Bioreactor’s Formula and Equation
The growth of cells is a highly complex and organized process that is expressed by the increase in cell number or cell mass. The process is highly dependent on the availability and transport of necessary nutrients. The environmental factors such as the amount of oxygen, temperature and pH also play a significant role in the process. In optimum condition, the growth of cells is most dependent on nutrient supply.
The chemical composition of the bioreactor is adjusted to control the cell growth and allow a continuous growth of the cell. After the completion of the four phases of cell growth, the cell number of the first generation determined as N0 x 21 while the second generation is given by, N0 x 22 so on up to the N0 x 2n.
Biomass Growth Rate
In calculating the biomass growth rate, the Monod’s model is used. The biomass concentration in a particular system (X) equals or is proportional to its formation (Rx). (Chung, Chen and Tseng 2007)
To calculate the specific growth constant rate, we use Michaelis-Menten (Tresoldi, Pellegata and Mantero 2015) kinetic form and depends on the limiting substrate concentration (S) the reaction is as follows;
This reaction ignores the cell mortality rate that must be part of mature cultures. A complete description of biomass formation is therefore, given by the formula:
Substrate Consumption Rate
In general, the substrate consumption rate is illustrated using the biomass production and the right yield coefficient. The yield coefficient may however, change depending on the conditions but is frequently used as a constant.
Oxygen Consumption Rate
The oxygen consumption rate is also expressed in regards to empirical yield coefficient. The reaction for the oxygen consumption rate is as follows:
Tresoldi, C., Pellegata, A.F. and Mantero, S., 2015. Cells and stimuli in small-caliber blood vessel tissue engineering. Regenerative medicine, 10(4), pp.505-527.
Chung, C.A., Chen, C.W. and Tseng, C.S., 2007. Enhancement of cell growth in tissue‐engineering constructs under direct perfusion: Modeling and simulation. Biotechnology and bioengineering, 97(6), pp.1603-1616.