TISSUE ENGINEERING: Part A Volume 20, Numbers 9 and 10, 2014 ª Mary Ann Liebert, Inc. DOI: 10.1089/ten.tea.2013.0345
Influence of the Temporal Deposition of Extracellular Matrix on the Mechanical Properties of Tissue-Engineered Cartilage Mehdi Khoshgoftar, PhD, Wouter Wilson, PhD, Keita Ito, MD, ScD, and Corrinus C. van Donkelaar, PhD
Enhancement of the load-bearing capacity of tissue-engineered (TE) cartilage is expected to improve the clinical outcome of implantations. Generally, cartilage TE studies aim to increase the total extracellular matrix (ECM) content to improve implant mechanical properties. Besides the ECM content, however, temporal variations in deposition rate of ECM components during culture may also have an effect. Using a computational approach, the present study aims to quantify possible effects of temporal variations in the deposition of glycosaminoglycan (GAG) at given collagen synthesis rates on the mechanical stiffness of cartilage TE constructs. Maturation of a cylindrical cartilage TE construct over 42 days of culture was simulated using a composition-based finite element model that accounted for the transient deposition of GAG and collagen. Results showed an effect of GAG deposition rate on the swelling behavior and the collagen network strain, which resulted in significant changes in the compressive stiffness of cartilage TE constructs. When collagen deposition was first allowed in the constructs while the GAG deposition was delayed for the first 2 or 4 weeks, the collagen more effectively restricted tissue swelling later during the culture. Consequently, while the ultimate amount of ECM at day 42 was identical between the constructs, those with delayed GAG deposition contained elevated internal osmotic swelling pressure (up to 48%). This increased the compressive stiffness (up to 60%) of cartilage TE constructs at day 42. These findings clarify similar, yet unexplained, experimental observations. By providing further insights into mechanical effects inside cartilage TE constructs, these analyses are expected to help in designing culture regimes for engineering TE cartilage with improved load-bearing properties.
Introduction
D
amage of the cartilage in articular joints is associated with pain and may lead to disability in affected patients.1 To restore joint functionality, replacing damaged cartilage with tissue-engineered (TE) cartilage is promising.2–5 However, the mid- to long-term clinical outcome is to be improved. Enhancement of the mechanical properties of TE cartilage implants may improve the long-term loadbearing capacity of these implants in vivo and lead to more satisfying implantations in clinical practice. Generally, cartilage TE studies aim to increase the extracellular matrix (ECM) content, as this is thought to determine the loadbearing properties of the cartilage.6–11 Besides the ECM content, variations in temporal deposition of ECM components during culture may have an effect on the mechanical functionality of TE cartilage.12,13 The mechanical equilibrium state of TE cartilage during culture depends on the balance between osmotic swelling pressure induced by negatively charged glycosaminoglycans (GAGs) immobilized in proteoglycans (PGs), and stress in the ECM, mainly in the col-
lagen fibrils. Swelling and increasing total amount of ECM over time result in construct growth. In addition, the increasing amount of ECM and the internal swelling pressure stiffen the constructs. These effects occur at the same time, but GAG and collagen deposition may occur at different rates.9,12 Generally, GAG deposition precedes collagen synthesis. Therefore, swelling is more prominent in the beginning of the engineering process, while collagen reinforcement occurs later. The effects that variations in such deposition rate could have on the mechanical functionality of cartilage TE constructs are not fully understood. It has been shown that temporary depletion of GAG content with chondroitinase ABC (CABC), which depolymerizes chondroitin and dermatan sulfate and thereby depletes GAG content,14 improves the mechanical properties of cartilage TE constructs.12 However, these effects were dependent to the culture period during which CABC was applied. When CABC was added from day 14 to 28, at day 42 of the culture the stiffness of the construct was significantly enhanced in contrast to that when CABC was applied from day 0 to 28. Since CABC changed both the time course of GAG accumulation and the total amount of GAG and collagen
Orthopaedic Biomechanics, Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
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in the constructs, the exclusive effect of the relative depletion or deposition rate of GAG and collagen on the mechanical properties of TE constructs remained unclear. We postulate that alteration in the deposition rates of GAG and collagen changes the balance between osmotic pressure and tension in the collagen fibrils as follows. Collagen fibrils (and other biomolecules) are assumed to be synthesized and incorporated locally into the ECM in their individual stress-free configurations.15,16 Collagen fibrils stretched beyond their stress-free configuration will bear load, while a fibril that is shortened with respect to this configuration will not. Rapid deposition of GAG compared to that of collagen during cartilage TE may lead to high strains in early deposited collagen fibrils while those fibrils that are produced at later stages remain unstrained. In contrast, if GAG synthesis is delayed early in the culture, then collagen fibers may first be synthesized in the construct. Later on in the culture, when GAG synthesis is also allowed, fibrils already present in the constructs contribute to the mechanical performance of the tissue by resisting against excessive swelling induced by GAGs. Whether this theoretical effect is quantitatively significant is however unclear. Therefore, it is the aim of this study to quantify effects of temporal variations in the GAG deposition on the osmotic swelling behavior and overall mechanical stiffness of cartilage TE constructs. As this is challenging to do experimentally, this objective is approached using a computational framework that accounts for the transient deposition of GAG and collagen, to simulate the maturation of a TE construct over time. By providing further insights into the internal mechanical conditions of cartilage TE constructs during culture, such as osmotic swelling pressure and collagen network strain field, these analyses are expected to help in improving the mechanical quality of TE cartilage. Materials and Methods General approach
A three-study design was used. The intention in study 1 was to establish the finite element (FE) framework to predict maturation of a TE construct during culture, including expansion and stiffening as a result of osmotic swelling and matrix synthesis. Study 2 explored whether simulations could predict similar effects of GAG content depletion on the mechanical properties of the constructs as those ob-
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served in experiments.12 Study 3 evaluated whether modulation of the rate of GAG deposition with respect to the collagen synthesis rate may increase or decrease the mechanical stiffness of cartilage TE constructs even though it contains the same amount of GAG and collagen. In study 1, GAG and collagen contents of the control cases were adopted from the measurements by Mauck et al.9 and Bian et al.,12 respectively (Fig. 1). Using these data as the input parameters for FE analysis, Young’s modulus of the constructs were calculated and compared with those achieved in the experiments. In study 2, GAG and collagen contents were adopted from the measurements by Bian et al.12 in which GAG content was depleted for 2 weeks from day 14 to 28 (weeks 2–4) and for 4 weeks from day 0 to 28 (weeks 1–4) (Fig. 2). FE calculations of Young’s modulus were compared with those measured in the experiments. Based on the study of Bian et al.,12 compared with the control case, GAG depletion not only altered the rate of the GAG deposition but also changed the total GAG and collagen contents. To explore the exclusive effect of GAG deposition rate rather than that combined with changes in the ECM content, study 3 was designed. Here, the total ECM content in all simulations was the same at day 42, but the rate of the GAG deposition was modulated. Therefore, for the case where GAG was depleted from day 14 to 28 (weeks 2–4), GAG content between day 14 and 28 was kept identical to day 14, and from day 28 to 42 there was a stepwise increase in GAG content to the control value at day 42. For the case where GAG was depleted for 4 weeks from day 0 to 28 (weeks 1–4), GAG content after day 28 was equal to those in the control case. GAG depletion did not change collagen content during culture, which was therefore identical in all simulations (Fig. 3). Further, in the experiments by Bian et al.,12 the 2-week GAG depletion was designed to start from day 14 to 28 during culture. To explore what would be the effect if GAG depletion was started from the beginning of the culture and ends at day 14, an additional case (weeks 1–2) was included in study 3 (Fig. 3). Material model
A composition-based material model for cartilage TE constructs that included the descriptions for agarose gel scaffold, swelling induced by GAGs, and fibril reinforcement by collagen was used.13,17 The governing stress equation was as follows:
FIG. 1. Glycosaminoglycan (GAG) content (a) and collagen content (b) in control cases measured in the experiments by Bian et al.12 and by Mauck et al.9 Here, these data were used as the input parameter of finite element (FE) simulations in study 1.
