Surface Vehicle Usv

F. Dettùa. S. Formentina And S. M. Savaresia

aDipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy.

Abstract

Vehicular control systems are required to be both extremely reliable and robust to different environmental conditions, e.g. load or tire-road friction. In this paper, we extend a new paradigm for state estimation, called Twin-in-the-Loop filtering (TiL-F), to the estimation of the unknown parameters describing the vehicle oper- ating conditions. In such an approach, a digital-twin of the vehicle (usually already available to the car manufacturer) is employed on-board as a plant replica within a closed-loop scheme, and the observer gains are tuned purely from experimental data. The proposed approach is validated against experimental data, showing to significantly outperform the state-of-the-art solutions.

Parameter estimation; state estimation; driving simulator; sensors; signal processing.

Ntroduction

The Twin-in-the-Loop (TiL) framework has been recently proposed for vehicle dynam- ics control and estimation of unknown states and variables . In this innovative framework, an high-fidelity off-the-shelf vehicle dynamics simulator is employed in a control/estimation loop - thanks to the recent developments in on-board hardware plat- forms 1. Being the simulator a commercial product, we assume it to be a black-box, i.e. we can only extract its outputs given some inputs, but we are not able to access its equations and update rules directly. With regards to the TiL estimator, the authors in showed how the presented algorithm is able to estimate both unmeasured states (e.g. vehicle sideslip) and other unknown variables, such as the tire-road forces. How- ever, they did not address the estimation of time-varying parameters; in fact, modern vehicle dynamics controllers are strongly based on time-domain models of the process . Due to the variability of conditions during the daily use of a vehicle - e.g.

the most common case being the payload - such controllers can underperform, or even destabilize the system, if such variations are not properly addressed. Hence, following a well established research trend on vehicle state and parameters estimation, we build 1For example, https://www.vi-grade.com/en/products/autohawk/.

Related works. Existing literature solutions for four-wheeled vehicles on-line pa- rameter estimation can be broadly split among direct sensing and software sensing ones. In the first class of solutions, a sensor for the measurement of the variable of interest is used (e.g. , where the mass is estimated via strain gauges on the suspensions).

The second class of solutions features instead the estimation of unmeasurable variables via production available sensors (i.e. without adding new piece of hardware). If we focus on software sensing algorithms, we find many solutions in the literature - where we cite here the most relevant contributions in the past years - , which can be categorized according to four axes: estimated quantities, employed sen- sors, used estimation algorithm, and employed model. Other important contributions design software sensing with an highly specific goal, like rollover risk evaluation : we do not consider them in this review.

On the estimated quantities side, the mass M is indeed the most important vehicle parameter, and is always considered in the cited works; vehicle yaw inertia Jzz is then considered in , while roll and pitch inertia Jxx, Jyy are considered in . Other estimated parameters include longitudinal , lateral or vertical center-of-mass position variation. The tire-road friction coefficient is estimated in - however, this parameter is different in nature from the other considered in the literature, as its variations are not imputable to a variation of the vehicle load conditions, but rather to the terrain.

With regards to the sensing layout, one common denominator is the use of classical production vehicle sensors, like gyroscopes or Inertial Measurement Units (IMU); yaw rate, which is a gyroscope output, is employed in all the cited articles but . Ac- celeration information is used in all references; use three acceleration sensors, to be placed above the unsprung masses. Other considered sensors include wheel angu- lar speed , suspension displacement , GPS position measurements and vehicle longitudinal speed .

Moving further to the considered estimation algorithm, most works are based on Kalman Filtering (KF) , specifically declined - except for - in its Dual formulation; Dual KF is based on two separated observers, one devoted to classical state filtering, and the other one solely devoted to parameter estimation, to be switched-offonce a good estimate of said parameters has been reached. propose a similar formulation, where the correction law is computed via a particle filter. On the other hand, propose a different approach, based on the use of free decay responses of the vehicle - more similar to a classic identification algorithm rather than to a state observer.

