Am I allowed to process data on a cloud server?

I have gathered some fMRI and eye tracking data, from several subjects.

I can process them using the server in our lab, but somehow, I'd like to take vantage of my own cloud servers on Linode and DigitalOcean, even EC2.

Before these data were gathered, in the consent form we didn't mention the possibilities that data might be processed / stored in the cloud, so I wonder, that in current regulations, am I allowed to use cloud servers to process these data. Does it makes any difference if these servers were purchased under my lab's name?

Thanks