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FIG. 2. GAG content (a) and collagen content (b) measured in the experiments by Bian et al.12 where GAG content was depleted for 2 weeks from day 14 to 28 (weeks 2–4) and for 4 weeks from day 0 to 28 (weeks 1– 4). Here, these data were used as the input parameter of FE simulations in study 2.
!!
totf f
rtot ¼ l I þ ns, 0
1 nagr þ + !
totf
þ nagr ragr þ + i¼1
nicol ricol
i¼1
nicol
rpgm (1)
DpI
where lf was the water chemical potential, Dp was the osmotic pressure gradient, I was the unit tensor, ns,0 was the initial solid volume fraction with respect to the total initial volume, nagr was the volume fraction of the agarose ground substance with respect to the total solid volume, ragr was the stress in the agarose ground substance, rpgm was the stress in the nonfibrillar PG matrix, ricol was the fibril stress in the ith fibril direction, nicol was the volume fraction of the collagen fibrils with respect to the total solid volume, i was the number of the fibril compartment, and totf was the total number of the fibrils. For more details on the material models of agarose, nonfibrillar PG matrix, and collagen fibrils, the reader is referred to Khoshgoftar et al.17,18 and Wilson et al.19–21 Here, the mathematical description of the osmotic swelling pressure gradient, calculations of the volume fractions, and implementation of the temporal ECM deposition are described. Osmotic swelling pressure. The osmotic pressure gradient Dp as a result of the fixed negative charge concentration in GAGs was given by22,23
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c 2 2 Dp ¼ /int RT c2F, exf þ 4 ext 2 cext 2/ext RTcext c int
(2)
The external salt concentration (cext) was 0.15 M, the temperature (T) was 310 K, and the gas constant (R) was 8.3145 N$m/mmol. Effective fixed charge density cF,exf based on the extra-fibrillar fluid fraction was given by cF, exf ¼
nf cF nexf
(3)
with nf the total fluid fraction, nexf the extra-fibrillar fluid fraction, and cF the normal fixed charge density in mEq per mL total fluid. Fixed charge density cF was expressed as a function of the tissue deformation as follows: cF ¼ cF, 0
nf , 0 nf , 0 1 þ J
(4)
Where nf,0 was the initial fluid fraction and cF,0 was the initial fixed charge density. Further details about determining the extrafibrillar fluid fraction, osmotic coefficient (/a), and activity coefficient (ca) can be found in Wilson et al.20 and Huyghe et al.23 Temporal ECM deposition. A previously developed material model17,20 was extended to account for temporal
FIG. 3. GAG content (a) and collagen content (b) as input parameter in study 3, where GAG content was kept constant for 2 weeks from day 14 to 28 (weeks 2–4), for 4 weeks from day 0 to 28 (weeks 1–4), and for 2 weeks from day 0 to 14 (weeks 1–4). GAG contents before and/or after the GAG depletion period were equal to those in the control case (Fig. 1). GAG depletion did not change the collagen content.
ECM TEMPORAL DEPOSITION AND MECHANICS OF TE CARTILAGE
FIG. 4. Schematic overview of the extracellular matrix (ECM) deposition model. Vagr was the agarose volume, Vf was the fluid volume, and VECM was the ECM volume, that is, the sum of VGAG and Vcol. effects that originate from transient deposition of GAG and collagen, similar to the approach previously chosen for modeling the deposition of ECM constituents.24 Deposition of ECM during cartilage TE was assumed to be homogenous and was modeled by updating the GAG and collagen contents per day of culture, that is, per time-step in the simulation. Tissue synthesis was then incorporated as follows. Newly synthesized collagen (DVcol ) or GAG (DVGAG ) volumes during a given day were added to the total collagen (Vcol (t)) or GAG (VGAG (t)) present at that day: VGAG (t þ 1) ¼ VGAG (t) þ DVGAG Vcol (t þ 1) ¼ Vcol (t) þ DVcol
(5)
The resulting increase in total solid content was compensated for by an artificial decrease in the fluid content, such that the total volume remained constant (Fig. 4). As a consequence of the increased GAG content and the loss of fluid, the fixed charges per fluid volume in the tissue were increased. To re-equilibrate the tissue, this was followed by a free swelling step in which the tissue was rehydrated, and therefore the fluid fraction and the total tissue volume increased. Thus, without introducing an additional growth tensor into the constitutive equations,25–27 the tissue grows and expands naturally because matrix is synthesized. During tissue development over time, it was assumed that the GAG and collagen that were synthesized in a particular day would be incorporated locally into the ECM in a stress-free configuration.15,16,28 Therefore, the deformation of the new ECM was considered zero at the day or time step in which they were synthesized. The constituents would only become strained upon further growth of the
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tissue, or when external loading would be applied. Also, collagen fibrils were assumed to form a quasi-isotropic matrix. At each integration point 13 fibrils were included: 3 running in the directions of the orthogonal axis, 6 running in directions between those axes with 45 from each of the two orthogonal axes in each plane, and 4 running in the spatial directions in between the orthogonal axes with 60 from each axis (Fig. 5a).19 When collagen content was updated, the added collagen content was equally divided between all fibril directions at each integration point. The logarithmic fiber strain was calculated as follows: ef ¼ log F ~ e f , 0
(6)
where F was the deformation gradient tensor and ~ ef , 0 was the initial fiber direction. Input parameters. The input parameters in Equation (1) for calculating the total tissue stress at each culture day were the initial (i.e., at the beginning of each culture day) solid volume fraction ns,0 with respect to the total initial volume Vtot,0, the volume fraction of collagen ncol and agarose ground substance nagr with respect to the total initial solid volume Vs,0, and the initial fixed charge density cF,0 to compute the osmotic pressure gradient Dp using Equations (2–4). For each culture day, collagen bcol and GAG bGAG wetweight fractions (ww%) were calculated from experiments. For this, experimental data for GAG and collagen wet-weight fractions were linearly interpolated between days 0, 14, 28, and 42 at which they were measured.9,12 Based on the calculated wet-weight fractions at each culture day, the volume of collagen Vcol and GAG VGAG in a construct with initial total volume Vtot,0 and total mass mtot was calculated as follows:
mcol q · Vcol ¼ col 0Vcol (t) mtot qtot · Vtot, 0 q · Vtot, 0 ¼ bcol · tot qcol mGAG qGAG · VGAG bGAG ¼ ¼ 0VGAG mtot qtot · Vtot, 0 q · Vtot, 0 ¼ bGAG · tot qGAG bcol ¼
(7)
with qtot construct mass density, mcol and mGAG collagen and GAG mass, and qcol and qGAG collagen and GAG mass density, respectively. Mass density of collagen and GAG
FIG. 5. Collagen fiber orientations at an arbitrary integration point in the matrix (a) and size and boundary conditions in the axisymmetric model of a cylindrical cartilage tissue-engineered construct (b).
