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Analysis of Polarized Dust Emission Using Data from the First Flight of SPIDER

,3 A. S. Bergman,3 R. Bihary,4 J. J. Bock,5, 6

J. R. BOND,7 J. A. BONETTI,6 S. BRYAN,8 H. C. CHIANG,9, 10 C. CONTALDI,11 O. DORÉ,5, 6 A. DUIVENVOORDEN

H. K. Eriksen,13 J. P. Filippini

,14 A. A. FRAISSE,3 K. FREESE,15, 16, 17 M. GALLOWAY,13 A. E. GAMBREL,18

J. Hartley

,23 M. HASSELFIELD,24 G. HILTON,25 W. HOLMES,6 V. V. HRISTOV,5 Z. HUANG,7 K. D. IRWIN,26, 27

W. C. Jones

,3 A. KARAKCI,13 C. L. KUO,26 Z. D. KERMISH,3 J. S.-Y. LEUNG,28, 29 S. LI

,3, 30 D. S. Y. Mak,11

P. V. MASON,5 K. MEGERIAN,6 L. MONCELSI,5 T. A. MORFORD,5 J. M. NAGY

,3 J. D. Soler,33 X. Song,3

A. TRANGSRUD,5, 6 C. TUCKER,1 R. S. TUCKER,5 A. D. TURNER,6 J. F. VAN DER LIST,3 A. C. WEBER,6 I. K. WEHUS,13

D. V. Wiebe,2 And E. Y. Young26, 27

5Division of Physics, Mathematics and Astronomy, California Institute of Technology, MS 367-17, 1200 E. California Blvd., Pasadena, CA 91125, USA 6Jet Propulsion Laboratory, Pasadena, CA 91109, USA 11Blackett Laboratory, Imperial College London, SW7 2AZ, London, UK 12Center for Computational Astrophysics, Flatiron Institute, New York, NY 10010, USA 16Weinberg Institute for Theoretical Physics, Texas Center for Cosmology and Astroparticle Physics, Austin, TX 78712, USA 19Steward Observatory, 933 North Cherry Avenue, Tucson, AZ, 85721, USA 20APC, Univ. Paris Diderot, CNRS/IN2P3, CEA/Irfu, Obs de Paris, Sorbonne Paris Cité, France 25National Institute of Standards and Technology, 325 Broadway Mailcode 817.03, Boulder, CO 80305, USA 27 SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA 33Max-Planck-Institute for Astronomy, Konigstuhl 17, 69117, Heidelberg, Germany

Spider Collaboration

Using data from the first flight of SPIDER and from Planck HFI, we probe the properties of polarized emission from interstellar dust in the SPIDER observing region. Component separation algorithms operating in both the spatial and harmonic domains are applied to probe their consistency and to quantify modeling errors associated with their assumptions. Analyses of diffuse Galactic dust emission spanning the full SPIDER region demonstrate i) a spectral energy distribution that is broadly consistent with a modified-blackbody (MBB) model with a spectral index of βd = 1.45 ± 0.05 (1.47 ± 0.06) for E (B)-mode polarization, slightly lower than that reported by Planck for the full sky; ii) an angular power spectrum broadly consistent with a power law; and iii) no significant detection of line-of-sight polarization decorrelation. Tests of several modeling uncertainties find only a modest impact (∼10% in σr) on SPIDER’s sensitivity to the cosmological tensor-to-scalar ratio. The size of the SPIDER region further allows for a statistically meaningful analysis of the variation in foreground properties within it. Assuming a fixed dust temperature Td = 19.6 K, an analysis of two independent sub-regions of that field results in inferred values of βd = 1.52 ± 0.06 and βd = 1.09 ± 0.09, which are inconsistent at the 3.9σ level. Furthermore, a joint analysis of SPIDER and Planck 217 and 353 GHz data within one sub-region is inconsistent with a simple MBB at more than 3σ, assuming a common morphology of polarized dust emission over the full range of frequencies. This evidence of variation may inform the component-separation approaches of future CMB polarization experiments.

1. Introduction

The polarization of the cosmic microwave background (CMB) contains a wealth of information about the contents, history, and origins of the Universe (Abazajian et al. 2016).

Observations of the E-mode (“gradient”, scalar, even-parity) polarization pattern reveal details of acoustic oscillations in the primordial plasma. A measurement of a cosmological B-mode (“curl”, pseudoscalar, odd-parity) pattern on large angular scales would imply the presence of a background of primordial gravitational waves, and thus provide remarkable new insights into early Universe models (Kamionkowski & Kovetz 2016; Seljak & Zaldarriaga 1997).

Precision studies of CMB polarization are complicated by polarized emission at similar frequencies from foreground sources within our own Galaxy, notably synchrotron radia- tion and thermal emission from dust particles (Dunkley et al.

2009). Even at the highest Galactic latitudes, foreground emission is known to be far brighter than any primordial B-mode signal (BICEP2/Keck, Planck Collaborations et al.

