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3D models of chondrocytes within biomimetic scaffolds: Effects of cell deformation from loading regimens
Journal Pre-proof 3D models of chondrocytes within biomimetic scaffolds: Effects of cell deformation from loading regimens
Erica Di Federico, Dan L. Bader, Julia C. Shelton PII:
S0268-0033(20)30049-8
DOI:
https://doi.org/10.1016/j.clinbiomech.2020.01.022
Reference:
JCLB 4972
To appear in:
Clinical Biomechanics
Received date:
4 July 2019
Accepted date:
28 January 2020
Please cite this article as: E. Di Federico, D.L. Bader and J.C. Shelton, 3D models of chondrocytes within biomimetic scaffolds: Effects of cell deformation from loading regimens, Clinical Biomechanics (2020), https://doi.org/10.1016/ j.clinbiomech.2020.01.022
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© 2020 Published by Elsevier.
Journal Pre-proof
Title: 3D models of chondrocytes within Biomimetic Scaffolds: effects of cell deformation from loading regimens
Running title: Cell deformations under loads
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Authors: Erica Di Federicoa,∗, Dan L. Baderb , Julia C. Sheltona
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Affiliations: a Institute of Bioengineering, School of Engineering and Materials Science, Queen Mary,
Faculty of Health Sciences, University of Southampton, UK
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University of London, London, UK
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Submitted to: Clinical Biomechanics Special Issue: Cartilage Biomechanics - towards clinical
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implementation
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Keywords: Finite Element Analysis, Cartilage Tissue Engineering, Scaffold, Cell deformation.
Total number of Figures: 7
Total word count: 3911 words (excluding references & acknowledgements) (Guide for author: The length should not normally exceed 4000 words with around six figures/tables)
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Journal Pre-proof ABSTRACT Background: Mechanical conditioning has been widely used to attempt to enhance chondrocyte metabolism for the evolution of functionally competent cartilage. However, although upregulation of proteoglycans have been reported through the application of uniaxial compression, minimal collagen has been produced.
The study is designed to examine whether alternative loading
regimens, equivalent to physiological conditions, involving shear in addition to compression can enhance collagen production.
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Methods: Finite element models were developed to determine how the local chondrocyte
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environments within agarose constructs were influenced by a range of static and dynamic loading
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regimens. 3-D poro-viscoelastic models were validated against experimental data. In particular, these models were used to characterise chondrocyte deformation in compression with and without
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shear superimposed, with special reference to the formation of pericellular matrix around the cells.
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Findings: The models of the hydrogel constructs under stress relaxation and dynamic cyclic compression conditions were highly correlated with the experimental data. The cell deformation
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(y/z) in the constructs was greatest in the centre of the constructs, increasing with magnitude of
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compression up to 25%. The superposition of shear however did not produce significant additional changes in deformation, with the presence of PCM reducing the chondrocyte deformation. Interpretation:
The use of FE models can prove important in the definition of appropriate,
optimised mechanical conditioning regimens for the synthesis and organisation of mature extra cellular matrix by chondrocyte-seeded constructs.
They will also provide insight into the
mechanisms relating cell deformation to mechanotransduction pathways, thereby progressing the development of functionally competent tissue engineered cartilage.
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Journal Pre-proof 1.0 INTRODUCTION Articular cartilage is a highly organised connective tissue consisting of chondrocytes surrounded by an extracellular matrix (ECM) composed of a proteoglycan gel, enclosed within a complex network of collagen fibres (Bader and Lee, 2000). The interaction of the proteoglycan gel and collagen fibres is critical in providing mechanical competence to support loads generated in normal joint activities (Langelier and Buschmann 2003), which involve a combination of compressive, shear and tensile modalities (Guo et al., 2015; Grodzinsky et al., 2000). Changes in the ECM composition can
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dramatically alter its load-bearing capacity, thereby initiating a process which can eventually result
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in its degradation (Mauck et al. 2000). Since articular cartilage is avascular it exhibits a very limited
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capacity to regenerate and repair. Accordingly, a number of clinical strategies have been established to repair partial thickness cartilage defects, all of which deliver metabolically active cells to the
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defect site. However, such interventions rarely provide long term functional stability, thereby
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motivating a number of tissue engineering strategies involving chondrocyte-seeded scaffolds for the in vitro development of neo-cartilage tissues prior to implantation (Buckwalter and Mankin, 1998).
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Although these strategies can result in neo-cartilaginous tissue, which resembles the morphological
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and biochemical appearance of the native cartilage, its functional competence has not been demonstrated within a clinically relevant timescale (Schöne et al., 2016; Johnstone et al., 2013; Ng et al., 2009; Freyria et al. 2005).
Mechanical conditioning has often been introduced to enhance the biosynthetic activity of chondrocytes within 3D constructs. Several studies have revealed that mechanically induced cell deformations influence chondrocyte metabolism and consequently the evolution of neo-cartilage structure and composition. The majority of the in vitro studies have employed uniaxial compression to modulate the response of chondrocytes (Chowdhury et al., 2008; Lee and Bader, 1997; Mauck et al., 2000; Kisiday et al., 2004; Davisson et al., 2002), reporting an up-regulation of proteoglycans but with an absence of any significant amounts of collagen. A few studies have suggested that the superposition of shear on compression, particularly in the form of intermittent loading, can enhance 3
Journal Pre-proof the production of collagen and lead to neo-cartilage properties which match that of the native tissue (Guo et al., 2015, Jin et al., 2001; Waldman et al., 2003). Indeed, the concept of the development of an intelligent bioreactor with the ability to adjust the mechanical stimulation according to the state of the tissue engineered construct has been previously proposed (Schultz et al, 2008). However, the relationship between the specific form of mechanical stimuli and cell activity has not been fully established. In a recent paper, the authors reported the effect of different conditioning regimens, involving
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compression (uniaxial stimulation) or shear imposed on compression (biaxial stimulation), on the
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synthesis of ECM, using a model of isolated chondrocytes seeded in agarose constructs (Heywood
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et al., 2004; Chowdhury et al., 2008; Di Federico et al., 2017 ). Our findings strongly suggested
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that proteoglycan and collagen synthesis can be triggered by uncoupled mechanosensitive cellular responses. In particular, continuous biaxial stimulation, as opposed to uniaxial stimulation, led to a
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significantly enhanced activity of the cells. However, the mechanism by which the stimulation of the
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cells deformed evoked the response remained undetermined. This highlighted the need for models to describe the behaviour of both the chondrocytes and the scaffolds in which they are embedded,
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under relevant loading regimes, in order to predict quantifiable parameters (e.g. cell deformation, stress stimuli, etc.), which are known to influence gene expression and the chondrocytes metabolism (Wong and Carter, 2003; Guilak et al., 2000). The biphasic poro-viscoelastic (BPVE) theory, originally developed to model articular cartilage (DiSilvestro and Suh, 2001; Olberding and Suh, 2006; Nagel and Kelly, 2010), has been demonstrated to accurately predict the compressive viscoelastic behaviour of various soft hydrogel-like materials (Suh and Bai, 1998; DiSilvestro and Suh, 2001). Nguyen et al (2008) predicted the mechanical behaviour of a single calcium alginate microsphere under stress-relaxation conditions using a porous linear viscoelastic model.
Although cells are characterised by a viscoelastic behaviour, it is
conventionally accepted that linear elastic models can be employed to investigate their overall mechanical response (Ofek et al., 2009). Solid models have been successfully used to describe the 4
Journal Pre-proof behaviour of chondrocytes (Haider and Guilak, 2000; Caille et al., 2002), including theirresponse during micropipette aspiration tests (Haider and Guilak, 2000), for the determination of Young’s modulus (Jones et al., 1999) and the stiffness of chondrocyte cytoplasm and nucleus (Ofek et al., 2009). Chondrocyte viscoelastic behaviour can be considered negligible under applied cyclic loading regimes of 1Hz are applied as these cells are characterised by a relaxation time of approximately 20 s (Darling et al., 2008). The aim of this study was to adopt a finite element modelling (FEM) approach to understand how
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the local chondrocyte environments are influenced by well-defined loads and deformations in a
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tissue engineered scaffold. In the current study, biphasic poro-viscoelastic computational models of
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our experimental system were developed to
predict cell distortion under biaxial loading regimens within 3D agarose constructs;
gain insight into how the development of the ECM may influence cell metabolic activity by
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evaluate chondrocytes deformation under a complex loading modality of shear superimposed
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on compression,
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The objectives of this study were to
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altering the mechanical strain distributions within and around the chondrocytes.
compare the deformation ratios of the cells in two different construct geometries.
