High Field Parahydrogen Induced Polarization of Succinate and Phospholactate

Abstract

The signal enhancement provided by the hyperpolarization of nuclear spins of metabolites is a promising technique for diagnostic magnetic resonance imaging (MRI). To date, most ¹³C-contrast agents are hyperpolarized utilizing a complex or cost-intensive polarizer. Recently, the in situ parahydrogen-induced ¹³C hyperpolarization was demonstrated. Hydrogenation, spin order transfer (SOT) by a pulsed NMR sequence, in vivo administration, and detection was achieved within the magnet bore of a 7 Tesla MRI system. So far, the hyperpolarization of the xenobiotic molecule 1-¹³C-hydroxyethylpropionate (HEP) and the biomolecule 1-¹³C-succinate (SUC) through the PH-INEPT+ sequence and a SOT scheme proposed by Goldman et al., respectively, was shown. Here, we investigate further the hyperpolarization of SUC at 7 Tesla and study the performance of two additional SOT sequences. Moreover, we present first results of the hyperpolarization at high magnetic field of 1-¹³C-phospholactate (PLAC), a derivate to obtain the metabolite lactate, employing the PH-INEPT+ sequence. For SUC and PLAC, ¹³C polarizations of about 1–2 % were achieved within seconds and with minimal equipment. Effects that potentially may explain loss of ¹³C polarization have been identified, i.e. low hydrogenation yield, fast T₁/T₂ relaxation and the rarely considered ¹³C isotope labeling effect.

Introduction

Magnetic Resonance Imaging (MRI) is a widely used clinical imaging modality due to its excellent soft tissue contrast and non-ionizing radiation. In clinical routine, however, the available signal-to-noise ratio (SNR) is limiting its application to imaging and probing the properties of the abundant protons (¹H) of water and lipids. While this is sufficient for important and essential diagnostics, many other applications such as sodium imaging¹ or metabolic imaging are not feasible in clinical routine. At room temperature and with currently available magnets, only a few out of a million nuclear spins effectively contribute to the Magnetic Resonance (MR) signal according to the Boltzmann distribution. For ¹H, the low polarization is compensated by a high concentration mostly in water and lipids. Hence, sufficient SNR is obtained and ¹H MRI is feasible. For metabolites or X-nuclei, i.e. a nucleus other than proton, such as ²³Na, ¹³C or ¹⁵N, the situation is different as their concentration, polarization, or natural abundance is much lower. Hence, in many cases, the MR signals of metabolites and X-nuclei are well below the detection limit and signal averaging is required.^1–4

The hyperpolarization, i.e. the creation of a non-equilibrium overpopulation of the Zeeman eigenstates, is a method to boost the polarization of MR active nuclei (and thus its signal) by many orders of magnitude.⁵ For instance, hyperpolarized pyruvate, lactate, and fumarate, have been successfully employed to visualize metabolic processes. Cancer was detected and response to treatment was measured in vivo by Magnetic Resonance Spectroscopy Imaging without background signal.^6–9 Because of the short lifetime of ¹³C hyperpolarization the sensitivity-enhanced detection of metabolic conversion is limited to a time-window of rarely more than two minutes.⁷

The most established and commercially available hyperpolarization technique is dissolution Dynamic Nuclear Polarization (d-DNP)^10,11. However, the method is time-consuming and expensive (10⁶ € or more). Typically, achieving a ¹³C polarization of P > 10 % requires > 30 min per sample.

Another hyperpolarization method is based on the spin order of parahydrogen, i.e. dihydrogen (H₂) enriched in its nuclear singlet state (PHIP).^12–14 Parahydrogen (pH₂) has a combined spin of zero, i.e. it is MR invisible. However, its perfectly ordered spin state can be used to achieve X-nuclei hyperpolarization in several ways. By adding pH₂ to an unsaturated molecule (hydrogenation), the spin order becomes available in the product molecules’ spin system. Under PASADENA¹³ conditions, the ¹H spin order can be transferred to ¹³C through evolution under J-coupling and spin manipulations by spin order transfer (SOT) pulse sequences.^15–24 These sequences consist of periods of free evolution and radiofrequency (RF) pulses applied to ¹H and ¹³C.

The pH₂ based hyperpolarization procedure is typically executed in an external device (the “polarizer”) operating at low magnetic fields in the range of a few milliTesla.^25–33 At these fields, the ¹³C hyperpolarization of lactate derivatives and (diethyl-) succinate as high as 15 % and 28 %, respectively, have been demonstrated.^{31,32,34–37} The hyperpolarization of lactate is promising, because high lactate concentrations are sustained well in living organisms and lactate may be used for the investigation of brain and energy metabolism.^9,38–40 Please note that purification of the solution from the catalyst and reaction side product is required prior rigorous in vivo application.

For metabolic imaging of molecules hyperpolarized by low-field PHIP or d-DNP, the samples are typically transferred to a high field detection site. During this transfer, T₁-relaxation reduces the precious signal enhancement.

Recently, the hyperpolarization of molecules at high field, in an NMR spectrometer or directly in an MRI, has made great progress. ¹³C polarizations of about 60 % and 9 % for esters of the metabolites acetate and pyruvate, respectively, have been achieved in an NMR spectrometer at 7 T.^22,41 Moreover, synthesis amid the magnet bore allows a dramatically enhanced nuclear alignment (SAMBADENA) and we demonstrated that high field methods can be employed to conduct a variant of PASADENA in an MRI system^42–44. Dispensing with the need of a transfer, we administrated and imaged an aqueous hyperpolarized solution within no more than 15 s after hyperpolarization.