2015).

Observations At Multiple Frequencies Can Be Used

to differentiate CMB from foreground emission based upon their differing spectral energy distributions (SEDs) (Wright et al. 1991; Brandt et al. 1994). Several such component separation methods have been developed: see, e.g., Planck Collaboration et al. (2020a) and references therein. In or- der to stitch together such multi-frequency data, these meth- ods must necessarily make assumptions about the nature of foregrounds: their spatial morphology, SED, or some com- bination thereof. Component separation is thus an imperfect process, and there are always some uncertainties due to these assumptions (Remazeilles et al. 2016; Hensley & Bull 2018).

At frequencies above 100 GHz, Galactic dust emission is the dominant polarized foreground on large angular scales (Planck Collaboration et al. 2016a).Dust grains, heated by stellar radiation to ∼20 K, thermally re-emit that energy with an efficiency that depends on the physical characteristics of the grains. Because emission is inefficient at wavelengths much larger than the grain itself, dust emissivity is expected to drop in the mm-wave regime where CMB measurements occur (Draine & Fraisse 2009). Aspherical grains that are ferro- or para-magnetic will preferentially align relative to the local magnetic field, leading to linearly-polarized emis- sion with large-scale correlations (Purcell 1975). Motivated by this picture, it is common to model the dust SED1 as a thermal blackbody at temperature Td, modified by a power-

Βd

B(ν,Td).

(1)

Here B is the Planck spectrum for a blackbody emitter, ν0 is some reference frequency, and τ0 is the optical depth at the reference frequency. Equation 1 is referred to as a modified blackbody (MBB).

Though widely-used, this simple model is unlikely to re- flect the full range of dust emission across the sky.

The

detailed nature of dust grains remains a subject of ongoing research (Hensley & Draine 2023; Draine & Fraisse 2009). Their composition, size distribution, and density are all ex- pected to vary from place to place, as are their radiative and magnetic environments. Thus, we may naturally expect different dust populations in our Galaxy to exhibit different SEDs. Such variation of the spatial morphology of a fore- ground component with observation frequency—or, equiva- lently, of the component SED across the sky—is often called frequency decorrelation. Furthermore, observations of the CMB constitute a collection of line-of-sight (LOS) integrals through the materials surrounding us, each of which may tra- 1 Note that, while Equation 1 may be used to model both the intensity and polarization of dust emission, the same model parameters need not apply to both; indeed, Planck has found a slightly steeper power law for polarization than for intensity in an all-sky analysis Planck Collaboration et al. (2020b).

3

verse heterogeneous populations. In addition to complicating the dust SED, such LOS decorrelation can yield variation in polarization angle with frequency even within a single map pixel (Tassis & Pavlidou 2015).

Decorrelation may significantly complicate efforts at com- ponent separation. For example, Poh & Dodelson (2017) have shown that naive extrapolation of dust templates made from 353 GHz data to lower frequencies can bias the recovery of the tensor-to-scalar ratio r ≤1.5×10−3. While an analysis by the BICEP team (BICEP/Keck Collaboration et al. 2023) showed no evidence of dust decorrelation within their ob- serving region, there is evidence for its presence in larger regions.

By Identifying Regions Of The Sky Likely To Con-

tain magnetically misaligned clouds, Pelgrims et al. (2021) demonstrate that LOS frequency decorrelation is detectable within the Planck dataset, largely in the Northern Galactic cap.

Ritacco et al. (2023) has further demonstrated LOS frequency decorrelation in large-scale regions close to the Galactic plane. It is thus critically important to test the as- sumptions behind common foreground separation techniques through detailed studies of dust polarization. Such studies will inform both the field of Galactic astrophysics as well as the prospects for foreground removal by future CMB exper- iments (Hensley et al. 2022; Hazumi et al. 2020; Abazajian et al. 2016).

This publication is part of a series describing results from the first flight of SPIDER, a balloon-borne CMB telescope optimized to search for B-modes on degree angular scales.

These data from SPIDER provide a measurement of the an- gular power spectra of 4.8% of the polarized sky at two frequencies: 95 and 150 GHz (SPIDER Collaboration et al.

2022). Dust emission is the dominant foreground at these at these frequencies. Since the first SPIDER instrument did not include a channel optimized for dust, the analysis of these data relies heavily on Planck 217 and 353 GHz maps for component separation. The published B-mode results from these data relied primarily on template subtraction using the XFaster power spectrum estimator (Section 2.1) along- side comparisons with alternate estimators and foreground- cleaning techniques (e.g., Section 2.2).

