Diffuser Flow Analysis Ansys

ABSTRACT: Data centers have become the backbone of an increasingly digitized world, supporting the rapid growth of cloud computing, big data, IoT, 5G, and other emerging IT technologies, with rising demand and innovations in AI and ML reinforcing their significance. Data centers are energy intensive, with data processing and storage accounting for 3 to 4% of global energy consumption, which continues to grow annually. Improving their efficiency is therefore a major industrial challenge, offering substantial cost savings. The modern data center involves an intricate interaction between non-linear interdependencies make it challenging to understand and optimize energy efficiency. In the present study, computational fluid dynamics (CFD) analysis is used to assess the cooling performance of a dynamically controlled data center hall with non-raised floor configuration and hot aisle containment (HAC) strategy. The operation of air-cooling units (ACUs) is dynamically regulated in response to the data hall IT load through an integrated network of sensors and controllers. These controllers modulate ACU fan speed and chilled water flow rates to maintain the IT cabinet inlet air temperature within each ACU’s zone of influence and below the specified threshold. This control strategy, informed by real-time temperature and pressure sensor data, ensures desired thermal conditions within the data hall while optimizing overall cooling power consumption. This study focuses on two modes of operation for the purpose of design analysis, i.e., normal mode (NM) and failure mode (FM). Based on CFD simulation results, the present paper highlights the effects of control strategy used for ACUs, cooling airflow leakage, recirculation of hot air on the performance of the data hall cooling design. Different simulation scenarios, which accommodate all possible combinations during NM and FM of operation i.e., with & without control and with & without leakages are evaluated to understand the significance of various design parameters, leading towards the right design. Results show that the control strategy delivers approximately 9.89% energy savings in normal mode, while leakages significantly degrade performance during failure mode.

KEYWORDS: CFD, Control strategy, Data center, Leakage

Ntroduction

The information technology (IT) sector and related technologies are changing at an exponential rate. Data centers have become a key infrastructure to support the rapid development of cloud computing, big data, internet of things (IoT), 5G, Metaverse etc. ; thus, data centers serve as the backbone of information in an increasingly digitized world . The demand for data center services has gone up rapidly . The advancements in technologies such as artificial intelligence (AI), machine learning (ML) leading to development of smart appliances, digitalization of transport, buildings and various industries simply

Intensive Buildings Whose Size And Number Have

increased in response to the growing demands of a digital economy . Data processing and storage represent 3 to 4% of global energy consumption, and this consumption is significantly growing year on year , , .

S. A. Surwase et al., CFD Analysis of Data Center Hall Cooling Performance

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Journal of Engineering Research and Sciences, 5(1): 09-28, 2026 Data centers consume a lot of energy. Due to the large energy demands, data center generates a large amount of heat. Thus, cooling is a major aspect of data center design.

Enhancing the efficiency of data centers is a significant challenge in the industry, as it can result in significant cost savings . The modern data center involves an intricate interaction between various mechanical, electrical and

Operating

configurations and non-linear interdependencies make it challenging to optimize energy efficiency .

Iterature Review

The concept of hot and cold aisles was first introduced and formalized in , where it was demonstrated that an

Aisles

significantly improves data center cooling efficiency compared to earlier layouts that lacked floor planning and applications of CFD to data center cooling was presented in , at a time when such studies were scarce. The study proposed an alternative cooling arrangement with ceiling

Saving

advantages over conventional modular air conditioning

Unit Designs. Using Experimentally Validated Cfd

simulations, the authors demonstrated the ability to predict system inlet temperatures and identify hot spots, highlighting the importance of CFD based design for reliable cooling in future high power and high density

Experimental Validation, Became A Benchmark For

subsequent academic and industrial CFD studies. The

Paper On Airflow And Cooling Within Data Center

provides one of the earliest comprehensive formulations

Of Airflow Management From A Fluid Mechanics

perspective. The study evaluated how raised floor height, CRAC unit, tile layout and open area, and underfloor obstructions influence plenum airflow, noting that deliberate obstructions such as inclined solid or perforated partitions can beneficially redirect flow. The work also addressed above floor management strategies to prevent hot air recirculation into rack inlets, including sufficient cold air supply, air curtains, partitions, drop ceilings, and ducted racks. The work established the theoretical foundation for many subsequent CFD studies.

N , A Literature Review Was Conducted To Examine

corridor isolation and the integration of Building Information Modelling (BIM) with Computational Fluid Dynamics (CFD) in data centers. The authors identified a

Research Gap In Studies Combining Bim And Cfd For

corridor isolation. Their findings revealed that hot aisle containment (HAC) provides greater cooling efficiency, lower power usage effectiveness (PUE), and improved working conditions compared to cold aisle containment (CAC). CFD simulations showed that leakage size and position, significantly influence airflow patterns and cooling capacity, while increased supply airflow does not mitigate leakage losses. Cold corridor isolation was found suitable for low-load data centers (up to 5 kW per cabinet) but can reduce personnel comfort, whereas hot aisle isolation is more efficient and preferred in high-load

Environments (Up To 10 Kw Per Cabinet). The Study

concluded that integrating BIM and CFD offers a reliable

Thermal

management in data centers.

