An effect of procaine (novocaine) on the structural and functional properties of somatic cell membranes was studied based on erythrocyte acidity resistance. To study the effect of different levels of procaine (novocaine) in the bloodstream, the dynamics of the red blood cells rupture was measured after the addition of hydrochloric acid to the red blood cell suspension. The measurements were taken every 15 seconds for 12 minutes. Since the response was sampled at a high frequency, it can be regarded as functional data. One of the research questions was to compare rates of hemolysis under different procaine (novocaine) dosages. We propose a new methodology to perform a pairwise comparison of rates of change based on the closure method and using an analysis of distance approach in a functional data setting. Our methodology allows the comparison of the first derivatives both region-wise in time and pairwise across treatment levels. A simulation study is carried out to compare the practical behavior of the proposed methodology.