Predicting the effect of reduced load level and cell infiltration on spatio-temporal Achilles tendon healing.

Mechanobiology plays an important role in tendon healing. However, the relationship between mechanical loading and spatial and temporal evolution of tendon properties during healing is not well understood. This study builds on a recently presented mechanoregulatory computational framework that couples mechanobiological tendon healing to tissue production and collagen orientation. In this study, we investigated how different magnitudes of mechanical stimulation (principal strain) affect the spatio-temporal evolution of tissue production and the temporal evolution of elastic and viscoelastic mechanical parameters. Specifically, we examined the effect of cell infiltration (mimicking migration and proliferation) in the callus on the resulting tissue production by modeling production to depend on local cell density. The model predictions were carefully compared with experimental data from Achilles tendons in rats, at 1, 2 and 4 weeks of healing. In the experiments, the rat tendons had been subjected to free cage activity or reduced load levels through intramuscular botox injections. The simulations that included cell infiltration and strain-regulated collagen production predicted spatio-temporal tissue distributions and mechanical properties similarly to that observed experimentally. In addition, lack of matrix-producing cells in the tendon core during early healing may result in reduced collagen content, regardless of the daily load level. This framework is the first to computationally investigate mechanobiological mechanisms underlying spatial and temporal variations during tendon healing for various magnitudes of loading. This framework will allow further characterization of biomechanical, biological, or mechanobiological processes underlying tendon healing.

A numerical framework for mechano-regulated tendon healing-Simulation of early regeneration of the Achilles tendon.

Mechano-regulation during tendon healing, i.e. the relationship between mechanical stimuli and cellular response, has received more attention recently. However, the basic mechanobiological mechanisms governing tendon healing after a rupture are still not well-understood. Literature has reported spatial and temporal variations in the healing of ruptured tendon tissue. In this study, we explored a computational modeling approach to describe tendon healing. In particular, a novel 3D mechano-regulatory framework was developed to investigate spatio-temporal evolution of collagen content and orientation, and temporal evolution of tendon stiffness during early tendon healing. Based on an extensive literature search, two possible relationships were proposed to connect levels of mechanical stimuli to collagen production. Since literature remains unclear on strain-dependent collagen production at high levels of strain, the two investigated production laws explored the presence or absence of collagen production upon non-physiologically high levels of strain (>15%). Implementation in a finite element framework, pointed to large spatial variations in strain magnitudes within the callus tissue, which resulted in predictions of distinct spatial distributions of collagen over time. The simulations showed that the magnitude of strain was highest in the tendon core along the central axis, and decreased towards the outer periphery. Consequently, decreased levels of collagen production for high levels of tensile strain were shown to accurately predict the experimentally observed delayed collagen production in the tendon core. In addition, our healing framework predicted evolution of collagen orientation towards alignment with the tendon axis and the overall predicted tendon stiffness agreed well with experimental data. In this study, we explored the capability of a numerical model to describe spatial and temporal variations in tendon healing and we identified that understanding mechano-regulated collagen production can play a key role in explaining heterogeneities observed during tendon healing.

Diminishing effects of mechanical loading over time during rat Achilles tendon healing.

Mechanical loading affects tendon healing and recovery. However, our understanding about how physical loading affects recovery of viscoelastic functions, collagen production and tissue organisation is limited. The objective of this study was to investigate how different magnitudes of loading affects biomechanical and collagen properties of healing Achilles tendons over time. Achilles tendon from female Sprague Dawley rats were cut transversely and divided into two groups; normal loading (control) and reduced loading by Botox (unloading). The rats were sacrificed at 1, 2- and 4-weeks post-injury and mechanical testing (creep test and load to failure), small angle x-ray scattering (SAXS) and histological analysis were performed. The effect of unloading was primarily seen at the early time points, with inferior mechanical and collagen properties (SAXS), and reduced histological maturation of the tissue in unloaded compared to loaded tendons. However, by 4 weeks no differences remained. SAXS and histology revealed heterogeneous tissue maturation with more mature tissue at the peripheral region compared to the center of the callus. Thus, mechanical loading advances Achilles tendon biomechanical and collagen properties earlier compared to unloaded tendons, and the spatial variation in tissue maturation and collagen organization across the callus suggests important regional (mechano-) biological activities that require more investigation.

Understanding how reduced loading affects Achilles tendon mechanical properties using a fibre-reinforced poro-visco-hyper-elastic model.