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was assumed to be 1.4 mg/mm3,21,29,30 and total mass density of the construct was assumed to be 1.02 mg/mm3 with negligible variations during the culture.31 Total solid volume Vs,0 at the beginning of each culture day was then calculated as follows: Vs, 0 ¼ Vagr þ Vcol þ VGAG
(9)
Vf , 0 nf , 0 ¼ Vtot, 0 and the initial solid fraction ns,0 with respect to total initial volume was then calculated as follows: ns, 0 ¼ 1 nf , 0
(10)
Collagen, GAG, and agarose volume fractions with respect to total solid matrix volume were calculated as follows: totf
ncol ¼ + nicol ¼ i¼1
Vcol Vs, 0
VGAG Vs, 0 nagr ¼ 1 (ncol þ nGAG ) nGAG ¼
ZCS · 0:77 ZKS · 0:23 mGAG · cF, 0 ¼ þ MWCS MWKS Vf , 0
(8)
where Vagr was volume of the solid agarose gel in the construct that was assumed to be constant during culture and equaled 2% of the total initial volume of the construct, that is, equal to the concentration of agarose used in the experiments from which input data are derived in the present study.9,12 Assuming biphasic saturation, initial fluid volume and fluid fraction at the current day were given as follows: Vf , 0 ¼ Vtot, 0 Vs, 0
To calculate the initial fixed charge density cF,0, it was assumed that GAGs contained 77% chondroitin sulfate (CS) and 23% keratan sulfate (KS).32 Initial fixed charge density was then calculated as follows:
(11)
where nGAG was the volume fraction of GAG with respect to total solid matrix volume.
(12)
with valencies zCS = 2 (mEq/mmol) and zKS = 1 (mEq/mmol) and molecular weights MWCS = 0.513 (g/mmol) and MWKS = 0.464 (g/mmol).32 Initial parameters of cell-seeded agarose constructs and material parameters of PG matrix and collagen fibers are summarized in Table 1. FE simulations
The finite element method (FEM) was used to solve the equations, and an axisymmetric FE mesh was created in ABAQUS (v6.9, Pawtucket, RI) (Fig. 5b). The height and radius of the FE mesh were 1.1 and 2.38 mm, respectively, similar to construct samples used in the literature.9,12 The nodal displacements of the nodes at the symmetry axis were confined in radial direction. The nodal displacements at the bottom plane were confined in the vertical direction. The material model was implemented in ABAQUS as a User Subroutine (UMAT). FEM simulations consisted of two parts. First, a culturing period was simulated in which daily ECM deposition was simulated. Following 0, 14, 28, or 42 days of free swelling culture, sample height was recorded and a 10% unconfined compression test was simulated to calculate equilibrium compressive Young’s modulus of the construct similar to the experimental data.9,12 During this mechanical test, in which the ECM content was constant, the mesh was first equilibrated under an axial compressive tare load of 0.02 N, followed by a stress relaxation test with a ramp displacement of 1 mm/s to 10% strain, based on the post tare load
Table 1. Initial Parameters of Cell-Seeded Agarose Constructs and Material Parameters of PG Matrix and Collagen Fibers Parameter Agarose construct Vtot,0 ns,0 nf,0 qss Eagra PG matrix qGAG Gma ZCS ZkS MWCS MWKS Collagen E1a K1a a
Description at day 0 Total initial volume Initial solid volume fraction Initial fluid fraction Construct mass density Agarose gel Young’s modulus GAG mass density Shear modulus Valency of chondroitin sulfate Valency of keratan sulfate Molecular weight of chondroitin sulfate Molecular weight of keratin sulfate Equilibrium modulus Strain dependency of the equilibrium modulus
Value (unit)
References
19.564 (mm3) 2% 98% 1.02 (mg/mm3) 0.015 (MPa)
Mauck et al.9 Mauck et al.9 Mauck et al.9 Kelly et al.31 Mauck et al.9
1.4 (mg/mm3)
Basser at al.29 Shapiro et al.30 Wilson et al.20 Narmoneva et al.32 Narmoneva et al.32 Narmoneva et al.32 Narmoneva et al.32
0.903 (MPa) 2.0 (mEq/mmol) 1.0 (mEq/mmol) 0.513 (g/mmol) 0.464 (g/mmol) 4.316 (MPa) 16.85
Mathematical equations for these parameters can be found in Khoshgoftar et al.13,17 and Wilson et al.19–21 GAG, glycosaminoglycan; PG, proteoglycan.
Wilson et al.20 Wilson et al.20
ECM TEMPORAL DEPOSITION AND MECHANICS OF TE CARTILAGE
thickness. After equilibrium was reached (2000 s), the compressive Young’s modulus was determined from the equilibrium response of the stress–relaxation test by dividing the equilibrium stress (minus the tare stress) by the applied strain.9 During the test, free fluid flow was allowed at the lateral edge of the construct. The FE mesh consisted of 2500 eight-node linear axisymmetric (2D) pore pressure elements (CAX8P). Mesh refinement was considered (Fig. 5b) close to the top surface (where compressive load is applied) and the periphery of the construct (where fluid was free to flow). This was important for achieving numerical convergence in the second part of the simulations where the mechanical test was simulated. In the first part of the simulations, where ECM deposition was simulated, the ECM deposition was assumed to occur homogeneously. Therefore, there was no difference in the ECM content and deposition rate between different integration points in the mesh. Results Study 1
Using GAG and collagen contents from the control case in the experimental study of Mauck et al.,9 the input parameters for the FEM simulations resulted in a Young’s modulus of 30, 38, and 59 kPa for the construct at days 14, 28, and 42, respectively. This was in agreement with the experimental data for all culture days (Fig. 6a). With GAG and collagen contents from the control case in the experimental study of Bian et al.,12 FEM simulations resulted in the Young’s modulus of 94, 277, and 281 kPa for the construct at days 14, 28, and 42, respectively. For days 14 and 28, there was a good agreement between FEM calculations and the experimental measurements, but the Young’s modulus at day 42 was lower than the 780 kPa measured12 (Fig. 6b). Study 2
Using GAG and collagen contents in a study where GAG was depleted from day 14 to 28,12 FEM calculations
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showed a substantial increase in the Young’s modulus from day 28 (99 kPa) to day 42 (561 kPa) (Fig. 7a), in agreement with the experimental data12 (Fig. 7b). Similar agreement was found when GAG was depleted during 4 weeks (Fig. 7a, b, weeks 1–4), which resulted in a lower Young’s modulus (81 kPa) compared with that in the control case (281 kPa). The pattern of changes in Young’s modulus (Fig. 7a) corresponded to those of the osmotic swelling pressure (Fig. 7c), suggesting a major influence of the osmotic pressure on the compressive stiffness of the constructs. Osmotic swelling pressure resulting from the GAGs induced a tensile strain on the collagen fibrils, which resisted the internal swelling pressure in the constructs. Due to the gradual deposition of GAG and, therefore, a gradual increase in the osmotic swelling pressure, strain in the collagen fibrils varied depending on their age in the culture period. Moreover, during culture, newly synthesized collagen fibrils were deposited with zero strain. Therefore, by culture time, the average strain in the collagen network had decreased because younger fibrils were not extensively strained, whereas older fibrils were. When GAG content was depleted from day 14 to 28, because of the reduced total osmotic swelling pressure, the maximum strain in the collagen fibrils reached 5.1%, whereas with continuous GAG depletion it reached only 1%. Here, strains of those fibrils that were deposited during culture in the radial direction of the construct are shown as the representative strain in the collagen fibril network (Fig. 7d). The strain in the fibrils deposited in other directions showed similar trends (data not shown). Study 3
Our FEM calculations showed that compared with the control case (shown in Fig. 7a), continuous depletion of GAG content in the first 2 weeks or first 4 weeks of culture initially decreased the Young’s modulus at day 28 and then increased the Young’s modulus of the construct by 75% and 81% at day 42, respectively (Fig. 8a). Our model suggests that the influence of GAG depletion from day 14 to 28 on
FIG. 6. Finite element method (FEM) results for Young’s modulus compared to those measured in the experiments by Mauck et al.9 (a) and those measured in the experiments by Bian et al.12 (b).