So far, the SAMBADENA hyperpolarization of the xenobiotic ¹³C agent 1-¹³C,2,3,3-²H₃-hydroxyethylpropionate (HEP) and the biomolecule 1-¹³C,2,3-²H₂-succinate (SUC) was shown. The different molecular structure of the two substrates required the application of two different SOT sequences for efficient polarization transfer. For hyperpolarization of HEP, the SOT sequence PH-INEPT+²³ was used, whereas for hyperpolarization of SUC, the sequence proposed by Goldman et al¹⁷. was employed. In both cases, ¹H and ¹³C RF pulses were played out for spin order transfer. Calculations in simplified models predicted a ¹³C polarization of 49 % and 99 % for HEP and SUC, respectively.^42,44,45 Experimentally, reduced ¹³C polarizations of about 20 % for HEP and 10 % for SUC were found.^42,44 The low SUC polarization was attributed to singlet-triplet mixing during hydrogenation that led to a 10-fold reduction of available singlet spin order.⁴⁴

Here, we present initial experiences of the SAMBADENA hyperpolarization of 1-¹³C-²H₂-phospholactate (PLAC) at 7 T in an MRI. Furthermore, we investigate the hyperpolarization of SUC with two other SOT sequences, denoted as ECHO^23,46 and ADAPT¹⁹. For both SUC and PLAC, we investigated the hydrogenation and SOT efficiency by varying hydrogenation durations and SOT sequence parameters. Moreover, the influence of pH buffer solutions on the PLAC polarization level was investigated. Quantum mechanical simulations were performed to understand experimental findings better.

Theory and Simulations

¹³C PASADENA Agents and Spin Order Transfer Sequences

Succinate

As the molecule SUC is expected to form an AA′X spin system to a good approximation,³⁷ spin order transfer sequences tailored to strongly coupled protons are well suited (Figure 1a). AA′X spin systems consist of two chemically equivalent but magnetically inequivalent protons A and A′. The values of the J-couplings were taken from literature as J₁₂ = 7.41 Hz, J₁₃ = −7.15 Hz, and J₂₃ = 5.82 Hz.³⁷ The isotropic chemical shifts of the two ¹H nuclei and ¹³C nucleus were determined by NMR spectroscopy and take the values δ₁(¹H) ≈ δ₂(¹H) ≈ 2.75 ppm, and δ₃(¹³C) = 176 ppm. The two protons experience a slightly different effective magnetic field because of isotopic ¹³C labeling and become chemically inequivalent, i.e. δ₁(¹H) ≠ δ₂(¹H). Simulations and experiments indicate that the actual difference of the Larmor frequencies at 7 T is about 4 Hz (Figure 5 and supplementary information). To our knowledge, this effect was not taken into account in simulations of SOT before. Please note that couplings to ²H spins are not considered as the ²H-¹H interactions are a factor of γ(¹H)/γ(²H) = 6 smaller than the ¹H-¹H couplings.⁴⁷ SUC is an intermediate in the tricarboxylic acid cycle and may be used for the diagnosis of brain cancer and potentially other diseases.^35,36,48

Figure 1: Hydrogenation reaction, J-coupling network, and SOT sequences for succinate and strongly coupled protons.

a) The pH₂ protons are added to fumarate (FUM) via a rhodium-based catalyst at 90°C and 20 bar, forming succinate (SUC). The values of the J-couplings read J₁₂ = 7.41 Hz, J₁₃ = −7.15 Hz, and J₂₃ = 5.82 Hz. The SOT sequences ADAPT¹⁹ (b) and ECHO^23,46 (c) were used to transfer the ¹H para order to ¹³C polarization and consist of RF pulses and free evolution times t_AD,α and t_E. Note that ADAPT requires heteronuclear decoupling during hydrogenation to preserve singlet state (red bars), whereas ECHO does not. The black bar denotes a 180° spin echo pulse along the x- or y-axis at t_E/2.

Figure 5: Experimental (squares) and computed (lines) ¹³C polarization of SUC as a function of t_E, the free evolution interval of the ECHO sequence.

The polarization yield of SUC was simulated with and without the effect of the ¹³C labeling on the ¹H chemical shift (red line: Δ_CS = 0 Hz, blue line: Δ_CS = 4 Hz). The simulated polarization yield was scaled by a constant factor 4.9 to match the maximum of the experimental data (SUC.E2). The simulations matched the experiments better if chemically inequivalent protons were assumed (blue line). All data points were measured three times and the error bars represent the standard deviation.

Here, two SOT sequences, denoted as ADAPT¹⁹ and ECHO^23,46, tailored to chemically equivalent protons were employed for hyperpolarization of SUC (Figure 1). In contrast to the recently reported hyperpolarization of SUC with Goldman’s sequence,^17,44,45 ECHO and ADAPT require ¹³C RF pulses only and less RF excitations. Hence, ECHO and ADAPT are expected to be less susceptible to erroneous flip angles and off-resonance effects than Goldman’s sequence. In addition, ECHO does not require heteronuclear decoupling during hydrogenation. This is of major importance for MR systems with limited power specifications of the transmit array.

The ADAPT sequence¹⁹ converts singlet spin order I₁I₂ = I_1zI_2z + I_1yI_2y + I_1xI_2x into detectable ¹³C magnetization (Figure 1b). Therefore, heteronuclear decoupling is essential during hydrogenation to preserve singlet state in the product system. Depending on the flip angle α_x ∈ (0°, 180°), the free evolution interval t_AD,α and number of ADAPT cycles n_α have to be set appropriately. In this contribution, the parameters were chosen as α_x = 90° and n_α = 2. Please note that according to the original description of the ADAPT sequence¹⁹, no 180° spin echo pulses are played out during free evolution. Another sequence, denoted as ECHO here, transfers (I_1z-I_2z)I_3z ¹H spin order into ¹³C polarization and requires neither decoupling during hydrogenation nor ¹H RF pulses (Figure 1c). After hydrogenation, a 90° ¹³C RF pulse followed by free evolution and a 180° spin echo pulse is played out.

Phospholactate

The molecule PLAC forms an ABDX 4-spin system at 7 T with two chemically inequivalent ¹H spins A and B, one ³¹P spin D, and one ¹³C spin X. The chemical shift difference of the two protons, 225 Hz at 7 T, is much larger than the mutual J-coupling of 6.90 Hz (Figure 2). The values of the chemical shifts δ_i in ppm and J-couplings J_ij in Hz were taken from literature³¹ and read δ₁(¹H) = 1.29, δ₂(²H) = 4.33, δ₃(¹³C) = 182.1, δ₄(³¹P) = 4.53, J₁₂ = 6.90, J₁₃ = 4.07, J₂₃ = 3.80, J₃₄ = 6.52, and J₂₄ = 8.60. The sequence PH-INEPT+²³ was employed for hyperpolarization as it was designed for systems containing weakly coupled protons. Originally, it was assumed that the singlet spin order I₁I₂ of pH₂ is converted into I_1zI_2z spin order by averaging of the transversal I_1yI_2y-and I_1xI_2x-components during hydrogenation at high field.^{23 1}H and ¹³C 180° spin echo pulses are played out in between the other pulses to compensate for different precession frequencies.

