Thread 3. Biomechanics at Micro- and Nanoscale Levels T3.1 Cell Mechanics $443

models. Particle evolution under the action of the peristaltic waves is quantified by the dispersion, spread, mixing, transport and distribution of particles. Mixing of particles with advected species such as enzymes is also quantified. Results show complex dynamics of particle scatter, clumping and sheet formation de- pending on the input parameters. Insights are obtained into the mechanics over a wide parameter space influencing mixing and transport in the gastrointestinal tract, including particle size, mass, initial placement of the bolus, frequency and amplitude of the peristaltic wave and wave train effects. The study has implications in the design of drug delivery systems as well as in understanding the mechanism of nutrition.

5037 Tu, 08:45-09:00 (P18) One-dimensional f lu id-s t ruc ture interact ion model o f human cystic ducts W.G. Li 1 , X.'~ Luo 2, N.A. Hill 2, A.G. Johnson 3, N. Bird 3, S.B. Chin 1 . 1Department of Mechanical Engineering, University of Sheffield, Sheffield, UK, 2Department of Mathematics, University of Glasgow, Glasgow, UK, 3Academic Surgical Unit, Royal Hallamshire Hospital, Sheffield, UK

It is generally accepted that prolonged stasis of bile in the gallbladder is a significant contributing factor to gallstone formation, suggesting that fluid mechanics, in particular, the pressure drop which is required to overcome the resistance of bile flow during emptying, may play an important role in gallstone formation. Unusually high gallbladder pressures could be a cause of acute pain observed in vivo, and also indicate that the gallbladder could not empty satisfactorily, increasing the likelihood of forming cholesterol crystals. Although detailed numerical study in 2D/3D cystic models can identify influ- ences of different baffle heights, numbers, and Reynolds numbers on the pressure drop, it is time consuming and limited to rigid cystic duct models. Now we propose a one-dimensional model of the human biliary system with an elastic cystic duct. Using this model, the effects of physical parameters such as the cystic duct length, diameter, baffle height ratio, number of baffles, the Young's modulus, and the bile viscosity, on the pressure drop can be quickly estimated. The model has been carefully validated with 3D numerical results for rigid cystic duct, and is found to be in excellent agreements for a wide range of parameters. The models can be further developed to provide some fast, qualitative estimates of pressure drop based on real time in vivo data of patients' biliary systems and therefore be used to aid clinical diagnosis in the longer term. The results show the diameter of the cystic is still the most significant factor in controlling the pressure drop. The elasticity of the duct plays an important role here, however, only when the Young's modulus is low enough: when the Young's modulus of the cystic duct is more than 400Pa, its effect on the pressure drop is negligible.

6203 Tu, 09:00-09:15 (P18) A mathematical model for the opening o f thick wal led elast ic tubes

J.G. Brasseur, S. Ghosh. The Pennsylvania State, University Park, University

A coupled fluid-structure mathematical model was developed to quantify rapid opening of thick-walled elastic tubes, a phenomenon underlying biological flows such as gastroesophageal reflux disease (GERD). The wall was mod- eled using non-linear finite deformation theory to predict space-time radial distention of an axisymmetric tube with luminal fluid flow. Anisotropic azimuthal and longitudinal muscle-induced stresses were incorporated, and interstitial material properties were assumed isotropic and linearly elastic. Fluid flow was modeled using lubrication theory with inertial correction. Opening and flow were driven by a specified inflow pressure and zero pressure gradient was specified at outflow. No-slip and surface force balance were applied at the fluid-wall interface. Viscoelasticity was modeled with ad hoc damping and the evolution of the tube geometry was predicted at mid-layer. As an example, we applied the model to sudden opening of the gastro-esophageal segment as occurs with GERD. A potentially important discovery was made: while material stiffness is of minor consequence, small changes in resting lumen distension (1-2mm) can have a strong effect on probability for opening and reflux. The implication is that pathological increases in wall compliance in this region might be a sensitive distinguishing feature of GERD.

