Atomic force microscopy characterization of collagen 'nanostraws' in human costal cartilage.

Costal cartilage, a type of hyaline cartilage that bridges the bony ribs and sternum, is relatively understudied compared to the load bearing cartilages. Deformities of costal cartilage can result in deformation of the chest wall, where the sternum is largely pushed toward or away from the spine, pectus excavatum and pectus carinatum, respectively, with each condition having significant clinical impact. In the absence of extensive literature describing morphological features of costal cartilage, we characterized a sample from the costal margin immunohistologically and through atomic force microscopy. We had previously observed the presence of collagen 'nanostraws' running the length of costal cartilage. Hypothesizing that these structures may be responsible for fluid flow within this thick, avascular tissue, and prior to microfluidic analysis, we estimated the diameters and measured Young's modulus of elasticity of the collagen nanostraws. We found significant differences in results between treatment type and fixation. Significant differences in nanostraw elasticity and diameter obviously affect nano-fluidic transport calculations, and therefore, we consider these results of importance to the scientific community relying upon measurements in the nanoscale.

Decorin expression, straw-like structure, and differentiation of human costal cartilage.

Costal cartilage is much understudied compared with the load-bearing cartilages. Abnormally grown costal cartilages are associated with the inherited chest wall deformities pectus excavatum and pectus carinatum resulting in sunken and pigeon chests, respectively. A lack of understanding of the ultrastructural and molecular biology of costal cartilage is a major confounder in predicting causes and outcomes of these disorders. This study analyzed the structure of marginal human costal cartilage (ribs 6-10) through scanning electron and atomic force microscopes and identified the presence of straw-like structures running longitudinally. We also demonstrated that chondrocytes tend to occur singly or as doublets and that centrally located cells produce high levels of aggrecan compared with more peripherally located cells measured using immunohistochemistry. Gene expression from mRNA extracted from cartilage showed high levels of decorin expression, likely associated with the large, complex tubular structures running through this cartilage type. COL2A1, ACAN, and TIMP1 also showed higher levels of expression compared with ACTB. Analysis of gene expression ratios demonstrate that costal cartilage is under differentiated compared with published ratios for articular cartilage, likely due to the vastly different biomechanical environments of each cartilage type. Further studies need to establish whether findings described here from the costal margins are significantly different than the cartilage of the "true ribs" and how these values change with age.

Analytical solution of time periodic electroosmotic flows: analogies to Stokes' second problem.

Analytical solutions of time periodic electroosmotic flows in two-dimensional straight channels are obtained as a function of a nondimensional parameter kappa, which is based on the electric double-layer (EDL) thickness, kinematic viscosity, and frequency of the externally applied electric field. A parametric study as a function of kappa reveals interesting physics, ranging from oscillatory "pluglike" flows to cases analogous to the oscillating flat plate in a semi-infinite flow domain (Stokes' second problem). The latter case differs from the Stokes' second solution within the EDL, since the flow is driven with an oscillatory electric field rather than an oscillating plate. The analogous case of plate oscillating with the Helmholtz-Smoluchowski velocity matches our analytical solution in the bulk flow region. This indicates that the instantaneous Helmholtz-Smoluchowski velocity is the appropriate electroosmotic slip condition even for high-frequency excitations. The velocity profiles for large kappa values show inflection points very near the walls with localized vorticity extrema that are stronger than the Stokes layers. This have the potential to result in low Reynolds number flow instabilities. It is also shown that, unlike the steady pure electroosmotic flows, the bulk flow region of time periodic electroosmotic flows are rotational when the diffusion length scales are comparable to and less than the half channel height.

Analytical solution of combined electroosmotic/pressure driven flows in two-dimensional straight channels: finite Debye layer effects.

Analytical results for the velocity distribution, mass flow rate, pressure gradient, wall shear stress, and vorticity in mixed electroosmotic/pressure driven flows are presented for two-dimensional straight channel geometry. We particularly analyze the electric double-layer (EDL) region near the walls and define three new concepts based on the electroosmotic potential distribution. These are the effective EDL thickness, the EDL displacement thickness, and the EDL vorticity thickness. We show that imposing Helmholtz-Smoluchowski velocity at the edge of the EDL as the velocity matching condition between the EDL and the bulk flow region is incomplete under spatial bulk flow variations across the finite EDL. However, the Helmholtz-Smoluchowski velocity can be used as the appropriate slip velocity on the wall. We discuss the limitations of this approach in satisfying the global conservation laws.