Figure 2: Hydrogenation reaction, J-coupling network, and PH-INEPT+ sequence used for PLAC.

By addition of pH₂, phosphoenolpyruvate (PEP) is converted to PLAC (a). By means of the PH-INEPT+ pulse sequence²³, spin order is transferred to ¹³C (b). In a simplified model, PLAC is a 4-spin system composed of two weakly coupled protons, one ¹³ C nucleus, and one ³¹P nucleus (blue) with the corresponding J-couplings J₁₂ = 6.90 Hz, J₁₃ = 4.07 Hz, J₂₃ = 3.80 Hz, J₃₄ = 6.52 Hz, and J₂₄ = 8.60 Hz.³¹ The sequence consists of two free evolution intervals and ¹H/¹³ C RF pulses. Black bars denote 180° spin echo pulses.

PLAC was previously hyperpolarized in low magnetic fields and a maximum polarization of up to 15 % was achieved inside a low-field polarizer.^{28,31,32,34,49} It was reported that the phosphate group in PLAC (Figure 2a, orange) is removed by blood dephosphorylation quickly after in vivo administration such that the metabolite 1-¹³C-lactate is obtained.⁴⁹ Please note, that for now, the PHIP-SAH strategy proposed by Reineri et al. is the only method by which pH₂ hyperpolarized 1-¹³C-lactate has been obtained.^50,51

Spin Hamiltonian, Density Matrix, and Strategy for SOT Computations

Spin Hamiltonian

The spin system was driven by the Zeeman interaction considering the isotropic chemical shift (δ_i) and J-couplings (J_ij). The Hamiltonian of PLAC in the laboratory frame of reference reads (ħ = 1)

$${\mathcal{H}}_{\mathrm{P}\mathrm{L}\mathrm{A}\mathrm{C}}=\mathrm{ }-{\mathrm{B}}_0\sum _{\mathrm{i}}{\mathrm{\gamma }}_{\mathrm{i}}\left(1+{\mathrm{\delta }}_{\mathrm{i}}\right){\mathbf{I}}_{\mathrm{i}\mathrm{z}}+2\mathrm{\pi }\sum _{\mathrm{i}<\mathrm{j}}{\mathrm{J}}_{\mathrm{i}\mathrm{j}}{\mathbf{I}}_{\mathrm{i}}{\mathbf{I}}_{\mathrm{j}}$$ (Equation 1)

where the summation runs over all spins and all coupling pairs with I_iI_j = I_ixI_jx + I_iyI_jy + I_izI_jz. Here, γ_i denotes the gyromagnetic ratios of ¹H, ¹³C, and ³¹P (γ₁ = γ₂ = γ_H, γ₃ = γ_C, and γ₄ = γ_P).

The Hamiltonian of SUC is of the form

$${\mathcal{H}}_{\mathrm{S}\mathrm{U}\mathrm{C}}=\mathrm{ }-{\mathrm{B}}_0\left[{\mathrm{\gamma }}_{\mathrm{H}}\left(1+{\mathrm{\delta }}_1\right)\left({\mathbf{I}}_{1\mathrm{z}}+{\mathbf{I}}_{2\mathrm{z}}\right)+{\mathrm{\gamma }}_{\mathrm{C}}\left(1+{\mathrm{\delta }}_3\right){\mathbf{I}}_{3\mathrm{z}}\right]+{\Delta }_{\mathrm{C}\mathrm{S}}{\mathbf{I}}_{2\mathrm{z}}+2\mathrm{\pi }\sum _{\mathrm{i}<\mathrm{j}}{\mathrm{J}}_{\mathrm{i}\mathrm{j}}{\mathbf{I}}_{\mathrm{i}}{\mathbf{I}}_{\mathrm{j}}$$ (Equation 2)

The factor Δ_CS was introduced to account for a difference of the ¹H Larmor frequencies induced by the ¹³C labeling and consequential symmetry breaking.⁵²

Density Matrix of PLAC and SUC

The density matrices representing the spin system after hydrogenation were obtained by numerical simulations. As the reaction takes place over a finite period of time t_hydr, each hydrogenated molecule experiences a different evolution time t. This condition is approximated by calculating the time-averaged density operator

$$\stackrel{-}{{\mathbf{\rho }}_0}=\mathrm{ }\frac{\sum _{\mathrm{t}=\mathrm{n}·\Delta \mathrm{t}}^{{\mathrm{t}}_{\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}}}\mathrm{p}\left(\mathrm{t}\right)\mathbf{Q}\left(\mathrm{t}\right){\mathbf{\rho }}_0{\mathbf{Q}\left(\mathrm{t}\right)}^{†}}{\sum _{\mathrm{t}=\mathrm{n}·\Delta \mathrm{t}}^{{\mathrm{t}}_{\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}}}\mathrm{p}\left(\mathrm{t}\right)}$$ (Equation 3)

where p(t) is a weighting function that reflects the amount of hydrogenated molecules at different points in time. Q is an operator that either describes free evolution (ECHO and PH-INEPT+, Figures 1 and 2) or heteronuclear MLEV16 decoupling⁵³ (ADAPT, Figure 1b). The free evolution operator is given by the matrix exponential of –i$\mathcal{H}$t. The exponential was computed numerically employing the MatLab function “expm”. Ideal RF pulses (on-resonant and instantaneous rotations) are approximated by the exponential of −iαI_jk where α denotes the flip angle and I_jk represents the spin operator of spin j in k-direction (k = x,y, or z). MLEV16 decoupling pulses of finite duration t_MLEV were approximated by a single rotation with subsequent time evolution t_MLEV. The pulse duration of a single 90° excitation within the MLEV16 pulse train was chosen as t_MLEV(90°) ≈ 1 ms in order to simulate the experimental conditions (Table 1).

Table 1: Performed experiments with SUC at 7 T and pH 2.9 using buffer B.1.

The hyperpolarization was investigated in three experimental series: In SUC.E1, ECHO was applied and the polarization was measured as a function of the hydrogenation duration by variation of t_delay with a fixed free evolution interval. In SUC.E2, the free evolution interval t_E was varied while t_delay was fixed. To investigate the polarization scheme of the ADAPT sequence, the free evolution interval t_AD,90° was varied with fixed hydrogenation duration t_hydr = 5 s (SUC.E3).

