Arduino Flood Alert System

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This version of the article has been published in the Journal of Flood Risk Management Robust blue-green urban flood risk management optimised with a genetic algorithm for multiple rainstorm return periods Asid Ur Rehman 1*, Vassilis Glenis 1, Elizabeth Lewis 2, Chris Kilsby 1, Claire Walsh 1

Abstract

Flood risk managers seek to optimise Blue-Green Infrastructure (BGI) designs to maximise return on investment. Current systems often use optimisation algorithms and detailed flood models to maximise benefit-cost ratios for single rainstorm return periods. However, the BGI scheme optimised for one return period (e.g., 100 years) may differ significantly from those optimised for others (e.g., 10 or 20 years).

This study aims to assess the effectiveness of single return period-based BGI design across multiple storm magnitudes and introduces a novel multi-objective optimisation framework that simultaneously incorporates five return periods (T = 10, 20, 30, 50, and 100 years). The framework combines a Non- dominated Sorting Genetic Algorithm II (NSGA-II) with a fully distributed hydrodynamic model to optimise the spatial placement and combined size of BGI features. For the first time, direct damage cost (DDC) and expected annual damage (EAD), calculated for various building types, are used as risk objective functions, transforming a many-objective problem into a multi-objective one. Performance metrics such as Median and Maximum Risk Difference (MedRD, MaxRD) between reference and trial Pareto fronts, capturing characteristic single values from the distribution of risk differences, and the Area Under Pareto Front (AUPF), indicating overall optimisation quality, reveal that a 100-year optimised BGI design performs poorly when evaluated for other return periods, particularly shorter ones. In contrast, a BGI design optimised using composite return periods enhances performance metrics across all return

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periods, with the greatest improvements observed in MedRD (22%) and AUPF (73%) for the 20-year return period, and MaxRD (23%) for the 50-year return period. Furthermore, climate uplift stress testing confirms the robustness of the proposed design to future rainfall extremes. This study advocates a paradigm shift in flood risk management, moving from single maximum to multiple rainstorms-based optimised designs to enhance resilience and adaptability to future climate extremes.

Keywords

multi-objective optimisation; genetic algorithm; blue-green infrastructure; multiple return periods; robust

Introduction

Flooding, a prevalent global natural disaster, exposes 1.47 billion people to 1-in-100-year risk, with annual losses rising from $6 billion in 2005 to an expected $60 billion by 2050 (Salhab & Rentschler, 2020). As urbanisation expands (Miller & Hutchins, 2017; Rentschler et al., 2023) and climate change intensifies, flood events are becoming more frequent and severe (Kendon et al., 2023; Robinson et al., 2021). Traditional urban flood risk management (FRM) approaches, primarily relying on subsurface drainage and designed by historical rainfall data, often struggle to handle extreme and varying rainfall patterns, leaving cities at unprecedented risk (Salinas-Rodriguez et al., 2018). This escalating risk to cities highlights the need for innovative and robust FRM designs to tackle the adverse impact of rainstorm events of varying intensities.

Grey Infrastructure (GI), such as drainage systems and concrete barriers, manages runoff but often fails during severe rainstorms due to limited capacity (D’Ambrosio et al., 2022; Salinas-Rodriguez et al., 2018). Expanding GI can increase capacity, but it is costly, unsustainable, impractical in dense urban areas, and potentially degrades ecosystems (Qin et al., 2013; Rosenbloom, 2018). Such limitations highlight the need for sustainable alternatives such as Blue-Green Infrastructure (BGI) or Low Impact Development (LID). These approaches use semi-natural features such as permeable surfaces, green roofs, rain gardens, and detention/retention ponds to enhance flood risk management by integrating natural hydrological processes like infiltration, evaporation, and temporary storage into urban planning (Alves et al., 2019; O’Donnell et al., 2020; Webber et al., 2020). Beyond managing floods, BGI proves beneficial

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in boosting biodiversity, mitigating heat islands, and improving urban environments (Ahiablame et al., 2012; Rodriguez et al., 2021). The adaptability, sustainability, and multifunctionality of BGI make it ideal for retrofitting flood management systems by complementing traditional GI methods and driving policy shifts in city councils towards ‘blue-green’ urban planning (Liberalesso et al., 2020; Manchester City Council, 2021; Wheeler, 2016).

