Swiftcomp Solid Model Composite

Detector With Horizontal Muons

Y. Abreu𝑏Y. Amhis𝑗L. Arnold𝑐G. BarberℎW. Beaumont𝑏S. Binet𝑎I. Bolognino𝑝M. Bongrand𝑗J. BorgℎD. Boursette𝑗V. Buridon𝑒B. C. Castle𝑘H. Chanal𝑎K. Clark𝑐B. Coupé𝑙P. Crochet𝑎D. Cussans𝑐J. D’Hondt𝑑D. Durand𝑒T. Durkin𝑚M. Fallot𝑖D.

Galbinski𝑒S. Gallego𝑜L. Ghys𝑙L. Giot𝑖K. GravesℎB. Guillon𝑒S. Hayashida𝑞D. Henaff𝑖 B. HosseiniℎS. Jenzer𝑗S. Kalcheva𝑙L.N. Kalousis𝑑R. Keloth𝑑L. Koch𝑘,𝑜M. Labare𝑔G. Lehaut𝑒S. Manley𝑐L. Manzanillas𝑗J. Mermans𝑙I. Michiels𝑔S. Monteil𝑎C. Moortgat𝑔,𝑙 D. Newbold𝑐,𝑚V. Pestel𝑒K. Petridis𝑐I. Piñera𝑏L. Popescu𝑙A. De Roeck𝑏, 𝑓N. Roy𝑗D.

Ryckbosch𝑔N. Ryder𝑘D. Saunders𝑐M.-H. Schune𝑗M. Settimo𝑖H. Rejeb Sfar𝑏L. Simard 𝑗,𝑛A. Vacheret𝑒G. Vandierendonck𝑔S. Van Dyck𝑙P. Van Mulders𝑑N. van Remortel𝑏S. Vercaemer𝑏,𝑑M. Verstraeten𝑟B. Viaud𝑖A. Weber𝑠,𝑜M. Yeresko𝑎F. Yermia𝑖 𝑎Université Clermont Auvergne, CNRS/IN2P3, LPCA, Clermont-Ferrand, France

𝑑vrije Universiteit Brussel, Brussel, Belgium

𝑒Normandie Univ, ENSICAEN, UNICAEN, CNRS/IN2P3, LPC Caen, Caen, France

𝑔universiteit Gent, Gent, Belgium

𝑖SUBATECH, Nantes Université, IMT Atlantique, CNRS/IN2P3, Nantes, France 𝑗IJCLab, Univ Paris-Sud, CNRS/IN2P3, Université Paris-Saclay, Orsay, France 𝑙SCK-CEN, Belgian Nuclear Research Centre, Mol, Belgium

𝑛institut Universitaire De France, Paris, France

𝑜Johannes Gutenberg-Universität Mainz, Mainz, Germany arXiv:2507.05180v4 [physics.ins-det] 22 Oct 2025 Abstract: SoLid is a neutrino experiment at very-short baseline searching for active-to-sterile oscillations of reactor antineutrinos. The detection principle is based on the pairing of two types of solid scintillators: polyvinyl toluene and 6Li:ZnS(Ag), which is a new technology used in this field of Physics. In addition to good neutron-gamma discrimination, this setup allows the detector to be highly segmented; the basic detection unit is a 5 cm cube. High segmentation provides numerous advantages including precise localisation of the Inverse Beta Decay (IBD) products, the derivation of an antineutrino energy estimator based on the isolated positron energy, and a powerful background reduction tool that relies on the topological signature of the signal. Finally, the system is read out by a network of wavelength-shifting fibres coupled to photosensors. A relative electromagnetic calibration is performed with horizontal cosmic muons. This source poses the simplest calibration problem in which a single detection unit is involved. In addition, large muon energy deposits allow us to perform a calibration at the most detailed level (i.e. per fibre) and to accurately define the fraction of energy escaping to neighbouring detection cells. A statistical precision at the sub-percent level is reached. The paper also discusses two methods to calibrate the absolute energy scale and presents their implementation and results. The first method relies on horizontal muons, though the precision is limited to around 10% because of the uncertainty in the energy distribution of such muons. A novel, alternative method based on the radioactive americium- beryllium source is proposed. It takes advantage of the electron-positron pair-production process and provides a calibration point at 3.4 MeV (i.e. in the core of the IBD positron spectrum). The paper is concluded with various cross-check including a determination of the energy spectrum of the standard cosmogenic background candle: 12B.

