The elementary flux modes (EFMs) approach is an efficient computational tool to predict novel metabolic pathways. Elucidating the physiological relevance of EFMs in a particular cellular state is still an open challenge. Different methods have been presented to carry out this task. However, these methods typically use little experimental data, exploiting methodologies where an a priori optimization function is used to deal with the indetermination underlying metabolic networks. Available "omics" data represent an opportunity to refine current methods. In this article we discuss whether (or not) metabolomics data from isotope labeling experiments (ILEs) and EFMs can be integrated into a linear system of equations. Aside from refining current approaches to infer the physiological relevance of EFMs, this question is important for the integration of metabolomics data from ILEs into metabolic networks, which generally involve non-linear relationships. As a result of our analysis, we concluded that in general the concept of EFMs needs to be redefined at the atomic level for the modeling of ILEs. For this purpose, the concept of Elementary Carbon Modes (ECMs) is introduced.