This paper exploits the sensitivity and sky coverage of the SPIDER data to explore the properties of the Galactic emis- sion and to quantify the impact of the methods and mod- els employed on component separation. Section 2 reviews both component separation techniques, and in Section 3 they are applied to two distinct subsets of the SPIDER region to probe for evidence of spatial variation in the nature of the diffuse polarized dust emission. The fidelity of the MBB model is tested in a comparison of the results from the two sub-regions using two Planck-derived dust templates (353- 100 GHz and 217-100 GHz). Section 4 examines different choices for modeling the dust SED within the full SPIDER region: the validity of the MBB model, the constancy of MBB parameters with angular scale, and the use of power- law models for the dust angular power spectrum. Section 5 searches for LOS decorrelation by developing a custom es- timator to look for evidence of variation of dust polarization angle with frequency in the SPIDER observing region. Fi- nally, Section 6 compares the measured dust power spectrum for this sky region to templates generated by the PySM fore- ground modeling package.

2. Component Separation Techniques

As in SPIDER Collaboration et al. (2022), our analy- ses in this paper rely on two main component separation techniques: foreground-template subtraction, and Spectral Matching Independent Component Analysis (SMICA). In this section, we present baseline versions of these methods.

In Sections 3 and 4 we explore variations in the assumptions presented below in order to test our understanding of the po- larized emission from interstellar dust.

2.1. Template Subtraction

In the baseline cosmological analysis of the SPIDER first flight data (SPIDER Collaboration et al. 2022), we remove polarized dust emission from the SPIDER 95 and 150 GHz maps by subtracting from them a scaled template for this

The Spider Imple-

mentation of foreground-template subtraction follows the ap- proach pioneered by Page et al. (2007) in the analysis of the WMAP polarization data. Within any given map pixel ob- served at frequency ν, the measured Stokes parameters, Sν, are each modeled as the sum of three components: CMB,

Ν0

+nν .

(2)

The uniform (pixel-independent) scaling factor Aν,ν0 con- nects the dust map at the observing frequency ν to that at the reference frequency ν0 = 353 GHz.

We construct our dust template by subtracting the Planck

Ν0 ≡Sν0 −S100. Since

the CMB component is independent of frequency in these units, this removes the CMB signal at the cost of a mod- est increase in noise. To produce a cleaned CMB map, we scale this dust template by a fitting parameter α and subtract

+ Nν −Αnt

ν0.

(3)

2 In both the analyses presented in SPIDER Collaboration et al. (2022) and in this publication, we use release 3.01 of the Planck data (Planck Collab- oration et al. 2020c) unless otherwise noted.

Spider Collaboration

Here nν is the noise component at the frequency ν, and nt

Ν0 ≡

nν0 −n100. Following SPIDER Collaboration et al. (2022), we use the XFaster algorithm (Gambrel et al. 2021) to fit for values of α = Aν,ν0/(1−A100,ν0) and the tensor-to-scalar ratio, r, in a si- multaneous fit to the SPIDER EE and BB spectra. Note that, before subtraction, the dust template is “reobserved,” i.e., in- jected as an input sky through the full SPIDER simulation pipeline; it is thus subjected to the same scan strategy, beam smoothing, time-domain filtering, and map-making as the sky observed by SPIDER. The reobserved template, like the SPIDER data, is corrected in map space for the temperature- to-polarization leakage induced by the pipeline.

The template method implements a single scalar-valued factor α for each SPIDER frequency multiplying the entire map.

Thus, This Method Assumes That The Morphology Of

the polarized dust emission is independent of frequency (at least between 353 GHz and 100 GHz) or, equivalently, that the dust SED is constant across the relevant sky area. Note, however, that this method does not impose assumptions on the dust SED itself. We will revisit this assumption in our analysis below, notably in Sections 3 and 5.

Spectral Matching Independent Component Analysis

(SMICA; Cardoso et al. 2008) is a method for construct- ing linear combinations among a collection of maps in or- der to isolate desired sky components (e.g., dust or CMB). In contrast to the map-space template analysis described above, SMICA operates in multipole space, acting on the spherical harmonic coefficients, aℓm, for each map. Given a collection of n input frequency maps,3 we construct Y = (y1,··· ,yn), where each yi is a row vector of aℓm coefficients for a sin- gle map i. We use the SMICA algorithm to construct the column vector of map weights, w, such that the linear combi- nation s ≡wTY is an estimate of the spherical harmonic coef- ficients for our desired sky component. Throughout this sec- tion, lower case letters denote vectors, and upper case bold letters denote matrices.

The weights are optimized with respect to some model of the assumed sky components.

Given A Column Vector, A,

containing the frequency scaling of a given sky component across the various maps (uniform for CMB, MBB for dust), the multipole-binned weights, wb, for this sky component are

(4)

3 Throughout this paper, n = 6: for each polarization mode we use maps at all four polarized Planck HFI frequencies (100, 143, 217, and 353 GHz) and the two SPIDER frequencies (95 and 150 GHz).

where eRb is the binned modeled covariance matrix containing CMB, dust, and noise components. These weights minimize the variance of the reconstructed harmonic map, var(s) =

B A = 1

(Hurier et al. 2013).

