Breast tumor formation is thought to arise from a scarce population of cells exhibiting similar functional properties and phenotypic traits as adult stem cells derived from the same tissue. Mutations within the adult stem cell population may adversely affect their ability to control their proliferation, thereby resulting in a cancer stem cell. The scarcity of Breast Cancer Stem Cells (BrCSCs) severely compromises research on these populations, since analyses are generally restricted to those needing only small cell numbers. This, in turn, has become a major impediment to the development of breast cancer therapeutics. In order to address the issue of BrCSC scarcity, a detailed investigation into the propagation of these cells as tissue aggregates, called tumorspheres, in suspension bioreactors have been conducted. A rigorous theoretical framework has been developed, in order to understand and characterize the implications of oxygen mass transfer within aggregates upon scale-up, and thereby provide a foundation for the scale-up of aggregate cultures. The effects of inoculation density and hydrodynamic shear upon cell yield and doubling times were also determined through a 22 factorial design experiment. We discovered that the culture of the murine aggregates in a relatively low shear environment (maximum shear = 0.20 Pa) and inoculated at 3.50x10^4 cells/mL resulted in the best yields for the range of conditions investigated in suspension bioreactors. Little or no mass transfer limitation of oxygen was observed within the aggregates, upon comparison of oxygen uptake rates of single cells and aggregates themselves. Furthermore, cells cultured in a process controlled 500 mL suspension bioreactor resulted in growth kinetics that were comparable to those observed in 125 mL spinner flasks. Doubling times in the 500 mL vessel were found to be 23.9 hours and attained a maximum cell density of 1.20x10^6 cells/mL. With greater attention being applied to breast cancer stem cells, their subsequent propagation in suspension bioreactors has the potential to play an essential role in enabling the development of more effective drugs and therapies specifically targeted for the eradication of these cells.