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FIG. 7. FEM results (a) and experimental measurements by Bian et al.12 (b) for Young’s modulus, and FEM calculation for osmotic swelling pressure (c) and representative strain in the collagen network during culture (d). GAG and collagen contents were taken from the experimental data of Bian et al.12
FIG. 8. Young’s modulus (a) and osmotic swelling pressure (b) during culture calculated in FEM simulations, where GAG depletion only changed the rate of GAG deposition rate and it did not change the total GAG and collagen content before or after the depletion period.
ECM TEMPORAL DEPOSITION AND MECHANICS OF TE CARTILAGE
enhancing the Young’s modulus at day 42 (297 kPa) compared with the control case (281 kPa) was not substantial. The changes of the Young’s modulus corresponded to those of the osmotic swelling pressure (Fig. 8b). Discussion
The present study introduces an approach to simulate TE cartilage development over time, which uses synthesized GAG and collagen contents as input parameters. Using this approach, which results in realistic tissue development (study 1), we showed that by modulating the deposition ratio of GAG versus collagen over time, the mechanical properties of TE cartilage constructs can be improved (study 2), in agreement with experimental data.12 In these experiments, however, GAG depletion from day 14 to 28 increases the total collagen content, whereas continuous depletion of GAG for 4 weeks of culture decreases the collagen content. The present numerical model allows selective adjustment of the deposition ratio between GAG and collagen, while ensuring that total GAG and collagen contents at day 42 of culture are identical between simulations. Our model suggests that indeed the stiffness of TE cartilage constructs improves as a consequence of the changes in matrix deposition rate, independent of the total matrix content (study 3). Consistent with previous findings in the literature, it is worth mentioning that reasonably both our and Nagel and Kelly’s33 studies share a conclusion that cartilage TE construct with enhanced compressive stiffness may be achieved by finding cues to further elevate internal osmotic swelling pressure of the constructs. Importantly, the computational approach exposes the underlying mechanism that explains this observation. Our model suggests that it is mainly associated with the interplay between osmotic swelling pressure and the strain field in the collagen network. When collagen deposition is first allowed in the TE constructs while the GAG deposition is delayed, less swelling occurs in the first period of culture. Therefore, the strain in the collagen fibrils remains low and more homogeneous than when the tissue swells gradually over time. When GAG is produced in the second stage of the culture, the collective fibers are more effective in resisting the internal osmotic swelling pressure. This results in less total swelling of the construct. As a consequence, the same amount of GAG is located in a smaller volume and therefore the resulting osmotic swelling pressure is higher. The osmotic pressure correlates closely with the effective tissue stiffness (Figs. 7a, c and 8). Consistent with previous findings in the literature,33 these results suggest that cartilage TE construct with enhanced compressive stiffness may be achieved by finding cues to further elevate internal osmotic swelling pressure of the constructs. The differences in collagen content depending on the duration of CABC treatment have been speculated to result from inhibiting effects of CABC on the beneficial effects of transforming growth factor (TGF)-b. However, an alternative explanation is proposed here. Our model suggests that when GAGs are depleted for the 4 initial weeks of culture, the strain in the collagen fibers remains low (studies 2 and 3). It is known that collagen is more susceptible to enzymatic degradation at strains below 4%.34–36 Therefore, synthesized collagen may have been degraded under
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low strain conditions that persist when CABC treatment is prolonged. The composition-based approach to account for temporal effects of the transient deposition of GAG and collagen during TE culture is promising, because it uses measurable collagen and GAG amounts over time as direct input. Also, the computed increase in tissue stiffness over time is in good agreement with the reference TE experiments, except for one single data point.12 In addition, the total increase in volume concurred with the experimental data [19% (Bian et al.12) vs. 16% (simulations) after 6 weeks of culture]. Although a good match between model predictions and most experimental data is obtained, after 42 days of culture with TGF-b supplementation, samples were stiffer in the experiments12 than that our model predicted. One explanation may be that the distribution of ECM in these constructs has changed from one in which islands of matrix are separated by scaffold material into one in which these islands coalesce. This is likely to occur after long-term culture and with TGF-b supplementation, which is known to produce more equally distributed matrix in TE constructs.37 Nonlinear effects caused by such changes in internal matrix distribution have been discussed elsewhere17,38,39 and are outside the scope of the present study. While the general agreements between the numerical predictions and the experimental measurements enforce the confidence in the present approach, refinement of the model and further quantitative validation is possible. For instance, mechanical properties of collagen and GAGs and their swelling behavior are chosen identical to those of mature cartilage,20–21 which may not be the case in immature constructs. Other examples of effects that were not yet accounted for, but have been included in former models and may be incorporated in the future, are effects of growth factors or nutrients,38 mechanical loading,18 and ECM diffusion.39 Because there is no evidence of collagen fiber reorganization in cartilage TE constructs during free swelling culture,31 in the present study collagen fibers were assumed to remain randomly oriented. When addressing loaded TE constructs where substantial collagen reorganization may occur, collagen remodeling algorithms28,40 may provide useful insights. In conclusion, the present article introduces a promising numerical approach to simulate TE cartilage development. This model is adopted to evaluate and explain the experimental observation that temporal GAG depletion during culture may result in stiffening of the ultimate TE cartilage construct.12 This insight in the effect of matrix synthesis rates on construct stiffness may help improving culturing regimes for TE cartilage, and the present model may be considered a valuable tool for designing optimized cartilage TE experiments. This is another step toward developing TE cartilage with native mechanical properties. Acknowledgment
This study was supported with funding from the Dutch Technology Foundation STW (VIDI-07970). Disclosure Statement
No competing financial interests exist.
