Urothelial cells line the bladder. If the urothelium is damaged, it is vital that it repairs itself quickly. Experimental results shedding light on how this repair process works are presented, revealing in particular the dependence of the response on the length of time for which the drug Troglitazone (TZ) is applied. A simple mathematical model for the basic mechanism (comprising ordinary differential equations) is then developed and analysed, seeking specifically to clarify and quantify the mechanisms governing the dependence of the cell differentiation response on the TZ administration time, rather than providing a comprehensive model of differentiation. Through biologically justified simplifications, analysis reveals that the model gives results in accord with the experimental observations, and suggests new experiments that may aid further understanding. Directions in which this preliminary modelling of the PPARγ (peroxisome proliferator activated receptor γ) pathway could be usefully extended are also indicated.