Application of mechanoregulatory models to simulate peri-implant tissue formation in an in vivo bone chamber

Micro/nanostructural properties of peri-implant jaw bones: a human cadaver study

PURPOSE

Many points concerning the structure of osseointegration and the surrounding jaw bone remain unclear, and its optimal histological form has yet to be identified. The aim of this study was to clarify the structural characteristics of peri-implant jaw bone on the micro- and nano-scales by quantitatively evaluating bone quality.

METHODS

Five samples of human mandibular bone containing dental implants and one dentate sample that had been in place for some years while the donors were still alive were collected. Bulk staining was performed, and 100-μm-thick polished specimens were prepared. The osteon distributions in peri-implant bone and mandibular cortical bone were measured, after which alignment analysis of biological apatite (BAp) crystallites and anisotropy analysis of collagen fiber orientation using second-harmonic generation imaging were carried out.

RESULTS

Osteons in the vicinity of the implant body ran parallel to it. In the cortical bone at the base of the mandible, however, most osteons were oriented mesiodistally. The preferential alignment of BAp crystallites was generally consistent with osteon orientation. The orientation of collagen fibers in peri-implant jaw bone resembled the concentric rings seen in normal cortical bone, but there were also fibers that ran orthogonally across these concentric fibers.

CONCLUSIONS

These results suggest that the mechanical strain imposed by implants causes the growth of cortical bone-like bone in areas that would normally consist of cancellous bone around the implants, and that its structural characteristics are optimized for the load environment of the peri-implant jaw bone.

Bone healing response in cyclically loaded implants: Comparing zero, one, and two loading sessions per day

When bone implants are loaded, they are inevitably subjected to displacement relative to bone. Such micro-motion generates stress/strain states at the interface that can cause beneficial or detrimental sequels. The objective of this study is to better understand the mechanobiology of bone healing at the tissue-implant interface during repeated loading. Machined screw shaped Ti implants were placed in rat tibiae in a hole slightly bigger than the implant diameter. Implants were held stable by a specially-designed bone plate that permits controlled loading. Three loading regimens were applied, (a) zero loading, (b) one daily loading session of 60 cycles with an axial force of 1.5 N/cycle for 7 days, and (c) two such daily sessions with the same axial force also for 7 days. Finite element analysis was used to characterize the mechanobiological conditions produced by the loading sessions. After 7 days, the implants with surrounding interfacial tissue were harvested and processed for histological, histomorphometric and DNA microarray analyses. Histomorphometric analyses revealed that the group subjected to repeated loading sessions exhibited a significant decrease in bone-implant contact and increase in bone-implant distance, as compared to unloaded implants and those subjected to only one loading session. Gene expression profiles differed during osseointegration between all groups mainly with respect to inflammatory and unidentified gene categories. The results indicate that increasing the daily cyclic loading of implants induces deleterious changes in the bone healing response, most likely due to the accumulation of tissue damage and associated inflammatory reaction at the bone-implant interface.

Time course of peri-implant bone regeneration around loaded and unloaded implants in a rat model

The time-course of cancellous bone regeneration surrounding mechanically loaded implants affects implant fixation, and is relevant to determining optimal rehabilitation protocols following orthopaedic surgeries. We investigated the influence of controlled mechanical loading of titanium-coated polyether-ether ketone (PEEK) implants on osseointegration using time-lapsed, non-invasive, in vivo micro-computed tomography (micro-CT) scans. Implants were inserted into proximal tibial metaphyses of both limbs of eight female Sprague-Dawley rats. External cyclic loading (60 or 100 μm displacement, 1 Hz, 60 s) was applied every other day for 14 days to one implant in each rat, while implants in contralateral limbs served as the unloaded controls. Hind limbs were imaged with high-resolution micro-CT (12.5 μm voxel size) at 2, 5, 9, and 12 days post-surgery. Trabecular changes over time were detected by 3D image registration allowing for measurements of bone-formation rate (BFR) and bone-resorption rate (BRR). At day 9, mean %BV/TV for loaded and unloaded limbs were 35.5 ± 10.0% and 37.2 ± 10.0%, respectively, and demonstrated significant increases in bone volume compared to day 2. BRR increased significantly after day 9. No significant differences between bone volumes, BFR, and BRR were detected due to implant loading. Although not reaching significance (p = 0.16), an average 119% increase in pull-out strength was measured in the loaded implants. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:997-1006, 2017.