When Reconstructing Component Maps, Each Harmonic

mode aℓm is scaled by the corresponding wb for its appro- priate bin. The reconstructed maps, S, are the inverse spheri- cal harmonic transform of these weighted collections of har- monic modes.

SMICA’s power and flexibility lie in the freedom to impose (or relax) different assumptions about the components in this model, and thus about the relationships among the weights.

As discussed in detail in SPIDER Collaboration et al. (2022), the SMICA implementation for the SPIDER B-mode analysis assumed a single dust component with a MBB SED. In this analysis we make two improvements to SMICA dust mod- eling: we do not impose an SED on the dust component, and we improve the power-spectrum estimation for the dust through a more accurate transfer function. Both changes are described further below.

In this analysis we do not assume a MBB dust SED, but instead fit for the dust a as for any other parameter of the model defining eRb (which includes the CMB, dust emission, and noise) using the same maximum-likelihood fitting pro- cedure as in SPIDER Collaboration et al. (2022). We choose the arbitrary overall normalization of a such that its 353 GHz element is set to 1.

Fitting For The Dust A In This Man-

ner effectively trades precision for accuracy: the frequency- dependence of the reconstructed dust component will not be biased by any assumptions about the dust SED, but the un- certainty on the other fitted parameters (e.g., the amplitude of the emission) will likely be larger; it could be smaller, but only if the SED we would otherwise assume were an espe- cially poor description of the data.

In previous analyses (SPIDER Collaboration et al. 2022), the sky components of eRb are corrected for effects from fil- tering, beam smoothing, and mode-coupling kernels through a Jbb′ transfer matrix, as per Leung et al. (2022). While this approach is accurate for CMB spectra, the different angular power spectrum of dust make it inaccurate for an unbiased recovery of the full-sky dust spectrum, especially at larger scales. In this paper we modify the model to apply Jbb′ only to the CMB component, and instead apply a diagonal Fb to the foreground component. Fb is the ratio of the output to in- put power for each bin and is constructed from an ensemble of reobserved Gaussian dust realizations. These realizations follow a power-law scaling of amplitude with angular scale, with an exponent γ = −2.30, pivoting around ℓ= 80.

Figure 1 shows the weights by which each SPIDER and Planck HFI frequency map contribute to the component maps computed by SMICA. For the dust component, the relative

Multipole ‘

Figure 1. SMICA derived EE (top) and BB (bottom) weights to recover cleaned CMB (left) and dust (right) component Q/U maps. The SPIDER 95 and 150 GHz maps contribute predominantly to- ward the CMB signal, recovered (dominant positive weights) in the left panels and removed (subdominant and/or negative weights) in the right panels. The Planck 217 and 353 GHz maps contribute pre- dominantly toward the dust signal, removed in the left panels and recovered in the right panels. The dust weights are scaled with the fitted dust amplitude fν to indicate their signal contribution.

contribution of the map at frequency ν is given by its SMICA

, The Ν-Component Of

the vector adust, the dust frequency scaling vector fitted to the data by SMICA. The main contributor to both the E-mode and B-mode dust signals in Figure 1 is the 353 GHz Planck map, which has the highest ratio of dust signal to noise. In the B-mode dust reconstruction, all contributions are positive, as expected in the absence of CMB B-mode power.

For the CMB, the SMICA weight for a given frequency map directly represents its relative contribution, since aCMB is the identity vector. The SPIDER maps provide the dominant contribution to both the E and B-modes, reflecting the higher ratios of CMB signal to noise in these maps than in any of the Planck HFI maps.

The Q and U maps derived by SMICA, along with their estimated uncertainties, are shown in Figures 2 and 3 for the CMB and dust components, respectively. The covariance σw of the weights and the noise covariance σY contribute in quadrature to the total per-pixel uncertainty on the estimates

Right Ascension

Figure 2. (top) SMICA derived component separated Stokes Q/U CMB maps computed with the CMB weights shown in the left pan- els of Figure 1. (middle) The contribution σw to the uncertainty in the CMB maps due to uncertainty in the SMICA weights. (bottom) The contribution σY to the CMB map uncertainty due to the uncer- tainty in the input SPIDER and Planck data maps. All maps are in units of µKCMB.

of the component maps S. The former represents the uncer- tainty due to signal reconstruction, while the latter (the dom- inant term) represents the per-pixel noise after a weighted average. Both are presented in separate panels of Figures 2 and 3.

Is Similar To Noise Esti-

mates for Planck 353 GHz, as that map dominates the weight.