Finally, when coming to employed plant replica, the simplest model is the single- track, which is however only used in , as it fails to capture most of vehicle dynamics non-linearities. The most common model is the double-track ; the latter can be enhanced with roll dynamics, as in , or wheel dynamics , depending on the estimation target or the available measurements. consider a full vehicle model - i.e. featuring also unsprung mass dynamics, roll and pitch dynamics. Finally, the most complex model is the one proposed in : the authors consider a multibody model - featuring 14 states.

Contributions. From the literature review, an important point emerges. As also pointed out in , classical vehicular state observers are based on simplified models of the variables to be estimated: an ad-hoc model for each variable is required, and each model has to be accurately calibrated. Given that approximately 75% of the time of a control system design project is devoted to modelling, as indicated in , the resulting procedure turns out to be cumbersome. Let this apart, consider that any estimator is based upon a set of hyperparameters controlling its behaviour - e.g.

the noise covariances in Kalman Filters. Generally speaking, the more complex an estimator is, the longer the hyperparameter selection is. Relying on simple correction laws is thus beneficial in the implementation phase.

In TiL framework we employ a single model - a digital twin - for each variable to be estimated: this solves the problem of designing ad-hoc models and of having many models running at run-time on the same estimation algorithm. The model calibration phase comes for free when using a digital twin, in the assumption that a car manu- facturer already has a library of simulators for their production vehicles. On the other hand, the correction algorithm complexity is now shifted to the model fidelity: the more faithful to the real system the model is, the less intense - and thus simple - the correction need to be. The authors in actually show as a linear and time-invariant correction law is sufficient to outperform the benchmark.

Matter-of-factly, the authors in consider an high-fidelity model of the plant as in TiL framework: however, being the considered model a white-box, the authors are able to directly compute the update rules via a Kalman Filter-like algorithm. This is not possible in TiL, as the underlying model is a black-box, and the correction law, although linear, has to be tuned via model-free approaches .

With respect to the research in , we extend the TiL framework to the estimation of varying parameters, providing insights on how the correction law has to be designed, and on the feasibility of the approach in terms of robustness to measurement noise and uncertainty.

The paper is structured as follows. In Section 2 we provide to the reader some preliminaries on the TiL estimator. Section 3 defines the problem of varying mass and moment of inertia, and its estimation. Then, in Section 4 we conduct an in-depth analysis of the parameters estimation problem by independently considering set of variables, providing sensitivity analyses to uncertainty and noise. Section 5 shows an application of the described and simulated framework on experimental data, while Section 6 concludes the manuscript with a few considerations.

Twin-In-The-Loop Observer Architecture

proposed an unified estimator for all the variables of interest in vehicle dynamics control. In such an architecture (see Fig. 1), the two main features are the following • The vehicle simulator, an high-fidelity plant replica, whose equations are a black- box.

• The closed-loop correction, based upon available measurements, perturbs the model in order to properly estimate unknown variables. The detailed architecture of the complete observer is given in Fig. 2. Generically speaking, the simulator states at time k are updated according to the following equa-

(1)

Figure 1. Twin-in-the-Loop estimation scheme. where f, g, h are unknown (possibly nonlinear) functions, y ∈Rny is the set of measurable outputs, x ∈Rnx is the set of internal states of the simulator, z ∈Rnz is a set of additional variables to be estimated and p is a set of constant parameters. We denote ˜νk an a-priori estimation for a certain variable νk: then closed-loop correction updates the a-priori estimates, and generates a-posteriori ones ˆνk - as in the widely known Kalman Filter formulation.

The authors in extend the state vector to estimate tire-road contact forces; more specifically, the additional variables z are estimated by correcting the nominal values

(2)

The artificial variable δˆzk is described by a fictitious constant dynamics equation δ˜zk+1 = δˆzk.

(3)

The latter assumption is widely used in case the parameters to be estimated are slowly varying. Overall, the set of states, including internal and extended ones, now reads

Δzt 

. At this point, the innovation term at step k, consisting in the mismatch among measured (yk) and a-priori estimated outputs (˜yk) is to be used to correct the state vector xaug. The innovation is mapped onto the states via a linear

(4)

However, we will show in the following that the linear formulation is inadequate for the estimation of certain parameters, e.g. the vehicle mass or inertia. Let us thus define a Figure 2. Twin-in-the-Loop complete estimation architecture, featuring correction of simulator states and augmented states.

