According to an observational study published in the journal eClinical Medicine, people living with long-term COVID who suffer from loss of smell show different patterns of activity in certain regions of the brain.

In the study, the researchers from the University College London used MRI scanning to compare the brain activity of people with long-term COVID who lost their sense of smell with the scan results of those whose sense of smell returned to normal after COVID infection and people who tested negative for COVID-19.

The findings of the study showed that people with long COVID smell loss had reduced brain activity and impaired communication between two parts of the brain, namely the orbitofrontal cortex and the prefrontal cortex. However, the researchers observed that this connection was not impaired in people who had regained their sense of smell after Covid.

Researchers explained that smell loss, known as anosmia, is linked to changes in the brain regions of a Long-Covid patient that prevent smells from being processed properly. They also indicated that patients with long-term COVID smell loss may be compensating for this lost sense by increasing connections with other sensory regions as their brains exhibited increased activity between portions of the brain that process smell and areas of the brain that process sight, i.e., the visual cortex. 

(Source: https://www.livemint.com/news/india/brain-activities-of-covid-patients-decline-who-suffer-from-loss-of-smell-study-11681775564535.html )