Sustainable FRM requires efficient resource allocation and robust designs that perform across varying rainstorm intensities (Sharma et al., 2021). The literature suggests that the cost-effectiveness and robustness of BGI largely depend on the hydrodynamic models and risk assessment functions used to evaluate design parameters such as BGI type, location, and size.(Maier et al., 2019; Seyedashraf et al., 2021; Wang et al., 2022). For instance, semi-distributed models like the Storm Water Management Model (SWMM) (Rossman, 2010) evaluate BGI efficiency and robustness by considering reduced peak flows and water volumes in drainage networks (Zhi et al., 2022), barely addressing surface flooding and related risks, usually termed stormwater management. Fully distributed models such as CityCAT (Glenis et al., 2018; Iliadis et al., 2023) explicitly simulate BGI to assess its effectiveness in reducing surface runoffs and associated risks to buildings, properties, and infrastructure, providing a more accurate representation of surface FRM. The literature reports that most BGI designs for FRM, developed using detailed flood models, often rely on limited options evaluated through multi-criteria (Alves et al., 2018; Joshi et al., 2021) or scenario-based designs (Abduljaleel & Demissie, 2021; D’Ambrosio et al., 2022; Iliadis et al., 2024; Vercruysse et al., 2019; Webber et al., 2020), which restrict BGI deployment options and may not ensure cost-effective designs. To address this challenge, a multi-objective optimisation algorithm is integrated with a fully distributed hydrodynamic flood model to systematically achieve the most cost- effective BGI design (Ur Rehman et al., 2024). In line with industry practice, a 100-year return period was initially used to optimise the permeable surfaces' location and overall size. However, the 100-year design performed poorly when tried for a 30-year return period, possibly due to a discrete risk objective function, which only accounts for BGI performance in risk reduction when a certain threshold is met. The outcomes highlight the need to investigate BGI optimisation further using continuous risk functions across different return periods. A continuous risk objective should capture the full range of risk reduction, from

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very minor to maximum. Furthermore, a novel approach is needed to optimise multiple return periods simultaneously, potentially leading to robust FRM. To the authors' knowledge, no such method has yet been developed or tested in multi-objective optimisation, highlighting a considerable research gap.

The prevailing approaches typically focus on a single design storm, often the maximum return period, which may not ensure reliable performance under more frequent or less intense events, raising a fundamental research question of whether this paradigm should be retained or replaced by a more comprehensive approach that integrates multiple rainstorm magnitudes. This study aims to answer this research question by evaluating the effectiveness of a BGI design optimised for a single maximum return period when applied to other return periods, and by developing and comparing a composite BGI design optimised using a range of rainstorm intensities. The novelty of this work lies in the simultaneous incorporation of multiple rainstorm return periods and the design of a continuous risk function for optimisation to develop a comprehensive blue-green flood risk management approach. The specific objectives of this study are to: (i) design a continuous risk objective function for optimisation and analyse subsequent optimisation results for distinct return periods, (ii) incorporate multiple return periods into a multi-objective optimisation framework to achieve a composite BGI design, (iii) quantitatively assess optimisation performance for individual and composite optimised BGI designs, (iv), calculate realistic cost-benefits for BGI lifespan and (v) conduct a stress test to evaluate the climate change resilience of the newly proposed FRM method. The rest of this paper is organised as follows: Section 2 covers the study area and detailed methodology; Section 3 presents the results; and Section 4 discusses the overarching findings, including their implications. Lastly, Section 5 provides the main concluding remarks along with the key limitations and future research directions.

Material And Methods

Figure 1 presents the research flow diagram, with each block representing a distinct stage of the study. Phase I involves BGI and rainstorm design for the selected study area. Phase II uses the outputs from Phase I to develop an optimisation framework by integrating the CityCAT model with an optimisation algorithm. Phase 3 processes the resulting Pareto fronts (a set of optimal solutions), generated for both single and composite return periods, and applies quantitative performance metrics to evaluate optimisation

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quality. The best-performing BGI design is then carried forward to Phase IV, where a lifetime benefit- cost analysis is conducted alongside stress testing based on projected future rainfall. Sections 2.1 to 2.4 explain each phase in detail.

Figure 1. Flow diagram showing the overall research design, including key components, processes, and their interactions. PF50y refers to the Pareto front optimised for a 50-year rainstorm event. PF(100y)50y and PF(Comp)50y denote Pareto fronts obtained by optimising BGI for a 100-year and a composite of multiple return periods rainfall events, respectively and then assessed for performance under a 50-year event. The same annotation applies to other return periods.