6430 Tu, 09:15-09:30 (P18) Hydrodynamic effects in osci l lat ing AFM microcantilevers

R.J. Clarke 3, J. Billingham 1 , P.M. Williams 2, A.P. Pearson 2, O.E. Jensen 1 . 1 Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, UK, 2Laboratory of Biophysics and Surface Analysis, School of Pharmacy, University of Nottingham, UK, 3School of Mathematical Sciences, University of Adelaide, SA, Australia

The atomic force microscope (AFM) is widely used to measure the mechanical and geometric properties of biological samples in their native liquid environ- ment. The AFM employs a microcantilever which oscillates at high frequencies

under either external forcing or thermal fluctuations. It is important to under- stand how hydrodynamic forces affect the cantilever's motion, both to enable accurate calibration and to interpret measurements. We present predictions of drag on a finite-length cantilever oscillating at small amplitude and high frequency near a plane wall, determined using the unsteady Stokes equations. The cantilever's slender geometry allows its motion to be described with a new formulation of slender body theory, extended to account for unsteady inertia. High oscillation frequencies and proximity to the wall are shown to screen the cantilever from three-dimensional flows. This justifies the use of a simpler two-dimensional theory that employs a boundary integral method to capture explicitly the shape of the cantilever's cross-section. The fluctuation-dissipation theorem (which captures memory effects in the Brownian forcing associated with unsteady fluid inertia) is then used to derive the cantilever's thermal power spectrum, allowing model predictions to be tested against experiment. This approach is shown to be more accurate than an existing popular method that neglect memory effects in the forcing by assuming equipartition of energy between the cantilever's in vacuo modes. The cantilever's distance from and orientation to the wall are also shown to have significant effects on the thermal spectrum.

5595 Tu, 09:30-09:45 (P18) Dynamic shear stress at cell 's membrane is governed by mechanical interaction between fluid and cell L.D. Blecha 1 , L. Rakotomanana 2, E Razafimahery 2, P.-Y Zambelli 3, D.P. Pioletti 1 . 1LBO, EPFL, Lausanne, Switzerland, 21RMAR, University of Rennes I, Rennes, France, 3 HOpital Orthop6dique de la Suisse Romande, Lausanne, Switzerland

Living cells interact chemically with its surrounding fluid and probably also in a mechanical way. In fact, the motion of the cell's surrounding fluid exerts a mechanical constrains on the cell's membrane. The constrains induces cells' deformation that simultaneousely changes the fluid flow pattern. As a result, the shear stress at the cell/fluid interface is a function of the cell and fluid physical properties. It is hypothetized in this study that coupling phenomena may play a role in mechanotransduction. The analytical resolution of a simplified one dimensional time dependent model showed that the mechanical interaction between a layer of cells and its surrounding fluid modulates the shear stress amplitude at their interface. A novel dimensionless number was found that characterises the coupling phe- nomenon. Depending on the fluid viscosity, the dynamical external excitation could be damped by a factor as large as 30 or conversely amplified at specific resonance frequency. In short, the fluid viscosity seems to play a key role in the modulation of the dynamic shear stress at the interface between cells and surrounding fluid.

Thread 3

B i o m e c h a n i c s at Micro- and N a n o s c a l e Levels

T3.1 Cell Mechanics

7231 Tu, 16:00-16:15 (P25) A system o f in situ osteocyte organ culture models for mechanobio log ica l s tudy o f bone

A.M. Sorkin 1 , M.L. Knothe Tate 1,2. 1. Department of Biomedical, 2Department of Mechanical & Aerospace Engineering, Case Western Reserve University, Cleveland, OH, USA

Osteocytes inhabit a complex mechanochemical ecology in which perturba- tions at the cellular level can have substantial impact on organ function. The factors required to maintain bone health remain largely undefined. Here we develop a tissue/organ culture model to determine how cells respond to specific in vivo-like mechanochemical cues. Bovine femur was sectioned into 200~tm slices, and stored under standard culture conditions in standard ~J,- MEM, or hypo-, hyper-, or iso-tonic formulations of phosphate buffered saline. Osteocyte viability was assessed with the Live/Dead assay. The integrity and condition of the osteocyte network were assessed with confocal microscopy following treatment with the membrane label DiO and a phalloidin stain for cytoskeletal actin. Network connectivity was measured by calculation of fractal dimension. Nitric oxide signaling was observed with 4-amino-5-methylamino- 2',7'-difluorfluorofluoroscein diacetate (DAF-FM). Cells remained 40%-50% viable over 6 days in all sections in PBS and ~J,-MEM. Short-term viability of cells was increased by exposure to non-isotonic PBS. In the presence of ~J,-MEM, osteocytes migrated to the inferior surface. An osteocytic network consistent with the lacunocanalicular system was observed in sections treated