W , Is Morpho-

logically distinct from the noise. In particular, the larger un-

Maps Does Not Trace

the reconstructed dust signal strength or the noise. This unex- pected structure could come from unidentified systematic er- rors in the input Planck or SPIDER maps, although evidence for the latter was not found in the expansive suite of null tests published in SPIDER Collaboration et al. (2022). A physi- cal origin is also possible: frequency decorrelation, in which dust emission at a given frequency is not well correlated with that at other frequencies, would prevent an accurate recon- struction of this emission by SMICA, as the formalism here assumes that a single frequency scaling factor applies to all pixels. Given a specific frequency decorrelation model, e.g., a mixture of two dust populations, each characterized by its own spectral index, simulations could be run through SMICA in an attempt to reproduce the structure observed in the dust

Right Ascension

Figure 3. (row 1) SMICA derived component separated Stokes Q/U dust maps, computed with the dust weights shown in the right panels of Figure 1, and scaled to the 353 GHz reference frequency. (rows 2 and 3) The 353 GHz and 217 GHz Planck map templates are re- observed and band-limited to ℓ∈. The SMICA dust map shows structure that is most consistent with the 353 GHz template, the predominant contribution to the component weights. (row 4) The contribution σw to the uncertainty in the SMICA dust maps due to uncertainty in the weights. (row 5) The contribution σY to the dust map uncertainty due to the uncertainty in the input SPIDER and Planck data maps. Note that the morphology of σY is inconsistent with that of σw. All maps are in units of µKCMB.

uncertainty maps. Such a study is beyond the scope of our analysis. Figure 3 also compares the SMICA dust component map

Ν0 Constructed With

ν0 = 353 GHz and ν0 = 217 GHz. The template maps have

353 Maps Look

very similar, which is not surprising since both are dominated

Than St

353, and lower signal-to-noise ratio. The visible struc- tures in these two template maps are similar but not identi- cal.

Emission Properties

In our baseline cosmological analysis (SPIDER Collabo- ration et al. 2022), we use foreground-template subtraction (Section 2.1) to subtract the polarized emission from inter- stellar dust from the SPIDER maps. As reflected in the scalar nature of Aν,ν0 (and therefore of α) in Equation 3, this pro- cedure assumes that the morphology of this emission is inde- pendent of frequency. This assumption could easily be inad- equate, e.g., if the temperature of dust grains changes across the SPIDER region, or if two or more dust populations— even if they are well mixed—permeate it. In Section 3.2, we perform foreground-template subtraction independently in two non-overlapping, physically motivated subregions of the SPIDER field (described in Section 3.1), and assess the consistency of the α values derived in the two subregions.

We discuss the physical interpretation of these results in Sec- tion 3.3.

3.1. Delineating Subregions

We define two physically motivated subregions within the SPIDER field based upon a SMICA-generated map of the to- tal polarized dust emission power, P2 = Q2 +U2 (Figure 4, top).

353

Stokes parameter maps described in Section 2.2 and shown in Figure 3. After smoothing this map with a Gaussian of 8◦FWHM, we separate the map into two complementary

Cmb Contour (Figure 4, Bot-

tom). We denote by Pd+ (Pd−) the subregion in which P2 is greater (less) than this threshold. This procedure produces two simply-connected subregions (prior to masking point sources) that are separated by a smooth boundary, features that facilitate power spectrum estimation (Gambrel et al.

2021). After point-source masking according to the proce- dure described in SPIDER Collaboration et al. (2022), Pd+ and Pd−cover roughly equal sky fractions of 2.4% and 2.3%, respectively. We note in passing that Pd−overlaps with the “Southern Hole,” a region of the Southern sky that has long been known to exhibit low total dust emission, and that has more recently been mapped with high polarization sensitiv- ity (BICEP/Keck Collaboration et al. 2021; Balkenhol et al.

2023). 3.2. Template Subtraction by Subregion: Evidence for

Spatial Variation

Following the procedure described in Section 2.1, we per- form foreground template subtraction independently on each

Cmb]

Figure 4. (top) The polarization P2 = Q2+U2 of the SMICA-derived dust component (first row of Figure 3). (bottom) Mask regions Pd

And Pd

−, containing more or less polarized dust, respectively, as in- ferred from the polarization map. of the two subregions defined in Section 3.1. The left panel of Figure 5 shows, for each subregion and for the entire SPIDER field, the resulting 1-D and 2-D likelihoods for the tensor-to- scalar ratio, r, and for the foreground-template fitting param- eters, α95 and α150, where the added indices refer to the SPI- DER frequencies to which we fit the Planck 353 GHz fore- ground template. Following the method in Section 4.3 of Gambrel et al. (2021), the results in this section are validated with a suite of 300 simulations with input r, α95, and α150 fixed to the maximum likelihood values in Figure 5. Each simulated map is constructed from ensembles of CMB plus SPIDER noise, along with either the 217 or 353 GHz Planck dust template. Fitted templates add noise from Planck FFP10 realizations. To produce robust estimates of the α parameters recovered from the SPIDER data, we correct the data likeli- hoods for a small (≪1σ) bias in the XFaster estimator, as measured from this validation suite.

