"So it's interesting to see that in all the patients so far they have improved slightly over the course of their involvement in the study."
The six patients suffered strokes between six months and five years before they were treated, and all had been left with limb weakness.
The patients were assessed using the National Institutes of Health Stroke Scale which ranked the first five patients with a median score of eight before the treatment and four points three months afterwards.
The sixth patient was treated less than three months ago. Six further patients will be treated as part of this Phase 1 trial.
Professor Muir said he was "intrigued" by the early results.
He added: "We know that if you're involved in a trial you are going to see patients change in behaviour, particularly if you're doing something invasive, so we need to be very cautious indeed in interpreting these results.
"However, that said, it is not something we'd anticipated seeing in this group of patients."
Further trials are needed to establish whether stem cells actually help the brain repair damaged tissue.
Michael Hunt, chief executive officer of the company developing the treatment, ReNeuron, said: "The clinical trial is primarily a safety study and we must therefore treat any of the observed early indications of functional benefit with considerable caution at this stage.
"That said, we remain encouraged by the results seen in the study to date and we look forward to providing further updates."
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Stem cell treatment helps heal stroke victims