From the article:

Current research has shown that (i) increased peripheral lactate levels (following high intensity exercise) are associated with increased peripheral BDNF levels, (ii) lactate infusion at rest can increase peripheral and central BDNF levels and (iii) lactate plays a very complex role in the brain’s metabolism. In this review, we summarize the role and relationship of lactate and BDNF in exercise induced neuroplasticity.

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Several trials have used blood lactate for the monitoring of exercise intensity. These studies indicate that higher lactate concentrations are associated with increased BDNF plasma and/or serum levels. Furthermore, current evidence indicates that high intensity interval training evokes larger BDNF levels compared to moderate and/or intensive continuous exercise […] Current research indicates that lactate transport from astrocytes to neurons plays a crucial role for memory formation and could be a link between exercise and neuroplasticity. Pharmacological inhibition of MCT 2 irreversibly impairs long-term memory. Van de Hall et al. have shown that lactate uptake in the brain increases from 8% at rest up to 20% during exercise.