A Comparative Cfd Analysis Of Three Airflow-

organization strategies: underfloor precision supply, inter-column supply, and rack backplane cooling was carried out in . The investigation introduced thermal performance indices such as ASE, ARE, MCRI, RTI, SHI and RHI to evaluate system effectiveness. Results showed

That Adopting Either Cac Or Hac Increased Ase And

reduced SHI values, while the backplane configuration

Eliminated Hot Spots Without Requiring Full Aisle

containment. Optimizing airflow organization scheme, significantly enhances cooling efficiency and energy utilization while minimizing hot spots. The HAC scheme

Showed The Best Thermal And Energy Performance,

offering valuable insights into selecting efficient cooling strategies. A similar numerical and experimental study

Compared Hac And Cac In Legacy Data Centers,

focusing on thermal performance and air leakage. The

Results Showed That Hac Outperformed Cac At A 15%

leakage rate, delivering a 24.9% thermal performance improvement and allowing the supply air temperature in the HAC system to be raised by 2°C. The authors also noted that accurately measuring and validating leakage is challenging and therefore used the IT supply temperature range as a practical indicator of relative leakage effects.

Furthermore, Conducted A Cfd Based Comparison Of

raised floor and hard floor configurations with HAC in high density data centers, demonstrating that the raised floor HAC system delivers superior thermal performance over hard floor HAC system. The results showed that adopting a raised floor improves air distribution efficiency by 28% and reduces recirculation ratio by around 40%.

In , a combined cooling system that integrates heat storage, waste-heat recovery and different renewable energy sources with conventional air conditioning was modeled. The proposed system reported approximately 16% annual energy savings, an increase in system COP from 3.9 to 4.6, and a reduction of PUE from 1.36 to 1.30.

The paper investigated two improvement methods to achieve a uniform temperature distribution in data centers using CFD: (i) installing adjustable underfloor deflectors beneath perforated tiles with varied opening ratios to balance cold-air distribution, and (ii) replacing standard floor grilles near cooling units with fan-floor modules to enhance airflow delivery. Simulation results showed that the deflector method increased airflow to front end cabinets by 18.1% and reduced rear end airflow by 5.1%, S. A. Surwase et al., CFD Analysis of Data Center Hall Cooling Performance

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Journal of Engineering Research and Sciences, 5(1): 09-28, 2026 while the fan-floor approach achieved a 4.9% increase and 3.8% reduction, respectively. Both methods improved thermal uniformity and showed that airflow is a key factor that influences cabinet temperature, reducing cabinet maximum outlet temperatures by up to 2.81°C.

The Kao Data Case Study Demonstrated The Use Of

CFD based digital twin modelling (via Future Facilities’

Sigmadcx) To Validate And Optimize The Indirect

evaporative cooling (IEC) design of a high-density, 100% free-cooled sustainable colocation data center. The study conducted both internal and external airflow analyses: internally, the data hall whitespace was evaluated under normal operation and failure mode scenarios to verify cooling efficiency and uniform airflow distribution; externally, a range of wind speeds and directions were simulated to assess the risk of recirculation. Simulation analyses confirmed that the IEC system could maintain target temperatures without mechanical refrigeration,

Highlighted The Value Of Cfd In Enabling Design

optimization and refining the decision-making process. AKCP illustrates the broader value of CFD to optimize data center airflow and thermal performance. The study emphasizes four key analyses: design airflow analysis to identify hotspots and uneven distribution, “Day One” analysis for early operational optimization, equipment switchover simulation to ensure resilience during cooling unit failures, and leakage analysis to reduce bypass losses and notes that simulation-driven optimization can lower operational costs and carbon footprint.

A new type of ducted HAC system for data center rack cooling was proposed and experimentally evaluated in . The authors studied the effects of different hot duct containment configurations, door states, diffuser types, blanking panel percentages, and airflow volume scenarios

Proposed Average Inlet Rack Temperature, Standard

deviation of temperature and temperature difference across rack as practical metrics instead of percentage leakage. Results showed that ducted containment offered performance close to that of full airtight containment but

At A Lower Cost. The Paper Combined Experimental

testing with physics based modelling to quantify cold air

Bypass And Determine The Optimal Dp Across Aisle

containment in data center. The results showed that even with containment, substantial bypass can occur through the rack itself, with bypass airflow reaching up to 20% of the ACU supply. The paper demonstrated that practical mitigation measures such as improved rack design and blocking leakage paths reduced power consumption by up to 8.8%, while optimizing the DP across the cold and hot aisles delivered up to a 16% reduction in power consumption. The authors of conducted a CFD study of a data center with cold aisle containment (CAC), validated by experiments, to assess the impact of leakage.

They argued for including realistic fan curves (both server

And Crac Fans) In Models, Noting That Fixed Flow

boundary conditions are a poor approximation in CAC cause an inlet temperature rise of about 4°C, and identified a critical leakage threshold of approximately 15%, above

Which The Containment Allows So Much Hot Air To

recirculate that the benefits of containment are completely lost. In , validated CFD modelling was used to assess airflow improvements in a raised floor data center, testing blanking panels, vertical partitions and partial cold aisle enclosure. Partial cold aisle enclosure produced the greatest benefit, allowing a 3°C increase in supply air temperature while maintaining acceptable rack inlet conditions, thereby improving energy efficiency. The study also noted that RTI can be unreliable for identifying bypass or recirculation in complex airflow scenarios. In

, The Effect Of Crac Unit Placement By Comparing

units placed in line with the rack rows to units placed perpendicular to the rack rows was investigated. Using RTI, SHI, and RHI as performance indicators, it was found that the perpendicular layout improves airflow uniformity from perforated tiles, reduces hot air recirculation and cold air bypass, and significantly enhances overall cooling performance.

