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

Journal of Biomechanics 44 (2011) 1051–1058

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Variability observed in mechano-regulated in vivo tissue differentiation can be explained by variation in cell mechano-sensitivity ¨ b, Per Aspenberg c, Patrick J. Prendergast a,n Hanifeh Khayyeri a, Sara Checa a, Magnus Tagil a

Trinity Centre for Bioengineering, School of Engineering, Trinity College Dublin, Ireland Department of Orthopaedics, Lund University Hospital, Lund, Sweden c Orthopaedics, IKE, Faculty of Health Sciences, Link¨ oping University Hospital, Link¨ oping, Sweden b

a r t i c l e i n f o

abstract

Article history: Accepted 7 February 2011

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., subjectspecific mechano-sensitivity) could be a reason for the different outcomes found when implants (or tissue engineered constructs) are used in a population. & 2011 Published by Elsevier Ltd.

Keywords: Mechano-regulation Mechanobiology Inter-specimen variability FE-model Lattice model

1. Introduction It has long been hypothesised that the differentiation of mesenchymal stem cells is regulated by the mechanical environment (Pauwels, 1960). Many animal experiments have corroborated the influence of mechanical stimuli on tissue phenotype (Duda et al., 2005; Goodship and Kenwright, 1985; Perren, 1979); however, many questions about mechano-regulation of tissue differentiation remain unravelled. Among these: Why is there often a significant degree of inter-specimen variability in tissue differentiation outcomes, even in well-controlled experiments? Several in vivo investigations of mechano-regulated tissue differentiation report a high variability between individuals (Geris et al., 2008; Guldberg et al., 1997; Reina-Romo et al., 2009). In some cases the variability is so great that the results become difficult to interpret (de Rooij et al., 2001; Tagil and Aspenberg, 1999).

n

Corresponding author. Tel.: + 353 1 896 3393. E-mail address: [email protected] (P.J. Prendergast).

0021-9290/$ - see front matter & 2011 Published by Elsevier Ltd. doi:10.1016/j.jbiomech.2011.02.003

The variable outcomes of tissue differentiation experiments can be explained as variation due to either environmental factors (differences in the mechanical loading, surgical procedure, nutrition, etc.) or variation in genetic factors between individuals of a population. It has been shown that variations in gene expression for recruiting skeletal progenitor cells in different strains of mice cause temporal variations in osteogenetic and chondrogenetic differentiation during endochondral bone formation (Jepsen et al., 2008). During mechanical loading, mechano-sensitive genes are up- or down-regulated and their expression patterns have been shown to affect cell activity rates in the course of tissue formation (Aspenberg et al., 2000; Barry et al., 2001; Kelly and Jacobs, 2010; Nowlan et al., 2008; Palomares et al., 2009; Provot and Schipani, 2005). In addition, mechano-sensitive genes are expressed with a large variation in animals of the same species compared to housekeeping genes (Balaburski and O’Connor, 2003). It has also been shown that mechano-sensitivity is positively correlated with bone turnover rates and negatively associated with bone mineral density (Judex et al., 2002), which in turn affects the course of tissue differentiation and fracture healing (Balaburski and O’Connor, 2003; Jepsen et al., 2008; Li et al., 2001; Manigrasso and O’Connor, 2008). It is therefore intriguing to wonder if

