application in Comm-MADRL [39, 40, 41, 42, 43].

Extensions With Communication

In the MADRL literature where communication is used, we notice two closely related research areas, which we will re- fer to with the terms emergent language and learning tasks with communication. The emergent language research area [18, 44, 45, 46, 47] aims at learning a language grounded on symbols in communities of interacting/communicating agents. This line of research tries to understand the evolution of the language in agents equipped with neural networks.

On the other hand, learning tasks with communication [16, 48, 49, 50] focuses primarily on solving multi-agent rein- forcement learning tasks with the aid of communication. Communication is often regarded as information exchange rather than learning a (human-like) language. Despite the distinction, when using MADRL techniques on specific domain tasks, languages might emerge, which can potentially enhance the learning system’s explainability in accom- plishing those tasks. We illustrate the research areas, emergent language and learning tasks with communication, along with their intersection learning tasks with emergent language in Figure 1. Notably, our survey focuses on learn- ing tasks with communication in multi-agent deep reinforcement learning, including the intersection with emergent

Emergent Language

Figure 1: An illustration depicting the scope of this survey. The focus of our survey is represented by the blue part. language.4 Within this focus, multiple agents often operate in partially observable environments and learn to share information encoded through neural networks. Furthermore, communication protocols, determining when and with whom to communicate, often leverage deep learning models to find the optimal choices that minimize communica- tion overhead and yield more targeted communication. A multitude of works have been proposed to handle these subproblems inherent in Comm-MADRL. Most research works model only one or a few aspects of Comm-MADRL while selecting a default approach for other aspects. Given that the common goal of Comm-MADRL approaches is to design an effective and efficient communication protocol to improve agents’ learning performance in the environment, the proposed Comm-MADRL approaches inevitably share similarities to some extent. Consequently, establishing a classification system for Comm-MADRL becomes crucial. Such a system would aid in categorizing critical ele- ments like contributions, targeted problems, and learning objectives, from which we can compare and analyse existing Comm-MADRL approaches.

In the emergent language literature, numerous works employ various forms of the Lewis game, often referred to as ref- erential games and operate under a cheap-talk setting , as highlighted in several surveys [10, 18].5 In these games, a goal, often represented as a target location, an image, or a semantic concept, is given to a sender agent but remains unrevealed from a receiver agent. The receiver agent must then either identify the correct goal based on the sender’s signaling [52, 53, 54, 47, 55, 56, 57, 58] or accomplish its single-agent task using the received signals (messages) [59, 60]. Research works in learning tasks with emergent language are grounded in a multi-agent environment where the joint actions of both sender and receiver agents impact environment transitions. Consequently, the learning tasks with emergent language literature considers multi-agent domain tasks [61, 62, 63, 64, 65], building on foundational concepts from MARL such as Dec-POMDPs or POSGs.

We further distinguish explicit versus non-explicit communication in the literature of MADRL with communica- tion. Explicit communication refers to communication through a set of messages separate from domain-level actions. Here, agents’ action policies are influenced by both their observations and the messages they receive. Such messages, crucial for supporting agents’ decision-making, are essential in both the training and execution phases. MADRL frameworks without explicit communication can still allow for communication through domain-level actions, such as the act of influencing the observations of one agent through the actions of another. Furthermore, without explicit com- munication, agents can transmit gradient signals, which facilitate centralized training (and decentralized execution) but are not utilized during execution phases. Specifically, in our survey, we focus on explicit and learnable communication.

Dec-POMDPs and POSGs are often extended to accommodate explicit communication. The communication can be integrated into the action set, adding a collection of communication acts alongside domain-level actions. Al- ternatively, a Dec-POMDP or a POSG can be extended to explicitly include a set of messages .

For In-

stance, the POSG can be expanded with a (shared) message space M, resulting in a POSG-Comm, defined as

, S, Ρ0, {Ai} , P, {Oi} , O, {Ri} , M

, where all components remain unchanged except for the added message space M. A Dec-POMDP-Comm can be defined as similar to the POSG-Comm with shared rewards. In both POSG- Comm and Dec-POMDP-Comm, action policies take into account both environmental observations and inter-agent messages. Research works in Comm-MADRL that expand upon a POSG or a Dec-POMDP can be seen in references such as [61, 63, 66, 65, 67].

4Throughout the remainder of our survey, Comm-MADRL will be used to specifically refer to the areas of our focus. 5In the emergent language research area, research works that do not adopt the cheap-talk setting but communicate through observable (domain-level) actions, are not included in our survey. Our survey focuses on explicit message transfer between agents.

Ommunication In Recent Surveys

Communication has attracted much attention in the field of multi-agent reinforcement learning (MARL). Previous surveys mentioning communication in MARL primarily focus on providing an overview of MARL’s development. These surveys view communication as a subfield in MARL, and no extensive and substantial progress is reported. In an early survey, Stone and Veloso classify MARL based on whether agents communicate and whether agents are homogeneous or not.6 They view learnable communication as a future research opportunity. Busoniu et al.

consider communication as a means to negotiate action choices and select equilibrium in the research direction of explicit coordination, without further classifying communication. With the advancement of deep learning, MARL has gradually incorporated deep neural networks such that recent developments are dominated by multi-agent deep reinforcement learning (MADRL). In the MADRL context, Hernandez-Leal et al. , Nguyen et al. , and Pa- poudakis et al. briefly review early Comm-MADRL methods, which have now become baselines in many recent works. Specifically, Hernandez-Leal et al. use learning communication to denote a new branch in MADRL.

