Hexapod Robot Project

Warsaw 2021

The Araucaria Project: Improving the cosmic distance scale Editorial board: Paulina Karczmarek, Megan Lewis, Grzegorz Pietrzyński Photo: All the authors, with the addition of Celeste Burgos and Michael Ramolla, are credited for the photos and images in this book.

Back Cover: Grzegorz Pietrzyński

Front cover: Merrillie Redden Photography – merrillie.com Layout, graphic design and printing: Wydawnictwo Aleksander Copyright© Nicolaus Copernicus Astronomical Center of the Polish Academy of Sciences, Warsaw 2021

Opyright© Wydawnictwo Aleksander, Pułtusk 2021

Published by: Nicolaus Copernicus Astronomical Center

Wolfgang Gieren And Grzegorz Pietrzyński

A brief history of the Araucaria Project ...................................................................... 8 Paulina Karczmarek, Wolfgang Gieren, Grzegorz Pietrzyński Optical survey of classical Cepheids ......................................................................... 18

Wolfgang Gieren

Near-infrared follow-up of extragalactic classical Cepheids previously discovered in optical photometric surveys ................................................... 21

Arek Górski

Tip of the Red Giant Branch stars as distance indicators ............................................... 25

Arek Górski

Red Clump stars as distance indicators ..................................................................... 28

Bartłomiej Zgirski

Distance determinations based on carbon stars .......................................................... 31

Paulina Karczmarek

RR Lyrae stars as near-infrared distance indicators to Local Group galaxies ..................... 34

Piotr Wielgórski

Type II Cepheids as distance indicators .................................................................... 37

Ouise Breuval

Impact of metallicity on the Leavitt Law .................................................................... 40

Ksenia Suchomska

Physical and orbital properties of Bulge late-type eclipsing binaries ................................ 43

Alexandre Gallenne

The role of interferometry in measuring high-precision distance and mass of binary stars ... 46

Grzegorz Pietrzyński

Distance to the Magellanic Clouds accurate to 1% from eclipsing binaries .......................... 49

Pierre Kervella

Multiplicity among classical Cepheids and RR Lyrae stars ............................................. 52

Gergely Hajdu

RR Lyrae stars in binary systems ............................................................................. 55

Bogumił Pilecki

High-precision astrophysics of Cepheids in binary systems .......................................... 58

Jesper Storm

The Baade-Wesselink technique and the effect of metallicity on the Leavitt law ................... 61

Nicolas Nardetto

The Nice contribution: The projection factor of Cepheids ............................................. 64

Rolf Kudritzki

Flux weighted gravity-luminosity relationship: A new distance indicator ........................ 67

Nicolas Nardetto

The Nice contribution: CHARA/VEGA and the SBCR of early-type stars ............................ 71

Ónica Taormina

Toward Early-type Eclipsing Binaries as Extragalactic Milestones .................................. 74

Fabio Bresolin

Metallicities of nearby galaxies ................................................................................ 77

Radosław Smolec

Modelling of classical pulsators ............................................................................... 80

Paulina Karczmarek And Radosław Smolec

Binary Evolution Pulsators – a new class of pulsating stars ............................................ 83

Weronika Narloch

Non-pulsating stars in the instability strip of classical Cepheids .................................... 86

Ezary Gałan

Atmospheric parameters and abundances of the eclipsing binary systems components from high-resolution spectra .................................................................................. 89

Weronika Narloch

Age-metallicity relation of star clusters in the Magellanic Clouds .................................... 92

Egan Lewis

Maser-derived parallax measurements of Miras ......................................................... 95

Nicolas Nardetto

The Nice contribution: The CHARA/SPICA interferometer ............................................ 97

Rolf Chini

Observatorio Cerro Armazones – the history, the present, and the future ....................... 100 Contributors ................................................................................................. 106 Beyond the Araucaria Project: hikes, social gatherings and conferences .............. 108

Up The Distance Scale. The Main Systematic

uncertainty in the HST Key Project seemed to be the largely unknown effect of environmental properties, mostly metallicity, on the luminosities of classical Ce­ pheid variables which had been extensively used by the Key Project to determine the distances to supernova Ia host galaxies, and to calibrate these SN Ia as standard candles reaching out into the unperturbed Hubble flow where the Hubble constant can be reliably determined.

