Aniform Double Diaphragm Forming

The Double Chooz Collaboration

H. de Kerret∗d, T. Abrah˜aoe, H. Almazano, J. C. dos Anjose, S. Appelv, J. Barrierek, I. Bekmana, T. J. Bezerrar, L. Bezrukovj, E. Blucherg, T. Brugi`ereq, C. Bucko, J. Busenitzb, A. Cabrera†1,d,aa, M. Cerradah, E. Chauveauf, P. Chimentie,†2, O. Corpacek, J. V. Dawsond, Z. Djurcicc, A. Etenkon, H. Furutas, I. Gil-Botellah, A. Givaudand, H. Gomezd, L. F. G. Gonzalezy, M. Goodmanc, T. Haram, J. Hasero, D. Hellwiga, A. Hourlierd,†3, M. Ishitsukat,†4, J. Jochumw, C. Jolletf, K. Kalef,q, M. Kanedat, M. Karakacd, T. Kawasakil, E. Kempy, D. Krynd, M. Kuzet, T. Lachenmaierw, C. E. Lanei, T. Lasserrek,d, C. Lastoriah, D. Lhuillierk, H. P. Lima Jre, M. Lindnero, J. M. L´opez-Casta˜noh, J. LoSeccop, B. Lubsandorzhievj, J. Maedau,m, C. Marianiz, J. Maricici,†5, J. Martinor, T. Matsubarau,†6, G. Mentionk, A. Meregagliaf, T. Miletici,†7, R. Milincici,†5, A. Minottik,†8, D. Navas-Nicol´ash, P. Novellah,†9, L. Oberauerv, M. Obolenskyd, A. Onillond,k, A. Oralbaevn, C. Palomaresh, I. Pepee, G. Pronostr,†10, J. Reichenbacherb,†11, B. Reinholdo,†5, S. Sch¨onertv, S. Schoppmanno, L. Scolak, R. Sharankovat, V. Sibillek,†3, V. Sinevj, M. Skorokhvatovn, P. Soldina, A. Stahla, I. Stancub, L. Stokesw, F. Suekanes,d, S. Sukhotinn, T. Sumiyoshiu, Y. Sunb,4, C. Veyssierek, B. Viaudr, M. Vivierk, S. Wagnerd,e, C. Wiebuscha, G. Yangc,†12, and F. Yermiar eCentro Brasileiro de Pesquisas F´ısicas, Rio de Janeiro, RJ, 22290-180, Brazil fCENBG, CNRS/IN2P3, Universit´e de Bordeaux, F-33175 Gradignan, France hCentro de Investigaciones Energ´eticas, Medioambientales y Tecnol´ogicas, CIEMAT, 28040, Madrid, Spain kIRFU, CEA, Universit´e Paris-Saclay, 91191 Gif-sur-Yvette, France oMax-Planck-Institut f¨ur Kernphysik, 69117 Heidelberg, Germany qIPHC, CNRS/IN2P3, Universit´e de Strasbourg, 67037 Strasbourg, France rSUBATECH, CNRS/IN2P3, Universit´e de Nantes, IMT-Atlantique, 44307 Nantes, France wKepler Center for Astro and Particle Physics, Universit¨at T¨ubingen, 72076 T¨ubingen, Germany yUniversidade Estadual de Campinas-UNICAMP, Campinas, SP, 13083-970, Brazil zCenter for Neutrino Physics, Virginia Tech, Blacksburg, Virginia 24061, USA

July 27, 2021

∗Deceased. † Laboratoire de l’Acc´el´erateur Lin´eaire (LAL), CNRS/IN2P3, F- 91405 Orsay, France, Universidade Estadual de Londrina, 86057- of Hawaii at Manoa, Honolulu, Hawaii 96822, USA, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki, Japan, side, PA 19038, Laboratoire d’Annecy-le-Vieux de physique des par- ticules (LAPP), CNRS/IN2P3 , 74940 Annecy-le-Vieux, France, In- stituto de F´ısica Corpuscular, IFIC (CSIC/UV), 46980 Paterna, Spain, versity of Tokyo, Kamioka, Gifu 506-1205, Japan, South Dakota School of Mines & Technology, 501 E. Saint Joseph St. Rapid City, SD Brook, NY, 11755, USA.

Neutrinos Were Assumed To Be Massless Particles

until the discovery of neutrino oscillation process.

Non-Zero Masses And The Mass Eigenstates (Ν1, Ν2,

ν3) are mixing of their flavour eigenstates (νe, νµ, ντ). The oscillations between different flavour eigen-

States Are Described By Three Mixing Angles (Θ12,

θ23, θ13), two differences of the square of neutrino

) And A Charge Conjugation

parity symmetry (CP) violating phase δCP.

Ouble Chooz (Dc) Experiment, Located Near The

Chooz Electricit´e de France reactors, France, mea- sures the oscillation parameter θ13 using reactor neu- trinos.