2.0 METHODS 2.1 Porous-biphasic viscoelastic models of agarose constructs Three dimensional solid models of two different 3% w/v agarose hydrogel construct geometries were constructed using a commercial software package (ABAQUS/Standard 6.12). The agarose gel was characterised as a fully-hydrated, incompressible, porous material with an intrinsically viscoelastic solid matrix, with both solid and fluid phases assumed to be incompressible. Its viscoelasticity is presented as a combination of both fluid flow-independent (intrinsic viscoelasticity
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Journal Pre-proof of the solid matrix) and fluid flow-dependent (diffusive interaction between the interstitial fluid and the porous solid matrix during deformation) mechanisms. The material properties of the hydrogel constructs were modelled using data derived from experiments (Di Federico, 2015, Lee and Knight, 2004). Two distinct construct geometries were examined involving either cylindrical (model 1, Figure 1A) or dumbell (model 2, Figure 1D) designs. An axisymmetric FE model consisting of stainless steel loading plates compressing the cylindrical construct (Model 1, Figure 1B) was subjected to both unconfined stress-relaxation and dynamic
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compression tests (Table1). The FE geometry and mesh of the construct and loading plate matched
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the sample dimensions in the experiment (Di Federico et al., 2017), with mesh optimisation accepted
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at a level of ±2%.
The solid matrix of the agarose gel was defined by an elastic component derived from the
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instantaneous compressive moduli and the viscous component calibrated in the time domain by a
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Prony series (S1) derived from stress-relaxation test data (Di Federico, 2015). The construct was considered fully and uniformly saturated (s = 1) and the isotropic permeability, k, was defined as a
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linear function of the saturation (i.e. k = 1 when s = 1). The material parameters were obtained
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either from the literature, or derived from tests performed in the host laboratory (Table 2). The model boundary conditions for the construct and loading plates were defined as follows. Displacement and rotation of the top loading plate both in the x and z directions were prevented, while the bottom plate was fully restrained. The interactions between the construct surfaces and the plates were defined as “simple contact” with tangential and normal behaviour directionally isotropic, and a friction coefficient set at 0.05 (Cobb, 2008). By contrast, no displacement constraints were imposed on the agarose construct, although its top and bottom surfaces were considered impermeable to simulate contact with the loading plates, while a “free draining condition” was defined at the outer diameter of the construct, corresponding to a pore pressure, p, equal to zero. After fully validating Model 1 through comparison with experimental data, a 3D solid model of a dumbell shaped cylindrical construct supported by nylon loading cup holders (Model 2), was 6
Journal Pre-proof implemented using the same material properties (Figure 1D & E). The Prony series coefficients describing the gel viscoelastic behaviour were obtained experimentally from a stress-relaxation test with this design. Differences in the construct geometry, volume and amount of fluid within the sample affected its fluid flow-dependent viscoelastic behaviour. The boundary conditions were similar for both models; the agarose directly in contact with the internal surfaces of the threaded loading cups were prescribed as impermeable and the contact surfaces between construct and loading cups were modelled as “simple contact” with a friction coefficient set at 0.30 (Chen et al.
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2000).
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The relationship between stress and time obtained for the simulations of both models were directly
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compared with the experimental data to evaluate the validity of the two models.
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2.2 Finite Element Model of Chondrocytes embedded in agarose hydrogel.
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The FE models 1 and 2 were both refined to incorporate chondrocytes into the construct geometries (Figure 1C & F, respectively). In Model 1, 45 chondrocytes were embedded in the cylindrical
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geometry, while a total of 73 chondrocytes were introduced into Model 2. As the cell density
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employed in the mechano-transduction experiments (Di Federico et al., 2017) do not to alter the mechanical response of the agarose construct (Heywood et al., 2004; Ahearne et al. 2005; Guilak and Mow, 2000), a relatively low cell number was introduced in the FE models to minimise the computational cost.
Model 2 was additionally modified by considering the effects of ECM deposition in the form of a pericellular matrix (PCM), forming a chondron-like structure around a cell diameter of 10 m and an outer diameter of 14 m (Figure 1G). This simulated the histological observation when chondrocyteseeded dumbell constructs were pre-cultured in the free-swelling state for 8 days (Di Federico et al., 2017). The chondrocyte and the associated PCM were each modelled as linear isotropic elastic materials (Guilak and Mow 2000; Haider and Guilak, 2000; Ahearne et al. 2005), with a Young’s modulus of 3.2 and 40 kPa and a Poisson’s ratio of 0.4 and 0.04, respectively (Table 2). An 7
Journal Pre-proof “embedding” constraint was employed to describe the interaction of both the cells and the PCM with the surrounding agarose gel. Models 1 and 2 were used to simulate the stress-relaxation tests previously performed in the host laboratory (Bader et al., 2002; Knight et al, 1998). In addition, Model 2 was employed to simulate 10% dynamic shear strain superimposed on a 15% dynamic compressive strain prescribed using different waveforms (Table 1). Results of the simulations were processed to estimate the deformation ratio of the cell diameters, a parameter previously estimated in the host laboratory
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(Knight et al, 1998).
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2.3 FE simulation solutions
The numerical problems defined in the FE simulations were solved using the standard implicit direct
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equation solver for both static and dynamic analyses. The numerical simulations were performed
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using the “soils step analysis” (Simulia ABAQUS 6.12 Documentation; 2012) with a transient consolidation for the pore fluid response. A full Newtonian solution technique with unsymmetrical
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matrix storage was adopted. Time-dependent behaviour was analysed using the "consolidation"
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parameter. The solver automatic stabilization process was based on the damping factors obtained from a previous general step, while a strain energy equal to 0.05 was considered as the maximum ratio of stabilization for the adaptive process. The analysis included a strain error tolerance of 0.1 for the viscoelastic behaviour (Simulia ABAQUS 6.12 Documentation; 2012). The mesh consisted of 10-node modified quadratic tetrahedrons for both construct geometries (Table S1). In the case of Model 2, the mesh was locally refined around the threads, the cells and the border of the PCM in order to maintain the accuracy of the FE approximation. A summary of the element numbers for each of the simulated geometries is found in Table S1.
2.4 Statistical Analyses
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Journal Pre-proof Mann-Whitney test was used to statistically compare numerical and experimental results. Frechet distance (D) between simulated and average experimental curves was also determined. Data are presented as mean ± standard deviation. A level of 5% was considered statistically significant in all tests (P<0.05).
3 RESULTS
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3.1 Stress-relaxation and Dynamic Compression Tests (Model 1)
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The simulated stress-relaxation curve obtained from the FE cylindrical model (Model 1A) was
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compared with the representative average curve from the experimental tests (n = 6, Di Federico, 2015), shown in Figure 2A. At each time point the stress values of the simulated curve was
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compared with the corresponding averaged experimental stress value, resulting in a high correlation
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between the model prediction and the experimental response of the agarose (P = 0.559, D = 1.472 and 1.462 for linear and relaxation regions, respectively).
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Results of the simulated stress-relaxation test showed that during the loading phase, the
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compressive displacement applied to the top surface of the construct generated a pore pressure gradient, which drove water out through the lateral surfaces of the construct. The magnitude of pore pressure gradually increased from the top surface in the direction of the application of the load (y-axis) reaching a uniform distribution and uniform fully developed pore effective velocity (FLVEL) of 1.25x10-4 ms-1 after 60 s, corresponding to the maximum displacement (point 3, Figure 2B). The gradual decrease in pore pressure during the relaxation phase was a result of the partial reabsorption of the exudate fluid, as demonstrated by the reversed FLVEL vectors, mainly through the lateral surface, with minimal values of 6.35x10-9 ms-1 occurring radially (point 6, Figure 2B). The porous-viscoelastic model of the cylindrical construct also accurately predicted the agarose mechanical behaviour under dynamic compression, Figure 3A (P = 0.999, D = 1.625). The peak stress amplitude decreased over time for both experimental and computational curves. A progressive
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Journal Pre-proof flattening of the trough shape, resulting from a loss of contact between the indenter and construct leading to lift-off (Figure 3A), such that after 20 cycles, the model predicted a permanent deformation of 0.20 mm, compared to a mean experimental value of 0.22 mm (Di Federico, 2015). Simulation results indicated that during the first cycle of dynamic compression, the resultant pore pressure gradient within the cylindrical construct progressively increased with applied load (Figure 3B). The water within the hydrogel flowed out through the lateral surface of the construct as indicated at points 1 - 4 (Figure 3B). A decrease in pore pressure as the load reduced to zero,
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corresponded to a reversal of the FLVEL vector (points 5 and 6) as the construct re-adsorbed fluid. At
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the start of the second cycle of dynamic compression (point 7), liquid flow occurred towards the
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outer surface of the construct in the top region, while the FLVEL vector was directed inwards tending towards the bottom of the construct.
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Since these results showed that simulations using the biphasic viscoelastic model yielded high
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agreement with the experimental data for both stress-relaxation and dynamic compression tests the
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same material parameters were employed to generate Model 2.
