How the signal-to-noise ratio influences hyperpolarized 13C dynamic MRS data fitting and parameter estimation

MRI Application and Challenges of Hyperpolarized Carbon-13 Pyruvate in Translational and Clinical Cardiovascular Studies: A Literature Review

Cardiovascular disease shows, or may even be caused by, changes in metabolism. Hyperpolarized magnetic resonance spectroscopy and imaging is a technique that could assess the role of different aspects of metabolism in heart disease, allowing real-time metabolic flux assessment in vivo. In this review, we introduce the main hyperpolarization techniques. Then, we summarize the use of dedicated radiofrequency 13C coils, and report a state of the art of 13C data acquisition. Finally, this review provides an overview of the pre-clinical and clinical studies on cardiac metabolism in the healthy and diseased heart. We furthermore show what advances have been made to translate this technique into the clinic in the near future and what technical challenges still remain, such as exploring other metabolic substrates.

Sensitivity schemes for dynamic glucose-enhanced magnetic resonance imaging to detect glucose uptake and clearance in mouse brain at 3 T

We investigated three dynamic glucose-enhanced (DGE) MRI methods for sensitively monitoring glucose uptake and clearance in both brain parenchyma and cerebrospinal fluid (CSF) at clinical field strength (3 T). By comparing three sequences, namely, Carr-Purcell-Meiboom-Gill (CPMG), on-resonance variable delay multipulse (onVDMP), and on-resonance spin-lock (onSL), a high-sensitivity DGE MRI scheme with truncated multilinear singular value decomposition (MLSVD) denoising was proposed. The CPMG method showed the highest sensitivity in detecting the parenchymal DGE signal among the three methods, while both onVDMP and onSL were more robust for CSF DGE imaging. Here, onVDMP was applied for CSF imaging, as it displayed the best stability of the DGE results in this study. The truncated MLSVD denoising method was incorporated to further improve the sensitivity. The proposed DGE MRI scheme was examined in mouse brain with 50%/25%/12.5% w/w D-glucose injections. The results showed that this combination could detect DGE signal changes from the brain parenchyma and CSF with as low as a 12.5% w/w D-glucose injection. The proposed DGE MRI schemes could sensitively detect the glucose signal change from brain parenchyma and CSF after D-glucose injection at a clinically relevant concentration, demonstrating high potential for clinical translation.

Application of low-rank approximation using truncated singular value decomposition for noise reduction in hyperpolarized 13 C NMR spectroscopy

Dissolution dynamic nuclear polarization allows in vivo studies of metabolic flux using ¹³ C-hyperpolarized tracers by enhancing signal intensity by up to four orders of magnitude. The T₁ for in vivo applications is typically in the range of 10-50 s for the different ¹³ C-enriched metabolic substrates; the exponential loss of polarization due to various relaxation mechanisms leads to a strong reduction of the signal-to-noise ratio (SNR). A common solution to the problem of low SNR is the accumulation/averaging of consecutive spectra. However, some limitations related to long delays between consecutive scans occur: in particular, following biochemical kinetics and estimate apparent enzymatic constants becomes time critical when measurement scans are repeated with the typical delay of about 3 T₁ . Here we propose a method to dramatically reduce the noise, and therefore also the acquisition times, by computing, via truncated singular value decomposition, a low-rank approximation to the individual complex time-domain signals. Moreover, this approach has the additional advantage that the phase correction can be applied to the spectra already denoised, thus greatly reducing phase correction errors. We have tested the method on (1) simulated data; (2) performing dissolution of hyperpolarized 1-¹³ C-pyruvate in standard conditions and (3) in vivo data sets, using a porcine model injected with hyperpolarized Na-1-¹³ C-acetate. It was shown that the presented method reduces the noise level in all the experimental data sets, allowing the retrieval of signals from highly noisy data without any prior phase correction pre-processing. The effects of the proposed approach on the quantification of metabolic kinetics parameters have to be shown by full quantification studies.

