Fig. 3.

Kinetic model for DGE ²H-MRS. A Modification of the model proposed by Kreis et al. (Kreis et al., 2020) for measuring the maximum rate of glucose consumption (V_max) for synthesis of lactate (V_lac) and glutamate-glutamine (V_glx): V_max = V_glx + V_lac. B Performance of V_glx and V_lac estimates (mM min⁻¹) when v (0–1) is taken as a model-free parameter of the kinetic model (model I) vs. when parameter v is fixed to the value obtained from DCE T1-w data (model II), demonstrated in two tumors: top, G4; bottom, G6. Different V_glx and V_lac estimates were obtained by running the fitting procedures with different initial guess estimates, which were uniformly sampled between maximum/minimum values of confidence interval range across all the samples. While for some samples model I and II estimates showed comparable results (G4: 0.301 and 0.252 for V_glx, and 0.766 vs 0.702 for V_lac, respectively), in other samples meaningful estimates were only obtained by fixing v to the value obtained from DCE T1-w data (G6: 0–600 and 0.117 for V_glx, and; 0–1200 and 0.437 for V_lac, respectively). C Precision of the model demonstrated by iteratively (x1000) adding random noise (1 %) to the parameter estimations obtained with v fixed (model II) and repeating the estimations with the same model at each step. While noisy estimates from different iterations render normal distributions, their values are around the initial estimates and consistently suggesting higher V_glx and V_lac for G4 compared to G6 (0.252 vs. 0.177, and 0.702 vs. 0.437, respectively). a₁, Glc concentration after the bolus injection (mM); k_p, effective rate constant of labeled glucose transfer to tissue (min⁻¹); k_g, apparent rate constant of glucose transfer between blood and tumor (min⁻¹); V_glx, maximum rate of Glc consumption for Glx synthesis (mM min⁻¹); k_glx, apparent rate constant of Glx elimination (min⁻¹); V_lac, maximum rate of Glc consumption for Lac synthesis (mM min⁻¹); k_lac, apparent rate constant of lactate elimination (min⁻¹); V_max, maximum rate of total Glc consumption (mM min⁻¹).