N This Paper, Dc Reports Its Latest Θ13 Re-

sult, sin2(2θ13) = 0.105 ± 0.014, exploiting its multi- detector configuration, iso-flux baseline, reactor-off

Sult Has Contributed To The Completion Of A Quest

of the neutrino oscillation studies lasting half a cen-

Date, Given By The Mean Cross Section Per Fission

⟨σf⟩= (5.71 ± 0.06) × 10−43cm2/fission. Due to transitions between neutrino flavours (νe, νµ, ντ), the neutrino masses are generated and the mass eigenstate of the neutrino system (ν1, ν2, ν3) becomes a superposition of the flavour eigenstate. When considering the simpler two flavour (να, νβ) case, the mass eigenstate (ν1, ν2) expresses as

(1)

If we started with να, we might observe a νβ at a certain distance L, due to neutrino oscillations. The probability of the νβ appearance as a function of the distance is

Is The Differ-

ence of square of ν2 and ν1 masses. The probability oscillates due to the interference between the amplitudes of propaga- tion; (να →ν1 →νβ) and (να →ν2 →νβ). The disappear-

Ance Probability Of Να Is Therefore Expressed As

P (να →να) = 1 −P (να →νβ) .

(3)

The first experimental evidence for neutrino oscillations and, still, most of the information today relies on high precision disappearance measurements with about 50 years of history.

Phe-

nomenon [1, 2, 3] came as a solution of atmospheric and solar neutrino anomalies around the year 2000. Those results had indicated two consequences: a new oscillation mode, labelled θ13, and the possibility to observe CP-violation, if θ13 was sizeable. The reactor neutrino experiments CHOOZ and Palo Verde set upper limit of sin2 2θ13 < 0.15 already be- fore 2001. The Double Chooz (DC) group was formed in 2006 to measure the θ13 more precisely making use of near and far detector configuration .

The Dc Experiment Has Played

a pioneering role in this oscillation channel by providing the first positive evidence, in 2011 , in combination with the

Νµ →Νe Appearance Results Of T2K And Minos Ex-

periments. The establishment of θ13 awaited the Daya Bay experiment’s observation in 2012 ; confirmed soon after

By The Reno Experiment . Today’S World Best Value

is driven by the statistical combination of the latest published θ13 results [13, 14, 15, 16, 17]. A reassuring feature for the field is that all reactor θ13 experiments are redundant which is critical to ensure a robust and unambiguous result. Therefore, multi-experimental validation framework is highly beneficial.

A working group formed by all three experiments is on-going with the goal to assess both internal consistency and coherent systematics treatment of each experiment.

Besides reactor experiments, neutrino beam experiments,

Such As T2K , Nova And Minos , Are Also Sen-

sitive to θ13 via the sub-dominant appearance νµ →νe and ¯νµ →¯νe oscillation modes. However, their ability for a high precision measurement of θ13 is limited by uncertainties and unknowns such as the δCP and θ23 octant degeneracy. Con- versely, this channel allows them to explore neutrino oscilla- tion CP-violation directly. Currently, the beam experiments provide the first CP-violation explorations [18, 19] by using the value of θ13 from reactor experiments as input. The latest data allow beam experiments to obtain the first hints of non- zero δCP. This result embodies a remarkable demonstration of synergy and compatibility across both reactor and beam measurements.

In this article, DC reports its multi-detector results for the first time with its 4th data release comprising 865 days ex- posure. DC measures reactor νe coming from EDF company Chooz twin reactors by identical near and far neutrino de- tectors. The θ13 value was extracted from the disappearance and spectrum distortion of the reactor νe caused by the base- line difference of the two detectors. Most of the systematic uncertainties are cancelled out by using functionally identi- cal detectors observing the same reactor νe sources. DC can provide clean analysis results by using several unprecedented techniques such as the exploitation of the effective iso-flux site geometry which cancels possible difference between the two reactors, a model-independent background estimation via re- actor power modulation including reactor-offdata and the total neutron capture detection technique which significantly increases the neutrino event statistics. Those analysis details are also explained. In addition, the DC near detector is used to characterise the rate and shape difference between data and predicted spectra, and measure the most precise neutrino flux to date, given by the mean cross-section per fission ⟨σf⟩.

The latter can be used as reference in other reactor neutrino experiments for an accurate neutrino event rate prediction.

The Double Chooz Experiment

The DC experiment relies on two identical detectors and two of the most powerful pressurised water reactors of the N4 plant series, whose full power is 8.5 GW thermal power

Figure 1:

LNCA (Laboratoire Neutrino Champagne-Ardenne) site allows for an almost iso-flux geometry (left) to the two identical DC detec- tors (right) yielding major inter-detector cancellation of reactor flux and detection systematics. Active BG rejection is achieved by the exploitation of the multi-layer (blue shaded) liquid-scintillator design whose light is read out by many photomulipliers via a Flash- ADC deadtime-less electronics The “Inner Detector” (ID) is sub- divided into 3 optically coupled volumes: i) ν-Target (GdT, 10 m3 liquid scintillator Gd 1 g/l loaded), ii) γ-Catcher ( GC, 23 m3 liq- uid scintillator), and iii) buffer (100 m3 non-scintillating oil). The “Inner Veto” (IV, 0.5 m thick liquid scintillator) fully surrounds the ID while the “Outer Veto” (OV, tracking plastic scintillator strip) is placed on the top. The IV tags external rock γ’s (anti- Compton veto), fast-neutrons and cosmic µ’s while the OV only sees cosmic µ’s, covering the ID chimney region. An external inert shield surround the IV: 15 cm steel (FD) and 1 m water (ND). The glove-box allows clean and safe deployment of the same calibration sources (252Cf, 60Co, 68Ge, 137Cs) in both the ND and FD.

