Latent growth process

#1
Hi,
I'm starting a study investigating the use of several medical imaging measurements taken pre-treatment to predict treatment outcome. Treatment outcome is measured using a continuous quantitative measure, not related to medical imaging. However, treatment outcome is measured 3 times over the course of 9 months.
I'm not a stats person but my research today has found the following:
1. I can simply group my subjects as responders and non-responders and use a t-test to determine if the groups have different mean imaging findings.
2. I can use linear regression to regress one outcome onto the imaging quantities. The outcome in this case could be the final outcome measurement or the mean of all 3, for example.
3. I can model the treatment response as a latent growth process, and regress the parameter estimates onto the imaging quantities.

I don't understand the 3rd option. How do I model the latent growth process? Is it simple linear regression? Polynomial? From there, how do I regress multiple parameters onto the imaging findings?
I am planning on using MATLAB for this. Your comments appreciated!