Advanced cooling control strategies for data centers with raised floors and HAC, proposing a decentralized MPC controller design to improve thermal management

Air

temperatures. The decentralized control system structure lowers the risk of failure associated with centralized

Inlet

temperatures while reducing cooling power consumption. In , the concept of a smart cooled data center with variable capacity cooling system to allocate cooling dynamically where and when required was proposed. The cooling system consists of adjustable vents, sensors for real

Time Temperature And Pressure Monitoring And Crac

units with VFD for fans speed and three way valves for

Chilled Water Control. Later, Implemented And

experimentally tested this distributed sensor network coupled with CRAC control in a raised floor data center, reporting a 50% reduction in cooling power consumption and a 25% cost reduction in space and power.

The thermal performance of air cooled data centers under raised floor and non-raised floor configurations was

Numerically Evaluated In . They Found That A Non-

raised floor design with overhead supply and overhead return strategy gives the best thermal performance. They also recommend using overhead supply and return even in raised floor setups, because obstructions (such as pipes and cables) in the underfloor plenum (should be used for only housing pipes and cable) significantly affect air flow S. A. Surwase et al., CFD Analysis of Data Center Hall Cooling Performance

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Journal of Engineering Research and Sciences, 5(1): 09-28, 2026 distribution. Importantly, their results showed that using a ceiling return is better than a room level return for both raised floor and non-raised floor design.

The Effect Of Air Flow Leakage From Hac System On

their cooling performance was analyzed by the author of . He evaluated the influence of leakage area, supply air ratio and rack cooling load on the performance of HAC system and found that leakage areas have the largest impact on the performance. An increase in leakage area raises the rate of air leakage, while the nature and location of the leakage paths alter airflow patterns, both of which negatively impact the cooling performance. He also finds that simply increasing supply airflow only reduces temperature of hot air exiting and does not mitigate leakage, and that varying rack cooling loads has little impact on leakage rates. The authors of investigated introduced a Leakage Impact Factor (LIF) to quantify and rank leakage paths such as gaps beneath racks, above racks, and around containment doors. They assumed no leakage through the racks to isolate the effect of containment leakage. Their results showed that leakage beneath racks is the largest contributor to unwanted heat transfer into cold spaces, and they concluded that slight over provisioning of pressure differential is required to mitigate leakage effects. The authors of motivated by experimental data showing air recirculation from the hot aisle to the cold aisle through the gap beneath server cabinets, investigated how tile perforation area, CRAC provisioning, leakage pressure gradients, and CAC affect cooling performance. Results indicate that even small under-cabinet leakage can reduce cooling effectiveness, with the effect being particularly sensitive to under provisioned conditions.

In , the authors demonstrated that properly sealed cold aisle containment (CAC) supports higher server heat loads (25.2 kW/cabinet) compared with standard hot aisle/cold aisle layouts (14.6 kW/cabinet). Their research also highlights the critical role of sealing accessories such as grommets and blanking panels, and unused U-slot

Closures Being Crucial For Improving Containment

performance. In , the authors evaluated the effect of partial aisle containment in both hard floor and raised floor data center layouts under two supply flow rates, 100% and 50%. Their results showed that at a 100% flow rate, the top or side cover fully prevented recirculation in the raised floor configuration, while only reducing it in the hard floor configuration. However, at 50% flow, hard floor setup developed hotspots at the row ends: The side cover improved performance for hard floor layouts and the top

Floor

configurations partial containment remained beneficial over an open aisle under reduced airflow, with the side cover offering the best results and the top cover providing little improvement.

A containerized data center using CAC with an airside heat exchanger and waterside evaporative water chiller to improve performance in tropical and subtropical regions

Was Demonstrated In . Cfd Simulations Evaluated

temperature distribution and thermal performance under varying inlet air temperatures and velocities. Results showed that supply air temperature had minor impact, while inlet air velocity strongly influenced air distribution

And Thermal Management. Overall, The Overhead

downward flow system with CAC significantly enhanced air distribution and thermal performance in large scale data centers. A comprehensive CFD based analysis of a real data center comprising 208 racks was conducted by

Authors Of To Assess How Airflow And Thermal

performance change under varying thermal loads and air supply velocities. They simulated four distinct case studies: two with spatially varying heat loads and two under uniform load, each tested with both maximum and minimum air velocity conditions. Their results showed that while operating CRAC units at maximum airflow can successfully cool the room, it does so at a high energy cost.

Consequently, the authors argue that instead of costly

Rac Upgrades, Sustainability Can Be Improved By

optimizing rack layout such as removing selected end of row racks and thereby eliminating hot spots by improving airflow.

According To The Authors Of , The Standard K–Ε

turbulence model is particularly well suited for turbulent flows due to its approach for calculating turbulent viscosity and conductivity. It is also the most extensively

Commercial Cfd Codes. Furthermore, Report That

previous studies have demonstrated the k–ε turbulence

Model Outperforms The Sst, K–Ω, Rsm, And Rng K–Ε

models. The paper focused on improving the accuracy of CFD simulations for data center airflow by comparing different turbulence models, including the widely used k– ε model, Reynolds Stress Model (RSM), and Detached Eddy Simulation (DES). Using a full-scale data center test facility, the CFD results were validated against the experimental measurements. The study found that while the k–ε model captures general flow patterns, it fails to predict low velocity zones present above server racks. The differences in flow fields predicted by the different turbulence models are mostly observed in areas far from the main components of the data center. RSM and DES produced very similar results, with RSM being more computationally efficient and thus recommended for data center airflow modeling. A CFD based study to enhance the design of water cooled data centers using a rear door air to liquid heat exchanger for a 40 kW server rack was conducted in . The simulation, performed with ANSYS and the RNG k-ε turbulence model, showed that inlet air temperature strongly affects rack thermal performance.

