Network Thermodynamic Modeling With Bond Graphs for Membrane Transport During Cell Freezing Procedures

Freezing procedures for preservation of living cells create osmotic stresses associated with the addition and removal of cryoprotective agents and with ice formation in the extracellular solution, causing a concomitant segregation of electrolytes into the remaining liquid phase. When these osmotic stresses are introduced, coupled flows of water and permeable solute are induced across the plasma membrane. A network thermodynamic model of this process is presented, based on development according to the principles of bond graphs. The model is a complete representation of the equations that describe the process, and the bond graph can be interpreted directly in terms of the relevant energy flows during membrane transport and the topology of the system. Determination of the transient cell volume during addition of glycerol to an erythrocyte suspension is used to demonstrate the model.