A data-driven approach for improved quantification of in vivo metabolic conversion rates of hyperpolarized [1-13C]pyruvate

Abstract

Purpose: Accurate quantification of metabolism in hyperpolarized (HP) ¹³C MRI is essential for clinical applications. However, kinetic model parameters are often confounded by uncertainties in radiofrequency flip angles and other model parameters.

Methods: A data-driven kinetic fitting approach for HP ¹³C-pyruvate MRI was proposed that compensates for uncertainties in the B₁ ⁺ field. We hypothesized that introducing a scaling factor to the flip angle to minimize fit residuals would allow more accurate determination of the pyruvate-to-lactate conversion rate (k_PL). Numerical simulations were performed under different conditions (flip angle, k_PL, and T₁ relaxation), with further testing using HP ¹³C-pyruvate MRI of rat liver and kidneys.

Results: Simulations showed that the proposed method reduced k_PL error from 60% to 1% when the prescribed and actual flip angles differed by 60%. The method also showed robustness to T₁ uncertainties, achieving median k_PL errors within ±3% even when the assumed T₁ was incorrect by up to a factor of 2. In rat studies, better-quality fitting for lactate signals (a 1.4-fold decrease in root mean square error [RMSE] for lactate fit) and tighter k_PL distributions (an average of 3.1-fold decrease in k_PL standard deviation) were achieved using the proposed method compared with when no correction was applied.

Conclusion: The proposed data-driven kinetic fitting approach provided a method to accurately quantify HP ¹³C-pyruvate metabolism in the presence of B₁ ⁺ inhomogeneity. This model may also be used to correct for other error sources, such as T₁ relaxation and flow, and may prove to be clinically valuable in improving tumor staging or assessing treatment response.

Keywords: flip angle correction; hyerpolarized C‐13 pyruvate; metabolic conversion analysis; metabolic imaging.

FIGURE 1

(A) Proposed data‐driven kinetic fitting model for a pyruvate‐to‐lactate conversion via k _PL and approach to determine k _PL. Pyruvate (Pyr) and lactate (Lac) magnetizations are lost via T₁ relaxation at a rate of R₁ and radiofrequency pulses (flip angle θ), which are scaled by a parameter, α. (B) In kinetic fitting, the root‐mean‐square error (RMSE) values for lactate fit at varying α were calculated, and k _PL was determined at α = α _optimal where the lowest RMSE is observed. (C) Results of the lactate fits.

FIGURE 2

Experimental setup for animal studies with hyperpolarized (HP) [1‐¹³C]pyruvate. Lac, lactate; Pyr, pyruvate.

FIGURE 3

(A,B) Distributions of α _optimal values obtained from k _PL fitting of simulated pyruvate and lactate signals (A) and k _PL errors that result when α _nominal (blue box plot) and α _optimal (orange box plot) are used in the presence of flip‐angle (θ) errors (B). The orange dashed line represents the case where α _optimal equals the true flip‐angle ratio. Simulation parameters: nominal (θ _Pyr, θ _Lac) = (10°, 30°), nominal R_1,Lac = 1/25 s⁻¹, k _PL = 0.02 s⁻¹, noise level = 0.1 (SNR_max,Lac = 10). SNR, signal‐to‐noise ratio.

FIGURE 4

(A–C) Median values of lactate root mean square error (RMSE; A), α _optimal (B), and k _PL errors (C) from the fitting of simulated pyruvate and lactate signals in the presence of R_1,Lac errors and flip‐angle uncertainties. The α _optimal is the value of α that leads to the minimum RMSE. Simulation parameters: nominal (θ _Pyr, θ _Lac) = (10°, 30°), nominal R_1,Lac = 1/25 s⁻¹, k _PL = 0.02 s⁻¹, noise level = 0.1 (SNR_max,Lac = 10). SNR, signal‐to‐noise ratio.

FIGURE 5

Average B₁ ⁺ scales obtained from the axial B₁ ⁺ field maps of the radiofrequency coil at varying distances through the z‐direction from the center of the coil. The corresponding B₁ ⁺ field map for each data point is displayed below them. The red dashed line corresponds to the B₁ ⁺ calibrated based on the peak power at 0.3 G for Bloch‐Siegert shift pulse.

FIGURE 6

Representative results of k _PL fitting using α _optimal and α _nominal to hyperpolarized [1‐ ¹³ C]lactate data acquired from left kidney (first row), right kidney (second row), and liver (bottom row) in three successive experiments conducted with (θ _Pyr, θ _Lac) = (10°, 30°) (“underflipped”), (15°, 45°), and (20°, 60°) (“overflipped”) radiofrequency pulses, shown in (A), (B), and (C) columns, respectively. Solid red and dashed blue curves overlaid on the acquired lactate signals show the lactate fits when α = α _optimal and α _nominal, respectively. The red and blue markers shown in the root mean square error (RMSE) plots respectively indicate α _optimal at the minimum RMSE and α _nominal = prescribed (θ _Pyr, θ _Lac)/(15°, 45°).

FIGURE 7

The k _PL values obtained from left/right kidneys and liver regions of interest on rats injected with hyperpolarized pyruvate in six animal studies (three experiments and three controls). Each study contains three data sets with varied or constant θ. (A,B) The k _PL results from using α _nominal (A) and α _optimal (B). Error bars represent a 95% confidence interval for the fits, and the dashed lines across the three k _PL values in each study represent the mean k _PL.