They provide a plausible laboratory model on which to investigate some clinical aspects of the human hypertension.

on which to do...是定语从句的省略表达。该句可以变成：

They provide a plausible laboratory model on which they (can) investigate some clinical aspects of the human hypertension.

【翻译】他们提供了一个可信的实验室模型，（他们）以此来研究人类高血压的一些临床情况。