Electric-field-enhanced nutrient consumption in dielectric biomaterials that contain anchorage-dependent cells

Abstract

This research contribution addresses electric-field stimulation of intra-tissue mass transfer and cell proliferation in viscoelastic biomaterials. The unsteady state reaction–diffusion equation is solved according to the von Kármán–Pohlhausen integral method of boundary layer analysis when nutrient consumption and tissue regeneration occur in response to harmonic electric potential differences across a parallel-plate capacitor in a dielectric-sandwich configuration. The partial differential mass balance with diffusion and electro-kinetic consumption contains the Damköhler (Λ 2) and Deborah (De) numbers. Zero-field and electric-field-sensitive Damköhler numbers affect nutrient boundary layer growth. Diagonal elements of the 2nd-rank diffusion tensor are enhanced in the presence of weak electric fields, in agreement with the formalism of equilibrium and nonequilibrium thermodynamics. Induced dipole polarization density within viscoelastic biomaterials is calculated via the real and imaginary components of the complex dielectric constant, according to the Debye equation, to quantify electro-kinetic stimulation. Rates of nutrient consumption under zero-field conditions are described by third-order kinetics that include local mass densities of nutrients, oxygen, and attached cells. Thinner nutrient boundary layers are stabilized at shorter dimensionless diffusion times when the zero-field intra-tissue Damköhler number increases above its initial-condition-sensitive critical value [i.e., {Λ 2 zero-field} critical ≥ 53, see Eq. (23)], such that the biomaterial core is starved of essential ingredients required for successful proliferation. When tissue regeneration occurs above the critical electric-field-sensitive intra-tissue Damköhler number, the electro-kinetic contribution to nutrient consumption cannot be neglected. The critical electric-field-sensitive intra-tissue Damköhler number is proportional to the Deborah number.