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October 31, 2018

First Microlensing Candidates From The MEGA Survey⋆Of M31 Jelte T.A. de Jong1, Konrad H. Kuijken2,1, Arlin P.S. Crotts3, Penny D. Sackett4, Will J. Sutherland5, Robert R. Uglesich3, Edward A. Baltz3, Patrick Cseresnjes3, Geza Gyuk6, and Lawrence M. Widrow7

(The Mega Collaboration)

3 Columbia Astrophysics Laboratory, 550 W 120th St., Mail Code 5247, New York, NY 10027, United States

Weston Act 2611, Australia

5 Institute of Astronomy, Madingley Rd, Cambridge CB3 0HA, United Kingdom

States

Received 24 September 2003 / Accepted 24 September 2003 Abstract. We present the first M31 candidate microlensing events from the Microlensing Exploration of the Galaxy and Andromeda (MEGA) survey. MEGA uses several telescopes to detect microlensing towards the nearby Andromeda galaxy, M31, in order to establish whether massive compact objects are a significant contribution to the mass budget of the dark halo of M31. The results presented here are based on observations with the Isaac Newton Telescope on La Palma, during the 1999/00 and 2000/01 observing seasons. In this data set, 14 variable sources consistent with microlensing have been detected, 12 of which are new and 2 have been reported previously by the POINT-AGAPE group. A preliminary analysis of the spatial and timescale distributions of the candidate events support their microlensing nature. We compare the spatial distributions of the candidate events and of long-period variable stars, assuming the chances of finding a long-period variable and a microlensing event are comparable. The spatial distribution of our candidate microlensing events is more far/near side asymmetric than expected from the detected long-period variable distribution. The current analysis is preliminary and the asymmetry not highly significant, but the spatial distribution of candidate microlenses is suggestive of the presence of a microlensing halo.

Key words. Gravitational lensing – M31: halo – Dark matter

1. Introduction

One of the astrophysical solutions to the galactic dark mat- ter problem would be the presence of a significant amount of undetected compact objects in the halos of galaxies. These MACHOs (Massive Astrophysical Compact Halo Objects) can be detected using gravitational microlensing (Paczynski 1986).

According to gravitational lensing theory the measured bright- ness of a background source will temporarily increase if a mas- sive compact object moves close enough through our line of sight towards the background source.

During the last decade, the MACHO (Alcock et al. 1993) and EROS (Aubourg et al. 1993) collaborations have been monitoring fields in the Large and Small Magellanic Clouds

E-Mail:

⋆Based on observations made with the Isaac Newton Telescope op- erated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de

Astrofisica De Canarias

(LMC and SMC) in order to detect such events. After 5.7 years of observing the MACHO group found 13-17 microlensing events towards the LMC, and concluded that up to 20% of the Milky Way dark halo may consist of compact objects of mass 0.15 - 0.9 M⊙(Alcock et al. 2000). The EROS collaboration has found 3 microlensing events towards the LMC and puts strong constraints on the fraction of dark matter in the form of com- pact objects (Lasserre et al. The results of both groups are, however, consistent with ∼10% of the dark halo mass con- sisting of compact objects of ∼0.5M⊙(e.g. Milsztajn 2002).

Looking for microlensing events in the nearby Andromeda galaxy (M31) has several advantages over Magellanic Clouds searches (Crotts 1992; Baillon et al. 1993). Because of the ge- ometry the microlensing optical depth can be up to ten times larger in parts of M31. In combination with the extremely high density of background stars, this results in a highly en- hanced microlensing rate. Due to the high inclination of the disk of M31, it should be possible to use microlensing to con- strain the mass contribution of compact objects to the dark halo (Baltz, Gyuk & Crotts 2003; Gyuk & Crotts 2000; Kerins et al.

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Jelte T.A. de Jong et al.: First Microlensing Candidates From The MEGA Survey Of M31 2001). In the presence of a significant microlensing halo, the microlensing rate should be asymmetric, with more microlens- ing taking place towards the far side of the disk than to the near side, because the line-of-sight through the halo is longer towards the far side.