Understanding tendon mechanobiology is important for gaining insight into the development of tendon pathology and subsequent repair processes. The aim of this study was to investigate how experimentally observed mechanobiological adaptation of rat Achilles tendons translate to changes in constitutive mechanical properties and biomechanical behavior. In addition, we assessed the ability of the model to simulate tendon creep and stress-relaxation. A three dimensional finite element framework of rat Achilles tendon was implemented with a fibre-reinforced poro-visco-hyper-elastic constitutive model. Stress-relaxation and creep data from Achilles tendons of Sprague Dawley rats that had been subjected to both daily loading and a period of reduced loading were used to determine the constitutive properties of the tendons. Our results showed that the constitutive model captures creep and stress-relaxation data from rat Achilles tendons for both loaded and unloaded tendons with good accuracy (normalized root mean square error between model and experimental data were 0.010-0.027). Only when the model parameters were fitted to data from both mechanical tests simultaneously, were we able to also capture similar increase in elastic energy (increased stiffness) and decreased viscoelasticity in response to unloading, as was reported experimentally. Our study is the first to show that experimentally observed mechanobiological changes in tendon biomechanics, such as stiffness and viscoelasticity, can be designated to mechanical quantities in a constitutive model. Further investigation in this direction has potential to discriminate tissue components responsible for specific biomechanical response, and enable targeted treatment strategies for tendon health.

Crack propagation in cortical bone is affected by the characteristics of the cement line: a parameter study using an XFEM interface damage model.

Bulk properties of cortical bone have been well characterized experimentally, and potent toughening mechanisms, e.g., crack deflections, have been identified at the microscale. However, it is currently difficult to experimentally measure local damage properties and isolate their effect on the tissue fracture resistance. Instead, computer models can be used to analyze the impact of local characteristics and structures, but material parameters required in computer models are not well established. The aim of this study was therefore to identify the material parameters that are important for crack propagation in cortical bone and to elucidate what parameters need to be better defined experimentally. A comprehensive material parameter study was performed using an XFEM interface damage model in 2D to simulate crack propagation around an osteon at the microscale. The importance of 14 factors (material parameters) on four different outcome criteria (maximum force, fracture energy, crack length and crack trajectory) was evaluated using ANOVA for three different osteon orientations. The results identified factors related to the cement line to influence the crack propagation, where the interface strength was important for the ability to deflect cracks. Crack deflection was also favored by low interface stiffness. However, the cement line properties are not well determined experimentally and need to be better characterized. The matrix and osteon stiffness had no or low impact on the crack pattern. Furthermore, the results illustrated how reduced matrix toughness promoted crack penetration of the cement line. This effect is highly relevant for the understanding of the influence of aging on crack propagation and fracture resistance in cortical bone.

An interface damage model that captures crack propagation at the microscale in cortical bone using XFEM.

Reliable tools for fracture risk assessment are necessary to handle the challenge with an aging population and the increasing occurrence of bone fractures. As it is currently difficult to measure local damage parameters experimentally, computational models could be used to provide insight into how cortical bone microstructure and material properties contribute to the fracture resistance. In this study, a model for crack propagation in 2D at the microscale in cortical bone was developed using the extended finite element method (XFEM). By combining the maximum principal strain criterion with an additional interface damage formulation in the cement line, the model could capture crack deflections at the osteon boundaries as observed in experiments. The model was used to analyze how the Haversian canal and the interface strength of the cement line affected the crack trajectory in models depicting osteons with three different orientations in 2D. Weak cement line interfaces were found to reorient the propagating cracks while models with strong interfaces predicted crack trajectories that penetrated the cement line and propagated through the osteons. The presented model is a promising tool that could be used to analyze how local, age-related material changes influence the crack trajectory and fracture resistance in cortical bone.

Linking multiscale deformation to microstructure in cortical bone using in situ loading, digital image correlation and synchrotron X-ray scattering.