2.1.1 Study Area

The study area, shown in Figure 2, is an urban catchment in Newcastle upon Tyne. The catchment has a total area of approximately 5.3 km, of which approximately 43% is green/permeable area, 32% is impervious surfaces, and 25% is buildings. Based on type, the building area is further classified into residential (10%) and non-residential (15%) categories. The catchment has a maximum elevation of 128 meters, with a relatively steep slope of 3.3% from northwest to southeast (see the elevation map in Supplementary Information S2). The high gradient allows rainstorm water to move relatively quickly from the upper catchment to the lower catchment, placing infrastructure and properties in the lower catchment at high risk.

Newcastle has experienced numerous flash floods due to heavy rainstorm events (Newcastle City Council, 2016), the most severe being 'Thunder Thursday', during which the city received 49 mm of rainfall in 2 hours (Environment Agency, 2012). This rainstorm was approximated as a 100-year return period event.

2.1.2 Permeable Surface Intervention Design

The current study builds on previous research (Ur Rehman et al., 2024), which assessed the cost- effectiveness of permeable surface interventions by dividing the entire catchment into zones of varying sizes and quantities. The best-performing scenario, featuring 80 permeable zones (shown in Figure 3), was selected for this case. The total permeable surface area is 0.74 km, comprising 31% parking areas

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and 69% roadside pavements and paths. As shown on the map, the sizes of permeable surface zones vary, but the optimisation process automatically normalises these differences through intervention costs. Figure 3. Permeable surface zonation for interventions: A total of 80 zones were defined, with red numbered boxes used to reference different parts of the catchment.

2.1.3 Rainstorm Design

The standard Depth-Duration-Frequency (DDF) model for the UK (Faulkner, 1999) was used to calculate the total rainfall amount for 100, 50, 30, 20, and 10-year return periods (T), each with a duration (t) of 30 minutes. The DDF model equation used for rainfall with a duration of 12 hours or less is given below: 𝑙𝑛(𝑅) = (𝑐𝑦+ 𝑑1) 𝑙𝑛(𝐷) + 𝑒𝑟+ 𝑓 𝑤ℎ𝑒𝑟𝑒 𝑟= −𝑙𝑛[−𝑙𝑛(1 −1

𝑇)]

R is the rainfall depth, D is the duration, r is the Gumbel reduced variate, T is the return period, and c, d1, e, and f are catchment descriptors. The hyetograph generation method from the Flood Studies Report (FSR) (Institute of Hydrology, 1975) was then applied to generate temporal distribution profiles for the given rainfall events in an urban catchment. The equation to create the rainfall distribution profile is given

1 −𝑎 𝑤ℎ𝑒𝑟𝑒 𝑧= 𝑥𝑏

Where: y is the fraction of the rainfall that drops within the proportion x of the total rainstorm duration. Parameters a and b have fixed values, and the profile is centred on the peak. The obtained rainfall totals

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and temporal distributions for the considered return periods with the same durations are shown in Figure 4. Figure 4. Design rainstorms for five return periods

Optimisation Framework

The optimisation framework integrates a Multi-Objective Optimisation Algorithm (MOOA) (Venter, 2010), called the Non-dominated Sorting Genetic Algorithm (NSGA-II) (Deb et al., 2002), with the CityCAT flood simulation model to identify the most cost-effective spatial combinations of permeable surface zones. MOOAs generally solve optimisation problems by iteratively changing the values of decision variables in a set of candidate solutions, called a population, to achieve better values for the considered objective functions. This iterative process, known as generations, continues until a termination criterion is reached. The result is a set of optimal solutions called the Pareto optimal front, representing the best trade-offs between objective functions. NSGA-II, in particular, uses non-dominated sorting to identify the optimal solutions and applies a crowding distance method to maintain population diversity to create better solutions in the new generation (Deb et al., 2002). For a detailed overview of a genetic algorithm, readers are encouraged to refer to the article by Maier et al. (2019). NSGA-II was selected over other optimisation algorithms due to its straightforward implementation and its ability to avoid trapping in local optima, thereby achieving a good balance between adaptability and optimisation efficiency.

