While the cytosolic fermentation pathway of lactate is well established, a novel feature of the lactate shuttle hypothesis is the oxidation of lactate in the mitochondria. Baba and Sherma (1971) were the first to identify the enzyme lactate dehydrogenase (LDH) in the mitochondrial inner membrane and matrix of rat skeletal and cardiac muscle. Subsequently, LDH was found in the rat liver, kidney, and heart mitochondria.  It was also found that lactate could be oxidized as quickly as pyruvate in rat liver mitochondria. Because lactate can either be oxidized in the mitochondria (back to pyruvate for entry into the Krebs’ cycle, generating NADH in the process), or serve as a gluconeogenic precursor, the intracellular lactate shuttle has been proposed to account for the majority of lactate turnover in the human body (as evidenced by the slight increases in arterial lactate concentration). Brooks et al. confirmed this in 1999, when they found that lactate oxidation exceeded that of pyruvate by 10-40% in rat liver, skeletal, and cardiac muscle.
In 1990, Roth and Brooks found evidence for the facilitated transporter of lactate, monocarboxylate transport protein (MCT), in the sarcolemma vesicles of rat skeletal muscle. Later, MCT1 was the first of the MCT super family to be identified.  The first four MCT isoforms are responsible for pyruvate/lactate transport. MCT1 was found to be the predominant isoform in many tissues including skeletal muscle, neurons, erythrocytes, and sperm.  In skeletal muscle, MCT1 is found in the membranes of the sarcolemma, peroxisome, and mitochondria.  Because of the mitochondrial localization of MCT (to transport lactate into the mitochondria), LDH (to oxidize the lactate back to pyruvate), and COX (cytochrome c oxidase, the terminal element of the electron transport chain), Brooks et al. proposed the possibility of a mitochondrial lactate oxidation complex in 2006. This is supported by the observation that the ability of muscle cells to oxidize lactate was related to the density of mitochondria.  Furthermore, it was shown that training increases MCT1 protein levels in skeletal muscle mitochondria, and that corresponded with an increase in the ability of muscle to clear lactate from the body during exercise.  The affinity of MCT for pyruvate is greater than lactate, however two reactions will ensure that lactate will be present in concentrations that are orders of magnitude greater than pyruvate: first, the equilibrium constant of LDH(3.6 x 104) greatly favors the formation of lactate. Secondly, the immediate removal of pyruvate from the mitochondria (either via the Krebs’ cycle or gluconeogenesis) ensures that pyruvate is not present in great concentrations within the cell.
LDH isoenzyme expression is tissue-dependent. It was found that in rats, LDH-1 was the predominant form in the mitochondria of myocardium, but LDH-5 was predominant in the liver mitochondria.  It is suspected that this difference in isoenzyme is due to the predominant pathway the lactate will take - in liver it is more likely to be gluconeogenesis, whereas in the myocardium it is more likely to be oxidation. Despite these differences, it is thought that the redox state of the mitochondria dictates the ability of the tissues to oxidize lactate, not the particular LDH isoform.