With the Planck 353 GHz template, we find the maximum- likelihood values for r and α95 to be consistent to better than 0.7σ and 2.0σ, respectively, between all three regions. How- ever, the maximum-likelihood values for α150 differ by 3.6σ between the two subregions, with a significantly higher value of α150 in Pd−than in Pd+. In other words, the template- correlated dust signal in the more diffuse region, Pd−, is brighter than would be inferred by scaling the template based upon observations of the region with more polarized dust emission, Pd+ (or of the combined region, where the fit is naturally driven by the brighter areas). We would thus expect residual dust signal after subtraction of a template that did not account for such variability.

Note that these data are not sufficient to establish any gen- eral causal relationship between variation in α150 and the in- tensity of the dust P map. This would require comparisons between a larger number of subregions, which is beyond the scope of this work.

We are able to reject a number of compact structures as the origin of this discrepancy. Two regions of particular in- terest are the Orion-Eridanus Superbubble (Finkbeiner 2003; Soler et al. 2018) and the Magellanic Stream (Mathewson et al. 1974).

The Former, Which Features Prominently In

Hα maps, occupies about 20% of the full SPIDER region, mostly located in Pd+. Although the Magellanic Stream falls mostly outside the SPIDER region, some high-velocity clouds have been mapped on the outskirts of its bottom-right cor- ner (HI4PI Collaboration et al. 2016). Even though we do not necessarily expect the dust emission from these regions to dominate the polarized emission in our maps, high lev- els of polarization along the edge of the Orion-Eridanus Su- perbubble and hints of variation in dust properties between the Galaxy and the Magellanic Clouds (Galliano et al. 2018) warrant caution. As documented in Appendix A, we find the measured spatial variation in α150 to be robust to masking aimed at probing the impact of these structures.

We further explore the discrepancy in α between subre- gions by repeating this template subtraction analysis with an alternate dust template, constructed by substituting the 217 GHz Planck map for the 353 GHz map. The 217 GHz data also contain substantial polarized dust emission, as evi- denced by the fact that they provide the second-largest con- tribution to the SMICA dust reconstruction (Figure 1). The right panel of Figure 5 shows the 1-D and 2-D likelihoods for r, α95, and α150 in this configuration. We again find r to be consistent (within 0.2σ) between the two subregions, a mod- erate discrepancy in α95 (2.7σ), and a larger discrepancy in α150 (3.5σ). However, while the latter discrepancy has sim- ilar significance to that found with the 353 GHz template, it is in the opposite direction: α150 is found to be lower in Pd− than in Pd+.

−

Figure 5. The XFaster likelihood contours for r, α95, and α150 with the combined SPIDER region in gray and Pd

−Subregions In Orange

and light blue, respectively, computed independently with the 353 GHz dust template (left) and the 217 GHz dust template (right). Central values and 1σ errors for each of the three regions are indicated in the titles for the α parameters. In the context of the simple MBB model of Equation 1, the template scaling parameter α is a function of the dust model parameters—the dust temperature, Td, and the spectral index of polarized emission, βd—as well as the frequencies of the maps used to build the dust template and the frequency of the map to which the template is fitted. Specifically,

(5)

where the superscript “d” added to the frequency of a map indicates that its effective band center is computed for a dust SED instead of the CMB SED, as discussed in Appendix B, and we have used the shorthand x ≡hν/(kTCMB).

Using this relationship, we can translate the 1-D likeli- hoods for α95 and α150 shown in Figure 5 into contour plots in (Td,βd). The results are shown in Figure 6. These parameter constraints allow us to perform several internal comparisons within the MBB model context, which are discussed in the paragraphs below.

Comparing SPIDER frequencies —The βd values inferred from the fitted α95 and α150 show excellent consistency (<1σ) with one another for either choice of dust template, except perhaps in Pd+ at the very lowest dust temperatures (Td ≲

7K).

In other words, if we confine ourselves to a single Planck-derived dust template, the SPIDER data provide no significant evidence of deviation from an MBB SED in ei- ther subregion.

Comparing subregions —The values of α150 obtained using the ν0 = 353 GHz dust template translate into lower values of βd in Pd−compared to Pd+ for any value of Td. Specifically, if we fix Td = 19.6K (Planck Collaboration et al. 2020b) through- out, we find βd = 1.52 ± 0.06 in Pd+ and 1.09 ± 0.09 in Pd−.

Importantly, the value of βd inferred independently from α95 is consistent with that of α150, with comparable significance. Taken at face value, this 3.9σ inconsistency in βd would in- dicate a spatial variation in dust composition between the Pd+ and Pd−subregions.

If we instead fix the dust spectral index to be βd = 1.53 (Planck Collaboration et al. 2020b) in both subre- gions, we find a large difference in implied dust temper-

−2.5 K In Pd+, Td = 9.2+1.1

−0.8 K in Pd−.

