Moisture Diffusion Composite Ansys

Abstract

Fiber reinforced polymer composite (FRPC) materials are extensively used in lightweight applications due to their high specific strength and other favorable properties including enhanced endurance and corrosion resistance. However, these materials are inevitably exposed to moisture, which is known to drastically reduce their mechanical properties caused by moisture absorption and often accompanied with plasticization, weight gain, hygrothermal swelling, and de-bonding between fiber and matrix.

Hence, it is important to understand the mechanics of moisture diffusion into FRPCs. The presence of fibers, especially impermeable like Carbon fibers, introduce tortuous moisture diffusion pathways through polymer matrix. In this paper, we elucidate the impact of fiber packing and morphology on moisture diffusion in FRPC materials. Computational models are developed within a finite element framework to evaluate moisture kinetics in impermeable FRPCs. We introduce a tortuosity factor for calculating the extent of deviation in moisture diffusion pathways due to impermeable fiber reinforcements. Two-dimensional micromechanical models are analyzed with varying fiber volume fractions, spatial distributions and morphology to elucidate the influence of internal microscale fiber architectures on tortuous diffusion pathways and corresponding diffusivities. Finally, a relationship between tortuosity and diffusivity is established such that diffusivity can be calculated using tortuosity for a given micro-architecture. Tortuosity can be easily calculated for a given architecture by solving steady state diffusion governing equations, whereas time-dependent transient diffusion equations need to be solved for calculating moisture diffusivity. Hence, tortuosity, instead of diffusivity, can be used in future composites designs, multi-scale analyses, and optimization for enabling robust structures in extreme moisture environments.

Keywords Moisture Diffusion · Diffusivity · Tortuosity · Finite Element Analysis · Micromechanics

Ntroduction

Fiber reinforced polymer composite (FRPC) materials are widely used in structural applications within the aerospace, automotive, civil and marine industries due to their high specific strength, improved durability and corrosion resistance. When used in such applications, FRPCs are inevitably exposed to extreme conditions: moisture, low and high temperatures, pH, UV radiation and salinity, among others. Moisture, in particular, is a key environmental factor due to 1) its prevalence, although to different extents; 2) polymer matrices having a relatively high polarity when compared to reinforcing fibers and therefore a high affinity for absorbing moisture in humid environments; 3) the drastic reduction of FRPC properties caused by moisture absorption and often accompanied with plasticization, weight gain, hygrothermal swelling, and de-bonding between fiber and matrix [1, 2]. This necessitates an in-depth study of the mechanisms and avenues of moisture ingression through FRPCs.

Most prior experimental research conducted on FRPCs for establishing the effect of moisture diffusion involves measuring the weight gain response with various reinforcing fiber types (continuous or textile) and materials (Carbon, Glass, Kevlar) . In most studies, FRPC samples are subjected to moisture (chamber, submerged in water/seawater) and their weight gain is measured periodically, and further plotted as weight gain vs. time graphs. Key information

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obtained are the effective diffusivity and moisture saturation for specific FRPCs. Such studies are very important for identifying the overall effect of moisture diffusion and the extent of moisture absorption, although they only provide a global understanding of moisture diffusion and the local mechanisms are poorly understood or rarely captured. To moisture diffusion through FRPCs . These frameworks have focused on predicting experimentally measured moisture diffusivities and global weight gain curves of FRPCs considering independent parameters like fiber volume fraction, fiber distribution and diffusivities of individual components (fiber and matrix). However, gaining a fundamental understanding of micro-scale moisture diffusion in terms of the effective fiber architecture has seldom been the focus.

