Computation of physiological loading induced interstitial fluid motion in muscle standardized femur: Healthy vs. osteoporotic bone.

BACKGROUND AND OBJECTIVES: Physiological loading-induced mechanical environments regulate bone modeling and remodeling. Thus, loading-induced normal strain is typically considered a stimulus to osteogenesis. However, several studies noticed new bone formation near the sites of minimal normal strain, e.g., the neutral axis of bending in long bones, which raises a question on how bone mass is maintained near these sites. Secondary mechanical components such as shear strain and interstitial fluid flow also stimulate bone cells and regulate bone mass. However, the osteogenic potential of these components is not well established. Accordingly, the present study estimates the distribution of physiological muscle loading-induced mechanical environments such as normal strain, shear strain, pore pressure, and interstitial fluid flow in long bones. METHODS: A poroelastic finite element muscle standardized femur (MuscleSF) model is developed to compute the distribution of the mechanical environment as a function of bone porosities associated with osteoporotic and disuse bone loss. RESULTS: The results indicate the presence of higher shear strain and interstitial fluid motion near the minimal strain sites, i.e., the neutral axis of bending of femoral cross-sections. This suggests that secondary stimuli may maintain the bone mass at these locations. Pore pressure and interstitial fluid motion reduce with the increased porosity associated with bone disorders, possibly resulting in diminished skeletal mechano-sensitivity to exogenous loading. CONCLUSIONS: These outcomes present a better understanding of mechanical environment-mediated regulation of site-specific bone mass, which can be beneficial in developing prophylactic exercise to prevent bone loss in osteoporosis and muscle disuse.

Modeling virus transport and dynamics in viscous flow medium.

In this paper, we developed a mathematical model to simulate virus transport through a viscous background flow driven by the natural pumping mechanism. Two types of respiratory pathogens viruses (SARS-Cov-2 and Influenza-A) are considered in this model. The Eulerian-Lagrangian approach is adopted to examine the virus spread in axial and transverse directions. The Basset-Boussinesq-Oseen equation is considered to study the effects of gravity, virtual mass, Basset force, and drag forces on the viruses transport velocity. The results indicate that forces acting on the spherical and non-spherical particles during the motion play a significant role in the transmission process of the viruses. It is observed that high viscosity is responsible for slowing the virus transport dynamics. Small sizes of viruses are found to be highly dangerous and propagate rapidly through the blood vessels. Furthermore, the present mathematical model can help to better understand the viruses spread dynamics in a blood flow.

Computational modeling for osteogenic potential assessment of physical exercises based on loading-induced mechanobiological environments in cortical bone remodeling.

Osteoporosis and disuse can cause bone loss which reduces the weight-bearing strength of long bones. Physical exercise or mechanical loading prevents bone loss as it promotes bone modeling through osteogenesis, i.e., new bone formation. Several studies have observed distinct bone remodeling responses to physical exercises; nevertheless, the underlying mechanism behind such responses is not well established. Loading-induced pore-pressure and fluid motion act as mechanobiological stimuli to bone cells namely osteocytes which further initiate osteoactivities. The shape of loading waveforms also affects the poromechanical environment of bone. Accordingly, the present study hypothesizes that loading waveforms associated with physiological exercises may expose the bone to different mechanobiological stimuli resulting in distinct bone remodeling. A poromechanical finite element model is developed to compute pore-pressure and interstitial fluid velocity in femoral cortical bone tissue (healthy and osteoporotic) subjected to loading waveforms of three physiological exercises namely walking, running, and jumping. The model also computes the mechanobiological stimulus as a function of fluid velocity. The outcomes indicate that pore-pressure and fluid velocity decrease significantly in osteoporotic bone tissue in comparison with healthy tissue. Jumping and running both improve pore-pressure and fluid velocity in healthy and osteoporotic tissues, whereas running significantly enhances mechanobiological stimulus in both the tissues which indicates a possible explanation for distinct bone remodeling to different physical exercises. The present work also suggests that running may be recommended as a potential biomechanical therapeutic to prevent bone loss. Overall, the present work contributes to the area of orthopedic research to develop effective designs of prophylactic exercises to improve bone health.

Alteration in membrane-based pumping flow with rheological behaviour: A mathematical model.