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1. Buckwalter, J.A., Saltzman, C., and Brown, T. The impact of osteoarthritis: implications for research. Clin Orthop 427, S6, 2004. 2. Risbud, M.V., and Sittinger, M. Tissue engineering: advances in in vitro cartilage generation. Trends Biotechnol 20, 351, 2002. 3. Kuo, C.K., Li, W.J., Mauck, R.L., and Tuan, R.S. Cartilage tissue engineering: its potential and uses. Curr Opin Rheum 18, 64, 2006. 4. Nesic, D., Whiteside, R., Brittberg, M., et al. Cartilage tissue engineering for degenerative joint disease. Adv Drug Deliv Rev 58, 300, 2006. 5. Noth, U., Steinert, A.F., and Tuan, R.S. Technology insight: adult mesenchymal stem cells for osteoarthritis therapy. Nat Clin Pract Rheum 4, 371, 2008. 6. Carver, S.E., and Heath, C.A. Influence of intermittent pressure, fluid flow, and mixing on the regenerative properties of articular chondrocytes. Biotechnol Bioeng 65, 274, 1999. 7. Vunjak-Novakovic, G., Martin, I., Obradovic, B., et al. Bioreactor cultivation conditions modulate the composition and mechanical properties of tissue-engineered cartilage. J Orthop Res 17, 130, 1999. 8. Mauck, R.L., Soltz, M.A., Wang, C.C., et al. Functional tissue engineering of articular cartilage through dynamic loading of chondrocyte-ceeded agarose gels. J Biomech Eng 122, 252, 2000. 9. Mauck, R.L., Wang, C.C-B., Oswald, E.S., et al. The role of cell seeding density and nutrient supply for articular cartilage tissue engineering with deformational loading. Osteoarthritis Cartilage 11, 879, 2003. 10. Lima, E.G., Bian, L., Ng, K.W., et al. The beneficial effect of delayed compressive loading on tissue-engineered cartilage constructs cultured with TGF-beta3. Osteoarthritis Cartilage 15, 1025, 2007. 11. Kock, L.M., Van Donkelaar, C.C., and Ito, K. Tissue engineering of functional articular cartilage: the current status. Cells Tissue Res 347, 613, 2012. 12. Bian, L., Crivello, K.M., Ng, K.W., et al. Influence of temporary chondroitinase ABC-induced glycosaminoglycan suppression on maturation of tissue-engineered cartilage. Tissue Eng Part A 15, 2065, 2009. 13. Khoshgoftar, M., Wilson, W., Ito, K., and van Donkelaar, C.C. The effect of tissue-engineered cartilage biomechanical and biochemical properties on its post-implantation mechanical behavior. Biomech Model Mechanobiol 12, 43, 2013. 14. Yamagata, T., Saito, H., Habuchi, O., et al. Purification and properties of bacterial chondroitinases and chondrosulfatases. J Biol Chem 243, 1523, 1968. 15. Humphrey, J.D., and Rajagopal, K.R. A constrained mixture model for growth and remodeling of soft tissues. Math Model Meth Appl Sci 12, 407, 2002. 16. Garikipati, K., Olberdingb, J.E., and Narayananc, H. Biological remodeling: stationary energy, configurational change, internal variables and dissipation. J Mech Phys Solid 54, 1493, 2006. 17. Khoshgoftar, M., Wilson, W., Ito, K., and van Donkelaar, C.C. Influence of tissue- and cell-scale extracellular matrix distribution on the mechanical properties of tissueengineered cartilage. Biomech Model Mechanobiol 12, 901, 2013.
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18. Khoshgoftar, M., van Donkelaar, C.C., and Ito, K. Mechanical stimulation to stimulate formation of physical collagen architecture in tissue-engineered cartilage; a numerical study. Comput Methods Biomech Biomed Engin 14, 135, 2011. 19. Wilson, W., Van Donkelaar, C.C., Van Rietbergen, B., et al. Stresses in the local collagen network of articular cartilage: a poroviscoelastic fibril-reinforced finite element study. J Biomech 37, 357, 2004. 20. Wilson, W., Huyghe, J.M., and Van Donkelaar, C.C. A composition-based cartilage model for the assessment of compositional changes during cartilage damage and adaptation. Osteoarthritis Cartilage 14, 554, 2006. 21. Wilson, W., Huyghe, J.M., and Van Donkelaar, C.C. Depth-dependent compressive equilibrium properties of articular cartilage explained by its composition. Biomech Model Mechanobiol 6, 43, 2007. 22. Huyghe, J.M., and Janssen, J.D. Quadriphasic theory of swelling incompressible porous media. Int J Eng Sci 35, 793, 1997. 23. Huyghe, J.M., Houben, G.B., Drost, M.R., and van Donkelaar, C.C. An ionised/non-ionised dual porosity model of intervertebral disc tissue. Biomech Model Mechanobiol 2, 3, 2003. 24. van Donkelaar, C.C., and Wilson, W. Mechanics of chondrocyte hypertrophy. Biomech Model Mechanobiol 11, 655, 2012. 25. Klisch, S.M., Chen, S.S., and Sah, R.L. A growth mixture theory for cartilage with application to growth-related experiments on cartilage explants. J Biomech Eng 125, 169, 2003. 26. Ficklin, T.P., Davol, A., and Klisch, S.M. Simulating the growth of articular cartilage explants in a permeation bioreactor to aid in experimental protocol design. J Biomech Eng 131, 041008, 2009. 27. Davol, A., Bingham, M.S., Sah, R.L., and Klisch, S.M. A nonlinear finite element model of cartilage growth. Biomech Model Mechanobiol 7, 295, 2008. 28. Nagel, T., and Kelly, D.J. Remodeling of collagen fibre transition stretch and angular distribution in soft biological tissues and cell-seeded hydrogels. Biomech Model Mechanobiol 11, 325, 2012. 29. Basser, P.J., Schneiderman, R., Bank, R.A., et al. Mechanical properties of the collagen network in human articular cartilage as measured by osmotic stress technique. Arch Biochem Biophys 351, 207, 1998. 30. Shapiro, E.M., Borthakur, A., Kaufman, J.H., et al. Water distribution patterns inside bovine articular cartilage as visualized by 1H magnetic resonance imaging. Osteoarthritis Cartilage 6, 533, 2001. 31. Kelly, T.A.N., Ng, K.W., Wang, C.C., et al. Spatial and temporal development of chondrocyte-seeded agarose constructs in free-swelling and dynamically loaded cultures. J Biomech 39, 1489, 2006. 32. Narmoneva, D.A., Wang, J.Y., and Setton, L.A. Nonuniform swelling-induced residual strains in articular cartilage. J Biomech 32, 401, 1999. 33. Nagel, T., and Kelly, D.J. Altering the swelling pressures within in vitro engineered cartilage is predicted to modulate the configuration of the collagen network and hence improve tissue mechanical properties. J Mech Behav Biomed Mater 22, 22, 2013. 34. Huang, C., and Yannas, I.V. Mechanochemical studies of enzymatic degradation of unsoluble collagen fibers. J Biomed Mater Res 11, 137, 1977.
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35. Nabeshima, Y., Grood, E.S., Sakurai, A., and Herman, J.H. Uniaxial tension inhibits tendon collagen degradation by collagenase in vitro. J Orthop Res 14, 123, 1996. 36. Ruberti, J.W., and Hallab, N.J. Strain-controlled enzymatic cleavage of collagen in loaded matrix. Biochem Biophys Res Commun 336, 483, 2005. 37. Kock, L.M., Geraedts, J., Ito, K., and van Donkelaar, C.C. Low agarose concentration and TGF-b3 distribute extracellular matrix in tissue-engineered cartilage. Tissue Eng Part A 19, 1621, 2013. 38. Sengers, B.G., Taylor, M., Please, C.P., and Oreffoa, R.O.C. Computational modelling of cell spreading and tissue regeneration in porous scaffolds. Biomaterials 28, 1926, 2007. 39. van Donkelaar, C.C., Chao, G.E., Bader, D.L., and Oomens, C.W.J. A reaction-diffusion model to predict the influence of neo-matrix on the subsequent development of tissue engineered cartilage. Comput Methods Biomech Biomed Engin 14, 425, 2011.
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40. Wilson, W., Driessen, N.J.B., van Donkelaar, C.C., and Ito, K. Prediction of collagen orientation in articular cartilage by a collagen remodeling algorithm. Osteoarthritis Cartilage 14, 1196, 2006.
