Composite Fatigue Life Ansys

Abstract

A microstructure-sensitive fatigue life prediction framework based on CP- FFT is proposed to study SLM fabricated Hastelloy-X. The microstructure enters in the model through the shape, size and orientation distributions of grains in the RVEs, which are generated from experimental EBSD data.

The framework has been applied to specimens built in two different direc- tions with different polycrystalline microstructures and is able to accurately predict their fatigue life, using just two experiments for calibration. The model reproduces the better fatigue performance found experimentally at high stresses for samples built in transverse direction, identifying the origin of this anisotropy in grain aspect ratios.

Ntroduction

Hastelloy-X is a nickel-based superalloy, primarily strengthened by adding solute elements W, Cr, and Mo [1, 2] which shows excellent oxidation and corrosion resistance at elevated temperatures, making it suitable for gas tur- bines and jet engine parts. Moreover, the alloy shows good formability and weldability, making it an ideal candidate for additive manufacturing fabrica- tion, mainly using a selective laser melting (SLM) route .

SLM is an additive manufacturing process that can achieve near net shapes of complex geometries with stable properties. In this process, a laser beam follows a predefined 2D path over a platform in a sequential manner.

Preprint submitted to International Journal of Fatigue

November 16, 2022

arXiv:2211.08305v1 [cond-mat.mtrl-sci] 15 Nov 2022 After one traverse of a laser beam, the platform is lowered by the prede- fined layer thickness. This procedure is repeated till the completion of the final 3D object . SLM fabrication allows tailoring of the microstructure by changing parameters such as laser energy , scanning strategy [2, 4] or build/sample geometries [2, 4]. The production of net-shape complex com- ponents of Hastelloy-X using a SLM process presents enormous potential for the industry, especially aerospace, which have already started to design and fabricate some jet engine parts using SLM fabricated Hastelloy-X. However, strong variability is found in the monotonic and cyclic/fatigue behavior of SLM components depending on the process parameters and part geometry.

This variability of properties is mainly attributed to the highly heteroge- neous microstructures resulting from the complex thermal cycles followed during fabrication [5, 6, 7, 8] . The most critical design parameter for po- tential high-temperature applications of SLM fabricated Hastelloy-X parts is the fatigue performance. Therefore, models able to predict the fatigue life for SLM components accounting for the effect the heterogeneous microstructure are fundamental for the progressive introduction of these components into industrial applications.

Multiple authors have studied the cyclic deformation and fatigue behavior of SLM components from an experimental viewpoint [9, 10, 11, 5, 12, 13, 14]. Most of these studies reported similar conclusions for a wide range of SLM alloys including IN718 or Ti-6Al-4V [5, 15], namely an inferior fatigue per- formance of the SLM component compared to wrought and cast ones. In some cases, the reduction of fatigue life can be larger than one order of mag- nitude [14, 16, 15, 7]. This worse fatigue performance of SLM components, particularly in as-built case, has been attributed to the porosity , surface roughness or residual stresses , and also to the resulting anisotropy of the part and its orientation with respect to the cyclic loading direction [19, 15]. However, some studies reported the mitigation methodologies for porosity, surface roughness and residual stresses effects on the fatigue lives by optimizing the processing parameters, heat treatment and powder composition. With respect to the specimen orientation, the fatigue life of vertically built specimens has been found to be inferior to horizontally built parts when loaded under stress control [22, 16, 12, 23, 19]. On the contrary, under strain-controlled loading, some studies show the oppo-

Site Effect,

vertically built samples having a superior fatigue performance than horizontally built samples. This fact is justified by the resulting elas- tic anisotropy, vertically built samples have lower elastic modulus and hence underwent lower stress amplitudes than horizontally built samples.