The incidence of fragility fractures is expected to increase in the near future due to an aging population. Therefore, improved tools for fracture prediction are required to treat and prevent these injuries efficiently. For such tools to succeed, a better understanding of the deformation mechanisms in bone over different length scales is needed. In this study, an experimental setup including mechanical tensile testing in combination with digital image correlation (DIC) and small/wide angle X-ray scattering (SAXS/WAXS) was used to study deformation at multiple length scales in bovine cortical bone. Furthermore, micro-CT imaging provided detailed information about tissue microstructure. The combination of these techniques enabled measurements of local deformations at the tissue- and nanoscales. The orientation of the microstructure relative to the tensile loading was found to influence the strain magnitude on all length scales. Strains in the collagen fibers were 2-3 times as high as the strains found in the mineral crystals for samples with microstructure oriented parallel to the loading. The local tissue strain at fracture was found to be around 0.5%, independent of tissue orientation. However, the maximum force and the irregularity of the crack path were higher when the load was applied parallel to the tissue orientation. This study clearly shows the potential of combining these different experimental techniques concurrently with mechanical testing to gain a better understanding of bone damage and fracture over multiple length scales in cortical bone. STATEMENT OF SIGNIFICANCE: To understand the pathophysiology of bone, it is important to improve our knowledge about the deformation and fracture mechanisms in bone. In this study, we combine several recently available experimental techniques with mechanical loading to investigate the deformation mechanisms in compact bone tissue on several length scales simultaneously. The experimental setup included mechanical tensile testing in combination with digital image correlation, microCT imaging, and small/wide angle X-ray scattering. The combination of techniques enabled measurements of local deformations at the tissue- and nanoscales. The study clearly shows the potential of combining different experimental techniques concurrently with mechanical testing to gain a better understanding of structure-property-function relationships in bone tissue.

Perturbed bone composition and integrity with disorganized osteoblast function in zinc receptor/Gpr39-deficient mice.

Changes in bone matrix composition are frequently found with bone diseases and may be associated with increased fracture risk. Bone is rich in the trace element zinc. Zinc was established to play a significant role in the growth, development, and maintenance of healthy bones; however, the mechanisms underlying zinc effects on the integrity of the skeleton are poorly understood. Here, we show that the zinc receptor (ZnR)/Gpr39 is required for normal bone matrix deposition by osteoblasts. Initial analysis showed that Gpr39-deficient ( Gpr39-/-) mice had weaker bones as a result of altered bone composition. Fourier transform infrared spectroscopy analysis showed high mineral-to-matrix ratios in the bones of Gpr39-/- mice. Histologic analysis showed abnormally high numbers of active osteoblasts but normal osteoclast numbers on the surfaces of bones from Gpr39-/- mice. Furthermore, Gpr39-/- osteoblasts had disorganized matrix deposition in vitro with cultures exhibiting abnormally low collagen and high mineral contents, findings that demonstrate a cell-intrinsic role for ZnR/Gpr39 in these cells. We show that both collagen synthesis and deposition by Gpr39-/- osteoblasts are perturbed. Finally, the expression of the zinc transporter Zip13 and a disintegrin and metalloproteinase with thrombospondin motifs family of zinc-dependent metalloproteases that regulate collagen processing was downregulated in Gpr39-/- osteoblasts. Altogether, our results suggest that zinc sensing by ZnR/Gpr39 affects the expression levels of zinc-dependent enzymes in osteoblasts and regulates collagen processing and deposition.-Jovanovic, M., Schmidt, F. N., Guterman-Ram, G., Khayyeri, H., Hiram-Bab, S., Orenbuch, A., Katchkovsky, S., Aflalo, A., Isaksson, H., Busse, B., Jähn, K., Levaot, N. Perturbed bone composition and integrity with disorganized osteoblast function in zinc receptor/Gpr39-deficient mice.

Achilles tendon compositional and structural properties are altered after unloading by botox.

Tendon function and homeostasis rely on external loading. This study investigates the biological mechanisms behind tendon biomechanical function and how the mechanical performance is affected by reduced daily loading. The Achilles tendons of 16 weeks old female Sprague Dawley rats (n = 40) were unloaded for 5 weeks by inducing muscle paralysis with botulinum toxin injections in the right gastrocnemius and soleus muscles. The contralateral side was used as control. After harvest, the tendons underwent biomechanical testing to assess viscoelasticity (n = 30 rats) and small angle X-ray scattering to determine the structural properties of the collagen fibrils (n = 10 rats). Fourier transform infrared spectroscopy and histological staining (n = 10 rats) were performed to investigate the collagen and proteoglycan content. The results show that the stiffness increased in unloaded tendons, together with an increased collagen content. Creep and axial alignment of the collagen fibers were reduced. Stress-relaxation increased whereas hysteresis was reduced in response to unloading with botox treatment. Our findings indicate that altered matrix deposition relies on mechanical loading to reorganize the newly formed tissue, without which the viscoelastic behavior is impaired. The results demonstrate that reduced daily loading deprives tendons of their viscoelastic properties, which could increase the risk of injury.

Effects of tissue fixation and dehydration on tendon collagen nanostructure.