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variation in mechano-sensitivity can explain the variation in tissue differentiation observed in vivo. Computer models can be used to test hypotheses regarding the origin of variability in differentiation outcomes by corroborating simulation output against experimental results. Mechano-regulation theories proposed by Carter et al. (1988), Claes and Heigele (1999) and Prendergast et al. (1997) have been able to capture the main features of the tissue differentiation process in various computational mechanobiology studies (Carter et al., 1998; Geris et al., 2008; Hayward and Morgan, 2009; Isaksson et al., 2006; Kelly and Prendergast, 2005; Khayyeri et al., 2009; Lacroix and Prendergast, 2002; Liu and Niebur, 2008). In a study of tissue differentiation inside a bone conduction chamber, the effects of environmental factors (loading, and surgical procedure) on the differentiation process were investigated in simulations of tissue differentiation. The results of the simulations showed that variation in environmental factors alone did not capture the variability to the extent that is observed in animal experiments (Khayyeri et al., 2009). In this paper we hypothesise that the variable outcomes observed in experiments of mechano-regulation of tissue differentiation can be explained, at least partly, by variation in the mechano-regulated cell activity rates for proliferation, differentiation and apoptosis. To test this hypothesis, we modelled a bone chamber experiment designed by Tagil and Aspenberg (1999) (Fig. 1a). The chamber has two ingrowth openings at the bottom of the implant that allow cells to migrate into the empty cylindrical chamber within which a piston applies mechanical loads to the growing tissues (Fig. 1b). The experiment was performed on male rats and they had no extra exercise than what the animal cages allowed for. The results from the animal experiment show a load-dependant tissue differentiation process and a dichotomous outcome—dichotomous in the sense that, 4 out of 7 of the loaded specimens developed a layer of cartilage on an underlying layer of bone, whereas 3 out of 7 of the loaded specimens showed mainly fibrous tissue, necrosis of whatever bone was present when loading started, and very sparse bone differentiation (Tagil and Aspenberg, 1999). Neither cartilage nor necrotic tissue was seen in unloaded control chambers (Tagil and Aspenberg, 1999). If our hypothesis, that variation in cell activity rates can capture the variability observed in the animal experiment, is corroborated it would suggest that it is important to include such variation in tissue differentiation simulations so as to get a clear picture of the probable outcomes rather than relying on deterministic simulations based on best-estimate parameters that are, in reality, subject to genetic variation. Computational models that simulate variability in outcomes would be more useful in tissue engineering applications.

2. Methods A computational framework of the bone chamber experiment was created using finite element modelling and a C++ interface. The cylindrical interior of the bone chamber was modelled consisting of 14,200 hexahedral finite elements (Fig. 1c), where each element contained a three-dimensional grid of 1000 lattice points (Fig. 1d). This lattice allowed for cell activities to be modelled, where each lattice point represented a possible position that a cell and its extracellular matrix could occupy in three dimensions (Byrne et al., 2007). Cell activities such as cell migration, proliferation, apoptosis, and differentiation were implemented as Monte Carlo processes that depended on the mechanical environment (Checa and Prendergast, 2009; Khayyeri et al., 2009; Perez and Prendergast, 2007). Angiogenesis (formation of new capillaries) was modelled according to Checa and Prendergast (2009), where capillaries are described as a ‘‘string’’ of lattice points occupied by endothelial cells with capillary growth in either of three directions: the previous direction, a random direction, or towards VEGF that is released by hypertrophic chondrocytes and acts as an angiogenic stimulator. Each capillary could branch stochastically, with the length of the capillary increasing its probability of branching. The growth of the capillaries was prevented in the event of anastomosis (fusion of two capillaries) or high mechanical stimulus. The mechano-regulation theory of Prendergast et al. (1997) was adopted to modulate mesenchymal stem cell (MSC) fate. A biophysical stimulus (S¼ g/a+v/b, a¼0.0375, b¼ 3 mm/s) described as a combination of interstitial fluid flow (v) and shear strain (g) determined the differentiation of MSCs into osteoblasts, chondrocytes or fibroblasts in the bone chamber. Different levels of biophysical stimulus encouraged differentiation of different cell lineages according to the following scheme:

IF (S43) Fibrous connective tissue differentiation IF (1oSo3) Cartilage differentiation IF (0.53oSo1) Immature bone differentiation IF (0.01oSo0.53) Mature bone differentiation IF (So0.01) Bone resorption END Mesenchymal stem cell differentiation was also regulated by oxygen availability, where the distance of the cell to the capillaries (D) determined the cell fate into either the osteogenetic or the chondrogenetic pathway according to a set of rules:

IF (0.01oSo1) AND IF (Do100 mm) THEN Osteogenesis ELSE IF (D 4100 mm) THEN Chondrogenesis END END

Fig. 1. (a) A picture of the bone chamber screw where the red arrow points at an ingrowth opening. (b) A simplified cross-section of the bone chamber where the thin red arrows point at the ingrowth openings and the thicker grey arrow shows the piston and the direction of loading. (c) The finite element model of the bone chamber (H¼ 5 mm, D ¼ 2 mm) illustrating the boundary conditions where the chamber wall was modelled as; mmmm: free fluid flow; ——: ux ¼ uy ¼ 0; - - - -: ux ¼ uy ¼uz ¼0. (d) A finite element containing 10  10  10 lattice points. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 2. Iterative computational scheme adopted in this model.

The time course of the tissue differentiation process inside the bone chamber was computed in a series of iterations, where each iteration represented a 12 h time interval (Fig. 2). The bone chamber was assumed to be filled with granulation tissue initially and MSCs and endothelial cells (ECs) were seeded on the lattice points representing the ingrowth openings. During each iteration, MSCs could migrate, proliferate and apoptose until they reached certain maturation age (6 days in this model). Thereafter, modulated by fluid flow and shear strain (computed using Abaqus poroelastic analysis) and the distance to capillaries, MSCs differentiated. New cell phenotypes proliferated and underwent apoptosis, with cell phenotype specific rates (Isaksson et al., 2008a). These cell activities occurred only when the cell was subjected to an appropriate stimulus, e.g. in a region of mechanical stimulus for cartilage, only chondrocyte differentiation and proliferation was allowed whilst other cell phenotypes underwent apoptosis. This allowed changes in cell activity rates to be directly associated with the specimen’s response to mechanical stimulus, where higher rates corresponded to a more mechano-sensitive response and vice versa. After 9 weeks, corresponding to the time of harvest in the in vivo experiments, the simulation, i.e. the iteration loop, was ended. Simulations of the bone chamber were carried out according to the in vivo experiments (Tagil and Aspenberg, 1999): (i) Loaded group—chamber kept unloaded (0.02 MPa in simulations) for 3 weeks and then loaded (2 MPa) with the piston for 6 following weeks and (ii) Control group—chamber kept unloaded for 9 weeks (0.02 MPa in simulations). A cell-phenotype specific sensitivity analysis was initially performed on differentiation and proliferation rates (see Table 1 for values used) to distinguish between the important parameters. Then to consider inter-specimen variability in cell activity rates in the model, a random number (R), describing up- or downregulation of an activity from its baseline value, was introduced; i.e. the rate of an activity was described as R times baseline rate and the value for R was randomly chosen from a uniform distribution such that, (i) RA[0.5, 1] if down regulation (ii) RA[1, 3] if up regulation. To investigate the variable nature of the outcomes, the three cell activities of differentiation, proliferation and apoptosis were performed with varied rates for all cell phenotypes. Because each simulation is stochastic due to the probabilistic

Table 1 List of parameters used for the sensitivity analysis. The values followed by (B) were also used as baseline rates in the variability simulations.

1

MSC differentiation (day ) MSC proliferation (day  1) OB proliferation (day  1) CC proliferation (day  1) FB proliferation (day  1)

High

Low

0.6 1.2 (A) 0.5 (A) 0.75 (A) 0.55 (B)

0.3 0.6 0.3 0.2 0.1

(B) (B) (B) (B) (A)

(A)—(Andreykiv et al., 2008), (B)—(Isaksson et al., 2008a) also baseline values.

modelling of cellular activities (e.g. random walk) and since the degree of up- or down-regulation could have a significant effect on the results, four simulations of each combination were run—since there are 3 activities and 4 simulations, the full permutation of simulations then requires 32 separate simulations, see Table 2. Furthermore, simulations according to those in Table 2, but excluding variations in MSC proliferation rate, were performed to investigate the effect of turning off variability in MSC activity—thus 64 simulations were done in total.