CityCAT was chosen for hydrodynamic modelling because of its advanced capabilities in accurately representing and modelling buildings, BGI, and other land use features (Iliadis et al., 2023), which enables precise calculation of water depths and velocities. While Sections 2.2.1 to 2.2.4 offer an overview of these

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topics, Ur Rehman et al. (2024) provide a thorough justification for prioritising NSGA-II, detailed insights into CityCAT’s functionality, and a step-by-step guide to integrating both tools within the context of flood risk optimisation.

The following sub-sections provide a concise overview of hydrodynamic modelling and the optimisation processes implemented in this study.

2.2.1 Hydrodynamic Flood Modelling

This study uses the advanced City Catchment Analysis Tool (CityCAT) (Glenis et al., 2018). CityCAT is a fully distributed, physically-based hydrodynamic model that uses a high spatial resolution Digital Elevation Model (DEM) to explicitly represent land use features, including buildings, permeable green spaces, and impervious areas. It also simulates the hydrodynamics of BGI, incorporating features such as permeable surfaces, green roofs, and water butts. Surface water elements like detention ponds and rivers are represented within the DEM. CityCAT takes rainfall, DEM, land use and BGI inputs and applies shallow water equations to simulate 2D water depths and velocities across the spatial domain. It can also integrate subsurface sewer networks to compute coupled surface-subsurface water flows and volumes, though this significantly increases computational time. Due to such computational constraints, this study only uses CityCAT's 2D surface flood simulation module. Further details on its role within the optimisation framework are provided in Section 2.2.3. For a comprehensive overview of CityCAT, refer to Ur Rehman et al. (2024), with detailed information in Glenis et al. (2018). A detailed description of the data used for BGI and flood modelling is provided in Supplementary Information S1.

CityCAT has been successfully validated in various studies using laboratory datasets (Glenis et al., 2018), on-the-ground flood depths derived from social media images (Kutija et al., 2014), and property-level flooding based on local authority surveys (Bertsch et al., 2022). More recently, Iliadis et al. (2023) validated CityCAT outputs for the 2012 "Thunder Thursday" flood event and found good agreement between the model and surveyed data. Notably, the validation area overlaps with the catchment considered in the present study. Therefore, the same CityCAT parameters were adopted for this study (see Table S3 in Supplementary Information S1).

2.2.2 Decision Variables And Objective Functions

The decision variables in this optimisation problem correspond to the spatial locations of 80 predefined permeable surface zones. Each candidate solution is encoded as a binary vector of length 80, where a value of 1 indicates the inclusion of a particular zone, and 0 indicates its exclusion. With 80 binary decision variables, the total solution space consists of 280 possible combinations, which is an extremely large number. However, the binary representation allows the algorithm to efficiently explore a limited range of spatial configurations to find the optimal set of solutions. The encoding strategy used in this study is described in detail by Ur Rehman et al. (2024).

The objective functions are the life cycle cost (LCC) of the permeable surface zones and the associated levels of risk (R) to properties. Based on these decision variables and objective functions (LCC, R), the optimisation

𝑀𝑖𝑛𝑚𝑖𝑠𝑒: 𝐹(𝐼) = (𝐹𝐿𝐶𝐶, 𝐹𝑅)

The LCC for the jth permeable zone can be computed using the following equation:

𝐿𝐶𝐶(𝐼𝑗) = (𝐶𝑐+ 𝐶𝑜) × 𝑆(𝐼𝑗) 𝑗= 1, . . . , 80

Cc and Co are the unit size capital and operational costs, respectively, and S(Ij) is the jth permeable surface zone area. The capital cost refers to the one-time installation expense, while the operational cost is the annual maintenance expense of the permeable surfaces over a specific lifetime.

The LCC per unit of permeable surface area was calculated following the guidelines from the UK Environment Agency (Gordon-Walker et al., 2007). LCC comprises one-time Capital Expenditures (CapEx) and recurring Operational Expenditures (OpEx) over the BGI lifetime. A lifespan of 40 years was assumed for permeable pavements. An average inflation rate of 2.9%, calculated from the UK Office for National Statistics’ Consumer Price Index (CPI) spanning 2007 to 2022, was applied to calculate the current and future costs using the equation below.

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Where: FV represents the future value, BV is the base year value, i is the inflation rate, and n is the number of maintenance years. For this study, the operational cost was multiplied by the lifespan of the permeable surface, which is 40 years, before being added to the capital cost. The calculated CapEx was £82.9 m-2, with an OpEx of £46.6 m-2, resulting in an LCC of £129.5 m-2.

