A process that combines the advantages of solid state fermentation (SSF) and submerged fermentation (SmF) could increase the efficiency of cellulase production required in the cellulosic ethanol industry. Due to the difficulty of measuring cellular biomass in the presence of solids, we developed a novel methodology for indirect quantification of biomass during production of the pre-culture for a combined fermentation process. Cultivation of Aspergillus niger was initiated as SSF using sugar cane bagasse as a solid substrate. Experiments were conducted in the absence of bagasse to determine growth kinetic parameters. Changes in glucose and biomass concentrations were measured. and the data were used for simulation employing a simple unstructured model. Parameters were estimated by applying a combination of Simulated Annealing (SA) and Levenberg-Marquardt (LM) algorithms to search for minimization of the error between model estimates and experimental data. Growth kinetics followed the Contois model, with a maximum specific growth rate (${mu}_{max}$) of 0.042/h, a yield coefficient for biomass formation ($Y_{x/s}$) of 0.30 g/g and a death constant ($k_D$) of 0.005/h. These parameters were used to simulate cellular growth in the solids-containing medium. The proposed model accurately described the experimental data and succeeded in simulating the cell concentration profile. The selected pre-culture conditions (24 h as SSF followed by 48 h as SmF) were applied for cellulase production using the combined fermentation process and resulted in an endoglucanase activity ($1,052{pm}34$ U/L) greater than that obtained using the conventional SmF procedure ($824{pm}44$ U/L). Besides the standardization of pre-culture conditions, this methodology could be very useful in systems where direct measurement of cell mass is not possible.