From the publication:

Our finding that supplementation of omega-3 fatty acids normalizes the protein levels of BDNF after TBI suggests that BDNF mediates the beneficial effects of omega-3 fatty acids on cognitive function.

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It is notable that fish oil supplementation increased BDNF but did not affect cognitive function in intact rats. It is possible that slight changes in BDNF may not significantly affect cognition under normal conditions. It seems likely, however, that under pathological weakness small decreases in BDNF can be a factor to further deteriorate cognitive function. This eventual possibility emphasizes the necessity to use therapeutic means, such as dietary supplementation of fish oil, to maintain normal levels of BDNF under challenging conditions.

Mitigation of oxidative stress as a mechanism of increased BDNF:

It has been shown that TBI can result in cumulative ROS, which may be associated with reduction of BDNF. Thus, DHA may help to counteract elevated levels of ROS with subsequent effects on the action of BDNF on synaptic plasticity and cognition after TBI.