3. Results The sensitivity study investigating cell phenotype specific proliferation and differentiation rates showed that the simulation outcomes are very sensitive to MSC proliferation rates, but are not significantly affected by variations in fibroblast, osteoblast and chondrocyte proliferation rates, or the rate of MSC differentiation. Higher MSC proliferation rates predicted an overall increase

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Table 2 List of 32 simulations with variable R-values, selected at random from uniform distributions. Simulation

1a 1b 1c 1d

2a 2b 2c 2d

3a 3b 3c 3d

4a 4b 4c 4d

5a 5b 5c 5d

6a 6b 6c 6d

7a 7b 7c 7d

8a 8b 8c 8d

Differentiation

Proliferation

Apoptosis

Down

Down

Down

0.95 0.77 0.76 0.78

0.55 0.92 0.87 0.64

0.77 0.85 0.93 0.60

Down

Down

Up

0.79 0.86 0.61 0.93

0.78 0.61 0.83 0.56

2.18 1.58 1.49 2.54

Down

Up

Down

0.80 0.77 0.63 0.75

2.24 1.25 2.57 1.11

0.64 0.81 0.71 0.80

Down

Up

Up

0.78 0.62 0.50 0.63

2.16 1.03 2.85 1.96

2.17 1.96 2.24 1.88

Up

Down

Down

2.27 1.85 2.50 2.21

0.82 0.93 0.55 0.77

0.82 0.71 0.50 0.90

Up

Down

Up

2.32 1.98 1.78 2.19

0.82 0.83 0.75 0.68

1.41 2.33 2.03 1.24

Up

Up

Down

2.32 1.59 1.03 1.89

2.35 1.05 2.64 1.11

0.84 0.80 0.67 0.72

Up

Up

Up

2.37 1.28 1.10 1.81

2.46 1.39 2.38 1.28

1.30 1.24 1.78 1.43

The R-values were multiplied with baseline rates (from Isaksson et al., 2008a) to simulate the up or down regulation of cell activities.

(up to 20%) in tissue differentiation inside the chamber. Our parametric model variations in the unloaded bone chamber (control group) simulations did not show a significant change in the tissue differentiation pathway when varying cell activity rates (variable cell activity rates predicted variable amount of osteoblasts in the chamber and never chondrocytes or fibroblasts). This corroborates the idea that the variability observed in the loaded chambers is caused by a difference in cellular response to mechanical loading, i.e. inter-animal differences in mechanosensitivity. The loaded simulations with variable cell activity rates for tissue formation/differentiation in the chamber showed, in general, a large amount of fibrous tissue at the bottom of the chamber

followed by endochondral ossification on top, after 9 weeks, see Fig. 3(i). Simulations with low cell activity rates predicted more fibrous tissue and chondrocytes but less osteoblasts (e.g., Fig. 3(i), simulation ref. no. 1d), whereas computations with higher cell activity rates showed the formation of an osteoblastic bridge across the chamber followed by a layer of chondrocytes on top (e.g., Fig. 3(i), simulation ref. no. 8c). The systematic variation of activity rates showed that the endochondral ossification inside the chamber was highly dependant on the rates for cell proliferation and apoptosis. Higher rates induced more osteoblast and chondrocyte formation; see Fig. 3(i). Simulations with variable cell activity rates excluding MSC proliferation still showed a variable result, but variation was considerably less (see Fig. 3(ii)). These results also show that apoptosis of cells—a process which makes space for new cells—influences the rate of endochondral ossification. Higher rates of apoptosis, relative to baseline rates, showed faster and more bone formation—to see this compare a low rate (e.g., ref. no. 3a in Fig. 3 and Table 2) with a high rate (e.g. ref. no. 4a in Fig. 3 and Table 2). The degree of variation, i.e. whether R-values were close to one (baseline values) or deviated largely from the baseline, influenced the variability of outcomes also within the different simulation groups (see Table 3). Turning off the variability of MSC proliferation rate showed much reduced variability within the simulation group compared to the simulations with it turned on. This shows the highly influential nature of MSC mechano-sensitivity on tissue differentiation outcomes. Such differences were not observed between turning on/off the variation of other cell phenotypical activity rates. The collection of simulations shows that variable cell activity rates predict variation also in the tissue differentiation pathways followed, see Fig. 4, and not just the final outcomes. The results also show that, simulations with constant MSC proliferation rate predict a dichotomy in the final outcomes, where two groups of outcome can be distinguished by the amounts of bone in the chamber, after 9 weeks (Fig. 5).