Keywords: Only keywords from JINST’s keywords list please

Absolute Calibration With The Horizontal Muons

Absolute calibration with the americium-beryllium source

Ntroduction

The SoLid (Search for Oscillations with a Lithium-6 Detector) experiment is located in the vicinity of the Belgian Reactor 2 (BR2) research reactor at the SCK CEN site in Mol, Belgium. The experiment aims to make a precise measurement of the reactor antineutrino flux at a very short baseline (6.3 - 8.9 m) to search for oscillations of neutrinos to a sterile state. The second goal is to study the 235U energy spectrum with regard to the “5 MeV bump” . The first measurement provides information on the so-called Reactor Antineutrino Anomaly (RAA) and the Gallium anomaly . In particular, it is possible to constrain the 3 + 1 model , which assumes the existence of an additional light sterile neutrino state. The SoLid experiment was designed to probe the best-fit region of the oscillation parameters with sin2(2𝜃𝑠) ≈0.1 and Δm2

𝑠≈1 Ev2. The Description Of The

design of the SoLid detector is beyond the scope of this article. The interested reader can consult the detailed discussion reported in Ref. . The following paragraph contains the executive summary required for the description of the calibration procedure.

The basic detection unit of the detector is a 5 cm side PolyVinyl Toluene (PVT) cube. PVT is a cheap plastic scintillator with a linear response over a wide range of energy. Each cube has two

– 1 –

neutron detection screens (microcomposite 6LiF:ZnS(Ag)) placed on adjacent faces. The detection units are combined into planes of 16 × 16 units each.

Each Cube Is Individually Wrapped In

Tyvek to prevent scintillation light from escaping. Furthermore, each plane is surrounded by two square Tyvek sheets, which optically decouple the planes by further preventing the passage of light between them [5, 6]. The latter is a very important feature for both calibration and reconstruction, since it simplifies the problem from 3D to 2D. Ten planes make up a module, and the detector comprises five modules in total. The scintillation light from the PVT cube is collected by two vertical and two horizontal WaveLength-Shifting (WLS) fibres that pass through each detection cell. One side of each WLS fibre is covered with a Mylar foil that acts as a mirror to reflect the incoming light. The second side is coupled with Multi-Pixel Photon Counters (MPPCs) that read out the light. The digitised version of the readout is the initial input received from the detector.

Figure 1 shows the schematic view of the SoLid detection unit and the detection plane. The origin of the coordinate system corresponds to the position of the reactor core. The 𝑥−𝑦coordinates are defined by the orientation of the detector planes, with 𝑥being the horizontal direction and 𝑦the vertical, respectively. The 𝑧axis is perpendicular to the detector planes.

Figure 1. A sketch of the SoLid basic detection unit (left) and detector plane (right). The SoLid detector uses the Inverse Beta Decay (IBD) process (¯𝜈𝑒+ 𝑝→𝑛+ 𝑒+) to detect antineutrinos. The necessary simultaneous detection of the neutron and positron signals justifies the use of two scintillators: neutron detection screens featuring 6LiF:ZnS(Ag) and PVT. On average, the IBD neutron receives a kinetic energy of 50 keV, which is much larger than the thermal neutron energy (25 meV). Thus, the neutron is first thermalised via elastic collisions with the nuclei in the PVT. After thermalisation, it is captured on the 6Li, which has a very large thermal neutron cross section of 936 b (compared to 0.3 b for hydrogen and 0.5 mb for carbon). The atom breaks into tritium and 𝛼particles, generating scintillation photons in the ZnS(Ag) crystals present in the detection screens. The PVT acts not only as a neutron moderator but also as a proton-enriched target

– 2 –

This light is subsequently captured by WLS fibres and read out by MPPCs. The high granularity of the detector allows the ionisation and annihilation gamma contributions from the positron to be distinguished. Hence, the antineutrino energy is defined from the IBD process as follows:

(1.1)

where 𝑚𝑝and 𝑚𝑛denote the masses of the scattered proton and the outgoing neutron, respectively, and 𝐸𝑖with 𝑖∈𝑒+, 𝑛, ¯𝜈denotes the kinetic energies of the corresponding particles. Neglecting 𝐸𝑛in the second equation is justified, since the neutron kinetic energies do not exceed 50 keV, much lower than the O(3) MeV antineutrino energy. Therefore, the antineutrino energy estimator relies on the measurement of the actual energy deposited by the positron, in contrast to the total prompt energy of the event in the case of liquid scintillators. The size of the cube in the SoLid geometry corresponds to the maximum path length of a 10 MeV positron. According to Geant4 (version 10.6.0) studies, the positron, in fact, deposits its energy in a single cube in 80% of events. Furthermore, the cube in which the annihilation occurred (Annihilation Cube or AC) is the most energetic cube of the event when the positron energy is above 1 MeV. Thus, an accurate reconstruction of the AC and an accurate calibration of its energy are key to a precise measurement of the antineutrino spectrum; which in turn is of the utmost importance for both oscillation analysis and the “5 MeV bump” exploration.

Figure 2. A sketch of the energy deposit (pink cube) in the SoLid detector plane with fired horizontal (red) and vertical (blue) fibres and impacted (pink and light pink) MPPC. However, the detector does not directly deliver the positron energy information at the cube level. The starting point for any analysis is the digitised readout from the MPPCs. Therefore, signal candidates must be defined from this input. More precisely, the MPPC response must be transformed back into the list of detection cubes involved in the event. This list of cubes contains the energy deposits from the annihilation gamma and positron if the mean path length of the

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annihilation gamma is enough to escape the AC. In addition to verifying the energy estimator suggested in Equation (1.1), the reconstructed annihilation gamma clusters also provide a very powerful background rejection tool. Figure 2 sketches the basics of the reconstruction problem. If there is an energy deposit 𝐸𝑗, then the WLS fibres act as linear projectors to transfer light to the MPPC. As mentioned above, the planes are optically decoupled; hence, the reconstruction problem can be posed for each plane individually. We postulate 𝑓𝑖𝑗as the projector from cube j to MPPC i (generally speaking, 𝑓𝑖𝑗represents the fraction of light generated in the given cube received by an individual fibre). The definition of 𝑓𝑖𝑗involves the absolute energy scale and the MPPC gain. It is discussed in more detail in Section 4. The readout value for this particular MPPC is calculated as

(1.2)

where 𝑝𝑖corresponds to one of the 64 readout projection values (twice the sum of the number of cubes in rows and columns) and 256 corresponds to the number of cubes in the plane. A similar equation can be written for each individual MPPC. Afterwards, the system of 64 equations can be

(1.3)

where p is the column vector of the readout projections. E is a column vector of unknown energy deposits that are determined by the reconstruction procedure. Finally, 𝐴64×256 is called the system matrix and embodies the best of our knowledge about the detector behaviour at each stage, from light generation to digitisation. Finally, it must be complemented with the absolute energy scale to transform the energy of the cubes from the Analogue-to-Digital Converter units (ADCs) to the physics units (MeV). The description of the methods for solving Equation (1.3) is beyond the scope of this article. The tools available on the market, together with the baseline choice made for the SoLid experiment, known as the CCube algorithm, are exhaustively discussed in Ref. . The equation is solved under the assumption that the system matrix is determined elsewhere. The derivation of this matrix and the determination of the absolute energy scale are the subject of this article.

Osmic Muons As The Calibration Source

The projector values 𝑓𝑖𝑗in Equation (1.2) are not constrained a priori. Their initial features are obtained from a simplified optical simulation. The simulation is performed with the GODDeSS extension framework for Geant4. It consists of one row of 16 identical PVT cubes without neutron detection screens, but wrapped in reflective Tyvek paper. Both horizontal and vertical WLS fibres are paired with MPPCs, which read out the number of arriving scintillation photons. A single muon is generated such that it crosses the central cube of the system. The setup is sketched in Figure 3.

