Min Yue^1,1, Jeanne C. Stachowiak^1,1,2,2, Arunava Majumdar^1,1,3,3

Molecular & Cellular Biomechanics, Vol.1, No.3, pp. 211-220, 2004, DOI:10.3970/mcb.2004.001.211

Abstract Microchips;ontaining arrays of cantilever beams have been used to mechanically detect and quantitatively analyze multiple reactions of DNA hybridization and antigen-antibody binding simultaneously. The reaction-induced deflection of a cantilever beam reflects the interplay between strain energy increase of the beam and the free energy reduction of a reaction, providing an ideal tool for investigating the connection between mechanics and chemistry of biomolecular reactions. Since free energy reduction is common for all reactions, the cantilever array forms a universal platform for label-free detection of various specific biomolecular reactions. A few such reactions and their implications in More >

Tanmay Lele^1,1, Philmo Oh^1,1, Jeffrey A. Nickerson^1,1,2,2, Donald E. Ingber^1,1,3,3

Molecular & Cellular Biomechanics, Vol.1, No.3, pp. 181-190, 2004, DOI:10.3970/mcb.2004.001.181

Abstract The estimation of binding constants and diffusion coefficients of molecules that associate with insoluble molecular scaffolds inside living cells and nuclei has been facilitated by the use of Fluorescence Recovery after Photobleaching (FRAP) in conjunction with mathematical modeling. A critical feature unique to FRAP experiments that has been overlooked by past mathematical treatments is the existence of an `equilibrium constraint': local dynamic equilibrium is not disturbed because photobleaching does not functionally destroy molecules, and hence binding-unbinding proceeds at equilibrium rates. Here we describe an improved mathematical formulation under the equilibrium constraint which provides a more… More >

J. P. Mills^1,1, L. Qie^2,2, M. Dao^1,1, C. T. Lim^2,2, S. Suresh^1,3

Molecular & Cellular Biomechanics, Vol.1, No.3, pp. 169-180, 2004, DOI:10.3970/mcb.2004.001.169

Abstract Studies of the deformation characteristics of single biological cells can offer insights into the connections among mechanical state, biochemical response and the onset and progression of diseases. Deformation imposed by optical tweezers provides a useful means for the study of single cell mechanics under a variety of well-controlled stress-states. In this paper, we first critically review recent advances in the study of single cell mechanics employing the optical tweezers method, and assess its significance and limitations in comparison to other experimental tools. We then present new experimental and computational results on shape evolution, force--extension curves, More >

K.Y. Volokh¹

Molecular & Cellular Biomechanics, Vol.1, No.2, pp. 147-160, 2004, DOI:10.3970/mcb.2004.001.147

Abstract A simple phenomenological framework for modeling growth of living tissues is proposed. Growth is defined as a change of mass and configuration of the tissue. Tissue is considered as an open system where mass conservation is violated and the full-scale mass balance is applied. A possible structure of constitutive equations is discussed with reference tosimple growing materials. 'Thermoelastic' formulation of the simple growing material is specified. Within this framework traction free growth of cylindrical and spherical bodies is examined. It is shown that the theory accommodates the case where stresses are not generated in uniform More >

Leo Q. Wan^1,1, Chester Miller^1,1, X. Edward Guo^2,2, Van C. Mow^1,1,3,3

Molecular & Cellular Biomechanics, Vol.1, No.1, pp. 81-100, 2004, DOI:10.3970/mcb.2004.001.081

Abstract The triphasic constitutive law [Lai, Hou and Mow (1991)] has been shown in some special 1D cases to successfully model the deformational and transport behaviors of charged-hydrated, porous-permeable, soft biological tissues, as typified by articular cartilage. Due to nonlinearities and other mathematical complexities of these equations, few problems for the deformation of such materials have ever been solved analytically. Using a perturbation procedure, we have linearized the triphasic equations with respect to a small imposed axial compressive strain, and obtained an equilibrium solution, as well as a short-time boundary layer solution for the mechano- electrochemical… More >

D.E. Ingber¹

Molecular & Cellular Biomechanics, Vol.1, No.1, pp. 53-68, 2004, DOI:10.3970/mcb.2004.001.053

Abstract This article is a summary of a lecture presented at a symposium on "Mechanics and Chemistry of Biosystems'' in honor of Professor Y.C. Fung that convened at the University of California, Irvine in February 2004. The article reviews work from our laboratory that focuses on the mechanism by which mechanical and chemical signals interplay to control how individual cells decide whether to grow, differentiate, move, or die, and thereby promote pattern formation during tissue morphogenesis. Pursuit of this challenge has required development and application of new microtechnologies, theoretical formulations, computational models and bioinformatics tools. These… More >

Huajian Gao^1,1, Baohua Ji^1,1, Markus J. Buehler^1,1, Haimin Yao^1,1

Molecular & Cellular Biomechanics, Vol.1, No.1, pp. 37-52, 2004, DOI:10.3970/mcb.2004.001.037

Abstract Bone-like biological materials have achieved superior mechanical properties through hierarchical composite structures of mineral and protein. Gecko and many insects have evolved hierarchical surface structures to achieve extraordinary adhesion capabilities. We show that the nanometer scale plays a key role in allowing these biological systems to achieve their superior properties. We suggest that the principle of flaw tolerance may have had an overarching influence on the evolution of the bulk nanostructure of bone-like materials and the surface nanostructure of gecko-like animal species. We demonstrate that the nanoscale sizes allow the mineral nanoparticles in bone to More >

Yoshihiro Ochiai¹, Vladimir Sladek²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.6, pp. 525-536, 2004, DOI:10.3970/cmes.2004.006.525

Abstract The conventional boundary element method (BEM) uses internal cells for the domain integralsCwhen solving nonlinear problems or problems with domain effects. This paper is concerned with conversion of the domain integral into boundary ones and some non-integral terms in a three-dimensional BIEM, which does not require the use of internal cells. This method uses arbitrary internal points instead of internal cells. The method is based on a three-dimensional interpolation method in this paper by using a polyharmonic function with volume distribution. In view of this interpolation method, the three-dimensional numerical integration is replaced by boundary More >

S. Callsen¹, O. von Estorff¹, O. Zaleski²

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.5, pp. 421-430, 2004, DOI:10.3970/cmes.2004.006.421

Abstract In standard boundary element formulations, singular integrals need to be solved as soon as the considered sources coincide with the collocation points at the boundary. Using a desingularized boundary element approach, the sources are distributed on a surface outside the acoustic domain which means that they are never located at the boundary. Consequently, all the resulting kernels are nonsingular which reduces the complexity of the numerical treatment of the boundary integral equations considerably. In the current contribution a desingularized formulation is given for both, the direct and the indirect boundary element method used to solve More >

Nam Mai-Duy¹

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.2, pp. 209-226, 2004, DOI:10.3970/cmes.2004.006.209

Abstract This paper is concerned with the use of the indirect radial basis function network (RBFN) method in solving partial differential equations (PDEs) with scattered points. Indirect RBFNs (Mai-Duy and Tran-Cong, 2001a), which are based on an integration process, are employed to approximate the solution of PDEs via point collocation mechanism in the set of randomly distributed points. The method is tested with the solution of Poisson's equations and the Navier-Stokes equations (Boussinesq material). Good results are obtained using relatively low numbers of data points. For example, the natural convection flow in a square cavity at More >