The rear door liquid cooling system effectively reduced S. A. Surwase et al., CFD Analysis of Data Center Hall Cooling Performance

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Journal of Engineering Research and Sciences, 5(1): 09-28, 2026 outlet air from about 40°C to near room temperature of 24°C, efficiently handling the full heat load without additional room cooling.

Centers Exhibits Inherently Complex Behavior With

recirculating flow. Considering an inlet velocity of 1 m/s at the supply vents and a rack height of 2.4 m, the resulting

Role Of Cfd In Data Center Design

The CFD simulation plays an important role in data

Center Design :

 Virtual Design and 3D Analysis: Minimize rework by

Testing The Design Or Design Changes Prior To

implementation. Helps to validate and analyze design effectiveness through detailed 3D analysis of air flow and heat transfer in a data center.

 Performance-Based Analysis: Identifies issues with data center performance, such as improper air flow (excess or insufficient supply of cold air, bypass, recirculation of hot air, mixing of cold and hot air) during the design phase.

 What-if Scenarios: Using predictive results provided by CFD simulation, design and what-if scenarios can be evaluated, minimizing risk of failure such as server overheating and helps in identification of potential failures, which leads to an accurate design.

1.3. Raised Floor Versus Non-Raised Floor Data Hall

Optimal Temperature For The Highest Efficiency Of

equipment. There are various cooling design approaches such as uncontained room cooling, CAC, HAC, in-row cooling, direct to chip cooling, immersion cooling each having advantages and disadvantages over one another.

Irrespective of the cooling approach used, a data hall can be either raised-floor or slab floor (non-raised floor). Researchers continue to debate whether raised floor or non-raised floor configurations provide a better supply air

Path, With No Clear Conclusion Yet. The Thermal

performance depends on the cooling conditions and IT environment, and although both approaches reduce loss of cooled air, they differ in practical implementation and operation . The topic of raised floor versus slab floor construction is a topic that often sparks heated discussions in the data center industry as both having advantages and disadvantages over one another. Earlier, almost all the data centers used raised floor. In recent years, non-raised floor data center have gained popularity. The decision to go with raised floor or non-raised floor data centers is now driven by operational objectives, business objectives, business needs and market demands .

Scope Of Study

In the present study, CFD analysis is used to assess the cooling performance of a dynamically controlled data hall with practical leakages, non-raised floor configuration and HAC strategy. The operation of air cooling units (ACUs) is dynamically regulated in response to the data hall IT

Load Through An Integrated Network Of Sensors And

controllers. These controllers modulate ACU fan speed and chilled water flow rates to maintain the IT cabinet inlet air temperature within each ACU’s zone of influence and below the specified threshold. This control strategy, informed by real-time temperature and pressure sensor data, ensures stable thermal conditions within the data hall while optimizing overall cooling power consumption.

This study focuses on two modes of operation for the purpose of design analysis, i.e., normal mode (NM) and failure mode (FM). In NM steady state operation, all the

Acus Are Functional. During Fm Of Operation, A

designated number of cooling equipment are offline in the worst-case scenario. Both modes operate with 100% IT loads with uniform distribution of load in data hall.

Based on CFD simulation results, the present paper highlights the effects of control strategy used for ACUs, cooling airflow leakages and recirculation of hot air on the performance of the data hall cooling design. Results from different simulation scenarios, which accommodate all possible combinations during NM and FM of operation i.e., with & without control and with & without leakages are evaluated to understand the significance of various design parameters, leading towards right design. Data center metrics such as ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers)

And Sla (Service Level Agreement) Compliance Are

plotted for all simulation scenarios.

Novelty And Contribution

While numerous prior studies have examined thermal behavior and airflow management in data centers, most rely on highly simplified models of data halls (e.g. limited number of IT Cabinets, idealized geometric layouts or

The

complexity of real operational environments. Existing

Configuration And Cac. Only A Few Investigations

addresses non-raised floor facilities with HAC designs, that gained popularity and are increasingly adopted in modern data centers but remain underrepresented and less thoroughly investigated. Moreover, most prior

Studies Typically Assume Fixed Acu Fan Speeds And

constant chilled water flow rates, failing to explore the dynamic optimization crucial for energy efficiency. To the author’s knowledge, studies that do incorporate control often omit details of the control strategy, leaving its impact largely unexplored.

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Journal of Engineering Research and Sciences, 5(1): 09-28, 2026 Addressing these gaps, the novelty of the present study lies in its comprehensive, holistic CFD simulation of a dynamically controlled, existing full-scale data hall comprising 308 IT cabinets configured with a non-raised floor and HAC design, thereby offering a level of practical

Complexity Rarely Addressed In Previous Works. A

dedicated control strategy for optimizing ACU fan speed and chilled water flow rate is developed, described in detail, and its impact on overall energy consumption is quantified. Finally, unlike prior studies, which typically examine leakage effects, equipment failures, or normal a holistic evaluation of data hall performance under both NM and FM, including the practical leakages and active control strategy. By integrating real scale, dynamic control and multi-scenario operation, these contributions advance the state of knowledge by offering practical insights into the design, operational control strategy, and optimization of large-scale modern data centers.