Our conclusion was that it was absolutely necessary to com­ plement the HST Key Project work with a thorough determi­ nation of environmental effects on Cepheids, and a more ac­ curate distance to the Large Magellanic Cloud which served as the anchor galaxy to the HST Key Project SN Ia host gal­ axy distances. The perfect laboratories to do this were the galaxies in the nearby Local and Sculptor Groups which offer a wide range of types, and environmental properties. Eventually, we thought that it would be of great interest to not only carry out studies aiming at improving classical Cepheids as standard candles, but also other stellar distance indicators like RR Lyrae stars,

Of The Araucaria Project

1 Universidad de Concepción, Departamento de Astronomia, Casilla 160-C, Concepción, Chile 2 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland In early 2000, Grzegorz Pietrzyński started to work with Wolfgang Gieren in Concepción. During this time the Hubble Space Telescope (HST) Key Project on the Extragalactic Distance Scale by Wendy Freedman and collaborators was about to finish, and the topic of distance determina­ tion was again, and very strongly, in the focus of the international astronomical community.

red clump stars, the Tip of the Red Giant Branch, Type II Cepheids, eclipsing binaries, and others. Another key consideration was to carry the stellar methods of distance determination, traditionally calibrated in the optical, to the near-infrared regime where extinction was much less a problem than in the optical spectral region, and where some previous theoretical studies had suggested that environmental dependences might be smaller as well. It was good timing for such studies Fig. 1. Araucaria tree in Conguillío National Park.

because excellent near-infrared cameras had just be­ come available at several observatories around the be­ ginning of the 21st century. When it became clear to us that we were starting a very ambitious and long-lasting project, we needed a name for it, and decided to call it the “Araucaria Project”, making reference to the place the first ideas were born (Araucaria trees are the most beautiful native trees in southern Chile).

N The Same Year, 2000, Wolfgang And Grzegorz

visited Rolf Kudritzki in Munich. Rolf was a leading expert on blue supergiant stars and had some ideas

In Mind About How To Use These Extremely Luminous

objects, visible in very distant galaxies, for distance

Determination. Wolfgang And Grzegorz Were Working

at this time, together with Pascal Fouqué, who was a visitor at the European Southern Observatory’s (ESO) branch in Chile, on a survey for Cepheids in the beau­ tiful spiral galaxy NGC 300 in the Sculptor Group us­

Ing Images Obtained With The Eso/Mpi Wide-Field

Imager at the 2.2-m telescope on La Silla, and it was evident from the blue images that NGC 300 contained a lot of bright blue stars. So we quickly agreed with Rolf that it would be a very nice project to test his spectro­ scopic method (which eventually became known as the “Flux-Weighted Gravity-Luminosity Relationship”) to determine distances using blue supergiants, and check their correctness by comparison with the distance we were about to determine from the NGC 300 Cepheids.

This way the Araucaria Project group saw its first ex­ pansion, by integrating Rolf Kudritzki and his close collaborators, Fabio Bresolin and Miguel Urbaneja in the project, who were to strongly contribute to the sci­ entific success of the project over the next two decades.

At The Same Time, Giuseppe Bono From Rome Ob­

servatory joined the project which opened up the op­ portunity to complement the observational work with theoretical model results and predictions, with mutual benefits for both approaches to study and understand pulsating variable stars. Another member of the Ar­ aucaria Project who joined our group in its very first years was Jesper Storm from AIP Potsdam. He, Wolf­

Gang And Pascal Fouqué Had Been Working For Some

years together to develop a near-infrared version of the classical Baade-Wesselink method, the Infrared Surface

Brightness (Irsb) Technique, And Now Went On With

this work as part of the Araucaria Project. Another two key members of the Project joined us some years later:

An Thompson From The Observatories Of The Carne­

joined our team in Concepcion. Ian and Darek became interested in collaborating with the Araucaria Project group when we started to extensively observe special

