Vericut Delamination Avoidance

Avoidance and Coalescence of Delamination Patterns

Zoe Budrikis

ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy

Stefano Zapperi

CNR-IENI, Via R. Cozzi 53, 20125 Milano, Italy and ISI Foundation, Via Alassio 11/c, 10126 Torino, Italy Delamination of coatings and thin films from substrates generates a fascinating variety of pat- terns, from circular blisters to wrinkles and labyrinth domains, in a way that is not completely understood. We report on large-scale numerical simulations of the universal problem of avoidance and coalescence of delamination wrinkles, focusing on a case study of graphene sheets on patterned substrates. By nucleating and growing wrinkles in a controlled way, we are able to characterize how their interactions, mediated by long-range stress fields, determine their formation and morphology.

We also study how the interplay between geometry and stresses drives a universal transition from conformation to delamination when sheets are deposited on particle-decorated substrates. Our re- sults are directly applicable to strain engineering of graphene and also uncover universal phenomena observed at all scales, as for example in geomembrane deposition.

Ntroduction

Delamination of a thin sheet from a substrate may be an undesirable effect, for example when plastic coatings peel from glass, but controlled delamination is of inter- est for a range of applications from flexible electronics to building micro- and nanofluidic devices [2, 3]. It is therefore of great technological importance to understand the role played by sheet properties and substrate geom- etry in determining delamination and sheet morphology.

In addition, delamination blisters and wrinkles form a rich variety of complex patterns, which are the subject of ongoing research. Examples include circular blisters, “telephone cord” buckles, parallel and radially organized

Wrinkles, And Labyrinth Patterns . In The Case Of

graphene sheets, patterning into networks of wrinkles us- ing nanopillars or particles on the substrate has been ex-

Perimentally Demonstrated . Previous Theoretical

work on thin sheet delamination has focused on the prop- erties of a single blister or wrinkle, looking for example at how blister growth is affected by substrate interac- tions and elastic instabilities [4, 10, 12, 18]. On the other hand, interactions between delaminated regions are fun- damental as strikingly illustrated by recent experiments by Yamamoto et al on graphene sheets.

Graphene Wrinkles Are Seen To Form Pairs That Ap-

proach each other but do not coalesce (see Fig. 1), as also confirmed by atomistic simulations . Avoiding wrinkle pairs are not just a curiosity of graphene sheets on patterned substrates, and in fact can be found not only in other thin films but even in macroscopic sheets such as geomembranes used to line landfills. Examples from the physics and engineering experimental literature are listed in Table I. Despite their ubiquitous nature, the physics leading to avoiding wrinkle pairs is largely unex- plored. It is remarkable that similar universal avoiding patterns are widely observed in cracks.

“En Passant”

cracks in films and plates have been recently shown to be display universal morphology, independent on the material properties . Do similar universal laws apply

To Avoiding Wrinkle Pairs?

Here we report a large-scale simulation study of avoid- ing and coalescing delamination wrinkles in graphene. The phenomena we describe are universal, but we have chosen to focus on graphene as a case study because it is an exemplary thin sheet, being truly two-dimensional and having a remarkably high ratio of bending rigidity

(∼1 Ev) To Tensile Rigidity (∼103 Ev/Nm2) ,

which allows narrow buckled morphological features to form. This makes it an ideal model system in which to explore the mechanics of membranes and fascinating in its own right .

Furthermore, Strain Engineering

of graphene promises control of electronic, optical and thermal properties, making it useful for a range of appli-

Cations , So That Understanding The Morphology

of graphene sheets on substrates is of value for building devices.

We Introduce A Coarse Grained Model For Mono- And

multilayer graphene, which we validate by comparing simulations of micron square sheets with existing exper- imental results . We then report on simulations of controlled growth of interacting delamination wrinkles, which are inspired by Fender et al’s experiments on cracks in plates . These reveal the role played by long range interactions in determining the shapes of wrinkles, and arXiv:1403.8063v1 [cond-mat.mtrl-sci] 31 Mar 2014 whether they form avoiding pairs or coalesce. We also discuss how coalescence of wrinkles can be used to in- duce delamination in rectangular regions. Our simula- tion studies illustrate the importance of free edges on the sheet for allowing lateral motion, without which it is impossible to model experimentally-observed phenomena correctly.

N-Layer Graphene Sheet

While atomistic simulations provide a useful bench- mark, their computational intensity limits their useful- are primarily interested in universal phenomena, rather than graphene-specific behavior.

We Therefore Develop

a linearized model that captures the essential physics of an ultrathin sheet interacting with a patterned substrate, and show below that it is capable of describing the me- chanical behavior of graphene in which we are interested.