4. Discussion One of the challenges in the engineering of musculo-skeletal tissues is to understand the processes behind mechano-regulated tissue differentiation. If simulations are to be useful for engineering design, one issue that needs to be addressed is the variable response between different individuals, which occurs even under the same level of loading and in a controlled environment. The results of this study corroborated the hypothesis that variation in cell mechano-sensitivity could be responsible for variation in tissue differentiation outcomes in mechano-regulated tissue differentiation in bone chambers. There can be many other biologically variable factors, such as variation in tissue mechanical properties, nutrition intake, bone density, chemotaxis and intrinsic cell activities, behind the large variability observed in the in vivo experiments. But despite these, generally, simulations with higher cell activity rates were in good correlation with the 4 out of 7 specimens (showing a layer of bone across the chamber covered by a layer of cartilage on top after 9 weeks), whereas simulations with lower cell activity rates corresponded to the remaining 3 out of 7 specimens in the experiment (predicting sporadic bone formation and a large amount of chondrocytes and fibrous tissue). Also, further unpublished data using the chamber described in Tagil and Aspenberg (1999) shows fibrous tissue formation, a region of chondrocytes and scattered bone islands after 9 weeks [unpublished in Tagil and Aspenberg (1999) but shown here in Fig. 6];

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Fig. 3. Cross-section of the bone chamber in which the results are presented: (i) A selection of the final outcomes from the simulations performed (Table 2) illustrating the effect of up and down regulation of cell activities, after 9 weeks. The higher amounts of fibrous tissue in some simulations is due to faster MSC proliferation rates that fill the entire chamber with MSCs. (ii) The results from the simulations with variable differentiation, proliferation and apoptosis rates, excluding variable MSC proliferation rate. The cross-sectional plots show a much smaller variation in fibrous tissue formation between the simulation groups (1–8) but still indicate a larger variation in the osteoblast and chondrocyte differentiation process. The coloured lattice points represent osteoblasts (OB), chondrocytes (CC), fibroblasts (FB), endothelial cells (EC) and mesenchymal stem cells (MSC). The regions that appear white in all sections are filled with granulation tissue.

this new data is similar to simulation results with the lowest cell activity rates. The model showed high sensitivity to MSC proliferation rates. Higher rates produced more MSCs in the chamber, and caused larger amounts of bone and fibrous tissue, and less cartilage. Variable MSC proliferation rates resulted not only in larger variability in the outcomes but also induced a higher sensitivity of the model to the degree of variation in all activity rates, i.e. identical simulations but with small differences in R-values showed quite different outcomes. This sensitivity to MSC activity is also observed in an in vivo experiment by Jepsen et al. (2008), where differences in the recruitment of progenitor cells affected the rate of fracture healing. In particular, they found that such differences in MSC recruitment caused variable endochondral ossification rates, a result which we also observed in our bone chamber simulations. Regarding limitations, it must be emphasised that, even though the outcomes of the simulations show that variable cell mechanosensivity results in predictions of variation in outcome similar to that observed in vivo, the results do not prove that variable mechano-sensitivity is the cause of such variation in reality. Furthermore, hematopoetic and fat cells that fill the marrow cavity in vivo are not incorporated in the computational

