Data from the English Longitudinal Study of Aging, in which nearly 4,000 older adults (60+) had their walking speed assessed on two occasions in 2002-2003 and in 2004-2005, those with a slower walking speed were more likely to develop dementia in the next 10 years. Those who experienced a faster decline in walking speed over the two-year period were also more likely to develop dementia.

https://www.eurekalert.org/pub_releases/2018-03/ags-oaw032318.php

A long-running study involving 175 older adults (70-79) found that slowing in walking speed over a 14-year period was associated with cognitive impairment, and with shrinkage of the right hippocampus specifically.

Gait slowing over an extended period of time was a stronger predictor of cognitive decline than slowing at a single time point. All the participants slowed over time, but those who slowed by 0.1 seconds more per year than their peers were 47% more likely to develop cognitive impairment.

The finding held even when the researchers took into account slowing due to muscle weakness, knee pain and diseases, including diabetes, heart disease, and hypertension.

Typically, a slowing gait is seen as a physical issue, but doctors should consider that there may be a brain pathology driving it.

http://www.futurity.org/gait-hippocampus-brains-dementia-1472892/