Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants

Peri-implant cell differentiation in delayed and immediately-loaded dental implant: A mechanobiological simulation

OBJECTIVE

This study aimed to investigate the effect of immediate versus delayed dental implant placement strategies on cell differentiation in a dental callus.

DESIGN

The implant was placed in the mandible with two nearby teeth using an idealized two-dimensional finite element model. Eight weeks after surgery, the mechanobiological modeling of healing was used to estimate cell differentiation. It was assumed that the callus was initially filled by mesenchymal cells. The model then transformed mechanical stimuli received by the callus from loadings in terms of distortional and dilatational strains into predictions of the cellular phenotypes, including fibroblasts, chondrocytes, and osteoblasts, or whether they would remain unchanged or die.

RESULTS

The results demonstrated that delayed loading led to greater bone formation than immediate loading. Osteoblast colonies were observed in the base of threads in the immediately-loaded implant, whereas the delayed loading caused distant bone formation from the surrounding bone side towards the implant. The osteoblasts were differentiated from both intramembranous and endochondral mechanisms of ossification. After eight weeks, approximately 61 % of the callus was ossified in the delayed placement model compared to 35 % in the immediate placement model, resulting in a greater amount of fibrocartilaginous tissue on the bone side of the callus.

CONCLUSIONS

Immediate and delayed loading models generated different results. In the delayed strategy, bone cells were supplied appropriately during the first few weeks following surgery, whereas the immediate loading caused fibrocartilaginous tissue differentiation. In the form of distant osseointegration, the secondary stability of the dental implant was higher and faster due to the delayed placement.

On computational predictions of fluid flow and its effects on bone healing in dental implant treatments: an investigation of spatiotemporal fluid flow in cyclic loading

Fluid flow in (porous) bone plays an important role in its maintenance, adaptation, and healing after an injury. Experimental and computational studies apply mechanical loading on bone to predict fluid flow development and/or to find its material properties. In most cases, mechanical loading is applied as a linear function in time. Multiple loading functions-with identical peak load and loading frequency-were used to investigate load-induced fluid flow and predict bone healing surrounding a dental implant. Implementing an instantaneous healing stimulus led to major differences in healing predictions for slightly different loading functions. Load-induced fluid flow was found to be displacement-rate dependent with complex spatial-temporal variations and not necessarily symmetrical during loading and unloading phases. Haversine loading resulted in more numerical stability compared to ramped/triangular loading, providing the opportunity for further investigation of the effects of various physiological masticatory loadings. It was concluded that using the average healing stimulus during cyclic loading gives the most robust bone healing predictions.

PCL strut-like scaffolds appear superior to gyroid in terms of bone regeneration within a long bone large defect: An in silico study

The treatment of large bone defects represents a major clinical challenge. 3D printed scaffolds appear as a promising strategy to support bone defect regeneration. The 3D design of such scaffolds impacts the healing path and thus defect regeneration potential. Among others, scaffold architecture has been shown to influence the healing outcome. Gyroid architecture, characterized by a zero mean surface curvature, has been discussed as a promising scaffold design for bone regeneration. However, whether gyroid scaffolds are favourable for bone regeneration in large bone defects over traditional strut-like architecture scaffolds remains unknown. Therefore, the aim of this study was to investigate whether gyroid scaffolds present advantages over more traditional strut-like scaffolds in terms of their bone regeneration potential. Validated bone defect regeneration principles were applied in an in silico modeling approach that allows to predict bone formation in defect regeneration. Towards this aim, the mechano-biological bone regeneration principles were adapted to allow simulating bone regeneration within both gyroid and strut-like scaffolds. We found that the large surface curvatures of the gyroid scaffold led to a slower tissue formation dynamic and conclusively reduced bone regeneration. The initial claim, that an overall reduced zero mean surface curvature would enhance bone formation, could not be confirmed. The here presented approach illustrates the potential of in silico tools to evaluate in pre-clinical studies scaffold designs and eventually lead to optimized architectures of 3D printed implants for bone regeneration.