	SOT	Timings / Parameters
SUC.E1	ECHO	tpH2 = 2 s, Variation of tdelay tE = 70.0 ms Setup 1, 90° C
SUC.E2	ECHO	tpH2 = 2 s, tdelay = 3 s Variation of tE Setup 1, 90° C
SUC.E3	ADAPT	tpH2 = 2 s, tbypass = 3 s αx = 90°, nα = 2 Variation of tAD,90° Setup 2, 90° C tMLEV(90°) = 1 ms

When simulating the hydrogenation process of PLAC numerically, the sudden addition of pH₂ was assumed, resulting in a density matrix of the form

$${\mathbf{\rho }}_0=\left|\mathrm{S}⟩\right.⟨\left.\mathrm{S}\right|\otimes {\text{ρ}}_{{}_{\mathrm{ }}{}^{13}\mathrm{C}}\mathrm{ }\otimes {\text{ρ}}_{{}_{\mathrm{ }}{}^{31}\mathrm{P}}$$ (Equation 4)

The first factor represents singlet state of the two protons, i.e.

$$\left|\mathrm{S}⟩\right.=\frac{1}{\sqrt{2}}\left(\left|\mathrm{\alpha }\mathrm{\beta }⟩\right.-\left|\mathrm{\beta }\mathrm{\alpha }⟩\right.\right)$$ (Equation 5)

in Zeeman basis. The density matrices of the target nucleus ${\text{ρ}}_{{}_{\mathrm{ }}{}^{13}\mathrm{C}}$ and ³¹P spin ${\text{ρ}}_{{}_{\mathrm{ }}{}^{31}\mathrm{P}}$ were assumed to be a normalized $2\times 2$ unity matrix, i.e. non-polarized, neglecting the low thermal ¹³C and ³¹P polarization.

For SUC, two different initial density matrices were considered. In an idealized model the density matrix of a single SUC-molecule was given by

$${\mathbf{\rho }}_0=\left|\mathrm{S}⟩\right.⟨\left.\mathrm{S}\right|\otimes {\mathbf{\rho }}_{{}_{\mathrm{ }}{}^{13}\mathrm{C}}\mathrm{ }$$ (Equation 6)

However, in previous experiments conducted at 7 T using the same hydrogenation catalyst as used in this work, singlet-triplet mixing during hydrogenation led to a significant decrease of singlet spin order.⁴⁴ Analysis of ¹H PASADENA spectra revealed that the amount of singlet and triplet $\left|{\mathrm{T}}_0⟩\right.\mathrm{ }=\frac{1}{\sqrt{2}}\left(\left|\mathrm{\alpha }\mathrm{\beta }⟩\right.+\left|\mathrm{\beta }\mathrm{\alpha }⟩\right.\right)$ spin order was about 55 % and 45 %, respectively. Hence, the density matrix ρ₀ of a single SUC-molecule directly after hydrogenation with pH₂ was further assumed to be of the form

$${\mathbf{\rho }}_0=\left[0.55\left|\mathrm{S}⟩\right.⟨\left.\mathrm{S}\right|+0.45\left|{\mathrm{T}}_0⟩\right.⟨\left.{\mathrm{T}}_0\right|\right]\otimes {\mathbf{\rho }}_{{}_{\mathrm{ }}{}^{13}\mathrm{C}}$$ (Equation 7)

Please note that analytical equations of the time-averaged density matrix were derived for AB and AA’X spin systems by Hübler et al. and Natterer et al.^54,55 In the latter paper, however, a potential ¹³C isotope effect was neglected.

Computations of SOT Sequences

To simulate the effect of free evolution and RF pulses on ¹H and ¹³C, rotation and time evolution operators were applied to the time-averaged density matrix $\stackrel{-}{{\mathrm{\rho }}_0.}$ For different initial states of the spin system (Equations 4–7) and different values of Δ_CS (Equation 2), the ¹³C polarization yield was calculated as a function of the free evolution intervals of the SOT sequences (0.05 ms time increments). Moreover, the influence of the ³¹P spin in PLAC was investigated as computations were conducted excluding or including the ³¹P spin. The transversal polarization was determined by taking the trace over the matrix product of the final density matrix (after application of the SOT sequence) and the polarization operator 2(I_3x+iI_3y). Relaxation effects, for instance due to dipole-dipole interaction or chemical exchange in hydroxyl groups, were neglected in all simulations.

Two-Site Kinetic Model of the Hydrogenation Reaction

To estimate the reaction kinetics and relaxation of ¹H spin order during hydrogenation experimentally, the ¹³C polarization was measured as a function of the total hydrogenation duration t_hydr. A model was developed to fit the data (Equation 8), consisting of an asymptotical increase of the hydrogenated molecules (∝ 1 − exp[−t_hydr/t_cat]), and a mono-exponential decay of the polarization due to relaxation (∝ exp[−t_hydr/t_spin].^42,56

$$P\left(t_{\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}}\right)=\mathrm{ }\frac{P_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\frac{t_{\mathrm{c}\mathrm{a}\mathrm{t}}}{t_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}}-1}\left[{\mathrm{e}}^{\frac{-\left(t_{\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}}-t_0\right)}{{\mathrm{t}}_{\mathrm{c}\mathrm{a}\mathrm{t}}}}-{\mathrm{e}}^{\frac{-\left(t_{\mathrm{h}\mathrm{y}\mathrm{d}\mathrm{r}}-t_0\right)}{{\mathrm{t}}_{\mathrm{s}\mathrm{p}\mathrm{i}\mathrm{n}}}}\right]$$ (Equation 8)

The coefficients P_max and t₀ represent fit parameters that allow the maximum polarization to be adjusted and to consider an activation delay between application of pH₂ pressure and the onset of the hydrogenation reaction, respectively. The time constants for hydrogenation and relaxation of the initial ¹H spin order are denoted by t_cat and t_spin, respectively.

Experiments

Enrichment of Parahydrogen

The fraction of pH₂ was enriched to ≈ 90 % using a custom-built pH₂ converter at a temperature of 21 K as described previously.^42–44,57 The pH₂-enriched gas was stored in 2.7 L steel or 0.5 L aluminum reservoirs at a pressure of 50 bar and was used within 10 hours.