Bond et al. investigated the influence of fiber spatial distribution on moisture diffusivity computationally and stated that diffusion coefficient is unaffected between regular and random fiber distribution. Hence, they suggested that the regular fiber model is adequate for estimating diffusion coefficients for composites. However, Joliff et al.

showed that fiber arrangement has a significant impact on moisture diffusion when the fibers are in contact with each other, thereby, forming an effective barrier against diffusion. The results also showed that the rate of diffusion is greatly modified during initial (short) exposure times because of fiber arrangement, where the diffusivity of randomly distributed array is lower compared to that of a regular array of fibers. Aditya et al. showed that moisture diffusivity is influenced by the cross-sectional shape of fibers. They computationally showed that the effective diffusivity is minimum for circular fibers, and it increases as the eccentricity of circular cross-section increases to become an elliptical cross-section. In their consecutive work , they considered computational models with many irregular shapes of fiber cross-section and determined that the percentage change in diffusivity when compared with circular fibers varies between -15.19% to 10.56%. In summary, prior research has shown that moisture diffusivity of fiber reinforced composites depends on fiber packing, fiber volume fraction, fiber cross-sectional shape and diffusion properties. Although these parameters are studied individually, further investigation is necessary to study the combined effect of these microscale fiber architecture on moisture diffusivity.

In this paper, we propose to capture the combined effect of fiber micro-architecture by introducing a tortuosity factor. Such a factor has previously been considered for capturing diffusive flow in porous electrodes . In this paper, we will numerically determine the effective diffusivity and compare that with the tortuosity factor to account for the influence of fiber architecture on moisture diffusion in FRPCs. Particularly, we used Finite Element Method (FEM) for studying the moisture ingression in impermeable fiber reinforced polymer composites. First, we developed two-dimensional micromechanical models with different fiber volume fractions and fiber distributions to establish the influence of fiber distribution and volume fraction on the effective moisture diffusivity and to determine the tortuosity factor for these composites. Then, we studied the influence of fiber morphology (shapes) on tortuosity. Finally, we established a relationship between tortuosity that captures the fiber architecture (combined effect of fiber volume fraction, fiber distribution and fiber shape) and diffusivity. This relationship was validated for a set of test fiber micro-architectures.

Otivation And Significance

The main objective of this paper is to study how moisture diffusion occurs in FRPC composites. In particular, our model system is Carbon fiber reinforced polymer matrix (CFRP) composites, where Carbon fibers are considered to be impermeable to moisture diffusion. Hence, they typically act as barriers that make moisture diffusion pathways tortuous, thereby, delaying moisture ingression and consequently reducing moisture diffusivity. Fiber spatial distribution and morphology induced hindrance to moisture diffusion is quantified using a tortuosity factor, where an increase in tortuosity implies greater resistance to moisture diffusion. The tortuosity is obtained by solving steady state diffusion governing equation, which is computationally less expensive compared to transient diffusion equation that is solved for obtaining moisture diffusivity. Hence, by establishing a relationship between tortuosity and diffusivity, we can directly obtain diffusivity from tortuosity values for a large range of fiber architecture without having to perform diffusion Further in this study, we consider one dimensional diffusion while modelling moisture kinetics. This is because FRPCs are typically used as large thin sheets or plates where thickness is very negligible compared to the in-plane dimensions.

When used in structures, the faces are exposed to moisture which results in primary moisture flow direction occurring along the through-thickness direction, as explained in Figure 1.

N Summary, The Novelty Of This Paper Is Twofold:

• We present a novel tortuosity factor within the realm of FRPCs that can capture the collective influence of fiber architecture. Although presented for 2D micromechanics models in this paper, the concept can be extended to 3D space and multiscale architectures. For example, our work can be extended to multi-scale analysis of 2D and 3D textile composites where the effect of weave patterns, tow cross-sections, tow waviness, etc. on moisture diffusion can be captured effectively by relating diffusivity and tortuosity.

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• By establishing a relationship between tortuosity and diffusivity, diffusivity can be readily estimated using tortuosity. Further, we can use tortuosity as a design parameter for FRPCs composites, within multi-scale analysis, and optimization problems instead of diffusivity. Such tortuosity factors can also be developed for calculating effective electrical and thermal properties.

Figure 1: Macroscale image (right) consists of a sandwich structure composed of Carbon fiber reinforced plain weave polymer composite facings with foam core. Mesoscale image (center) shows a Scanning Electron Microscopy image of the cross-section of one of the facings. Microscale image (left) shows the representative volume element model of a fiber bundle present within a facing. Exposure to moisture occurs on either of the facings along to the thickness direction. As a result, at the microscale, moisture diffusion occurs primarily in the direction perpendicular to the fiber direction.