Al-

though we certainly expect some lack of uniformity in dust temperature—stemming from spatial variation in the dust’s radiative environment—such a large variation in the temper- ature of the diffuse interstellar medium at high Galactic lat- itude may be unphysical given our current understanding of dust physics (Li & Draine 2001; Draine & Li 2007).

A similar discrepancy between subregions (though of op- posite sign) is visible with the 217 GHz dust template, as shown in the middle panel of Figure 6. Fixing Td = 19.6K with the α150 constraint results in βd = 1.37 ± 0.08 in Pd+

And 2.1+0.3

−0.2 in Pd−, a 3.2σ discrepancy. Alternatively, fixing

−2 K For Pd+, But No Value Of Td Accom-

modates βd = 1.53 within Pd−.

−—The Values Of Βd Derived

from α150 within the Pd−subregion using the ν0 = 217 GHz

˛D Discrepancy Significance [Ff]

Figure 6. 1σ contours of possible Td and βd for the α values found with the XFaster framework and presented in Figure 5. (top) Using

−Region. (Bottom) Mutual

significance of the discrepancy in βd between the two templates, as a function of assumed Td. The βd values found in the Pd

−Region

are discrepant at > 3σ, while the significance of the discrepancy is

< 2Σ In The Pd

+ region. The Planck 2018 all-sky best fit parameters (βd = 1.53, Td = 19.6 K) are also shown for reference (dotted lines). dust template are inconsistent with those derived using the ν0 = 353 GHz template. The bottom panel of Figure 6 shows the significance of this discrepancy as a function of dust tem- perature: it exceeds 3σ (4σ) for any Td ≳5K (Td ≳15K).

Under the assumption that the morphology of the polarized emission from interstellar dust is identical in both templates, this result corresponds to a statistically significant break in βd for any physical Td, with the index having a lower value at the higher frequency. Such an interpretation is compli- cated, however, by a comparison between subregions: the inferred values of βd are lower in Pd−than Pd+ when using the 353 GHz template, but higher when using the 217 GHz template. We can nonetheless infer a statistically significant deviation from a single MBB spectrum within Pd−.

Discussion —Taken together, the observations above point to- ward a more complex picture of the polarized emission from interstellar dust in the SPIDER region than that provided by a single-component MBB model. To summarize: i) Unless Td exhibits large variations at high Galactic latitudes, the spa- tial variation in α between Pd+ and Pd−may be evidence of multiple dust populations (i.e., differing compositions, and thus emissivities); ii) The inconsistency in the value of α de- rived in Pd−with one template and that found in the same subregion with the other template requires either a deviation from an MBB spectrum or a discrepancy in the morphology of polarized dust emission between the two templates, or both.

Such a discrepancy in morphologies could arise from a spa- tially varying dust SED, e.g., due to the presence of multi- ple dust populations. The possible presence of multiple dust populations within Pd−is perhaps not surprising, given the spatial variation in α between Pd−and Pd+ detected with the ν0 = 353 GHz template.

Evaluating this rather complex picture will require more data. Deep observations between 150 and 353 GHz (such as the SPIDER 280 GHz maps) will be particularly valuable in distinguishing between frequency-dependent dust morphol- ogy and complexity in the dust SED. If deviations from an MBB model are borne out, this may provide new insights into the properties of the interstellar medium, and associated modeling uncertainties would need to be taken into account in upcoming searches for cosmological B-modes.

4. Testing Standard Dust Modeling

The SMICA framework offers a high degree of flexibility in modeling the characteristics of dust. The SMICA pipeline implemented for the analysis in SPIDER Collaboration et al.

(2022) incorporates a MBB model for the dust foreground

Component With The Following Characteristics:

• A single βd parameter that is common across all mul-

Tipoles And Polarizations,

• A dust amplitude Ad that is free to vary across multi-

Poles And Polarizations,

• A δ-function prior of Td = 19.6K to fix the dust tem-

Perature At The Planck All-Sky Value, And

• A Gaussian prior on βd centered at the Planck all-sky value βd = 1.53, with a generous width of σβd = 1.5.

Spider Collaboration

Table 1. The best-fit dust amplitude Ad for each of the input fre- quency maps relative to that of the Planck 353 GHz map. The val- ues tabulated here are also plotted in Figure 7. Best-fit values are computed as the median of the posterior distribution, with 1σ errors determined from the 68% interval on either side of the median.

0.123 ± 0.014

In this section, we quantify how these foreground model- ing choices impact the best-fit CMB and foreground param- eters recovered with the combined SPIDER and Planck data.

Throughout this section, we leave the dust temperature fixed, due to a lack of sufficient constraining power and frequency coverage to simultaneously estimate both βd and Td, while varying the constraints on Ad and/or βd. Here, unlike the dis- cussion in Section 3.3, we apply the analysis to the full SPI- DER region. The results in this section are therefore driven by the higher signal-to-noise component, corresponding ap- proximately to the Pd+ contours of Figure 6.