We model the graphene sheet as a triangular lattice of particles connected by springs with rest length a = 5˚A,

S Is The Stiff-

ness for a graphene sheet composed by n layers, with

K∗

s = 20 eV/˚A2 [22, 23]. Bending rigidity is implemented as an energy that depends on the angle φ between two neighbouring triangles and is minimized when the sheet

A Distinct Advantage Of These

simulations over atomistic simulations is that sheet thick- ness enters as a change in parameters, without a change in the number of particles simulated. This allows us to study any number of layers as long as the assumptions of thin-sheet elasticity hold.

The sheet is attracted to the substrate via a down- ward force applied on all particles that is independent of height, but the substrate itself has a radial repulsive interaction with the sheet, to form a hard barrier. The strength of these forces has been selected to give qualita- tive agreement with experiments (see below). This sub- strate interaction guarantees a substrate solid enough to deposit particles on, and behaves in a reasonable way

Even If The Specific Choice Is Rather Arbitrary

Open boundary conditions are used, so that the sheet is able to expand and shrink laterally. As discussed be- low, an adequate accounting for lateral deformation of the sheet is essential to capture the physics of the system.

In order to reduce spurious edge effects and allow for ef- fects of friction between the sheet and substrate, particles near the sheet edge are coupled to their original lateral positions with harmonic springs, to constrain their lateral (but not vertical) motion. The simulation is performed

Using The Molecular Dynamics Package Lammps And

is conducted at zero temperature, with damping applied to slowly drain energy from the system. Further details are given in Appendix A.

Wrinkle Networks On Decorated Substrates

We verify our model through comparison with experi- mental studies of graphene sheets deposited on substrates decorated with nanoparticles of diameter ∼10 nm, as published recently by Yamamoto et al . We simulate 1×1 µm2 regions of monolayer and 5-layer graphene, with particles of radius 8 nm placed at positions determined by digitizing the atomic force micrograph that was obtained

By Yamamoto Et Al For A System With Nanoparticle

density of 90 µm−2. As seen in Fig. 1, the agreement be- tween monolayer simulation and experiment is good, with both systems displaying similar networks of long narrow wrinkles connecting particles. We note that agreement is only expected in the center of the region simulated, because the experimental image is a sample of a larger region so that wrinkles near the edges are affected by particles that are not shown in the limited field of view.

Importantly, our linearized simulations exhibit avoid- ing pairs of wrinkles, an example of which is highlighted in Fig. 1(d,e). The pairs are stable for long simulation times (up to at least 2×106 time steps) and occur under a range of downward forces on the sheet. In addition, like Yamamoto et al, we find that increasing the thickness of the graphene sheet hinders its conformation to the sub- strate (compare our Fig. 1(a,b) with Fig. 6 of Ref. ).

This is especially apparent in regions where close-spaced particles are positioned on the vertices of a polygon, as in the region indicated in Fig. 1(a,b). As highlighted in Fig. 1(f,g), the sheet in this region “pops up” when its thickness (and hence ratio of bending to stretching costs) increases. In the rest of this paper, we study these two characteristic behaviors in greater detail.

Beyond Visual Comparisons, We Compare Simulation

and experiment statistically, by measuring the distribu- tion of the number of wrinkles emanating from each parti- cle for the grpahene monolayers, as plotted in Fig. 1(h).

The agreement is good, although the simulations have a slightly larger mean number of wrinkles per particle (2.48 for simulation, vs 2.15 for experiment). However, this may simply be because the lower noise levels in the simulation data allow more wrinkles to be detected.

Orphology Of Wrinkle Pairs

We first study the growth and interactions of wrinkles, with a focus on avoiding pairs. In order to character-

± 0.06 M C

a c.f. Fig. 1 of main text. b Based on the average wrinkle width being approximately the nanoparticle diameter . c As quoted in Ref. .

TABLE I. Examples of avoiding pairs of wrinkles in the literature, sorted by sheet thickness. This is not intended to be an exhaustive list, but rather to give a sense of the variety of situations in which avoiding pairs occur. ize and understand these pairs, we require a controlled method for creating and growing them. Inspired by stud- ies of interacting cracks grown from a pair of notches , we study propagating and interacting wrinkles using sim- ulations in which an initially flat sheet of dimensions 600×600 nm2 is subject to upward pulling in well-defined “wrinkle nuclei” regions. The tips of the nuclei are sepa- rated by distances X and Y as defined in Fig. 2(a), which are our control parameters. We set the upward force to 0.01 eV/˚A, a factor of 10 larger than the downward force that is applied to the whole sheet. Because the nuclei are long and narrow and the sheet has high stretching cost, the upward driving primarily causes the wrinkle to prop- agate forward, with minimal lateral broadening, as shown in Fig. 2. We run each simulation until a stable configu- ration is attained, which occurs when the applied upward forces are balanced by stresses in the sheet. We have also tested simulations where the upward force is increased slowly, rather than turned on instantaneously, and find that although this allows smoother initial wrinkle growth, the final configurations attained are not strongly affected, as seen in example movies in Supplemental Material .