Eclipsing Binary Systems In The Magellanic Clouds

which were composed of pairs of red giants. These very rare systems had been discovered by the OGLE Project

At Las Campanas Observatory And Needed Radial Ve­

locity follow-up observations to confirm their physical reality, and derive their properties and distances. Ian not only added his experience in eclipsing binary stud­ ies to the Project but also, through his special access to the Magellan telescopes at Las Campanas Observatory in Chile, helped to start very ambitious observing cam­ paigns on these faint objects which, after a decade or more of continued data collection, led to the most ac­ curate-ever distance determination to both Magellanic Clouds. Darek was taking care of precision modeling Fig. 3. Araucaria Meeting in Potsdam, Germany, 2010.

Through The Years, A Number Of Very Talented And

motivated young scientists joined the Araucaria Proj­ ect. Igor Soszynski from Warsaw worked for two years

Working In Concepción Were Olaf Szewczyk, Nicolas

Nardetto and Marek Górski. Olaf started to work on the improvement of RR Lyrae stars as distance indi­ cators using near-infrared photometry, and eventually obtained good distance determinations to both Mag­ ellanic Clouds. Nicolas was working on the modeling of classical Cepheid atmospheres mainly to better un­ derstand how observed Cepheid radial velocities could be transformed to the pulsation velocities of these vari­ ables, a central problem in the IRSB method to be over­ come in order to yield reliable distances from this tech­ nique. Marek was working on red clump stars and the

Trgb Method To Improve Our Understanding Of How

these stellar methods of distance determination de­ pend on age and metallicity, and also became involved in the IRSB work led by Wolfgang and Jesper.

N 2006 Grzegorz Decided To Go Back To Poland. It

was a very difficult decision because he was extremely happy working and living in beautiful southern Chile.

However This Decision Turned Out To Have A Strong

positive impact on the Araucaria Project. Thanks to generous support from the Foundation of Polish Sci­

Warsaw. Many Talented Researchers Joined Our Team

thanks to these funds including Bogumił Pilecki, Pauli­ na Karczmarek, Piotr Konorski, Mónica Taormina and Ksenia Suchomska. Since then the Araucaria team has been able to expand research on several different kinds of eclipsing binaries and even pulsating stars in eclips­ ing binaries.

Fig. 4. Araucaria Meeting in Nice, France, 2013.

Arek Graczyk Has Been Leading The Project On

eclipsing binaries in the Solar neighborhood, and also kept working on binaries in the Magellanic Clouds. Bogumił managed to very carefully model several clas­ sical and Type II Cepheids in eclipsing binaries lead­ ing to the determination of their physical parameters

With Unprecedented Accuracy. Grzegorz And Darek

discovered a very special pulsating star which mimics a classical RR Lyrae star but is the product of binary evolution. Mónica obtained very interesting results on

Very Promising Eclipsing-Binary Systems Composed

of early-type stars. Ksenia dedicated a lot of work to studying Milky Way eclipsing binaries composed of gi­ ants. Paulina performed simulations to study in detail also gained another important collaborator, an expert on eclipsing binaries - Pierre Maxted. All these scientif­ ic projects opened a new era in the Araucaria project.

Most of them have been continued until today (2021) and resulted in several dozen publications, including 4 papers published in the prestigious Nature journal.

Another Important Expansion Of Our Research Line

was possible due to the start of a close collaboration with Pierre Kervella and Nicolas Nardetto in 2003, and Alexandre Gallenne in 2008. Thanks to their expertise in interferometry we were now able to conduct several new projects which gave us the opportunity to improve Fig. 5. Araucaria Meeting in the Royal Restaurant Wierzynek in Kraków, Poland, 2017.

A Brief History Of The Araucaria Project

on previous results. By the year 2018, we managed to very precisely measure angular diameters of some 50 red clump stars which, in tandem with high quality near-IR data collected for the same stars at the South African Astronomical Observatory, that allowed us to improve the calibration of the surface brightness-col­ or relationship for stars in the Cepheid color range, an effort which complemented our hectic efforts on eclipsing binaries very well. This is just one very good example of the strong synergy we now had within our group. Alexandre and Pierre worked on several very interesting astrometric binary systems in the Milky Way containing classical Cepheids, work which com­ plements our efforts to study Cepheids in eclipsing bi­ naries in the Large Magellanic Cloud.