(i.e. ∼1021 ¯νe/s flux). The near (ND) and far (FD) detectors are located at the respective average distance of ∼400 m and ∼1050 m to the Chooz reactors (B1 and B2). The θ13 sig- nature manifests itself as a rate deficit with an up to ∼10% spectral distortion in the FD relative to the almost undis- torted ND spectrum.

Thus, Dc Performs A “Rate+Shape”

θ13 measurement whose statistical uncertainty is dominated by the FD. There are three types of sources of systematic uncertainties: detection (including the estimation of the neu- trino energy) and background are internally constrained with DC data, while the reactor flux relies on an external reactor model. The model is commonly used by most reactor exper- iments while here it is customised to the specific DC reactor conditions. The simple Chooz multi-reactor site geometry en- ables to place the ND at the effective iso-flux1 position relative 1The detector locations are slightly offfrom iso-flux while this has negligible impact.

Reactor Flux Uncertainties On The Signal

Normalisation. Both rate and shape flux uncertainties are treated via covariance matrices as predicted by the data- driven reactor flux model [26, 27, 29] used by DC. The Bugey4 experiment (B4) provides an independent rate constraint via its ⟨σf⟩and therefore extra precision via the cancellation of the reactor-detector baselines is negligible (< 0.01%). The unknown inter-reactor correlations are assumed to be corre- lated for the reactor power (Pth) and the fission fractions (αf) in the SD case and uncorrelated for any MD configuration in general (combined uncertainty of Pth and αf is 0.83%). These assumptions are made to minimise the θ13 sensitivity to be conservative. In the DC case with two reactors the uncertain- ties on Pth and αf are reduced by about a factor of

Only

the uncorrelated terms are relevant for the specific MD case in DC (ND/FD-I and ND/FD-II). to the FD. This implies meeting the condition LB1-ND/LB1-FD ≈LB2-ND/LB2-FD for each reactor-detector pair distance (L).

This way, both the FD and the ND are exposed to both re- actors with the same fraction. From the single-detector (SD) to the multi-detector (MD) configurations, major systematics cancellation occurs by virtue of correlations due to identical detectors (detection systematics) and the iso-flux reactor ge- ometry (flux systematics). The site and detectors are briefly described in Fig. 1 – see Appendix for details. In this release, 481 days of data from single detector operation (FD-I, April 2011 until January 2013) previous to commissioning of the ND and 384 days of data with both detectors FD and ND (FD-II, January 2015 until April 2016) are combined. The result presented here supersedes our previous [13, 14].

Each N4 reactor typically runs at maximum power allowing the lowest power uncertainty (0.5%), or else they stop a few weeks once per year to refuel. The Chooz total reactor power modulation allows for “2-reactors” (both on), “1-reactor” (ei- ther on) and the unique BG only “0-reactor” (both off) data sets. An exposure of ∼25 days of 0-reactor data is avail- able. Past FD-I SD results [13, 14] employed the Bugey4 ex- periment data to compensate the ND absence, improving the overall systematics.

The ND monitors the rate+shape of the flux, thus reducing the θ13 uncertainty from most of the reactor physics and run- ning configuration. The ND is a direct reactor monitor of the FD-II (iso-flux) and indirect to the FD-I. The iso-flux implies that the neutrino fluxes are expected to be largely correlated across detectors, with negligible impact from reactor power or composition variations.

This Correlation Translates Into

an almost total rate+shape flux-error cancellation [6, 24]; a

Tnc

Figure 2: The TnC Detection Principle.

The Ibd Accep-

tance criteria are widely opened to integrate over all capture-γ’s: ∼2.2 MeV (H-n), ∼5.0 MeV (C-n) and ∼8 MeV (Gd-n). The over- whelming accidental BG (ND) is rejected over >4 orders of mag- nitude below 3.5 MeV (top) using vetoes and the ANN selection.

Excellent data (blue points) to MC (red area) agreement is found in the delayed energy distribution after the rejection. The energy scale uncertainty has negligible impact (<0.05%) due to 1.3 MeV cut. The selection efficiency (bottom) of the Gd-only (left) confines IBD’s to the Gd presence. The TnC (right) yields detec- tion in the full volume; i.e. GdT (>95%) and GC (>80%). The relative yields are ∼61.3% H-n, ∼38.2% Gd-n and ∼0.5% C-n.

unique DC feature as compared to other reactor-θ13 experi- ments . Instead, the FD-I benefits only from partial error cancellation. The ND provides the reference oscillation spec- trum for both FD-I and FD-II for the θ13 measurement. The shape differences between the FD-I and ND due to the differ- ent fuel composition are less than 0.5%. The flux systematics reduce from 2.27% (1.68% with Bugey4 data – see Table 1) in the SD case to ≤0.83% in MD configurations. The uncor- related uncertainty between the ND and FD-I predictions is estimated to be 0.66%. It strongly reduces to ∼0.1% between the ND and FD-II predictions because of the iso-flux config- uration and simultaneous data taking. In brief, the unique DC geometry grants a framework for a high-precision mea- surement by cancellation of the flux systematics.