Schulte R, Laustsen C. Comprehensive Literature Review of Hyperpolarized Carbon-13 MRI: The Road to Clinical Application

This review provides a comprehensive assessment of the development of hyperpolarized (HP) carbon-13 metabolic MRI from the early days to the present with a focus on clinical applications. The status and upcoming challenges of translating HP carbon-13 into clinical application are reviewed, along with the complexity, technical advancements, and future directions. The road to clinical application is discussed regarding clinical needs and technological advancements, highlighting the most recent successes of metabolic imaging with hyperpolarized carbon-13 MRI. Given the current state of hyperpolarized carbon-13 MRI, the conclusion of this review is that the workflow for hyperpolarized carbon-13 MRI is the limiting factor.

Kinetic Modeling of Hyperpolarized Carbon-13 Pyruvate Metabolism in the Human Brain

Kinetic modeling of the in vivo pyruvate-to-lactate conversion is crucial to investigating aberrant cancer metabolism that demonstrates Warburg effect modifications. Non-invasive detection of alterations to metabolic flux might offer prognostic value and improve the monitoring of response to treatment. In this clinical research project, hyperpolarized [1-¹³C] pyruvate was intravenously injected in a total of 10 brain tumor patients to measure its rate of conversion to lactate ( k_PL ) and bicarbonate ( k_PB ) via echo-planar imaging. Our aim was to investigate new methods to provide k_PL and k_PB maps with whole-brain coverage. The approach was data-driven and addressed two main issues: selecting the optimal model for fitting our data and determining an appropriate goodness-of-fit metric. The statistical analysis suggested that an input-less model had the best agreement with the data. It was also found that selecting voxels based on post-fitting error criteria provided improved precision and wider spatial coverage compared to using signal-to-noise cutoffs alone.

Spectral data de-noising using semi-classical signal analysis: application to localized MRS

In this paper, we propose a new post-processing technique called semi-classical signal analysis (SCSA) for MRS data de-noising. Similar to Fourier transformation, SCSA decomposes the input real positive MR spectrum into a set of linear combinations of squared eigenfunctions equivalently represented by localized functions with shape derived from the potential function of the Schrödinger operator. In this manner, the MRS spectral peaks represented as a sum of these 'shaped like' functions are efficiently separated from noise and accurately analyzed. The performance of the method is tested by analyzing simulated and real MRS data. The results obtained demonstrate that the SCSA method is highly efficient in localized MRS data de-noising and allows for an accurate data quantification.

A comparison of quantitative methods for clinical imaging with hyperpolarized (13)C-pyruvate

Dissolution dynamic nuclear polarization (DNP) enables the metabolism of hyperpolarized (13)C-labelled molecules, such as the conversion of [1-(13)C]pyruvate to [1-(13)C]lactate, to be dynamically and non-invasively imaged in tissue. Imaging of this exchange reaction in animal models has been shown to detect early treatment response and correlate with tumour grade. The first human DNP study has recently been completed, and, for widespread clinical translation, simple and reliable methods are necessary to accurately probe the reaction in patients. However, there is currently no consensus on the most appropriate method to quantify this exchange reaction. In this study, an in vitro system was used to compare several kinetic models, as well as simple model-free methods. Experiments were performed using a clinical hyperpolarizer, a human 3 T MR system, and spectroscopic imaging sequences. The quantitative methods were compared in vivo by using subcutaneous breast tumours in rats to examine the effect of pyruvate inflow. The two-way kinetic model was the most accurate method for characterizing the exchange reaction in vitro, and the incorporation of a Heaviside step inflow profile was best able to describe the in vivo data. The lactate time-to-peak and the lactate-to-pyruvate area under the curve ratio were simple model-free approaches that accurately represented the full reaction, with the time-to-peak method performing indistinguishably from the best kinetic model. Finally, extracting data from a single pixel was a robust and reliable surrogate of the whole region of interest. This work has identified appropriate quantitative methods for future work in the analysis of human hyperpolarized (13)C data.