Ethodology

The air flow and temperature distribution within the data center are governed by the fundamental principles of conservation of mass, momentum, and energy. The full mathematical formulation and derivation of the Navier-

Stokes Equations (Momentum Conservation) And The

energy conservation equation are omitted here, as these

And

comprehensively documented in standard CFD books and

Literature , , , . However, The Underlying

physics, key assumptions, the selection of the turbulence model, and the details of the computational approach

And

convergence criteria critical to this simulation are discussed in detail in the following sections.

The Computational Model Is Based On Conservation

laws, specifically the continuity, momentum, and energy equations, supplemented by the ideal gas equation of state. These equations collectively describe the steady state motion of an incompressible Newtonian fluid (air) and the associated heat transfer by the active information

Technology (It) Equipment, Along With Significant

auxiliary sources such as uninterruptible power supplies dimensional domain. Key assumptions include modeling the working fluid air as an ideal gas, treating the fluid flow as incompressible and turbulent, and assuming steady- state heat transfer process.

The mass balance (or continuity equation) ensures that mass is conserved within the fluid domain . It dictates that for any control volume within the simulation, the rate at which mass enters must equal the rate at which it leaves, plus any change in mass stored inside. This balance is

Incompressible Flows And The Density Changes In

compressible flows, ensuring a physically realistic flow pattern. The momentum balance applies Newton's second law to fluid motion, stating that the net force on a fluid element equals its rate of momentum change. These forces include surface forces like pressure gradients, viscous stresses (internal friction), and body forces like gravity. By solving this balance, CFD determines the fluid's velocity field which along with the pressure field describes the flow dynamics. The energy balance ensures that total energy is conserved by accounting for all energy transfers based on first law of thermodynamics. It relates changes in internal energy to heat transfer (conduction and convection) and the work done by pressure and viscous

Forces. This Equation Is Solved To Determine The

temperature distribution throughout the fluid domain, making it essential for simulations involving heat transfer, and fluid property variations caused by temperature changes.

Modeling air as an ideal gas allows the simulation to

Necessary Density Variation Caused By Changes In

temperature and pressure within the flow field. The equation of state is crucial for solving the system of governing equations, as it provides a way to calculate the

Equations, Based On The Pressure And Temperature

calculated by the momentum and energy equations. A steady state analysis is performed by setting all the time derivatives to zero (𝜕𝜕/𝜕𝜕𝜕𝜕 = 0). This choice is justified because the primary objective is to predict the long term, time averaged thermal equilibrium and characteristic mean operating temperatures of the data hall, providing a computationally efficient approach.

As air velocities in the data hall are typically low (with Mach number, Ma < 0.3), incompressible flow assumption is applied. This neglects density variations due to pressure changes, which is a significant simplification used in the continuity and momentum equations.

The Air Flow Patterns In Data Centers Are Highly

complex and recirculating. Based on typical operating conditions such as an air inlet velocity of 1 m/s at supply vent and IT cabinet height of 2.4 m, the Reynolds number is approximately 105, clearly indicating a turbulent flow regime .

To Computationally Model The Inherently Turbulent

flow characteristic of large indoor spaces such as data hall, these fundamental principles are typically expressed in their Reynolds-Averaged Navier–Stokes (RANS) form.

Rans Models Decompose Each Instantaneous Flow

variable (e.g., velocity, pressure, temperature etc.) into a S. A. Surwase et al., CFD Analysis of Data Center Hall Cooling Performance

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Journal of Engineering Research and Sciences, 5(1): 09-28, 2026

Time-Averaged Mean Component And A Fluctuating

component. This time-averaging process introduces the

′) Into The Momentum

equations, which represents the effective momentum transfer due to turbulent fluctuations. Since the Reynolds stress terms are unclosed (i.e., they introduce more unknowns than available equations), a turbulence model is required. Specifically, the Reynolds stress tensor, is a symmetric second-order tensor and thus introduces six independent unknown components into the

Three Rans Momentum Equations. These Six Unknowns

cannot be determined solely by the existing four RANS equations (continuity and three momentum equations).

A Common And Robust Approach Is To Employ The

Boussinesq turbulence hypothesis, which postulates that the Reynolds stresses are directly proportional to the mean rate of strain tensor, analogous to the relationship between viscous stress and strain for a laminar flow. This hypothesis effectively replaces these six unknowns with a single scalar quantity, the eddy viscosity (𝜇𝜇𝑡𝑡). The major drawback of this hypothesis is that it assumes the turbulent flow is isotropic (the same in all directions), which is often not true for complex engineering flows and cannot accurately predict stresses in highly anisotropic

Flows Where Turbulent Stress And Mean Strain Are

misaligned (e.g., highly swirling or separating flows). Despite this simplification, it works remarkably well for a vast range of engineering applications, including the data center flows.

(1)

Where, 𝑆𝑆̅𝑖𝑖𝑖𝑖 is the mean rate of strain tensor, 𝜌𝜌 is the fluid density, 𝑘𝑘 is the turbulent kinetic energy , 𝛿𝛿𝑖𝑖𝑖𝑖 is the Kronecker delta. With the six Reynolds stress components now expressed in terms of 𝑆𝑆̅𝑖𝑖𝑖𝑖, and the new variable 𝜇𝜇𝑡𝑡 (which itself depends on 𝑘𝑘), the closure problem is reduced from six unknowns to one primary unknown, the eddy viscosity 𝜇𝜇𝑡𝑡.