Address correspondence to: Corrinus C. van Donkelaar, PhD Orthopaedic Biomechanics Department of Biomedical Engineering Eindhoven University of Technology PO Box 513 Eindhoven 5600 MB The Netherlands E-mail: [email protected] Received: June 9, 2013 Accepted: December 4, 2013 Online Publication Date: April 14, 2014
Influence of the Temporal Deposition of Extracellular Matrix on the Mechanical Properties of Tissue-Engineered Cartilage Mehdi Khoshgoftar, PhD, Wouter Wilson, PhD, Keita Ito, MD, ScD, and Corrinus C. van Donkelaar, PhD
Enhancement of the load-bearing capacity of tissue-engineered (TE) cartilage is expected to improve the clinical outcome of implantations. Generally, cartilage TE studies aim to increase the total extracellular matrix (ECM) content to improve implant mechanical properties. Besides the ECM content, however, temporal variations in deposition rate of ECM components during culture may also have an effect. Using a computational approach, the present study aims to quantify possible effects of temporal variations in the deposition of glycosaminoglycan (GAG) at given collagen synthesis rates on the mechanical stiffness of cartilage TE constructs. Maturation of a cylindrical cartilage TE construct over 42 days of culture was simulated using a composition-based finite element model that accounted for the transient deposition of GAG and collagen. Results showed an effect of GAG deposition rate on the swelling behavior and the collagen network strain, which resulted in significant changes in the compressive stiffness of cartilage TE constructs. When collagen deposition was first allowed in the constructs while the GAG deposition was delayed for the first 2 or 4 weeks, the collagen more effectively restricted tissue swelling later during the culture. Consequently, while the ultimate amount of ECM at day 42 was identical between the constructs, those with delayed GAG deposition contained elevated internal osmotic swelling pressure (up to 48%). This increased the compressive stiffness (up to 60%) of cartilage TE constructs at day 42. These findings clarify similar, yet unexplained, experimental observations. By providing further insights into mechanical effects inside cartilage TE constructs, these analyses are expected to help in designing culture regimes for engineering TE cartilage with improved load-bearing properties.
Introduction
D
amage of the cartilage in articular joints is associated with pain and may lead to disability in affected patients.1 To restore joint functionality, replacing damaged cartilage with tissue-engineered (TE) cartilage is promising.2–5 However, the mid- to long-term clinical outcome is to be improved. Enhancement of the mechanical properties of TE cartilage implants may improve the long-term loadbearing capacity of these implants in vivo and lead to more satisfying implantations in clinical practice. Generally, cartilage TE studies aim to increase the extracellular matrix (ECM) content, as this is thought to determine the loadbearing properties of the cartilage.6–11 Besides the ECM content, variations in temporal deposition of ECM components during culture may have an effect on the mechanical functionality of TE cartilage.12,13 The mechanical equilibrium state of TE cartilage during culture depends on the balance between osmotic swelling pressure induced by negatively charged glycosaminoglycans (GAGs) immobilized in proteoglycans (PGs), and stress in the ECM, mainly in the col-
lagen fibrils. Swelling and increasing total amount of ECM over time result in construct growth. In addition, the increasing amount of ECM and the internal swelling pressure stiffen the constructs. These effects occur at the same time, but GAG and collagen deposition may occur at different rates.9,12 Generally, GAG deposition precedes collagen synthesis. Therefore, swelling is more prominent in the beginning of the engineering process, while collagen reinforcement occurs later. The effects that variations in such deposition rate could have on the mechanical functionality of cartilage TE constructs are not fully understood. It has been shown that temporary depletion of GAG content with chondroitinase ABC (CABC), which depolymerizes chondroitin and dermatan sulfate and thereby depletes GAG content,14 improves the mechanical properties of cartilage TE constructs.12 However, these effects were dependent to the culture period during which CABC was applied. When CABC was added from day 14 to 28, at day 42 of the culture the stiffness of the construct was significantly enhanced in contrast to that when CABC was applied from day 0 to 28. Since CABC changed both the time course of GAG accumulation and the total amount of GAG and collagen
Orthopaedic Biomechanics, Department of Biomedical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands.
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in the constructs, the exclusive effect of the relative depletion or deposition rate of GAG and collagen on the mechanical properties of TE constructs remained unclear. We postulate that alteration in the deposition rates of GAG and collagen changes the balance between osmotic pressure and tension in the collagen fibrils as follows. Collagen fibrils (and other biomolecules) are assumed to be synthesized and incorporated locally into the ECM in their individual stress-free configurations.15,16 Collagen fibrils stretched beyond their stress-free configuration will bear load, while a fibril that is shortened with respect to this configuration will not. Rapid deposition of GAG compared to that of collagen during cartilage TE may lead to high strains in early deposited collagen fibrils while those fibrils that are produced at later stages remain unstrained. In contrast, if GAG synthesis is delayed early in the culture, then collagen fibers may first be synthesized in the construct. Later on in the culture, when GAG synthesis is also allowed, fibrils already present in the constructs contribute to the mechanical performance of the tissue by resisting against excessive swelling induced by GAGs. Whether this theoretical effect is quantitatively significant is however unclear. Therefore, it is the aim of this study to quantify effects of temporal variations in the GAG deposition on the osmotic swelling behavior and overall mechanical stiffness of cartilage TE constructs. As this is challenging to do experimentally, this objective is approached using a computational framework that accounts for the transient deposition of GAG and collagen, to simulate the maturation of a TE construct over time. By providing further insights into the internal mechanical conditions of cartilage TE constructs during culture, such as osmotic swelling pressure and collagen network strain field, these analyses are expected to help in improving the mechanical quality of TE cartilage. Materials and Methods General approach
A three-study design was used. The intention in study 1 was to establish the finite element (FE) framework to predict maturation of a TE construct during culture, including expansion and stiffening as a result of osmotic swelling and matrix synthesis. Study 2 explored whether simulations could predict similar effects of GAG content depletion on the mechanical properties of the constructs as those ob-
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served in experiments.12 Study 3 evaluated whether modulation of the rate of GAG deposition with respect to the collagen synthesis rate may increase or decrease the mechanical stiffness of cartilage TE constructs even though it contains the same amount of GAG and collagen. In study 1, GAG and collagen contents of the control cases were adopted from the measurements by Mauck et al.9 and Bian et al.,12 respectively (Fig. 1). Using these data as the input parameters for FE analysis, Young’s modulus of the constructs were calculated and compared with those achieved in the experiments. In study 2, GAG and collagen contents were adopted from the measurements by Bian et al.12 in which GAG content was depleted for 2 weeks from day 14 to 28 (weeks 2–4) and for 4 weeks from day 0 to 28 (weeks 1–4) (Fig. 2). FE calculations of Young’s modulus were compared with those measured in the experiments. Based on the study of Bian et al.,12 compared with the control case, GAG depletion not only altered the rate of the GAG deposition but also changed the total GAG and collagen contents. To explore the exclusive effect of GAG deposition rate rather than that combined with changes in the ECM content, study 3 was designed. Here, the total ECM content in all simulations was the same at day 42, but the rate of the GAG deposition was modulated. Therefore, for the case where GAG was depleted from day 14 to 28 (weeks 2–4), GAG content between day 14 and 28 was kept identical to day 14, and from day 28 to 42 there was a stepwise increase in GAG content to the control value at day 42. For the case where GAG was depleted for 4 weeks from day 0 to 28 (weeks 1–4), GAG content after day 28 was equal to those in the control case. GAG depletion did not change collagen content during culture, which was therefore identical in all simulations (Fig. 3). Further, in the experiments by Bian et al.,12 the 2-week GAG depletion was designed to start from day 14 to 28 during culture. To explore what would be the effect if GAG depletion was started from the beginning of the culture and ends at day 14, an additional case (weeks 1–2) was included in study 3 (Fig. 3). Material model
A composition-based material model for cartilage TE constructs that included the descriptions for agarose gel scaffold, swelling induced by GAGs, and fibril reinforcement by collagen was used.13,17 The governing stress equation was as follows:
FIG. 1. Glycosaminoglycan (GAG) content (a) and collagen content (b) in control cases measured in the experiments by Bian et al.12 and by Mauck et al.9 Here, these data were used as the input parameter of finite element (FE) simulations in study 1.