First, the simulation shows that the scintillation light is not contained within a single cube. A significant fraction of the photons (∼10%) are propagated to the neighbouring cubes, in particular through the holes created by the WLS positioning tolerances. This effect will be referred to as

– 4 –

Figure 3. An optical simulation setup with a single muon track launched through the central cube. Light Leaks (LL) in the following. The fraction of photons that end up two cubes away from the crossed cube is at a subpercent level, and thus neglected. Therefore, each energy deposit has only 12 non-zero projector values associated with it. Four of them are related to the fibres in the main cube, where the energy deposit has occurred, and another eight are related to the four neighbouring cubes (2 on the horizontal axis and 2 on the vertical) created by the LL. Secondly, the simulation reveals asymmetries in light sharing between the fibres. These asymmetries are observed between the horizontal and vertical fibres. Moreover, the amount of light shared between the two horizontal (vertical) fibres that cross the same cube is not equivalent either. Thus, a per-fibre determination of the System Matrix elements, i.e. calibration, is desirable. The final stage of the simplified optical simulation scrutiny is related to the impact of the WLS groove size. The width of the groove is 5 mm, while the diameter of the fibre is 3 mm. In the modified version of the simulation, the width of the groove is changed to match the size of the WLS fibre, so that there is no air gap between the two. This modification demonstrated a drastic change in the distributions of scintillating light, which, in turn, indicates miscalibrations due to the actual geometry of the detector. This effect also varies from cube to cube. Other effects such as temperature or the detector displacements triggered by the movement of the calibration sources can also influence the detector response. The modelling of the miscalibrations cannot therefore rely solely on physics assumptions such as attenuation length or coupling effect. Since all detection units are identical in the Geant4 simulation, the modelling cannot rely on it either. There are two ways to address this problem: develop a much more detailed simulation or alternatively use the data directly.

In summary, the optical simulation shows that the calibration in the SoLid experiment must be performed on the per-fibre level. In addition, the calibration source must provide a way to determine the LL. Accurate measurement of light-sharing features contributes to a precise reconstruction of the positions of the cubes and their energies. Events can therefore be categorised on the basis of their topological characteristics. These calibration requirements are further complemented by the

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fact that the detector is a dynamic system; e.g. the PVT is exposed to ageing, which decreases the number of generated photons and therefore modifies the energy response during data taking. As such, the calibration procedure must be performed regularly, with a frequency defined by the precision of the method. This in turn provides the third requirement: the precision of the approach has to be at the percent level, which requires enough statistics for all the fibres. Finally, let us return to Equation (1.2). In the case of the unique energy deposit 𝐸𝑗, for the projection 𝑝𝑖, the equation

(2.1)

where 𝑝𝑖is the direct output of the detector. Hence, if the total energy deposited in the plane is known, the projector value 𝑓𝑖𝑗is the only unknown. Therefore, in such a case, all 12 projector values associated with the cube, where the energy deposit occurs, can be measured directly. Cosmic muons can meet all the requirements listed above. On average, muons deposit 1.6 MeV/cm (which translates to 8 MeV for the SoLid detection unit size of 5 cm). As such, it is possible to accurately measure both the light-sharing properties within the main cube traversed by a muon and in the neighbouring cubes impacted by the LL. Furthermore, the muon track typically crosses several cubes in the detector. Thus, it is possible to use a single track to calibrate multiple cubes. However, to fit the condition of the single energy deposit in the plane, only a subset of the cosmic muon sample is considered for calibration purposes. It consists of parts of the muon tracks that are horizontal enough to cross only one cube in a plane.

Selection Of Horizontal Muons

Horizontal muon candidates are selected from both reactor-off (ROff) and reactor-on (ROn) samples. The selection itself is implemented in the SoLid Analysis Framework (Saffron2). The main objective of the tool is to cluster the waveforms recorded by detectors that are close in time and space. The waveforms within a cluster are divided into three mutually exclusive categories: muons, nuclear signals, and electromagnetic signals. The latter two are aimed at selecting the signals originating from the IBD neutron (nuclear) and positron together with annihilation gammas (electromagnetic), respectively. The exhaustive description of the Saffron2 software can be found in Ref. . As for muon clusters, they are searched for in the first place that satisfies a single requirement on the fibre read-out: the presence of high-energy channels with an amplitude greater than 200 ADC counts.

If the number of these channels is less than 11, the muon candidate is tagged as a Type 0 muon. In most cases, Type 0 muons correspond to the so-called clipping muons, which cross only a few cubes on the edge of the detector. In other cases, the muon candidate deposits energy in a larger number of cubes that most likely form a track. The latter assumption is checked with two weighted least-squares linear fits (vertical and horizontal projections).

The candidates are further divided into two categories according to the convergence of the fits: Type 1 if either one of the fits has failed; Type 2 if both fits were successful. The horizontal muons used for the calibration were selected exclusively from the Type 2 muon sample. It is important to mention that the fits are performed solely with the fibre-level information, i.e. the reconstruction algorithm is not involved in determining the positions of the cubes on the track. Therefore, one

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can simultaneously solve Equation (1.3) and determine the System Matrix.