Despite the ND, the reactor ¯νe prediction model remains an important element to the analysis, key for the FD-I. The same strategy employed in past publications is adopted.

An external reactor ¯νe prediction model is used [26, 27] where 235U, 239Pu, 241Pu fissile isotope contributions rely on ILL data . DC uses a measurement for the 238U predic- tion, while Daya Bay and RENO use summation methods.

Dedicated Chooz reactor simulations provide the fission frac- tion (αf) evolution considering the thermal power data (Pth) and re-fuel inventories. Bugey4 data aid both to constrain the predicted rate and to improve the precision.

Apture

Since the discovery of the neutrino, reactor ¯νe are typically detected via the inverse-beta-decay (IBD: ¯νe+p →n+e+) interactions on free protons (i.e. H nuclei) via a coincidence technique, where the prompt trigger (e+) is followed by the delayed trigger (neutron capture) several tens of µs later. The mean capture time τ capture is ∼200 µs in a metal-free organic liquid scintillator. The coincidence aids IBD identification as DC e+ recognition is impractical relative to radiogenic (e−, γ, α) or cosmogenic (p recoil or cosmic µ’s) BGs. In DC, the Gd is employed via scintillator loading (1 g/l). Gd’s high n- capture probability reduces the mean capture time (τ capture ≈ 30 µs) and provides a unique n-capture tag (∼8 MeV total energy) allowing for major BG rejection.

Another IBD detection approach opens with the Total Neu- tron Capture (TnC) technique presented here for the first time. The TnC relies on a larger delayed energy range inte- grating over the γ-peaks of all capturing elements available, H-n, C-n and Gd-n shown in Fig. 2. Thus, TnC combines past Gd-only and H-only selections. The main challenge is the control of larger BGs. The IBD space-time coincidence definition relies on a multi-variable ANN (Artificial Neural Network) thus rejecting random (uncorrelated) BG coinci- dences – see Appendix for details. More than two orders of magnitude of accidental background rejection is possible while keeping high the average selection efficiency at 86.78 ± 0.21% (MC: 86.75±0.01%) and at 85.47±0.08% (MC: 85.54±0.02%) averaged over the prompt energy spectra of the FD and ND, respectively. The selection efficiency is defined as the inclu- sive ratio of IBD candidates with the standard and loose ANN cuts. Thus, the denominator integrates over ∼98% of the de- tectable IBD’s. The ∼1.3% ND to FD difference, matched by the MC within 0.1%, is due to the ANN definition which is slightly different to ensure the prompt energy selection effi- ciency is identical across detectors.

The novel TnC has several remarkable features. Mainly, the TnC integrates all n-capture elements, thus the ¯νe detection is independent from specific capture details. This implies that the detection volume expands to both the GdT (Gd-target) and GC (gamma-catcher), as shown in Fig. 1, so the TnC vol- ume increases ∼3× as compared to Gd-only. This boost in statistics2 is critical for the DC sensitivity. In addition, the statistical limitation of the selection systematics is reduced as the selection efficiency per volume increases close to 100% in GdT and ∼80% in GC due to the ANN accidental rejec- tion. The wider TnC acceptance integrates over most MC inaccuracies, including the complex spill-in/out effect across the GdT-to-GC boundary. The only relevant boundary is the simpler GC-to-buffer with only H-C on both sides. So, TnC matches MC better while all element-dependent terms, such as Gd or H fractions, are irrelevant. A small concentration of Gd was found inside the GC of the ND due to leakage from the GdT. The described element independence also makes the TnC leak insensitive demonstrating selection stability within 0.1% in both the ND and FD.

2∼900 IBD/day (ND) and ∼140 IBD/day (FD) with 2 reactors on.

≤0.05

Table 2: Detection Uncertainties. The central column shows the uncertainties on the signal normalisation for the single detec- tor (SD) case. The multi detector (MD) case in the column on the right shows the uncertainty on the ratio of the signal rates (FD/ND) assuming simultaneous operation (not fully representa- tive for DC fit configuration). The total systematics is dominated by the uncertainty of the number of protons for IBD interactions (mainly the GC). This is to be re-measured upon future detector dismantling. The TnC reduces selection systematics as compared to the element dependent detection, since it is not sensitive to the knowledge of the Gd/H fraction of neutron captures. Boundary systematics relying on the modeling of spill-in/out events at vol- ume interfaces in the MC are assumed fully correlated between detectors. The selection systematics rely on an IBD data-driven method, thus inclusively accounting and averaging over selection and energy scale (stability, uniformity and linearity) variations.