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3.2 Stress-relaxation Tests (Model 2)
The data from the simulation of stress-relaxation test on the dumbell construct with nylon holders demonstrated good agreement with an average of 10 sets of experimental data (Figure 4A). Indeed the differences between the two sets of temporal stress values were not statistically different (P = 0.169, D = 1.863 and 4.248 for linear and relaxation regions, respectively). Pore pressure gradient and fluid flow within the construct during the simulated stress-relaxation test were comparable in trend and magnitude to those observed in Model 1 (Figure 3B). Close examination of the data revealed that the FLVEL values were higher in the outer region of the construct compared to its core (point 3 and 4, Figure 4B).
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Cell Deformation Analysis (Models 1 & 2) 10
Journal Pre-proof Comparison of the stress relaxation data from the two models (Figure 2A and 4A) revealed that the presence of the loading cups in model 2 resulted in a 36% reduction in the maximum stress at the end of the ramp loading phase. The overall differences in viscoelastic behaviour in the two geometries clearly influenced the mechanical environment in which the chondrocytes were embedded within the constructs. This effect was evaluated by comparing the diameter ratios measured in all three planes for each chondrocyte at the end of the stress-relaxation simulation. Table 3 summarises the absolute diameters and resultant diameter ratios for one simulation for
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model 1 and three simulations for model 2. For the former, where symmetry is assumed in the x
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and z directions, the mean diameter ratios y/x and y/z were 0.71. The corresponding ratio value for
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model 2 yielded a value of 0.92 with considerably greater variability resulting from the nature of the dumbell construct. There is only a small reduction in diameter ratio for both dynamic loading
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conditions with no obvious effects of the superposition of shear strain. This is also reflected when
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the data is presented as continuum maps (derived from the individual discrete cell deformation data) of the y/z diameter ratio for cells subjected to compressive strain in the presence or absence
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of shear strain(Figure 5). In particular, there was considerable change in the diameter ratios in the
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centre of the construct when compressive strains of between 15% and 25% were applied in the absence of shear. However, when shear strains of 5 and 10% were superimposed there was little additional change in the y/z ratios.
An alternative mode of data presentation for diameter ratios is shown in Figure 6 for two test conditions (15% compression and 15% compression with 10% shear) with and without pericellular matrix (PCM). In the two test conditions the presence of the PCM reduced both diameter ratios across the dimensions of the construct. For example, in the centre (y = 0) the y/z diameter ratio was reduced by approximately 10% and 5% for compression in the absence and presence of shear, respectively. In a separate series of simulation, the effects of different loading modalities, for both dynamic compression and shear were examined (Figures 7B and C), in terms of the resulting diameter ratios 11
Journal Pre-proof (y/z and z/x) (Figure 7A). Some clear differences were apparent. For example, when compression was applied as in the original experiment (Di Federico et al, 2017) the y/z diameter ratio was 0.93 in the central region of the construct compared to 0.89 when compression was applied in a sinusoidal waveform. The z/x diameter ratios as a function of the y coordinate showed smaller differences between the loading regimens (Figure 7A), although, in all cases, modality (i) yielded the greatert inplane deformation of the cells. It is interesting to note that the combination of waveform for compression and shear in modality (ii), depicted in Figure 7C, yielded similar cell diameter ratios to
DISCUSSION
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those found for compression alone.
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The study was designed to investigate the chondrocyte deformation and the fluid flow within two agarose construct morphologies, under varying complex mechanical loading regimens and
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boundaries conditions using dedicated computational models. The poro-viscoelastic biphasic FE
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models were also used to investigate the role of pericellular matrix (PCM) in altering the load perceived by the chondrocytes as measured by the cell deformation ratios.
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The implemented models were shown to provide an accurate prediction of the mechanical
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behaviour of both cylindrical and dumbbell-shaped constructs under stress relaxation and dynamic compression tests. The selected material properties allowed a precise estimation of the construct deformation and the permanent deformation induced by dynamic compressive loading (Figures 2, 3 & SM1). The FE simulations also provided an estimation of the pressure gradient and pore fluid velocity within the cylindrical construct, offering insight into how the mechanical regimens influence the transport of fluid within loaded agarose constructs (Figures 2 & 3). The FE models also provided an accurate assessment of the cell deformations as a function of the applied loading regimen and identified differences due to their location within the two constructs morphologies (Figures 5 - 7). The computational models revealed that the cells located in the core of the dumbbell construct were exposed to higher deformations than those elsewhere, in particular within the loading cups ((Figure 6). Differences in the cell deformation between the two construct 12
Journal Pre-proof morphologies (Model 1 vs 2) were approximately 10%. Small differences in the cell deformation ratios were predicted dependent on the modality by which the loading regimen was applied to the construct (Figure 7). The simultaneous application of shear and compression to the dumbell construct yielded different cell deformations in each of the planes compared to compression alone, with corresponding values 5% smaller and 4% higher for y/z and z/x, respectively. When an alternative loading regime was simulated using a trapezoidal (compression) and semi-sinusoidal (shear) waveform respectively, modality (ii), the cell distortions in the YZ and XZ planes were found
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to be similar to those predicted when the chondrocytes were exposed to compression alone (Figure
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7). This insight, derived from modelling, would not be possible with experimental techniques alone.
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In agreement with previous studies (De Vries et al., 2014; Appelman et al., 2011), results of the simulations confirmed that the PCM has a strain shielding effect on the cells. Its presence
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significantly decreases the maximum strain values within the embedded cells by 10% and 7%, for
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compression alone and shear superimposed on compression, respectively (Figure 6). The ability to predict the strain magnitude on chondrocytes seeded in a matrix provides a means to define
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appropriate conditioning regimes in order to up-regulate the ECM synthesis and its organisation.
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Earlier studies have suggested that cell deformation may mediate alterations in matrix synthesis (Jeon et al., 2013; Bader and Knight, 2008) and cell deformation is known to activate regulatory mechanisms involving, for example, various forms of stretch-sensitive ion channels in the cell membrane (Ramage et al., 2009; Chowdhury et al., 2008). The deposition of PCM around chondrocytes shield the chondrocytes from direct loading, thereby minimising the risk of cell death (Appelman et al., 2011), although, it is frequently observed that the collagen and proteoglycan upregulation in engineered cartilage constructs is small (Di Federico et al., 2017; Davisson et al., 2002; Jin et al., 2001). However, by maintaining the level of cell/membrane deformation with culture time, despite the generation of the protective PCM, the mechanotransduction mechanisms which underpin the up-regulation of ECM, in particular the collagen component, might be sustained.
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Journal Pre-proof Thus, the use of predictive FE models may play a critical role in developing appropriate culture regimens for cartilage tissue engineering by producing substantial insight into how chondrocytes within constructs remodel their local environment in order to redistribute mechanical signals. The developed FE models could be essential in determining how to vary the applied mechanical load during culture time to ensure that the stimulation of cells in the construct remains sufficient and appropriate for the development of functional tissues. This provides value to the further development of an intelligent bioreactor (Schultz et al 2008), which is sensitive to the measurement
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of both metabolic activity and could incorporate a feedback loop to inform the appropriate
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mechanical stimulation to ensure the most effective evolution of tissue engineered cartilage.
CONCLUSION
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Computational modelling represents a valuable addition to the experimental approach employed in
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recent studies (Di Federico et al., 2017) in that it can both interpret biological responses and predict critical parameters, such as cell deformation, which are difficult to estimate experimentally.
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The study describes the successful development and implementation of a model which simulates the
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experimental culture system (Di Federico et al., 2017). It has enabled the accurate prediction of cell deformations in 3 planes as a result of the mechanical loading regimen applied to the construct and the location of chondrocytes within it. This method can inform further insight into the mechanisms by which cell deformation, determined by external mechanical stimuli, is related to the resulting chondrocyte synthetic activity, enabling future studies to investigate the role of cell deformation in mechanotransduction. Considerable advantages may be derived by the application of FE models in the definition of appropriate mechanical conditioning regimes aimed to up-regulate the ECM synthesis and organisation, while addressing the structural and mechanical adaptation of the chondrocytes to those different stimuli. The present computational approach represents the first to account for the
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Journal Pre-proof effects of different loading regimens and of the cell location within the sample on the deformation modalities of chondrocytes embedded in different morphologies of agarose constructs.
Acknowledgements
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The support of Orthopaedic Research UK is gratefully acknowledged.