Several Additional

requirements are applied to Type 2 muons to increase the quality of the sample and ensure that there is indeed a single cube hit in the plane. First, the start and end cubes of the track have to be on the detector border. This requirement allows muons that are captured while crossing the detector (stopping muons) and as such have different stopping power to be rejected. Second, the muon track length must be greater than or equal to 7 cubes. This rejects candidates that are likely excited nuclei.

Third, the slopes 𝑥/𝑧and 𝑦/𝑧must provide cos 𝜃less than 0.8, where 𝜃is the polar angle of the muon track (approximately 40◦). The development of muon selection is discussed in Ref. . An example of a Type 2 muon track that meets all the listed conditions is shown in Figure 4.

However, not all cubes along this track are used in the calibration procedure. To select the planes in which the muon has indeed deposited its energy in a single detection unit, the cube is kept if and only if the reconstructed track enters and exits the cube through a fiducial window. This window is shown in pink in Figure 5 and represents the area which is at least 10% (of the cube size) away from each border. It lifts the ambiguity of a choice of the cube of interest when the track passes close to the border. The set of such cubes from the dedicated muon tracks is referred to as horizontal muons in the following.

Figure 4. An example of the horizontal muon track obtained from ROff data. There are 4 fibres traversing each SoLid cube. If there is an energy deposit in the cube, each fibre should receive a fraction of the scintillating photons. However, there are several scenarios for which this is not the case. The first one appears when the energy contribution is not enough for the

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Figure 5. The entrance and exit windows (shown in pink), that the reconstructed muon track must follow. fibre photons to meet the threshold level; since muons typically deposit large amounts of energy on average, this is not the main case. Another appears when one or more fibres are dead, i.e. that the fibre does not transport the photons to the MPPC. About 1% of the fibres are permanently dead (most of these dysfunctional fibres are concentrated in Module 5. This module is the farthest from the reactor core, and hence receives the least statistics), or temporarily in dysfunction.

Figure 6. The time evolution of the number of cubes reconstructed with different number of fibres within a run of ROff data. The total number of cubes (blue) is shared among 4 (red), 3 (purple) and 2 (green) fibres. The second scenario occurs if a fibre receives too many scintillating photons (e.g. stopping muons) to the extent that it exceeds the processing capacity of the electronics.

According To

ROff studies, a single channel saturates at 15700 ADC counts. When a channel saturates, the corresponding event buffer is required to be reset in order to transmit again normally the read-out information. This reset occurs only at the beginning of a new physics run that lasts 8 minutes.

Therefore, a saturated fibre remains dead until the end of the current run. The time evolution of the number of candidates reconstructed with different numbers of fibres is presented in Figure 6. The sample unit of the 𝑥-axis corresponds to 25 ns. Hence, the figure represents a single physics run of

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8 minutes. As a side note, the dying fibre effect also impacts Equation (1.3). If the fibre dies during the run, the corresponding projector values a𝑖𝑗are switched to zero and restored with the fibre at the beginning of the next run.

Relative Calibration

As discussed in Section 2, a sample of horizontal muons is considered to obtain the system matrix elements that define a cell-by-cell calibration. For each fibre, projection 𝑝𝑖is calculated by multiplying projector 𝑓𝑖𝑗by the energy deposit made in the cube 𝐸𝑗. The definition of 𝑓𝑖𝑗involves the multiplication of three factors: the MPPC gain (𝑔𝑖), the absolute energy scale (𝛽𝑗, which shows the number of photoavalanches generated per unit of energy) and the fraction of light received by the fibre (𝑎𝑖𝑗). The result of the multiplication of 𝐸𝑗by 𝛽𝑗is the total number of scintillation photons (denoted as 𝑛plane) in the given cube, which matches the number of photons in the given plane (since, by construction, horizontal muons hit a unique cube in the plane). The gain for the entire SoLid detector was equalised at the beginning of each data-taking period . As discussed in Section 5, the absolute scale factors are homogenised for all detection cells. Therefore, it is equivalent (up to a scaling factor) to fill the system matrix with the values of 𝑓𝑖𝑗or 𝑎𝑖𝑗. We arbitrarily chose the latter.