Omputational Models

Finite element method is used here for studying moisture diffusion in FRPCs. Two-dimensional representative volume element (RVE) micromechanical models are developed for understanding the effect of fiber distribution and fiber volume fraction on moisture diffusivity and tortuosity. These models consist of different spatial distribution of fibers in polymer matrix with a range of fiber volume fractions. Then, the influence of fiber morphology/shape on moisture diffusion is elucidated using a unit cell model. Finally, the combined effect of fiber architecture on moisture diffusivity and tortuosity is studied by modelling RVEs of real microstructures of FRPCs. Although the interphase between fibers and matrix could impact moisture diffusion, we have only considered two-phase (fiber and matrix) models in this paper due to lack of sufficient characterization of interphase chemistry in the literature. Having said that, the approach and models can be easily extended to three-phase models to include fiber-matrix interphases.

In this paper, the influence of fiber architecture on moisture diffusion and tortuosity is investigated first in two steps: 1) fiber volume fraction and spatial distribution, and 2) fiber morphology. Next, real microstructures from FRPCs are considered to capture the combined effect of fiber architecture on moisture diffusion and tortuosity.

Fiber volume fraction and spatial distribution: 2D micromechanical finite element models of RVEs with spatially distributed fibers are considered as shown in Figure 2(a). Figure 2(b)shows a representative cross-sectional image of a carbon fiber-reinforced polymer laminate with five plies where the dimensions along the y-axis are larger than dimensions along the z-axis. Here, A-D shows possible RVE types. In general, RVEs like A and C are not considered while modeling the effective elastic properties due to the boundary effect, and only RVEs like B and D which are in the bulk of the material are considered . In our case, since the interest is in modeling the moisture diffusion from the boundary to the interior of the material, we consider RVEs like A and C that are at the boundary. In this work, only the moisture ingression that occurs along the thickness direction is considered since the composite’s length and width are orders of magnitude larger than the thickness. Therefore, the material periodicity in our 2D models is considered only in the y-direction for numerical simulations. Although, geometric periodicity is considered along the y-axis, we have not considered periodic boundary conditions in our models. Typically, there are three types of boundary conditions used for numerical homogenization in diffusion (conduction) problems, which are uniform concentration gradient boundary condition, uniform flux boundary condition, and periodic boundary condition. In this work, we have considered uniform concentration gradient boundary condition to calculate the tortuosity, which is the average flux along the z-axis, while the other surfaces are insulated. This process needs to be repeated depending upon the direction of interest. Further, these three boundary conditions converge to the same effective properties when the model is sufficiently large . In our model, the size of the RVE is large enough such that the influence of either of the three types of boundary conditions

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mentioned above on the effective properties are minimal. Next, we discuss how we determined the converged size for our RVE.

(B)

Figure 2: (a) Illustration of a 2D micromechanical model (left) with material domains and boundaries highlighted. Cross-sectional view of a real microstructure (right) within a CFRP composite at the microscale, and (b) Representation of different types of RVEs with (A, C) and without (B, D) boundary effect.

The overall domain of the models, Ω, is the union of fibers and matrix regions given by Ωf + Ωm. The dimensions of the entire domain, Ω, is 100µm x 100 µm and the fiber diameter is 7µm. The exterior boundaries of the domain are Γi, where i = 1 −4. We used a numerical statistical approach to determine the size of the RVE, where 2D square models with edge (characteristic) length of 25, 45, 70, 100, and 200 µm are first considered. For every RVE size mentioned above, five random fiber distributions each are generated for three fixed fiber volume fractions (30, 50 and 70 %). We then determined the effective diffusion properties in terms of tortuosity as described later in section 4.3. The mean value and standard deviation for all the RVEs for each volume fractions considered are calculated and plotted in Figure 3. We notice that the mean value of tortuosity converges to a plateau as the sample size increases. From this approach, RVE sample size of 100 µm x 100 µm is considered, which has less than 3% error compared to the largest RVE size.

