Abstract

It is well established that the primary substrate for brain energy metabolism is glucose, but accumulating evidence suggests that lactate can also be considered as an energy substrate for the brain. Additionally, it has been shown that lactate is linked to memory, epilepsy, and traumatic brain injury, which emphasizes the importance of lactate. Considering the effects of lactate and the complexity of imaging its dynamics in neurons and glial cells, researchers are motivated to explore lactate dynamics using mathematical modeling. In this thesis, we propose a new mathematical model for brain lactate exchanges which includes four compartments. In summary, our model consists of four ordinary differential equations explaining interactions between neuronal, astrocytic, capillary, and extracellular space compartments. We simulate this model to assess its abilities to reproduce different qualitative behaviors of lactate dynamics in the brain. These scenarios include increased lactate transport to the brain due to physical exercise and increased lactate production inside neurons and astrocytes. Also, parameter estimation becomes crucial for these types of models due to its effect on the model’s ability to reproduce correct physiological and pathological behavior of the brain. Some parameters can be determined from the experiments in the literature. However, for some of them, there is not a consensus over the values. In this case, an optimization can be done to determine the parameters. In this thesis, we fixed the parameter values for lactate transport and optimized the lactate production and consumption parameters.