We have also tested changing the nucleus orientation rel- ative to the sheet edges (and therefore lattice), but do not find any lattice effects.

Whereas an isolated wrinkle propagates directly for- ward, parallel to its nucleus, nearby wrinkles interact via long-range stresses in the sheet. This leads to wrinkles ei- ther joining or forming an avoiding pair. For fixed driving conditions, we find that whether a pair of wrinkles join is controlled by the separation of their nuclei. As shown in Fig. 2(b), this can be characterized by aspect ratio X/Y and distance R. When X > Y , the joining condition is simply a distance threshold of ∼30 nm. However, for X < Y , wrinkle merging becomes more favourable and the minimum distance required for the formation of an avoiding pair increases rapidly.

In addition to the conditions for avoiding pair forma- tion, we also characterize how the morphology of such pairs depends on wrinkle nuclei separation. Typical wrin- kle shapes are shown in Fig. 2(c), for fixed X/Y = 1. For small R, wrinkles are directed toward each other, but for larger R they are initially repelled before being attracted.

To quantitatively describe the wrinkle shapes, we focus on two characteristics which are indicated in Fig. 2(a):

Μ2 + Ν2

from base to tip, and aspect ratio µ/ν. For fixed X/Y , ξ depends on R and is maximized at a distance ∼230 nm, as shown in Fig. 2(d). As shown in Fig. 2(e), the maximum extension decreases with increasing X/Y , so that avoiding pairs of wrinkles formed by nearly head- on nuclei are substantially longer than wrinkles formed from nuclei that are separated in the X direction. Re- markably, for nucleus separations R ≳200 nm, X/Y has little effect on the aspect ratio µ/ν of wrinkles, which decreases approximately linearly with R.

Nteractions Of Wrinkle Pairs

In order to understand how wrinkle interactions af- fect their shape, we characterize the stresses induced by wrinkles, via the trace of the stress tensor Tr(σ) = σxx + σyy + σzz. (The calculation of the stress tensor is described in Appendix A.) We first consider a single wrinkle. As shown in Fig. 3, the stresses emanating from the tip of a wrinkle are compressive (Tr(σ) < 0), which causes the wrinkle to grow via buckling of the sheet, so that deformation occurs as bending rather than stretch- ing which is highly unfavourable for graphene.

As indicated in Fig. 3(b), the stress distribution dis- plays an angular dependence and compressive stresses are largest along a line parallel to the wrinkle. We have also calculated the stresses generated by an idealized wrin- kle in an infinite sheet under the assumption of zero in-plane deformation by imposing a wrinkle shape and numerically calculating the stresses using standard thin- plate elasticity, as described in Appendix D. As shown in

Simulated 1 × 1 Μm2 (A) Monolayer And (B) 5-Layer

graphene sheet on a substrate decorated with spherical parti- cles of diameter 8 nm, placed in positions determined by dig- itization of the experimental micrograph shown in panel (c).

Red dots indicate the particle centres. (c) Atomic force mi- showing a 1×1 µm2 region of graphene exfoliated onto a sub- strate decorated with nanoparticles of mean diameter 7.4nm.

(d,e) Close-ups of an example avoiding pair of wrinkles found in experiment and simulation, as highlighted by the blue boxes in panels (a) and (c).

(F,G) Close-Ups Of A Region In

which the monolayer sheet conforms to the substrate but the 5-layer sheet delaminates, as indicated by the green ellipses in panels (a) and (b). (h) Histograms of the number of wrinkles emanating from each particle, as counted from the images in panels (a) and (c). Error bars correspond to the square root of each count.

Fig. 3(c,d), the idealized wrinkle also generates a stress field with an angular dependence. Far from the wrinkle tip, the stresses decay as a power law with exponent 1 along the wrinkle axis and 2 perpendicular to the wrinkle axis.

When Two Wrinkles Are Grown In Proximity To Each

other, their behavior is determined by the superposition of their stress fields. A video showing the evolution of stresses for a growing pair of wrinkles is provided as Sup- plemental Materials . As shown in Fig. 4, wrinkles

Fig. 2.

