Electrical analogs for Kelvin & Maxwell viscoelastic materials: Applications to cornea & sclera

Abstract

Purpose: The purpose of this report is to develop analog electrical circuits, using resistors, capacitors, and constant current sources, which automatically calculate the stress and strain-rate response of viscoelastic biomaterials in response to arbitrary loading history, and to compare these with experimental strain-rate results from sclera subjected to constant and square-wave pressure loads. Methods: Electro-mechanical models of reversible and irreversible viscoelasticity are analyzed, using series and parallel combinations of springs and dashpots from the Kelvin-Voigt, Maxwell, and Jeffrey's viscoelastic models. Experiments include strain-rate response of the sclera, applicable to the development of axial myopia. Results: The resulting strain ε(t) versus time t is shown to vary exponentially for Kelvin-Voigt, as a linear step-ramp for Maxwell, and as a curved step-ramp for Jeffrey's materials, consistent with experimental observations from cornea and sclera, corresponding to output voltage at the analog circuit capacitor V(t) in response to a step change in applied load σ(t) from 0 to σ o and a step change in applied current from 0 to Io at time t = 0. The cornea and sclera are rate-sensitive viscoelastic materials which stretch up to 12% in response to constant or repetitive loads. This is equivalent to an accumulated-9.00 diopters of axial myopia. Conclusions: The resulting analog equivalent circuits can be used as general purpose analog computers, to calculate system strain-rate ε(t), in response to arbitrary applied stress loading σ(t), including ramps, steps, sinusoids, and square waves, with variable intermittency factor. Results are applicable to collagen, cornea, sclera.