(13)C metabolic flux analysis: Classification and characterization from the perspective of mathematical modeling and application in physiological research of neural cell

(13)C metabolic flux analysis ((13)C-MFA) has emerged as a forceful tool for quantifying in vivo metabolic pathway activity of different biological systems. This technology plays an important role in understanding intracellular metabolism and revealing patho-physiology mechanism. Recently, it has evolved into a method family with great diversity in experiments, analytics, and mathematics. In this review, we classify and characterize the various branch of (13)C-MFA from a unified perspective of mathematical modeling. By linking different parts in the model to each step of its workflow, the specific technologies of (13)C-MFA are put into discussion, including the isotope labeling model (ILM), isotope pattern measuring technique, optimization algorithm and statistical method. Its application in physiological research in neural cell has also been reviewed.