Mathematical correlation between biomaterial and cellular parameters—Critical reflection of statistics

For mathematical modelling of the biomaterial-cell contact, it is necessary to find both parameters characterizing physical and chemical properties of the material surface and also such describing the reaction of the adhering cells. Only those material and cell parameters that correlate with each other are applicable to model this contact mathematically. Only few papers are dealing with this special problem.The aim of this paper is to present results of physical/chemical and biological investigations made on differently modified rough titanium implant surfaces in order to find out only the correlating parameters. Furthermore we discuss several ways to apply statistical methods to the correlation problem.Only few ones of all investigated parameters both on material and on cellular side were applicable for correlation. For example we found in our studies that fractal structure parameter topothesy has influence on the spreading behaviour of the osteoblastic cells. However the value of the correlation coefficient and its statistical significance heavily depend on the method of averaging the available data. Especially the biological data (spreading area) were afflicted with relatively high error up to 30%. Averaging of this data masks the true facts. That is why the correlation coefficient considerably decreases if the biological parameters are not averaged. On the other hand, the statistical reliability increases due to the higher number of investigated cases.Critical error discussion is necessary in statistical correlation between material and biological parameters. Often the results are heavily influenced by the statistical handling of data, especially if only few data are available. May be that new unconventional methods like bootstrap method can show a way out of this dilemma.