The vetoes play a negligible role as they were optimized to maxi- mize the selection efficiency while adding a negligible systematic. All detection systematics are summarised in Table 2 for

Both Sd And The Ideal Md Case With Nd And Fd Tak-

ing data simultaneously. The θ13 uncertainty is dominated by the uncertainty on the number of protons in the tar- get/detection volume (or “proton-number”). The higher GC proton-number uncertainty (1.1%) as compared to the GdT (∼0.3%) is because at the time of the filling of the detectors we did not consider that precise IBD detection in the GC was possible. The selection systematics estimation uses an IBD data-driven inclusive approach. Thus, the estimator simul- taneously integrates and averages over a) IBD spectrum and volume, b) ANN selection correlations and dependences, c) energy scale systematics including uniformity, stability and The robustness of the IBD-based methodology was demon- strated with two methods using independent data: one was based on 252Cf data sampling in the GdT while the other was based on fast-neutrons data in both the ND and FD over the full volume.

No Deviations Of More Than 1Σ (Re-

spectively 0.1% and 0.3%) were observed. Lastly, the TnC selection was challenged to per mille precision by estimat- ing the known 252Cf neutron multiplicity .

Agreement

across ND and FD is within 0.1% (1σ). Thus, the uncertainty on the selection efficiency is demonstrated <0.3% (MD) and <0.4% (SD) excluding the dominant proton-number uncer- tainty. The proton-number will be re-evaluated with higher precision upon detector dismantling. In brief, the TnC tech- nique provides a robust IBD detection framework with better selection systematics for both SD and MD physics.

The Ibd Signal & Backgrounds

The BG consists of all physical events mimicking the IBD time-space coincidence implied by the TnC selection. This

Signal To Bg

Table 3: IBD Candidates Background. The rate+shape θ13 extraction depends on the precise knowledge of each (exclusive) BG rate and shape (i.e.

The Impact Of

BG in the FD is larger due to the lower signal rate. The data are consistent with a BG model with three components, shown in Fig.3, accidental, fast-neutron and 9Li. All other BGs are found or made (via vetoes) negligible. The BG component accuracy can be demonstrated by providing several independent measurements including 0-reactor data. This is very valuable for the least precise 9Li rate (∼10% uncertainty), where an additional measure- ment is possible via its time correlation to µ’s (“µ-tag” indicated).

The lower signal to BG ratio is ∼11 as compared to the Gd-only (∼25) due to the larger (>40×) accidentals. The total BG preci- sion is 3.2%FD and 3.9%ND. The total BG (Σ-exclusive) compu- tation implies a model assumption. The comparison and agree- ment found between Σ-exclusive (model-dependent) and inclusive (model-independent) measurements provide unique validation of the model itself as well as the BG rates. The inclusive measure- ment uses ∼17 days of 0-reactor data, not used for θ13 extraction.

includes accidental and correlated BGs. BG rejection is much harder whenever there is a neutron in the final state. Due to the small overburden3, cosmogenic BGs are dominant: fast- neutrons and unstable isotopes produced from 12C spallation, such as 9Li. The signature of fast-neutrons is a recoil on H, as prompt, followed by the n-capture, as delayed.

One Or

more neutrons can participate in a fast-neutrons coincidence. 9Li undergoes a β-n decay (including α’s), but no indica- tions of 8He production are found . Since the detector chimney is an effective tagging hole to vertical µ’s, there is a potential background when they stop inside the active detec- tor volume. Both µ decay at rest (Michel e±) and µ capture have been carefully studied and rejected to a negligible level. Lastly, the accidental BG is caused by two independent events, mainly from radioactive isotopes inside or around the detectors.

An offline 1.25 ms veto is imposed after each tagged µ, thus rejecting the resulting fast neutrons’ captures (>5×τ capture) and stopping-µ’s. The live time loss is 5.4% (FD) and 25.5% (ND). DC has developed a multi-veto method yielding large BG rejection: a rejection factor of 200 is reached for the FD and 35 for the ND as compared to simple time coincidence.

The vetoes are defined identically across ND and FD. Cosmo- genic BG rejection relies on direct µ and/or neutron tagging 3ND and FD are, respectively, at ∼30 m and ∼100 m rock overburden depth, so their cosmic µ rates are, respectively, ∼240 s−1 and ∼45 s−1.

using ID (inner detector), IV (inner-veto) and OV (outer- veto) detectors’, as shown in Fig. 1. A fraction of 9Li and most 12B are tagged by identifying spallation activity via correlated neutrons upon each tracked µ . Fast-neutron rejection exploits direct neutron tagging in the IV or the primary µ using the OV. The ANN discards most accidentals with a rejection factor >300. Since IBD’s extend to the GC, about 25% of external γ’s are tagged in the IV acting as anti-Compton veto. Stopped µ’s are fully suppressed based on Michel e± discrimination using informa- tion of the ID pulse-shapes and goodness of fit information from the position reconstruction. Any veto using the ID only affects delayed triggers to prevent any prompt spectral dis- tortion affecting θ13. The IBD inefficiency for all vetoes com- bined is 4.5% (FD) and 5.7% (ND) with negligible (<0.05%) systematics. See Appendix for further complementary selec- tion and veto details.

Table 3 summarises the remaining BG estimates including several independent measurements employed to validate the accuracy. The BG rates, larger compared to Gd-only , have negligible impact on the determination of θ13.

The

BG subtraction impact is small for signal-to-background >10 while the dominant statistical BG uncertainty is reduced. The vetoed BG samples provide copious data-driven spectra, which contain BG information independent of MC simula- tions.