model. This causes the simulations to predict a large amount of fibrous tissue formation in regions where bone marrow is observed in vivo. As investigated by Isaksson et al. (2009), tissue mechanical properties, such as permeability and Young’s modulus, are highly influential, which makes model predictions of this kind sensitive to these parameters. Nagel and Kelly (2010) have further shown that including the anisotropic behaviour of tissues and the re-organisation of collagen fibres as a function of mechanical stimulus is of significance for mechano-regulated tissue differentiation predictions. As Fig. 5 indicates, the applied piston loading after 3 weeks initiates a high degree of osteoblast apoptosis, which can be difficult to corroborate quantitatively with the available data. The inhibition of osteoblast differentiation and initiation of osteoblast apoptosis predicted by the model (due to the higher stimuli environment caused by the loading) is in agreement with in vivo experimental findings, which showed that high mechanical strains decrease osteoblast formation (Meyer et al., 2001) and high fluid flows induce bone resorption (Skripitz and Aspenberg, 2000). In vitro studies have further shown that stretch-induced osteoblast apoptosis rate is higher when subjected to immature bone cells, compared to mature (Weyts et al., 2003) and that high compressive forces can increase apoptosis of human osteoblast-like cells as much

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as 30% in 24 h (Goga et al., 2006). Also, species-specific parameter values are crucial for more accurate simulations and data on the distribution of cell activity rates within the population are necessary to discern the relationship between cell activity rates and tissue differentiation more precisely, and to evaluate the predictive ability of cell phenotype specific modelling. Moreover sensitivity studies were not performed on cell phenotype specific apoptosis rates or cell migration. Parameters related to the mechano-regulation algorithm could also contribute to variability in the outcomes, particularly since these could not only be individual-specific but most probably also species-specific; this aspect needs further investigation. The scope of this study was, however, to test the hypothesis that variable cell activity rates could explain variability in the mechano-regulated tissue Table 3 The amount of different cell phenotypes occupying the chamber volume after 9 weeks of simulation, where the variation in the simulation groups is caused by the degree of variation in cell activity rates, i.e. R-value, and the stochastic behaviour of cells in the lattice modelling approach. Simulation ref. no. Osteoblasts according to Table 2 Mean St. d (%) (%)

Chondrocytes

Fibroblasts

Mean (%)

St. d (%)

Mean (%)

St. d (%)

2.6 0.9 2.7 1.1 2.6 0.9 4.0 2.3

40.1 24.6 62.1 44.3 46.2 37.8 62.0 58.6

10.2 11.7 7.8 6.3 7.8 2.3 5.8 7.3

MSCs 0.3 0.3 0.4 0.1 0.2 1.3 0.5 0.9

50.1 37.5 49.2 35.9 53.1 43.2 52.1 44.1

0.9 1.5 0.7 0.8 0.3 4.5 0.7 3.5

Variability of mechano-sensitivity in all cells 1a–d 0.5 0.6 2.4 2a–d 0.3 0.6 0.7 3a–d 9.0 3.8 9.8 4a–d 15.7 7.3 2.8 5a–d 1.1 1.0 2.9 6a–d 2.0 1.9 1.7 7a–d 7.4 3.8 10.6 8a–d 13.8 6.1 5.6 Variability of mechano-sensitivity in all cells except 1a–d 1.8 0.2 5.9 2a–d 11.9 0.8 3.1 3a–d 1.7 0.2 5.8 4a–d 10.5 1.3 3.2 5a–d 2.9 0.2 6.9 6a–d 11.9 0.4 4.1 7a–d 2.5 0.4 4.0 8a–d 10.3 2.9 4.2

