This study investigates the influence of key biomass parameters on specific oxygen uptake rate (SOUR) in a sponge submerged membrane bioreactor (SSMBR) to develop mathematical models of biomass viability. Extra-cellular polymeric substances (EPS) were considered as a lumped parameter of bound EPS (bEPS) and soluble microbial products (SMP). Statistical analyses of experimental results indicate that the bEPS, SMP, mixed liquor suspended solids and volatile suspended solids (MLSS and MLVSS) have functional relationships with SOUR and their relative influence on SOUR was in the order of EPS > bEPS > SMP > MLVSS/MLSS. Based on correlations among biomass parameters and SOUR, two independent empirical models of biomass viability were developed. The models were validated using results of the SSMBR. However, further validation of the models for different operating conditions is suggested. (C) 2015 Elsevier Ltd. All rights reserved.