The Shape Of Cosmogenic Bg Is Found To Be Identi-

cal across ND and FD within statistical uncertainties. The non-flat energy spectrum of the fast neutrons was carefully evaluated as it could mimic the θ13 signature.

Ts Spectra

was characterised over an extended window up to 100 MeV. The overall impact of BG on θ13 is marginal.

The Domi-

nant BG systematic is the 9Li uncertainty. The BG model accuracy was scrutinised independently with ∼17 days of in- clusive 0-reactor data samples in both ND and FD-II. Thus, these data are not used in the θ13 fit. No non-statistical bias or tension (<1σ) is found on the measured BG-model, rates and/or spectral shapes.

The Θ13 Measurement

The θ13 measurement is obtained by contrasting the observed IBD rate+shape spectral distortion against the specific neu- trino oscillation model prediction, similar to Eq.3, in which the rate reduces following the flux modulation given by

(4)

where sin22θ13 is the unknown. L(m) is the baseline distance between each reactor-detector pair, E¯νe(MeV) is the neutrino energy obtained from the prompt energy deposition or Visible

Ee| =

(2.484 ± 0.036) × 10−3eV2 is used as input to the fit. The θ13 rate+shape fit measurement uses all detectors data simultaneously. The nominal fit considers the input from each SD fit (data to its MC) including pertinent constraints and correlations. The SD fit is shown in Fig. 3-(bottom). In our MD analysis, all SD fits (FD-I, FD-II and ND) are simulta- neously performed, constrained by the inter-detector corre- lations such as BG (shape), detection (rate), energy (shape) and flux (rate+shape). Thus, the common ND provides di- rect and almost un-oscillated rate+shape reference spectrum.

Systematic uncertainties cancel due to correlations with both FD-I and FD-II. The iso-flux FD-II benefits from the max- imum error cancellation. The θ13 measurement is, in prin- ciple, independent from any common or correlated contribu- tions across the MC and detectors. Fig. 4-(left) illustrates the inter-detector ratio fit exhibiting the expected θ13 flux modu- lation and demonstrating the suppression of the spectral dis- tortion against the MC. The common MC serves both as link to the neutrino energy (E¯νe) and an inter-detector compar- ison mediator. The non-trivial role of the reactor model is scrutinised later on. This is a delicate point since the data to prediction comparison exhibits clear distortions uncovered by the uncertainties such as the 5 MeV excess shown in Fig 3.

The BG constraints benefit from ∼8 days of FD-I 0-reactor data (taken in 2011 and 2012) and the 20 MeV range exten- sion. The systematics are treated both via covariance matri- covariance treatment data points and uncertainty bands in figures do not fully represent the fit constraints upon minimi- sation. Pull terms are also used in the χ2 minimisation and give access to physical observables (BG rates, inter-detector normalisation, etc) as well as insight to the fit consistency.

There is negligible (<1σ) tension in all fit output values. The fit strategy follows an unbiasing scheme where performance and robustness to θ13 measurements are scrutinised using MC and fixed prior to the final data fit.

The best fit value is sin22θ13=0.105 ± 0.014 (13.3% preci- sion) with χ2/DoF = 182/112 with a p-value of 3.2×10−5. The expected total uncertainty (i.e. sensitivity) was 0.014.

The statistical precision is 0.005, so systematics largely dom- inate. The large χ2/DoF is caused by the mismatch between data and prediction, which is not covered by the model uncer- tainties. This topic is addressed later on. The 9Li rate is un- constrained in the fit. This is because the fit 9Li sample is up to 50% statistically correlated to the one used for 9Li estima- tion (µ-to-IBD time correlation), as summarised in Table 3.

The rate+shape spectral distortion is shown in Fig. 4 (right). An empirical fit to the spectral distortion residual appears to resolve a structure consistent with a slope and one or two Gaussian peaks. Their origin remains unknown. The common normalisation across all detectors can be measured as output of the fit. The value is 1.004 ± 0.008, while the input value was constraint by the uncertainty of the Bugey4 measurement (1.4%) . The sizeable smaller output uncertainty indicates that DC holds valuable independent information about rate normalisation.

Table 4 summarises the contributions to the total uncer- tainty in the oscillation fit. The FD drives the overall statis- tical precision (∼90k IBD’s). Because the FD-I data set still represents a large fraction of the data analysed here, the flux systematics are the largest contribution to the uncertainty on θ13. However, the operation of the two detectors in iso- flux configuration during FD-II lead to a large reduction of the systematics and this phase drives the overall sensitivity.