BACKGROUND AND OBJECTIVE: Blood is complex fluids exhibits the non-Newtonian characters and rheological properties of the blood vary person to person. Typically, the rheological properties of blood are very similar to Carreau fluids which is considered in the present model. The main objective of this study is to examine how a typical membrane-based pumping model will function with varying rheological properties (shear-thinning, Newtonian, and shear-thickening) of fluids. METHODS: A mathematical formulation is constructed for the membrane-based pumping model using the conservation principles of mass and momentum, and stress-strain relationship based on Carreau fluids model. Velocity slip condition is adopted for this model to discuss the possibility of fluids velocity at the wall surface. The perturbation method is employed to derive the series solution for the governing equations subjected to physical boundary conditions with suitable assumptions. RESULTS: From numerical results, it is found that the pressure inside the microchannel reduces for the shear-thinning fluid and increases for the shear-thickening fluid with increasing the Weissenberg. In the membrane region, the chaos of the flow field is occurred due to the local pressure gradient by the rhythmic membrane propagation. It is further reported that shear-driven flow is responsible for the decrement in fluid velocity. CONCLUSIONS: This model provides a framework for estimating the effects of rheological properties and velocity slip for membrane-based pumping model which help in designing the smart pumps for various needs in the fields of biomedical engineering and fluid industries.

Blood-based graphene oxide nanofluid flow through capillary in the presence of electromagnetic fields: A Sutterby fluid model.

Pumping devices with the electrokinetics phenomena are important in many microscale transport phenomena in physiology. This study presents a theoretical and numerical investigation on the peristaltic pumping of non-Newtonian Sutterby nanofluid through capillary in presence of electromagnetohydrodynamics. Here blood (Sutterby fluid) is taken as a base fluid and nanofluid is prepared by the suspension of graphene oxide nanoparticles in blood. Graphene oxide is extremely useful in the medical domain for drug delivery and cancer treatment. The modified Buongiorno model for nanofluids and Poisson-Boltzmann ionic distribution is adopted for the formulation of the present problem. Constitutive flow equations are linearized by the implementation of approximations of low Reynolds number, large wavelength, and the Debye-Hückel linearization. The numerical solution of reduced coupled and nonlinear set of equations is computed through Mathematica and graphical illustration is presented. Further, the impacts of buoyancy forces, thermal radiation, and mixed convection are also studied. It is revealed in this investigation that the inclusion of a large number of nanoparticles alters the flow characteristics significantly and boosts the heat transfer mechanism. Moreover, the pumping power of the peristaltic pump can be enhanced by the reduction in the width of the electric double layer which can be done by altering the electrolyte concentration.

Mathematical modeling and simulation of electromagnetohydrodynamic bio-nanomaterial flow through physiological vessels.

Gold-based metal nanoparticles serve a key role in diagnosing and treating important illnesses such as cancer and infectious diseases. In consideration of this, the current work develops a mathematical model for viscoelastic nanofluid flow in the peristaltic microchannel. Nanofluid is considered as blood-based fluid suspended with gold nanoparticles. In the investigated geometry, various parametric effects such as Joule heating, magnetohydrodynamics, electroosmosis, and thermal radiation have been imposed. The governing equations of the model are analytically solved by using the lubrication theory where the wavelength of the channel is considered large and viscous force is considered more dominant as compared to the inertia force relating the applications in biological transport phenomena. The graphical findings for relevant parameters of interest are given. In the current analysis, the ranges of the parameters have been considered as: 0<κ<6,0<λ1<0.6,2

Response of vaccination on community transmission of COVID-19: a dynamical approach.

Due to the severity of COVID-19, vaccination campaigns have been or are underway in most parts of the world. In the current circumstances, it is obligatory to examine the response of vaccination on transmission of the SARS-CoV-2 virus when there are many vaccines available. Considering the importance of vaccination, a dynamic model has been proposed to provide an insight in the same direction. A mathematical model has been developed where six population compartments viz. susceptible, infected, vaccinated, home-isolated, hospitalized and recovered population are considered. Moreover, two novel parameters are included in the model to ascertain the effectiveness and speed of the vaccination campaign. Reproduction number and local stability of both the disease-free and endemic equilibrium points are studied to examine the nature of population dynamics. Graphical results for the community stage of COVID-19 infection are simulated and compared with real data to ascertain the validity of our model. The data is then studied to understand the impact of vaccination. These numerical results evidently demonstrate that home isolation and hospitalization should continue for the infected people until the transmission of the virus from person to person reduces sufficiently after completely vaccinating every nation. This model also recommends that all type of prevention measures should still be taken to avoid any type of critical situation due to infection and also reduce the death rate.