(5)

where K ∈Rnx×ny maps the innovation onto the nominal states, and K (yk) ∈Rnz×ny maps the innovation onto the extended states. 3. A parameter estimation case study: the uncertain load setting Figure 3. Vehicle top view, considering differently added additional masses.

Among the physical parameters defining a vehicle, mass and inertia might signif- icantly change due to different load conditions, while being extremely important in estimating such parameters in a road vehicle via the TiL estimator architecture. Con- sider the 5-seats vehicle in Fig. 3. Such vehicle can be loaded with additional masses.

On the mathematical perspective, we assume each of the mi, i = 1, . . , M to be a point mass, characterized by a certain position pmi =

In The Refer-

ence frame defined by axes X, Y, Z - as displayed in Fig. 3. If we assume that the vehicle chassis can be modeled as a rigid body with its mass concentrated in a single point - a common assumption in vehicle dynamics - the center-of-mass of such system

(6)

whereas m0 denotes the original lumped mass of the chassis. Indeed, the center-of- mass including additional masses - CM = (dx, dy, dz) - is going to be different from the original one - CM0 = (d0,x, d0,y, d0,z). The new lumped mass is then simply defined

(7)

Consequently, the chassis moments and products of inertia change due to the mass variation and the re-defined center-of-mass . Considering the Huygens-Steiner the- orem , we obtain the new moments/products of inertia, defined with respect to CM; this is done starting from the ones defined in CM0 and taking into account the newly added masses. E.g., for the moments of inertia - Jxx, Jyy, Jzz - one has

(8)

whereas Jxx,0, Jyy,0, Jzz,0 represent the chassis nominal moment of inertia, and δ (x1, x2) = (x1 −x2)2. Also product of inertia variations - e.g. Jxy- can be quanti- fied analytically in a similar way; for the load conditions considered in the case study - realistic ones for road vehicles - we don’t have significant variations of these parameters.

Now, let us consider again scheme of Fig. 1: the high-fidelity digital twin is modelled with a set of nominal parameters, i.e. lumped mass, inertia, and center-of-mass loca- tion. The real vehicle is instead loaded with additional masses, and thus ”perturbed” from the nominal parameters set.

In , the authors design a closed-loop correction so as to force the simulator states to be identical to the ones of the real vehicle, regardless of the reasons leading to differences between the two instances of the vehicle. On the other hand, in the present work we shift the philosophy, trying to estimate also the exact differences among the two instances.

Table 1. Nominal Vehicle Mass, Inertia

and CM parameters. Additional load param.

Kg

Table 2. Additional load parameters. In this Section, we demonstrate the TiL methodology for the case study of Section 3. For a better assessment of the potentialities and limitations of the present method, we conduct a preliminary analysis in a controlled simulation environment. The nom- inal chassis parameters of the considered vehicle are given in Table 1. Said nominal parameters also include the presence of a driver (md in Fig. 3). The parameters are those of a generic sport utility vehicle, which is modeled in VI-CarRealTime (CRT) simulation environment . The nominal vehicle model is perturbed by adding masses according to the scheme of Fig. 3; the values of such loads are given in Table 2. For this new configuration, the center-of-mass, mass and inertia can be analytically com- puted according to what described in Section 3; the new values for the most relevant parameters are in Table 3.

We apply the TIL architecture to the problem herein, defining the complete extended Perturbed param.

+5.3 %

Table 3. Perturbed vehicle parameters.

(9)

where x is the set of VI-CarRealTime states, x ∈R. In this simulation analysis, only extended states - parameters - are going to be corrected, as we want to focus on the feasibility of parameters correction. Each extended state represents the deviation of said parameter from the nominal value provided by the simulator as an output. Joint state and parameter correction will be considered in an experimental case study in Section 5.