Mechanical regulation of bone regeneration: theories, models, and experiments

How mechanical forces influence the regeneration of bone remains an open question. Their effect has been demonstrated experimentally, which has allowed mathematical theories of mechanically driven tissue differentiation to be developed. Many simulations driven by these theories have been presented, however, validation of these models has remained difficult due to the number of independent parameters considered. An overview of these theories and models is presented along with a review of experimental studies and the factors they consider. Finally limitations of current experimental data and how this influences modeling are discussed and potential solutions are proposed.

The emergence of mechanoregulated endochondral ossification in evolution

The differentiation of skeletal tissue phenotypes is partly regulated by mechanical forces. This mechanoregulatory aspect of tissue differentiation has been the subject of many experimental and computational investigations. However, little is known about what factors promoted the emergence of mechanoregulated tissue differentiation in evolution, even though mechanoregulated tissue differentiation, for example during development or healing of adult bone, is crucial for vertebrate phylogeny. In this paper, we use a computational framework to test the hypothesis that the emergence of mechanosensitive genes that trigger endochondral ossification in evolution will stabilise in the population and create a variable mechanoregulated response, if the endochondral ossification process enhances fitness for survival. The model combines an evolutionary algorithm that considers genetic change with a mechanoregulated fracture healing model in which the fitness of animals in a population is determined by their ability to heal their bones. The simulations show that, with the emergence of mechanosensitive genes through evolution enabling skeletal cells to modulate their synthetic activities, novel differentiation pathways such as endochondral ossification could have emerged, which when favoured by natural selection is maintained in a population. Furthermore, the model predicts that evolutionary forces do not lead to a single optimal mechanoregulated response but that the capacity of endochondral ossification exists with variability in a population. The simulations correspond with many existing findings about the mechanosensitivity of skeletal tissues in current animal populations, therefore indicating that this kind of multi-level models could be used in future population based simulations of tissue differentiation.

A mathematical model for cell differentiation, as an evolutionary and regulated process

We introduce an approach which allows one to introduce the concept of cell plasticity into models for tissue regeneration. In contrast to most of the recent models for tissue regeneration, cell differentiation is considered a gradual process, which evolves in time and which is regulated by an arbitrary number of parameters. In the current approach, cell differentiation is modelled by means of a differentiation state variable. Cells are assumed to differentiate into an arbitrary number of cell types. The differentiation path is considered as reversible, unless differentiation has fully completed. Cell differentiation is incorporated into the partial differential equations (PDEs), which model the tissue regeneration process, by means of an advection term in the differentiation state space. This allows one to consider the differentiation path of cells, which is not possible if a reaction-like term is used for differentiation. The boundary conditions, which should be specified for the general PDEs, are derived from the flux of the fully non-differentiated cells and from the irreversibility of the fully completed differentiation process. An application of the proposed model for peri-implant osseointegration is considered. Numerical results are compared with experimental data. Potential lines of further development of the present approach are proposed.

Variability observed in mechano-regulated in vivo tissue differentiation can be explained by variation in cell mechano-sensitivity

Computational simulations of tissue differentiation have been able to capture the main aspects of tissue formation/regeneration observed in animal experiments-except for the considerable degree of variability reported. Understanding and modelling the source of this variability is crucial if computational tools are to be developed for clinical applications. The objective of this study was to test the hypothesis that differences in cell mechano-sensitivity between individuals can explain the variability of tissue differentiation patterns observed experimentally. Simulations of an experiment of tissue differentiation in a mechanically loaded bone chamber were performed. Finite element analysis was used to determine the biophysical environment, and a lattice-modelling approach was used to simulate cell activity. Differences in cell mechano-sensitivity among individuals were modelled as differences in cell activity rates, with the activation of cell activities regulated by the mechanical environment. Predictions of the tissue distribution in the chambers produced the two different classes of results found experimentally: (i) chambers with a layer of bone across the chamber covered by a layer of cartilage on top and (ii) chambers with almost no bone, mainly fibrous tissue and small islands of cartilage. This indicates that the differing cellular response to the mechanical environment (i.e., subject-specific mechano-sensitivity) could be a reason for the different outcomes found when implants (or tissue engineered constructs) are used in a population.

