Is the prayer of one who urinated in a vessel because he was prevented from going to the bathroom due to the long duration of being hooked up to heart rate monitoring devices, and prayed by gesturing, valid?

If you pray in the aforementioned condition, being unable to purify yourself and perform the pillars of prayer, then your prayer is valid and you are not required to repeat it. This is because you have done what you are capable of, and Allah does not burden a soul beyond its capacity.