Besides these advantages, M31 microlensing also has some problems. Because of the large distance the stars are faint and generally unresolved from the ground. However, using spe- cial techniques, it is possible to detect microlensing in M31 (e.g. Crotts & Tomaney 1996; Paulin-Henriksson et al. 2003; Calchi Novati et al. 2003). Three collaborations are currently working on microlensing surveys in M31, namely POINT- AGAPE (Auri`ere et al. 2001), WeCAPP (Riffeser et al. 2001) and MEGA (Crotts et al. 2001).

And

Andromeda (MEGA) collaboration has performed an in- tensive four-year survey of two large fields in M31 plus extended baseline observations in order to measure the mi- crolensing optical depth due to a possible MACHO halo.

In this paper we present the first microlensing candidates resulting from the analysis of the 1999-2000 and 2000-2001 season data obtained at the Isaac Newton Telescope at La Palma. In section 2 we briefly describe the dataset and methods used. The microlensing candidates are presented in section 3. Our discussion and conclusions are presented in section 4.

Finally, future work is outlined in section 5.

2.1. Dataset

MEGA uses several telescopes to monitor two wide fields, cov- ering a total area of 0.57 square degrees. For the current analy- sis, observations done with the Wide Field Camera (WFC) on the Isaac Newton Telescope (INT) were used. The layout of the WFC chips on M31 is shown in Figure 1. We present mi- crolensing events from the 1999/2000 and 2000/2001 observ- ing seasons. The observations in the first season (99/00) were spread over 57 nights between August 1st 1999 and January 4th 2000 and were taken in the Sloan r′, g′ and i′ broad bands.

The r′ dataset is the largest with 57 epochs, whilst the g′ and i′ datasets contain 41 and 24 epochs respectively. During the second observing season (00/01) 90 epochs were obtained in both r′ and i′, between August 1st 2000 and January 23 2001.

Observations were spread equally over both fields. The expo- sure time per epoch ranges between 5 and 30 minutes and is typically 10 minutes. Because the WFC is not always mounted on the INT, the epochs tend to cluster in blocks of two to three weeks. Part of the data from the 2001/2002 season has been used as well. From this third season, 19 epochs in r′ and i′ taken between August 13th 2001 and November 18th 2001 were used to extend the baselines of the events from the first two seasons in order to exclude long period variable stars. These data were not used to detect more microlensing events.

Fig. 1. The layout of the two INT Wide Field Camera (WFC) fields in M31 used for the microlensing search described in this paper. The WFC has four 2048x4100 pixel chips with a pixel scale of 0.333′′, offering a field of view of approximately 0.25□o. With this field layout we cover a large part of the far side (SE) of the disk of M31 as well as part of the near side.

Also plotted are the positions of the candidate microlensing events in our sample (full circles). Note that our events 7 and 11 correspond to the events PA-99-N2 and PA-00-S4 reported previously by POINT-AGAPE. Part of the south field close to the bulge is not used for our analysis, since the image subtrac- tion is not of high quality in this very high surface brightness area. This region is indicated in the uppermost chip of the south field. The two POINT-AGAPE events not present in our sample are indicated with the open circles.

2.2. Data Reduction

Standard data reduction, including bias subtraction, trimming and flatfielding was performed in IRAF. Because of the high stellar density in M31 and its large distance, the background source stars are usually resolved only while they are be- ing lensed and sufficiently magnified. To detect microlensing events in these fields, we use the Difference Image Photometry (DIP) method as described by Tomaney & Crotts (1996). This method involves subtracting individual images from a high quality reference image, resulting in difference images in which variable objects show up as residuals.

Below we outline the steps of the DIP pipeline that was used. All operations are done in IRAF, using the DIFIMPHOT package written primarily by Austin Tomaney, unless explic- Jelte T.A. de Jong et al.: First Microlensing Candidates From The MEGA Survey Of M31

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itly stated otherwise.

• Astrometric Registration And Stacking Of Images

All images are transformed to a common astrometric reference frame. By stacking high quality images from the 1999 season, a high signal-to-noise reference image was made. Per night all exposures are combined separately for each band. Each epoch corresponds to the combination of all frames taken in the same band in one night. The Julian date of the epoch is taken as the weighted average of the Julian dates of the individual frames.