(a) Schematic of wrinkle interaction tests shown on a close-up of the central region of a sheet. Elongated “wrinkle nuclei”, indicated by green lines, are lifted with constant force, to cause wrinkles to propagate towards the centre of the sheet.

We investigate how changing the nucleus separations X and Y affects the wrinkle shape, which is characterized by µ and ν. The scale bar indicates 50 nm. (b) Whether two wrinkles join or remain separate depends on nucleus separations, here characterized by aspect ratio X/Y and distance. When the nuclei are nearly head on (X/Y small), even distant pairs join, but the maximum distance for joining drops offrapidly as the aspect ratio is increased. (c) Wrinkle shapes for X = Y , for a range of R values. The wrinkle nucleus is excluded, and wrinkles are transformed so the end of the nucleus (the base of the wrinkle) is situated at (x = 0, y = 0) and the tip of the wrinkle is to the right of its base. (d) The extension of

Μ2 + Ν2, Is Maximised For A Separation Of

∼220 nm, but decreases with increasing aspect ratio.

(E)

Remarkably, when X/Y ≥1, the aspect ratio of the wrinkle, µ/ν depends only on nucleus tip separation R. propagate along the steepest stress gradient in front of them. Pairs of wrinkles propagate in a spiral around the centre of the line joining their tips. As seen in Fig. 4(a,b), the wrinkle tips initially propagate outwards slightly, and the high-stress central region expands. As the tips pass each other, their motion changes to an inwards propaga- tion, as seen in Fig. 4(c), and the high-stress region con- tracts. The wrinkles continue to propagate around the centre of the line joining their tips, and come to a stop in the configuration seen in Fig. 4(d). This configuration

Fig. 3.

(a) Trace of the stress tensor from a single wrinkle in the coarse grained model, showing tension behind the tip and compression in front, concentrated at the tip. The scale bar represents 100 nm. (b) Slices of the stress trace parallel and perpendicular to the wrinkle direction, as indicated by red and blue lines in panel (a). (c) σxx +σyy for an infinite sheet with an idealized wrinkle imposed, as described in Appendix D. (d) Slices of σxx + σyy parallel and perpendicular to the wrinkle direction, as indicated by red and blue lines in panel (c). For clarity, in panels (a) and (c) the interiors of the wrinkles, defined by a height threshold of 2 ˚A, are not shown.

is stabilized by the balance between applied forces and stresses in the sheet. However, even for larger upward forces on the wrinkle nuclei, the deformations required to merge two wrinkles are highly unfavourable. This is consistent with the observation of stable avoiding pairs of wrinkles in simulation and experimental stud- ies of graphene deposited on nanoparticles. The depen- dence of wrinkle extension on nucleus tip distance seen in Fig. 2(c) can be accounted for by noting that when nuclei are close, wrinkle propagation is limited by wrin- kles blocking each other, but as nuclei distance increases, stresses decrease and the rate of wrinkle propagation de- creases accordingly.

Finally, We Observe That, As Expected For A Thin

plate , the stresses induced by wrinkles act in-plane. As shown in Fig. 4(e), σzz is zero outside the wrinkle, and even on the wrinkle boundary has a value two orders of magnitude smaller than σxx + σyy. In other words, wrinkle growth is driven by buckling induced by in-plane compressive stresses.

Suspended On Four Particles

Finally, we consider a situation where wrinkle merging is of great relevance, namely the transition from con- formation to delamination of a graphene sheet placed on a substrate decorated with nanoparticles. To study

Fig. 4.

(a–d) Contour lines of the stress trace during the evolution of an avoiding pair of wrinkles, with a field of view that excludes the sheet edges. The nucleus separations are X = Y = 56.6 nm. The line joining the wrinkle tips is a local maximum in the stress distribution and the tips propagate around the centre of this line, which is a saddle point. (e) Contour lines of σzz, for the same wrinkle configuration as shown in panel (d). For clarity, the interiors of the wrinkles (defined by a height threshold of 2 ˚A) are not shown.

All

images have the same scale; the scale bar, shown in panel (a), represents 100 nm. this transition in a systematic way, we simulate a 600 × 600 nm2 graphene sheet deposited on a substrate with four nanoparticles of diameter 8 nm, arranged in a rect- angle with aspect ratio close to unity and a range of side lengths ℓ, with center close to the sheet center. (We use this configuration, rather than a square centered exactly, in order to avoid spurious effects arising from symme-

Example Movies Of Deposition Are Shown In The

Supplemental Material . Here, we examine the role of both the inter-particle distance and the sheet’s mechan- ical properties, which are controlled by its thickness.