In the particular case of AM Hastelloy-X, a few recent studies can be found in the literature which cover its fatigue analysis. Han et al. studied the effect of hot isostatic pressing (HIP) on the fatigue life of AM Hastelloy-X and concluded that the fatigue life could be significantly improved by HIP due to closure of internal pores and relief of residual stresses. Esmaeilizadeh et al. studied the fatigue life of AM Hastelloy-X as a function of laser scanning speed at room temperature and concluded that fatigue lives could be improved by optimizing the processing parameters. Wang et al. high- lighted the importance of HIP on fatigue life improvement and reported that the part orientation does not play a significant role in the fatigue life for low applied stress level; however, at higher loads, observed that the fatigue resis- tance of vertically orientated specimen is inferior to its horizontally oriented counterpart. Lindstrom et al. reported that the fracture surface of the horizontally oriented specimen had shown more plastic deformation than the vertically oriented specimen.

From the modelling view point, empirical models such as Basquin, Coffin Manson, etc., have been used with experimental data to correlate the fatigue life of different additive manufactured alloys [27, 28, 29], including the study of SLM Hastelloy-X by Esmaelizadeh et al..

However, It Is Well Known

that there is a strong influence of the microstructure in the fatigue life of an alloy, and these models cannot account for it because they are empirical and calibrated with experimental data without considering any microstructural aspect.

The influence of the microstructure in the fatigue performance is mainly affecting the nucleation of a crack. The repeated deformation of the poly- crystal induces the localization of plasticity at the grain level in persistent slip bands which degenerate finally in microscopic fatigue cracks . The regions of the microstructure in which these bands and subsequent cracks are more prone to appear correlate with the points in which some variable related with cyclic plastic deformation is localizing. In order to consider the effect of the microstructures resulting from SLM fabrication in the fatigue life prediction, micromechanical models which model this mechanisms have to be used.

In particular, the approaches relying on the use of polycrystalline com- putational homogenization to estimate the number of cycles for crack nucleation allow to analyze crack nucleation as a function of the mi- crostructure from a statistical viewpoint. Under the microstructure sensitive fatigue life approach, fatigue life is predicted by cyclic accumulation of plas- tic slip and localized stresses that act as a driving force for fatigue crack nucleation on persistent slip bands. The driving force is quantified using Fatigue Indicator Parameters (FIP) that are based on accumulated plastic slip [33, 34], stored strain energy [35, 36, 37], dissipated energy [38, 39, 40, 41] or in general any combination of stress, strain and plastic slip fields .

The FIP is evaluated at each material point by varying local micro-fields and internal variables, and fatigue life is calculated based on the maximum FIP (hot-spots) in the domain. These models include the relevant microstruc- tural features of the polycrystal under study into Representative Volume El- ements (RVE) of the microstructure. The mechanical response of the RVEs under a macroscopic cyclic history is then simulated using crystal plasticity and some computational homogenization approach to obtain some fatigue indicator parameter that is the driving force for crack nucleation.

These

micromechanics-based fatigue life prediction models have been successfully applied to a large number of alloys produced by standard fabrication routes, as wrought Ni-based superalloys [33, 43, 40]. Most of the micromechanical studies of fatigue rely on finite element simulation and only recently Fast Fourier Transform (FFT) solvers have been introduced as an alternative to FEM [42, 44, 32]. The use of FFT-homogenization methods allow accurate prediction of the micro-field response over many cycles at a fraction of the cost of FE based solvers, making it possible to simulate larger RVEs and consider more accurate microstructural features .

The application of crystal plasticity models to investigate the effect of the resulting microstructures of AM metals in their fatigue performance is a trending topic nowadays. These models have already been applied to some SLM fabricated superalloys [45, 46, 47, 48]. In some cases the life prediction is focused on crack propagation stage. Other studies consider crack nu- cleation but the life prediction model is directly linked with the macroscopic cyclic response [25, 20, 27], without making use of the distribution of micro- scopic fields obtained. Only a few studies on AM alloys are available which rely on the use of micromechanical fields through fatigue indicator parame- ters (FIPs) to estimate the fatigue life assuming crack nucleation controlled fatigue. Among these studies, in some cases the real microstructures are not considered and simplified random textures are assumed [49, 50]. In other cases, the actual microstructures obtained from EBSD data are included in the model [51, 46, 52, 53] but the study is focused only on a particular fa- tigue regime, either LCF [46, 51, 53] or HCF [54, 55], and a particular loading control, either strain or stress control.

