Multi Robot Coordination

Compositional Coordination for Multi-Robot Teams with Large

Anguage Models

Zhehui Huang1, Guangyao Shi1, Yuwei Wu2, Vijay Kumar2, Gaurav S. Sukhatme1 Abstract— Multi-robot coordination has traditionally relied on a mission-specific and expert-driven pipeline, where natural language mission descriptions are manually translated by domain experts into mathematical formulation, algorithm design, and executable code. This conventional process is labor- intensive, inaccessible to non-experts, and inflexible to changes in mission requirements. Here, we propose LAN2CB (Language to Collective Behavior), a novel framework that leverages large language models (LLMs) to streamline and generalize the multi-robot coordination pipeline. LAN2CB transforms natural language (NL) mission descriptions into executable Python code for multi-robot systems through two core modules: (1) Mission Analysis, which parses mission descriptions into behavior trees, and (2) Code Generation, which leverages

To

generate robot control code. We further introduce a dataset of natural language mission descriptions to support development

And

real-world environments demonstrate that LAN2CB enables robust and flexible multi-robot coordination from natural language, significantly reducing manual engineering effort and supporting broad generalization across diverse mission types.

Ntroduction

Problem: Multi-robot coordination for complex collective behaviors, including coverage, formation, foraging, and ex- ploration, has been extensively studied for decades –.

However, most prior coordination methods target a specific and narrowly defined coordination task. This highlights the need for a general and unified framework that can address a wide range of coordination problems in a systematic way.

The conventional multi-robot development pipeline starts with a natural language (NL) problem description, enabling both expert and non-expert users to specify objectives and constraints. An expert translates this description into a math- ematical formulation, typically as an optimization problem, which inevitably requires additional assumptions. Following this, a domain expert designs algorithms to solve the for- mulated problem, which are subsequently implemented and validated on robotic hardware. However, this pipeline has three limitations: It is labor-intensive, inaccessible to non- experts, and inflexible. The first two limitations are apparent due to the significant use of skilled experts, despite the repet- itive nature of problem formulation, algorithm design, and code implementation. The third becomes apparent when even 1 Zhehui Huang, Guangyao Shi, and Gaurav S. Sukhatme are with

Ission Description

Fig. 1. LAN2CB is an LLM-assisted multi-robot framework that converts mission descriptions into structured representations (e.g., behavior trees), assigns roles and priorities to each robot, and automatically generates executable code to accomplish complex missions. A mission change does not require human intervention since new code is generated automatically.

NL means natural language. user- or expert-provided content.

-

generated mission representations. LLM-generated code. minor changes to the problem statement or new requirements emerge, as the entire pipeline must be manually redesigned.

Claim: We posit that recent advances in large language models (LLMs) can be leveraged to alleviate these three lim- itations. Specifically, the use of such models can significantly reduce human expert effort and enhance the flexibility of multi-robot coordination systems –.

Background: LLMs are trained on massive amounts of text data to understand and generate human-like language, allowing them to interpret natural language prompts, perform contextual reasoning, and produce coherent responses or

Actions In Both Visual And Linguistic Tasks –. In

robotics, LLMs are increasingly being used to improve high- level decision-making, task planning, and human-robot in- teraction –. Applications include interpreting natural language instructions, generating structured plans, assisting in code generation for robot control, and enabling dialogue- advantages of LLMs in robotics include their flexibility, ability to adapt to new tasks without extensive retraining, and capacity to bridge the gap between human intent and machine execution, thereby significantly reducing the need for manual programming and domain-specific engineering.

Contributions: 1. We propose, implement, and thoroughly evaluate an LLM-based framework, Language to Collective Behavior (LAN2CB), which addresses the limitations of the traditional pipeline and turns natural language mission descriptions into executable plans and Python code for robot

Arxiv:2507.16068V3 [Cs.Ro] 22 Oct 2025

first module is MISSION ANALYSIS, which takes the mission specified in natural language as input, identifies the necessary tasks to be completed, and analyzes the dependency between tasks. The output of the first module, all ready-to-run nodes from a behavior tree, is given to the second module CODE GENERATION, together with a pre-constructed knowledge base, to generate executable code for robots. 2. We design a dataset of natural language mission specifications for multi- robot coordination. 3. Our experiments, both in simulation and hardware, demonstrate that LAN2CB produces effective multi-robot coordination from natural language. They also show that LAN2CB is flexible and extendable, obviating the need to design from scratch whenever the mission changes and providing a standard format to incorporate existing knowledge into its knowledge base.

