Comparison of biophysical stimuli for mechano-regulation of tissue differentiation during fracture healing

Most long-bone fractures heal through indirect or secondary fracture healing, a complex process in which endochondral ossification is an essential part and bone is regenerated by tissue differentiation. This process is sensitive to the mechanical environment, and several authors have proposed mechano-regulation algorithms to describe it using strain, pore pressure and/or interstitial fluid velocity as biofeedback variables. The aim of this study was to compare various mechano-regulation algorithms' abilities to describe normal fracture healing in one computational model. Additionally, we hypothesized that tissue differentiation during normal fracture healing could be equally well regulated by the individual mechanical stimuli, e.g. deviatoric strain, pore pressure or fluid velocity. A biphasic finite element model of an ovine tibia with a 3mm fracture gap and callus was used to simulate the course of tissue differentiation during normal fracture healing. The load applied was regulated in a biofeedback loop, where the load magnitude was determined by the interfragmentary movement in the fracture gap. All the previously published mechano-regulation algorithms studied, simulated the course of normal fracture healing correctly. They predicted (1) intramembranous bone formation along the periosteum and callus tip, (2) endochondral ossification within the external callus and cortical gap, and (3) creeping substitution of bone towards the gap from the initial lateral osseous bridge. Some differences between the effects of the algorithms were seen, but they were not significant. None of the volumetric components, i.e. pore pressure or fluid velocity, alone were able to correctly predict spatial or temporal tissue distribution during fracture healing. However, simulation as a function of only deviatoric strain accurately predicted the course of normal fracture healing. This suggests that the deviatoric component may be the most significant mechanical parameter to guide tissue differentiation during indirect fracture healing.     

A dynamical study of the mechanical stimuli and tissue differentiation within a CaP scaffold based on micro-CT finite element models

The control of the mechanical stimuli transmitted to the cells is critical for the design of functional scaffolds for tissue engineering. The objective of this study was to investigate the dynamics of the mechanical stimuli transmitted to the cells during tissue differentiation in an irregular morphology scaffold under compressive load and perfusion flow. A calcium phosphate-based glass porous scaffold was used. The solid phase and the fluid flow within the pores were modeled as linear elastic solid material and Newtonian fluid, respectively. In the fluid model, different levels of viscosity were used to simulate tissue differentiation. Compressive strain of 0.5% and fluid flow with constant inlet velocity of 10 μm/s or constant inlet pressure of 3 Pa were applied. Octahedral shear strain and fluid shear stress were used as mechano-regulatory stimuli. For constant inlet velocity, stimuli equivalent to bone were predicted in 80% of pore volume for the case of low tissue viscosity. For the cases of high viscosity, fluctuations between stimuli equivalent to tissue formation and cell death were predicted due to the increase in the fluid shear stress when tissue started to fill pores. When constant pressure was applied, stimuli equivalent to bone were predicted in 62% of pore volume when low tissue viscosity was used and 42% when high tissue viscosity was used. This study predicted critical variations of fluid shear stress when cells differentiated. If these variations are not controlled in vitro, they can impede the formation of new matured tissue.     

Micromotion-induced peri-prosthetic fluid flow around a cementless femoral stem

Micromotion-induced interstitial fluid flow at the bone-implant interface has been proposed to play an important role in aseptic loosening of cementless implants. High fluid velocities are thought to promote aseptic loosening through activation of osteoclasts, shear stress induced control of mesenchymal stem cells differentiation, or transport of molecules. In this study, our objectives were to characterize and quantify micromotion-induced fluid flow around a cementless femoral stem using finite element modeling. With a 2D model of the bone-implant interface and full-factorial design, we first evaluated the relative influence of material properties, and bone-implant micromotion and gap on fluid velocity. Transverse sections around a femoral stem were built from computed tomography images, while boundary conditions were obtained from experimental measurements on the same femur. In a second step, a 3D model was built from the same data-set to estimate the shear stress experienced by cells hosted in the peri-implant tissues. The full-factorial design analysis showed that local micromotion had the most influence on peak fluid velocity at the interface. Remarkable variations in fluid velocity were observed in the macrostructures at the surface of the implant in the 2D transverse sections of the stem. The 3D model predicted peak fluid velocities extending up to 2.2 mm/s in the granulation tissue and to 3.9 mm/s in the trabecular bone. Peak shear stresses on the cells hosted in these tissues ranged from 0.1 to 12.5 Pa. These results offer insight into mechanical stimuli encountered at the bone-implant interface.     

A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 microm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 microm/s of inlet fluid velocity and 1.45 Pas viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5)Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.     