To summarize, on one hand, there are no available micromechanics based fatigue life prediction approaches available which consider both strain and stress control and a wide range of fatigue lives. On the other hand, there is still a lack of understanding of the effect that the building direction has on the fatigue performance of SLM alloys, originated in the different microstructures developed during SLM fabrication.

In this work, we present a micromechanics based fatigue life prediction approach valid for stress and strain control and a wide range of fatigue lives. From a numerical viewpoint, FFT based polycrystalline homogenization is used to simulate the cyclic response of the specimen. This framework is then applied to analyze the effect of the SLM resulting microstructures, including grain aspect ratios and orientation distributions. The model is applied to study the fatigue life of Hastelloy-X specimens built in different directions including its validation using experimental data under strain and stress control at 750 ◦C for a wide range of fatigue cycles from very low LCF to more than 105 cycles.

Aterial And Fabrication

This work uses a selective laser melting(SLM) route to manufacture the Hastelloy-X samples, whose nominal composition is given in . The bulk samples were built layerwise in the Z direction using the Ren- ishaw RenAM 500Q machine, keeping a constant layer thickness of 60 µm and a rotation of the laser scanning direction between consecutive layers of 67◦(see Fig. 1). Hastelloy-X powder was made via the Ar gas atomization process, providing a powder size in the range of 15 µm to 53 µm. The pa- rameters of the SLM process, such as laser power, scan speed, hatch distance, and volumetric energy density, were well optimized to achieve the maximum part density. The different fatigue specimens were fabricated through the SLM process by ITP Aero in the shape of bulk blocks. The bulk samples were fabricated in two different orientations (see Fig.1): • Bulk Z specimen is built in a cylindrical shape, oriented parallel to the build direction.

• Bulk X specimen is printed with a rectangular shape with dimensions 15 mm×15 mm×100 mm, oriented perpendicular to the build direction. Figure 1: The SLM platform shows different orientations of the bulk samples fabricated using the SLM process along with the build direction.

Coupons necessary for fatigue tests were machined from above-built bulk samples in cylindrical dog-bone shapes with the same gauge length (12.7 mm) and diameter (5.08 mm) shown in Fig.2.

Finally, The Samples Were

heat treated at 1170◦C / 30 minutes and followed by gas cooling.

The

SLM thermal history was removed by this treatment and the SLM process dendrites were dissolved.

This Annealing Also Significantly Minimises The

residual stresses of Hastelloy-X, as observed in Karapuzha et al. .

T Is

also interesting to note that precipitates were found in significant quantities in the Ni-based as-build samples, but after the heat treatment the presence of precipitates in the alloy was strongly reduced or even suppressed.

Icrostructure

The resulting porosity was obtained using a microCT analysis and was be-

Figure 2:

The cylindrical dog-bone-shaped specimen, used for the uniaxial tensile fatigue test. low 1% in all the samples. With respect to the polycrystalline microstructure, it is well known that changes in the printing process parameters generate mi- crostructures with different grain elongation and textures. The bulk samples showed different grain structures in BD than in the XY plane. The elongated grains are observed in the build direction. The direction of epitaxial grain growth depends on the direction of maximum heat flow. The maximum heat flow in the SLM process is observed in the building direction. However, the equiaxed grains are observed in the lateral direction.

The grain size, shape, and orientation distributions were obtained using Electron Backscatter Diffraction(EBSD) imaging technique. Concerning the grain morphology, the Bulk Z sample reveals elongated grain arrangement in the build direction along with an equiaxed grain setup in the XY section (see Fig. 4). The Bulk X specimen exhibits more equiaxed grain arrangement in both sections. The average grain aspect ratio was 1/1/2 and 1/1/1.5 in X-Y-Z axis, for Bulk-Z and Bulk-X samples respectively.

The diameter of the equiaxed grains in the XY plane follows the log- normal distribution. The log-normal distribution parameters(mean and stan- dard deviation) for both bulk samples are enlisted in Table 1. The surface roughness is always present in the SLM samples due to partially melted and unmelted powder on the surface. Therefore, the samples are machined from all directions to minimize the surface roughness impact on the fatigue test.