Propagation of H1N1 virus through saliva movement in oesophagus: a mathematical model.

H1N1 (Swine flu) is caused by the influenza A virus which belongs to the Orthomyxoviridae family. Influenza A is very harmful to the elderly, and people with chronic respiratory disease and cardiovascular disease. Therefore, it is essential to analyse the behaviour of virus transmission through the saliva movement in oesophagus. A mathematical paradigm is developed to study the saliva movement under the applications of transverse magnetic field. Jeffrey fluid model is considered for saliva to show the viscoelastic nature. The flow nature is considered creeping and assumptions of long wavelength and low Reynolds number are adopted for analytical solutions. The Basset-Boussinesq-Oseen equation is employed to understand the propagation of H1N1 virus through saliva under the effect of applicable forces such as gravity, virtual mass, basset force, and drag forces. The suitable data for saliva, oesophagus and H1N1 virus are taken from the existing literature for simulation of the results using MATLAB software. From the graphical results, it is observed that the susceptibility to viral infections is less because the magnetic field reduces the motion of the virus particle. Further, the chances of infections in males are more as compared to females and children due to variation in viscosity of saliva. Such findings provide an understanding of the mechanics of the virus floating through the saliva (viscoelastic fluids) in the oesophagus.

Electroosmotic modulated unsteady squeezing flow with temperature-dependent thermal conductivity, electric and magnetic field effects.

Modern lubrication systems are increasingly deploying smart (functional) materials. These respond to various external stimuli including electrical and magnetic fields, acoustics, light etc. Motivated by such developments, in the present article unsteady electro-magnetohydrodynamics squeezing flow and heat transfer in a smart ionic viscous fluid intercalated between parallel plates with zeta potential effects is examined. The proposed mathematical model of problem is formulated as a system of partial differential equations (continuity, momenta and energy). Viscous dissipation and variable thermal conductivity effects are included. Axial electrical distribution is also addressed. The governing equations are converted into ordinary differential equations via similarity transformations and then solved numerically with MATLAB software. The transport phenomena are scrutinized for both when the plates move apart or when they approach each other. Also, the impact of different parameters such squeezing number, variable thermal conductivity parameter, Prandtl number, Hartmann number, Eckert number, zeta potential parameter, electric field parameter and electroosmosis parameter on the axial velocity and fluid temperature are analysed. For varied intensities of applied plate motion, the electro-viscous effects derived from electric double-capacity flow field distortions are thoroughly studied. It has been shown that the results from the current model differ significantly from those achieved by using a standard Poisson-Boltzmann equation model. Axial velocity acceleration is induced with negative squeeze number (plates approaching,S< 0) in comparison to that of positive squeeze number (plates separating,S> 0). Velocity enhances with increasing electroosmosis parameter and zeta potential parameter. With rising values of zeta potential and electroosmosis parameter, there is a decrease in temperatures forUe> 0 for both approaching i.e. squeezing plates (S< 0) and separating (S> 0) cases. The simulations provide novel insights into smart squeezing lubrication with thermal effects and also a solid benchmark for further computational fluid dynamics investigations.

Bioinspired Pumping Flow Driven by Rhythmic Membrane Propulsion in a Porous Medium.

Investigation concerning the bioinspired pumping flow of viscous fluids in the porous region using Darcy's law is demonstrated in the present article. The rhythmic membrane contraction propels fluids in the porous microchannel. The periodic contraction of the membrane is utilized in the present analysis to introduce the unique pumping mechanism. For small pattern, width to channel height ratio (i.e., the channel is substantially longer than its width) and at low Reynolds numbers, the governing equations are solved by an analytical approach. In light of porous effects, we noticed the implications of rheological limitations on pumping and trapping processes. The porosity has a dynamic role in the augmentation of membrane-based pumping. These outcomes may be productive in various bioengineering (drug delivery schemes) applications.