A. Multi-Robot Coordination

Multi-robot systems can solve large tasks efficiently through cooperation, coordination, or collaboration . Prior work has shown that these approaches enable robots to contribute effectively to overall team performance, either through global control strategies or by relying on local observations and decentralized decision-making [31, 32].

As tasks become more complex, task-level coordination has received growing attention, where high-level goals are decomposed into interdependent sub-tasks that are allocated

And Executed Collaboratively By The Team –. For

example, Messing et al. introduced a four-layer structure covering task planning, allocation, scheduling, and motion planning to simplify decision-making. More recent work applied learning-based methods to multi-robot coordination by leveraging neural architectures such as graph attention

Networks For Scheduling And Heterogeneous Policy

networks for communication and collaboration in diverse robot teams . However, most existing approaches remain limited to specific tasks and lack the generalization to handle more dynamic objectives, understand natural language, or perform higher-level reasoning abilities.

B. Integrating Llms In Robotics

1) Single-Robot Integration: Recent work has explored integrating LLMs with single robots to enable more intuitive human-robot interaction and high-level task planning. These approaches leverage the language understanding and reason- ing capabilities of LLMs to interpret natural language com- mands and translate them into executable actions. Because natural language is inherently tied to contexts and semantics, LLMs are particularly effective in understanding tasks such as navigation, exploration, and instruction following. In these scenarios, LLMs can help robots ground language inputs into spatial or semantic representations that guide behavior

In Complex, Partially Known Environments –. In

addition, real-time resilience and anomaly detection have been integrated into LLM-based robotic pipelines to improve robustness in dynamic and unforeseen situations.

2) Team-Level Integration: Extending LLMs to multi- robot systems introduces challenges in coordination, com- munication, and scalability, with research still in the early stages exploring their use for flexible, robust multi-robot coordination . Some works use LLMs to translate natural language into formal representations –, but they are limited to simple missions and cannot handle multi-robot teams or decomposable long-horizon tasks. Others propose prompt-based frameworks for multi-robot coordination us- ing LLMs [27, 28]. For instance, Zhao et al. introduced RoCO , where robots coordinate via interactive dia- logues. However, such frameworks face limitations with large robot teams (e.g., ≥10) and complex language-based mis-

Sions. Shyam Et Al. Proposed Smart-Llm , An Llm-

based task planner for multi-robot teams with task decompo- sition and allocation, but it lacks domain knowledge, limits generalization beyond in-context examples, and cannot han- dle motion-level language commands. Our work is closely related to GenSwarm , which translates natural language task descriptions into executable Python code. While both aim to enable language-driven multi-robot coordination, our framework differs in two key ways. First, our modular design supports a broader range of coordination problems, including multi-team tasks with interdependencies and trigger events, unlike GenSwarm’s focus on simple, single-team scenarios.

Second, we incorporate a structured knowledge base to guide the LLM, enhancing extensibility, whereas GenSwarm relies solely on in-context learning, limiting generality.

Problem Statement

Consider an environment with N robots. Given natural language mission descriptions from users, our goal is to develop a system that can automatically control robots to accomplish these missions without further human interven- tion. We focus on two fundamental categories of missions: 1) goal-approaching missions, such as geometric formation or region visitation, and 2) herding missions, where robots must guide dynamic objects into specific regions or achieve a specific coverage percentage of an area. Mission diversity is introduced by systematically varying key dimensions,

Resulting In A Broad Spectrum Of Possible Tasks:

1) Coordination Strategies: Missions may require robots to coordinate, form a range of geometric patterns (e.g., lines, circles, characters), visit assigned regions, track dynamic targets, or herd dynamic objects.

2) Motion Patterns: Robots may be required to execute various motion trajectories, such as moving in straight lines, zigzagging, or spiral paths.

3) Constraints: Additional requirements can be imposed, such as entering a region from a specific direction or adhering to prescribed durations for actions.

4) Trigger: Tasks can include trigger conditions that allow actions to be terminated or modified in response to environmental events. For example, if a robot comes within a specified distance (e.g., 1 meter) of a forbidden region, it needs to switch to another task.

