Today, we will study data obtained using three techniques: Micropipette aspiration Force range: 10 pN – 1000 nN soft cells hard cells Optical tweezers Force range: 0 pN – 200 pN human blood cells Atomic force microscopy (AFM) Force range: 1 pN – 1000 nN atrial myocytes and endothelial cells (soft cells) hair fibers (composite hard materials) Lecture 18,

Linear Viscoelasticity: Summary of Key Points In viscoelastic materials stress depends on strain and strain-rate They exhibit creep, relaxation and hysteresis Viscoelastic models can be derived by combining springs with syringes 3-parameter linear models (e.g. Kelvin Solid) have exponentially decaying creep and relaxation functions; time constants are the ratio of elasticity to damping The instantaneous elastic modulus is the stress:strain ratio at t=0 The asymptotic elastic modulus is the stress:strain ratio as t→∞

Simple Linear Viscoelastic Models Stress depends on strain and strain-rate: Kelvin Solid Voigt Solid Maxwell Fluid T  T E T1T1 T2T2  T T E 11 22 "" T T E" E' Elastic stress depends on strain (spring) Viscous stress depends on strain-rate (dashpot) Strains add in series, stresses are equal Stresses add in parallel, strains are equal

Quasilinear Viscoelasticity: Summary of Key Points The stress-strain relation is not unique, it depends on the load history. The elastic modulus depends on the load history, e.g. the instantaneous elastic modulus E 0 at t=0 is not, in general, equal to the asymptotic elastic modulus E  at t= . The instantaneous elastic response T (e) (t) = E 0  (t). Creep, relaxation and recovery are all properties of linear viscoelastic models. Creep solution can be normalized by the initial strain to give the reduced creep function J(t). J(0)=1. Relaxation solution can be normalized by the initial stress to give the reduced relaxation function G(t). G(0)=1.

Two micropipettes in a chamber. A pneumatic micromanipulator controls the movement of a micropipette along three orthogonal axes. (a) A spherical cell being aspirated into a micropipette with a suction pressure *P. (b) An attached cell being aspirated into a pipette. (c) A closely fitting cell or bead moving freely in a pipette like a piston in a cylinder. When static, the suction pressure times the cross-sectional area of the pipette equals the attachment force F. Where  h: hydrostatic head height = 2.5  m  P: suction pressure The force F on a static cell in a micropipette F = P x

A simple expression for the calculation of viscosity η

Blood Cell mechanics with Optical tweezers

Optical traps can be used to direct neurite extension Ehrlicher et al. (2002) Proc. Natl. Acad. Sci. USA,