Unlike molecular viscosity (𝜇𝜇), eddy viscosity is a flow property, not a fluid property, which varies throughout

The Flow Field And Is Computed From Averaged Flow

variable , necessitating the use of two-equation models for closure. For instance, the widely-adopted Standard 𝑘𝑘− 𝜀𝜀model solves two auxiliary RANS transport equations, one for the turbulent kinetic energy (𝑘𝑘) and another for turbulent kinetic energy dissipation rate (𝜀𝜀) . These two variables are then used to calculate the turbulent viscosity, 𝜇𝜇𝑡𝑡, thus achieving closure for the RANS equations.

While The Standard 𝑘𝑘−𝜀𝜀model Is Utilized For Its

robustness and wide applicability, it is essential to acknowledge its inherent limitations. The model is known to perform less accurately for flow with strong adverse pressure gradients, substantial boundary layer separation, rotating fluid flows or flow over curved surfaces. This model also assumes a fully turbulent flow regime, an assumption that may not hold across all regions of the airflow within the data center.

The standard 𝑘𝑘−𝜀𝜀 turbulence model remains the most commonly used approach for CFD simulations of data centers despite its well-known limitations because it offers

A Uniquely Advantageous Combination Of Numerical

robustness, computational efficiency, and extensive historical validation. Its exceptional stability makes it unlikely to diverge or crash even on complex or coarse meshes, an attribute that is particularly valuable in data center design where many preliminary configurations must be evaluated rapidly and stability is prioritized over

Marginal Increases In Accuracy. The Model Is Also

computationally inexpensive, adding only two additional transport equations to the RANS formulation, whereas more advanced models such as the Reynolds stress model (RSM) require solving seven additional equations (six for the Reynolds stress tensor components plus one for epsilon), significantly increasing memory requirements and runtime for the large computational domains typical of data halls. Furthermore, the 𝑘𝑘−𝜀𝜀 model’s empirical constants have been calibrated over decades against a

Implementations

extensively, reinforcing its position as an industry- standard model . Although it fails to perfectly capture the physics of small, highly anisotropic eddies with high fidelity, it typically provides sufficiently accurate

Characterize

recirculation, and support overall decision making. In practice, higher-fidelity alternatives such as the realizable or RNG 𝑘𝑘−𝜀𝜀, the 𝑘𝑘 - 𝜔𝜔 SST model, or the RSM are employed when detailed accuracy in near-wall behavior, swirl, turbulence anisotropy or modeling of flow inside a server rack is required, but for large-scale airflow in typical data halls, the standard 𝑘𝑘−𝜀𝜀 model continues to offer the most effective balance between stability, computational cost, and engineering reliability and practicality.

Approach For Near-Wall Modeling. This Coupling Is

necessary because resolving the steep velocity profiles within the thin viscous sublayer of a turbulent boundary layer requires an extremely fine mesh (viscous sublayer resolving approach, 𝑦𝑦+ ≈1), leading to prohibitively high computational cost. Moreover, the SKE model is not S. A. Surwase et al., CFD Analysis of Data Center Hall Cooling Performance

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Journal of Engineering Research and Sciences, 5(1): 09-28, 2026 formulated for low Reynolds number wall treatment, its core assumptions specifically the local isotropy of turbulence (turbulence is highly anisotropic near wall) and the validity of the 𝜀𝜀 - transport equation (The 𝜀𝜀 - transport equation is unsuitable near the wall because it is derived under the assumption of high local Reynolds numbers. But near the wall, viscous effects dominate, leading to low local Reynolds numbers) break down in the

Achieve

computational feasibility, wall functions are used. These are semi-empirical formulas based on the universal law of the wall, effectively bypassing the need to resolve the viscous sublayer with the mesh. The universal law of the wall describes the mean velocity profile of turbulent flow close to the wall, stating that when the mean flow velocity (𝑢𝑢ത) and distance from the wall (𝑦𝑦) are scaled using friction velocity and kinematic viscosity to yield the dimensionless velocity ( 𝑢𝑢+ ) and dimensionless distance ( 𝑦𝑦+ ), the resulting relationship becomes universally constant and

Independent Of The Overall Reynolds Number. This

universal velocity profile is characterized by a linear relationship in the viscous sublayer , transitioning through a buffer region and a logarithmic relationship in the log layer.

This approach requires the first grid cell center to be located within the turbulent logarithmic region of boundary layer, satisfying the meshing guideline of 30 < 𝑦𝑦+ < 300 . This compromise is acceptable for data hall flows, which are generally high Reynolds number and attached.

Although A Highly Accurate Thermal Model Could

include the heat source at individual servers, a black box approach was utilized for each IT cabinet in this study, as the inclusion of server level heat details only offered a marginal contribution to overall data center thermal accuracy .

Furthermore, Buoyancy Effects, Which Are Highly

significant in thermally stratified air cooled data halls, are incorporated using the Boussinesq approximation. This approximation simplifies the equations by treating the fluid density (𝜌𝜌) as constant in all equations, except within the gravity (buoyancy) term of the momentum equation.

In this term, density is assumed to vary linearly with temperature.

(3)

where 𝜌𝜌ref, 𝛽𝛽 and 𝑇𝑇ref are the reference density, thermal expansion coefficient and reference temperature. This simplification is valid provided air properties are constant, the flow is incompressible and exhibits small temperature-induced density variations resulting from a small temperature difference (ΔT). The use of this approximation is strongly justified for this study because data hall operates with a maximum design ΔT of 12 ± 1°C between the supply and return air. This value is well within the widely accepted limit (typically < 20 K) for air . This assumption enables the accurate prediction of temperature and buoyancy driven airflow patterns such as the thermal plume rising from IT equipment without solving the full compressible Navier - Stokes equations, thereby reducing computational costs.