Kinetic analysis of hyperpolarized data with minimum a priori knowledge: Hybrid maximum entropy and nonlinear least squares method (MEM/NLS)

PURPOSE

To assess the feasibility of using a hybrid Maximum-Entropy/Nonlinear Least Squares (MEM/NLS) method for analyzing the kinetics of hyperpolarized dynamic data with minimum a priori knowledge.

THEORY AND METHODS

A continuous distribution of rates obtained through the Laplace inversion of the data is used as a constraint on the NLS fitting to derive a discrete spectrum of rates. Performance of the MEM/NLS algorithm was assessed through Monte Carlo simulations and validated by fitting the longitudinal relaxation time curves of hyperpolarized [1-(13) C] pyruvate acquired at 9.4 Tesla and at three different flip angles. The method was further used to assess the kinetics of hyperpolarized pyruvate-lactate exchange acquired in vitro in whole blood and to re-analyze the previously published in vitro reaction of hyperpolarized (15) N choline with choline kinase.

RESULTS

The MEM/NLS method was found to be adequate for the kinetic characterization of hyperpolarized in vitro time-series. Additional insights were obtained from experimental data in blood as well as from previously published (15) N choline experimental data.

CONCLUSION

The proposed method informs on the compartmental model that best approximate the biological system observed using hyperpolarized (13) C MR especially when the metabolic pathway assessed is complex or a new hyperpolarized probe is used.

Multisite Kinetic Modeling of (13)C Metabolic MR Using [1-(13)C]Pyruvate

Hyperpolarized ¹³C imaging allows real-time in vivo measurements of metabolite levels. Quantification of metabolite conversion between [1-¹³C]pyruvate and downstream metabolites [1-¹³C]alanine, [1-¹³C]lactate, and [¹³C]bicarbonate can be achieved through kinetic modeling. Since pyruvate interacts dynamically and simultaneously with its downstream metabolites, the purpose of this work is the determination of parameter values through a multisite, dynamic model involving possible biochemical pathways present in MR spectroscopy. Kinetic modeling parameters were determined by fitting the multisite model to time-domain dynamic metabolite data. The results for different pyruvate doses were compared with those of different two-site models to evaluate the hypothesis that for identical data the uncertainty of a model and the signal-to-noise ratio determine the sensitivity in detecting small physiological differences in the target metabolism. In comparison to the two-site exchange models, the multisite model yielded metabolic conversion rates with smaller bias and smaller standard deviation, as demonstrated in simulations with different signal-to-noise ratio. Pyruvate dose effects observed previously were confirmed and quantified through metabolic conversion rate values. Parameter interdependency allowed an accurate quantification and can therefore be useful for monitoring metabolic activity in different tissues.

Hyperpolarized magnetic resonance as a sensitive detector of metabolic function

Hyperpolarized magnetic resonance allows for noninvasive measurements of biochemical reactions in vivo. Although this technique provides a unique tool for assaying enzymatic activities in intact organs, the scope of its application is still elusive for the wider scientific community. The purpose of this review is to provide key principles and parameters to guide the researcher interested in adopting this technology to address a biochemical, biomedical, or medical issue. It is presented in the form of a compendium containing the underlying essential physical concepts as well as suggestions to help assess the potential of the technique within the framework of specific research environments. Explicit examples are used to illustrate the power as well as the limitations of hyperpolarized magnetic resonance.

Assessing radiotracer kinetics in the Langendorff perfused heart

BACKGROUND

The Langendorff perfused heart is a physiologically relevant and controllable model with potential for assessing the pharmacokinetics of new radiotracers under a range of pathophysiological conditions.. We assess the feasibility of extending the methods validated for in vivo PET data analysis to the characterisation of PET tracer kinetics applied to Langendorff perfused hearts.

METHODS

Monte Carlo simulations were used to study the accuracy and reproducibility of linear and non-linear spectral analysis (SA/NLSA), the Patlak graphical method and normalised tissue activity (NA). The methods were used to analyse time-activity curves of two widely used PET tracers, [18 F]-FDG and [18 F]-FMISO, acquired ex vivo from Langendorff perfused rat hearts under normoxic and hypoxic conditions.