A mechano-regulation model for tissue differentiation during fracture healing: analysis of gap size and loading

Bone has a capability to repair itself when it is fractured. Repair involves the generation of intermediate tissues, such as fibrous connective tissue, cartilage and woven bone, before final bone healing can occur. The intermediate tissues serve to stabilise the mechanical environment and provide a scaffold for differentiation of new tissues. The repair process is fundamentally affected by mechanical loading and by the geometric configuration of the fracture fragments. Biomechanical analyses of fracture healing have previously computed the stress distribution within the callus and identified the components of the stress tensor favouring or inhibiting differentiation of particular tissue phenotypes. In this paper, a biphasic poroelastic finite element model of a fracture callus is used to simulate the time-course of tissue differentiation during fracture healing. The simulation begins with granulation tissue (post-inflammation phase) and finishes with bone resorption. The biomechanical regulatory model assumes that tissue differentiation is controlled by a combination of shear strain and fluid flow acting within the tissue. High shear strain and fluid flows are assumed to deform the precursor cells stimulating formation of fibrous connective tissue, lower levels stimulate formation of cartilage, and lower again allows ossification. This mechano-regulatory scheme was tested by simulating healing in fractures with different gap sizes and loading magnitudes. The appearance and disappearance of the various tissues found in a callus was similar to histological observation. The effect of gap size and loading magnitude on the rate of reduction of the interfragmentary strain was sufficiently close to confirm the hypothesis that tissue differentiation phenomena could be governed by the proposed mechano-regulation model.     

Mechanical interaction between cells and fluid for bone tissue engineering scaffold: Modulation of the interfacial shear stress

An analytical model of the fluid/cell mechanical interaction was developed. The interfacial shear stress, due to the coupling between the fluid and the cell deformation, was characterized by a new dimensionless number N_fs. For N_fs above a critical value, the fluid/cell interaction had a damping effect on the interfacial shear stress. Conversely, for N_fs below this critical value, interfacial shear stress was amplified. As illustration, the role of the dynamic fluid/cell mechanical coupling was studied in a specific biological situation involving cells seeded in a bone scaffold. For the particular bone scaffold chosen, the dimensionless number N_fs was higher than the critical value. In this case, the dynamic shear stress at the fluid/cell interface is damped for increasing excitation frequency. Interestingly, this damping effect is correlated to the pore diameter of the scaffold, furnishing thus target values in the design of the scaffold. Correspondingly, an efficient cell stimulation might be achieved with a scaffold of pore size larger than 300 μm as no dynamic damping effect is likely to take place. The analytical model proposed in this study, while being a simplification of a fluid/cell mechanical interaction, brings complementary insights to numerical studies by analyzing the effect of different physical parameters.     

The relation between surface roughness and interfacial shear strength for bone-anchored implants. A mathematical model.

A rough bone implant surface was conceptualized as being built up of pits of different sizes and of different shapes. Hypotheses were formulated regarding the mechanical strength of the interfacial bone based upon the present knowledge of the character of the tissues adjacent to endosseous implants and the mechanical characteristics of different bone constituents. A surface roughness parameter was derived, the pit effectivity factor (fpe), which describes how effective the individual pits of the rough surface are as retention elements with regard to shear. Another surface roughness parameter was defined, the pit density factor (fpd), the value of which depends upon how densely packed the pits are. The interfacial shear strength of a rough implant surface with known microgeometry can be estimated by means of these two surface roughness parameters. The effectiveness of pits of different sizes and of different shapes was investigated using this model.     

Effect of surface roughness on slip flows in hydrophobic and hydrophilic microchannels by molecular dynamics simulation

The influences of surface roughness on the boundary conditions for a simple fluid flowing over hydrophobic and hydrophilic surfaces are investigated by molecular dynamics (MD) simulation. The degree of slip is found to decrease with surface roughness for both the hydrophobic and hydrophilic surfaces. The flow rates measured in hydrophobic channels are larger than those in hydrophilic channels with the presence of slip velocity at the walls. The simulation results of flow rate are correlated with the theoretical predictions according to the assumption of no slip boundary condition. The slip boundary condition also strongly depends on the shear rate near the surface. For hydrophobic surfaces, apparent fluid slips are observed on smooth and rough surfaces. For simple fluids flowing over a hydrophobic surface, the slip length increases linearly with shear rate for both the smooth and rough surfaces. Alternately, the slip length has a power law dependence on the shear rate for the cases of hydrophilic surfaces. It is observed that there is a no-slip boundary condition only when shear rate is low, and partial slip occurs when it exceeds a critical level.     

