Mathematical principles and methods of biological surface lubrication with phospholipids bilayers

This paper presents a mini-review of investigations performed by the authors in the field of hydrodynamic theory of lubrication of biological systems and synthetic processing of results to indicate the influence of biologically live material properties on biological liquid viscosity variations. The goal of the presented study was to demonstrate a new principle of a general mathematical theory applied to the mechanism of hydrodynamic lubrication of human joint cartilage surfaces with phospholipids bilayer and to indicate analytical solutions of hydrodynamic pressure, temperature and bio-fluid velocity components. Moreover, 3D variations of dynamic synovial fluid viscosity are assessed, particularly its variations across the entire film thickness. A new 3D analytical and numerical model has been elaborated on the basis of tribology methods, based on the assumptions of an ultra-thin boundary layer of non-Newtonian fluid. The analysed elements also included phospholipid concentrations, power hydrogen ion and collagen fiber concentrations in synovial, biological fluids, as well as electrostatic field, cartilage or biological surface wettability. The obtained results of our analysis demonstrate relationships which occur among hydrodynamic pressure, human joint load carrying capacity and phospholipid bilayer in the cartilage superficial layer. According to the best knowledge of the Authors, the obtained results may find applications in a broad scope of spatiotemporal models in biology and health science.