Hi Nicole. In my opinion, some things in fitness may not need a research study or article to support them 🙂 Your client’s work on the treadmill, like any other exercising, can be explained in simple terms related to ‘exercise intensity,’ and “overload.”
If your client’s goal is to IMPROVE their cardiovascular fitness they need to up their intensity in order to progressively overload their system – period. I use analogies a lot in explaining concepts to my clients. One I like to use regarding overload and intensity is I will take out a pencil and say “there is no doubt that this pencil has weight – right? So, what if everyday I came to the gym, lifted this pencil 150 times – do you think that I will start to get stronger?” Of course this is a ridiculous example, but the underlying message is clear – you improve through manipulating the intensity of your exercise in order to overload your system.
I hope that this helps.