Papoudakis et al. consider communication as an approach to handle the non-stationary problem in MADRL, as agents can exchange information to stabilize their training. Compared to the aforementioned surveys, OroojlooyJadid and Hajinezhad provide a more detailed review of Comm-MADRL, covering a significant number of existing works. They view communication as a way to solve cooperative MADRL problems but did not propose a catego- rization model for Comm-MADRL. Zhang et al. and Yang et al. review communication from a theoretical share information through a time-varying network, aiming to reach consensus on learned value functions or policies.

Despite this, no further classification of communication is made. Two more recent surveys in MADRL, proposed by Gronauer and Diepold and Wong et al. , focus on classi- fying existing works on communication. Gronauer and Diepold classify early research works in Comm-MADRL into Broadcasting, Targeted, and Networked communication, based on whether messages are received from all agents, a subset of agents, or a network of agents. Wong et al., similar to the survey of Papoudakis et al. , view commu- nication as a method to address the issues of non-stationarity and partial observability. In the survey of Wong et al., research works on communication are categorized into three groups from a high-level perspective: communication as the primary learning goal, communication as an instrument to learn a specific task, and peer-to-peer teaching. How- ever, they do not delve into how agents utilize communication to enhance learning. These surveys focus on limited aspects of communication, making their categorizations too narrow to distinguish recent works effectively, given the fact that many existing works share similar assumptions and conditions. To the best of our knowledge, only one survey exclusively focuses on communication issues in MADRL. They review algorithms for communication and coop- eration, including efforts to interpret languages developed through communication. Despite this, their survey mainly covers early models without proposing a categorization framework.

The literature has investigated communication from other perspectives. Shoham and Leyton-Brown investigate communication from a game-theoretic perspective. They introduce several theories of communication in multi-agent systems, with the particular concern that agents can be self-motivated to convey information, driven by underlying incentives (e.g., the knowledge of game structure), or communicate in a pragmatic way analogous to human com- munication. Deep neural networks and deep reinforcement learning techniques have greatly widened the scope of emergent language, aiming to establish effective human-machine communication. As highlighted in section 2.2, the primary goal of emergent language research is to learn a human-like language from scratch. The goal of our survey is, however, to classify the literature on learning tasks with communication that aims at exploiting communication to accomplish multi-agent tasks.

In summary, existing surveys in Comm-MADRL lack coverage of the latest developments. These surveys also do not elaborate on the fact that communication itself is a combinatorial problem. Importantly, communication models engage with MADRL algorithms across various processes, including learning and decision-making. To effectively distinguish between existing Comm-MADRL approaches, it is crucial to analyze and classify them from a wider range of perspectives. In the following section, we delve into the field of Comm-MADRL through multiple dimensions, each linked to a unique research question pertinent to system design. These dimensions allow us to provide a fine-grained classification, highlighting the differences between Comm-MADRL approaches even within similar domains.

6Homogeneous agents have the same internal structure including goals, domain knowledge, and possible actions. Table 1: Proposed dimensions and associated research questions.

Earning Tasks With Communication In Madrl

In our survey, we consider explicit communication where action policies of agents are conditioned on communica- tion that is learnable and dynamic, rather than static and predefined. Therefore, both the content of the messages and the chances of communication occurrences are subject to learning. As agents engage in multi-agent tasks, they learn domain-specific action policies and their communication protocols concurrently. As a result, learning tasks with communication becomes a joint learning challenge, where agents employ reinforcement learning to maximize envi- ronmental rewards and simultaneously utilize various machine learning techniques to develop efficient and effective communication protocols.

Learning tasks with communication in multi-agent deep reinforcement learning (Comm-MADRL) is a significant research problem, particularly as communication can lead to higher rewards. Numerous studies have emerged, devel- oping effective and efficient Comm-MADRL systems, often sharing similarities. Our review begins with the seminal works such as DIAL, RIAL, and CommNet, and then expands to include the most relevant research works presented at major AI conferences and journals like AAMAS, AAAI, NeurIPS, and ICML, totaling 41 models in Comm-MADRL. To better distinguish among these models, we propose classifying them based on several dimensions in Comm-MADRL system design. These dimensions aim to comprehensively cover the current literature, allowing us to project the research works into a space where their similarities and differences become clear. We start by focus- ing on three key components of Comm-MADRL systems: problem settings, communication processes, and training processes. Problem settings encompass both communication-specific settings (e.g., communication constraints) and non-communication-specified settings (e.g., reward structures). Communication processes include common communi- cation procedures, such as deciding whether to communicate and what messages to communicate. Training processes cover the learning of both agents and communication within MADRL. Based on the three key components, we iden- tify and summarize 9 research questions that commonly arise in Comm-MADRL system design, corresponding to 9 dimensions as detailed in Table 1. These research questions and dimensions are designed to capture various aspects of Comm-MADRL, covering the learning objectives of agents and communication, the processes by which messages are generated, transmitted, integrated, and learned within the MADRL framework. We outline a systematic procedure The procedure allows us to organize the dimensions, demonstrate their relevance in system design, and guide the creation of customized Comm-MADRL systems in a step-by-step manner.

As outlined in Procedure 1, N reinforcement learning agents employ communication throughout their learning and decision-making. Initially, the learning objective for the N agents is set, defining rewards that induce cooperative, competitive, or mixed behaviors, as captured by dimension 1. We then consider potential communication-specified settings like limited resources, addressing the need for realistic scenarios as described in dimension 2. Dimension 3 identifies potential communicatees, determining the agents for messages to be received, which varies across domains.