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Figure 3: Convergence study to determine the RVE size with five realizations for each characteristic length and three different volume fractions. Extensive prior research has been performed using regular arrays of fiber distribution or by considering a unit cell in a 2D micromechanical model to determine the effective diffusivity of composites. In this paper, our model comprises of random fiber distribution and different volume fractions that closely captures the essence of the microstructure of a real composite shown in Figure 2(a) (right). One of the primary reasons for choosing such a representation is to emphasize the vital role of volume fraction, fiber distribution and associated tortuosity on moisture ingression in composite materials reinforced with fibers. We hypothesize that the tortuosity is enhanced by higher fiber volume fractions and more disorderliness in fiber arrangement, which reduces the effective diffusivity of moisture ingression into composites, thus, increasing the time needed for complete degradation of the material. Therefore, 2D models with different fiber distributions and volume fractions are created as shown in Figures 4(a), 4(b) and 4(c). Randomly distributed models with high fiber volume fractions like 60, 65 and 70% are created using a microstructure generation tool - VIPER . These models are then imported into finite element framework for further analysis. A transient moisture diffusion boundary value problem is solved within the finite element framework in ABAQUS to determine the effective diffusivity of each composite model considered. This time-dependent moisture diffusion is based on Fick’s second law, which will be discussed later in Section 4.

(C)

Figure 4: Spatial distribution of fibers (green) in matrix (cream): (a) Random array; (b) Square array; (c) Hexagonal

Array

Fiber morphology: The morphology of fiber cross-section in FRPCs can play an important role on moisture diffusivity and tortuosity[37, 38]. In order to gain an in-depth understanding of the influence of fiber morphology on tortuosity, the morphological features have been further subdivided into 1) fiber cross-sectional perimeter (2D) or fiber cross-sectional surface area (3D) and 2) fiber orientation. For the fiber perimeter study, different fiber shapes like square, asteroid, octagon and circle are chosen such that the tortuosity is the same along the x and y directions. Then, to study the influence of fiber cross-section angle, an elliptical cross-section is chosen and the tortuosity is determined for different fiber cross-sectional angle starting at 0 degrees to 90 degrees of the major axis to the x axis. However, since the real

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microstructure is a combination of circular and deformed shapes, different bean curved cross-sectional shapes are considered using the following parametric equations:

(1)

where, r is the radius, a and b are morphology parameters. Few unit cell models with deformed fiber cross-sections having constant cross-sectional area and different morphology parameters are shown in Figure 5.

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Figure 5: Unit cell models with constant fiber cross-sectional area, but with different fiber morphology parameters a and b: (a) a=1, b=3 ; (b) a=1, b=5; (c) a=1, b=7; (d) a =3, b=3 Real microstructure: Diffusivity and tortuosity of real microstructures within FRPCs are determined next by develop- ing their microscale models. To that end, images of CFRP composites at the microscale are obtained using a Zeiss LEO 1550 VP (Carl Zeiss Jena GmbH–Planetariums, Germany) field emission scanning electron microscope (SEM) at UW-Madison. Specimen cross-sections are polished thoroughly using SiC grinding paper up to 1200 grit size followed by polishing using DACRON II polishing cloth with 1-0.1 mm diamond solution. Then, the cross-section of these specimens are examined under 15 kV electron beam and secondary electron detector to obtain different magnified images with high resolution. The polished gray scale cross-section images similar to the one shown in Figure 6(a) from SEM are converted into two-phase binary images as shown in Figure 6(b) using an image processing tool. These binary images are imported into MATLAB and converted into finite element mesh using im2mesh and MESH2D, which is a simplified version of the mesh generation algorithm presented in [45, 46].

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Figure 6: Process of converting real microstructure image of FRPC into a finite element meshed model: (a) SEM image of a CFRP composite; (b) Two phase binary image; (c) Meshed Finite Element Method model

Governing Equations And Input Properties

The governing equation for transient moisture diffusion is given by,

(2)

where, C is the moisture concentration, J is the flux associated with moisture and D is the diffusion coefficient of moisture or diffusvitiy. The total domain Ω= Ωf + Ωm, where Ωf is the fiber domain and Ωm is the matrix domain as

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shown in Figure 2(a). The exterior boundary of this domain, Γ = Γ1 ∪Γ2 ∪Γ3 ∪Γ4. Equation 2 cannot be directly applied to composites because of material heterogeneity. Therefore, a normalized concentration φ term is used for the diffusion analysis in order to overcome the discontinuities at multi-material interfaces. The normalized concentration and corresponding flux are defined in Equation 3.