All These Advances Allowed Us To Formulate More

ambitious science goals and apply for, and eventual­ ly obtain, important new funding from the European Research Council (ERC) in the form of a prestigious ERC advanced grant. This grant, realized from 2016 to 2021, allowed us to build an even stronger science

Team. Many Very Valuable Collaborators Joined Our

project including Weronika Narloch, Piotr Wielgórski, Bartek Zgirski, Gergely Hajdu, Wojtek Pych, Mikołaj

Kałuszyński, Czarek Gałan, Gonzalo Rojas, Megan

Lewis, Louise Breuval, Simon Borgniet, Boris Trahin,

And Behnam Javanmardi. Louise, Piotr, And Bartek

worked mostly on pulsating stars. They produced very precise fiducial period-luminosity relations for classi­ cal Cepheids, Type II Cepheids, and RR Lyrae stars in different environments. Gergely studied mostly RR Ly­ rae stars, and Megan Miras in the Milky Way. Mikołaj and Gonzalo modeled eclipsing binaries. Simon, Boris, and Wojtek worked on spectroscopic data, while Beh­ nam used archival Hubble Space Telescope data to in­ dependently determine the Cepheid distance to one of the key SN host galaxies, using new algorithms which allowed a valuable check on the results and methods Meanwhile we realized that, in order to take full ad­ vantage of the huge amount of precision data from sat­ ellite missions like Gaia, TESS, or Kepler to improve the extragalactic distance scale, one needs to complement these satellite data with very precise ground-based data. The only way to do that given the extremely large amount of data needed, is to collect them with dedi­ cated telescopes at a very good site. A breakthrough in our project occurred around 2016 when we started to closely collaborate with Rolf Chini’s group who oper­ ated their own telescopes at Cerro Armazones in north­

Ern Chile. Our Team Members Not Only Had A Unique

opportunity to obtain the required observations but

From Bochum Including Martin Hass, Michael Ramo­

lla, Francisco Pozo, Moritz Heckstein, Christian West­

Hues, Catalina Sobrino Figuaredo, Sadegh Noorozi,

and others. This particularly successful collaboration allowed us to start a few instrumental projects funded by the Polish Ministry of Science and Higher Educa­ tion, including building a few new modern telescopes.

On the basis of all our previous work we successful­ ly applied for an ERC Synergy grant on the continua­ tion and extension of the Araucaria Project. Within this grant which started in late 2021, we will build a 2.5m telescope which will extend enormously our observing capabilities, and together with our smaller telescopes, will enable us to collect an enormous amount of high quality photometric and spectroscopic data for eclips­ ing binaries, pulsating stars, and also for Active Galac­ tic Nuclei which offer a completely different and inde­ pendent route to build the extragalactic distance scale and extend it out to enormous distances, observing and measuring galaxies in an era when the Universe was only half as old as today. Therefore, our scientific panorama for the next 6 years looks extremely promis­ ing, paving the way to a solid measurement of Hubble constant, reaching a 1% accuracy, and even tracing the possible variation of its value over cosmic time.

The Araucaria Project has so far produced about 200 papers in the most prestigious astronomical journals, and it is far beyond the scope of this article to mention all the science results it has produced over the two de­ cades since its start in 2000. A few highlights however

Should Be Mentioned Here:

- in 2001, the first successful survey for classical Ce­ pheids in NGC 300 was finished, pushing the number of known Cepheids in this galaxy from 18 to 117, and demonstrating that our discovery strategy was suc­

Cessful (Pietrzyński Et Al. 2002, Aj, 123, 789)

- in the same year, we discovered and obtained spec­ tra for a large number of blue supergiants in NGC 300 which were later used to calibrate blue supergiants as distance indicators (Bresolin et al. 2002, ApJ, 567, 277) - in 2003, a first study on environmental effects on red clump stars in optical and near-infrared bands was published (Pietrzyński et al. 2003, AJ, 125, 2494) - in 2005, the most accurate-ever (at the time) distance to a galaxy was derived for NGC 300 by applying the multiband optical/near-infrared photometric method developed by the Araucaria Project to its Cepheid vari­