Tissue differentiation in an in vivo bioreactor: in silico investigations of scaffold stiffness

Scaffold design remains a main challenge in tissue engineering due to the large number of requirements that need to be met in order to create functional tissues in vivo. Computer simulations of tissue differentiation within scaffolds could serve as a powerful tool in elucidating the design requirements for scaffolds in tissue engineering. In this study, a lattice-based model of a 3D porous scaffold construct derived from micro CT and a mechano-biological simulation of a bone chamber experiment were combined to investigate the effect of scaffold stiffness on tissue differentiation inside the chamber. The results indicate that higher scaffold stiffness, holding pore structure constant, enhances bone formation. This study demonstrates that a lattice approach is very suitable for modelling scaffolds in mechano-biological simulations, since it can accurately represent the micro-porous geometries of scaffolds in a 3D environment and reduce computational costs at the same time.

Mathematical modeling in bone biology: from intracellular signaling to tissue mechanics

Although conceptual and experimental models are historically well incorporated in bone biology studies, mathematical modeling has been much less-frequently utilized. This review aims to introduce mathematical modeling to readers who are not familiar with the concept underlying this methodology, to outline how mathematical models can help to improve current understanding of bone biology and to discuss examples where mathematical modeling was used to provide new insights into important questions of bone biology.

Cancellous bone osseointegration is enhanced by in vivo loading

Biophysical stimuli may be an effective therapy to counteract age-related changes in bone structure that affect the primary stability of implants used in joint replacement or fracture fixation. The influence of controlled mechanical loading on osseointegration was investigated using an in vivo device implanted in the distal lateral femur of 12 male rabbits. Compressive loads (1 MPa, 1 Hz, 50 cycles/day, 4 weeks) were applied to a porous titanium foam implant and the underlying cancellous bone. The contralateral limbs served as nonloaded controls. Backscattered electron imaging indicated that the amount of bone ingrowth was significantly greater in the loaded limb than in the nonloaded control limb, whereas the amount of underlying cancellous periprosthetic bone was similar. No significant difference in the mineral apposition rate of the bone ingrowth or periprosthetic bone was measured in the loaded compared to the control limb. Histological analysis demonstrated newly formed woven bone in direct apposition to the implant coating, with a lack of fibrous tissue at the implant-periprosthetic bone interface in both loaded and nonloaded implants. The lack of fibrous tissue demonstrates that mechanical stimulation using this model significantly enhanced cancellous bone ingrowth without the detrimental effects of micromotion. These results suggest that biophysical therapy should be further investigated to augment current treatments to enhance long-term fixation of orthopedic devices. Additionally, this novel in vivo loading model can be used to further investigate the influence of biophysical stimulation on other tissue engineering approaches requiring bone ingrowth into both metallic and nonmetallic cell-seeded scaffolds.

Corroboration of mechanobiological simulations of tissue differentiation in an in vivo bone chamber using a lattice-modeling approach

It is well established that the mechanical environment modulates tissue differentiation, and a number of mechanoregulatory theories for describing the process have been proposed. In this study, simulations of an in vivo bone chamber experiment were performed that allowed direct comparison with experimental data. A mechanoregulation theory for mesenchymal stem cell differentiation based on a combination of fluid flow and shear strain (computed using finite element analysis) was implemented to predict tissue differentiation inside mechanically controlled bone chambers inserted into rat tibae. To simulate cell activity, a lattice approach with stochastic cell migration, proliferation, and selected differentiation was adopted; because of its stochastic nature, each run of the simulation gave a somewhat different result. Simulations predicted the load-dependency of the tissue differentiation inside the chamber and a qualitative agreement with histological data; however, the full variability found between specimens in the experiment could not be predicted by the mechanoregulation algorithm. This result raises the question whether tissue differentiation predictions can be linked to genetic variability in animal populations.