In order to reproduce a simulation environment the closer to a real scenario, we introduce measurement noise. The noise is introduced on the signals coming from an - simulated in CRT - inertial measurement unit (IMU) placed near the vehicle CM. The

(10)

where s is a signal coming from an IMU, and σs is the standard deviation of a suitable white noise. In the simulation case study, x-axis acceleration ax and x, y, z axes angular rates ωx,y,z are employed as measurements in the observer, hence, only these signals are perturbed with noise. When not specified, the snr is tuned to be ≈10: however, we also conduct sensitivity analyses to verify the impact of measurement noise onto the estimator.

When quantifying the observer performance, we consider as a metric the root mean square estimation error in the last w = 1 seconds of test, as the dynamics of the estimated parameters are rather slow, and considering larger windows would take into account transient effects.

(11)

Where Ns is the number of samples in an experiment, fs [Hz] is the sampling frequency, and ν is a suitable parameter or variable to be estimated, e.g. ν = δM. On the other hand, we also consider the percentage version of rmsw, in order to quantify the amount of error within the parameters values. This metric is defined as

(12)

Where ν0 is the nominal value of a variable to be estimated; e.g. in our case, the nominal value for δM is the difference among the perturbed value in Table 3 and the nominal value in Table 1.

In the following, we consider as acceptable a percentage rms smaller than the 10 % of a perturbated variable.

Enter-Of-Mass Position Identification

The CM position is perturbed from CM0 in the modified layout, as evident from Table 3. Most significant displacement occur along x and z axes, as y axis variation are mostly due to extremely unbalanced - on the left-right direction - loads, which are not common in road vehicles. Given that the digital twin computes the torque and force balances referring to the center-of-mass, a not exact knowledge of CM might be detrimental for estimating the other parameters.

Two Possible Ways Of Solving This Problem Exist:

• Insert the variables dx, dy, dz onto the augmented state vector xaug, and conse- quently correct the mismatch from the nominal values; • Identify in a traditional way - see e.g. - dx, dy, dz on-line via available data and simplified models.

In the present work, we decide to follow the second approach, as we want to concentrate onto the estimation of mass and inertia: hence, we assume correct knowledge of CM. However, we also perform sensitivity analyses to check the effect of a wrong CM onto the estimation performance: in general, we will show as for the considered load conditions, which are reasonable for a passenger car, the performance loss is negligible even in case of wrong CM estimation.

Ehicle Mass Estimation

(a) Mass estimation in an urban driving context. (b) Urban driving commands. Figure 4. Mass estimation in an urban driving like context, with noisy measurements.

Estimated mass for different initial conditions. Vehicle chassis mass can be estimated by suitably exciting the longitudinal dynamics. Consider the following simplified longitudinal dynamics balance for a road vehicle Mchassis · ax = Ftrac −Fbrake −Froll −Faero.

(13)

It is clear that, provided that roughly the same forces act on the vehicle, an increased mass yields a lower longitudinal acceleration. Hence, if the digital twin is characterized by a smaller mass than the real vehicle, a suitable correction can be based upon the difference between longitudinal accelerations. Indeed, if the terms on the right hand side of Eq. (13) are significantly different, we are not able to determine whether an

Table 4. Mass Estimation Performance In

different conditions. acceleration variation is due to a mass difference or rather to an error in modelling the brake system or the tire-road interaction. For this reason, in this simulation analysis the sole modelling difference among the two simulated instances of the vehicle lie in the mass perturbation. In Section 5 we will test the mass estimation on real data, where other modelling differences might exist.

(14)

Where Kax,δM is a suitable gain to be tuned and sgn (·) extracts the sign of the argu- ment. Note as K (yk) = Kax−δM · sgn(ax,k) in this context. The importance of the sign operator is easily understood with a simple example.

Consider a coasting down - deceleration due to inertia ax < 0 - event: if the vehicle has an higher mass than the simulator, it will coast down faster, thus (ax −˜ax) < 0. Correcting δM proportionally to (ax −˜ax), with the same sign, would lead to a decrement of the extended state: however, δM should instead increase to compensate for the greater mass on the vehicle. Thus, the introduction of the sign operator accounts for this issue, an introduces a necessary non-linearity in the correction law.