• Image Subtraction

From the single epoch images the high signal-to-noise ref- erence image is subtracted, after photometric calibration and matching of the point spread function (PSF) between the im- ages (Tomaney & Crotts 1996). The shape of the PSF is mea- sured from bright, unsaturated stars in the images that are being matched. By dividing the PSFs in Fourier space a convolution kernel is calculated with which the better seeing image (usually the reference image) is degraded.

• Variable Object Detection

The resulting difference images are dominated by shot noise in which variable sources show up as positive or negative residu- als, depending on the flux difference of the object between the single epoch image and the reference image. Due to fringing, the i′ difference images are of poorer quality than the r′ dif- ference images. SExtractor (Bertin & Arnouts 1996) is used to detect residuals in all r′ difference images from the first two observing seasons. The catalogs with residuals are cross- correlated to obtain a catalog with all variable objects in the surveyed fields. As a first selection to get rid of noisy detec- tions, we demand that objects have to be detected in at least two epochs.

• Lightcurves And Epoch Quality

Lightcurves for the variable sources are obtained by perform- ing PSF fitting photometry on the residuals in the difference images, using the PSF shape measured from the bright unsatu- rated stars. Several epochs turned out to give problematic dif- ference images for a number of different reasons. Epochs with seeing worse than 2.0′′ do not give clean difference images and were discarded. A small number of epochs were overexposed and had to be discarded as well.

Lightcurves were also produced at “empty” positions, i.e. posi- tions were no variability was detected. Flat line fits were done to these empty lightcurves to check the error bars on the fluxes derived from statistics of the PSF fitting photometry. For each epoch, the distribution of the deviations from the flat lightcurve fits weighted by the error bar returned by the photometry rou- tine was examined. In some cases this distribution showed broad non-gaussian wings, and these epochs were discarded.

Typically they were associated with highly variable seeing be- tween the individual exposures. In other cases, the normalized error distribution was gaussian, but with dispersion higher than one. In these cases the error bars were renormalized appropri- ately.

The typical number of epochs that were left after the pro- cedure described above are tabulated in table 1 for each filter and field for the 99/00 and 00/01 seasons. From these epochs the lightcurves were constructed that were used for the analysis presented in this paper.

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Table 1. Overview of the number of epochs used for seasons 1 and 2, field and filter. F1 is the north field and F2 is the south field.

2.3. Event Selection

The final dataset consists of lightcurves of 118,424 variable sources, practically all of which are periodic variable stars. Finding candidate microlensing events in such a large num- ber of lightcurves is no trivial problem. A procedure to se- lect lightcurves that are compatible with microlensing must be aimed at recognizing the characteristics of a microlensing lightcurve while taking into account computing speed, and the quality of the available data. Since the quality of the i′ band data was clearly poorer than the quality of the other bands, and since g′ data were only available for the first season, we de- cided to use the r′ data as the main basis for candidate selec- tion. Another advantage of the r′ data is that they have much better sampling density in the first season than do i′ and g′ data separately. Thus, the first steps of the filtering process involved only r′ data, after which the i′ data are used to further analyse the r′ microlensing candidates.

A microlensing event caused by a single lens has a char- acteristic shape and a flat baseline. The selection steps based purely on the r′ lightcurves are aimed at selecting lightcurves with flat baselines and well sampled, significant peaks which fit the characteristic microlensing shape well. A detailed descrip- tion of these steps is given in Appendix A1. To make sure these selection steps do a good job selecting microlensing events and rejecting long-period variable stars, Monte Carlo simula- tions of microlensing events and long-period variables were performed and used to fine tune the selection procedure. Based on just the r′ data we select 1,347 lightcurves.

Colour information can be used for the microlensing can- didate selection for several reasons. Contrary to variable stars, microlensing events are intrinsically achromatic, meaning that the colour of the observed difference flux remains the same during the event. Furthermore, long-period variable stars that might be mistaken for microlensing are very red. Because of this, the brightness variations are also more pronounced in i′ than in r′. Further selection steps, described in more de- tail in Appendix A2, include a colour cut designed to reject long-period variables and a goodness of fit criterion for the i′ lightcurve. For the latter, the i′ lightcurves are fit with a stan- dard microlensing lightcurve with the shape parameters found for the r′ lightcurves, as a test for achromaticity.