Sample Preparation

1-¹³C,2,3-²H₂-succinate was formed by hydrogenation of 1-¹³C,2,3-²H₂-fumarate (FUM, 118.08 g/mol molecular weight, CAS: 24461–32-3, Cambridge Isotope Laboratories, deionized H₂O as solvent).

By hydrogenation of the precursor 1-¹³C-²H₂-phosphoenolpyruvate (PEP, 170.0 g/mol, in-house synthesis as described in literature³², D₂O as solvent) PLAC is obtained.

For hyperpolarization experiments, reaction solutions were prepared with different concentrations of substrate (c_FUM = 5 mM, c_PEP = 10 mM) and catalyst (c_cat ≈ 2 mM) using a Schlenk line and degassing as described previously^42–44. The catalyst was obtained by mixing 1,4-bis-[(phenyl-3-propane sulfonate) phosphine] butane disodium salt (≈ 2.2 mM, Q36333, 562.5 g/mol, Sigma Aldrich) with bis(norbornadiene)rhodium (I) tetrafluoroborate (≈ 2.0 mM, CAS: 36620–11-8, StremChemicals).

Previous reports of pH₂-induced polarization of SUC and PLAC suggested adjusting the pH value to either low (3–4) or high (10–11) pH for well-resolved J-couplings, to reduce relaxation due to chemical exchange, and to achieve a high hydrogenation yield.^32,37 Hence, different substances B.1-B.3 were used to buffer the reaction solution to a pH of 3 for SUC and about 10 for PLAC.

B.1: A pH buffer based on potassium dihydrogen phosphate (KH₂PO₄, CAS: 7778–77-0) and phosphoric acid (H₃PO₄, CAS: 7664–38-2) for experiments with SUC was prepared (c_KH2PO4 = 40 mM, c_H3PO4 = 3 mM). A pH value of 2.9 was measured at room temperature and before hydrogenation (HI 83141, Hanna Instruments).

B.2: For hyperpolarization of PLAC, sodium phosphate in a powdery form was added to the precursor solution until a pH of 10.6 was measured (Na₃PO₄, CAS: 7601–54-9, Sigma Aldrich). The final Na₃PO₄ concentration was ≈ 22 mM.

B.3: A commercially available stock buffer solution based on boric acid, potassium chloride, and sodium hydroxide with a pH value of 10.0 at 20°C was used for experiments with PLAC (material number 9438, Merck).

Experimental Setup, Workflow, and Performed Experiments

As the experimental setup, workflow, and hydrogenation reactor were described in detail in several previous reports^42–44, only a brief overview is provided here. The experimental setup consists of a 7 T preclinical MRI system (Biospec 70/20, Bruker) and a linearly polarized ¹H-¹³C volume coil (Rapid Biomed). The hyperpolarization experiments were conducted with the help of two or three electromagnetic valves V (type 124, Bürkert) that were controlled with a custom written software (MatLab, National Instruments, Figure 3). To start the experiment, gaseous pH₂ at a pressure of 20 bar was injected into a reactor filled with substrate solution through an inlet at the bottom of the reactor. After the experiment and data acquisition, pressure was released through an outlet at the top. Prior to experiments, the reactor was heated in a 60° C or 90° C water bath.

Figure 3: Experimental setups and timetables showing the actuation of the magnetic valves.

Setup 1: The pH₂ reservoir was connected to the inlet of the reaction chamber via a pressure regulator (PR), valve V1, and a non-metallic check valve. V1 was opened for a period of t_pH2 to initialize the chemical reaction. The SOT sequence was executed after an additional delay (t_delay), resulting in a total hydrogenation time t_hydr. The outlet valve V2 was closed during the entire hydrogenation and hyperpolarization process. After signal detection, V2 was opened and the solution was flushed out from the reactor and caught in a water bath (blue). Setup 2 was identical to setup 1 but an additional valve (V3) was installed to bypass the reactor for equilibration of the pressure between in- and outlet. This valve was opened after t_pH2 for a period of t_bypass to stop the pH₂ injection and to prevent the formation of gas bubbles. When heteronuclear decoupling was required, decoupling was played out only during t_bypass.

The MRI system was adjusted by placing the reactor filled with 1 mL of deionized H₂O in the isocenter of the MRI. The RF coil was tuned and matched manually. The field homogeneity was improved by an automatic first order shimming routine provided by the manufacturer. For experiments with SUC, the ¹H center frequency was set to the resonance frequency of the SUC-protons at ≈ 2.8 ppm. For hyperpolarization of PLAC, the ¹H frequency was centered between the two resonances of the pH₂-nascent protons at 4.33 and 1.29 ppm, i.e. at ≈ 2.8 ppm. The durations of the ¹H and ¹³C SOT RF pulses were chosen as 0.5 ms in all experiments. When heteronuclear decoupling during hydrogenation was required, the ¹H MLEV16 decoupling scheme was applied. The pulse length of a single 90° ¹H RF pulse of the MLEV16 sequence was set to 1 ms.

After hyperpolarization experiments, the ¹³C polarizations were quantified by comparing the hyperpolarized ¹³C signals with a thermally polarized acetone reference sample (4 mL, 13.5 M, 1.1 % ¹³C, 50 averages, 90° excitation, numerical integration with TopSpin, Bruker) assuming a full conversion to SUC and PLAC.

For SUC and ECHO (Figure 1), the hydrogenation reaction was initialized by injecting pressurized pH₂ gas into the reaction chamber by opening the pH₂ valve (V1) for time duration t_pH2 = 2 s (Figure 3, setup 1). After an additional delay of t_delay, i.e. a total hydrogenation duration t_hydr = t_pH2 + t_delay, spin order was transferred.

For SUC/ADAPT and PLAC/PH-INEPT+ (Figures 1 and 2), another setup and workflow was used. This was of particular importance when employing the ADAPT sequence: As previously reported,⁴⁴ heteronuclear decoupling is strongly disturbed during pH₂ injection. Distortions of the field homogeneity because of susceptibility gradients induced by the gas bubbles in aqueous solution during t_pH2 lead to erroneous RF excitations. Therefore, ¹H MLEV16 decoupling pulses were only applied during t_bypass using setup 2. Thus, the total hydrogenation duration was t_hydr = t_pH2 + t_bypass.