Together, The Rans Formulation, The Boussinesq

turbulence hypothesis, the Standard 𝑘𝑘−𝜀𝜀 model, wall function, and the Boussinesq approximation establish a practical and robust framework for predicting the steady state distribution of air velocity, temperature, and pressure within data center spaces.

The set of coupled, non-linear partial differential

Equations (Pdes) Comprising The Rans Momentum,

mass, energy, and turbulence equations cannot be solved analytically. They are solved using a computational approach. A computational approach based on the Finite Volume Method (FVM) was employed to discretize and solve the equations numerically. In FVM, the physical domain of the data hall is first divided into a finite number of non-overlapping continuous sub-regions, known as control volumes (or the computational mesh). In FVM, the governing PDEs are integrated over each control volume.

This integration converts the differential equations into a system of linear algebraic equations that link the value of a variable (e.g., velocity or temperature) at the center of one control volume to the values in its neighboring control

Volumes. A Primary Challenge In Solving The Rans

equations is the inherent coupling between the pressure field and the velocity field, as the mass conservation (continuity) equation does not explicitly contain a term for pressure. This requires a specialized iterative algorithm for solution. For this steady state simulation, the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm, or a similar segregated scheme, was utilized.

This algorithm iteratively adjusts the pressure and velocity fields until the mass and momentum equations are simultaneously satisfied throughout the entire domain. The system of algebraic equations is solved iteratively until a converged steady state solution is achieved. Convergence is confirmed when the residuals

Which Represent The Imbalance In The Conservation

equations for each control volume have reduced to a specified level. Specifically, the simulation was considered converged when the residuals for pressure, velocity, temperature and turbulence parameters (𝑘𝑘 and 𝜀𝜀) tended to 1. Furthermore, monitoring key performance metrics, such as the return air temperature to cooling unit, ensured

That These Values Stabilized And Ceased To Change

significantly between iterations. S. A. Surwase et al., CFD Analysis of Data Center Hall Cooling Performance

Alidity Of Cfd Simulation

‘DataCenterDesignPro’ which is an industry standard data center specific CFD software (Previously recognized as ‘6SigmaRoom’ Release 16.3, which is the latest version at the time of analysis) is used for modeling and CFD simulation. The software is a physics based simulation tool for data center design that utilizes digital twin models. It enables the rapid and accurate creation of digital twins, which serve as virtual representations of existing or planned data centers. These models allow the exploration of multiple design configurations and failure scenarios, supporting the optimization of new data center designs as well as the reevaluation of legacy facilities. By leveraging CFD simulations, the software facilitates the entire design

Process, From Conceptual Prototyping To Detailed

engineering . It includes a comprehensive database of IT equipment and cooling systems, with information collected and verified directly by the respective manufacturers. This capability enables accurate modeling of real data center.

The software incorporates the latest cooling technologies and offers greater flexibility in addressing a wide range of design challenges compared to other commercial CFD tools and emerges as the most extensive and feature rich.

It is widely recognized as the most accurate tool in the industry for data center design. It is used by several global

Including

Facebook, Microsoft, and IBM, in their data center projects

, , , , , , , Demonstrating The

reliability of its CFD results.

A Mesh Independence Study Is A Fundamental

requirement in all CFD simulations. It is conducted to confirm that the numerical solution is insensitive to further mesh refinement indicating that the discretization

Error Due To The Mesh Size Has Been Minimized And

therefore represents the correct underlying physical behavior. The regions with high gradients are typically assigned a finer mesh. While a finer mesh enhances solution accuracy, it leads to a substantial increase in

Computational Time. By Progressively Refining The

computational grid and comparing key solution variables, it is possible to determine the point at which additional refinement produces negligible changes in the results.

The automatic grid generation feature of the software was used to generate the unstructured hexahedral mesh. Five different meshes were generated, and variables such as ACU return air temperature, cabinet inlet and outlet temperatures, and room temperature were monitored for each mesh size. The mesh containing 7,288,454 cells was

Found To Be Optimal, As Further Refinement Caused

negligible variation in the selected variable values, and was thus chosen for analysis. This method ensures the accuracy and reliability of the simulation results while avoiding unnecessary computational cost.

The essential components of the data hall (such as ACUs, PDUs, IT Cabinets etc.) can be added either from the software’s built-in library or through a neutral data format. This approach ensures the accuracy of simulation, as the mesh independence study of these components is already validated. Achieving grid independence alone does not guarantee simulation accuracy. The correctness of boundary conditions and the choice of turbulence model also significantly affect the simulation results.

Ata Center Hall

A data hall layout with non-raised floor configuration and HAC strategy as shown in Figure 1, 2 and 3 is used for the CFD analysis. The data hall measures approximately 41 m in length and 20 m in width, with a total floor area of 810 m. The floor to ceiling height is 5.7 m. The number of IT Cabinet are 308 and the corresponding total IT load is 1920 kW (6.23 kW per cabinet). Each cabinet has a height of 2.4 m and a footprint of 0.6 m×1.2 m.

The cabinets are organized into 14 rows in face-to-face and back-to-back configurations, with the back sides of the cabinets facing each other to form HAC of varying sizes.

Data hall layout is with caging. The cages are used to create enclosed areas within the data hall which provides an additional layer of security for IT cabinets in a colocation data center. The doors are provided in the containment to allow access to the rear of the cabinets.