This complete automated selection procedure results in 126 candidate microlensing events from the 99/00 and 00/01 ob- serving seasons. Unfortunately, rather lenient χ2 cuts had to be used for the goodness of fit criteria. This is due to the photome- try being too sensitive to nearby variable sources, as described

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Jelte T.A. de Jong et al.: First Microlensing Candidates From The MEGA Survey Of M31 Fig. 2. Lightcurves of the 14 microlensing candidate events. This page shows candidates 1 through 5, with the r′ lightcurves plotted in the upper panel and the i′ lightcurves in the lower panel. The Julian Date of the zeropoint of the time axis is 2451393, which corresponds to August 1st 1999.

Jelte T.A. de Jong et al.: First Microlensing Candidates From The MEGA Survey Of M31

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Fig. 3. Data points from the baseline of event 10, but now the ∆Flux is plotted as function of the seeing. During the period from which these points are taken, a variable source located about 7 pixels away from the event caused a strong residual in the difference images. There clearly is a trend with worse seeing corresponding to lower fluxes.

in more detail in Appendix A. Because of this, the sample still contains lightcurves with slightly variable baselines. The lightcurves and the difference image residuals of these candi- date events had to be inspected visually to establish whether any additional variability was intrinsic to the variable source or was caused by nearby sources. An effort to improve the photometry in the presence of neighbours is underway. The lightcurves with baseline variability that could not be attributed to nearby variable sources, in total 67, were thrown out. In a further 39 cases, the detected candidate event was actually caused by bad pixels and these were discarded as well, so af- ter visual inspection, 21 events remain that are consistent with microlensing based on the 2 year lightcurves. Finally, part of the data from the third (01/02) season were used to extend the baselines of these 21 events, 7 of which showed variability in the third season. The final set of candidate microlensing events consists therefore of the 14 events described in the following section.

3. Results

The lightcurves of the 14 candidate microlensing events are shown in figure 2; their positions are plotted in figure 1. August 1st 1999 was taken as the zero point of the time scale in the lightcurve plots. The important fit parameters are tabulated in table 2. For illustration we show in figure 4 thumbnails of the difference images and single epoch images for events 5, 7 and 11. All difference image thumbnails for all events are available on-line at http://www.astro.rug.nl/∼jdejong/eventtn.

Inspection of the lightcurves in figure 2 indicates that the baselines are not always completely flat, this is especially the case for the i′ lightcurves. When looking at the difference im- ages, it becomes clear that for these events, secondary bumps in the lightcurve are caused by variable objects very close to the position of the event, rather than by variability in the events themselves. For example, the bump around day 100 in the lightcurve of candidate event number 2, is caused by a bright- ening source located only 4 pixels away from the event. In the i′ data, this problem occurs more frequently because of the higher density of detected variable sources and the effect is stronger because of the stronger variability at longer wavelengths.

Not only can nearby variable sources result in trends in the lightcurves, they can also increase the scatter in the flux. The size of the aperture and the ring that is used for sky subtraction depends on the seeing, meaning that a nearby variable does not always influence the photometry and also not necessarily in the same way. As an example of this, we show in figure 3 the flux as a function of the seeing for the part of the baseline of event 10.

Clearly, differences in seeing between the epochs will create extra scatter in the baseline. Below we discuss the possible reasons for additional vari- ability in each of the event lightcurves.

Event 1: This event has a bright periodic variable star at a dis- tance of 5 pixels, which is probably the cause of the noisy base- line in both r′ and i′.

Event 2: This event also has close variable neighbours. In the r′ difference images a variable source is located at only 3 pix- els from the event. This source peaks around day 100, causing a bump in the r′ lightcurve. In the i′ difference images there are two additional bright variables, both of them at about 10 pixels distance. These sources cause the noisy nature of the i′ baseline.