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FIG. 2. GAG content (a) and collagen content (b) measured in the experiments by Bian et al.12 where GAG content was depleted for 2 weeks from day 14 to 28 (weeks 2–4) and for 4 weeks from day 0 to 28 (weeks 1– 4). Here, these data were used as the input parameter of FE simulations in study 2.
!!
totf f
rtot ¼ l I þ ns, 0
1 nagr þ + !
totf
þ nagr ragr þ + i¼1
nicol ricol
i¼1
nicol
rpgm (1)
DpI
where lf was the water chemical potential, Dp was the osmotic pressure gradient, I was the unit tensor, ns,0 was the initial solid volume fraction with respect to the total initial volume, nagr was the volume fraction of the agarose ground substance with respect to the total solid volume, ragr was the stress in the agarose ground substance, rpgm was the stress in the nonfibrillar PG matrix, ricol was the fibril stress in the ith fibril direction, nicol was the volume fraction of the collagen fibrils with respect to the total solid volume, i was the number of the fibril compartment, and totf was the total number of the fibrils. For more details on the material models of agarose, nonfibrillar PG matrix, and collagen fibrils, the reader is referred to Khoshgoftar et al.17,18 and Wilson et al.19–21 Here, the mathematical description of the osmotic swelling pressure gradient, calculations of the volume fractions, and implementation of the temporal ECM deposition are described. Osmotic swelling pressure. The osmotic pressure gradient Dp as a result of the fixed negative charge concentration in GAGs was given by22,23
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi c 2 2 Dp ¼ /int RT c2F, exf þ 4 ext 2 cext 2/ext RTcext c int
(2)
The external salt concentration (cext) was 0.15 M, the temperature (T) was 310 K, and the gas constant (R) was 8.3145 N$m/mmol. Effective fixed charge density cF,exf based on the extra-fibrillar fluid fraction was given by cF, exf ¼
nf cF nexf
(3)
with nf the total fluid fraction, nexf the extra-fibrillar fluid fraction, and cF the normal fixed charge density in mEq per mL total fluid. Fixed charge density cF was expressed as a function of the tissue deformation as follows: cF ¼ cF, 0
nf , 0 nf , 0 1 þ J
(4)
Where nf,0 was the initial fluid fraction and cF,0 was the initial fixed charge density. Further details about determining the extrafibrillar fluid fraction, osmotic coefficient (/a), and activity coefficient (ca) can be found in Wilson et al.20 and Huyghe et al.23 Temporal ECM deposition. A previously developed material model17,20 was extended to account for temporal
FIG. 3. GAG content (a) and collagen content (b) as input parameter in study 3, where GAG content was kept constant for 2 weeks from day 14 to 28 (weeks 2–4), for 4 weeks from day 0 to 28 (weeks 1–4), and for 2 weeks from day 0 to 14 (weeks 1–4). GAG contents before and/or after the GAG depletion period were equal to those in the control case (Fig. 1). GAG depletion did not change the collagen content.
ECM TEMPORAL DEPOSITION AND MECHANICS OF TE CARTILAGE
FIG. 4. Schematic overview of the extracellular matrix (ECM) deposition model. Vagr was the agarose volume, Vf was the fluid volume, and VECM was the ECM volume, that is, the sum of VGAG and Vcol. effects that originate from transient deposition of GAG and collagen, similar to the approach previously chosen for modeling the deposition of ECM constituents.24 Deposition of ECM during cartilage TE was assumed to be homogenous and was modeled by updating the GAG and collagen contents per day of culture, that is, per time-step in the simulation. Tissue synthesis was then incorporated as follows. Newly synthesized collagen (DVcol ) or GAG (DVGAG ) volumes during a given day were added to the total collagen (Vcol (t)) or GAG (VGAG (t)) present at that day: VGAG (t þ 1) ¼ VGAG (t) þ DVGAG Vcol (t þ 1) ¼ Vcol (t) þ DVcol
(5)
The resulting increase in total solid content was compensated for by an artificial decrease in the fluid content, such that the total volume remained constant (Fig. 4). As a consequence of the increased GAG content and the loss of fluid, the fixed charges per fluid volume in the tissue were increased. To re-equilibrate the tissue, this was followed by a free swelling step in which the tissue was rehydrated, and therefore the fluid fraction and the total tissue volume increased. Thus, without introducing an additional growth tensor into the constitutive equations,25–27 the tissue grows and expands naturally because matrix is synthesized. During tissue development over time, it was assumed that the GAG and collagen that were synthesized in a particular day would be incorporated locally into the ECM in a stress-free configuration.15,16,28 Therefore, the deformation of the new ECM was considered zero at the day or time step in which they were synthesized. The constituents would only become strained upon further growth of the
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tissue, or when external loading would be applied. Also, collagen fibrils were assumed to form a quasi-isotropic matrix. At each integration point 13 fibrils were included: 3 running in the directions of the orthogonal axis, 6 running in directions between those axes with 45 from each of the two orthogonal axes in each plane, and 4 running in the spatial directions in between the orthogonal axes with 60 from each axis (Fig. 5a).19 When collagen content was updated, the added collagen content was equally divided between all fibril directions at each integration point. The logarithmic fiber strain was calculated as follows: ef ¼ log F ~ e f , 0
(6)
where F was the deformation gradient tensor and ~ ef , 0 was the initial fiber direction. Input parameters. The input parameters in Equation (1) for calculating the total tissue stress at each culture day were the initial (i.e., at the beginning of each culture day) solid volume fraction ns,0 with respect to the total initial volume Vtot,0, the volume fraction of collagen ncol and agarose ground substance nagr with respect to the total initial solid volume Vs,0, and the initial fixed charge density cF,0 to compute the osmotic pressure gradient Dp using Equations (2–4). For each culture day, collagen bcol and GAG bGAG wetweight fractions (ww%) were calculated from experiments. For this, experimental data for GAG and collagen wet-weight fractions were linearly interpolated between days 0, 14, 28, and 42 at which they were measured.9,12 Based on the calculated wet-weight fractions at each culture day, the volume of collagen Vcol and GAG VGAG in a construct with initial total volume Vtot,0 and total mass mtot was calculated as follows:
mcol q · Vcol ¼ col 0Vcol (t) mtot qtot · Vtot, 0 q · Vtot, 0 ¼ bcol · tot qcol mGAG qGAG · VGAG bGAG ¼ ¼ 0VGAG mtot qtot · Vtot, 0 q · Vtot, 0 ¼ bGAG · tot qGAG bcol ¼
(7)
with qtot construct mass density, mcol and mGAG collagen and GAG mass, and qcol and qGAG collagen and GAG mass density, respectively. Mass density of collagen and GAG
FIG. 5. Collagen fiber orientations at an arbitrary integration point in the matrix (a) and size and boundary conditions in the axisymmetric model of a cylindrical cartilage tissue-engineered construct (b).