At each time step, agents decide when and with whom to communicate, as highlighted in dimension 4. The patterns of communication occurrences are structured like a graph, where links, either undirected or directed, aid information ex- change. Subsequently, messages that encapsulate agents’ understanding of the environment are generated and shared, relating to dimension 5. Given that agents often receive multiple messages, they must decide on how to combine these messages effectively. This process, crucial for integrating messages into their policies or value functions, is captured in dimensions 6 and 7. In cases of Comm-MADRL studies focusing on emergent language (i.e., learning tasks with emergent language), where messages are modeled as communicative acts emitted alongside domain-level actions, a specific rearrangement of the procedure is required. Here, messages are not observed by other agents until the next time step. Therefore, the processes outlined in dimensions 6 and 7 (lines 8 and 9) are moved to the front of those in dimension 4 (line 6). This rearrangement allows agents to combine and integrate messages from the previous time step before initiating new communication. As a result, agents make decisions and perform actions in the environment based not only on their environmental observations but also on information obtained from other agents (lines 10 and 11). During the training phase, experiences from both environmental interactions and inter-agent communication are utilized to train how agents will behave and communicate, i.e., agents’ policies, value functions, and communication processes, as characterized in dimensions 8 and 9 (line 14).

In the following sections, we make an extensive survey on Comm-MADRL based on each dimension and classify the literature when we focus on a specific dimension. We finally provide a comprehensive table to frame recent works with the aid of the 9 dimensions.

:

Perform in the environment (and store experiences)

:

Update agents’ policies, value function, and communication processes

: End For

influences interaction with the environment and training phases.

Ontrolled Goal

With a given reward configuration, reinforcement learning agents are guided to achieve their designated goals and interests. As agents communicate in order to obtain higher rewards, the goal of communication and the goal of achieving domain-specific tasks are inherently aligned. The emergent behaviors of agents can be summarized into three types: cooperative, competitive, and mixed [96, 23], each corresponding to different reward configurations and goals. Notably, some Comm-MADRL methods have been tested in more than one benchmark environment to show their flexibility and scalability, where the reward configurations may vary [49, 81, 89, 77, 92]. Furthermore, a multi-agent environment may consist of both fixed opponents and teammates, which typically do not participate in communication. Therefore, we exclude fixed agents when identifying reward configurations. Consequently, we focus on (learnable) agents involved in communication and classify their behaviors that are desired to emerge, aligning them with associated reward configurations (summarized in Table 2).

Ooperative

In cooperative scenarios, agents have the incentive to communicate to achieve better team performance. Cooperative settings can be characterized by either a global reward that all agents share or a sum of local rewards that could be different among agents. Communication is usually used to promote cooperation as a team. Thus, in the literature, a team of agents can receive a global reward [73, 48, 61, 88, 39, 89, 40, 41, 43, 74, 31, 75, 66, 76, 63, 77, 78, 79, 90, 32, 91, 92, 93, 80, 64, 33, 94], which does not account for the contribution of each agent. The agents can also receive local rewards, with designs to make the reward depend on teammates’ collective performance [50, 88, 81, 49, 42, 82, 83, 87, 91], to penalize collisions [39, 81, 82, 83, 90, 86, 92, 93], or to share the reward with other agents for encouraging mutual cooperation [84, 85, 65].

There are a variety of cooperative environments where communication has shown performance improvements, from small-scale games to complex video games. In early works, Foerster et al. developed two simple games, named Table 2: The category of controlled goals.

Sc ; Magic ;

Switch Riddle and MNIST Games, for their proposed models, DIAL and RIAL. Sukhbaatar et al. used Traffic Junction for evaluating CommNet, which has become a popular testbed in recent works [88, 89, 49, 83, 79, 90, 92]. Among them, MAGIC achieved higher performance on Traffic Junction with local rewards compared to two early works, CommNet , IC3Net , and one recent work, GA-Comm . StarCraft [97, 98, 99] is another benchmark environment in cooperative MARL with relatively flexible settings. BiCNet and MS-MARL-GCM are evaluated on an early version of StarCraft . Then, a new version of StarCraft, SMAC, has become popular in recent works [31, 75, 66, 32, 33, 94]. By controlling a team of agents, the cooperative goal in SMAC is to defeat enemies on easy, hard, and super hard maps. FCMNet and MAIC are two recent works that surpass multiple communication methods and value decomposition methods (e.g., QMIX) on different maps. Google research football is an even more challenging game with a physics-based 3D soccer simulator. Only MAGIC has reported performance on this platform with communication, and more investigations on this environment are needed. Compared to the above approaches in Comm-MADRL, ATOC has been examined using a significantly larger number of learning agents in the predator-prey domain. Predator-prey is a grid world game with a long history in MARL. It has been developed with several versions [101, 102, 7], while still viewed as a standard test environment due to its flexibility and customizability. ATOC reports performance on this platform with continuous state and action spaces. In the subfield learning tasks with emergent language, cooperative scenarios are popularly used. They are mostly based on grid world or particle environments and have explicit role assignments, e.g., senders and receivers [61, 63, 65, 64].