Numerical modeling of cell differentiation and proliferation in force-induced substrates via encapsulated magnetic nanoparticles

BACKGROUND AND OBJECTIVE

Cell migration, differentiation, proliferation and apoptosis are the main processes in tissue regeneration. Mesenchymal Stem Cells have the potential to differentiate into many cell phenotypes such as tissue- or organ-specific cells to perform special functions. Experimental observations illustrate that differentiation and proliferation of these cells can be regulated according to internal forces induced within their Extracellular Matrix. The process of how exactly they interpret and transduce these signals is not well understood.

METHODS

A previously developed three-dimensional (3D) computational model is here extended and employed to study how force-free substrates and force-induced substrate control cell differentiation and/or proliferation during the mechanosensing process. Consistent with experimental observations, it is assumed that cell internal deformation (a mechanical signal) in correlation with the cell maturation state directly triggers cell differentiation and/or proliferation. The Extracellular Matrix is modeled as Neo-Hookean hyperelastic material assuming that cells are cultured within 3D nonlinear hydrogels.

RESULTS

In agreement with well-known experimental observations, the findings here indicate that within neurogenic (0.1-1kPa), chondrogenic (20-25kPa) and osteogenic (30-45kPa) substrates, Mesenchymal Stem Cells differentiation and proliferation can be precipitated by inducing the substrate with an internal force. Therefore, cells require a longer time to grow and maturate within force-free substrates than within force-induced substrates. In the instance of Mesenchymal Stem Cells differentiation into a compatible phenotype, the magnitude of the net traction force increases within chondrogenic and osteogenic substrates while it reduces within neurogenic substrates. This is consistent with experimental studies and numerical works recently published by the same authors. However, in all cases the magnitude of the net traction force considerably increases at the instant of cell proliferation because of cell-cell interaction.

CONCLUSIONS

The present model provides new perspectives to delineate the role of force-induced substrates in remotely controlling the cell fate during cell-matrix interaction, which open the door for new tissue regeneration methodologies.

Role of Mechanical Cues in Cell Differentiation and Proliferation: A 3D Numerical Model

Cell differentiation, proliferation and migration are essential processes in tissue regeneration. Experimental evidence confirms that cell differentiation or proliferation can be regulated according to the extracellular matrix stiffness. For instance, mesenchymal stem cells (MSCs) can differentiate to neuroblast, chondrocyte or osteoblast within matrices mimicking the stiffness of their native substrate. However, the precise mechanisms by which the substrate stiffness governs cell differentiation or proliferation are not well known. Therefore, a mechano-sensing computational model is here developed to elucidate how substrate stiffness regulates cell differentiation and/or proliferation during cell migration. In agreement with experimental observations, it is assumed that internal deformation of the cell (a mechanical signal) together with the cell maturation state directly coordinates cell differentiation and/or proliferation. Our findings indicate that MSC differentiation to neurogenic, chondrogenic or osteogenic lineage specifications occurs within soft (0.1-1 kPa), intermediate (20-25 kPa) or hard (30-45 kPa) substrates, respectively. These results are consistent with well-known experimental observations. Remarkably, when a MSC differentiate to a compatible phenotype, the average net traction force depends on the substrate stiffness in such a way that it might increase in intermediate and hard substrates but it would reduce in a soft matrix. However, in all cases the average net traction force considerably increases at the instant of cell proliferation because of cell-cell interaction. Moreover cell differentiation and proliferation accelerate with increasing substrate stiffness due to the decrease in the cell maturation time. Thus, the model provides insights to explain the hypothesis that substrate stiffness plays a key role in regulating cell fate during mechanotaxis.

Prediction of fracture healing under axial loading, shear loading and bending is possible using distortional and dilatational strains as determining mechanical stimuli

Numerical models of secondary fracture healing are based on mechanoregulatory algorithms that use distortional strain alone or in combination with either dilatational strain or fluid velocity as determining stimuli for tissue differentiation and development. Comparison of these algorithms has previously suggested that healing processes under torsional rotational loading can only be properly simulated by considering fluid velocity and deviatoric strain as the regulatory stimuli. We hypothesize that sufficient calibration on uncertain input parameters will enhance our existing model, which uses distortional and dilatational strains as determining stimuli, to properly simulate fracture healing under various loading conditions including also torsional rotation. Therefore, we minimized the difference between numerically simulated and experimentally measured courses of interfragmentary movements of two axial compressive cases and two shear load cases (torsional and translational) by varying several input parameter values within their predefined bounds. The calibrated model was then qualitatively evaluated on the ability to predict physiological changes of spatial and temporal tissue distributions, based on respective in vivo data. Finally, we corroborated the model on five additional axial compressive and one asymmetrical bending load case. We conclude that our model, using distortional and dilatational strains as determining stimuli, is able to simulate fracture-healing processes not only under axial compression and torsional rotation but also under translational shear and asymmetrical bending loading conditions.