Simulations with constant MSC proliferation rate show smaller standard deviations and thus reduced variability within the simulation groups.

differentiation process. A previous computational mechanoregulation study that varied cellular and biological parameters using factorial analysis (Isaksson et al., 2008b), has shown very low sensitivity to MSC proliferation rates, contrary to observations in this study, but higher sensitivity to initial MSC concentrations in the model. In our simulations, where MSC proliferation rates are kept at baseline, the model shows some sensitivity to parameters related to bone and cartilage formation and apoptosis, similar to that reported by Isaksson et al. (2008b). However, the differences in parameter sensitivity could also depend on the tissue differentiation scenario investigated. In this study, the bone chamber is sensitive to MSC proliferation rates because the chamber is not fully filled with MSCs when the differentiation process starts, therefore the amount of MSCs occupying the chamber significantly affects the differentiation patterns. The simulations suggest that differences in mechano-sensitivity in the form of differences in mechano-regulated cell activity rates between animals have a strong influence on the tissue differentiation process. These simulation results are along the same line as previous findings in animal studies of variation in bone traits—they found that variation in mechano-sensitivity in different strains of mice affect the rate of bone apposition during mechanical loading (Robling and Turner, 2002) and that differences in growth patterns and rate of bone formation influences fracture risk and bone fragility throughout life (Price et al., 2005). Other experimental findings have further shown differences in the rate of fracture healing between different strains of mice, indicating that variability in mechano-sensitive cell activity rates that control endochondral ossification can be due to genetic variations in an animal population (Jepsen et al., 2008; Li et al., 2001). In conclusion, this study expands a computational framework of mechano-regulated tissue differentiation by showing that variable cell mechano-regulation gives simulation outcomes matching the variability observed experimentally. The results corroborate the mechano-regulation theory of Prendergast et al. (1997) not only because the model captures the load-dependant tissue differentiation process but also because the variability in the cell activity parameters returns a variability similar to that observed in vivo. Computational models that can accurately capture intra- and inter-species variations in response to loading are essential for a better understanding of mechanobiology and this investigation illustrates how variability can be included in simulations of tissue differentiation.

Fig. 4. Amount of different cell phenotypes differentiated in the bone chamber over time (from day 1–day 63). The variable cell activity rates also induced a variation in differentiation pathways and outcomes (a). Excluding variable MSC proliferation rate in the simulations predicted less variable pathways and outcomes (b), but indicates a similar trend in the endochondral ossification process.

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Fig. 5. Number of osteoblasts inside the chamber over time (a) for different cell activity rates showing a large variability in the final outcomes. (b) with MSC proliferation rates kept constant and variability in differentiated cell activity rates showing a dichotomous result in the amount of bone formation. The high amount of osteoblasts predicted in the original simulations (a) at the time of loading is a direct result of the higher amounts of MSCs occupying the chamber volume due to faster MSC proliferation rate that is independent of the mechanical stimulus. Note that the peak predicted at day 21 in both (a) and (b) is caused by the change in loading (from 0.02 MPa as assumed blood pressure to 2 MPa applied by the piston). The higher mechanical loading changed the biophysical environment favouring fibroblasts and chondrocytes – initiating osteoblast apoptosis – which generates the drop in osteoblast population after 21 days.

Fig. 6. Additional histology of the bone chamber experiment. The result slice, from the mid-cross-section of the chamber, shows a large amount of fibrous tissue formation but also a region of cartilage cells across and at the centre of the chamber. The enlargement shows the line of cartilage surrounded by fibrous tissue but also some newly formed bone islands.

Conflicts of interest statement The authors have no conflicts of interest to declare.

Acknowledgements ˚ The authors would like to thank Inger Martensson and Mea Pelkonen for their technical assistance with the animal experiments. This material is based upon works supported by the Science Foundation Ireland under Grant no. SFI/06/IN.1/B86.

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