Ompetitive

In case agents need to compete with each other to occupy limited resources, they are assigned com- petitive learning objectives. In some competitive games, such as zero-sum games, one player wins and the others lose and therefore rational agents do not have the incentive to communicate. Nevertheless, in other competitive scenarios where agents compete for long-term goals, communication can allow for low-level cooperation among agents before the (long-term) goals are achieved. Based on our observations, only one work, IC3Net , tests competitive set- tings and enables agents to compete for rewards.7 IC3Net shows that competitive agents communicate only when it is profitable, e.g., before catching prey in the predator-prey domain. R-MACRL considers communication from malicious agents to improve the worst-case performance. In R-MACRL, the whole environment is cooperative while agents learn to defend against malicious messages. Although the environment is cooperative, we classify this work under the competitive category as the learning goal between malicious agents and other agents is competitive.

Ixed

For a MAS where we care about self-interest agents, individual rewards can be designed and distributed to each agent [81, 89, 49, 75, 77, 92, 94]. Therefore, cooperative and competitive behaviors coexist during learning, which may show more complex communication patterns. Specifically, DGN considers a game where each agent gets positive rewards by eating food but gets higher rewards by attacking other agents. However, being attacked will get a high punishment. With communication, agents can learn to share resources collaboratively rather than attacking each other. IC3Net , TarMAC and MAGIC are evaluated on a mixed version of Predator-prey, and agents learn to communicate only when necessary. NDQ is examined in an independent search scenario, where two 7IC3Net has been tested in several settings, including cooperative, competitive, and mixed scenarios, with different reward configurations.

Table 3: The category of communication constraints.

Al ; Diff Discrete; Dcss ; R-Macrl ;

agents are rewarded according to their own goals, and shows that agents learn to not communicate in independent scenarios. IC considers a scenario in which sender and receiver agents have different abilities to complete the goal. The sender agents have more vision but cannot clean obstacles, while receiver agents have limited vision but are able to clear obstacles. With communication, agents show collaborative behaviors to get higher rewards.

Ommunication Constraints

Practical concerns such as communication cost and noisy environment impair Comm-MADRL systems from embrac- ing realistic applications more than simulations. This dimension, Communication Constraints, determines which type of communication concerns are handled in a Comm-MADRL system. We categorize recent works on this dimension into the following categories (summarized in Table 3).

Unconstrained Communication

In this category, communication processes, including communication channels, the content and transmission of messages, and the decisions of whether to communicate or not, are not explicitly restricted. In principle, agents can communicate as much as information they can without any decision to disallow communication in order to prevent communication overhead [48, 50, 88, 81, 89, 40, 42, 90, 91, 80, 94]. Specifically, several works consider blocking communication through predefined or learnable decisions of whether to communicate or not, while aiming to differentiate useful communicated information [39, 41, 49, 82, 74, 83, 77, 84, 85, 79, 92, 93].

We also put those works under this category as they do not explicitly assume that communication is limited by cost.

Onstrained Communication

In this category, communication processes are explicitly constrained by cost or noise. Thus, agents need to utilize communication resources efficiently to promote learning. We further identify two practical concerns that have been considered in the literature.

• Limited Bandwidth. In this category, communication bandwidth is limited by channel capacity. Thus, communi- cation needs to be used more efficiently, both in the number of times that agents can communicate and the size of communicated information. Early works focus on transmitting succinct messages to avoid communication overhead.

RIAL and DIAL are proposed to communicate very little information (i.e., a binary value or a real number) at every time step to reduce the bandwidth needed. MD-MADDPG considers a fixed-size memory, which is shared by all agents. Agents communicate through the shared memory instead of ad hoc channels. VBC and TMC reduce communication costs by using predefined thresholds to filter unnecessary communication, and both show lower communication overhead. NDQ cuts 80% of messages by ordering the distributions of messages according to their means and drops accordingly to prevent meaningless messages. MAIC also cuts messages by examining several message pruning rates. In MAIC, messages are encoded to consider their respective importance. Sent messages are ordered and then pruned with a given pruning rate. IMAC explicitly models bandwidth limitation as a constraint to optimization. An upper bound of the mutual information between messages and observations is derived according to bandwidth constraint, which turns out to minimize the entropy of messages.

Then agents learn not only to maximize cumulative rewards but also to generate low-entropy messages. The number of agents to communicate can also be restricted to reduce the total amount of communication. SchedNet con- siders a scenario of a shared channel together with limited bandwidth. Only a subset of agents are chosen to convey their messages according to their importance. Gated-ACML learns a probabilistic gate unit to block messages transmitting between each agent and a centralized message coordinator, with the extra cost of learning optimal gates.

Inspired by Gated-ACML and IMAC, ETCNet puts constraints on the behaviors of deciding whether to send messages or not. A penalty term is added to the environment rewards, and an additional reinforcement learning algorithm is used to optimize the sending behaviors. Variable-length Coding also utilizes a penalty term while encouraging short messages. When learning tasks with emergent language, symbolic languages are acquired for communication through a limited number of tokens. Therefore, we classify those works under limited bandwidth [61, 62, 63, 65].