Collagen is the most prominent protein in biological tissues. Tissue fixation is often required for preservation or sectioning of the tissue. This may affect collagen nanostructure and potentially provide incorrect information when analyzed after fixation. We aimed to unravel the effect of 1) ethanol and formalin fixation and 2) 24h air-dehydration on the organization and structure of collagen fibers at the nano-scale using small and wide angle X-ray scattering. Samples were divided into 4 groups: ethanol fixed, formalin fixed, and two untreated sample groups. Samples were allowed to air-dehydrate in handmade Kapton pockets during the measurements (24h) except for one untreated group. Ethanol fixation affected the collagen organization and nanostructure substantially and during 24h of dehydration dramatic changes were evident. Formalin fixation had minor effects on the collagen organization but after 12h of air-dehydration the spatial variation increased substantially, not evident in the untreated samples. Generally, collagen shrinkage and loss of alignment was evident in all samples during 24h of dehydration but the changes were subtle in all groups except the ethanol fixed samples. This study shows that tissue fixation needs to be chosen carefully in order to preserve the features of interest in the tissue.

Mechanobiological modelling of tendons: Review and future opportunities.

Tendons are adapted to carry large, repeated loads and are clinically important for the maintenance of musculoskeletal health in an increasing, actively ageing population, as well as in elite athletes. Tendons are known to adapt to mechanical loading. Also, their healing and disease processes are highly sensitive to mechanical load. Computational modelling approaches developed to capture this mechanobiological adaptation in tendons and other tissues have successfully addressed many important scientific and clinical issues. The aim of this review is to identify techniques and approaches that could be further developed to address tendon-related problems. Biomechanical models are identified that capture the multi-level aspects of tendon mechanics. Continuum whole tendon models, both phenomenological and microstructurally motivated, are important to estimate forces during locomotion activities. Fibril-level microstructural models are documented that can use these estimated forces to detail local mechanical parameters relevant to cell mechanotransduction. Cell-level models able to predict the response to such parameters are also described. A selection of updatable mechanobiological models is presented. These use mechanical signals, often continuum tissue level, along with rules for tissue change and have been applied successfully in many tissues to predict in vivo and in vitro outcomes. Signals may include scalars derived from the stress or strain tensors, or in poroelasticity also fluid velocity, while adaptation may be represented by changes to elastic modulus, permeability, fibril density or orientation. So far, only simple analytical approaches have been applied to tendon mechanobiology. With the development of sophisticated computational mechanobiological models in parallel with reporting more quantitative data from in vivo or clinical mechanobiological studies, for example, appropriate imaging, biochemical and histological data, this field offers huge potential for future development towards clinical applications.

Comparison of structural anisotropic soft tissue models for simulating Achilles tendon tensile behaviour.

The incidence of tendon injury (tendinopathy) has increased over the past decades due to greater participation in sports and recreational activities. But little is known about the aetiology of tendon injuries because of our limited knowledge in the complex structure-function relationship in tendons. Computer models can capture the biomechanical behaviour of tendons and its structural components, which is essential for understanding the underlying mechanisms of tendon injuries. This study compares three structural constitutive material models for the Achilles tendon and discusses their application on different biomechanical simulations. The models have been previously used to describe cardiovascular tissue and articular cartilage, and one model is novel to this study. All three constitutive models captured the tensile behaviour of rat Achilles tendon (root mean square errors between models and experimental data are 0.50-0.64). They further showed that collagen fibres are the main load-bearing component and that the non-collagenous matrix plays a minor role in tension. By introducing anisotropic behaviour also in the non-fibrillar matrix, the new biphasic structural model was also able to capture fluid exudation during tension and high values of Poisson׳s ratio that is reported in tendon experiments.

A fibre-reinforced poroviscoelastic model accurately describes the biomechanical behaviour of the rat Achilles tendon.

BACKGROUND: Computational models of Achilles tendons can help understanding how healthy tendons are affected by repetitive loading and how the different tissue constituents contribute to the tendon's biomechanical response. However, available models of Achilles tendon are limited in their description of the hierarchical multi-structural composition of the tissue. This study hypothesised that a poroviscoelastic fibre-reinforced model, previously successful in capturing cartilage biomechanical behaviour, can depict the biomechanical behaviour of the rat Achilles tendon found experimentally. MATERIALS AND METHODS: We developed a new material model of the Achilles tendon, which considers the tendon's main constituents namely: water, proteoglycan matrix and collagen fibres. A hyperelastic formulation of the proteoglycan matrix enabled computations of large deformations of the tendon, and collagen fibres were modelled as viscoelastic. Specimen-specific finite element models were created of 9 rat Achilles tendons from an animal experiment and simulations were carried out following a repetitive tensile loading protocol. The material model parameters were calibrated against data from the rats by minimising the root mean squared error (RMS) between experimental force data and model output. RESULTS AND CONCLUSIONS: All specimen models were successfully fitted to experimental data with high accuracy (RMS 0.42-1.02). Additional simulations predicted more compliant and soft tendon behaviour at reduced strain-rates compared to higher strain-rates that produce a stiff and brittle tendon response. Stress-relaxation simulations exhibited strain-dependent stress-relaxation behaviour where larger strains produced slower relaxation rates compared to smaller strain levels. Our simulations showed that the collagen fibres in the Achilles tendon are the main load-bearing component during tensile loading, where the orientation of the collagen fibres plays an important role for the tendon's viscoelastic response. In conclusion, this model can capture the repetitive loading and unloading behaviour of intact and healthy Achilles tendons, which is a critical first step towards understanding tendon homeostasis and function as this biomechanical response changes in diseased tendons.

