Utilization of spline functions for smoothing fermentation data and for estimation of specific rates

A response surface method of smoothing fermentation data with spline functions is presented. The available electron balance is used to optimally select the values of the smoothing parameters associated with the spline functions. The method is applied to six sets of anaerobic fermentation data in which pure and mixed cultures are grown in batch followed by fed batch culture. Lactobacillus bulgaricus and Streptococcus thermophilus are cultured on 3% dry milk. Measured concentrations of biomass, lactose, galactose, lactic acid, and other acid products are smoothed using spline functions. Values of specific growth rate, specific lactose consumption rate, specific galactose formation rate, and specific acid product formation rate are estimated and the consistency of the results is examined using the available electron balance. The results show that the method works reasonably well, but that an upper bound should be used for the smoothing parameters to obtain accurate estimates of the derivative quantities.