• Corrupted Messages. In this category, messages transmitted among agents can be corrupted due to environmental noise or malicious intentions. DIAL shows that during training, adding Gaussian noise to the communication channel can push the distribution of messages into two modes to convey different types of information. Diff Discrete considers how to backpropagate gradients through a discrete communication channel (between 2 agents) with unknown noise. An encoder/channel/decoder system is modeled, where the encoder is used to discretize a real- valued signal into a discrete message to pass through the discrete communication channel, and the decoder is used to compute an approximation of the original signal. Later they show that the encoder/channel/decoder system is equivalent to an analog communication channel with additive noise. With the additional assumption that training is centralized, the gradient of the receiver with respect to real-value messages from the sender can be computed to allow backpropagation. DCSS also considers a noisy setting. They prove that representing messages as one-hot vectors may not be optimal when the environment becomes noisy. Inspired by word embedding in the NLP field, they propose to generate a semantic representation of discrete tokens that are communicated among agents. The results show that such representation is robust in noisy environments and benefits human understanding of communication. Different from noisy environments, R-MACRL assumes that an agent holds a malicious messaging policy, producing adversarial messages that can mislead other agents’ action selections. Therefore, other agents need to prevent being exploited by learning a defense policy in order to filter the messages.

Ommunicatee Type

Communicatee Type determines which type of agents are assumed to receive messages in a Comm-MADRL system. We found that in the literature, communicatee type can be classified into the following categories based on whether agents in the environment communicate with each other directly or not.

Agents In The Mas

In this category, the set of communicatees consists of agents in the environment, and they di- rectly communicate with each other. Nevertheless, due to partial observability, agents may not be able to communicate with every agent in the MAS, and thus we further distinguish the types of communicatees as follows: • Nearby Agents. In many Comm-MADRL systems, communication is only allowed between neighbors. Nearby agents can be defined as observable agents , agents within a certain distance [81, 74, 77] or neighboring agents on a graph . GAXNet labels observable agents and enables communication between them. DGN limits communication within 3 closest neighbors while using a distance metric to find them. Agent-Entity Graph also uses distance to measure whether agents are nearby or not. As long as two agents are close to each other, they will be allowed to communicate. LSC enables agents within a cluster radius to decide whether to become a leader agent. Then all non-leader agents in the same cluster will only communicate with the leader agent. NeurComm and IP, communicatees are restricted to neighbors on the graph. MAGNet-SA-GS-MG uses a pre-trained graph to limit communication and restricts communication on neighboring agents. Neighboring agents can also emerge during learning instead of being predetermined, as proposed in GA-Comm , MAGIC and FlowComm , which explicitly learn a graph structure among agents. Specifically, in GA-Comm and MAGIC , a central unit (e.g., GNN) learns a graph inside and coordinates messages based on the (complete) graph simultaneously. In this case, agents do not communicate with each other directly; instead, they communicate through a virtual agent who does not affect the environment. Therefore, we categorize these two works into the proxy category.

• Other (Learning) Agents. If nearby agents are not identified, the set of communicatees typically consists of other (learning) agents. Specifically, IC3Net enables communication between learning agents and their opponents. Experiments indicate that these opponents eventually learn to not communicate to avoid being exploited. Some works assume explicit role assignments, i.e., senders and receivers. The role of the receiver can be taken by a disjoint set of agents separate from the senders [62, 63, 64] or by all other agents in the environment [61, 65]. In both cases, agents communicate with each other directly.

Proxy

A proxy is a virtual agent that plays an essential role (e.g., as a medium) in facilitating communication but does not directly affect the environment. Using a proxy as the communicatee means that agents will not directly communicate with each other, instead viewing the proxy as a medium, coordinating and transforming messages for specific purposes. MS-MARL-GCM utilizes a master agent that collects local observations and hidden states from agents in the environment and sends a common message back to each of them. Similarly, HAMMER employs a central proxy that gathers local observations from agents and sends a private message to each agent.

Table 4: The category of communicatee type.

Agent 5

Figure 2: Three communicatee types in the same system. MD-MADDPG maintains a shared memory among agents, learning to selectively store and retrieve local observations from the memory. IMAC defines a scheduler that aggregates encoded information from all agents and sends individual messages to each agent. These works primarily focus on how to encode messages through the proxy without determining whether to send or receive messages. By contrast, ATOC , Gated-ACML , GA-Comm and MAGIC are all designed for agents to decide whether to communicate with a message coordinator. In ATOC and Gated-ACML, each agent’s decisions are made locally based on individual observations, with messages aggregated from nearby agents and from the entire MAS, respectively. Both GA-Comm and MAGIC develop a global communication graph, coupled with a graph neural network (GNN) to aggregate messages by weights and send new messages back to each agent, informing action selection in the environment.

Table 4 summarizes recent works on communication types in MAS. To illustrate these categories, we present an example of different communication methods used in a Comm-MADRL system in Figure 2. The system consists of five agents and one proxy. Agent 3 is the nearby agent of Agent 1, while Agent 4 is the nearby agent of Agent 2. Agent 5 is out of the view range of Agents 1 and 2. If communication is limited to nearby agents, Agent 1 will communicate only with Agent 3, and Agent 2 will communicate only with Agent 4. However, if communication involves a proxy, all agents can send their messages to the proxy and receive coordinated messages.

Ommunication Policy

Communication Policy determines when and with which agents (i.e., communicatees) to communicate in order to enable message transmission. A Communication Policy defines a set of communication actions, which can be modeled in different ways. For example, a communication action can be represented as a vector of binary values, where each value indicates whether communication with one of the other agents is allowed at a certain time step. These actions form communication links between pairs of agents, which can be represented as a communication graph among agents.

