An axisymmetric boundary integral model for incompressible linear viscoelasticity: Application to the micropipette aspiration contact problem

The micropipette aspiration test has been used extensively in recent years as a means of quantifying cellular mechanics and molecular interactions at the microscopic scale. However; previous studies have generally modeled the cell as an infinite half-space bz order to develop an analytical solution for a viscoelastic solid cell. In this study, an axisymmetric boundary inte gral formulation of the governing equations of incompressible linear viscoe lasticity is presented and used to simulate the micropipette aspiration con tact problem. The cell is idealized as a homogenous and isotropic continuum with constitutive equation given by three-parameter (E, tau (1), tau (2)) standard linear viscoelasticity. The formulation is used to develop a compu tational,model via a "correspondence principle" in which the solution is wr itten as the sum of a homogeneous (elastic part and a rzollhonrpgerzeous pa rt, which depends only on past values of the solution. Via a time-marching scheme, the solution of the viscoelastic problem is obtained by employing a rt elastic boundary element method with modified boundary conditions. The a ccuracy and convergence of the time-marching scheme are verified using an a nalytical solution. An incremental reformulation of the scheme is presented to facilitate the simulation of micropipette aspiration, a nonlinear conta ct problem. In contrast to the halfspace model (Sato et al, 1990), this com putational model accounts for nonlinearities in the cell response that resu lt from a consideration of geometric factors including the finite cell dime nsion (radius R), curvature of the cell boundary, evolution of the cell-mic ropipette contact region, and curvature of the ed,Ses of the micropipette ( inner radius a edge curvature radius epsilon). Using 60 quadratic boundary elements, a micropipette aspiration creep test with ramp time t* =0.1s and ramp pressure p*/E=0.8 is simulated for the cases a/R =0.3, 0.4, 0.5 using mean parameter values for primary chondrocytes. Comparisons to the half-spa ce model indicate that the computational model predicts an aspiration lengt h that is less stiff during the initial ramp response (t=0-1 s) but more st iff at equilibrium (t =200 s) Overall, rite ramp and equilibrium prediction s of aspiration length by the computational model are fairly insensitive to aspect ratio a/R but can differ from the half-space model by np to 20 per- cent. This computational approach may be readily extended to account for mo re complex geometries or inhomogeneities in Cellular-properties.