Event 3: Although the r′ baseline is very clean, the i′ baseline shows quite some variability, especially in the second season. Again this is caused by a very close variable source, at 3 pixels distance. This source has a bright episode between days 440 and 470, which causes the high fluxes in this period in the i′ lightcurve.

Event 4: The baselines of this event look quite flat, but the peak in the i′ data is not very symmetric. The sudden drop in flux after day 420 coincides with the sharp brightening of a bright variable source at 14 pixels distance.

Event 5: This event has several variable sources nearby. Unfortunately the closest one, at about 4 pixels, is also the brightest, which especially in the i′ lightcurve causes a lot of noise. See figure 4 for thumbnails of this event.

Event 6: In the second season the baseline shows a periodic variability, which is caused by a periodic variable star at 6 pix- els from the event. A second close variable, at 5 pixels, shows up only in the first season in r′, but pops up also in the second season in i′ and is very bright in the first season. Together, these variables cause the i′ baseline to be be rather messy.

Event 7: The baselines of this very high S/N event are quite well behaved in both r′ and i′, but there is a quite bright variable source located at 15 pixels, which may cause some deviations.

However, the deviations in the i′ data from the Paczynski fit between days 100 and 150 are too large to be caused by these near neighbours. Also from this event, some thumbnails are shown in figure 4.

0.3 ± 0.4

Table 2. Fit parameters for the 14 candidate microlensing events. The tmax and tFWHM values are based on full parameter fits to the r′ lightcurves. Also listed are the magnitude of the difference flux at maximum amplification and the r′-i′ colours where possible. For the short events, i.e. tFWHM in the order of a few days, the uncertainties are large, because the time sampling of the data is relatively sparse compared to the width of the peak. Peak times are in days after August 1st 1999.

Event 8: Even though there is a variable source located at 7 pixels distance from this event, the baselines are quite well be- haved.

Event 9: Two faint variables are located at about 4 and 8 pixels distance from this event, and a bright one at 12 pixels. The lightcurves do not appear to be affected substantially.

Event 10: Here the noisy baseline in i′ and the two deviating points in the r′ lightcurve around day 100 can be attributed to the same variable source 7 pixels away.

Event 11: While the r′ baseline of this high amplification event is well behaved, the i′ baseline is not completely flat. In the difference images there is a hint of a weak variable source a few pixels away, which is probably the cause of the small baseline wiggle. See figure 4 for thumbnails of this event.

Event 12: The r′ lightcurve of this event is quite well behaved and there are no nearby variable sources. The reason for the noise in the i′ lightcurve is not clear.

Event 13: A fairly bright variable source is situated 16 pixels away from this event, but the lightcurves in both r′ and i′ are well behaved.

Event 14: The noise in the lightcurves and more particularly the small bump in the i′ lightcurve around day 370 is due to a variable source 3 pixels away from the event.

3.1. Point-Agape Events

The POINT-AGAPE group uses the same data for their mi- crolensing survey towards M31, although their pixel lensing technique is different (Paulin-Henriksson et al. 2003). Based on the same two-year dataset, they find four high signal-to-noise microlensing events. Two of these events are also present in our sample, namely PA-99-N2, our event number 7, and PA-00-S4, our event number 11.

The fact that our sample of candidate microlensing events is much larger is caused by the severe selection criteria used Fig. 5. The lightcurves in r′ (upper panel) and i′ (lower panel) of the microlensing event PA-99-N1, reported by POINT- AGAPE. In the i′ data the variability in the baseline, caused by nearby variables, is high enough to give a χ2 which is too high to pass our selection procedure.

by POINT-AGAPE, that limit the number of events found. For example, POINT-AGAPE demands FWHM timescales smaller than 25 days and much higher signal-to-noise than we. The fol- lowing two events reported by the POINT-AGAPE team are not in our sample of candidate microlensing events.

• Pa-99-N1

This event did not pass our filtering procedure because of too large variability in the i′ baseline caused by a very closeby vari- able star. Our lightcurves of this event are shown in figure 5.

• Pa-00-S3

Very close to the bulge of M31 the surface brightness becomes very high and our difference images become very noisy and of low quality. This event is located in a part of the field that is not used for the current analysis for this reason. In figure 1 the region that is not used in our analysis is indicated.