N Summary, The Projection 𝑝𝑖is Defined As:

𝑝𝑖= 𝐸𝑗· 𝑓𝑖𝑗= 𝐸𝑗· 𝛽𝑗· 𝑎𝑖𝑗· 𝑔𝑖= 𝑛plane · 𝑎𝑖𝑗· 𝑔𝑖= 𝑛𝑖· 𝑔𝑖= 𝑛𝑖· 𝑔,

(4.1)

where 𝑛𝑖represents the number of scintillating photons reaching the MPPC 𝑖. The sum of all projections 𝑝𝑖in the given plane (denoted as 𝑝plane) is the only missing piece to compute 𝑎𝑖𝑗. It is

(4.3)

This formula is equivalent for all fibres (shown in Figure 7) of the main cube that is traversed by the muon track, and of the neighbouring cubes that are affected by LL. This formula provides a single value for the projector 𝑎𝑖𝑗of a single muon. Once all muons crossing a cube are considered, the distribution of the projector values is obtained. The value 𝑎𝑖𝑗that goes into the System Matrix is determined from a fit of a Landau model to the distribution. A transformation that deals with the outliers and ensures a Gaussian behaviour of the distribution is applied, and is described in the next section.

Kl Divergence

The left panel of Figure 8 shows the raw distribution of the 𝑎𝑖𝑗values for one of the fibres in the adjacent cube (due to LL). A fit to this distribution with a Landau function would allow us to determine the 𝑎𝑖𝑗values. However, the presence of outliers compromises the goodness of fit. There are multiple approaches to address outliers, and the Kullback–Leibler (KL) divergence method

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Figure 7. The calibration problem posed by horizontal muon. Scintillation light shared between the hit cube (in pink) with fibre projectors p𝑖and the cubes affected by the LL (light pink) with projectors p 𝑗. is one of them. The KL divergence method is a type of statistical distance (or dissimilarity test), which quantifies how much a probability distribution 𝑝1 is different from a reference probability distribution 𝑝2. In the case of the SoLid experiment, both distributions must obey the Poisson law; hence, the KL divergence, slightly modified with respect to Ref. , is given by:

(4.4)

This class of equations is solved with a Lambert function 𝑊. This is a multivalued function with different branches. In our implementation, 𝜆1 is either 22.5% (main cube with four fibres) or 1.25% (adjacent cubes, 8 fibres). The parameter 𝑚is the mean of a Gaussian model fit to the initial distribution of 𝑥. Equation (4.4) is solved for 𝜆2 (mean value of the measured distribution)

(4.5)

As a result, it is not the distribution of 𝑎𝑖𝑗values that is fit. Instead, we fit the statistical distance for each set of projector values from the Poisson law. The outliers in the transformed distribution are much more pronounced and can be straightforwardly excluded from the fit. The result of the application of the KL divergence method is shown in Figure 8. As such, the total sum of the light-sharing fractions from the four fibres of the main cube and the eight fibres of the adjacent cubes improves from 96% to 99%.

Homogenisation Of The Response

The second stage of the relative calibration is the homogenisation of the response from individual cubes. The characteristics of the detection units (namely the absolute energy scale 𝛽𝑗) differ, causing a variation in the response of the detector. The energy loss of the muon serves as a calibration reference. The sum of the projections of the 12 fibres involved within the plane is considered as the

– 10 –

Figure 8. The distributions of the light fraction observed by one of the fibres in the neighbouring cubes (triggered by LL) before (left) and after (right) application of the KL divergence method. representation of the energy deposit made by the muon while crossing it (as in the variable 𝑝plane from Equation (4.2)). In addition, all muon candidates are selected from Type 2 muons, for which there is a successfully reconstructed track. The path length of the muon within a certain plane is determined from this track information and is further denoted as 𝑥track. Thus, the energy loss is

(4.6)

Figure 9. The energy loss distribution before(left) and after (right) application of the 4 active fibre cut. The energy loss distribution for a given cube is obtained by applying Equation (4.6) to the subset of muons that cross it. A muon is rejected if the cube is not reconstructed with 4 fibres (except for the cases where the fibre is permanently dead). This additional selection compensates for the dying fibre effect presented in Section 3. The result of the selection is shown in Figure 9. A Landau function convoluted with a Gaussian is fit to the resulting energy loss distribution. The model has

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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