Bioengineered bioreactors: a review on enhancing biomethane and biohydrogen production by CFD modeling.

Computational fluid dynamics (CFD) is numerical strategy developed for simulating the behavior of liquid and gas flow. CFD may be applied starting from aerospace, engine design, vehicle aerodynamics, power plants and chemical industries for analyzing and solving relevant system design and process issues. Biogas produced during anaerobic digestion (AD) is sustainable and renewable alternative to fossil fuels. AD may improve the controlled production of biogas and offers significant environmental benefits. This review focuses on research outcomes relevant for enhanced biogas production by exploring the possible applications of CFD in AD technology. CFD-related research performed in AD conditions in order to improve mixing performance, reduce power consumption, and understand the effects of total solid (TS) concentrations on flow behavior have been discussed. In addition, the use of AD for bio-hydrogen production, wastewater treatment, and sludge treatment are looked in. This review also identifies novel areas for AD technology advancement where there is potential for economic improvement in renewable energy production. Finally, future research needs have been identified, focusing on the opportunities to integrate conceptual and mathematical models for advancing CFD simulations for bioenergy.

Double-diffusion convective biomimetic flow of nanofluid in a complex divergent porous wavy medium under magnetic effects.

We explore the physical influence of magnetic field on double-diffusive convection in complex biomimetic (peristaltic) propulsion of nanofluid through a two-dimensional divergent channel. Additionally, porosity effects along with rheological properties of the fluid are also retained in the analysis. The mathematical model is developed by equations of continuity, momentum, energy, and mass concentration. First, scaling analysis is introduced to simplify the rheological equations in the wave frame of reference and then get the final form of equations after applying the low Reynolds number and lubrication approach. The obtained equations are solved analytically by using integration method. Physical interpretation of velocity, pressure gradient, pumping phenomena, trapping phenomena, heat, and mass transfer mechanisms are discussed in detail under magnetic and porous environment. The magnitude of velocity profile is reduced by increasing Grashof parameter. The bolus circulations disappeared from trapping phenomena for larger strength of magnetic and porosity medium. The magnitude of temperature profile and mass concentration are increasing by enhancing the Brownian motion parameter. This study can be productive in manufacturing non-uniform and divergent shapes of micro-lab-chip devices for thermal engineering, industrial, and medical technologies.

Physiological Loading-Induced Interstitial Fluid Dynamics in Osteon of Osteogenesis Imperfecta Bone.

Osteogenesis imperfecta (OI), also known as "brittle bone disease," is a genetic bone disorder. OI bones experience frequent fractures. Surgical procedures are usually followed by clinicians in the management of OI. It has been 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 stimulate bone remodeling activities. Several studies have characterized strain environment in OI bones, whereas very few studies attempted to characterize the interstitial fluid flow. OI significantly affects bone micro-architecture. Thus, this study anticipates that canalicular fluid flow reduces in OI bone in comparison to the healthy bone in response to physiological loading due to altered poromechanical properties. This work attempts to understand the canalicular fluid distribution in single osteon models of OI and healthy bone. 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 the 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. This work attempts to identify the plausible explanation behind the diminished mechanotransduction capability of OI bone. This work may further be extended for designing better biomechanical therapies to enhance the fluid flow in order to improve osteogenic activities in OI bone.

Anatomical variations in cortical bone surface permeability: Tibia versus femur.

Cortical bone surfaces (periosteal and endosteal) exhibit differential (re)modelling response to mechanical loading. This poses a serious challenge in establishing an in silico model to predict site-specific new bone formation as a function of mechanical stimulus. In this regard, mechanical loading-induced fluid motion in lacunar-canalicular system (LCS) is assumed osteogenic. Micro-architectural properties, especially permeability regulate canalicular fluid motion within the bone. The knowledge of these properties is required to compute flow distribution. Along the same line, it is possible that cortical surfaces may experience differential fluid distribution due to anatomical variations in microarchitectural properties which may induce distinct new bone response at cortical surfaces. Nevertheless, these properties are not well reported for cortical surfaces in the literature. Accordingly, the present study aims to measure microarchitectural properties especially permeability at different anatomical locations (medial, lateral, anterior, and posterior) of periosteal and endosteal surfaces using nanoindentation. A standard poroelastic optimization technique was used to estimate permeability, shear modulus, and Poisson's ratio. The properties are also compared for two weight-bearing bones i.e. tibia and femur. Endosteal surface was found more permeable as compared to the periosteal surface. Tibial endosteal surface had shown greater permeability values at most of the anatomical locations as compared to femoral endosteal surface. The outcomes may be used to precisely predict site-specific osteogenesis in cortical bone as a function of canalicular flow distribution. This work may ultimately be beneficial in designing the loading parameters to stimulate desired new bone response for the prevention and the cure of bone loss.

