Cell life-cycle and motility analysis is one of the fundamental tasks in many biological research activities, and its automation is a challenging problem. To solve the cell tracking problem using a Bayesian stochastic filter, one needs to properly incorporate all the information available about the cell behavior within the filter. This includes its movements, changes during mitosis process (up to splitting) and death. This paper demonstrates an effective way to perform this task for a particular family of cells (Chinese Hamster Ovarian (CHO) cells) that are known to have a commonly elliptic shape, and elongate during their mitosis. We model this by incorporating an ellipse-based state variable, a particular spawning process and an intuitive adaptive (measurement-driven) birth process that are added to the prediction step of a multi-Bernoulli filter. Our numerical experimental results involving microscopic images of living cells demonstrate significant improvement in tracking performance as a result of the proposed additions.