The detection uncertainties are dominated by the large GC proton-number uncertainty. The BG has a small role, thanks to the statistics and since the 9Li rate is constrained in the

Ulti Detector Uncertainty

Uncertainty is the square root of the covariance matrix diagonal terms

Ulti Detector Uncertainty

Uncertainty is the square root of the covariance matrix diagonal terms Figure 3: ND and FD Spectra & SD Ratios. Both ND (∼210k IBD’s) and FD (∼90k IBD’s) spectra are shown (top) within the fit [1.0,20.0] MeV range, including the un-oscillated MC prediction (red) and the BG model: accidentals (clear grey), 9Li (grey) and fast-neutron (dark grey). Cosmogenic BGs are estimated during the fit since 9Li (unconstraint) dominates in the [7.0,12.0] MeV region and fast-neutrons above 12 MeV. The impact of accidentals to the θ13 measurement is negligible. The data (BG subtracted) to prediction ratio is shown (bottom). The best fit solution (blue) contrasts with the no-oscillation hypothesis (red). Two dominant spectral distortions can be appreciated: the θ13 signature (mainly FD) and a common 5 MeV excess, leading to a large χ2/DoF of 182/112. Bugey4 constrains the prediction rate. The normalisation with this constraint is lower as compared to the prediction rate not using the Bugey4 information. The cancellation of both common distortions and correlated uncertainties takes place from the SD (yellow) to the MD (green) configurations. The covariances used (not shown) play an important role during the fit.

oscillation fit due to the spectral shape above ∼7 MeV. The non-linearity uncertainty is lower than 0.6% thanks to the re- liable Flash-ADC linearity control. The impact of deviations from response stability and uniformity is negligible. Using the common 252Cf source fission prompt spectrum, the response linearity was found identical between detectors with no slope greater than 0.1%. The impact of the uncertainty on |∆m2

Ast, Some Degree Of Degeneracy Among Sys-

tematics exists and leads to correlations. This increases the impact of some terms (see Table 4). To conclude, the reactor (FD-I) and the detection systematics dominate. More data are expected to reduce the impact of most systematic errors and correlations between them because the relative impact of the FD-I phase is reduced. A <0.010 precision on the sin2 2θ13 measurement is possible using the full data exposure, if the proton-number systematics were to be improved.

Iscussion & Implications

Our reported MD θ13 exhibits an up to 48% higher central value whose significance is <2.0 σ’s compared to all other measurements. The latest published values of θ13 are shown

In Fig. 5. Nova And Minos Are Also Sensitive To

θ13. Since the statistical uncertainties in reactor experiments are small, a simple statistical fluctuation is unlikely to be the sole cause of the difference. Differences are however today consistent within the context of the dominant systematics un- certainties. The consistency among the DC, DYB and RENO reactor measurements remains critical check for the θ13 final global value used everywhere else.

Systematic Uncertainty Scrutiny

The reported θ13 result deserves thorough scrutiny to ensure that the accuracy (i.e. any bias) is controlled well within the quoted uncertainties. In order to do this, DC has performed

Odel Systematics

Figure 4: The Spectral Ratios. The FD to ND ratio (left) represents a clean θ13 rate+shape disappearance evidence used by the fit for parameter extraction. No traces of any remaining distortion are found, demonstrating the expected inter-detector cancellation key to ensure the θ13 accuracy. Instead, ND data to MC prediction ratio (right) allows for precise extraction of the spectral distortion, which is common in FD and ND as seen in Fig.3. Both the rate and shape effects are visible so rate+shape feature extraction is possible. An empirical structure is examined by fitting with two models: one and two empirical Gaussian peaks with a common slope.

Both models reproduced data. The origin of those empirical features remains unknown. Shape-only analysis is described in Appendix.

Sin22Θ13 Measurement Uncertainties Break-

down. The match between the θ13 uncertainty from data (0.0139) and the predicted sensitivity (0.0141) allows for a MC uncertainty breakdown. In the central column the fractional uncertainties of the different systematics (x) are given. They were calculated from the sensitivity assuming just one systematic contribution in addi- tion to the statistical uncertainty. The statistical part was then subtracted in quadrature. The total is larger than the square root of the sum of the individual squared uncertainties because of cor- relations. The difference corresponds to a (0.0065)2 term. The column on the right shows the total uncertainty when the corre- sponding single systematics is removed. The impact of background and in particular of the energy scale on the sensitivity is higher than one might expect from the values given in the central column.

Again, this is due to the correlations. several independent checks. This is only possible for internal systematics; i.e. those relying on the experiment’s data. This was reported in previous sections for the case of detection, en- ergy and BG systematics. The case of the reactor flux model is exceptional, as it cannot be tested directly with DC data.

Today’s IBD data exhibit a significant discrepancy in terms of both rate (i.e. deficit) and shape (i.e. possible slope and ex- cess around ∼5 MeV), as illustrated in Fig. 4 – see Appendix for details. While there is so far an unsettled debate on its origin , here we shall focus on the empirical impact on the θ13 determination. Thus, the remaining discussion addresses the subtle role of the reactor model and its systematics on the reported θ13 measurement.

Impact of Reactor Model on θ13.

Since Dc Data Has A

limited ability to test the validity of the model, the stability of the θ13 measurement is scrutinised and demonstrated against the behaviour of the reactor model for both the SD and MD configurations as explained in Fig. 6.

The SD case is more illustrative as a stronger dependence on the model biases is expected due to the lack of a ND. Also, past DC results with data from the FD only can be directly validated4. Indeed, we demonstrate that a measure- ment of θ13 is compromised using the standard rate+shape model prescription due to the large data to model mismatch.