Ables (Gieren Et Al. 2005, Apj, 628, 695)

- also in 2005, an in-depth pulsation modeling study of classical Cepheids yielded a period-age relation for these stars which up to now has become the standard reference in the field (Bono et al. 2005, ApJ, 621, 966) - in 2006 we published the first paper reporting results from an improved TRGB application to red giants in NGC 300, with data obtained with the Advanced Cam­ era for Surveys onboard the Hubble Space Telescope

Wolfgang Gieren, Grzegorz Pietrzyński

- in 2008, we obtained an accurate distance to the Large Magellanic Cloud using RR Lyrae stars in the near-in­

Frared (Szewczyk Et Al. 2008, Aj, 136, 272)

- also in 2008, the Araucaria Project published a defin­ itive calibration of the FGLR spectroscopic method for blue supergiants which was later used to determine the distances to most of the Araucaria Project target galax­ ies, with results mostly in excellent agreement with the Cepheid distances (Kudritzki et al. 2008, ApJ, 681, 269) - in 2009, a first paper analyzing one of the rare eclipsing binary systems in the LMC consisting of a pair of red gi­ ants was published, demonstrating the extraordinary po­ tential these systems have for a super-accurate distance determination (Pietrzyński et al. 2009, ApJ, 697, 862) - also in 2009, a study was published which compared the metallicities and metallicity gradients in NGC 300 as derived from young stars to those derived from H II regions, showing that within very small uncertainties the two methods yield identical results. This is a very important result in the context of distance determina­ tion, which needs information about metallicities in the target galaxies whose distances are to be measured

(Bresolin Et Al. 2009, Apj, 700, 309)

- in the same year, 2009, we published an accurate Ce­ pheid-based distance determination to the so-far most distant galaxy in our project, NGC 247 in the Sculptor

Group (Gieren Et Al. 2009, Apj, 700, 1141)

- in 2010, our group finished the analysis of the first classical Cepheid discovered in an eclipsing binary sys­ tem in the LMC. The paper reported the first dynamical mass determination of a classical Cepheid ever, accu­ rate to one percent, and in this way resolved the famous mass discrepancy problem for classical Cepheids show­ ing that the masses predicted by pulsation theory were correct (Pietrzyński et al. 2010, Nature, 468, 542) - in 2011, we published a re-calibration of the IRSB Baade-Wesselink method using for the first time a large sample of Large Magellanic Cloud Cepheids which set additional constraints on the calibration not available from Galactic Cepheids alone. This new calibration represented a very significant improvement over the

(Storm Et Al. 2011, A&A, 534, A94 And A95)

-in 2012, we published precision near-IR photometry of some 200 nearby red clump stars. This opened the road to improve the surface brightness-color relation for late-type stars and was a necessary condition to mea­ sure a 1% distance to the LMC in the future. (Laney et

Al. 2012, Mnras, 419, 103)

- also in 2012, we announced the discovery of a new class of pulsating stars, called Binary Evolution Pulsa­ tors. (Pietrzyński et al. Nature, 484, 75). Pulsating mod­ els for such stars were then developed by Araucaria scientist Radek Smolec et al. (2013, MNRAS, 428, 3034) while Paulina Karczmarek studied in detail possible evolutionary channels for such stars.

- in 2013 we presented a 2% distance determination to the LMC based on eclipsing binaries (Pietrzyński et al. 2013, Nature, 495, 56) which was the most precise-ev­ er distance measured to the LMC at the time. The dis­ tance to the SMC based on the same technique could be measured by our team with a precision of 3% (Graczyk et al. 2014, ApJ, 780, 59). These were the first very solid results from our decade-long (at that time!) observing efforts on this project and received outstanding atten­ tion from the international astronomical community.

- in 2014 we presented the results of the analysis of a very exotic eclipsing binary system which revealed that it is composed of two classical Cepheids (Gieren et al. 2014, 786, 80). It was (and still is) the first-ever firm­ ly established binary system with two Cepheid stars orbiting each other.