The risk objective function (FR) in this study represents two scenarios: (i) a risk function based on a single return period and (ii) a composite risk function incorporating multiple return periods. According to the Intergovernmental Panel on Climate Change (IPCC) Sixth Assessment Report, flood risk results from the combination of hazard, exposure, and vulnerability of affected systems (IPCC, 2023):

𝑅𝑖𝑠𝑘𝐼𝑃𝐶𝐶= 𝐻𝑎𝑧𝑎𝑟𝑑 × Exposure × Vulnerability

Previously, Ur Rehman et al. (2024) approximated flood hazard by extracting flood depths using hydrodynamic simulations. These depths were used as inputs into a building-level exposure tool (Bertsch et al., 2022) to estimate the number of buildings exposed to flooding. The resulting building count served as a proxy for flood risk within the objective function. However, this approach presents two key limitations. First, it omits building vulnerability, thereby failing to capture the true nature of flood risk.

Second, the exposure tool produces discrete outputs, classifying buildings as "exposed" only when both the 90th percentile and the mean of maximum flood depths exceed predefined thresholds. This binary classification leads to a discrete risk function, which only recognises BGI effectiveness when these thresholds are surpassed. Consequently, it may underestimate the efficiency of BGI interventions and produce inconsistent performance across varying storm intensities.

To address these limitations, this study adopts a revised approach by adapting the risk estimation methodology outlined in the Multi-Coloured Manual (MCM) for the Economic Appraisal of Flood Risk (Penning-Rowsell et al., 2014). The MCM defines flood risk as:

𝑅𝑖𝑠𝑘𝑀𝐶𝑀= Probability × Consequence

When aligned with the IPCC framework, probability in the MCM corresponds to hazard, while consequence encompasses both exposure and vulnerability. Although the MCM does not explicitly define vulnerability, it is implicitly embedded within the consequence term, which is calculated as:

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Consequence = ∑𝐹𝑙𝑜𝑜𝑑 𝑑𝑒𝑝𝑡ℎ × 𝑃𝑟𝑜𝑝𝑒𝑟𝑡𝑦 𝑡𝑦𝑝𝑒× 𝐷𝑎𝑚𝑎𝑔𝑒 𝑓𝑎𝑐𝑡𝑜𝑟 In this formulation, flood depth and property type represent exposure, whereas the damage factor is linked to building vulnerability. The consequence term is operationalised through depth-damage curves, which are derived from empirical data and express the percentage of damage relative to the asset value across varying flood depths, as illustrated in Figure 5.

Figure 5. Depth damage curves for (a) residential and (b) non-residential buildings (Source: Penning-Rowsell et al., 2014). The adaptation of depth-damage curves enables a continuous and more representative estimation of flood risk, capturing the varying susceptibility of different building types to damage across a spectrum of flood depths (i.e. hazard severity). Using these curves, this study calculates Direct Damage Cost (DDC) and Expected Annual Damage (EAD) as risk objective functions for optimisation under single and multiple return periods.

According to the MCM, DDC is calculated per property for residential buildings (Figure 5a) and per unit area for non-residential buildings (Figure 5b), with the latter multiplied by the total floor area to obtain total damage to the building (see Section 2.2.3). EAD is then computed by integrating DDC values across different return periods (see Section 2.2.4 for details). While DDC represents only the consequence component of risk, EAD accounts for both probability and consequence, offering a more comprehensive measure of flood risk.

2.2.3 Single Return Period-Based Bgi Optimisation

The schematic diagram of the multi-objective optimisation framework is illustrated in Figure 6. It comprises NSGA-II, CityCAT, and Risk Modules. Initially, NSGA-II (Figure 6a) randomly generates 'P- 2' candidate solutions, each representing different combinations of permeable surface zones. The first candidate solution, with no permeable zones, defines the baseline scenario, while the P th candidate solution, with all permeable zones, represents the maximum intervention scenario. Next, NSGA-II passes these candidate solutions to the objective functions for fitness evaluation. The cost function calculates the LCC of each candidate solution using the formula provided below:

𝑗=1

LCC(Sz) is the life cycle cost for the zth candidate solution, and LCC(Ij) is the life cycle cost of the jth permeable intervention zone. Similarly, the risk function processes the 'P' candidate solutions sequentially using the CityCAT module (Figure 6b). This module consolidates geometry files of the available permeable surface zones in each solution. Then, it incorporates standard inputs such as rainfall, DEM, and geometries of green areas and building footprints to compute maximum water depths. These water depths are then forwarded to the risk module (Figure 6c), which is adapted from Bertsch et al. (2022). The risk module creates a buffer around each building at 150% of the DEM grid cell dimension. The buffer polygons are overlaid on the flood depth map to extract flood depth cells surrounding each building. The risk module then calculates the 90th percentile and mean of maximum depth values within each building buffer area to determine whether the building Bi (where i = 1, 2, …, m) is at risk or not at risk. If Bi is categorised as at risk, the DDC is calculated using the 90th percentile of the water depth value, which helps tackle outliers in maximum flood depth values. The building classification approach helps avoid extra DDC for buildings with negligible water depths. The total risk is the sum of DDCs for 'm’ buildings, calculated using the following equations:

1 𝑑𝑚_𝑖< 0.1 𝑚 𝐴𝑁𝐷 𝑑90𝑡ℎ_𝑖< 0.3 𝑚

𝑂𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝐵𝑖 𝑛𝑜𝑡 𝑎𝑡 𝑟𝑖𝑠𝑘

Where:

• DDC(Sz) is the direct damage cost (risk level) for the zth candidate solution. • IR_i is the risk index, a function of the mean maximum depth (dm_i) and the 90th percentile of maximum depths (d90th_i) around the ith building Bi. The criterion for IR_i is adapted from the exposure classification scheme presented by Bertsch et al. (2022).

• DDCres_d90th_i is the direct damage cost for a residential building based on the 90th percentile of maximum flood depths around Bi. • ABi is the area of Bi, and DDCnon-res_d90th_i is the direct damage cost per unit area for a non- residential building, depending upon the 90th percentile of maximum flood depths around Bi.

After receiving the LCCs and DDCs for ‘P’ candidate solutions, the NSGA-II module evaluates their fitness based on their ability to minimise both LCC and DDC simultaneously. The algorithm then checks the generation number as a termination criterion and stops if it is met. Otherwise, evolutionary operations, including parent selection, crossover, and mutation (Ur Rehman et al., 2024), create a new set of ‘P’ offspring. These offspring are evaluated for cost and risk objectives to determine their LCCs and DDCs.

NSGA-II combines the LCCs and DDCs of both parent and offspring populations, selects the ‘P’ best solutions, and forms a new generation of parents. This process repeats for N generations to achieve optimal solutions with the lowest LCC and DDC.

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Figure 6. The optimisation framework for individual return periods. The NSGA-II module (a) generates a population of candidate solutions, calculates the life cycle cost (LCC) for each solution, and forwards them one by one to the CityCAT module (b), which simulates each solution to determine maximum flood depths. These depths are then used by the Risk module (c) to identify the number of buildings at risk and estimate the associated direct damage cost (DDC). The total damage cost for each solution is calculated and returned to the NSGA-II module, which evaluates LCC versus DDC to identify better- performing solutions and evolves them to create a new population. This process continues until the termination criteri on is met, ultimately providing the optimal solutions.

2.2.4 Multiple return period-based BGI optimisation For multiple return periods, each return period has an associated direct damage cost (DDC), resulting in multiple DDC objectives. Traditional multi-objective algorithms are typically limited to handling up to three objectives efficiently. A potential alternative is a many-objective optimisation algorithm (Deb & Jain, 2014), which extends multi-objective methods to accommodate and tackle a larger number of objectives. However, the implementation of such algorithms is complex, and, in this case, assigning equal

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weight to DDCs for frequent and rare events does not reflect real-world risk priorities, making this approach unsuitable for the current study. Instead, a weighted aggregation of DDCs into a single risk objective function, such as expected annual damage (EAD), is more appropriate. EAD, calculated using the trapezoidal rule, assigns weights to respective DDCs based on their exceedance probability (Bilskie et al., 2022). Five return periods (T = 10, 20, 30, 50, and 100 years) were selected to balance accuracy and computational cost, as Ward et al. (2011) noted that using very few return periods may overestimate EAD. Adopting EAD as a risk objective function provides a more accurate representation of risk and enables the calculation of realistic lifetime cost benefits for BGI. The following equation from the Scottish