This mission consists of two robot groups working in parallel with a trigger mechanism. Group 1: ['/robot_0', '/robot_1', '/robot_2'], Group 2: ['/robot_3', '/robot_4', '/robot_5']. Group 1 robots must visit the following points: [-1.0, 5.0], [1.0, 5.0], [0.0, 6.0].

Group 2 robots must form a circular formation around region_1. Circle center: located at the center coordinates of region 1; Circle radius: (half the size of region_1) + 1.0. The three robots should be evenly distributed around the circle perimeter (120 degrees apart).

If any robot from Group 1 comes within 1.5 units of any forbidden region, Group 1 robots immediately stop visiting positions and move to region 0. Group 2 continues their circle formation task normally. After Group 2 completes their circular formation, it takes over the original Group 1 point visitation task.

Ission Structuring Template

Please polish and structure the mission description using the following template:

**Mission Description:**

This mission consists of [number_of_phases] phases focused on [brief_phase_overview].

- **Task [Task_Number]:** [Task Title]

* task_description: [Detailed description of which specific robots perform what

Actions.]

* finish_condition: [Clear criteria that indicate when this task is successfully

**Mission Description:**

This mission consists of 2 phases, executed in parallel initially, focused on point visitation and circle formation with an intermediate trigger-based handoff mechanism. **Phase 1: Parallel Group Tasks with Trigger Mechanism**

- **Task 1: Target Point Visitation By Group 1**

* task_description: Robots '/robot_0', '/robot_1', and '/robot_2' (Group 1) each visit their designated points: - '/robot_0' to [-1.0, 5.0] - '/robot_1' to [1.0, 5.0] - '/robot_2' to [0.0, 6.0]. * trigger_condition: If any Group 1 robot approaches within 1.5 units of the edge of 'forbidden_0' region, all Group 1 robots must immediately cease point visitation and relocate to the center of 'region_0', each with a unique 0.5-unit offset from the center to avoid collisions.

* finish_condition: Each robot is within 0.1 units of their assigned target point, unless preempted by the trigger condition. ....

Ependency Description

Action Nodes: Group 1 ('/robot_0', '/robot_1', '/robot_2') visits assigned points ([-1.0, 5.0], [1.0, 5.0], [0.0, 6.0]) Group 2 ('/robot_3', '/robot_4', '/robot_5') forms a circle around region 1.

"Status": "Idle",

"robot_ids": ["/robot_0", "/robot_1", "/robot_2"], "points": [[-1.0, 5.0], [1.0, 5.0], [0.0, 6.0]], "region_ids": [], "trigger_condition": "Trigger if any robot comes within 1.5 units of the edge of any forbidden region, Once triggered, group 1 robots need to stop visiting points and move to region_0, and group 2 robots need to take

Over Visiting Points After Form Circle.",

"finish_condition": "Finish if all robots visit their assigned points.", ... }, ...

"Key_Action": "",

"task_name": "Group 1 visit points, Group 2 forms circle",

"Status": "Idle",

"finish_condition": "Finish if all children nodes are finished.", ...

"Status": "Idle",

"robot_ids": ["/robot_0", "/robot_1", "/robot_2"],

"Region_Ids": [],

"trigger_condition": "Trigger if any robot comes within 1.5 units of the edge of any forbidden region, Once triggered, group 1 robots need to stop visiting points and move to region_0, and group 2 robots need to take over visiting points after form circle.", "finish_condition": "Finish if all robots visit their assigned points.",

Def Mission_Finish_Condition_Generation(

robot_positions: Dict[str, List[float]], object_positions: Dict[str, List[float]], forbidden_region_info: Dict[str, Dict[str, Any]], regular_region_info: Dict[str, Dict[str, Any]], room_range: Dict[str, float], done_info_dict: Dict[str, Any]

# Returns: Tuple Containing:

# - bool: Mission has finished or not. True if finished, False if not finished. # - Dict[str, Any]: Updated done_info_dict with persistent state information. This is used to track the progress of the mission. ...

Trigger Condition Code

def trigger_condition_generation( robot_positions: Dict[str, List[float]], object_positions: Dict[str, List[float]], forbidden_region_info: Dict[str, Dict[str, Any]], regular_region_info: Dict[str, Dict[str, Any]], room_range: Dict[str, float], action_node_list: List[Any], done_info_dict: Dict[str, Any]) -> Dict[int, bool]: # Returns: Dictionary mapping each action node index to a boolean indicating whether the trigger condition is satisfied (True) or not (False).