RESULTS

Monte Carlo simulations showed NLSA to be superior to SA in identifying and quantifying the presence of irreversible trapping component (αo), for low values of αo. The performance of NLSA and SA for high values of trapping was comparable. NLSA was also more precise than SA in determining the absence of trapping over the range of simulated kinetics and SNR. Simulations also suggest that the semi-quantitative method NA is adequate for the evaluation of trapping, and it was found to be more accurate than Patlak. The values of α0 estimated with NLSA from the time series of both [18 F]-FDG and [18 F]-FMISO increased significantly from normoxia to hypoxia in agreement with previous studies. The values of trapping derived using SA increased but not significantly, reflecting the larger error associate with this method. Patlak estimated from the experimental datasets increased from normoxia to hypoxia but was not significant. NA estimated from the [18 F]-FDG data increased from normoxia to hypoxia, but was not significant, whilst NA calculated for [18 F]-FMISO time-activity curves increased significantly.

CONCLUSIONS

Monte Carlo simulations suggested that spectral-based quantitative analysis methods are adequate for the kinetic characterisation of time-activity curves acquired ex vivo from perfused hearts. The uptake rate Patlak and the index NA also represent a good alternative to the SA and NLSA algorithms when the aim of the kinetic analysis is to measure changes in the amount of tracer trapped in the irreversible compartment in response to external stimuli. For low levels of trapping, NLSA and NA were subject to lower errors than SA and Patlak, respectively.

Model free approach to kinetic analysis of real-time hyperpolarized 13C magnetic resonance spectroscopy data

Real-time detection of the rates of metabolic flux, or exchange rates of endogenous enzymatic reactions, is now feasible in biological systems using Dynamic Nuclear Polarization Magnetic Resonance. Derivation of reaction rate kinetics from this technique typically requires multi-compartmental modeling of dynamic data, and results are therefore model-dependent and prone to misinterpretation. We present a model-free formulism based on the ratio of total areas under the curve (AUC) of the injected and product metabolite, for example pyruvate and lactate. A theoretical framework to support this novel analysis approach is described, and demonstrates that the AUC ratio is proportional to the forward rate constant k. We show that the model-free approach strongly correlates with k for whole cell in vitro experiments across a range of cancer cell lines, and detects response in cells treated with the pan-class I PI3K inhibitor GDC-0941 with comparable or greater sensitivity. The same result is seen in vivo with tumor xenograft-bearing mice, in control tumors and following drug treatment with dichloroacetate. An important finding is that the area under the curve is independent of both the input function and of any other metabolic pathways arising from the injected metabolite. This model-free approach provides a robust and clinically relevant alternative to kinetic model-based rate measurements in the clinical translation of hyperpolarized (13)C metabolic imaging in humans, where measurement of the input function can be problematic.

Quantitative measurement of cancer metabolism using stimulated echo hyperpolarized carbon-13 MRS

PURPOSE

Magnetic resonance spectroscopy of hyperpolarized substrates allows for the observation of label exchange catalyzed by enzymes providing a powerful tool to investigate tissue metabolism and potentially kinetics in vivo. However, the accuracy of current methods to calculate kinetic parameters has been limited by T1 relaxation effects, extracellular signal contributions, and reduced precision at lower signal-to-noise ratio.

THEORY AND METHODS

To address these challenges, we investigated a new modeling technique using metabolic activity decomposition-stimulated echo acquisition mode. The metabolic activity decomposition-stimulated echo acquisition mode technique separates exchanging from nonexchanging metabolites providing twice the information as conventional techniques.

RESULTS

This allowed for accurate measurements of rates of conversion and of multiple T1 values simultaneously using a single acquisition.

CONCLUSION

The additional measurement of T1 values for the reaction metabolites provides further biological information about the cellular environment of the metabolites. The new technique was investigated through simulations and in vivo studies of transgenic mouse models of cancer demonstrating improved assessments of kinetic rate constants and new T1 relaxation value measurements for hyperpolarized (13) C-pyruvate, (13) C-lactate, and (13) C-alanine.