4. Discussion

Due to the nature of M31 microlensing, it is very difficult to de- termine the nature of the lensing object in individual microlens- ing events. In classical microlensing the mass of the lens, the relative motion of the lens with respect to the source and the distance to the lens are usually unknown and degenerate pa- rameters. In difference-image lensing there is an additional un- known, namely the unlensed flux of the source. If a conclusion about the existence and/or nature of a MACHO population in the halo of M31 is to be drawn from a microlensing survey, statistical methods have to be used.

By modeling the population of stars that can be lensed and the population of objects that can act as lenses, predictions can be made about the rate of occurrence, the spatial distributions, and the timescales of microlensing events. All these data can be used to constrain the lens populations responsible for ob- served microlensing events (Baltz, Gyuk & Crotts 2003, here- after BGC; Kerins et al. 2001).

To compare our sample of candidate microlensing events with rate maps as published by BGC, the detection efficien- cies and observing characteristics have to be carefully modeled, which will be done in a future paper. Instead of a full statistical analysis of the current sample, we restrict our discussion to a simple analysis of the spatial and timescale distributions of the candidate events to see if they are consistent with predictions for halo lensing and lensing by stars in M31.

4.1. Timescale Distribution

The timescale of a microlensing event depends on the relative velocities of the source and the lens and the size of the Einstein radius, which in turn depends on the mass of the lens and the geometry (eq. A.2). In the case of M31 microlensing we can assume that DOL = DOS and since the Einstein ring crossing

(1)

where vperp is the relative speed between lens and source pro- jected on the sky. The tFWHM that we measure is related to tE according to equation A.5.

For self-lensing, i.e. lensing by stars, this translates into a timescale distribution that varies spatially. In the bulge, veloc- ities are relatively high and distances between lens and source relatively short (compared to lensing by halo objects), therefore event durations will be relatively short. In the disk, relative ve- locities are much slower and event durations longer than in the bulge. On top of that, the timescales are expected to rise when going to larger radii, since the random velocities of the stars in a galactic disk are proportional to the root of the surface den- Fig. 6. For the 14 candidate microlensing events, the logarithms of the FWHM timescales are plotted against the local r′ surface brightnesses. At high surface brightnesses the timescales tend to be shorter than in low surface brightness regions.

sity (Bottema 1993). Roughly speaking we can say that aver- age self-lensing timescales are inversely correlated with surface brightness; in higher surface brightness regions the timescales are expected to be shorter.

For halo lensing, relative velocities are higher than for disk- disk lensing, but because of the larger lens-source distance the event durations are still relatively long. Because the relative ve- locities and distances do not change much within the observed field, the timescale distribution of halo-lensing events should be spatially uniform. Plots of the expected timescale distribu- tions for different lines of sight towards M31 are given by BGC for stellar self-lensing and halo lensing combined and reflect these trends.

In figure 6 we plot for our 14 microlensing candidates the logarithm of tFWHM versus the r′ surface brightness at their locations. The candidate events close to the center of M31, in locations with surface brightness brighter than 19.5 magr′ arcsec−2, all have event durations in the order of a few days. Most of the candidates in the low surface brightness re- gions have significantly longer timescales. That this distribu- tion is exactly what is expected for microlensing and the fact that the timescales are consistent with the timescales predicted by BGC are further indications that our sample of candidates consists of actual microlensing events.

4.2. Spatial Distribution

The expected spatial distribution of stellar self-lensing events is strongly concentrated to the center because both the density of possible source stars and lenses is highest there. Furthermore, the spatial distribution is nearly symmetric from the far to the near side of the disk of M31 (BGC), so in the case of only

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Jelte T.A. de Jong et al.: First Microlensing Candidates From The MEGA Survey Of M31 self-lensing the number density of events should be the same at the same radius on both the far and near side. The stellar halo of M31 has not been taken into account by BGC, but is not expected to change the symmetry significantly, since, like the bulge, it acts both as a lens and as a source population. If the spheroid has the same M/L as the disk, for every event caused by a spheroid-lens and disk-source pair, there is a disk-lens and spheroid-source pair event, as is the case with disk-bulge and bulge-disk lensing (BGC). In case of heavy extinction in the disk, the spheriod could induce an asymmetry in the lensing rate.