- in 2016 Gallenne et al. (A&A, 586, 35), presented a very precise and accurate distance measurement to the binary system TZ For, based on a combination of its astrometric and spectroscopic orbits.

- also in 2016 another important study on chemical abundances in the high-metallicity spiral galaxy M83 was published by Bresolin et al. (ApJ, 830, 64), while Kudritzki et al. (ApJ, 829, 70) reported another distance

A Brief History Of The Araucaria Project

- in 2017 Nardetto et al. published an extensive theoret­ ical study on the p-factor problem in the Baade-Wes­ selink technique. The important conclusions reached in this paper were based on high-resolution spectroscop­ ic data for the Cepheid prototype star Delta Cephei

(A&A, 597, 73).

- also in 2017 a new distance determination to the For­ nax dwarf galaxy from near-IR photometry of RR Ly­ rae stars was announced by Paulina Karczmarek et al.

(AJ, 154, 263). This work concluded our long-term ef­ fort on determining improved distances to nearby gal­ axies from this method.

- also in 2017 a new and improved calibration of the FLGR method based on the detailed study of blue su­ pergiants in the LMC, was published by Urbaneja et al.

(Aj 154, 102).

- in 2018, an extremely precise determination of the physical parameters for six classical Cepheids mem­

Bers In Eclipsing Binary Systems In The Lmc Was

presented (Pilecki et al. ApJ, 862, 43). This work has yielded the most accurate masses and radii known to date for this important class of pulsating stars. It also concluded our long term efforts on studying classical Cepheids in eclipsing binaries.

- also in 2018 the effect of metallicity on the brightness of classical Cepheids was precisely estimated from a Baade-Wesselink analysis of Cepheids in the Milky Way, LMC and SMC (Gieren et al. A&A, 620, A99). For the first time, a very sizable sample of metal-poor Ce­ pheids in the SMC could be included in the analysis thanks to data which were obtained over five years as part of an ESO Large Programme.

- also in 2018 a new multi-band calibration of the ab­

Solute Magnitude Of The Trgb Was Published By Our

group (Górski et al. AJ, 156, 278). This work demon­ strated that the TRGB absolute magnitude can be pre­ cisely and fully empirically calibrated with multiband photometric data.

- in 2019 several results regarding the binarity fraction of Cepheids (Kervella et al. A&A, 623, 110, Gallenne et al. 2019, A&A, 622, A164) and RR Lyrae stars (Kervella et al. A&A, 623, A116) were published which strongly expanded our previous efforts on this topic.

- also in 2019 we published our most precise LMC dis­ tance from eclipsing binaries (Pietrzyński et al. Na­ ture, 567, 200). We managed to achieve a 1% precision, which makes the LMC the best anchor for the extraga­ lactic distance scale at the present time. This paper has been enthusiastically received by the community and has become the standard reference in both cosmologi­ cal studies and studies on astrophysical objects in the Large Magellanic Cloud.

- Also In 2019 And Based On Strömgren Photometry,

Narloch et al. (MNRAS, 489, 3285) detected many candi­ dates for non-pulsating stars located in the main Cephe­ id instability strip. The physical nature of these objects remains unclear so far but is potentially very interesting.

- also in 2019 the first paper on eclipsing binaries con­

Sisting Of Early Type Components Was Published By

Taormina et al. (ApJ, 886, 111). Apart from interesting results on the physical parameters of massive stars in the LMC, these results point towards the possibility to use such systems to extend the calibration of the sur­ face brightness-color relation to very early type, hot stars, opening a window for using bright, hot stars in galaxies to determine their distances rather precisely.

- in 2020 we published extended reddening maps of the

And Smc Which Are Very Important And Useful

for most of the studies of these galaxies (Górski et al. ApJ, 889, 179). - also in 2020 an important advance on the empirical calibration of the SBCR based on interferometric data was presented by Nardetto et al. (2020, A&A, 639, A67).