# Check The Trigger Condition Of Each Action Node

# If the trigger_condition is an empty string, return False. # If the trigger_condition is not an empty string, implement the logic.

For Action_Node In Action_Node_List:

trigger_condition = getattr(action_node, 'trigger_condition', '') ...

Action Node(S) Finish Condition Code

def finish_condition_generation(robot_positions: Dict[str, List[float]], object_positions: Dict[str, List[float]], forbidden_region_info: Dict[str, Dict[str, Any]], regular_region_info: Dict[str, Dict[str, Any]], room_range: Dict[str, float], action_node_list: List[Any], robot_details_dict: Dict[str, List[Dict[str, Any]]]) ->

Ict[Str, Bool]:

# Returns: Dictionary mapping robot namespaces to completion status (True if finished). ... def all_robot_execution(robot_positions: Dict[str, List[float]], object_positions: Dict[str, List[float]], forbidden_region_info: Dict[str, Dict[str, Any]], regular_region_info: Dict[str, Dict[str, Any]], room_range: Dict[str, float], robot_key_action_dict: Dict[str, str]) -> Dict[str, List[Dict[str, Any]]]: # Returns: Dict mapping robot IDs to their motion plans with waypoints and constraints # --- Step 0: Filter robots to only those in this node's group --- group_1_robot_ids = ['/robot_0', '/robot_1', '/robot_2'], group_2_robot_ids = ... ; group_1_robot_positions = {rid: robot_positions[rid] for rid in group_1_robot_ids if rid in robot_positions}, group_2_robot_positions ...

# --- Step 1: Goal Generation ---

visit_point_list = [[-1.0, 5.0], [1.0, 5.0], [0.0, 6.0]], group_1_goal_positions = visit_points_func(...

# --- Step 2: Goal Allocation ---

group_1_allocated_goal_positions = default_goal_allocation(group_1_robot_ids, group_1_goal_positions) ...

# --- Step 3: Generate Robot Goal Condition ---

# No constraints, just use the allocated goals as conditions with direct goal_positions. group_1_robot_goal_condition = group_1_allocated_goal_positions

# --- Step 4: Group Robot Motion Generation ---

motion_info_dict = motion_generation(group_1_robot_positions, group_1_robot_goal_condition, object_positions, regular_region_info, forbidden_region_info, room_range, group_1_robot_goal_condition) ...

Node Reselection

Fig. 2. A comprehensive demonstration of LAN2CB. human-provided content.

LLM-generated mission descriptions. LLM-generated code. 5) Task Finish Condition: Each atomic task has a clearly defined completion criterion, such as reaching a des- ignated position within a user-specified tolerance or herding objects within a given range of the target region.

6) Mission Finish Condition: Mission completion is de- fined more broadly, either by the successful completion of all constituent atomic tasks or by satisfying higher- level objectives (e.g., achieving at least 60% coverage of a specified region).

Ethod

The LAN2CB workflow consists of the following stages,

Illustrated In Fig. 1:

1) Mission Analysis: Given natural language mission

Descriptions From Users, The Llm Autonomously De-

composes missions into atomic task specifications and analyze inter-task dependencies. For each task, the LLM extracts robot assignments, relevant constraints, triggers, finish conditions, contextual hints, and other contextual requirements. Tasks that are immediately executable are then identified and forwarded to the next stage.

2) Code Generation: Based on the mission description, the system first generates the mission finish condition, which is generated once for the entire mission cycle.

For each selected task, considering its constraints, trig- ger conditions, finish conditions, and hints, the system separately generates code for: (a) robot execution, (b) trigger conditions, and (c) task finish conditions.

3) Execution: The generated code is deployed to the robots for execution. During run-time, if any trigger condition or task finish condition is met, the workflow transitions to stage 4. If the overall mission finish condition is satisfied, it proceeds directly to stage 5.

4) Mission Progress Update: Upon receiving execution results, the system uses the LLM to update the status of each task, then returns to stage 1 for further analysis and potential replanning if necessary.

5) Mission Completion: Once the mission finish condition is met, the mission is formally marked as complete.

Node Type

Parallel | Sequence | Action.

Task Name

Concise task description of the node.

Status

Idle | Running | Success | Failure.

Finish Condition

Condition(s) for determining task completion.