(3)

𝐷(𝑆𝑧)𝐼𝑁𝐹𝐼𝑁= 𝐷𝐷𝐶(𝑆𝑧)𝑇100 + (𝐷𝐷𝐶(𝑆𝑧)𝑇100 − 𝐷𝐷𝐶(𝑆𝑧)𝑇50) × (( 1

(4)

The term 𝐷(𝑆𝑧)𝐼𝑁𝐹𝐼𝑁 is used to get proportionate direct damage contributions from the 100-year return period in the absence of the next longer return period. The adaptation of a multi-objective optimisation framework for composite return periods is shown in Figure 7. While the processes in the NSGA-II module remain unchanged, the CityCAT and risk modules evaluate each candidate solution across all return periods, calculating individual DDCs and then the EAD for each solution. This process is repeated ‘P’ times to generate ‘P’ EADs. The NSGA-II module then optimises over N generations using the LCC and EAD values of the candidate solutions.

Table S4 in Supplementary Information S4 provides the NSGA-II parameters and values used for single- and multiple-return-period optimisation.

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Figure 7. The optimisation framework for the composite of multiple return periods. The optimisation process functions similarly to that described in Figure 6. The key difference is that instead of using a single direct damage cost (DDC) as the risk function, the Risk module calculates the expected annual damage (EAD) by combining DDC values across multiple return periods. The NSGA-II module then evaluates life cycle cost (LCC) against EAD.

Optimisation Performance Quantification

Three metrics, Maximum Risk Difference (MaxRD), Median Risk Difference (MedRD), and Area Under Pareto Front (AUPF), were developed to quantify the performance and robustness of Pareto fronts obtained for the 100-year and composite return period optimisation (trialled Pareto fronts). Pareto fronts obtained by optimising BGI for individual return periods were used as a reference.

Maximum Risk Difference (MaxRD) and Median Risk Difference (MedRD) quantify the largest and median disparity in risk (DDC) between the reference and trialled Pareto fronts at any BGI cost (LCC). MedRD represents the central tendency of the risk discrepancies, providing a robust measure less sensitive to extreme deviations than the maximum difference. The formulas for these metrics are provided below:

(5)

𝑀𝑒𝑑𝑅𝐷= 𝑚𝑒𝑑𝑖𝑎𝑛 (|𝑅𝑡𝑟𝑖𝑎𝑙(𝑐1) − 𝑅𝑟𝑒𝑓(𝑐1)|, |𝑅𝑡𝑟𝑖𝑎𝑙(𝑐2) − 𝑅𝑟𝑒𝑓(𝑐2)| , . . , |𝑅𝑡𝑟𝑖𝑎𝑙(𝑐𝑛) − 𝑅𝑟𝑒𝑓(𝑐𝑛)|)

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Rref (c) and Rtrial (c) represent the risk value (DDC) on the reference and trialled Pareto fronts for a given cost c. C = {c1, c2, . . , cn} denotes the set of all cost values (LCC) where the solutions of Pareto fronts are evaluated.

MaxRD and MedRD metrics can also be expressed as percentages of the total risk range to get normalised values. The total risk range (Rrange) is defined as the difference between the risk of the baseline or no intervention solution (DDCBaseline) and the maximum intervention solution with the highest LCC (DDCMax- int).

(9)

Area Under Pareto Front (AUPF) measures the total area beneath a Pareto front in the objective space, defined by the BGI cost (LCC) and risk (DDC). This metric captures the performance of the entire Pareto front distribution. A smaller area typically indicates a more optimal front, representing lower cost and risk. AUPF is computed using the trapezoidal rule, as defined in the equation below:

Where:

C= {c1, c2, . . , cn} represents the set of sorted cost values (LCC) and R(ci) = risk value (DDC) at cost ci. The difference in underneath areas (∆AUPF) between the reference (AUPFref) and trialled Pareto fronts (AUPFtrial) reflects the overall disparity in the trialled set of solutions. This disparity can be expressed as a percentage of the reference AUPF to get normalised values.