4.1. Sed Modeling Of Polarized Dust Emission

We begin by testing the SED model of dust emission by fitting an independent amplitude Ad at each frequency, oper- ating under the assumption that this amplitude remains con- sistent across multipoles. As discussed in SPIDER Collabo- ration et al. (2022), dust and noise exhibit similar scaling be- haviors with frequency, making it challenging for the SMICA algorithm to distinguish between the two components. By relaxing the prior constraint on βd and fitting for the dust am- plitudes directly, we are able to circumvent this noise/dust scaling degeneracy. The resulting amplitudes can then be fit to a MBB model to recover the best-fit βd value.

The dust amplitudes recovered with this algorithm are listed in Table 1 for each of the SPIDER and Planck fre- quency bands, and the resulting MBB model fit is illustrated in Figure 7. Fitting a spectral index to each set of six fre- quency maps results in a best-fit value of βd of 1.45 ± 0.05 (1.47±0.06) for the EE (BB) components, with χ2 values of 0.7 (3.0), respectively.4 With approximately four degrees of freedom, these χ2 values indicate that a single-component MBB model is an adequate description of the SPIDER + 4 For comparison, we note that the template fit in the combined region from Section 3.3 corresponds to a value βd = 1.50 ± 0.05 for the combined EE & BB spectra.

Bb: ˛D = 1:47 ± 0:06, Ffl2 = 3:0

Figure 7. Testing the fidelity of the MBB dust model in the SPI- DER high-latitude region for E- (top) and B- (bottom) modes. All data are plotted relative to the best-fit MBB model for that polar- ization component (gray band indicates the 1σ fit envelope), and account for the detector bandpass at each frequency. The horizon- tal error bars indicate the effective detector bandwidth over which the amplitudes are computed. The SMICA best-fit dust amplitudes (+) are consistent with the best-fit MBB model. The SPIDER data (red) have smaller error bars on Ad, and therefore more constraining power, than the Planck data (black) in nearby bands.

Planck dataset, thus justifying the use of the MBB model for constraining foreground power in the CMB B-mode analy- sis. Additionally, Figure 7 illustrates the improved constrain- ing power of the SPIDER data at 95 and 150 GHz in this re- gion of the sky relative to that of the nearby Planck bands at 100 and 143 GHz.

4.2. Angular Scale Dependence of Dust Spectral Index Next we test the assumption of a scale-independent SED by fitting the MBB model independently for each polariza- tion as a function of ℓ.

The Results Of This Fit For Βd Are

shown in Figure 8. The best-fit spectral index values agree to within ∼0.5σ between the E and B polarization components across all angular scales, providing no evidence for includ- ing a polarization-dependence in the model. Comparing the best-fit βd values averaged over larger (ℓ< 140) and smaller (ℓ> 140) angular scales shows agreement to within 2σ.

When analyzed over the full SPIDER region, the data do not reveal any strong evidence of variations in spectral index

Authors:

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

94143, Usa.

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

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

14Jlvmi Consulting Llc, Dousman, Wi, Usa

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

Abstract

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

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

Introduction

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

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

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

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

●

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

●

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

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

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

Hyperpolarized 13C-Pyruvate Preparation

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

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

General Considerations

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

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

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

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

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

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

Personnel

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

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

Equipment And Facility

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

Material Handling

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

Pharmacy Kit Filling And Assembling

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

Quality Control And Dose Release

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

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

The Final Dose Release And Injection

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

Some Key Challenges

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

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

Current Practices

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

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

In House

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

Summary

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

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

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

Mri System Setup And Calibrations

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

Imaging System

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

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

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

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

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

Rf Coils

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

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

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

Provide B1 Transmit Across The Fov (B1

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

B1

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

+ Profile But Has Been Used Because Of

relatively easy integration into the scanner bore. B1

+ Variation Results In Variations In The Flip

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

Homogeneous B1

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

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

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

(1)

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

Tx = Transmit

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

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

Phantoms

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

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

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

+) And Receive (B1

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

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

Prescan Calibration

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

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

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

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

+ Inhomogeneity As Well

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

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

Power [Kw]

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

8

13C-bicarbonate doped with dimethyl silicone, various

Maximum Values

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

Summary

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

+ Profiles. The

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

For Calibration Of B1

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

Acquisition And Reconstruction

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

+ Inhomogeneity,

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

Acquisition And Reconstruction Methods

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

Mrs/I Methods Specifically

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

Chemical Shift

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

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

Their Application To Different

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

The Majority Of

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

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

Prostate Studies

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

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

Heart Studies

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

Brain Studies

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

Abdomen And Breast Studies

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

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

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

1H Imaging

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

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

Reported Study Parameters

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

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

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

(B)

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

Summary

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

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

Data Analysis And Quantification

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

Metrics

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

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

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

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

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

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

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

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

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

Visualization

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

Metrics

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

Parameter Encoding

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

Anatomical Context

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

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