There are 11 ACUs separated by partition walls and 28 power distribution units (PDUs) which are located inside the data hall.

Fd Model Of The Data Hall With It Cabinets

The 3D view of the data hall CFD model is shown in Figure 1. The data hall consists of ACUs, PDUs, IT cabinets, cages, hot aisle enclosure, power cables, data cables, lighting, structural beam, structural column, partition walls, walls, temperature and pressure sensors etc. as shown in Figure 2 and 3.

The CFD model of the data hall was fully constructed using the tools and options available in the software ‘DataCenterDesignPro’, with the CAD layout used as a reference. This CAD layout of the data hall was imported into the software to guide the modeling process, ensuring that the virtual representation accurately reflected the physical layout and arrangement of the data hall.

The ACU is custom built based on the manufacturer's specifications and all other important elements such as PDUs, IT Cabinets etc. are imported from software’s built- in library. The other details such as power cables and data cables are included in the model as flow obstructions.

Figure 2: Plan View Of Data Hall Cfd Model

Figure 3: Plan view of data hall CFD model with sensor locations 3.1.1.

N Data Hall Cfd Simulations, Accurately Defining

material properties is essential because these parameters directly influence heat transfer, and overall thermal performance.

Thermal

conductivities, densities, and heat capacities respond differently to temperature loads, affecting how heat is absorbed, stored, and dissipated within the space. Since data halls contain diverse architectural and equipment surfaces that interact with cooling systems, neglecting realistic material properties can lead to significant

Deviations Between Simulated And Actual Thermal

conditions. Therefore, incorporating correct material characteristics ensures more reliable predictions of temperature distribution, airflow patterns, and cooling

Thermal

management and design optimization. The walls of the data hall are constructed from cement mortar. The HAC, partition wall and panels are fabricated from polycarbonate. The column, floor and ceiling are composed of concrete. The IT cabinets, ACUs and I-beam are made of mild steel. The key material properties include density, thermal conductivity and specific heat capacity and are listed in Table 1.

The Temperature And Pressure Sensors Are Used To

monitor and control the conditions of the data hall. The aim is to ensure not only the sufficient air flow is provided for each IT cabinet but also efficiently cooling them without wastage of energy. The control strategy is developed in such a way that an efficient operation of data hall is achieved while ensuring all SLA temperature requirement are also being met.

The SLA sensors are placed at 0.9m & 1.5m off floor and 0.3m away from IT cabinet air intake side. The top- level sensors are placed at 2.4m off floor level (IT cabinet top level) and 0.3m away from IT cabinet air intake side.

The pressure sensors are placed at the far end of each cabinet row. One pressure sensor is placed in the room while another is placed in hot aisle to measure the pressure differential across the IT cabinet. The room temperature sensors are placed in cages to measure room temperature.

One on-coil temperature sensor is placed in front and one off-coil temperature sensor is placed behind each heat exchanger of an ACU. In this case, on-coil temperature is defined as the temperature of hot return air from the conditioned space of data hall (after passing over IT

Cabinet And Removing Heat Thereby Cooling It) And

entering the heat exchanger (cooling coil) of an ACU. The off-coil temperature is defined as the temperature of air leaving the heat exchanger of an ACU after getting cooled to the design value by exchanging heat with chilled water supplied by the chillers.

The Acus Supply Cold Air At The Design Supply

temperature and it fills the data hall room. The cold air then passes through the IT cabinets and takes away heat generated by them. The hot air then gets collected in hot aisle enclosure. The hot return air from IT cabinets then

Authors:

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

94143, Usa.

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

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

14Jlvmi Consulting Llc, Dousman, Wi, Usa

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

Abstract

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

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

Introduction

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

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

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

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

●

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

●

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

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

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

Hyperpolarized 13C-Pyruvate Preparation

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

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

General Considerations

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

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

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

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

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

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

Personnel

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

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

Equipment And Facility

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

Material Handling

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

Pharmacy Kit Filling And Assembling

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

Quality Control And Dose Release

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

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

The Final Dose Release And Injection

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

Some Key Challenges

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

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

Current Practices

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

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

In House

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

Summary

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

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

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

Mri System Setup And Calibrations

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

Imaging System

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

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

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

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

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

Rf Coils

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

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

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

Provide B1 Transmit Across The Fov (B1

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

B1

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

+ Profile But Has Been Used Because Of

relatively easy integration into the scanner bore. B1

+ Variation Results In Variations In The Flip

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

Homogeneous B1

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

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

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

(1)

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

Tx = Transmit

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

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

Phantoms

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

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

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

+) And Receive (B1

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

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

Prescan Calibration

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

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

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

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

+ Inhomogeneity As Well

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

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

Power [Kw]

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

8

13C-bicarbonate doped with dimethyl silicone, various

Power [Kw]

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

Maximum Values

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

Summary

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

+ Profiles. The

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

For Calibration Of B1

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

Acquisition And Reconstruction

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

+ Inhomogeneity,

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

Acquisition And Reconstruction Methods

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

Mrs/I Methods Specifically

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

Chemical Shift

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

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

Their Application To Different

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

The Majority Of

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

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

Prostate Studies

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

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

Heart Studies

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

Brain Studies

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

Abdomen And Breast Studies

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

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

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

1H Imaging

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

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

Reported Study Parameters

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

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

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

(B)

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

Summary

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

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

Data Analysis And Quantification

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

Metrics

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

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

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

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

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

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

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

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

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

Visualization

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

Metrics

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

Parameter Encoding

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

Anatomical Context

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

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