A series of different hyperpolarization experiments were performed, where the hydrogenation duration, i.e. t_delay, or free evolution intervals, i.e. t_IN,1/2, t_E, t_AD,α, were varied (Tables 1 and 2). Furthermore, the influence of different pH buffer materials on the PLAC polarization was investigated. The ¹H/¹³C relaxation times and the hydrogenation yield were determined by NMR spectroscopy after hyperpolarization experiments on a 7 T NMR spectrometer (see supplementary information).

Table 2: Performed experiments with PLAC using setup 2 and PH-INEPT+.

First, the hydrogenation conditions, i.e. hydrogenation duration and temperature, were optimized (PLAC.E1 and PLAC.E2). The free evolution intervals t_IN,1 and t_IN,2 of the sequence were varied in another experiment PLAC.E3 with a fixed hydrogenation duration t_hydr = 5 s. The influence of the buffer solutions B.2 and B.3 was examined in an additional set of experiments (PLAC.E4).

	Buffer	Timings / Parameters
PLAC.E1	B.2	tpH2 = 2 s, Variation of tbypass tIN,1 = 60.0 ms, tIN,2 = 50.0 ms 60° C
PLAC.E2	B.2	tpH2 = 2 s, Variation of tbypass tIN,1 = 60.0 ms, tIN,2 = 70.0 ms 90° C
PLAC.E3	B.2	tpH2 = 2 s, tbypass = 3 s Variation of tIN,1 and tIN,2 90° C
PLAC.E4	B.2/3, or no buffer	tpH2 = 2 s, tbypass = 3 s tIN,1 = 87.8 ms, tIN,2 = 70.7 ms 90° C

Results

Hyperpolarization of Succinate

Optimization of the Hydrogenation Duration

SUC was successfully polarized using both ECHO and ADAPT, however, to a lesser degree compared to the results obtained with Goldman’s sequence.⁴⁴ When SUC was polarized with different hydrogenation durations t_hydr (SUC.E1), an optimum was found between 3 s and 6 s (Figure 4). By fitting Equation 8 to the data, the relaxation time of pH₂-nascent spin order t_spin and the hydrogenation constant t_cat were determined as t_spin = (13 ± 5) s and t_cat = (1.4 ± 0.9) s, respectively. This implies that after 5 s of hydrogenation about (97 ± 6) % of all FUM molecules were hydrogenated. Examination of the hydrogenation kinetics by ¹H PASADENA/ALTADENA experiments was not feasible on the MRI system because the ¹H resonances were not resolved due to poor field homogeneity and baseline of the MR spectra.

Figure 4: ¹³C polarization of SUC polarized with ECHO (squares) as a function of the hydrogenation duration t_hydr and fit (line).

FUM (5 mM) was hydrogenated at 90° C and 20 bar pH₂ pressure for different durations (t_hydr) before ECHO (t_E = 70.0 ms) was applied and the polarization was measured (SUC.E1). A function was fitted to the data to extract the hydrogenation and relaxation constant t_cat and t_spin (Equation 8).

Performance of the ECHO Sequence

Computations assuming pure time-averaged singlet state after hydrogenation and chemically equivalent protons, i.e. 100 % $\left|\mathrm{S}⟩\right.$ before time-averaging and Δ_CS = 0 Hz (Equations 2, 3 and 6), predicted a maximum polarization of P = 48.0 % for t_E = 67.7 ms. These is a quite promising result given that the sequence is simple and short. However, when singlet-triplet mixing was taken into account in computations (Equation 7), a 10-fold decrease in polarization was observed (P = 4.8 % for t_E = 67.7 ms). Considering the ¹³C isotope effect with Δ_CS = 4 Hz did not lead to significantly different values for t_E ≤ 100 ms. However, less polarization was found for tE greater than 100 ms (Figure 5, red and blue lines).

To verify the simulations, experiments with varying evolution intervals t_E were conducted. Experimentally, a maximum polarization of P = (0.97 ± 0.15) % was found for t_E = 60.0 ms and 70.0 ms after a t_hydr = 5 s hydrogenation (SUC.E2, Figure 5, squares).

The experimental data was similar to the simulations without isotope effect (Δ_CS = 0 Hz), with singlet-triplet mixing, in the range of t_E ≤ 110 ms and t_E = 190 ms, except for an overall constant scaling factor of 4.94. Significant deviations were observed for t_E = 130, 150, and 170 ms (Figure 5, red line and squares). When the isotope effect was taken into account (Δ_CS = 4 Hz), good agreement was found for all values of t_E (except for t_E = 170 ms) and the same overall scaling factor of 4.94 (Figure 5, blue line and squares). An identical value of Δ_CS was found by comparing experimental and simulated ¹H PASADENA spectra (see supplementary information).

Performance of the ADAPT Sequence

The performance of the ADAPT sequence for hyperpolarizing SUC was investigated in simulations and experiments.

First, a simplified model was assumed, where decoupling was applied for the entire hydrogenation, neglecting reaction intermediates, and relaxation (Equation 6). Here, a polarization of P = 85.3 % was obtained for t_AD,90° = 33.63 ms and Δ_CS = 0 Hz. By adding singlet-triplet mixing (Equation 7), a significant decrease in ¹³C polarization to P = 8.5 % was observed (P = 5.7 % with S-T₀ mixing and without decoupling).

Next, we investigated the hyperpolarization as a function of t_AD,90° (Figure 6). Here, we found that the distribution of the polarization was shifted by ≈ 8 ms to smaller t_AD,90° if the isotope effect was considered (Δ_CS = 4 Hz and decoupling on). The maximum polarization was ≈ 5 % with S-T₀ mixing.

Figure 6: Experimental and simulated (normalized) ¹³C polarization of SUC using ADAPT.

The polarization yield was simulated assuming decoupling during the entire hydrogenation reaction for chemically equivalent (black) and non-equivalent (blue) protons. Experimentally, decoupling was applied only for 3 s after a 2 s delay (squares). The corresponding simulations yielded an oscillating pattern (red). Experimentally, a maximum polarization of ≈ 1.9 % was observed (squares), while the simulations yielded ≈ 5 %. All measured data points represent the mean of three measurements and the error bars correspond to the standard deviation (except for t_AD,90° = 23.0 ms which was measured only once). All simulated polarization yields were scaled by an overall factor to match the experimental data (black, blue, and red lines).