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Gu, W. Y. & Justiz, M. A. (2002). Apparatus for measuring the swelling dependent electrical conductivity of charged hydrated soft tissues. Journal of Biomechanical Engineering 124:790-793. 10.1115/1.1516571 Guilak, F. and V. C. Mow (2000). "The mechanical environment of the chondrocyte: a biphasic finite element model of cell-matrix interactions in articular cartilage." Journal of Biomechanics 33(12): 1663-1673. https://doi.org/10.1016/S0021-9290(00)00105-6 Guo, T., L. Yu et al. (2015). “Effect of dynamic culture and periodic compression on human mesenchymal stem cell proliferation and chondrogenesis”. Ann Biomed Eng 44:2103–2113. doi 10.1007/s10439015-1510-5 Haider, M. A. and F. Guilak (2000). "An axisymmetric boundary integral model for incompressible linear viscoelasticity: Application to the micropipette aspiration contact problem." Journal of Biomechanical Engineering 122(3): 236-244. doi 10.1115/1.429654 Heywood, H. K., Sembi, P. K., Lee, D. A. & Bader, D. L. (2004). Cellular utilization determines viability and matrix distribution profiles in chondrocyte-seeded alginate constructs. Tissue engineering 10:146779. 10.1089/ten.2004.10.1467 Jeon, J. E., K. Schrobback et al. (2013). “Effect of preculture and loading on expression of matrix molecules, matrix metalloproteinases, and cytokines by expanded osteoarthritic chondrocytes”. Arthritis Rheum 65:2356–2367. https://doi.org/10.1002/art.38049 Jin, M., E. H. Frank, et al. (2001). "Tissue shear deformation stimulates proteoglycan and protein biosynthesis in bovine cartilage explants." Archives of Biochemistry and Biophysics 395(1): 41-48. https://doi.org/10.1006/abbi.2001.2543 Johnstone, B., M. Alini, et al. (2013). "Tissue engineering for articular cartilage repair - the state of the art." European Cells & Materials 25: 248-267. doi 10.22203/eCM.v025a18 Jones, W.R., H. P. Ting-Beall et al. (1999). “Alterations in the Young’s modulus and volumetric properties of chondrocytes isolated from normal and osteoarthritic human cartilage”. J Biomechanics 32:119–127. https://doi.org/10.1016/S0021-9290(98)00166-3 Kisiday, J. D., M. Jin, et al. (2004). "Effects of dynamic compressive loading on chondrocyte biosynthesis in self-assembling peptide scaffolds." Journal of Biomechanics 37(5): 595-604. https://doi.org/10.1016/j.jbiomech.2003.10.005 Knight, M. M., D. A. Lee, et al. (1998). "The influence of elaborated pericellular matrix on the deformation of isolated articular chondrocytes cultured in agarose." Biochimica et Biophysica Acta 1405(1-3): 67-77. https://doi.org/10.1016/S0167-4889(98)00102-5 Langelier, E. and M. D. Buschmann (2003). "Increasing strain and strain rate strengthen transient stiffness but weaken the response to subsequent compression for articular cartilage in unconfined compression." Journal of Biomechanics 36(6):853-859. https://doi.org/10.1016/S00219290(03)00006-X Lee D.A. and M.M. Knight (2004) Mechanical Loading of Chondrocytes Embedded in 3D Constructs. In: Sabatini M., Pastoureau P., De Ceuninck F. (eds) Cartilage and Osteoarthritis. Methods in Molecular Medicine™, vol 100. Humana Press. https://doi.org/10.1385/1-59259-810-2:307 Lee, D. A. and D. L. Bader (1997). "Compressive strains at physiological frequencies influence the metabolism of chondrocytes seeded in agarose." Journal of Orthopaedic Research 15(2): 181-188. https://doi.org/10.1002/jor.1100150205 Mauck, R. L., M. A. Soltz, et al. (2000). "Functional tissue engineering of articular cartilage through dynamic loading of chondrocyte-seeded agarose gels." Journal of Biomechanical Engineering 122(3): 252-260. doi 10.1115/1.429656 Nagel, T. and D. J. Kelly (2010). "The influence of fiber orientation on the equilibrium properties of neutral and charged biphasic tissues." Journal of Biomechanical Engineering 132(11). doi 10.1115/1.4002589 Ng, K. W., L. E. Kugler, et al. (2009). "Scaffold degradation elevates the collagen content and dynamic compressive modulus in engineered articular cartilage." Tissue Eng Part A 15:2315–2324. https://doi.org/10.1016/j.joca.2008.06.013 17
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Nguyen, V.B., C.X. Wang et al. (2009). “Mechanical properties of single alginate microspheres determined by microcompression and finite element modelling”. Chemical Engineering Science 64(5):821-829. https://doi.org/10.1016/j.ces.2008.10.050 Ofek, G., R. M. Natoli, et al. (2009). "In situ mechanical properties of the chondrocyte cytoplasm and nucleus." Journal of Biomechanics 42(7): 873-877. https://doi.org/10.1016/j.jbiomech.2009.01.024 Olberding, J. E. and J. K. F. Suh (2006). "A dual optimization method for the material parameter identification of a biphasic poroviscoelastic hydrogel: Potential application to hypercompliant soft tissues." Journal of Biomechanics 39(13): 2468-2475. https://doi.org/10.1016/j.jbiomech.2005.07.019 Ramage, L., G. Nuki, et al. (2009). "Signalling cascades in mechanotransduction: cellmatrix interactions and mechanical loading." Scandinavian Journal of Medicine & Science in Sports 19(4): 457-469. https://doi.org/10.1111/j.1600-0838.2009.00912.x Schöne, M., N. Männicke et al. (2016). “3D ultrasound biomicroscopy for assessment of cartilage repair tissue: Volumetric characterisation and correlation to established classification systems”. Eur Cell Mater 31:119–135. doi 10.22203/eCM.v031a09 Schulz, R. M., Wüstneck, N., van Donkelaar, C. C., Shelton, J. C., & Bader A. (2008). Development and validation of a novel bioreactor system for load- and perfusion-controlled tissue engineering of chondrocyte-constructs. Biotechnol Bioeng, 101(4), 714-728. doi:10.1002/bit.21955 Simulia (2012). ABAQUS 6.12 Documentation. Suh, J. K. and S. Bai (1998). "Finite element formulation of biphasic poroviscoelastic model for articular cartilage." Journal of Biomechanical Engineering 120(2): 195-201. doi 10.1115/1.2798302 Tasci, A., Ferguson, S. J. & Buchler, P. (2011). Numerical assessment on the effective mechanical stimuli for matrix-associated metabolism in chondrocyte-seeded constructs. Journal of tissue engineering and regenerative medicine 5:210-219. https://doi.org/10.1002/term.307 Waldman, S. D., C. G. Spiteri, et al. (2003). "Effect of biomechanical conditioning on cartilaginous tissue formation in vitro." Journal of Bone and Joint Surgery- American Volume 85A: 101-105. doi 10.2106/00004623-200300002-00013 Wong, M. and D. R. Carter (2003). “Articular cartilage functional histomorphology and mechanobiology: a research perspective”. Bone 33(1):1–13. https://doi.org/10.1016/S8756-3282(03)00083-8
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Journal Pre-proof Figure captions Figure 1. Meshed cylindrical agarose construct model with (A) and without (B) impermeable metal loading plates. Meshed dumbell shaped agarose construct with (D) and without (E) nylon loading cup holders. Schematic drawing indicating the location of the chondrocytes (red dots) in Model 1, the cylindrical construct geometry (C) and in Model 2, the dumbell shaped agarose construct (F). Dimensions of meshed chondrocyte and pericellular matrix (PCM) (G). Figure 2. Comparison of predicted stress vs. time curve obtained from the simulated stress-relaxation test (Model 1A) and the average curve of five sets of experimentally determined data (A). Contour of the pore fluid effective velocity (FLVEL, mm/s) vector within the cylindrical geometry employed in Model 1A at different step times of the simulated stress-relaxation test (B). Insets indicate local directions of FLVEL in selected regions.
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Figure 3. Comparison of predicted stress vs. time curve obtained from the simulated dynamic compression test (Model 1A) and the average curve of five sets of experimentally determined data (A). Contour of the pore fluid effective velocity (FLVEL, mm/s) vector within the cylindrical geometry employed in Model 1A at different step times of the simulated dynamic compression test (B). Insets indicate local directions of FLVEL in selected regions.
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Figure 4. Comparison of predicted stress vs. time curve obtained from the simulated stress-relaxation test (Model 2A) and the average curve of five sets of experimentally determined data (A). Contour of the pore fluid effective velocity (FLVEL, mm/s) vector within the dumbbell geometry employed in Model 2A at different step times of the simulated stress-relaxation test (B). Insets indicate local directions of FLVEL in selected regions in six time points.
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Figure 5. Continuum maps of the y/z diameter ratio as a function of cell position in the dumbbell construct, following application of compressive strain (0 – 25 %) and shear strain (0 – 10 %) using Model 2B. The maps were generated using cells within the core of the agarose geometry (0 mm < z < 2 mm and -5 mm < y < 5mm).