Thermal, microrotation, electromagnetic field and nanoparticle shape effects on Cu-CuO/blood flow in microvascular vessels.

A thermal analysis of Cu-CuO/ blood nanofluids flow in asymmetric microchannel propagating with wave velocity is presented in this study. For the blood, a micropolar fluid model is considered to investigate the microrotation effects of blood flow. Thermal radiation effects and the influence of nanoparticle shape, electric double layer thickness, and electromagnetic fields on the flow are studied. Three types of nanoparticles shapes namely cylinder, bricks and platelets are taken into account. Governing equations are solved under the approximations of long wavelength, low Reynolds number, and Debye-Hückel linearization. Numerical computations are performed for the axial pressure gradient, axial velocity, spin velocity and temperature distribution. The effects of various physical parameters on flow and thermal characteristics are computed and their physical interpretation is also discussed. The outcomes indicate that the axial velocity of Cu-CuO/blood nanoparticles strongly depends on applied electromagnetic field and microrotation. The model's finding will be applicable in designing the smart electromagnetic micro pumps for the hemodialysis and lungs-on-chip devices for the pumping of the blood.

Blood-based graphene oxide nanofluid flow through capillary in the presence of electromagnetic fields: A Sutterby fluid model.

Pumping devices with the electrokinetics phenomena are important in many microscale transport phenomena in physiology. This study presents a theoretical and numerical investigation on the peristaltic pumping of non-Newtonian Sutterby nanofluid through capillary in presence of electromagnetohydrodynamics. Here blood (Sutterby fluid) is taken as a base fluid and nanofluid is prepared by the suspension of graphene oxide nanoparticle in blood. Graphene oxide is extremely useful in the medical domain for drug delivery and cancer treatment. The modified Buongiorno model for nanofluids and Poisson-Boltzmann ionic distribution is adopted for the formulation of the present problem. Constitutive flow equations are linearized by the implementation of approximations low Reynolds number, large wavelength, and the Debye-Hückel linearization. The numerical solution of reduced coupled and nonlinear set of equations is computed through Mathematica and graphical illustration is presented. Further, the impacts of buoyancy forces, thermal radiation, and mixed convection are also studied. It is revealed in this investigation that the inclusion of a large number of nanoparticles alters the flow characteristics significantly and boosts the heat transfer mechanism. Moreover, the pumping power of the peristaltic pump can be enhanced by the reduction in the width of the electric double layer which can be done by altering the electrolyte concentration.

Signalling molecule transport analysis in lacunar-canalicular system.

Mechanical loading-induced fluid flow in lacunar-canalicular space (LCS) of bone excites osteocyte cells to release signalling molecules which initiate osteo-activities. Theoretical models considered canaliculi as a uniform and symmetrical space/channel in bone. However, experimental studies reported that canalicular walls are irregular and curvy resulting in inhomogeneous fluid motion which may influence the molecular transport. Therefore, a new mathematical model of LCS with curvy canalicular walls is developed to characterize cantilever bending-induced canalicular flow behaviour in terms of pore-pressure, fluid velocity, and streamlines. The model also analyses the mobility of signalling molecules involved in bone mechanotransduction as a function of loading frequency and permeability of LCS. Inhomogeneous flow is observed at higher loading frequency which amplifies mechanotransduction; nevertheless, it also promotes trapping of signalling molecules. The effects of shape and size of signalling molecules on transport behaviour are also studied. Trivially, signalling molecules larger in size and weight move slower as compared to molecules small in size and weight which validates the findings of the present study. The outcomes will ultimately be useful in designing better biomechanical exercise in combination with pharmaceutical agents to improve the bone health.