Mathematical Model

We modeled the cell growth in bioreactor with an exponential model. Since perfusion provides constant supply of nutrients and removal of waste, we can assume approximately unlimited nutrients. With a requirement of selecting a starting cell density such that the cells remain less than 80% confluent throughout the entire experiment, we can also assume approximately unlimited space.

This model was implemented in a MATLAB program. The user inputs experiment specific parameters, such as starting cell density, growth rate, target metabolite concentrations, and metabolite consumption rates. The program generates a list of media flow rates needed to maintain the target nutrient concentrations during cell growth. The list is pasted into an Arduino program to run the pumps.