Deep Learning Improves Robustness of Voxelwise Kinetic Modeling for Hyperpolarized Carbon-13 MRI

To evaluate whether deep learning improves the robustness of voxelwise kinetic parameter estimation from hyperpolarized (HP) ¹³C MRI compared with nonlinear least-squares (NLLS) fitting.

A hybrid neural network (NN) was trained on synthetic pyruvate/lactate time courses generated from an open-system two-compartment HP ¹³C signal model to estimate the pyruvate-to-lactate conversion rate ( $k_{\mathrm{PL}}$ ), vascular-extravascular exchange rate ( $k_{\mathrm{VE}}$ ), and vascular volume fraction ( $v_B$ ). NN performance was compared with NLLS across flip-angle schemes, SNR levels, perturbations in acquisition parameters, and in vivo. Matched-ratio simulations tested whether model-estimated ( $k_{\mathrm{PL}}$ ) retained information beyond the Lac/Pyr area-under-the-curve ratio, ${\mathrm{AUC}}_{\mathrm{Lac}/\mathrm{Pyr}}={\mathrm{AUC}}_{\mathrm{Lac}}/{\mathrm{AUC}}_{\mathrm{Pyr}}$ .

In simulations, NLLS and NN performance were comparable for $k_{\mathrm{PL}}$ estimation at high SNR, whereas the NN outperformed NLLS at low SNR and for the weakly identifiable parameters $k_{\mathrm{VE}}$ and $v_B$ . In vivo, NN maps were more spatially coherent than NLLS maps: $k_{\mathrm{PL}}$ corresponded with ${\mathrm{AUC}}_{\mathrm{Lac}/\mathrm{Pyr}}$ , while $k_{\mathrm{VE}}$ and $v_B$ corresponded with pyruvate AUC. In matched-ratio simulations, NLLS-derived $k_{\mathrm{PL}}$ discriminated the metabolic classes better than NN-derived $k_{\mathrm{PL}}$ , although both model-based estimates retained discriminatory information.

NLLS is effective for $k_{\mathrm{PL}}$ estimation under ideal model-matched conditions, whereas the NN provides more stable voxelwise maps, especially for weakly identifiable parameters and under low-SNR or in vivo conditions. Prospective biological or repeatability validation is needed to establish quantitative accuracy.