Primary cilia mechanics affects cell mechanosensation: A computational study.

Primary cilia (PC) are mechanical cell structures linked to the cytoskeleton and are central to how cells sense biomechanical signals from their environment. However, it is unclear exactly how PC mechanics influences cell mechanosensation. In this study we investigate how the PC mechanical characteristics are involved in the mechanotransduction process whereby cilium deflection under fluid flow induces strains on the internal cell components that regulate the cell׳s mechanosensitive response. Our investigation employs a computational approach in which a finite element model of a cell consisting of a nucleus, cytoplasm, cortex, microtubules, actin bundles and a primary cilium was used together with a finite element representation of a flow chamber. Fluid-structure interaction analysis was performed by simulating perfusion flow of 1mm/s on the cell model. Simulations of cells with different PC mechanical characteristics, showed that the length and the stiffness of PC are responsible for the transmission of mechanical stimuli to the cytoskeleton. Fluid flow deflects the cilium, with the highest strains found at the base of the PC and in the cytoplasm. The PC deflection created further strains on the cell nucleus but did not influence microtubules and actin bundles significantly. Our results indicate that PC deflection under fluid flow stimulation transmits mechanical strain primarily to other essential organelles in the cytoplasm, such as the Golgi complex, that regulate cells' mechanoresponse. The simulations further suggest that cell mechanosensitivity can be altered by targeting PC length and rigidity.

Corroboration of computational models for mechanoregulated stem cell differentiation.

Do computational models contribute to progress in mechanobiology? Jacobs and Kelly (in Advances on Modelling in Tissue Engineering, p. 1-14, 2011) suggest that they do, but at the same time propose a limitation in the form of the 'paradox of validation', whereby the information needed to validate mechanoregulation theories obviates the need for them in the first place. In this article, the corroboration of theories describing mechanoregulation of tissue differentiation is reviewed. Considering the falsifiability of computational models derived using the theories as a measure of their predictive power, it is shown that the predictive power of some theories is poor and that models based on these theories fall into the 'paradox of validation'. Week theories for any phenomenon would succumb to such a paradox. We argue that mechanobiology needs theories that can have more potentially falsifying experiments and that perhaps the discipline does suffer from theories that are a priori designed to minimise falsifiability. However, several theories do have predictive power beyond the data used to validate them, so a paradox of validation should disappear as the subject develops.

Substrate stiffness and oxygen availability as regulators of mesenchymal stem cell differentiation within a mechanically loaded bone chamber.

Mechanical stimuli such as tissue deformation and fluid flow are often implicated as regulators of mesenchymal stem cell (MSC) differentiation during regenerative events in vivo. However, in vitro studies have identified several other physical and biochemical environmental cues, such as substrate stiffness and oxygen availability, as key regulators of stem cell fate. Hypotheses for how MSC differentiation is regulated in vivo can be either corroborated or rejected based on the ability of in silico models to accurately predict spatial and temporal patterns of tissue differentiation observed experimentally. The goal of this study was to employ a previously developed computational framework to test the hypothesis that substrate stiffness and oxygen availability regulate stem cell differentiation during tissue regeneration within an implanted bone chamber. To enable a prediction of the oxygen levels within the bone chamber, a lattice model of angiogenesis was implemented where blood vessel progression was dependent on the local mechanical environment. The model successfully predicted key aspects of MSC differentiation, including the correct spatial development of bone, marrow and fibrous tissue within the unloaded bone chamber. The model also successfully predicted chondrogenesis within the chamber upon the application of mechanical loading. This study provides further support for the hypothesis that substrate stiffness and oxygen availability regulate stem cell differentiation in vivo. These simulations also highlight the indirect role that mechanics may play in regulating MSC fate by inhibiting blood vessel progression and hence disrupting oxygen availability within regenerating tissues.

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.

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.

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.