Measuring local flow velocities and biofilm structure in biofilm systems with magnetic resonance imaging (MRI)

The characterization of substrate transport in the bulk phase and in the biofilm matrix is one of the problems which has to be solved for the verification of biofilm models. Additionally, the surface structure of biofilms has to be described with appropriate parameters. Magnetic resonance imaging (MRI) is one of the promising methods for the investigation of transport phenomena and structure in biofilm systems. The MRI technique allows the noninvasive determination of flow velocities and biofilm structures with a high resolution on the sub-millimeter scale. The presented investigations were carried out for defined heterotrophic biofilms which were cultivated in a tube reactor at a Reynolds number of 2000 and 8000 and a substrate load of 6 and 4 g/m2d glucose. Magnetic resonance imaging provides both structure data of the biofilm surface and flow velocities in the bulk phase and at the bulk/biofilm interface. It is shown that the surface roughness of the biofilms can be determined in one experiment for the complete cross section of the test tubes both under flow and stagnant conditions. Furthermore, the local shear stress was calculated from the measured velocity profiles. In the investigated biofilm systems the local shear stress at the biofilm surface was up to 3 times higher compared to the mean wall shear stress calculated on the base of the mean flow velocity.     

Stochastic Interdigitation as a Toughening Mechanism at the Interface between Tendon and Bone

Reattachment and healing of tendon to bone poses a persistent clinical challenge and often results in poor outcomes, in part because the mechanisms that imbue the uninjured tendon-to-bone attachment with toughness are not known. One feature of typical tendon-to-bone surgical repairs is direct attachment of tendon to smooth bone. The native tendon-to-bone attachment, however, presents a rough mineralized interface that might serve an important role in stress transfer between tendon and bone. In this study, we examined the effects of interfacial roughness and interdigital stochasticity on the strength and toughness of a bimaterial interface. Closed form linear approximations of the amplification of stresses at the rough interface were derived and applied in a two-dimensional unit-cell model. Results demonstrated that roughness may serve to increase the toughness of the tendon-to-bone insertion site at the expense of its strength. Results further suggested that the natural tendon-to-bone attachment presents roughness for which the gain in toughness outweighs the loss in strength. More generally, our results suggest a pathway for stochasticity to improve surgical reattachment strategies and structural engineering attachments.     

Mixed-mode failure strength of implant-cement interface specimens with varying surface roughness

Aseptic loosening at the implant-cement interface is a well-documented cause of failure in joint arthroplasty. Traditionally, the strength of the implant-cement interface is determined using uni-axial normal and shear loading tests. However, during functional loading, the implant fixation sites are loaded under more complex stress conditions. For this purpose, the strength of the implant-cement interface under mixed-mode tensile and shear loading conditions was determined in this study using interface specimens with varying interface roughness. For the lowest roughness value analyzed (R(a)=0.89 μm), the interface strength was 0.40-1.95 MPa at loading angles varying between pure tension and shear, whereas this was 4.90-9.90 MPa for the highest roughness value (R(a)=2.76 μm). The interface strength during pure shear (1.95-9.90 MPa) was substantially higher than during pure tension (0.58-6.67 MPa). Polynomial regression was used to fit a second-order interpolation function through the experimental interface strength data (R2=0.85; p<0.001), relating the interface strength (S [MPa]) to the interface loading angle (α [degrees]) and interface roughness (R(a) [μm]): S(α,R(a))=0.891R2(a)+0.001α2-0.189R(a)-0.064α-0.060. Finally, an interface failure criterion was derived from the interface strength measurements, describing the risk of failure at the implant-cement interface when subjected to a certain tensile and shear stress using only the interface strength in pure tensile and shear direction. The findings presented in this paper can be used in numerical models to simulate loosening at the implant-cement interface.     

Surface roughness parameters as predictors of anchorage strength in bone: a critical analysis

The surface roughness of a bone implant was defined parametrically. The values of the parameters defining the surface were varied. Some traditionally used surface roughness parameters were calculated. By means of a theoretical model the bone-implant interfacial shear strength was estimated. No simple correlation between the values of the surface roughness parameters and the estimated interfacial shear strength was found. It was concluded that the value of the traditional surface roughness parameters as predictors of interfacial shear strength is limited. If however a change of the surface topography of an implant is restricted to scale a positive correlation was found between the theoretical interfacial shear strength and some surface roughness parameters. It is suggested that the bone-implant interfacial shear strength in the general case be estimated by means of strength analyses based upon a study of the size, shape and density of the individual elements constituting the rough surface.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

The breakup of intravascular microbubbles and its impact on the endothelium

Encapsulated microbubbles (MBs) serve as endovascular agents in a wide range of medical ultrasound applications. The oscillatory response of these agents to ultrasonic excitation is determined by MB size, gas content, viscoelastic shell properties and geometrical constraints. The viscoelastic parameters of the MB capsule vary during an oscillation cycle and change irreversibly upon shell rupture. The latter results in marked stress changes on the endothelium of capillary blood vessels due to altered MB dynamics. Mechanical effects on microvessels are crucial for safety and efficacy in applications such as focused ultrasound-mediated blood–brain barrier (BBB) opening. Since direct in vivo quantification of vascular stresses is currently not achievable, computational modelling has established itself as an alternative. We have developed a novel computational framework combining fluid–structure coupling and interface tracking to model the nonlinear dynamics of an encapsulated MB in constrained environments. This framework is used to investigate the mechanical stresses at the endothelium resulting from MB shell rupture in three microvessel setups of increasing levels of geometric detail. All configurations predict substantial elevation of up to 150 % for peak wall shear stress upon MB breakup, whereas global peak transmural pressure levels remain unaltered. The presence of red blood cells causes confinement of pressure and shear gradients to the proximity of the MB, and the introduction of endothelial texture creates local modulations of shear stress levels. With regard to safety assessments, the mechanical impact of MB breakup is shown to be more important than taking into account individual red blood cells and endothelial texture. The latter two may prove to be relevant to the actual, complex process of BBB opening induced by MB oscillations.     

