Population Balances in Biomedical Engineering: Segregation Through the Distribution of Cell States

| Symbol | Variable | Units |
|---|---|---|
| ? | Cell age | Time |
| C P | Product concentration | Concentration |
| C S | Substrate concentration | Concentration |
| C Sf | Substrate feed concentration | Concentration |
| D | Dilution rate | Time -1 |
| f( z, t) | Normalized distribution of states with respect to cell state parameter z | Inverse units of z |
| h( z) | A priori distribution of division states | Inverse units of z |
| m | Cell mass | Mass |
| M n | nth moment of f( z, t) | |
| N( t) | Cell number concentration | Inverse volume |
| p( z, | Distribution of birth states | Inverse units of z |
| r | Single-cell growth rate | (Unit of the state parameter)/time |
| t | Time | Time |
| W( z, t) | Cell number concentration distribution of states | (Volume units of z) -1 |
| Y | Yield | (Rate of formation of z)/(rate of substrate consumption) |
| z | Arbitrary cell state parameter | |
| ?( z) | Division intensity | Time -1 |
| ?( z) | Dirac delta function | |
| ?( z) | Death intensity | Time -1 |
| ? | Specific growth rate of a population of cells | Time -1 |
| v | Specific growth rate of a single cell | Time -1 |
| ?( z) | Distribution of division states | Inverse units of z |