Dark halo lensing on the other hand will induce an asym- metric microlensing distribution, because it only acts as a lens population. Due to the longer line-of-sight through the M31 halo towards the far side of the disk, the microlensing opti- cal depth is much higher on the far side than on the near side.

Therefore, an asymmetry in the density of microlensing events between the far and near side is a strong indication of a mi- crolensing halo. Halo lensing is also more likely near the center because of the higher surface density of possible source stars, but drops offmuch more slowly, since the surface density of halo lenses should not drop offvery quickly.

Without knowing the detection efficiency of microlensing events, the number of detected candidate events is hard to in- terpret quantitavely. Since the detection efficiency might vary with position, their spatial distribution is also hard to interpret.

However, if we assume that the spatial distribution of variable stars is symmetric over M31, we can get an idea of the variation of the detection efficiency with position by looking at the spa- tial distribution of the detected variable stars. The variable stars that are most likely to be mistaken for microlensing are vari- ables with periods longer than 150 days. In table 3 we present the detected numbers of variables with periods between 150 and 600 days, for 300x324′′ subregions in our field of view.

For each subregion the actual area, corrected for area lost due to bright stars and diffraction spikes, is also tabulated. In figure 7 we show the corresponding variable star density map, with the positions of the 14 candidate events plotted on top.

To select the long-period variables (LPVs) from the com- plete set of lightcurves, all lightcurves were checked for peri- odic behaviour using the Numerical Recipes (Press et al. 1992) algorithm based on the Lomb method (1976) for spectral anal- ysis of unevenly sampled data. The lightcurves for which a pe- riodicity between 150 and 600 days was found with very high significance were selected. In total 32,841 variables were se- lected, excluding the part of the south field close to the bulge and one other small part at the edge of the south field, where a very bright foreground star is located.

In the spatial distribution of the LPVs we see no surprises. The surface density of these objects is correlated with the sur- face brightness. Since we are interested in a possible asymme- try in the distribution of the candidate microlensing events, we compare the relative distributions of variables and events over the near and the far side of M31. We assume that the LPVs are a good tracer of the population of possible microlensing source stars and that the chances of detecting LPVs and microlens- ing events are the same. The detection efficiencies of both will Fig. 8. Upper panel: histogram of the surface densities of long- period variable stars (LPVs) in small 150x162′′ regions on the far side of the M31 disk. The thin, black bars show in which LPV surface density bins the far side microlensing candidate events are located. Lower panel: histogram of the surface den- sities of LPVs in small 150x162′′ regions on the near side. The thin, shaded bars show the numbers of candidate microlensing events predicted by scaling the numbers of far side events with the ratio of regions on the near and far side in each LPV density bin. In total 6 events are expected on the near side, but only 2 are detected, shown by the thin, black bars.

depend on the surface brightness of the disk and be subject to extinction effects. To investigate the different parts of the far and near side of the M31 disk that we sample, we divide each subregion in table 3 in 4 smaller 150x162′′ pieces. In the upper panel of fig- ure 8 we plot the distribution of the LPV surface densities of these small subregions. The smaller, black histogram shows the distribution of the far side candidate events over the LPV den- sity bins. If the microlensing rates are intrinsically near/far side symmetric, as we assume the LPVs to be, the expected number of candidate events on the near side can be determined for each LPV density bin, by scaling the number of far side events. We can only do this for the low surface density bins, since the high surface density bins are not populated sufficiently. However, since close to the center of M31 the microlensing optical depth is dominated by stellar self-lensing they should not affect the symmetry of the spatial distribution. The lower panel of figure 8 shows the distribution of the subregions on the near side over the LPV density bins. The shaded histogram shows the distri- bution of the far side candidate events scaled to the near side LPV density distribution, and the black histogram the actual near side candidate events.

Whereas 6 near side candidate events are predicted from the distribution of the 9 far side events in areas with fewer than 10 LPVs per square arcsec, only 2 are detected. Thus,

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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