Deep Learning Improves Robustness of Voxelwise Kinetic Modeling for Hyperpolarized Carbon-13 MRI.
Authors
Affiliations (4)
Affiliations (4)
- Department of Physics and Astronomy, Howard University, Washington, DC, USA.
- Department of Mathematics, Howard University, Washington, DC, USA.
- College of Medicine, Howard University, Washington, DC, USA.
- Department of Radiation Oncology, Johns Hopkins Medicine, Washington, DC, USA.
Abstract
To evaluate whether deep learning improves the robustness of voxelwise kinetic parameter estimation from hyperpolarized (HP) <sup>13</sup>C 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 <sup>13</sup>C signal model to estimate the pyruvate-to-lactate conversion rate ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>PL</mi></msub> </mrow> </math> ), vascular-extravascular exchange rate ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>VE</mi></msub> </mrow> </math> ), and vascular volume fraction ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>v</mi> <mi>B</mi></msub> </mrow> </math> ). 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 ( <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>PL</mi></msub> </mrow> </math> ) retained information beyond the Lac/Pyr area-under-the-curve ratio, <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>AUC</mi> <mrow><mi>Lac</mi> <mo>/</mo> <mi>Pyr</mi></mrow> </msub> <mo>=</mo> <msub><mi>AUC</mi> <mi>Lac</mi></msub> <mo>/</mo> <msub><mi>AUC</mi> <mi>Pyr</mi></msub> </mrow> </math> . In simulations, NLLS and NN performance were comparable for <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>PL</mi></msub> </mrow> </math> estimation at high SNR, whereas the NN outperformed NLLS at low SNR and for the weakly identifiable parameters <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>VE</mi></msub> </mrow> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>v</mi> <mi>B</mi></msub> </mrow> </math> . In vivo, NN maps were more spatially coherent than NLLS maps: <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>PL</mi></msub> </mrow> </math> corresponded with <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>AUC</mi> <mrow><mi>Lac</mi> <mo>/</mo> <mi>Pyr</mi></mrow> </msub> </mrow> </math> , while <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>VE</mi></msub> </mrow> </math> and <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>v</mi> <mi>B</mi></msub> </mrow> </math> corresponded with pyruvate AUC. In matched-ratio simulations, NLLS-derived <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>PL</mi></msub> </mrow> </math> discriminated the metabolic classes better than NN-derived <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>PL</mi></msub> </mrow> </math> , although both model-based estimates retained discriminatory information. NLLS is effective for <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><msub><mi>k</mi> <mi>PL</mi></msub> </mrow> </math> 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.