[verb ます-stem] + 通す [verb ます-stem] + 通し
通す after a verb's ます-stem means "keep doing it all the way through": the action runs to the end without stopping or giving up. The result is an ordinary godan verb – やりとおすやり通す, やりとおしたやり通した, やりとおさないやり通さない.
The verb goes in the ます-stem, not the dictionary form: ×走る通す.
With a stretch of time, 通す says the action filled all of it.
With a belief, an opinion or a lie, 通す means keeping it up to the end against pressure.
These go beyond the verb 通す.
The ます-stem plus とおし通し, read どおし, is a noun: "doing it the whole time". It takes だ and is used mostly with standing, walking and working.