Computer-aided design and finite-element modelling of biomaterial scaffolds for bone tissue engineering

Scaffold biomaterials for tissue engineering can be produced in many different ways depending on the applications and the materials used. Most research into new biomaterials is based on an experimental trial-and-error approach that limits the possibility of making many variations to a single material and studying its interaction with its surroundings. Instead, computer simulation applied to tissue engineering can offer a more exhaustive approach to test and screen out biomaterials. In this paper, a review of the current approach in biomaterials designed through computer-aided design (CAD) and through finite-element modelling is given. First we review the approach used in tissue engineering in the development of scaffolds and the interactions existing between biomaterials, cells and mechanical stimuli. Then, scaffold fabrication through CAD is presented and characterization of existing scaffolds through computed images is reviewed. Several case studies of finite-element studies in tissue engineering show the usefulness of computer simulations in determining the mechanical environment of cells when seeded into a scaffold and the proper design of the geometry and stiffness of the scaffold. This creates a need for more advanced studies that include aspects of mechanobiology in tissue engineering in order to be able to predict over time the growth and differentiation of tissues within scaffolds. Finally, current perspectives indicate that more efforts need to be put into the development of such advanced studies, with the removal of technical limitations such as computer power and the inclusion of more accurate biological and genetic processes into the developed algorithms.

In silico biology of bone modelling and remodelling: regeneration

Bone regeneration is the process whereby bone is able to (scarlessly) repair itself from trauma, such as fractures or implant placement. Despite extensive experimental research, many of the mechanisms involved still remain to be elucidated. Over the last decade, many mathematical models have been established to investigate the regeneration process in silico. The first models considered only the influence of the mechanical environment as a regulator of the healing process. These models were followed by the development of bioregulatory models where mechanics was neglected and regeneration was regulated only by biological stimuli such as growth factors. The most recent mathematical models couple the influences of both biological and mechanical stimuli. Examples are given to illustrate the added value of mathematical regeneration research, specifically in the in silico design of treatment strategies for non-unions. Drawbacks of the current continuum-type models, together with possible solutions in extending the models towards other time and length scales are discussed. Finally, the demands for dedicated and more quantitative experimental research are presented.

Numerical Simulation of Bone Regeneration in a Bone Chamber

While mathematical models are able to capture essential aspects of biological processes like fracture healing and distraction osteogenesis, their predictive capacity in peri-implant osteogenesis remains uninvestigated. We tested the hypothesis that a mechano-regulatory model has the potential to predict bone regeneration around implants. In an in vivo bone chamber set-up allowing for controlled implant loading (up to 90 μ m axial displacement), bone tissue formation was simulated and compared qualitatively and quantitatively with histology. Furthermore, the model was applied to simulate excessive loading conditions. Corresponding to literature data, implant displacement magnitudes larger than 90 μ m predicted the formation of fibrous tissue encapsulation of the implant. In contradiction to findings in orthopedic implant osseointegration, implant displacement frequencies higher than 1 Hz did not favor the formation of peri-implant bone in the chamber. Additional bone chamber experiments are needed to test these numerical predictions.

Sensitivity of tissue differentiation and bone healing predictions to tissue properties

Computational models are employed as tools to investigate possible mechano-regulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The aim was to clarify the importance of the assumed tissue material properties in a computational model of tissue differentiation during bone healing. An established mechano-biological model was employed together with a statistical approach. The model included an adaptive 2D finite element model of a fractured long bone. Four outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at specific time points, (3) total time until healing, and (4) mechanical stability at specific time points. Statistical analysis based on fractional factorial designs first involved a screening experiment to identify the most significant tissue material properties. These seven properties were studied further with response surface methodology in a three-level Box-Behnken design. Generally, the sequential events were not significantly influenced by any properties, whereas rate-dependent outcome criteria and mechanical stability were significantly influenced by Young's modulus and permeability. Poisson's ratio and porosity had minor effects. The amount of bone formation at early, mid and late phases of healing, the time until complete healing and the mechanical stability were all mostly dependent on three material properties; permeability of granulation tissue, Young's modulus of cartilage and permeability of immature bone. The consistency between effects of the most influential parameters was high. To increase accuracy and predictive capacity of computational models of bone healing, the most influential tissue mechanical properties should be accurately quantified.