Table 1: The lognormal distribution of grain diameter of the bulk samples

Standard Deviation

To obtain the orientation distribution of each grain in the microstructure, the EBSD analysis was performed on the samples before the fatigue testing. For this purpose, a SEM with an EBSD detector was used. A confidence index (CI) criteria was used to ensure the accuracy of the measured Euler angles. The Euler angles are measured only if the CI at a pixel is greater than 0.02. The OIM analysis software generates the resultant EBSD orientation maps and M-TEX generates corresponding pole figures in Z-direction, which are depicted in Fig.3 and 4 for the XY and XZ sections of Bulk Z and Bulk X samples respectively. The colors in the EBSD maps that follow the IPF triangle gives the orientation of the building direction concerning the crystal reference frame, and the colors in the pole figures follow the color bar shown at the bottom of Fig.3 and 4. The pole figures depict that both bulk samples have a random texture along the XY and XZ sections.

Echanical Characterization

The uniaxial cyclic performance of SLM fabricated Hastelloy-X at 750◦ was experimentally determined by cyclic tests performed in a wide range of strain and stress amplitudes. The tests were carried out according to the standards PrEN3874-98 and ASTM E606. The results of the fatigue testing campaign will be presented in the result section.

3. Micromechanics Based Fatigue Life Prediction Model A computational polycrystalline homogenization framework based on the crystal plasticity and FFT homogenization (CP-FFT) is used to simulate the cyclic response for SLM Hastelloy-X under strain and stress-controlled loading.

The FFT-based homogenization code FFTMAD is used to simulate the cyclic response of Representative Volume Elements (RVE) of the microstructures considered.

The synthetic RVEs contain grain size distribution, grain aspect ratio, and orientations representative of the actual SLM microstructures experimentally

Figure 3:

EBSD images of Bulk Z (top) specimen in XY and XZ sections respectively. The colors of the maps suggest the orientation of the building direction compared to the reference frames following the IPF triangle. Pole figures using all the orientations (second) and a reduced set obtained after sampling the ODF(bottom), for Bulk Z specimen.

Figure 4:

EBSD images of Bulk X (top) specimen in XY and XZ sections respectively. The colors of the maps suggest the orientation of the building direction compared to the reference frames following the IPF triangle. Pole figures using all the orientations (second) and a reduced set obtained after sampling the ODF(bottom), for Bulk X specimen.

characterized. This section will describe the RVE generation, crystal plas- ticity model that accounts for the cyclic deformation of grains, the FFT homogenization framework, and the quantification methodology to predict fatigue life based on the FIP.

Rve Generation

The digital representation of RVE corresponding to the SLM Hastelloy-X microstructure is done to statistically include the grain size, shape, and orien- tations obtained from the EBSD. The detailed RVE generation methodology is enclosed in our previous work , and briefly recalled here for complete- ness.

The 2D grain size distribution is experimentally obtained from the XY section of EBSD images (see Fig 4) and is first converted to the apparent 3D grain size, assuming spherical grains, using the software GrainSizeTools.

. The 3D distributions are then used as input to generate digital RVEs consisting of equiaxial polycrystals. To this aim, a cloud of points and their corresponding weights are generated to define a weighted Voronoi tessellation which reproduced the targetgrain size distribution .

Finally, RVEs are scaled proportional to the aspect ratios measured. The resulting synthetic RVEs are shown in Fig.5 with XY and XZ sections.

Rystal Plasticity Model

The crystal plasticity (CP) model developed by Cruzado et al. for the cyclic response of Inconel 718 is used in this study to simulate the elasto- viscoplastic cyclic behavior of Hastelloy-X crystals. This model allows to reproduce the isotropic and kinematic hardening and mean stress relaxation effects which might appear under cyclic loading.

The Model Selected Is Size

independent because the differences in grain sizes are below 10%, which would have a negligible influence in the fatigue life. Moreover, kinematic hardening is considered by a flow rule, in contrast to some strain gradient models used in the context of fatigue in which kinematic hardening is obtained as a result of the computing explicitly the GNDs. The reason for this simplification is having a computationally efficient model which allow us to fulfil the two main requirements of our study (1) the use of realistic, statistically representative and well discretized microstructures and (2) considering fatigue life prediction in a statistical manner.