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Figure 6. Comparison of the mean diameter ratios (y/z and z/x) as a function of the cell position in the dumbbell construct, after application of 15% compression alone and with 10% shear strain superimposed. The simulations were modelled using Model 2 (chondrocyte with no PCM, red) and (chondrocyte with PCM, green). Figure 7. Comparison of the diameter ratios (y/z and z/x) as a function of the cells position in the dumbbell construct, following the application of 15% compression and two bi-axial loading regimens (10% shear strain superimposed on 15% compressive strain), B & C. The simulations were modelled using Model 2B.
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Table 1. Model components and implemented simulations.
Geometry
MODEL 1
Model ID
Chondrocyte
PCM
A
✗
✗
B
✓
✗
A
✗
✗
Cylindrical
✓
B MODEL 2
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Dumbell C
1
Simulations
u o
rn ✓
✓
J
Stress-relaxation test1 Dynamic compression test2
Stress-relaxation test1
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e
r P ✗
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Stress-relaxation test1 Stress-relaxation test1 Compression (0 - 25%) with 0 - 10% superimposed shear2,3 15% compression 15% compression and 10% shear
20% compressive strain applied at a ramp rate of 20%/min and dwell period of 10 minutes. 2 Sinusoidal displacement between 0 and 1 mm of the top plate at a frequency of 1 Hz for 20 cycles. 3 Shear and Compression both applied using different waveforms (Figure 7)
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Table 2. Mechanical (Tab 2A) and physical (Tab 2B) properties employed in the numerical simulations.
Table 2A Agarose
Nylon
316L SS
Chondrocyte
PCM
3.2 kPa†
40 kPa
0.4††
0.04 †††
90 kPa
2.8 GPa
(GPa) Poisson ratio
0.49
0.4
485 GPa 0.3
Density (g/mL)
1.64
1.14
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Mechanical property Young’s modulus
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5·10-12†
Porosity
97%††††
Void ratio
33
Saturation
1 21
-
††† (Alexopoulos et al.,
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† (Tasci et al., 2011) †† (Ofek et al. 2009; Knight et al., 2002) 2005) †††† (Gu et al., 2002)
-
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Fluid (water) bulk moduli (k Pa) Fluid (water) specific weight (N/m3)
9731
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†††† (Gu et al., 2002)
Table 3. Mean (± standard deviation) cell diameter along x, y and z directions and associated diameter ratios calculated at the end of the simulated loading regimes. Values determined in the internal region of the construct (Figure 1F). Diameter (μm)
Diameter ratio
x
y
z
y/x
z/x
y/z
Model 1 Stress-relaxation
11.20 ± 0.01
8.00 ± 0.01
11.20 ± 0.01
0.71 ± 0.001
1.00 ± 0.001
0.71 ± 0.001
Model 2 Stress-relaxation
10.24 ± 0.476
9.32 ± 0.734
10.25 ± 0.491
0.92 ± 0.106
1.00 ± 0.017
0.92 ± 0.107
Model 2 15% dynamic compressive strain
10.12 ± 0.165
9.62 ± 0.282
10.20 ± 0.188
0.95± 0.041
1.00 ± 0.012
0.94 ± 0.043
Model 2 15% dynamic
10.10 ± 0.184
9.60 ± 0.275
10.10 ± 0.170
0.95 ± 0.041
1.00 ± 0.024
0.96 ± 0.035
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compressive strain & 10% shear strain
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Journal Pre-proof Highlights
FE models can predict chondrocyte deformation in constructs under static and dynamic loading
Superposition of shear on compression does not produce significant changes in cell deformation Pericellular matrix resulting from cell activity reduces chondrocyte deformation
Modelling highlights the importance of cell deformation in mechanotransduction
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Modelling offers the potential of optimising the development of functional cartilage
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pathways
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Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Erica Di Federico, Dan L. Bader, Julia C. Shelton PII:
S0268-0033(20)30049-8
DOI:
https://doi.org/10.1016/j.clinbiomech.2020.01.022
Reference:
JCLB 4972
To appear in:
Clinical Biomechanics
Received date:
4 July 2019
Accepted date:
28 January 2020
Please cite this article as: E. Di Federico, D.L. Bader and J.C. Shelton, 3D models of chondrocytes within biomimetic scaffolds: Effects of cell deformation from loading regimens, Clinical Biomechanics (2020), https://doi.org/10.1016/ j.clinbiomech.2020.01.022
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
© 2020 Published by Elsevier.
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Title: 3D models of chondrocytes within Biomimetic Scaffolds: effects of cell deformation from loading regimens
Running title: Cell deformations under loads
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Authors: Erica Di Federicoa,∗, Dan L. Baderb , Julia C. Sheltona
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Affiliations: a Institute of Bioengineering, School of Engineering and Materials Science, Queen Mary,
Faculty of Health Sciences, University of Southampton, UK
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b
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University of London, London, UK
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Submitted to: Clinical Biomechanics Special Issue: Cartilage Biomechanics - towards clinical
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implementation
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Keywords: Finite Element Analysis, Cartilage Tissue Engineering, Scaffold, Cell deformation.
Total number of Figures: 7
Total word count: 3911 words (excluding references & acknowledgements) (Guide for author: The length should not normally exceed 4000 words with around six figures/tables)
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Journal Pre-proof ABSTRACT Background: Mechanical conditioning has been widely used to attempt to enhance chondrocyte metabolism for the evolution of functionally competent cartilage. However, although upregulation of proteoglycans have been reported through the application of uniaxial compression, minimal collagen has been produced.
The study is designed to examine whether alternative loading
regimens, equivalent to physiological conditions, involving shear in addition to compression can enhance collagen production.
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Methods: Finite element models were developed to determine how the local chondrocyte
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environments within agarose constructs were influenced by a range of static and dynamic loading
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regimens. 3-D poro-viscoelastic models were validated against experimental data. In particular, these models were used to characterise chondrocyte deformation in compression with and without
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shear superimposed, with special reference to the formation of pericellular matrix around the cells.
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Findings: The models of the hydrogel constructs under stress relaxation and dynamic cyclic compression conditions were highly correlated with the experimental data. The cell deformation
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(y/z) in the constructs was greatest in the centre of the constructs, increasing with magnitude of
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compression up to 25%. The superposition of shear however did not produce significant additional changes in deformation, with the presence of PCM reducing the chondrocyte deformation. Interpretation:
The use of FE models can prove important in the definition of appropriate,
optimised mechanical conditioning regimens for the synthesis and organisation of mature extra cellular matrix by chondrocyte-seeded constructs.
They will also provide insight into the
mechanisms relating cell deformation to mechanotransduction pathways, thereby progressing the development of functionally competent tissue engineered cartilage.
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Journal Pre-proof 1.0 INTRODUCTION Articular cartilage is a highly organised connective tissue consisting of chondrocytes surrounded by an extracellular matrix (ECM) composed of a proteoglycan gel, enclosed within a complex network of collagen fibres (Bader and Lee, 2000). The interaction of the proteoglycan gel and collagen fibres is critical in providing mechanical competence to support loads generated in normal joint activities (Langelier and Buschmann 2003), which involve a combination of compressive, shear and tensile modalities (Guo et al., 2015; Grodzinsky et al., 2000). Changes in the ECM composition can
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dramatically alter its load-bearing capacity, thereby initiating a process which can eventually result
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in its degradation (Mauck et al. 2000). Since articular cartilage is avascular it exhibits a very limited
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capacity to regenerate and repair. Accordingly, a number of clinical strategies have been established to repair partial thickness cartilage defects, all of which deliver metabolically active cells to the
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defect site. However, such interventions rarely provide long term functional stability, thereby
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motivating a number of tissue engineering strategies involving chondrocyte-seeded scaffolds for the in vitro development of neo-cartilage tissues prior to implantation (Buckwalter and Mankin, 1998).
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Although these strategies can result in neo-cartilaginous tissue, which resembles the morphological
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and biochemical appearance of the native cartilage, its functional competence has not been demonstrated within a clinically relevant timescale (Schöne et al., 2016; Johnstone et al., 2013; Ng et al., 2009; Freyria et al. 2005).
