The regulation of mitochondrial respiration in the intact heart may differ from that of isolated mitochondria if intracellular diffusion is restricted. Here we consider which factors may hinder diffusion in vivo and, based on computational analysis, design a reverse engineering approach to estimate the role of diffusional resistance in mitochondrial regulation from an experiment on the intact heart. Computational analysis of respiration measurements on skinned heart fibers shows that the outer mitochondrial membrane does not hinder diffusion enough to cause ADP gradients of tens of micromolars. A diffusion model further shows that the mesoscale structure of the myofibrillar space also does not hinder diffusion appreciably. However, ADP gradients are suggested by the measured activation time of oxidative phosphorylation and may be caused by diffusion restriction of other intracellulax structures or the in vivo microstructure of networks of physically interacting proteins. Based on computational modeling we propose an experiment on the intact heart that allows to estimate the effective diffusion restriction between ATP producing and consuming sites in the cardiac cell.