Low oxygen tension is a more potent promoter of chondrogenic differentiation than dynamic compression

During fracture healing and microfracture treatment of cartilage defects mesenchymal stem cells (MSCs) infiltrate the wound site, proliferate extensively and differentiate along a cartilaginous or an osteogenic lineage in response to local environmental cues. MSCs may be able to directly sense their mechanical environment or alternatively, the mechanical environment could act indirectly to regulate MSC differentiation by inhibiting angiogenesis and diminishing the supply of oxygen and other regulatory factors. Dynamic compression has been shown to regulate chondrogenesis of MSCs. In addition, previous studies have shown that a low oxygen environment promotes in vitro chondrogenesis of MSCs. The hypothesis of this study is that a low oxygen environment is a more potent promoter of chondrogenic differentiation of MSCs embedded in agarose hydrogels compared to dynamic compression. In MSC-seeded constructs supplemented with TGF-beta3, GAG and collagen accumulation was higher in low oxygen conditions compared to normoxia. For normoxic and low oxygen culture GAG accumulation within the agarose hydrogel was inhomogeneous, with low levels of GAG measured in the annulus of constructs maintained in normoxic conditions. Dynamic compression did not significantly increase GAG or collagen accumulation in normoxia. However under low oxygen conditions, dynamic compression reduced GAG accumulation compared to free-swelling controls, but remained higher than comparable constructs maintained in normoxic conditions. This study demonstrates that continuous exposure to low oxygen tension is a more potent pro-chondrogenic stimulus than 1h/day of dynamic compression for porcine MSCs embedded in agarose hydrogels.

Correlations between local strains and tissue phenotypes in an experimental model of skeletal healing

Defining how mechanical cues regulate tissue differentiation during skeletal healing can benefit treatment of orthopaedic injuries and may also provide insight into the influence of the mechanical environment on skeletal development. Different global (i.e., organ-level) mechanical loads applied to bone fractures or osteotomies are known to result in different healing outcomes. However, the local stimuli that promote formation of different skeletal tissues have yet to be established. Finite element analyses can estimate local stresses and strains but require many assumptions regarding tissue material properties and boundary conditions. This study used an experimental approach to investigate relationships between the strains experienced by tissues in a mechanically stimulated osteotomy gap and the patterns of tissue differentiation that occur during healing. Strains induced by the applied, global mechanical loads were quantified on the mid-sagittal plane of the callus using digital image correlation. Strain fields were then compared to the distribution of tissue phenotypes, as quantified by histomorphometry, using logistic regression. Significant and consistent associations were found between the strains experienced by a region of the callus and the tissue type present in that region. Specifically, the probability of encountering cartilage increased, and that of encountering woven bone decreased, with increasing octahedral shear strain and, to a lesser extent, maximum principal strain. Volumetric strain was the least consistent predictor of tissue type, although towards the end of the four-week stimulation timecourse, cartilage was associated with increasingly negative volumetric strains. These results indicate that shear strain may be an important regulator of tissue fate during skeletal healing.

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.

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.