(3)

where, S is the solubility.

(4)

This approach of normalized concentration can be verified using interfacial chemical equilibrium law, where a wetness fraction (normalized concentration) function is introduced in the paper by Wong et al. Here, we schematically explain the need for a normalized concentration approach for composites. Consider a bi-material domain as shown in Figure 7 which is representative of a FRPC material with different solubility limits for fiber and matrix. Saturation concentration of fiber is not equal to that of the matrix, which introduces a discontinuity at the interface. Figure 7 shows a schematic of the concentration in the fiber and matrix regions upon solving the original Fick’s law with concentration is the variable. There exists a discontinuity at the interface between the two materials.

Here, Sm and Sf are the solubility limits (saturation concentration) of the matrix and fiber, respectively, and Cm and Cf are the moisture concentration of matrix and fiber, respectively. Due to this discontinuity, it is not possible to solve for the concentrations using traditional finite element method.

(B)

Figure 7: Heterogeneous medium with discontinuous concentration at the fiber-matrix interface: (a) Unsaturated (b)

Saturated

Upon normalizing the concentrations with their respective solubilities, the discontinuity at the interface is removed and φ becomes continuous according to the Nernst partition rule . Figure 8 represents the normalized concentration

(B)

Figure 8: Heterogeneous medium with normalized concentration approach at fiber-matrix interface: (a) Unsaturated

And (B) Saturated

The boundary conditions for the 2D micromechanical model are:

(6)

The transient diffusion governing equations described in Equations 2 and 6 are solved using finite element method to determine effective diffusivity of moisture in micromechanical models. Quadratic triangular elements (DC2D6) within ABAQUS are used for mesh generation, and a convergence study is performed to determine the optimal mesh. The material properties for both fiber and matrix (resin) are given in Table 1. Here, the diffusivity for fibers is considered to be 0 since the diffusivity of fibers is very negligible compared to that of the matrix . This assumption is valid for Carbon and Glass fibers, whereas invalid for Kevlar fibers as they absorb significant amount of moisture. Material properties of Epoxy Resin (LY 556) with HT 972 Hardener were obtained from .

Effective Diffusivity Calculation

For calculating the coefficient of diffusion or moisture diffusivity for FRPCs, we used the theory proposed by Shen and Springer that predicts the coefficient of diffusion under constant temperature and moisture content. They developed an equation that relates moisture content in composites as a function of time with directional diffusivities, geometrical properties and saturation concentration. The percentage moisture gain in composites is given by,

(7)

where, Wd is the weight of a dry specimen after manufacturing, that is, at t = 0. W(t) is the weight of the specimen at a later time instant t.

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Figure 9: Schematic of moisture gain vs time response used for calculating effective diffusivity. Slope of the initial linear region and the plateau moisture saturation value is used in Equation 11.

(8)

where, Msat is the moisture concentration at saturation. Dx, Dy and Dz are the moisture diffusivities along x,y and z directions, respectively. t is time, and h, W and L are the thickness, width and length of the composite, respectively. Shen and Springer considered a composite exposed to moisture on the top and bottom surfaces perpendicular to the thickness h direction. They also assumed that the dimensions of the composite along the x and y directions to be infinite, which makes the concentration change along the x and y directions to be negligible. In our current study, since the diffusion is considered to occur primarily along thickness h direction, in addition to h being very small compared to the in-plan dimensions, the moisture gain is considered to primarily occur in the z direction. Hence, the terms h/L and h/W are neglected from Equation 8 making Dz = Deff. Equation 8 is rewritten to relate the effective diffusivity

(9)

Considering time instants t = t1 and t = t2 in the initial linear region of the moisture gain response, we pick their corresponding moisture gains M1 and M2. Hence, we have,

(10)

Subtracting the above two equations and rearranging gives:

(11)

Diffusivity is numerically calculated by first performing transient moisture diffusion analysis on micromechanical models. Moisture gain percentage the mass concentration at the centroid of each element. These values are averaged over the entire domain at several time instants to obtain the moisture gained by the composite over a time period until it attains moisture saturation concentration. Using the initial slope of the moisture gain curve, thickness along the flow direction and Msat, the effective diffusivity Deff is calculated using Equation 11. An empirical method for calculating effective diffusivity was also proposed by Shen and Springer based on the similarities between heat conduction and

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mass diffusion. Here, they modified the analytical equation proposed by Springer and Tsai for heat conduction to mass diffusion analysis. The transverse diffusivity is given by,

(12)

where Dm and Vf are the diffusion coefficient of resin and fiber volume fraction, respectively.

Tortuosity Calculation

Tortuosity has been predominantly used in electrochemical devices with highly complex electrode microstructure, which results in very tortuous electrolyte flow that plays an important role in ionic conductivity . Tortuosity in a porous media is a significant parameter that characterizes diffusive flow within hydraulic transport, mass transport, electric, heat or ionic conduction. Several porosity-tortuosity associations have previously been published based on experiments, and a detailed review is given by Shen .

Tortuosity is geometrically defined as the ratio of the length of a convoluted path of a diffusive flow in a porous medium to the length of the shortest path in a homogeneous media.

(13)

where, Le is the length of a convoluted path and L is the length of the shortest. Originally, Epstein coined a tortuosity factor that accounts for both the path length and change in diffusivity in a porous media. In their work , they use tortuosity factor within diffusion theory, where effective diffusivity Deff of a porous medium is calculated based on the bulk diffusion coefficient.

(14)

where, Deff , Dbulk, ϵ and τ are the effective diffusivity, bulk diffusivity, pore volume fraction and tortuosity, respectively. In 1935, Bruggeman proposed a Porosity-Tortuosity empirical relationship shown in Equation 15, which is commonly recognized in the field of porous media flow and is often used to derive materials’ effective properties. They assumed that the heterogeneous media consisted of only spherical particles.

(15)

Both geometrical and flux based algorithms have been developed by researchers for determining the tortuosity factor. In geometry based algorithms[56, 57], tortuosity is calculated as defined in Equation 13 using the shortest pathway for which the pore centroid method and the fast marching method are commonly used. Whereas, in flux-based algorithms, the tortuosity factor is calculated by considering diffusion behaviour. In addition, flux based paper, where we perform finite element analysis to determine flux in heterogeneous media as described next. Mesh sensitivity analysis is performed to reduce the effect of the finite element mesh on the tortuosity calculation.

(B)

Figure 10: (a) Schematic representation of diffusive flow in heterogeneous medium with impermeable inclusions; (b) Micromechanical model with regions and boundaries defined For calculating tortuosity factor, we run steady state diffusion analyses on micromechanical models with different fiber volume fractions as well as a model with matrix only. The governing equation and the boundary conditions are as

(16)

Since tortuosity depends on the flow path, we obtained a tortuosity factor in the direction in which the moisture ingression occurs. By solving the Laplace equation shown in Equation 16 using finite element method, volume average of flux J in the heterogeneous medium is determined. The volume average of flux JMF in a homogeneous medium free of barriers (in our case, fibers) is also calculated. The tortuosity factor is determined using the expression shown in Equation 17, which is the same as Equation 14.

(17)

Here, V is the volume of the heterogeneous domain, τ is the tortuosity factor and ϵ is generally termed as porosity or in our case the volume fraction of domain that is available for the movement of flux. In this paper, since we consider that only the matrix absorbs moisture, ϵ can be defined as 1-Vf where Vf is the fiber volume fraction.

Results And Discussion

Effect of Fiber Volume Fraction and Spatial Distribution on Tortuosity and Moisture Diffusivity Our micromechanical model was first validated against experimental results from Vaddadi et al. by comparing the rate of moisture gain and moisture saturation. These 2D micromechanical model comprised of carbon fibers and epoxy matrix system. This numerical model for validation considers moisture ingression for the case of temperature = 85°C

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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