Experimentally, it was necessary to wait for 2 s after the injection of pH₂ before the decoupling was tuned on to avoid inhomogeneous B₀ and ill - defined pulses because of the bubbles.⁴⁴ This means that decoupling was switched off and on, resulting in two different density matrices. Using the results from the above experiments (Equation 8 and Figure 4), we estimated that about 75% of FUM was hydrogenated in the first 2 s without decoupling, and 22 % during the following 3 s with decoupling (resulting in 97% total hydrogenation in 5 s). We used these fraction and density matrixes to simulate the expected total polarization as follows:

$$\mathrm{P}=\frac{0.754·{\mathrm{P}}_{\mathrm{N}\mathrm{o}\mathrm{D}\mathrm{e}\mathrm{c}.}+0.216·{\mathrm{P}}_{\mathrm{D}\mathrm{e}\mathrm{c}.}}{0.97}$$ (Equation 9)

These simulations yielded a similar distribution of the polarization as function of t_AD,90° as the simplified model, but with an oscillation up to about 10% of the absolute value (Figure 6, red line). The maximum polarization was found to be 5.2 % for ≈ 32 ms.

Experimentally, a similar distribution of the polarization was found. The experiments were most similar to the simulations considering the isotope effect. The maximum polarization was about 1.9 % at t_AD,90° = 23.0 ms (SUC.E3, squares).

Hyperpolarization of Phospholactate

SAMBADENA for PLAC was simulated with the SOT sequence PH-INEPT+. When the hydrogenation process was calculated numerically (Equations 3 and 4), the resulting time-averaged 4-spin density matrix was given by pure longitudinal ¹H double spin order, i.e. by

$$\stackrel{-}{{\mathrm{\rho }}_0}=\mathrm{ }\left[\frac{1}{4}\mathbb{E}-\mathbb{ }{\mathrm{I}}_{1\mathrm{z}}{\mathrm{I}}_{2\mathrm{z}}\right]\otimes {\text{ρ}}_{{}_{\mathrm{ }}{}^{13}\mathrm{C}}\mathrm{ }\otimes {\text{ρ}}_{{}_{\mathrm{ }}{}^{31}\mathrm{P}}$$ (Equation 10)

to a good approximation. Based on this density matrix, simulations of the PH-INEPT+ sequence ex- or including the ³¹P spin predicted a maximum ¹³C polarization level of P = 41.2 % for t_IN,1 = 87.8 ms and t_IN,2 = 70.7 ms in both cases.

Optimization of the Hydrogenation Duration

To obtain the optimal hydrogenation duration, we varied t_hydr in the range of 1 to 30 s. When using buffer B.2 and 90° C or 60° C hydrogenation temperature, a maximum polarization of about 0.7 % or 1.2 %, respectively, was found for t_hydr = 5 s (PLAC.E1/2). For 90°C reaction temperature, the lifetime of transferred spin order t_spin and the hydrogenation constant t_cat were determined as (1.3 ± 0.8) s and (17.9 ± 8.8) s, respectively (Equation 8, data not shown). Note that this is quite different to the values obtained for SUC. Fitting the two-site kinetic model to the MRI PLAC data suggested that only (24 ± 10) % of all precursor molecules were hydrogenated after t_hydr = 5 s at 90° C with a hydrogenation constant of t_cat = (17.9 ± 8.8) s. Assuming a (24 ± 10) % hydrogenation yield, an effective ¹³C polarization of (4.2 ± 0.4) % was reached following Gaussian propagation of errors. This is 10-fold less than predicted by simulations (41.2 %). A 63 % hydrogenation yield was measured by high-resolution NMR spectroscopy of the same samples several hours after initializing the hydrogenation (see supplementary information). This indicates an ongoing hydrogenation after the hyperpolarization experiment and an effective polarization yield of about 1.6 %.

Variation of the Free Evolution Intervals

The simulated parameters for PH-INEPT+ yielded a polarization yield of P = (0.63 ± 0.11) % for t_IN,1 = 87.8 ms and t_IN,2 = 70.7 ms using the sodium phosphate buffer B.2 at 90° C (PLAC.E3, Figure 7). By varying t_IN,1 and t_IN,2, we found that the experimental polarization increased slightly to P = (0.82 ± 0.11) % when shorter intervals were used, i.e. t_IN,1 = 60.0 ms and t_IN,2 = 50.0 ms. The measured ¹³C polarizations were identical for 10 ms ≤ t_IN,2 ≤ 110 ms, except for t_IN,2 = 50.0 ms. However, the values were identical within two error intervals.

Figure 7: Experimental and theoretical ¹³C-PLAC polarization as a function of the free evolution intervals of PH-INEPT+.

The intervals were empirically optimized (squares) and compared to simulations (red line). The computations did not suit the experimental outcome after scaling. The mean values and standard deviations are shown.

Please note that the measured polarization yield is about a factor of 65 smaller than predicted by computations. By comparing scaled simulated values and experimental data, mismatches were found for the first and second evolution interval (Figure 7).

Influence of pH Buffer Solution

The hyperpolarization experiments were repeated in differently buffered solutions with t_IN,1 = 87.8 ms, t_IN,2 = 70.70 ms, and a hydrogenation time of t_hydr = 5 s at 90° C (PLAC.E4). When adjusting the pH value to 10.6 through the sodium phosphate buffer (B.2), a maximum polarization yield of P = (0.62 ± 0.11) % was found. When a pH buffer based boric acid (B.3, pH 10.0) was used, a decreased polarization of P = (0.17 ± 0.15) % was found. At neutral pH of 7 before hydrogenation when no buffer solution was added to the solution, a mean polarization of P = (0.16 ± 0.05) % was observed.

¹H and ¹³C PLAC relaxation times

The relaxation times of thermally equilibrated PLAC in the B.2 solution at pH 10.6, room temperature, and 7 T were determined as T₁ = (6.8 ± 0.4) s for the methyl and T₁ = (5.5 ± 0.7) s for methine proton after a hyperpolarization experiment. The T₂ relaxation time of the methyl proton at 1.25 ppm was determined as T₂ = (3.5 ± 0.2) s. T₁ = (31.0 ± 1.0) s and T₂ ≈ 2 s were found for the ¹³C nucleus. See supplementary information for more details.

Discussion

In a previous SAMBADENA related publication, a fundamental hurdle for hyperpolarization of SUC, i.e. singlet-triplet mixing, has been identified.⁴⁴ Here, the loss of polarization due to the ¹³C isotope effect, poor hydrogenation, and fast T₁/T₂ relaxation is discussed for both of the SUC- and PLAC-molecules.

