Regressions of a/b against b?


I want to determine how increase in one variable (b) influences the ratio of another variable (a) against b (ie a/b). Without going into technical details of my project, I'll give a simple every-day example: Does the ratio of body height to girth change with increasing girth?

However, the literature indicates that this may yield spurious results since the independant variable is used to calculate the dependant variable.

Is there a way around this?