In the literature, communication policies can be either predefined or learned, allowing communication with all other agents or only a subset of agents. Furthermore, communication policies can be centralized, controlling communication among all agents, or decentralized, enabling individual agents to control whether to communicate. Therefore, we first categorize the literature based on whether communication policies are predefined or learned. We find that in predefined communication policies, the literature often uses either full communication among agents, where the communication

An

Figure 3: Four types of communication policy with agents (shown as A) in the environment and a possible proxy (shown as P). graph becomes complete, or a partial graph structure to incorporate constraints on communication policies. On the other hand, in learnable communication policies, we identify two distinct categories: individual control and global control. In individual control, communication policies are learned by each agent independently, whereas in global a result, we have identified four subcategories within the dimension of communication policy: Full Communication, (Predefined) Partial Structure, Individual Control, and Global Control. These categorizations are summarized in Table 5.

We present examples of how agents form communication links in the four categories of communication policy, as illustrated in Figure 3. Both Full Communication and Partial Structure rely on a predefined communication policy to determine communication actions. In contrast, Individual Control and Global Control involve the learning of a local communication policy and a global communication policy, respectively, to establish communication links between agents or a potential proxy. If a proxy is involved, it coordinates messages from agents choosing to communicate through this proxy. The categories and their associated research works are introduced as follows:

Full Communication

In this category, every pair of agents is connected so that messages are transmitted in a broad- cast manner. Full communication can be regarded as a fully connected graph, often used in early works on Comm- MADRL. DIAL , RIAL , CommNet , and BiCNet learn a communication protocol which connect all agents together. Inspired by BiCNet, FCMNet uses multiple RNNs to link all agents together with different sequences, allowing agents to benefit from communication flow from various directions. In contrast, Diff Discrete and Variable-length Coding focus on two-agent cases but do not learn to block messages from each other.

TarMAC and IS learn meaningful messages while using a broadcast way to share messages, thus still adher- ing to full communication. DCC-MD and R-MACRL introduce a strategy to drop out received messages without specifying whether to send messages. Specifically, DCC-MD drops out messages with a fixed probability to reduce input dimensions, and R-MACRL learns to drop out adversary messages through a defense policy. In Comm- MADRL methods like IMAC , MS-MARL-GCM and HAMMER , a central proxy that receives local observations or encoded messages is always connected with agents in the MAS. In addition, GCL and AE-Comm learn a language grounded on discrete tokens among agents, where all agents have the capability to send and receive messages.

(Predefined) Partial Structure

In this category, the communication between agents is captured by a predetermined partial graph to reduce overall communication. Then, each agent communicates with a limited number of agents within the MAS, rather than with every agent. NeurComm and IP operate in a networked multi-agent environment, randomly generating a communication network while maintaining a fixed average number of connections per agent during the learning process. DGN , MAGNet-SA-GS-MG , and GAXNet restrict communication to a certain proximity of agents. The Agent-Entity Graph employs a pre-trained graph to capture agent relationships.

Comm-MADRL approaches like VBC , NDQ , TMC , and MAIC utilize handcrafted thresholds or pruning rates to limit communication opportunities. In IC , Bias , and DCSS , disjoint sets of agents are designated as either senders or receivers, facilitating unidirectional communication from senders to receivers only.

Ndividual Control

In this category, each agent actively and individually determines whether to communicate with other agents, implicitly forming a graph structure. A common method employed in Comm-MADRL studies within this category is a learnable gate mechanism, which aids agents in making the decision to communicate. For instance, IC3Net and ATOC use a gate mechanism that enables agents to decide whether to broadcast their messages, in a deterministic and probabilistic manner, respectively. ETCNet also implements a gate unit but limits the overall probability of message-sending behaviors. If a proxy, such as a message coordinator, is present, Gated-ACML introduces a learning mechanism for each agent to decide whether to communicate with the proxy, as opposed to direct communication with other agents. Diverging from the gate function approach, I2C allows each agent to unilaterally decide on communication with other agents, based on evaluating the impact of those agents on its own policy. LSC allows each group of agents, defined by a specific radius, to compare their weights in order to elect a leader. This system then facilitates communication from each group to their respective leaders and from leader to leader. Notably, the leader agent in this model is not considered a proxy, as it still directly interacts with the environment.

Global Control

In this category, a globally shared communication policy is learned, providing more complete con- trol over the communication links between agents. SchedNet employs a global scheduler that limits the number of agents allowed to broadcast their messages, thereby reducing overall communication. FlowComm learns a di- rected graph among agents, enabling unilateral or bilateral communication between them. Similarly, GA-Comm and MAGIC develop an undirected and a directed graph for communication, respectively. These Comm-MADRL systems incorporate an additional message coordinator to coordinate and transform messages sent by the agents.

Ommunicated Messages

After establishing communication links among agents through a communication policy, agents should determine which specific information to communicate. This information can derive from historical experiences, intended actions, or future plans, enriching the messages with valuable insights. Consequently, the communicated information can expand the agents’ understanding of the environment and enhance the coordination of their behaviors. In the dimension of communicated messages, an important consideration is whether the communication includes future information, such as intentions and plans. This kind of information, being inherently private, often requires an (estimated) model of the environment to effectively simulate and generate conjectured intentions and plans. Accordingly, we categorize recent studies in this dimension into two categories, as summarized in Table 6.