- also in 2020 our group published a 2% geometric dis­ tance to the SMC from late type eclipsing binary sys­ tems (Graczyk et al. 2020, ApJ, 904, 13). This work im­ proved on our 2014 result and concluded our 15-year- long project, which was one of the most important ones in the Araucaria Project. It has already become the stan­ dard reference for the SMC distance in the literature.

- in 2021 we continued studies on binarity of Cepheids and RR Lyrae stars. Pilecki et al. 2021 (ApJ, 910, 118)

Wolfgang Gieren, Grzegorz Pietrzyński

detected a numerous population of double-lined bina­ ries in the LMC hosting a Cepheid component; Hajdu et al. (ApJ, 915, 50) presented a very detailed study of binaries containing RR Lyrae stars as detected from a study of their period variability.

- also in 2021, thanks to our geometrical distances and Gaia DR3 parallaxes another precise determination of the Cepheid metallicity effect was derived and pub­ lished (Breuval et al. ApJ, 913, 38). The results are in excellent agreement with those found in a complete­ ly independent way by our group before (Gieren et al.

, A&A, 620, A99).

- also in 2021 the first calibration of the SBCR from eclipsing binaries and Gaia DR3 parallaxes was pub­ lished (Graczyk et al. A&A, 649, A109). The results show the great potential of this approach.

The Araucaria Project Team Members Held Several

internal workshops over the years (sometimes enriched by external collaborators) which proved to provide excellent opportunities for brainstorming, and social events which helped to strengthen the spirit of friend­ ship among our group, including the ever-increasing number of graduate students who became part of the project over the years.

Fig. 7. Araucaria Meeting in Sopot, Poland, in 2021, twenty-one years after founding.

Candles: Classical Cepheids, Blue Supergiants,

tip of the red giant branch stars, eclipsing binaries, and where one can study a lot: the metallicity gradient in the disc from the spectroscopic analysis of blue supergi­ ants (Bresolin et al. 2002), the effect of metallicity on the intrinsic brightness of classical Cepheids, but above all, the distances determined independently from different standard candles, especially from classical Cepheids (hereafter just Cepheids). The only problem before the year 2002 was that NGC 300 was virtually uncharted territory, and the reported population of classical Ce­

Pheids Was Only 18 (Graham 1984). Why Has Ngc 300

not been studied thoroughly? A few reasons stacked up. NGC 300 is a large galaxy in terms of angular size (19’ x 13’), and covering such an area on the sky required a large field camera, which before the year 1999 simply hadn’t existed. In 1999 the Wide Field Imager (WFI, FoV: 34’ x 33’) on MPG/ESO 2.2-m telescope at the La Silla Ob­ servatory, Chile, was commissioned, making the obser­ vations of spatially extended objects feasible and very time-efficient. The enormous images produced by the WFI required dedicated time and human resources to be properly processed and analyzed, which meant that Paulina Karczmarek1, Wolfgang Gieren1, Grzegorz Pietrzyński2

Optical Survey Of Classical Cepheids

1 Universidad de Concepción, Departamento de Astronomía, Casilla 160-C, Concepción, Chile 2 Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland of the Universidad de Concepción was announced.

A resourceful and ingenious Polish astronomer, Grze­ gorz Pietrzyński, joined the team of Wolfgang Gieren, and they embarked on a scientific journey to find more Cepheids in NGC 300.

Prompted By The Fact That Ngc 300 Shows Signs Of

recent, massive star formation, and therefore should host a significant number of Cepheids, Wolfgang ap­ plied for observing time at ESO and was awarded the generous number of 29 nights between July 1999 and January 2000. During this time around 150 images of NGC 300 in each of B, V, I bands were collected. From around 32,000 observed stars Grzegorz selected targets of specific color index (0.4 mag < (B-V) < 1.5 mag), that showed the asymmetrical sawtooth light curves typi­ cal for classical Cepheids, and that had larger pulsa­ tion amplitudes in the B-band than in the V-band, with

The B-Band Amplitude Exceeding 0.4 Mag. Crawling

through a database of tens of thousands objects took

Some Time But Every Now And Then, A Cepheid Would

pop out! Soon not only had we recovered all previous­

Ly Known 18 Cepheids, But We Increased The Known

sample by a factor of six, resulting in a collection of 117 Cepheids (Pietrzyński et al. 2002). The Araucaria Project began from, and gained momentum with, a study of a graceful galaxy in the Sculptor Group, NGC 300. It is a spiral, near face-on galaxy, with a metallicity gradient ranging from solar-like in the center to SMC-like on the peripheries.