Assessment of a mechano-regulation theory of skeletal tissue differentiation in an in vivo model of mechanically induced cartilage formation

Mechanical cues are known to regulate tissue differentiation during skeletal healing. Quantitative characterization of this mechano-regulatory effect has great therapeutic potential. This study tested an existing theory that shear strain and interstitial fluid flow govern skeletal tissue differentiation by applying this theory to a scenario in which a bending motion applied to a healing transverse osteotomy results in cartilage, rather than bone, formation. A 3-D finite element mesh was created from micro-computed tomography images of a bending-stimulated callus and was used to estimate the mechanical conditions present in the callus during the mechanical stimulation. Predictions regarding the patterns of tissues—cartilage, fibrous tissue, and bone—that formed were made based on the distributions of fluid velocity and octahedral shear strain. These predictions were compared to histological sections obtained from a previous study. The mechano-regulation theory correctly predicted formation of large volumes of cartilage within the osteotomy gap and many, though not all patterns of tissue formation observed throughout the callus. The results support the concept that interstitial fluid velocity and tissue shear strain are key mec- hanical stimuli for the differentiation of skeletal tissues.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone-soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone-soft tissue interface, resulting in bone resorption.     

Peristaltic transport in a channel with a porous peripheral layer: model of a flow in gastrointestinal tract

Peristaltic transport in a two dimensional channel, filled with a porous medium in the peripheral region and a Newtonian fluid in the core region, is studied under the assumptions of long wavelength and low Reynolds number. The fluid flow is investigated in the waveframe of reference moving with the velocity of the peristaltic wave. Brinkman extended Darcy equation is utilized to model the flow in the porous layer. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. A shear-stress jump boundary condition is used at the interface. The physical quantities of importance in peristaltic transport like pumping, trapping, reflux and axial velocity are discussed for various parameters of interest governing the flow like Darcy number, porosity, permeability, effective viscosity etc. It is observed that the peristalsis works as a pump against greater pressure in two-layered model with a porous medium compared with a viscous fluid in the peripheral layer. Increasing Darcy number Da decreases the pumping and increasing shear stress jump constant beta results in increasing the pumping. The limits on the time averaged flux Q for trapping in the core layer are obtained. The discussion on pumping, trapping and reflux may be helpful in understanding some of the fluid dynamic aspects of the transport of chyme in gastrointestinal tract.     

Fluid-induced osteolysis: modelling and experiments

A model to calculate bone resorption driven by fluid flow at the bone–soft tissue interface is developed and used as a basis for computer calculations, which are compared to experiments where bone is subjected to fluid flow in a rat model. Previous models for bone remodelling calculations have been based on the state of stress, strain or energy density of the bone tissue as the stimulus for remodelling. We believe that there is experimental support for an additional pathway where an increase in the amount of the cells directly involved in bone removal, the osteoclasts, is caused by fluid pressure, flow velocity or other parameters related to fluid flow at the bone–soft tissue interface, resulting in bone resorption.     

Modeling pulsatile flow in aortic aneurysms: effect of non-Newtonian properties of blood

Pulsatile flow in an axisymmetric rigid-walled model of an abdominal aorta aneurysm was analyzed numerically for various aneurysm dilations using physiologically realistic resting waveform at time-averaged Reynolds number of 300 and peak Reynolds number of 1607. Discretization of the governing equations was achieved using a finite element scheme based on the Galerkin method of weighted residuals. Comparisons with previously published work on the basis of special cases were performed and found to be in excellent agreement. Our findings indicate that the velocity fields are significantly affected by non-Newtonian properties in pathologically altered configurations. Non-Newtonian fluid shear stress is found to be greater than Newtonian fluid shear stress during peak systole. Further, the maximum shear stress is found to occur near the distal end of AAA during peak systole. The impact of non-Newtonian blood flow characteristics on pressure compared to Newtonian model is found insignificant under resting conditions. Viscous and inertial forces associated with blood flow are responsible for the changes in the wall that result in thrombus deposition and dilation while rupture of AAA is more likely determined by much larger mechanical stresses imposed by pulsatile pressure on the wall of AAA.