We use our framework to model two physiologically relevant test systems: 1) advection–dispersion dynamics of glucose transport in the microvasculature and 2) advection–dispersion-reaction dynamics of glucose–lactate exchange in the functionally coupled tissue–vascular domains (glucose–lactate dynamics is relevant in tumor metabolism where metabolic activity alters in tumor microenvironments (Yang et al., 2021) and in modeling fuel-stimulated insulin secretion (Jiang et al., 2007; Prentki et al., 2013)). This evidence concerns the gene INS and neoplasm.