The Discovered Cepheids Span A Broad Range Of

pulsation periods, from 115 to 5.4 days, with a period uncertainty of only 0.005-0.01 days, thanks to greatly extended time baseline since the first epoch observa­ tions (Graham 1984), which now corresponds to about 76-1000 pulsation cycles. The high accuracy of our data is reflected by the uncertainties of the photometric zero points, which in both B- and V-bands are with­ in 0.03 mag, and agree very well with those present­ ed by Freedman et al. (2002). The completeness of our sample drops suddenly for objects fainter than about 22.5 mag in the V-band, corresponding to a pulsation period of around 10 days. In other words, our survey is virtually complete for Cepheids with periods longer than 10 days. The spatial distribution of Cepheids, that shows how they trace the spiral arms of the galaxy, can be appreciated in Figure 1, together with finding charts and light curves of five exemplary Cepheids.

Of Five Exemplary Cepheids. Figure Assem­

bled from figures 1, 3, 5 of Pietrzyński et al. (2002).

Optical Survey Of Classical Cepheids

Figure 2 shows that all 117 Cepheids follow the pe­ riod-luminosity relation in the B- and V-band, howev­ er the spread is too large to accurately determine the distance to NGC 300 from the visual passbands alone.

A much more accurate distance determination can be achieved in the near-infrared (NIR) domain, where the Cepheids follow the period-luminosity relation more tightly and are less affected by the reddening. The idea of carrying out NIR observations has been integrated into

A Large Programme That We Applied For At Eso In

2003. A survey in the visual passbands was necessary to find Cepheids by their large amplitude, asymmet­ rical light curves, and pick the best sample for a fol­

Distance And Reddening Simultaneously, And Derive

a true, dereddened distance of superior accuracy (Gie­ ren et al. 2005 and in this volume).

Authors:

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

94143, Usa.

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

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

14Jlvmi Consulting Llc, Dousman, Wi, Usa

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

Abstract

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

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

Introduction

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

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

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

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

●

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

●

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

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

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

Hyperpolarized 13C-Pyruvate Preparation

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

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

General Considerations

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

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

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

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

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

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

Personnel

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

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

Equipment And Facility

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

Material Handling

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

Pharmacy Kit Filling And Assembling

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

Quality Control And Dose Release

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

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

The Final Dose Release And Injection

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

Some Key Challenges

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

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

Current Practices

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

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

In House

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

Summary

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

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

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

Mri System Setup And Calibrations

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

Imaging System

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

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

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

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

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

Rf Coils

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

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

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

Provide B1 Transmit Across The Fov (B1

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

B1

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

+ Profile But Has Been Used Because Of

relatively easy integration into the scanner bore. B1

+ Variation Results In Variations In The Flip

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

Homogeneous B1

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

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

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

(1)

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

Tx = Transmit

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

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

Phantoms

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

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

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

+) And Receive (B1

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

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

Prescan Calibration

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

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

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

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

+ Inhomogeneity As Well

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

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

Power [Kw]

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

8

13C-bicarbonate doped with dimethyl silicone, various

Power [Kw]

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

Maximum Values

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

Summary

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

+ Profiles. The

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

For Calibration Of B1

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

Acquisition And Reconstruction

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

+ Inhomogeneity,

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

Acquisition And Reconstruction Methods

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

Mrs/I Methods Specifically

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

Chemical Shift

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

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

Their Application To Different

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

The Majority Of

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

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

Prostate Studies

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

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

Heart Studies

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

Brain Studies

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

Abdomen And Breast Studies

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

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

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

1H Imaging

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

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

Reported Study Parameters

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

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

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

(B)

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

Summary

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

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

Data Analysis And Quantification

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

Metrics

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

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

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

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

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

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

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

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

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

Visualization

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

Metrics

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

Parameter Encoding

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

Anatomical Context

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

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