Mechanical conditioning has often been introduced to enhance the biosynthetic activity of chondrocytes within 3D constructs. Several studies have revealed that mechanically induced cell deformations influence chondrocyte metabolism and consequently the evolution of neo-cartilage structure and composition. The majority of the in vitro studies have employed uniaxial compression to modulate the response of chondrocytes (Chowdhury et al., 2008; Lee and Bader, 1997; Mauck et al., 2000; Kisiday et al., 2004; Davisson et al., 2002), reporting an up-regulation of proteoglycans but with an absence of any significant amounts of collagen. A few studies have suggested that the superposition of shear on compression, particularly in the form of intermittent loading, can enhance 3
Journal Pre-proof the production of collagen and lead to neo-cartilage properties which match that of the native tissue (Guo et al., 2015, Jin et al., 2001; Waldman et al., 2003). Indeed, the concept of the development of an intelligent bioreactor with the ability to adjust the mechanical stimulation according to the state of the tissue engineered construct has been previously proposed (Schultz et al, 2008). However, the relationship between the specific form of mechanical stimuli and cell activity has not been fully established. In a recent paper, the authors reported the effect of different conditioning regimens, involving
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compression (uniaxial stimulation) or shear imposed on compression (biaxial stimulation), on the
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synthesis of ECM, using a model of isolated chondrocytes seeded in agarose constructs (Heywood
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et al., 2004; Chowdhury et al., 2008; Di Federico et al., 2017 ). Our findings strongly suggested
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that proteoglycan and collagen synthesis can be triggered by uncoupled mechanosensitive cellular responses. In particular, continuous biaxial stimulation, as opposed to uniaxial stimulation, led to a
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significantly enhanced activity of the cells. However, the mechanism by which the stimulation of the
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cells deformed evoked the response remained undetermined. This highlighted the need for models to describe the behaviour of both the chondrocytes and the scaffolds in which they are embedded,
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under relevant loading regimes, in order to predict quantifiable parameters (e.g. cell deformation, stress stimuli, etc.), which are known to influence gene expression and the chondrocytes metabolism (Wong and Carter, 2003; Guilak et al., 2000). The biphasic poro-viscoelastic (BPVE) theory, originally developed to model articular cartilage (DiSilvestro and Suh, 2001; Olberding and Suh, 2006; Nagel and Kelly, 2010), has been demonstrated to accurately predict the compressive viscoelastic behaviour of various soft hydrogel-like materials (Suh and Bai, 1998; DiSilvestro and Suh, 2001). Nguyen et al (2008) predicted the mechanical behaviour of a single calcium alginate microsphere under stress-relaxation conditions using a porous linear viscoelastic model.
Although cells are characterised by a viscoelastic behaviour, it is
conventionally accepted that linear elastic models can be employed to investigate their overall mechanical response (Ofek et al., 2009). Solid models have been successfully used to describe the 4
Journal Pre-proof behaviour of chondrocytes (Haider and Guilak, 2000; Caille et al., 2002), including theirresponse during micropipette aspiration tests (Haider and Guilak, 2000), for the determination of Young’s modulus (Jones et al., 1999) and the stiffness of chondrocyte cytoplasm and nucleus (Ofek et al., 2009). Chondrocyte viscoelastic behaviour can be considered negligible under applied cyclic loading regimes of 1Hz are applied as these cells are characterised by a relaxation time of approximately 20 s (Darling et al., 2008). The aim of this study was to adopt a finite element modelling (FEM) approach to understand how
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the local chondrocyte environments are influenced by well-defined loads and deformations in a
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tissue engineered scaffold. In the current study, biphasic poro-viscoelastic computational models of
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our experimental system were developed to
predict cell distortion under biaxial loading regimens within 3D agarose constructs;
gain insight into how the development of the ECM may influence cell metabolic activity by
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evaluate chondrocytes deformation under a complex loading modality of shear superimposed
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on compression,
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The objectives of this study were to
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altering the mechanical strain distributions within and around the chondrocytes.
compare the deformation ratios of the cells in two different construct geometries.
2.0 METHODS 2.1 Porous-biphasic viscoelastic models of agarose constructs Three dimensional solid models of two different 3% w/v agarose hydrogel construct geometries were constructed using a commercial software package (ABAQUS/Standard 6.12). The agarose gel was characterised as a fully-hydrated, incompressible, porous material with an intrinsically viscoelastic solid matrix, with both solid and fluid phases assumed to be incompressible. Its viscoelasticity is presented as a combination of both fluid flow-independent (intrinsic viscoelasticity
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Journal Pre-proof of the solid matrix) and fluid flow-dependent (diffusive interaction between the interstitial fluid and the porous solid matrix during deformation) mechanisms. The material properties of the hydrogel constructs were modelled using data derived from experiments (Di Federico, 2015, Lee and Knight, 2004). Two distinct construct geometries were examined involving either cylindrical (model 1, Figure 1A) or dumbell (model 2, Figure 1D) designs. An axisymmetric FE model consisting of stainless steel loading plates compressing the cylindrical construct (Model 1, Figure 1B) was subjected to both unconfined stress-relaxation and dynamic
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compression tests (Table1). The FE geometry and mesh of the construct and loading plate matched
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the sample dimensions in the experiment (Di Federico et al., 2017), with mesh optimisation accepted
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at a level of ±2%.
The solid matrix of the agarose gel was defined by an elastic component derived from the
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instantaneous compressive moduli and the viscous component calibrated in the time domain by a
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Prony series (S1) derived from stress-relaxation test data (Di Federico, 2015). The construct was considered fully and uniformly saturated (s = 1) and the isotropic permeability, k, was defined as a
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linear function of the saturation (i.e. k = 1 when s = 1). The material parameters were obtained
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either from the literature, or derived from tests performed in the host laboratory (Table 2). The model boundary conditions for the construct and loading plates were defined as follows. Displacement and rotation of the top loading plate both in the x and z directions were prevented, while the bottom plate was fully restrained. The interactions between the construct surfaces and the plates were defined as “simple contact” with tangential and normal behaviour directionally isotropic, and a friction coefficient set at 0.05 (Cobb, 2008). By contrast, no displacement constraints were imposed on the agarose construct, although its top and bottom surfaces were considered impermeable to simulate contact with the loading plates, while a “free draining condition” was defined at the outer diameter of the construct, corresponding to a pore pressure, p, equal to zero. After fully validating Model 1 through comparison with experimental data, a 3D solid model of a dumbell shaped cylindrical construct supported by nylon loading cup holders (Model 2), was 6
Journal Pre-proof implemented using the same material properties (Figure 1D & E). The Prony series coefficients describing the gel viscoelastic behaviour were obtained experimentally from a stress-relaxation test with this design. Differences in the construct geometry, volume and amount of fluid within the sample affected its fluid flow-dependent viscoelastic behaviour. The boundary conditions were similar for both models; the agarose directly in contact with the internal surfaces of the threaded loading cups were prescribed as impermeable and the contact surfaces between construct and loading cups were modelled as “simple contact” with a friction coefficient set at 0.30 (Chen et al.
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2000).
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The relationship between stress and time obtained for the simulations of both models were directly
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compared with the experimental data to evaluate the validity of the two models.
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2.2 Finite Element Model of Chondrocytes embedded in agarose hydrogel.
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The FE models 1 and 2 were both refined to incorporate chondrocytes into the construct geometries (Figure 1C & F, respectively). In Model 1, 45 chondrocytes were embedded in the cylindrical
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geometry, while a total of 73 chondrocytes were introduced into Model 2. As the cell density
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employed in the mechano-transduction experiments (Di Federico et al., 2017) do not to alter the mechanical response of the agarose construct (Heywood et al., 2004; Ahearne et al. 2005; Guilak and Mow, 2000), a relatively low cell number was introduced in the FE models to minimise the computational cost.
Model 2 was additionally modified by considering the effects of ECM deposition in the form of a pericellular matrix (PCM), forming a chondron-like structure around a cell diameter of 10 m and an outer diameter of 14 m (Figure 1G). This simulated the histological observation when chondrocyteseeded dumbell constructs were pre-cultured in the free-swelling state for 8 days (Di Federico et al., 2017). The chondrocyte and the associated PCM were each modelled as linear isotropic elastic materials (Guilak and Mow 2000; Haider and Guilak, 2000; Ahearne et al. 2005), with a Young’s modulus of 3.2 and 40 kPa and a Poisson’s ratio of 0.4 and 0.04, respectively (Table 2). An 7
Journal Pre-proof “embedding” constraint was employed to describe the interaction of both the cells and the PCM with the surrounding agarose gel. Models 1 and 2 were used to simulate the stress-relaxation tests previously performed in the host laboratory (Bader et al., 2002; Knight et al, 1998). In addition, Model 2 was employed to simulate 10% dynamic shear strain superimposed on a 15% dynamic compressive strain prescribed using different waveforms (Table 1). Results of the simulations were processed to estimate the deformation ratio of the cell diameters, a parameter previously estimated in the host laboratory
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(Knight et al, 1998).