Existing Knowledge

In this category, agents share their knowledge of the environment (e.g., past observations), previous movements, or policies to assist other agents in selecting actions. As historical information accumulates, agents use a low-dimensional encoding of their knowledge as messages to reduce communication overhead. Notably, the RNN family (e.g., LSTM and GRU) is commonly used as an encoding function, capable of selectively retaining and forgetting historical observations [48, 50, 88, 89, 49, 42, 83, 79, 92, 93, 33, 94], action-observation histories [73, 50], or action-observation-message histories [62, 63]. When a proxy is present, messages are generated and transformed from agents to the proxy, and then from the proxy to agents. Thus, local observations can either be encoded [42, 66, 83, 76, 92] or directly sent [88, 91] to the proxy. The proxy, after gathering these local (encoded) observations, can generate a unified message for all agents , or individualized messages for each agent [42, 66, 83, 76, 91, 92].

Both methods provide a message containing global information, relieving agents from the task of combining multiple received messages. In Comm-MADRL systems without a proxy, messages are sent directly to each agent. Specifically, in MADDPG-M , agents communicate local observations without an encoding of them. On the other hand, DIAL and RIAL encode past observations, actions, and current observations as messages. BiCNet encodes methods such as simple feed-forward networks [43, 78, 86, 87], MLP [40, 31, 32, 95], autoencoders , CNNs , RNNs [48, 89, 49, 79, 93, 33, 94], or GNNs [74, 77] to encode local observations as messages. Furthermore, agents can communicate more specific information, such as in GAXNet , where agents coordinate their local attention Table 6: The category of communicated messages.

; Agent-Entity Graph ; Vbc ; Ndq ; Imac ; Ga-Comm

; Gated-ACML ; Bias ; LSC ; Diff Discrete; I2C ; ETC- Net ; Variable-length Coding ; TMC ; HAMMER ; MAGIC ;

Atoc ; Neurcomm ; Ip ; Is ;

Table 7: The category of message combination.

Al ; Rial ; Commnet ; Gcl ; Ic ; Maddpg-M ;

IC3Net ; SchedNet ; VBC ; NDQ ; Bias ; Diff Discrete; IS ; ETCNet ; Variable-length Coding ; FlowComm ; AE-Comm

Bicnet ; Ms-Marl-Gcm ; Atoc ; Dgn ; Tarmac ;

MAGNet-SA-GS-MG ; MD-MADDPG ; DCC-MD ; Agent-Entity

; R-Macrl ; Maic ; Fcmnet ;

weights, integrating hidden states from neighboring agents. Messages can also be modeled as random variables, as seen in NDQ , where messages are drawn from a multivariate Gaussian distribution to maximize expressiveness by maximizing mutual information between messages and receivers’ action selection. In learning tasks with emergent language, agents often communicate goal-related information, such as the goal’s location [61, 62, 63, 65, 64].

Magined Future Knowledge

In this context, Imagined Future Knowledge refers to aspects such as intended actions , policy fingerprints (i.e., action probabilities in a given state) [85, 84], or future plans . Since intentions are related to the current environment state, recent works often combine intended actions with local observations to produce more relevant messages. The concept of future plans extends this idea further by utilizing an approximated model of the environment and the behavior models of other agents. This approach enables the generation of a sequence of possible future observations and actions . Such knowledge is shared among agents, allowing the receivers to consider the potential future outcomes of the senders’ actions.

Essage Combination

When agents receive more than one message, current works often aggregate all received messages to reduce the input for the action policy. Message Combination determines how to integrate multiple messages before they are processed by an agent’s internal model. If a proxy is involved, each agent receives already coordinated and combined messages from the proxy, eliminating the need for further message combination. If no proxy is presented, each agent independently determines how to combine multiple messages. Since communicated messages encode the senders’ understanding of the learning process or the environment, some messages can be more valuable than others. As shown in Table 7, recent works in the dimension of message combination are categorized based on how agents prioritize received messages.

Equally Valued

In this category, messages received by agents are treated without preference, meaning they are assigned equal weights or simply no weights at all. Without having preferences, agents can concatenate all messages, ensuring no loss of information, though it may significantly expand the input space for the action policy [73, 61, 62, 41, 43, 75, 78, 90, 86, 87]. Recent research involving concatenated messages typically represent the sent messages either as single values [73, 62, 87, 86] or as short vectors [61, 41, 43, 75, 78, 90]. Alternatively, messages can be combined by averaging [48, 49, 31] or summing , under the assumption that messages from different agents have the same dimension. In some cases, particularly in two-agent scenarios, no explicit preferences are assigned to messages [63, 65, 64].

Table 8: The category of inner integration.

Ommnet ; Gcl ; Ms-Marl-Gcm ; Atoc ; Magnet-Sa-

GS-MG ; IC3Net ; MD-MADDPG ; SchedNet ; IMAC ; GA- Comm ; Gated-ACML ; Diff Discrete; IP ; I2C ; IS ; ETCNet ; Variable-length Coding ; HAMMER ; FlowComm ;

Policy- And Value-Level

BiCNet ; IC ; TarMAC ; MADDPG-M ; Agent-Entity Graph ;

Unequally Valued

In this category, messages are assigned distinct preferences, which potentially impose differences on sender agents. DCC-MD and TMC use handcrafted rules to prune received messages. In DCC-MD, each received message can be dropped out with a certain probability. TMC stores the received messages and checks whether they are expired or not within a preset time window. Only valid messages are integrated into an agent’s model. Instead of using fixed rules, R-MACRL learns a gate unit to decide whether to use a received message. An attention mechanism can also be learned to assign weights to received messages and then combine them, rather than filtering messages out, as seen in research works [89, 40, 74, 33]. Moreover, a neural network can aggregate received messages into a single message or a low-dimensional vector, which implicitly imposes preferences on messages during the mapping. Feedforward neural networks [66, 76, 91], CNNs , LSTMs (or RNNs) [50, 88, 39, 42, 84, 79, 80, 94], and GNNs [83, 77, 85, 92] have been used as aggregators. Among them, GNNs utilize a learned graph structure of agents and assign different weights to neighboring agents.