Computational mechanobiology to study the effect of surface geometry on peri-implant tissue differentiation

The geometry of an implant surface to best promote osseointegration has been the subject of several experimental studies, with porous beads and woven mesh surfaces being among the options available. Furthermore, it is unlikely that one surface geometry is optimal for all loading conditions. In this paper, a computational method is used to simulate tissue differentiation and osseointegration on a smooth surface, a surface covered with sintered beads (this simulated the experiment (Simmons, C., and Pilliar, R., 2000, Biomechanical Study of Early Tissue Formation Around Bone-Interface Implants: The Effects of Implant Surface Geometry," Bone Engineering, J. E. Davies, ed., Emsquared, Chap. A, pp. 369-379) and established that the method gives realistic results) and a surface covered by porous tantalum. The computational method assumes differentiation of mesenchymal stem cells in response to fluid flow and shear strain and models cell migration and proliferation as continuum processes. The results of the simulation show a higher rate of bone ingrowth into the surfaces with porous coatings as compared with the smooth surface. It is also shown that a thicker interface does not increase the chance of fixation failure.

"May the force be with you": 14th Samuel Haughton lecture

This paper presents the 14th Samuel Haughton lecture delivered on the 26th of January 2008. The lecture began by describing Haughton's research on animal mechanics. Haughton opposed Charles Darwin's theory of natural selection using the argument that the skeleton obeys the 'principle of least action' and therefore must have been designed with that principle in mind. In the course of his research he dissected many animals, including albatrosses, cassowaries, llamas, tigers, jackals and jaguars. He took anatomical measurements and did calculations to prove that muscle attachment sites were optimally located. The relationship between optimality and evolution continues to be studied. Computer simulations show optimality is difficult to achieve. This is because, even if optimality could be defined, the gene recombinations required to evolve an optimal phenotype may not exist. The drive towards optimality occurs under gravitational forces. Simulations to predict mechano-regulation of tissue differentiation and remodelling have been developed and tested. They have been used to design biomechanically optimized scaffolds for regenerative medicine and to identify the mechanoregularory mechanisms in osteoporosis. It is proposed that an important development in bioengineering will be the discovery of algorithms that can be used for the prediction of mechano-responsiveness in biological tissues.

Angiogenesis in bone fracture healing: a bioregulatory model

The process of fracture healing involves the action and interaction of many cells, regulated by biochemical and mechanical signals. Vital to a successful healing process is the restoration of a good vascular network. In this paper, a continuous mathematical model is presented that describes the different fracture healing stages and their response to biochemical stimuli only (a bioregulatory model); mechanoregulatory effects are excluded here. The model consists of a system of nonlinear partial differential equations describing the spatiotemporal evolution of concentrations and densities of the cell types, extracellular matrix types and growth factors indispensable to the healing process. The model starts after the inflammation phase, when the fracture callus has already been formed. Cell migration is described using not only haptokinetic, but also chemotactic and haptotactic influences. Cell differentiation is controlled by the presence of growth factors and sufficient vascularisation. Matrix synthesis and growth factor production are controlled by the local cell and matrix densities and by the local growth factor concentrations. Numerical simulations of the system, using parameter values based on experimental data obtained from literature, are presented. The simulation results are corroborated by comparison with experimental data from a standardised rodent fracture model. The results of sensitivity analyses on the parameter values as well as on the boundary and initial conditions are discussed. Numerical simulations of compromised healing situations showed that the establishment of a vascular network in response to angiogenic growth factors is a key factor in the healing process. Furthermore, a correct description of cell migration is also shown to be essential to the prediction of realistic spatiotemporal tissue distribution patterns in the fracture callus. The mathematical framework presented in this paper can be an important tool in furthering the understanding of the mechanisms causing compromised healing and can be applied in the design of future fracture healing experiments.