The considered experiment for the mass estimation is an urban driving one - see Fig. 4b: in said test, only the correction of Eq. (14) is applied. The results - in case of noisy data and correct center-of-mass - can be appreciated in Fig. 4a: the mass is correctly estimated even by starting from different initial condi- tions, and the estimate eventually converges to the correct value. Table 4 reports the estimation performance in different conditions: as one can notice, the mass estimate is highly robust both to measurement noise and to imperfect knowledge of the center-of- mass. In the worst case, rmsM = 0.68 %: since δM = 355 kg, the error is smaller than 3 kg.

Figure 5 compares the estimator performance for an snr growing from 5 to 20: we can conclude that for reasonable noise levels, the estimator performance does not drop below the 10%, which was originally set to be our limit.

Finally, note that δM converges to the real value even if we are not correcting δJxx, δJyy, δJzz: this highlights the good decoupling among the estimated variables, without the need for designing a separated model for each of them.

Yaw Inertia And Roll Inertia Estimation

(a) Correct center-of-mass estimation case. (b) Wrong center-of-mass estimation case. Figure 6. Roll and yaw inertia estimation by means of a swept steer experiment, with noisy measurements. The upper plot depicts the estimated parameters in case the center-of-mass is exactly known, while the lower one depicts them in case the CM is not exactly known.

Figure 8. Yaw Inertia Estimation With

varying noise levels. Roll and yaw inertia can be estimated by exciting lateral dynamics and left-to-right load transfer, which often come together, e.g. while negotiating a curve. A proper experiment to estimate both variables at the same time is a swept steer maneuver, at constant speed, from 0 to 4 Hz. The non-linear correction law to be applied onto δJxx and δJzz follows from what described in Section 4.2 for the mass ∆δJxx,kk = K ˙ωx−δJxx( ˙ωx,k −˜˙ωx,k) · sgn( ˙ωx,k), ∆δJzz,kk = K ˙ωz−δJxx( ˙ωz,k −˜˙ωz,k) · sgn( ˙ωz,k).

(15)

Where the angular accelerations ˙ω are employed - such signals are easily obtained from the angular rates via differentiation. Note that while estimating Jxx and Jzz, δM could have been already estimated as described before. Same goes for the center-of- mass. Figure 6a depicts the estimation results in case of noisy measurements, wrong mass estimate, and correct center-of-mass; only corrections in Eq. (15) are applied. The Table 5. Roll and yaw inertia estimation performance in different conditions.

Wrong Mass;

Wrong CM. estimates converge to the true value, even starting from different initial conditions. On the other hand, Fig. 6b depicts the estimation of the same variable, in case the nominal center-of-mass is kept within the digital twin: as expected, we note a steady-state error in the estimated inertia - mostly noticeable for Jzz.

Table 5 quantifies the estimation performance in different cases. One can notice as the error on Jxx is generally higher and grows faster as the uncertainty increases. This is easily explained as the nominal value and the variation of Jxx are much smaller than for the other inertia. Finally, Fig. 7 and Fig. 8 show the estimator performance when considering different noise levels on the employed measurements. As expected, Jxx estimation performance significantly drops, and is never within the 10% limit. On the other hand, Jzz estimation shows good performance up to snr ≈7.5, which is a reasonable bound for yaw acceleration noise.

Pitch Inertia Estimation

As done above, pitch inertia Jyy can be estimated by suitably exciting the corre- sponding dynamics. The most straightforward way of exciting pitch dynamics is the excitation of the vehicle body with a non-zero road profile: hence, we assume that the vehicle is being driven at constant speed on a paved road. The road profile at front

(16)

Where σz = 0.01 m, and WN is the realization of a white noise. Consequently, the profile on the rear wheels is equal to zr(t) = zf(t−v/wb), with v the vehicle longitudinal speed, and wb the wheelbase.

The real vehicle, whose load is unknown and has to be estimated, is fed with the gen- erated road profile. The digital twin is then fed with the same road profile. In pratice, we are considering that the road profile at the current time is known; this information

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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