Action Type

visit points | follow targets | herd.

Robot Ids

List of robot IDs this action node will control.

Object Ids

List of object IDs related to the action node.

Region Ids

List of region IDs related to the action node.

Points

List of points related to the action node.

A. Mission Analysis

Mission analysis consists of two key phases: mission un- derstanding and ready-to-run action node selection. However, user-provided natural language mission descriptions often omit explicit definitions of atomic tasks and their execu- tion dependencies. As a result, directly prompting LLMs for general mission understanding can yield incomplete or ambiguous task specifications and may overlook critical execution dependencies. To address these challenges, the mission understanding phase begins by standardizing the mission description using an expert-provided template. We then perform dependency analysis to explicitly extract task relationships, which serve as the basis for a comprehensive mission analysis. Afterward, the LLM selects ready-to-run action nodes based on the results of the dependency and comprehensive mission analyses.

Dependency Analysis: To initiate dependency analysis, we prompt the LLM to extract all atomic tasks from the mis- sion description, initially disregarding trigger conditions and any tasks that may be activated post-trigger. The LLM then analyzes the dependency relationships among these atomic tasks. If triggers are activated during execution, we re-invoke the LLM to update the dependency analysis accordingly.

Comprehensive Mission Analysis: Building on the results of dependency analysis, we combine these atomic tasks and their dependencies with the standardized mission description to prompt the LLM for comprehensive mission analysis. The mission is represented in a behavior tree structure, with the overall mission as the root and atomic tasks as action nodes.

Non-leaf nodes of type Parallel or Sequence capture task execution topologies according to dependencies. For each node, we instruct the LLM to generate a unique index, identify the node type, task name, status, constraints, trigger conditions, finish conditions, hints, and children. For action nodes, the LLM also specifies the action type as well as the associated robots, objects, regions, and points. See Tab. I for detailed field descriptions of the BehaviorTreeNode.

Ready-to-Run Action Node(s) Selection: After construct- ing the complete behavior tree and integrating the depen- dency analysis results, we ask the LLM to identify action nodes that are immediately executable. Specifically, these are nodes for which all preconditions are met. The ready-to-run action nodes are then selected and forwarded for downstream processing, code generation. This approach ensures that robot actions are initiated only when all prerequisite tasks and constraints have been resolved, thereby supporting safe and efficient mission execution. After selecting action nodes that are ready-to-run, we instruct the LLM to update the status of all nodes in the behavior tree, marking the selected nodes and their parent nodes as Running.

B. Code Generation

After mission analysis and the identification of ready-to- run action nodes, we prompt the LLM to generate Python code to control all robots in the environment. The code generation process consists of four key components, executed synchronously with the robots’ control loop (Fig. 1 and 2): 1) Robot execution code generation; 2) Trigger condition code generation; 3) Action node finish condition code gen- eration; 4) Mission finish condition code generation.

Robot Execution Code Generation: Recent works have shown that LLMs can effectively assist code generation – . However, to improve success rates and mitigate hallu- cinations, it is more effective to provide core functions in advance and expose them as APIs, rather than asking the LLM to generate all code from scratch . To this end, we construct a meta behavior library for robot execution. To ensure flexibility and the capability to process multiple action nodes simultaneously, the meta-behavior library comprises

Three Sub-Libraries:

• Goal Generation: Provides primitives for three fun- damental behaviors: (a) visiting points, (b) following targets, and (c) herding.

• Goal Allocation: Offers two strategies for mapping generated goals to robots: (a) a default mapping that assigns goal positions based on robot IDs, and (b) a minimal conflict strategy that assigns goals to minimize trajectory intersections, assuming straight-line move- ment from start to goal.

• Motion Generation: Generates feasible paths from start to goal, considering environmental constraints. For each waypoint, the function not only outputs the position but also constraints such as maximum speed for approach.

This modular design allows the LLM to compose robust execution code for all selected action nodes, promoting Trigger Condition Code Generation: For each action node, LLMs are prompted to implement the corresponding trigger condition. If no trigger is specified, the function always returns False. Otherwise, the LLM encodes the trigger logic using available environmental information, in- cluding robot and object states and region properties.

Action Node Finish Condition Code Generation: For

each selected action node, the LLM generates code to evaluate whether the node’s specified finish condition has been met. For example, if the task is to visit three points, the action node is considered complete when all three points have been visited.

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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