Succinate:

The experimentally observed ¹³C polarization yield of about 1 % through the ECHO or ADAPT sequence was significantly lower than predicted by simulations considering singlet-triplet mixing, i.e. about 5 % for ECHO and 8 % for ADAPT, respectively (Figures 5 and 6). However, the simulated and measured dependencies on the free evolution intervals were in satisfying agreement when an overall scaling factor was introduced, when chemically inequivalent SUC-protons were hypothesized, and when the experimental workflow was considered. The scaling factor may be explained by ≈ 90 % pH₂ enrichment and deviating flip angles within the sample volume. The ¹³C isotope leads to a break of symmetry within the molecule, resulting in different Larmor frequencies of both protons. The assumed difference of Δ_CS = 4 Hz, i.e. a few ppb, is in accordance with previously detected ¹³C-induced shifts of the ¹H Larmor frequency.^58,59 Despite optimization of the free evolution intervals and hydrogenation duration, the herein reported polarization yields of 1 % are substantially lower than those previously achieved through Goldman’s sequence, i.e. 10 %.⁴⁴ However, given the simplicity of ECHO, i.e. ¹³C RF only and no decoupling, the sequence maybe beneficial for low-budget MR units.

Phospholactate:

The experimental polarization yield of about 1 % is lower than expected from computations where a ¹³C-PLAC polarization of roughly 41 % was predicted (Figure 7). ¹H-³¹P and ¹³C-³¹P J-coupling interaction did not affect the polarization yield in simulations.

Evidence for relaxation of spin order was found by variation of the intervals t_IN,1 and t_IN,2 as the experimental maximum was observed for shorter t_IN,1 intervals than predicted by simulations. Contrary, no prominent shift was observed by variation of the t_IN,2 interval. This finding is conclusive as the t_IN,2 interval of the PH-INEPT+ sequence serves for the transformation of ¹³C out-phase in ¹³C in-phase magnetization where only relaxation of ¹³C is important.²³

Please note that in previous studies, ¹³C-HEP was polarized to about 20 % through the same SOT sequence at 7 T using a similar setup.⁴² Comparing the relaxation times and polarization levels of HEP and PLAC leads to the assumption that relaxation may partly explain the tremendous loss of ¹³C-PLAC polarization. First, the longitudinal relaxation times of PLAC, about 6 s for ¹H and 35 s for ¹³C, are a factor of 2 or 5 lower than for HEP⁵⁶ (27 s for ¹H and 75 s for ¹³C in aqueous solution with the same catalyst). Second, the polarization transfer was about a factor of 17 more efficient in HEP than in PLAC. This follows by comparison of the simulated and measured HEP⁴² and PLAC polarization levels, i.e. P_HEP,Sim. ≈ 49 %, P_HEP,Exp. ≈ 20 %, P_PLAC,Sim. ≈ 42 %, and P_PLAC,Exp. ≈ 1 %.

Relaxation in PLAC is potentially more pronounced because of dipole-dipole interaction with the additional ³¹P spin and by the adjacency of the lactate-OH group (Figure 2). This hypothesis is supported by the fact that relaxation times depend on the field strength, temperature, and molecular environment.⁶⁰ For instance, shorter T₁ relaxation times, i.e. 4.3 s for ¹H and 16.2 s for ¹³C, were measured at 9.4 T in earlier studies.³⁴

The observed dependency of the polarization yield on reaction temperature and buffer solution might be caused by changes in the relaxation times and hydrogenation yields.

The experimental polarization yield of 1 % is significantly lower than the 15 % achieved in previous studies conducted at 5.75 mT³² and related to the ¹H-¹³C transfer efficiency, to the hydrogenation reaction, and relaxation times. The achieved signal enhancement of about 1800 at 7 T is likely too low for interesting in vivo applications. Here, faster hydrogenation may prove advantageous to boost ¹³C polarization yields to make this agent suitable for in vivo studies. Please note, that ions (due to the presence of a pH buffer) may lead to the cancellation of hyperpolarized signals as described in literature.⁶¹

Future PHIP Agents and their Application in Biomedical Research

Beside unsaturated double or triple bonds for permanent addition of pH₂, additional requirements need to be fulfilled for the generation of PASADENA hyperpolarized ¹³C agents for biomedical applications. First, chemically inequivalent protons are desirable to prevent polarization loss due to singlet-triplet mixing, challenges with decoupling sequences at high field⁴⁴, and potential isotope labeling effects. Second, molecules with relatively long ¹H and ¹³C relaxation times are preferable to provide high ¹³C polarization since the loss of spin coherence during hydrogenation and SOT is less dominant. The influence of relaxation during spin order transfer might be addressed by appropriate choice of the solvents and pH buffer solutions. Third, PASADENA agents with OH-groups close to the pH₂-nascnet protons and ¹³C should be avoided to decrease the influence of spin exchange induced relaxation. When the requirements are (partly) fulfilled, ¹³C polarization yields of metabolites at high field with pulsed SOT is feasible, e.g. 60 % of ethyl acetate and 9 % of pyruvate, respectively.^22,41 SAMBADENA would allow to perform the hyperpolarization directly in the MRI, at low cost, and next to the application target reducing loss by relaxation.

Conclusion and Outlook

In this contribution, the initial experience with the SAMBADENA hyperpolarization of PLAC, a derivate to obtain hyperpolarized 1-¹³C-lactate, was shown. Moreover, we investigated the hyperpolarization of SUC by means of the ECHO and ADAPT sequences. The low polarizations about 1 % were attributed to a) the ¹³C isotope effect, b) low T₁/T₂ relaxation times, and c) low hydrogenation yields. The symmetry of SUC is broken due to ¹³C labeling (Figure 1a). Consequently, the two SUC-protons precess with different Larmor frequencies (Δ_CS = 4 Hz) and the efficiency of spin order transfer is reduced. The value of Δ_CS was obtained from simulations and experiments (Figure 5 and supplementary information). In the case of PLAC, low relaxation times of the PLAC-protons and low hydrogenation yields may explain the loss of ¹³C polarization. These results are of significance for hyperpolarization with SOT sequences at high magnetic fields. Higher hydrogenation yields and precursor molecule concentrations than in recent SAMBADENA experiments are achievable with a more sophisticated reactor design and experimental setup in future work.