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2.3 FE simulation solutions
The numerical problems defined in the FE simulations were solved using the standard implicit direct
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equation solver for both static and dynamic analyses. The numerical simulations were performed
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using the “soils step analysis” (Simulia ABAQUS 6.12 Documentation; 2012) with a transient consolidation for the pore fluid response. A full Newtonian solution technique with unsymmetrical
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matrix storage was adopted. Time-dependent behaviour was analysed using the "consolidation"
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parameter. The solver automatic stabilization process was based on the damping factors obtained from a previous general step, while a strain energy equal to 0.05 was considered as the maximum ratio of stabilization for the adaptive process. The analysis included a strain error tolerance of 0.1 for the viscoelastic behaviour (Simulia ABAQUS 6.12 Documentation; 2012). The mesh consisted of 10-node modified quadratic tetrahedrons for both construct geometries (Table S1). In the case of Model 2, the mesh was locally refined around the threads, the cells and the border of the PCM in order to maintain the accuracy of the FE approximation. A summary of the element numbers for each of the simulated geometries is found in Table S1.
2.4 Statistical Analyses
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Journal Pre-proof Mann-Whitney test was used to statistically compare numerical and experimental results. Frechet distance (D) between simulated and average experimental curves was also determined. Data are presented as mean ± standard deviation. A level of 5% was considered statistically significant in all tests (P<0.05).
3 RESULTS
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3.1 Stress-relaxation and Dynamic Compression Tests (Model 1)
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The simulated stress-relaxation curve obtained from the FE cylindrical model (Model 1A) was
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compared with the representative average curve from the experimental tests (n = 6, Di Federico, 2015), shown in Figure 2A. At each time point the stress values of the simulated curve was
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compared with the corresponding averaged experimental stress value, resulting in a high correlation
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between the model prediction and the experimental response of the agarose (P = 0.559, D = 1.472 and 1.462 for linear and relaxation regions, respectively).
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Results of the simulated stress-relaxation test showed that during the loading phase, the
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compressive displacement applied to the top surface of the construct generated a pore pressure gradient, which drove water out through the lateral surfaces of the construct. The magnitude of pore pressure gradually increased from the top surface in the direction of the application of the load (y-axis) reaching a uniform distribution and uniform fully developed pore effective velocity (FLVEL) of 1.25x10-4 ms-1 after 60 s, corresponding to the maximum displacement (point 3, Figure 2B). The gradual decrease in pore pressure during the relaxation phase was a result of the partial reabsorption of the exudate fluid, as demonstrated by the reversed FLVEL vectors, mainly through the lateral surface, with minimal values of 6.35x10-9 ms-1 occurring radially (point 6, Figure 2B). The porous-viscoelastic model of the cylindrical construct also accurately predicted the agarose mechanical behaviour under dynamic compression, Figure 3A (P = 0.999, D = 1.625). The peak stress amplitude decreased over time for both experimental and computational curves. A progressive
9
Journal Pre-proof flattening of the trough shape, resulting from a loss of contact between the indenter and construct leading to lift-off (Figure 3A), such that after 20 cycles, the model predicted a permanent deformation of 0.20 mm, compared to a mean experimental value of 0.22 mm (Di Federico, 2015). Simulation results indicated that during the first cycle of dynamic compression, the resultant pore pressure gradient within the cylindrical construct progressively increased with applied load (Figure 3B). The water within the hydrogel flowed out through the lateral surface of the construct as indicated at points 1 - 4 (Figure 3B). A decrease in pore pressure as the load reduced to zero,
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corresponded to a reversal of the FLVEL vector (points 5 and 6) as the construct re-adsorbed fluid. At
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the start of the second cycle of dynamic compression (point 7), liquid flow occurred towards the
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outer surface of the construct in the top region, while the FLVEL vector was directed inwards tending towards the bottom of the construct.
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Since these results showed that simulations using the biphasic viscoelastic model yielded high
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agreement with the experimental data for both stress-relaxation and dynamic compression tests the
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same material parameters were employed to generate Model 2.
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3.2 Stress-relaxation Tests (Model 2)
The data from the simulation of stress-relaxation test on the dumbell construct with nylon holders demonstrated good agreement with an average of 10 sets of experimental data (Figure 4A). Indeed the differences between the two sets of temporal stress values were not statistically different (P = 0.169, D = 1.863 and 4.248 for linear and relaxation regions, respectively). Pore pressure gradient and fluid flow within the construct during the simulated stress-relaxation test were comparable in trend and magnitude to those observed in Model 1 (Figure 3B). Close examination of the data revealed that the FLVEL values were higher in the outer region of the construct compared to its core (point 3 and 4, Figure 4B).
4
Cell Deformation Analysis (Models 1 & 2) 10
Journal Pre-proof Comparison of the stress relaxation data from the two models (Figure 2A and 4A) revealed that the presence of the loading cups in model 2 resulted in a 36% reduction in the maximum stress at the end of the ramp loading phase. The overall differences in viscoelastic behaviour in the two geometries clearly influenced the mechanical environment in which the chondrocytes were embedded within the constructs. This effect was evaluated by comparing the diameter ratios measured in all three planes for each chondrocyte at the end of the stress-relaxation simulation. Table 3 summarises the absolute diameters and resultant diameter ratios for one simulation for
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model 1 and three simulations for model 2. For the former, where symmetry is assumed in the x
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and z directions, the mean diameter ratios y/x and y/z were 0.71. The corresponding ratio value for
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model 2 yielded a value of 0.92 with considerably greater variability resulting from the nature of the dumbell construct. There is only a small reduction in diameter ratio for both dynamic loading
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conditions with no obvious effects of the superposition of shear strain. This is also reflected when
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the data is presented as continuum maps (derived from the individual discrete cell deformation data) of the y/z diameter ratio for cells subjected to compressive strain in the presence or absence
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of shear strain(Figure 5). In particular, there was considerable change in the diameter ratios in the
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centre of the construct when compressive strains of between 15% and 25% were applied in the absence of shear. However, when shear strains of 5 and 10% were superimposed there was little additional change in the y/z ratios.
An alternative mode of data presentation for diameter ratios is shown in Figure 6 for two test conditions (15% compression and 15% compression with 10% shear) with and without pericellular matrix (PCM). In the two test conditions the presence of the PCM reduced both diameter ratios across the dimensions of the construct. For example, in the centre (y = 0) the y/z diameter ratio was reduced by approximately 10% and 5% for compression in the absence and presence of shear, respectively. In a separate series of simulation, the effects of different loading modalities, for both dynamic compression and shear were examined (Figures 7B and C), in terms of the resulting diameter ratios 11
Journal Pre-proof (y/z and z/x) (Figure 7A). Some clear differences were apparent. For example, when compression was applied as in the original experiment (Di Federico et al, 2017) the y/z diameter ratio was 0.93 in the central region of the construct compared to 0.89 when compression was applied in a sinusoidal waveform. The z/x diameter ratios as a function of the y coordinate showed smaller differences between the loading regimens (Figure 7A), although, in all cases, modality (i) yielded the greatert inplane deformation of the cells. It is interesting to note that the combination of waveform for compression and shear in modality (ii), depicted in Figure 7C, yielded similar cell diameter ratios to
DISCUSSION
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those found for compression alone.
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The study was designed to investigate the chondrocyte deformation and the fluid flow within two agarose construct morphologies, under varying complex mechanical loading regimens and
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boundaries conditions using dedicated computational models. The poro-viscoelastic biphasic FE
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models were also used to investigate the role of pericellular matrix (PCM) in altering the load perceived by the chondrocytes as measured by the cell deformation ratios.
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The implemented models were shown to provide an accurate prediction of the mechanical
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behaviour of both cylindrical and dumbbell-shaped constructs under stress relaxation and dynamic compression tests. The selected material properties allowed a precise estimation of the construct deformation and the permanent deformation induced by dynamic compressive loading (Figures 2, 3 & SM1). The FE simulations also provided an estimation of the pressure gradient and pore fluid velocity within the cylindrical construct, offering insight into how the mechanical regimens influence the transport of fluid within loaded agarose constructs (Figures 2 & 3). The FE models also provided an accurate assessment of the cell deformations as a function of the applied loading regimen and identified differences due to their location within the two constructs morphologies (Figures 5 - 7). The computational models revealed that the cells located in the core of the dumbbell construct were exposed to higher deformations than those elsewhere, in particular within the loading cups ((Figure 6). Differences in the cell deformation between the two construct 12
Journal Pre-proof morphologies (Model 1 vs 2) were approximately 10%. Small differences in the cell deformation ratios were predicted dependent on the modality by which the loading regimen was applied to the construct (Figure 7). The simultaneous application of shear and compression to the dumbell construct yielded different cell deformations in each of the planes compared to compression alone, with corresponding values 5% smaller and 4% higher for y/z and z/x, respectively. When an alternative loading regime was simulated using a trapezoidal (compression) and semi-sinusoidal (shear) waveform respectively, modality (ii), the cell distortions in the YZ and XZ planes were found
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to be similar to those predicted when the chondrocytes were exposed to compression alone (Figure
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7). This insight, derived from modelling, would not be possible with experimental techniques alone.
