To date, there has been only limited application of the triphasic model to cell mechanics (Gu et al., 1997). At mechanochemical equilibrium in vitro, many cells are known to exhibit a passive volumetric response corresponding to an ideal osmometer. For an ideal osmometer, cell volume and inverse osmolality (normalized to their values in the iso-osmotic state) are linearly related via the Boyle van’t Hoff relation. The resulting states of mechanochemical equilibrium of the cell exhibit an internal balance between mechanical and chemical stresses. The triphasic model, in the absence of electrical fields, gives rise to the mixture momentum equation:

where σ is the mixture stress and σE is the extra stress in the solid phase. The balance of electrochemical potentials for intracellular and extracellular water gives rise to the Donnan osmotic pressure relation:

where T is the temperature, ϕ and ϕ are the intracellular and extracellular osmotic activity coefficients, and c and c are the intracellular and extracellular ion concentrations, respectively (R is the universal gas constant). To close the system of governing equations (Eqs. 5.11–5.12), the intracellular extra stress and the intracellular ion concentration need to be characterized. While the former may be postulated via a constitutive description for the subcellular components (such as nucleus, cytoskeleton, membrane), the latter necessitates a detailed analysis of electrochemical ion potentials inside a cell that accounts for intracellular ionic composition and biophysical mechanisms such as the selective permeability of the bilayer lipid membrane, and the nontransient activity of ion pumps and ion channels.

The strength of this type of mixture theory approach was recently illustrated in a study modeling the transient swelling and recovery behavior of a single cell subjected to an osmotic stress with neutrally charged solutes (Ateshian et al., 2006). A generalized “triphasic” formulation and notation (Gu et al., 1998) were used to account for multiple solute species and incorporated partition coefficients for the solutes in the cytoplasm relative to the external solution. Numerical simulations demonstrate that the volume response of the cell to osmotic loading is very sensitive to the partition coefficient of the solute in the cytoplasm, which controls the magnitude of cell volume recovery. Furthermore, incorporation of tension in the cell membrane significantly affected the mechanical response of the cell to an osmotic stress. Of particular interest was the fact that the resulting equations could be reduced to the classical equations of Kedem and Katchalsky (1958) in the limit when the membrane tension is equal to zero and the solute partition coefficient in the cytoplasm is equal to unity. These findings emphasize the strength of using more generalized mixture approaches that can be selectively simplified in their representation of various aspects of cell mechanical behavior.

Analysis of cell mechanical tests

Similar to other experiments of cell mechanics, the analysis of cell multiphasic properties has involved the comparison and matching of different experimental