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

Several mechanoregulatory tissue differentiation models have been proposed over the last decade. Corroboration of these models by comparison with experimental data is necessary to determine their predictive power. So far, models have been applied with various success rates to different experimental set-ups investigating mainly secondary fracture healing. In this study, the mechanoregulatory models are applied to simulate the implant osseointegration process in a repeated sampling in vivo bone chamber, placed in a rabbit tibia. This bone chamber provides a mechanically isolated environment to study tissue differentiation around titanium implants loaded in a controlled manner. For the purpose of this study, bone formation around loaded cylindrical and screw-shaped implants was investigated. Histologically, no differences were found between the two implant geometries for the global amount of bone formation in the entire chamber. However, a significantly larger amount of bone-to-implant contact was observed for the screw-shaped implant compared to the cylindrical implant. In the simulations, a larger amount of bone was also predicted to be in contact with the screw-shaped implant. However, other experimental observations could not be predicted. The simulation results showed a distribution of cartilage, fibrous tissue and (im)mature bone, depending on the mechanoregulatory model that was applied. In reality, no cartilage was observed. Adaptations to the differentiation models did not lead to a better correlation between experimentally observed and numerically predicted tissue distribution patterns. The hypothesis that the existing mechanoregulatory models were able to predict the patterns of tissue formation in the in vivo bone chamber could not be fully sustained.

Bone regeneration during distraction osteogenesis: mechano-regulation by shear strain and fluid velocity

Corroboration of mechano-regulation algorithms is difficult, partly because repeatable experimental outcomes under a controlled mechanical environment are necessary, but rarely available. In distraction osteogenesis (DO), a controlled displacement is used to regenerate large volumes of new bone, with predictable and reproducible outcomes, allowing to computationally study the potential mechanisms that stimulate bone formation. We hypothesized that mechano-regulation by octahedral shear strain and fluid velocity can predict the spatial and temporal tissue distributions seen during experimental DO. Variations in predicted tissue distributions due to alterations in distraction rate and frequency could then also be studied. An in vivo ovine tibia experiment evaluating bone-segment transport (distraction, 1 mm/day) over an intramedullary nail was used for comparison. A 2D axisymmetric finite element model, with a geometry originating from the experimental data, was created and included into a previously developed model of tissue differentiation. Cells migrated and proliferated into the callus, differentiating into fibroblasts, chondrocytes or osteoblasts, dependent on the biophysical stimuli. Matrix production was modelled with an osmotic swelling model to allow tissues to grow at individual rates. The temporal and spatial tissue distributions predicted by the computational model agreed well with those seen experimentally. In addition, it was observed that decreased distraction rate (0.5 mm/d vs. 0.25 mm/d) increased the overall time needed for complete bone regeneration, whereas increased distraction frequency (0.5 mm/12 h vs. 0.25 mm/6 h) stimulated faster bone regeneration, as found in experimental findings by others. Thus, the algorithm regulated by octahedral shear strain and fluid velocity was able to predict the bone regeneration patterns dependent on distraction rate and frequency during DO.

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.

Implant design and intraosseous stability of immediately placed implants: a human cadaver study

OBJECTIVE

The objective of this study was to explore effects of implant macrodesign and diameter on initial intraosseous stability and interface mechanical properties of immediately placed implants.

MATERIAL AND METHOD

Mandibular premolars of four fresh-frozen human cadavers were extracted. Ø 4.1/4.8 mm ITI TE, Ø 4.1 and 4.8 mm solid screw synOcta ITI implants were placed into freshly prepared extraction sockets. Resonance frequency analysis was conducted to quantify primary implant stability quotient (ISQ). Installation torque value (ITV) and removal torque value (RTV) of the implants were measured using a custom-made strain-gauged torque wrench connected to a data acquisition system at a sample rate of 10,000 Hz. The vertical defect depth around the collar of each implant was measured directly by an endodontic spreader. The bone-implant contact was determined in digitalized images of periapical radiographs and expressed as percentage bone contact.

RESULTS

The ISQ values of the TE implant was higher than the Ø 4.1 mm implant (P<0.01), and comparable with the Ø 4.8 mm implants (P>0.05). ITVs and RTVs of TE and Ø 4.8 mm implants were higher than the Ø 4.1 mm implant, although the differences between groups were statistically insignificant (P>0.05). The vertical defect depths around all types of implants were similar. In the radiographic analyses, percentage bone-implant contact of the TE and Ø 4.8 mm implants were comparable at the marginal bone region and both were higher than that of the Ø 4.1 mm ITI implant. Nonparametric correlations between groups revealed a significant correlation between ITV and RTV (r=0.838; P<0.001), but not between ISQ values and ITVs and RTVs (P>0.05).

CONCLUSION

Immediately placed ITI TE implant leads to initial intraosseous stability and interface mechanical properties comparable with a wide diameter implant.