Figure 5:

3D images of RVEs of polycrystalline SLM Hastelloy-X for Bulk Z (top left) and Bulk X (top right). Note that colors indicate the grain numbers. EBSD maps of Bulk Z(bottom left) and Bulk X (bottom right) samples in XY and XZ sections.The colors of the maps suggest the orientation of the building direction compared to the reference frames following the IPF triangle.

A multiplicative decomposition of the deformation gradient F into its elastic (Fe) and plastic (Fp) components is assumed,

(1)

The plastic velocity gradient Lp is computed in the intermediate (relaxed) configuration as function of the shear rates ˙γα on all the slip systems α,

(2)

where, sα and mα are the slip and slip normal directions, respectively, in the initial configuration. The second Piola-Kirchoffstress S depends linearly on the Green-Lagrange strain Ee through the elastic stiffness tensor C, which is given by

(4)

, being Je the determinant of Fe. A power-law is used to define the slip rate in each slip system as,

(5)

where ˙γ0 and m are, respectively, the reference strain rate and the strain rate sensitivity parameters. τ α is the resolved shear stress, defined as, τ α = S : (sα ⊗mα).

(6)

The functions gα and χα are the critical resolved shear stress and backstress on the α slip system respectively. The evolution of the backstress on each slip system defines the kinematic hardening. In the present model , a simplified version of the Ohno Wang

(7)

where c, d, and k are material parameter. k controls the mean stress re- laxation, while c and d stand for direct hardening and dynamic recovery modulus, respectively.

The evolution of the Critical Resolved Shear Stress (CRSS) for a given slip system, gα, defines the isotropic hardening and is given by

(8)

where qαβ are the latent hardening coefficients and h is the self hardening modulus which follows the Voce hardening model , given by

(9)

where, τ0, τs, h0 and hs are the hardening parameters and the accumulated

(10)

3.3. FFT based computational homogenization framework The FFT homogenization code, FFTMAD [44, 59] is used to perform the virtual fatigue test that provide the homogenized performance of polycrystals and the localized stress and strain fields.

The polycrystal response is obtained by simulating the RVEs generated, which are discretized into a regular array of voxels. The constitutive model summarized in the previous section enters through a UMAT subroutine . The FFT homogenization problem in finite strains is solved using the Galerkin FFT method [64, 65, 66]. The differential operators in the FFT solver used a finite differentiation approach using the rotated scheme devel- oped in . Strain, stress and mixed control macroscopic boundary condi- tions are introduced following the technique proposed by Lucarini et al. .

According to this technique, the external macroscopic loading is controlled in terms of macroscopic deformation gradient F ij(t) or first Piola-Kirchoffstress components P IJ(t), for strain and stress-controlled fatigue respectively .

The loading process is discretized in increments and the resulting non-linear system of equations for each time increment defines the deformation gradient which provides stress equilibrium. The non-linear equation is solved using Newton Raphson and the conjugate gradient method is used as linear solver for each Newton iteration.

3.4. Fatigue Indicator Parameters and Life Prediction The successive deformation of the polycrystal induces the localization of plasticity in persistent slip bands which degenerate finally in microscopic fatigue cracks . The areas of the microstructure in which these bands and subsequent cracks will appear correlate with regions where some Fatigue Indicator Parameter (FIP) is maximum. Moreover, quantifying the value of this FIP in that hot-spots allows to estimate the number of cycles to crack nucleation.

In the current study, the Fatigue Indicator Parameter through the microstructure is obtained from computation homogenization of a full cycle. The FIP distribution within the RVE was computed from the variation of micro-fields and the state variables at every material point. This distribution defines the hot-spots in which fatigue cracks are more likely to appear and the fatigue life is predicted based on the most critical point. The most common FIPs found in the literature are, accumulated plastic strain per cycle [33, 30, 34], the plastic stored energy per cycle [35, 37], accumulated internal strain energy and some other parameters.

In this work, plastic work per cycle Wcyc(x) is chosen as local FIP, as it has shown to correlate well the fatigue life in many different materials [38, 39, 40, 41]. This election is merely practical and other FIP would probably lead to similar results. As an example, the stored energy criterion [35, 37], would provide very close number of cycles, since the stored energy is a small fraction of the total plastic work per cycle.