Despite the constraint on the rate from Bugey4, the shape distortion biases the fit via the shape-only term. This effect grows with statistics. The new empirical prescription for FD- I+FD-II data explained in Fig. 6 yields sin22θ13=0.108±0.028 (χ2/DoF = 53/74) matching the MD result. This is the best SD θ13 measurement to date. Conversely, the standard re- actor uncertainty leads to sin22θ13=0.122 ± 0.022 (χ2/DoF: 105/74). Thus, SD is proved a fragile measurement frame- work due to the unavoidable dependence on the rate+shape reactor model deviations and systematics.

The MD case is demonstrated a robust θ13 measurement. With the ND, the inter-detector cancellation protects θ13 largely from any common or correlated rate+shape bias. The 4The risk to compromise SD accuracy was already suspected in , so a rate-only θ13 measurement was conservatively adopted as baseline.

∆

Figure 5: Latest Published θ13 Measurements. The most precise published reactor measurements from DC MD TnC (this work), DYB [15, 16], and RENO are shown. The latest DC result is consistent with previous ones. Our result exhibits an up to 48% higher central value whose significance ranges <2.0 σ’s. The latest T2K is shown for comparison, whose larger uncertainty considers the marginalisation over the θ23-octant and CP violation.

model uncertainty underestimation mainly manifests as the larger χ2/DoF tension due to the large ND statistical preci- sion. The increase on the uncertainty of the reference spec- trum causes both a more robust θ13 value (<1% effect) and the alleviation of the χ2 tension. The latter was corroborated with data, in which χ2 went from 182 to 93 (DoF: 112). In- stead, the increase of the model uncertainty has almost no impact on the θ13 precision, as shown in Fig. 6.

Our studies allow a few empirical observations linked to today’s model limitations whose origins remain unknown. i) The 1σ envelope for today’s prediction appears insufficient to accommodate the mismatch between data and model for both rate and shape. A better understanding of the origin of model deviations remains critical. In the meantime, the adop- tion of IBD data driven methods is the only way to bypass the model limitations. Here DC demonstrates that Bugey4 (or alike) can be used to bypass the rate model bias with few per mille accuracy. However, the same is less evident for the spectral shape bias or distortion due to unresolved remain- ing differences among experiments at the few % level today – see Appendix. ii) the DC IBD data prescription favours the increase of today’s shape-only uncertainty to extend the empirical model, as described in Fig. 6. Unless new physics proves otherwise, significant reactor model progress is needed to attain SD precision below ∼6%.

Iii) The Spectral-Based

bias is expected to depend on the relative position between the dominant features, such as the ∼5 MeV excess, and the energy range where the θ13 oscillations affect the spectrum.

Rate and Shape Decomposition.

Since The Θ13 Mea-

surement exploits both the rate and the shape, further in-

∆

Figure 6: Reactor Model Uncertainty Impact on θ13. Asi- mov data is used here to illustrate the spectral distortion impact on θ13 when considering a similar distortion as that found in data.

Bugey4 is needed to correct the SD (black) rate normalisation. Else, an unbiased θ13 measurement is impossible, even if arbitrar- ily increasing the uncertainties. The SD θ13 value exhibits a strong dependence on the shape uncertainty of the reactor model due to the spectral distortion. Both SD and MD (blue) match to the input θ13 only when considering an increase of up to 4σ of this uncertainty. This increase provides an IBD-based empirical new prescription which yields a robust θ13 measurement in both bases.

The extra uncertainty accommodates the otherwise unaccounted 5 MeV spectral excess. This is corroborated with data (see text). While this behaviour is specific to the θ13 signature, the main pat- tern remains: any shape-dependent SD result might be spurious due to the reactor model dependences. The θ13 from MD data is found to vary <1.0% thus demonstrating its better stability. The model uncertainty underestimation arises in the MD case mainly via the reported χ2/DoF tension due to the ND statistical preci- sion. This tension vanishes when similarly increasing the model uncertainty.

sight comes from splitting the measurement into the rate- only (16% precision) and shape-only (43% precision) contri- butions. The main θ13 constraint is due to rate-only (sys- tematics dominated).

The Shape-Only Information Has En-

hanced significantly due to the higher statistics in the FD as compared to previous DC results . No tension is found between rate and shape measurements (<0.5σ). The shape- only θ13 fit value is about 20% lower as compared to our main result whereas the rate-only fit is higher. This indicates shape effects as the observed spectral distortions do not intro- duce a bias towards a higher θ13. The shape stability of the

−0.49)×10−3Ev2 Are

obtained. A loss in precision is expected due to the DC non- optimal baseline. See Appendix for further cross-checks. FD-I and FD-II Decomposition.

Thanks To The Direct

iso-flux monitoring, the reactor flux prediction of FD-II is largely correlated with the ND (∼0.1% uncorrelated nor- malisation uncertainty), hence the precision on θ13 is much better as compared to FD-I. It is interesting to decompose the θ13 measurement into the statistically independent FD-I (22% precision) and FD-II (15% precision) samples. Indeed, FD-II drives the reported central value of θ13. Using the SD, the FD-I and FD-II samples are demonstrated to be statisti- cally consistent (∼0.7σ). FD-II (46% of data) is expected to dominate future DC results.

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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