(12)

Interpretation of performance evaluation metrics requires analysing their values in synergy. Percent MaxRD and MedRD capture characteristic single values from the distribution of risk differences and thus represent local improvements. In contrast, the percent ∆AUPF quantifies the overall gap in trialled solutions, representing global improvements. Referring to Table 1, it is also important to note that ∆AUPF (%) has an unbounded upper limit; therefore, it should not be interpreted in isolation and must be considered alongside other metrics to enable meaningful comparisons. To achieve optimal performance, all three metrics should ideally be as close as possible to their minimum values. A combination of low MedRD (%) and ∆AUPF (%) with a high MaxRD (%) suggests overall good optimisation performance with a few poorly performing trialled solutions. Conversely, moderate ∆AUPF (%) alongside high MedRD (%) and MaxRD (%) indicates inconsistent optimisation, where some trialled solutions are highly effective but majority may differ significantly from the reference front. High values for all three metrics imply that the trialled solutions are totally incompatible with the reference set.

Unbounded (Depends On Deviation Severity)

Table 1. Upper and lower bounds of performance metrics

Benefit-Cost And Resilience Assessment

2.4.1 Benefit-cost analysis of composite optimised BGI design Integrating BGI LCC and EAD in multiple-return periods-based optimisation provides an opportunity to calculate more realistic benefit-cost ratios by accounting for the lifespan of the BGI. The following equation was used to compute benefit-cost ratios for optimised solutions:

20

• B/C represents the benefit-cost ratio. • BGI lifespan is the time (in years) when substantial maintenance or overhauling of the BGI is required. • BGI LCC is the life cycle cost of the BGI, calculated based on its lifespan.

• EADBaseline is the expected annual damage for the baseline flooding scenario (i.e., without BGI intervention). • EADBGI is the expected annual damage after implementing a specific BGI solution.

2.4.2 Bgi Design Resilience Assessment

A stress test using three climate change uplifts, classified as low, medium, and high, assessed the resilience of the proposed FRM design. Based on Chan et al. (2023), rainfall increases of 15%, 30%, and 45% were applied to baseline return periods for each uplift. Figure 8 shows how these uplifts can be considered equivalent to an increase in the return period. For example, a 45% rainfall increase for a 100- year storm equates to a 360-year return period on the baseline scale.

Figure 8. Different climate uplifts drawn on baseline return periods (percent uplifts were adapted from Chan et al. (2023))

Optimisation For Individual Return Periods

The BGI optimisation results for individual return periods are shown in Figure 9a-e. Referring to the scatter plots, the x- and y-axes represent the BGI life cycle cost (LCC) and the buildings’ direct damage cost (DDC), respectively. Grey dots in the plots depict solutions generated throughout the evolutionary

21

process of NSGA-II, whereas the coloured dots indicate the optimal or best solutions achieved by the final generation. The optimal solutions for each return period form a curve, representing the Pareto optimal front. On each Pareto front, the solution positioned at the top-left represents the baseline scenario, while the bottom-right solution corresponds to the maximum intervention scenario. The latter indicates that the solution has the most permeable surface zones with the highest LCC. Additionally, for each return period, an individual spatial map highlights the contribution of each permeable surface zone to the optimal solutions. Zones with the highest contribution, indicated in dark blue, are considered highly cost-effective, while zones in orange shades are the least cost-effective. Zones with no contribution to risk reduction are shown in white.

Figure 9a-e highlights BGI’s performance in reducing DDC and identifying the best zones for permeable interventions. The Pareto curve for the 50-year return period achieves greater depth than any other return period, indicating that optimal solutions with smaller LCCs (up to ~£10 million) result in a higher reduction in total DDC than other return periods with similar LCCs. In contrast, the Pareto curve for the 30-year return period has relatively low curvature towards the minimal value.

22

Figure 9. Optimisation of permeable zones for (1) 100-year, (b) 50-year, (c) 30-year, (d) 20-year, and (e) 10-year rainstorm return periods. Each map illustrates the contribution (in percent) of each zone to the number of solutions in the respective Pareto front, with higher contributions indicating greater cost-effectiveness. Grey-outlined points represent all solutions evaluated during the optimisation process, while coloured points denote the optimised solutions for the respective return period. Tinny blue arrows along the y-axis indicate abrupt gaps between consecutive solutions along the Pareto fronts.

23

Figure 10. Maximum flood depths and direct damage cost to buildings calculated for baseline (left) and after implementing maximum BGI intervention (right) for (a) 100-year, (b) 50-year, (c) 30-year, (d) 20-year and (e) 10-year return periods, (f) shows the DDC ranges reduced by maximum intervention for considered return periods.

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

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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