(11)

at each point x in the RVE being τα and ˙γα the resolved shear stress and shear strain rate respectively. Eq.11 is applied at the center of each voxel to obtain a local map of FIP values in the RVE.

However, the crack initiation on the persistent slip bands is a non-local phenomenon, as shown for example in Castelluccio et al. .

For This

reason, and considering also the strong mesh dependence of the local FIP maps, non-local FIP maps are defined as the volume averaged of local FIPs over the grains or bands within a grain parallel to the slip planes with a constant thickness [43, 40].

This Type Of Non-Local Variable Corresponds To

an non-local integral type model. Alternative non-local FIP by means of gradient approaches can be derived, as proposed in The estimation of the number of cycles for crack nucleation is done based on the most critical point of an RVE. In this work, the maximum of the non- local FIPs defined at each band in the RVE is taken as driving force. More details on the geometrical definition in bands can be found in . Each grain is divided in four families of bands, being nb the total number of bands in the RVE. The FIP of the full RVE is then defined as

(12)

where 1 ≤i ≤nb refers to each of the bands in the RVE, βi = 1, 2, 3, corresponds to the three different slips systems contained in the slip plane parallel to that band and Vi is the volume of the band.

Normally, crack nucleation is directly related to the cyclic FIP obtained from Eq.12 using some empirical relations. However, in this work, a different methodology has been used to predict both fatigue life for stress- and strain- controlled loading, keeping a similar definition of FIP.

Strain Controlled Loading

The value of the FIP in a stable cycle can be used to estimate, based on extrapolation, the number of cycles for crack nucleation. The relation between this value and the number of cycles for nucleation can be based on a linear extrapolation or on other relation, as the power law in [40, 41].

In the latter case, the value of the FIP in a stable cycle, Wcyc, is linked to

(13)

where Wcrit and m are two parameters of the material. This biparametric fatigue life prediction law requires the use of two independent fatigue exper- iments to be calibrated.

The use of the previous approach implies direct simulation of the RVE deformation until a stable hysteresis cycle is reached. Under strain control, hysteresis evolves from cycle to cycle, and stabilization can be reached after a few cycles in some cases to thousands of cycles in other cases, depending on the material and loading conditions . To limit the computational cost of these simulations, different strategies have been developed in the context of polycrystalline homogenization, such as the wavelet transformation-based multi-time scaling algorithm (WATMUS) or the linear extrapolation of internal variables or cycle jumps .

Stress Controlled Loading

Contrary to strain-controlled tests, under stress-control loading, the plas- tic flow is concentrated mainly in the first few cycles. From a computational point of view, this usually results in a relatively fast transition to an approx- imate elastic cyclic macroscopic response. Although microplasticity can still be observed after the shakedown regime, the associated FIPs are three to four orders of magnitude lower than the FIPs in plastic regimes, too small for an accurate prediction of crack nucleation based on the extrapolation approaches used for strain control.

As an alternative, we consider that the total accumulated plastic defor- mation (also related to the stored energy) until the shakedown limit is the precursor to the nucleation of a crack. Therefore, in this work, the total

, Is Proposed As Fip To Correlate The

number of cycles for crack nucleation and the microplasticity effects after shaking are neglected in this correlation. The approach proposed here first introduces a criterion to quantify, based on microscopic fields in an RVE simulation, the number of cycles n = ns at which elastic shakedown occurs.

ns such that Wcyc(n = ns) = 10−4Wcyc(n = 1).

(14)

where Wcyc(n) is the FIP value in the RVE (Eq. 12 ) on the nth cycle. Then,

(15)

A power-law function is proposed (Eq. 16) which also includes two fitting

Σ

, and nk to link the accumulated plastic FIP, W acc

, And

the fatigue crack initiation life Ni.

Experimental Results

Uniaxial tensile fatigue tests were performed using strain control in the case of Bulk X samples and under stress control for both Bulk X and Bulk Z. The cylindrical-shaped bulk sample (Bulk Z) was subjected to uniaxial tensile cyclic loading in the building direction (Z), while the rectangular- shaped sample ( Bulk X) was subjected to uniaxial tensile cyclic loading in the X-direction. In the case of strain controlled tests, the hysteresis stress- strain cycle was registered cycle by cycle in order to obtain the cyclic plastic response. From now on, due to the confidentiality agreement signed with the industrial partner, all data are normalized by constant normalization factors.