Nner Integration

Inner Integration determines how to integrate (combined) messages into an agent’s learning model, such as a policy or a value function. In most existing literature, messages are viewed as additional observations. Agents take messages as extra input to a policy function, a value function, or both. Thus, in the dimension of inner integration, we classify recent works into categories based on the learning model that is used to integrate messages. These categories are summarized in Table 8.

Policy-Level

By exploiting information from other agents, each agent will no longer act independently. Policies can be learned through policy gradient methods like REINFORCE, as seen in studies [48, 61, 88, 49, 83], which collect rewards during episodes and train the policy models at the end of episodes. Moreover, the Comm-MADRL approaches that utilize actor-critic methods [39, 40, 42, 43, 66, 76, 78, 85, 79, 90, 86, 87, 91, 93, 80, 95] assume that a critic model (i.e., a Q-function) guides the learning of an actor model (i.e., a policy network).

Alue-Level

In this category, a value function incorporates messages as input, and a policy is derived by selecting the action with the highest Q-value. Most works in this category employ DQN-like methods to train their value functions [73, 81, 82, 31, 75, 77, 32, 33]. Specifically, Comm-MADRL approaches like VBC , NDQ , TMC , and MAIC are based on value decomposition methods in cooperative scenarios (with global rewards). These methods involve learning to decompose a joint Q-function.

Policy- And Value-Level

Integrating messages using both a policy function and a value function typically relies on actor-critic methods. In Comm-MADRL approaches within this category, received messages can be treated as extra inputs for both the actor and critic models [50, 74, 64]. Alternatively, messages can be combined with local observations to generate new internal states, which are then shared with both the actor and critic models [62, 89, 41, 63, 84, 92, 65, 94].

Earning Methods

Learning methods determine which type of machine learning techniques is used to learn a communication protocol. The learning of communication is at the center of modern Comm-MADRL and can benefit from the advancements in the machine learning field. If proper assumptions about communication are made, such as being able to calculate the derivatives with respect to the message generator function and the communication policy, then the training of communication can be integrated into the overall learning process of agents. This integration allows for the use of fully differentiable methods for backpropagation. Other machine learning techniques, including reinforcement learning, Table 9: The assumptions behind different learning methods.

Fully Differentiable

The messages or the communication actions are generated by a differ- entiable function and thus backpropagation is used everywhere.

Supervised Learning

True labels (or the ground truth) are assumed to be given or defined to guide the learning of communication policy or messages.

Reinforcement Learning

Environment rewards or self-defined rewards are used to update com- munication policy or messages incrementally.

Regularizers

Regularizations such as entropy inspired from information theory are added to agents’ optimization objectives to regularize the learning of communication.

Table 10: The category of learning methods.

; Tarmac ; Magnet-Sa-Gs-Mg ; Md-Maddpg ; Dcc-Md

; Agent-Entity Graph ; VBC ; GA-Comm ; Diff Discrete; NeurComm ; IP ; IS ; Variable-length Coding ; TMC ;

Ndq ; Imac ; Bias ; Ae-Comm ; Maic ;

supervised learning, and regularizations, can also be utilized to incorporate our requirements and available ground truth into the learning of communication, each carrying respective assumptions. The assumptions used in the literature are summarized in Table 9. For instance, supervised methods require defining true labels for communication (e.g., the correct information to share or the right agents to communicate with). In contrast, reinforced methods use rewards as learning signals. Regularized methods, which use neither true labels nor rewards, employ an additional learning objective by using regularizers, such as minimizing the entropy of messages to reduce stochasticity. Therefore, we classify recent works based on how they differ in the learning of communication (summarized in Table 10).

Ifferentiable

In this category, communication is learned and improved by backpropagating gradients from agent to agent. When the communication policy is predefined, such as in full communication [73, 48, 61, 50, 88, 89, 42, 82, 78, 90, 87, 94] or by communicating with a subset of agents [81, 40, 74, 31, 84, 85, 32, 80, 64], agents learn the content of messages through backpropagation. Several recent studies [61, 83, 92, 93, 64] address the issue of non-differentiable communication actions by utilizing gradient estimators like Gumbel-softmax , which replaces non-differentiable samples with a differentiable approximation during training, albeit requiring additional parameter tuning. Specifically, both GCL and DCSS employ a differential message function in their approaches. Additionally, GCL inte- grates auxiliary rewards, and DCSS utilizes labeled messages for training communication policies. Thus, they are cat- egorized under the Differentiable category, each additionally aligning with the Reinforced and Supervised categories respectively. Freed et al. propose an alternative method, Diff Discrete, to address the challenge of continuous messages versus discrete channels. This method models message transmitting as an encoder/channel/decoder system, where the receiver decodes the messages and reconstructs the original signals. These reconstructed signals enable the calculation of derivatives with respect to the sender, allowing gradients to be sent back to the sender.

Supervised

In this category, additional efforts need to be made to define the true label for when and what informa- tion to communicate. ATOC and Gated-ACML use the difference in Q-values between actions chosen with and without a message to define a label of communication actions. If the difference exceeds a threshold, the message is

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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