1 PERFORM Centre, Concordia University, Montreal, Canada; Electrical and Computer Engineering Department, Concordia University, Montreal, Canada. Electronic address: milad.soltanzadeh@mail.utoronto.ca.
2 University of Rennes, INSERM, LTSI-UMR 1099, F-35000, Rennes, France. Electronic address: solenna.blanchard@gmail.com.
3 PERFORM Centre, Concordia University, Montreal, Canada; Brain Imaging Centre, Montreal Neurological Institute, McGill University, Montreal, Canada. Electronic address: jean-paul.soucy@mcgill.ca.
4 PERFORM Centre, Concordia University, Montreal, Canada; Electrical and Computer Engineering Department, Concordia University, Montreal, Canada. Electronic address: habib.benali@concordia.ca.

It is well known that glucose serves as the main energy substrate for the brain, and emerging evidence emphasizes its involvement in both physiological processes and disease (traumatic brain injury, memory, epilepsy, etc.). Furthermore, the usefulness of mathematical modeling in deciphering underlying dynamics of the brain to investigate lactate roles and mechanisms of action has been well established. Here, we analyze a novel mathematical model of brain lactate exchanges between four compartments: neurons, astrocytes, capillaries, and extracellular space. A system of four ordinary differential equations is proposed to explain interactions between these compartments. We first optimize the model's parameters under normal, resting state conditions, and then use it to simulate changes linked to elevated arterial lactate. Our results show that even though increased arterial lactate results in increased uptake by astrocytes and release to the extracellular space, it cannot strongly recover the initial drop in neuronal lactate concentration. Also, we show that the direction of lactate transport between the compartments is influenced by the maximum astrocyte production rate and the transport rate between astrocytes and extracellular space.