An analytical study of microvascular non-Newtonian blood flow is conducted incorporating the electro-osmosis phenomenon. Blood is considered as a Bingham rheological aqueous ionic solution. An externally applied static axial electrical field is imposed on the system. The Poisson-Boltzmann equation for electrical potential distribution is implemented to accommodate the electrical double layer in the microvascular regime. With long wavelength, lubrication and Debye-Hückel approximations, the boundary value problem is rendered non-dimensional. Analytical solutions are derived for the axial velocity, volumetric flow rate, pressure gradient, volumetric flow rate, averaged volumetric flow rate along one time period, pressure rise along one wavelength and stream function. A plug swidth is featured in the solutions. Via symbolic software (Mathematica), graphical plots are generated for the influence of Bingham plug flow width parameter, electrical Debye length and Helmholtz-Smoluchowski velocity (maximum electro-osmotic velocity) on the key hydrodynamic variables. This study reveals that blood flow rate accelerates with decreasing the plug width (i.e. viscoplastic nature of fluids) and also with increasing the Debye length parameter.
Osteogenesis Imperfecta (OI), also known as 'brittle bone disease', is a genetic bone disorder. OI bones experience frequent fractures. It is observed physical activity is equally beneficial in reducing OI bone fractures in both children and adults as mechanical stimulation improves bone mass and strength. Loading-induced mechanical strain and interstitial fluid flow stimulates bone remodeling activities. Several studies have characterized strain environment in OI bones, whereas, a very few studies attempted to characterize the interstitial fluid flow. OI significantly affect bone microarchitecture. Thus, the present study anticipates that canalicular fluid flow reduces in OI bone in comparison to healthy bone in response to physiological loading due to altered poromechanical properties. Hence, this work attempts to understand the canalicular fluid distribution in the single osteon model of OI and healthy bones. A poromechanical model of osteon is developed to compute pore-pressure and interstitial fluid flow as a function of gait loading pattern reported for OI and healthy subjects. Fluid distribution patterns are compared at different time-points of stance phase of the gait cycle. It is observed that fluid flow significantly reduces in OI bone. Additionally, flow is more static than dynamic in OI osteon in comparison to healthy subjects. The present work attempts to identify the plausible explanation behind low mechano-transduction capability of OI bone. This work may further be extended in designing better biomechanical strategies to enhance fluid flow in order to improve osteogenic activities in OI bone.
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