Growing and culturing stem cells in scalable quantities is of significant interest for both research and therapy. In this paper, a computational population balance model is developed and validated for the description of specified inter/intra-cellular related stem cell properties of interest (e.g. cell number, mass, size, age). The model describes the effects of extra-cellular variables; (A) bioreactor batch mode initial concentrations (substrate (1.5-5 g/l), dissolved oxygen (hypoxic (5%), normoxic (21%), and hyperoxic (35%)), (B) inoculum (3.75 x 10(4)-5.0 x 10(5) cells/ml), and (C) fed-batch mode conditions (media feed rate (10-100 ml/h) and air inlet flow rate 0.5-5l/min). The highest cell concentration achieved within the analysed simulation variable ranges is found to be approximately 1.9 x 10(6) cells/ml. Importantly, the results imply the existence of an optimum (maximum) cell concentration within the extra-cellular variable space, and identifying such optimality is non-trivial and would require a computational optimisation approach for this stem cell bioreactor process. (C) 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.