The normalization factor ∆ϵmin corresponds to the minimum applied strain range under strain loading conditions. For stress, the normalization factor is the critical resolved shear stress, τ0, identified for Hastelloy-X grains at

◦C.

The cyclic uniaxial tests under strain control were carried out with strain

∆Ε

∆ϵmin= 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7 and, 1.8 under strain ratio Rϵ=0. The hysteresis cycles show a combination of isotropic and kine- matic hardening and finally collapse in a stable cycle. An example of these experimental results is represented in Fig. 6, where the stress-strain cycle for the first and N = 2000 cycles (when the cycle became stable) is represented

∆Εmin= 1.6 (Fig.6(B)). The Rest

of the results will be represented together with the model predictions in the next section. In the case of stress-controlled tests, the applied uniaxial stress range

∆Σ

τ0 = 3.2, 3.57, 3.93, 4.29, 4.64, and 5 under stress ratio Rσ=0.03. Both stress and strain controlled tests were carried out at 750°C using a trapezoidal (1s-1s-1s-1s) waveform with a frequency of 0.25Hz and a stress concentration factor (Kt = 1).

The fatigue ε-N curve obtained for strain control and S-N curve for stress control are represented in Fig.7(a) and Fig. 7(b), respectively.

N These

curves, the fatigue life N corresponds to the cycle in which the final fracture is reached on the specimen. The fatigue performance of the samples built in the X and Z directions 7(b) is different, especially for high stress levels where Bulk X samples present longer fatigue life. This result is in agreement with previous studies by Wang et al. where the better performance of the samples built in the X direction is also observed for high stresses.

To observe the mechanism of fatigue failure, a fractography analysis was performed for the two samples loaded with cyclic strain amplitude ∆ϵ/∆ϵmin, 1 and 1.6 at 750◦C. The fracture surfaces obtained are shown in Fig.8(a), and Fig.8(b) respectively, showing the crack initiation (flat areas origin of prop- agating cracks), propagation (beach marks), and final fracture regions (dim-

(B)

Figure 6: Under strain controlled loading, the stress-strain cycle for the first(shown in red color), and N = 2000 cycles(shown in blue color) are represented for two strain ranges,

(B)

Figure 7: The experimental fatigue (a)strain-life curve obtained using strain control loading for Bulk X and (b)stress-life curve obtained using stress control loading for Bulk X and Bulk Z samples.

ples). It is observed that the dominant crack initiation sites were subsurface areas that have some small defects (both unmelted particles or very small pores have been observed), as they act as stress concentration sites. For low strain amplitude ∆ϵ/∆ϵmin=1, multiple crack initiation sites were observed, while at higher applied strains,∆ϵ/∆ϵmin=1.6, a single and well-defined crack initiation site was observed.

Multiple crack initiation sites for small strain amplitude (∆ϵ/∆ϵmin=1) implies that very small heterogeneities near the surface are enough to nucleate a crack and therefore the expected scatter in these cases is greater.

Figure 8: An overall view of the specimen subjected to cyclic strain amplitude, ∆ϵ/∆ϵmin= a) 1 and b) 1.6, %s showing crack initiation, propagation, and final fracture regions. The number of cycles for propagation can be qualitatively estimated by the number of beach marks observed in the propagation area. The crack propagation area for both strain ranges is similar, but since the width of the beach marks is smaller for the lower strain amplitude, the propagation regime is slightly larger for the smaller strain range. A rough estimation of the number of propagation cycles is around 0.01Nf for ∆ϵ/∆ϵmin = 1 and 0.1Nf for ∆ϵ/∆ϵmin=1.6, where Nf is the experimental fatigue life. In both cases, the ratio of propagation to total life is small and nucleation can be considered as the most dominant fatigue mechanism for both applied strains.

This fact validates the modeling approach followed, in which fatigue life is estimated based on the number of cycles for nucleation. The final fracture of the samples was reached when the crack reached the

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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