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In agreement with previous studies (De Vries et al., 2014; Appelman et al., 2011), results of the simulations confirmed that the PCM has a strain shielding effect on the cells. Its presence
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significantly decreases the maximum strain values within the embedded cells by 10% and 7%, for
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compression alone and shear superimposed on compression, respectively (Figure 6). The ability to predict the strain magnitude on chondrocytes seeded in a matrix provides a means to define
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appropriate conditioning regimes in order to up-regulate the ECM synthesis and its organisation.
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Earlier studies have suggested that cell deformation may mediate alterations in matrix synthesis (Jeon et al., 2013; Bader and Knight, 2008) and cell deformation is known to activate regulatory mechanisms involving, for example, various forms of stretch-sensitive ion channels in the cell membrane (Ramage et al., 2009; Chowdhury et al., 2008). The deposition of PCM around chondrocytes shield the chondrocytes from direct loading, thereby minimising the risk of cell death (Appelman et al., 2011), although, it is frequently observed that the collagen and proteoglycan upregulation in engineered cartilage constructs is small (Di Federico et al., 2017; Davisson et al., 2002; Jin et al., 2001). However, by maintaining the level of cell/membrane deformation with culture time, despite the generation of the protective PCM, the mechanotransduction mechanisms which underpin the up-regulation of ECM, in particular the collagen component, might be sustained.
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Journal Pre-proof Thus, the use of predictive FE models may play a critical role in developing appropriate culture regimens for cartilage tissue engineering by producing substantial insight into how chondrocytes within constructs remodel their local environment in order to redistribute mechanical signals. The developed FE models could be essential in determining how to vary the applied mechanical load during culture time to ensure that the stimulation of cells in the construct remains sufficient and appropriate for the development of functional tissues. This provides value to the further development of an intelligent bioreactor (Schultz et al 2008), which is sensitive to the measurement
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of both metabolic activity and could incorporate a feedback loop to inform the appropriate
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mechanical stimulation to ensure the most effective evolution of tissue engineered cartilage.
CONCLUSION
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Computational modelling represents a valuable addition to the experimental approach employed in
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recent studies (Di Federico et al., 2017) in that it can both interpret biological responses and predict critical parameters, such as cell deformation, which are difficult to estimate experimentally.
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The study describes the successful development and implementation of a model which simulates the
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experimental culture system (Di Federico et al., 2017). It has enabled the accurate prediction of cell deformations in 3 planes as a result of the mechanical loading regimen applied to the construct and the location of chondrocytes within it. This method can inform further insight into the mechanisms by which cell deformation, determined by external mechanical stimuli, is related to the resulting chondrocyte synthetic activity, enabling future studies to investigate the role of cell deformation in mechanotransduction. Considerable advantages may be derived by the application of FE models in the definition of appropriate mechanical conditioning regimes aimed to up-regulate the ECM synthesis and organisation, while addressing the structural and mechanical adaptation of the chondrocytes to those different stimuli. The present computational approach represents the first to account for the
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Journal Pre-proof effects of different loading regimens and of the cell location within the sample on the deformation modalities of chondrocytes embedded in different morphologies of agarose constructs.
Acknowledgements
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The support of Orthopaedic Research UK is gratefully acknowledged.
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Journal Pre-proof References
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Journal Pre-proof Figure captions Figure 1. Meshed cylindrical agarose construct model with (A) and without (B) impermeable metal loading plates. Meshed dumbell shaped agarose construct with (D) and without (E) nylon loading cup holders. Schematic drawing indicating the location of the chondrocytes (red dots) in Model 1, the cylindrical construct geometry (C) and in Model 2, the dumbell shaped agarose construct (F). Dimensions of meshed chondrocyte and pericellular matrix (PCM) (G). Figure 2. Comparison of predicted stress vs. time curve obtained from the simulated stress-relaxation test (Model 1A) and the average curve of five sets of experimentally determined data (A). Contour of the pore fluid effective velocity (FLVEL, mm/s) vector within the cylindrical geometry employed in Model 1A at different step times of the simulated stress-relaxation test (B). Insets indicate local directions of FLVEL in selected regions.
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Figure 3. Comparison of predicted stress vs. time curve obtained from the simulated dynamic compression test (Model 1A) and the average curve of five sets of experimentally determined data (A). Contour of the pore fluid effective velocity (FLVEL, mm/s) vector within the cylindrical geometry employed in Model 1A at different step times of the simulated dynamic compression test (B). Insets indicate local directions of FLVEL in selected regions.
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Figure 4. Comparison of predicted stress vs. time curve obtained from the simulated stress-relaxation test (Model 2A) and the average curve of five sets of experimentally determined data (A). Contour of the pore fluid effective velocity (FLVEL, mm/s) vector within the dumbbell geometry employed in Model 2A at different step times of the simulated stress-relaxation test (B). Insets indicate local directions of FLVEL in selected regions in six time points.
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Figure 5. Continuum maps of the y/z diameter ratio as a function of cell position in the dumbbell construct, following application of compressive strain (0 – 25 %) and shear strain (0 – 10 %) using Model 2B. The maps were generated using cells within the core of the agarose geometry (0 mm < z < 2 mm and -5 mm < y < 5mm).
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Figure 6. Comparison of the mean diameter ratios (y/z and z/x) as a function of the cell position in the dumbbell construct, after application of 15% compression alone and with 10% shear strain superimposed. The simulations were modelled using Model 2 (chondrocyte with no PCM, red) and (chondrocyte with PCM, green). Figure 7. Comparison of the diameter ratios (y/z and z/x) as a function of the cells position in the dumbbell construct, following the application of 15% compression and two bi-axial loading regimens (10% shear strain superimposed on 15% compressive strain), B & C. The simulations were modelled using Model 2B.
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Table 1. Model components and implemented simulations.
Geometry
MODEL 1
Model ID
Chondrocyte
PCM
A
✗
✗
B
✓
✗
A
✗
✗
Cylindrical
✓
B MODEL 2
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Dumbell C
1
Simulations
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rn ✓
✓
J
Stress-relaxation test1 Dynamic compression test2
Stress-relaxation test1
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e
r P ✗
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Stress-relaxation test1 Stress-relaxation test1 Compression (0 - 25%) with 0 - 10% superimposed shear2,3 15% compression 15% compression and 10% shear
20% compressive strain applied at a ramp rate of 20%/min and dwell period of 10 minutes. 2 Sinusoidal displacement between 0 and 1 mm of the top plate at a frequency of 1 Hz for 20 cycles. 3 Shear and Compression both applied using different waveforms (Figure 7)
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Table 2. Mechanical (Tab 2A) and physical (Tab 2B) properties employed in the numerical simulations.
Table 2A Agarose
Nylon
316L SS
Chondrocyte
PCM
3.2 kPa†
40 kPa
0.4††
0.04 †††
90 kPa
2.8 GPa
(GPa) Poisson ratio
0.49
0.4
485 GPa 0.3
Density (g/mL)
1.64
1.14
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Mechanical property Young’s modulus
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5·10-12†
Porosity
97%††††
Void ratio
33
Saturation
1 21
-
††† (Alexopoulos et al.,
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† (Tasci et al., 2011) †† (Ofek et al. 2009; Knight et al., 2002) 2005) †††† (Gu et al., 2002)
-
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Fluid (water) bulk moduli (k Pa) Fluid (water) specific weight (N/m3)
9731
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†††† (Gu et al., 2002)
Table 3. Mean (± standard deviation) cell diameter along x, y and z directions and associated diameter ratios calculated at the end of the simulated loading regimes. Values determined in the internal region of the construct (Figure 1F). Diameter (μm)
Diameter ratio
x
y
z
y/x
z/x
y/z
Model 1 Stress-relaxation
11.20 ± 0.01
8.00 ± 0.01
11.20 ± 0.01
0.71 ± 0.001
1.00 ± 0.001
0.71 ± 0.001
Model 2 Stress-relaxation
10.24 ± 0.476
9.32 ± 0.734
10.25 ± 0.491
0.92 ± 0.106
1.00 ± 0.017
0.92 ± 0.107
Model 2 15% dynamic compressive strain
10.12 ± 0.165
9.62 ± 0.282
10.20 ± 0.188
0.95± 0.041
1.00 ± 0.012
0.94 ± 0.043
Model 2 15% dynamic
10.10 ± 0.184
9.60 ± 0.275
10.10 ± 0.170
0.95 ± 0.041
1.00 ± 0.024
0.96 ± 0.035
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compressive strain & 10% shear strain
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Journal Pre-proof Highlights
FE models can predict chondrocyte deformation in constructs under static and dynamic loading
Superposition of shear on compression does not produce significant changes in cell deformation Pericellular matrix resulting from cell activity reduces chondrocyte deformation
Modelling highlights the importance of cell deformation in mechanotransduction
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Modelling offers the potential of optimising the development of functional cartilage
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pathways
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Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7