Figure 5(a–d) shows typical configurations for close- spaced and distant particles, for a monolayer (panels a and b) and a 5-layer sheet (panels c and d). When the particles are close together, the sheet is delaminated in the center of the rectangle, but as their spacing is in- creased, it is able to conform to the substrate. Increas- ing the sheet thickness “smooths” the sheet and increases the size of features, as can be seen by comparing panels

Typical Configurations Of A Sheet Deposited On

four nanoparticles: (a) monolayer sheet, particle spacing 60 nm, (b) monolayer sheet, particle spacing 160 nm, (c) 5-layer sheet, particle spacing 60 nm, (d) 5-layer sheet, particle spac- ing 160 nm. Panels (e–h) show the trace of the stress tensor corresponding to the configurations. Where the stress is above 15 GPa, the color scale has been clipped (black regions on top of the particles). All eight panels have the same scale, and the scale bar, shown in panel (a), represents 100 nm. (i) Height of the center of the graphene sheet as a function of particle spacing, for 1, 2, 5 and 10 layer sheets.

(J) As A First Ap-

proximation, the delamination transition occurs at a particle spacing s∗∼n1/4. (a,b) and (c,d) of Fig. 5. It also reduces stresses in the sheet, as seen in panels (e–h) which show the trace of the stress tensor.

Near The Particles, Stresses Are Ten-

sile (Tr(σ) > 0), but compressive regions exist inside the wrinkles and especially at the wrinkle tips. The effect of the finite sheet size is also seen, with the stress fields clearly modified by the sheet edges.

The delamination transition is quantified in Fig. 5(i), which shows the height of the center of the sheet as a function of particle spacing s, for 1-, 2-, 5- and 10-layer sheets. In all cases, a sharp transition is observed at a particle spacing s∗that depends on sheet thickness. As a first approximation, one can estimate the dependence on sheet thickness under the assumption that bending rigidity does not enter the problem and the sheet de- forms purely via stretching.

N That Case The Delami-

nated region of an n-layer sheet around a protrusion has radius R ≈r(4nE2D/3Γ)1/4 [16, 37], where r is the par- ticle radius, E2D is the tensile rigidity of the sheet and Γ characterizes the adhesion energy. Under the assump- tion that delamination in the center occurs when delam- inated regions meet, the critical particle spacing scales as s∗∼n1/4. As seen in Fig. 5(j), this scaling collapses the 1- and 2-layer curves very well, but already breaks down for the 5-layer sheet. This is to be expected, be- cause argument does not take into account the existence of long-range stresses and wrinkles connecting the parti- cles.

Interacting Cracks

Delamination is a form of fracture, so it is not sur- prising that our interacting delamination wrinkles are reminiscent of interacting cracks.

Single Wrinkles And

cracks have different fracture modes, since propagation of a crack due to pulling orthogonal to the crack direction is purely mode I fracture, whereas wrinkle propagation is inherently a mixture of modes I and II, due to the com- pressive stresses in front of the wrinkle tip (as shown in Fig. 3). Nonetheless, when interactions with other cracks or wrinkles are introduced, both types of fracture propa- gation involve mixed modes I and II loading, and in both cases fracture proceeds as rotation of the line connecting their tips, which is a local stress maximum , tensile for cracks and compressive for wrinkles.

Gelatine

plates reveal a universal shape for the lenticular region cut out by two interacting cracks, described by y(x) = √x.

N Those Experiments, Notch Lateral

separation (equivalent to our X, see Fig. 2(a)) was varied over an order of magnitude, with fixed separation along the direction of the notches (equivalent to our Y in Fig. 2(a)).

By Way Of Contrast, We Are Unable

to identify a universal shape in our data on avoiding wrinkle pairs, as is obvious from visual inspection of Fig. 2(c), in which some wrinkles are almost straight and others are substantially curved.

Furthermore, In

those experiments, cracks were found to only deviate from straight paths when their tips pass each other, whereas we find wrinkle shapes that are curved even at the wrinkle nuclei. We attribute these differences in behavior to differences in the long range stress fields.

In addition to fundamental differences between crack and wrinkle tips, in our simulations stresses are strongly affected by system edges, as we discuss below.

Experiments by Cortet et al on cracks in paper also reveal crack shapes controlled by interactions . Their experimental geometry is more complex, consisting of two lines of equidistant slits. The cracks are grown by pulling the paper perpendicular to the slit direction. The slits and their spacing are both fixed, and the control pa- rameter is the distance d between the two lines. For small d, cracks typically repel each other during their initial growth, before becoming attracted. For larger d, repul- sion is seen less frequently, until a transition inter-line distance above which cracks from different lines do not interact. As seen in the wrinkle shape data for X/Y = 1

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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