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was assumed to be 1.4 mg/mm3,21,29,30 and total mass density of the construct was assumed to be 1.02 mg/mm3 with negligible variations during the culture.31 Total solid volume Vs,0 at the beginning of each culture day was then calculated as follows: Vs, 0 ¼ Vagr þ Vcol þ VGAG
(9)
Vf , 0 nf , 0 ¼ Vtot, 0 and the initial solid fraction ns,0 with respect to total initial volume was then calculated as follows: ns, 0 ¼ 1 nf , 0
(10)
Collagen, GAG, and agarose volume fractions with respect to total solid matrix volume were calculated as follows: totf
ncol ¼ + nicol ¼ i¼1
Vcol Vs, 0
VGAG Vs, 0 nagr ¼ 1 (ncol þ nGAG ) nGAG ¼
ZCS · 0:77 ZKS · 0:23 mGAG · cF, 0 ¼ þ MWCS MWKS Vf , 0
(8)
where Vagr was volume of the solid agarose gel in the construct that was assumed to be constant during culture and equaled 2% of the total initial volume of the construct, that is, equal to the concentration of agarose used in the experiments from which input data are derived in the present study.9,12 Assuming biphasic saturation, initial fluid volume and fluid fraction at the current day were given as follows: Vf , 0 ¼ Vtot, 0 Vs, 0
To calculate the initial fixed charge density cF,0, it was assumed that GAGs contained 77% chondroitin sulfate (CS) and 23% keratan sulfate (KS).32 Initial fixed charge density was then calculated as follows:
(11)
where nGAG was the volume fraction of GAG with respect to total solid matrix volume.
(12)
with valencies zCS = 2 (mEq/mmol) and zKS = 1 (mEq/mmol) and molecular weights MWCS = 0.513 (g/mmol) and MWKS = 0.464 (g/mmol).32 Initial parameters of cell-seeded agarose constructs and material parameters of PG matrix and collagen fibers are summarized in Table 1. FE simulations
The finite element method (FEM) was used to solve the equations, and an axisymmetric FE mesh was created in ABAQUS (v6.9, Pawtucket, RI) (Fig. 5b). The height and radius of the FE mesh were 1.1 and 2.38 mm, respectively, similar to construct samples used in the literature.9,12 The nodal displacements of the nodes at the symmetry axis were confined in radial direction. The nodal displacements at the bottom plane were confined in the vertical direction. The material model was implemented in ABAQUS as a User Subroutine (UMAT). FEM simulations consisted of two parts. First, a culturing period was simulated in which daily ECM deposition was simulated. Following 0, 14, 28, or 42 days of free swelling culture, sample height was recorded and a 10% unconfined compression test was simulated to calculate equilibrium compressive Young’s modulus of the construct similar to the experimental data.9,12 During this mechanical test, in which the ECM content was constant, the mesh was first equilibrated under an axial compressive tare load of 0.02 N, followed by a stress relaxation test with a ramp displacement of 1 mm/s to 10% strain, based on the post tare load
Table 1. Initial Parameters of Cell-Seeded Agarose Constructs and Material Parameters of PG Matrix and Collagen Fibers Parameter Agarose construct Vtot,0 ns,0 nf,0 qss Eagra PG matrix qGAG Gma ZCS ZkS MWCS MWKS Collagen E1a K1a a
Description at day 0 Total initial volume Initial solid volume fraction Initial fluid fraction Construct mass density Agarose gel Young’s modulus GAG mass density Shear modulus Valency of chondroitin sulfate Valency of keratan sulfate Molecular weight of chondroitin sulfate Molecular weight of keratin sulfate Equilibrium modulus Strain dependency of the equilibrium modulus
Value (unit)
References
19.564 (mm3) 2% 98% 1.02 (mg/mm3) 0.015 (MPa)
Mauck et al.9 Mauck et al.9 Mauck et al.9 Kelly et al.31 Mauck et al.9
1.4 (mg/mm3)
Basser at al.29 Shapiro et al.30 Wilson et al.20 Narmoneva et al.32 Narmoneva et al.32 Narmoneva et al.32 Narmoneva et al.32
0.903 (MPa) 2.0 (mEq/mmol) 1.0 (mEq/mmol) 0.513 (g/mmol) 0.464 (g/mmol) 4.316 (MPa) 16.85
Mathematical equations for these parameters can be found in Khoshgoftar et al.13,17 and Wilson et al.19–21 GAG, glycosaminoglycan; PG, proteoglycan.
Wilson et al.20 Wilson et al.20
ECM TEMPORAL DEPOSITION AND MECHANICS OF TE CARTILAGE
thickness. After equilibrium was reached (2000 s), the compressive Young’s modulus was determined from the equilibrium response of the stress–relaxation test by dividing the equilibrium stress (minus the tare stress) by the applied strain.9 During the test, free fluid flow was allowed at the lateral edge of the construct. The FE mesh consisted of 2500 eight-node linear axisymmetric (2D) pore pressure elements (CAX8P). Mesh refinement was considered (Fig. 5b) close to the top surface (where compressive load is applied) and the periphery of the construct (where fluid was free to flow). This was important for achieving numerical convergence in the second part of the simulations where the mechanical test was simulated. In the first part of the simulations, where ECM deposition was simulated, the ECM deposition was assumed to occur homogeneously. Therefore, there was no difference in the ECM content and deposition rate between different integration points in the mesh. Results Study 1
Using GAG and collagen contents from the control case in the experimental study of Mauck et al.,9 the input parameters for the FEM simulations resulted in a Young’s modulus of 30, 38, and 59 kPa for the construct at days 14, 28, and 42, respectively. This was in agreement with the experimental data for all culture days (Fig. 6a). With GAG and collagen contents from the control case in the experimental study of Bian et al.,12 FEM simulations resulted in the Young’s modulus of 94, 277, and 281 kPa for the construct at days 14, 28, and 42, respectively. For days 14 and 28, there was a good agreement between FEM calculations and the experimental measurements, but the Young’s modulus at day 42 was lower than the 780 kPa measured12 (Fig. 6b). Study 2
Using GAG and collagen contents in a study where GAG was depleted from day 14 to 28,12 FEM calculations
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showed a substantial increase in the Young’s modulus from day 28 (99 kPa) to day 42 (561 kPa) (Fig. 7a), in agreement with the experimental data12 (Fig. 7b). Similar agreement was found when GAG was depleted during 4 weeks (Fig. 7a, b, weeks 1–4), which resulted in a lower Young’s modulus (81 kPa) compared with that in the control case (281 kPa). The pattern of changes in Young’s modulus (Fig. 7a) corresponded to those of the osmotic swelling pressure (Fig. 7c), suggesting a major influence of the osmotic pressure on the compressive stiffness of the constructs. Osmotic swelling pressure resulting from the GAGs induced a tensile strain on the collagen fibrils, which resisted the internal swelling pressure in the constructs. Due to the gradual deposition of GAG and, therefore, a gradual increase in the osmotic swelling pressure, strain in the collagen fibrils varied depending on their age in the culture period. Moreover, during culture, newly synthesized collagen fibrils were deposited with zero strain. Therefore, by culture time, the average strain in the collagen network had decreased because younger fibrils were not extensively strained, whereas older fibrils were. When GAG content was depleted from day 14 to 28, because of the reduced total osmotic swelling pressure, the maximum strain in the collagen fibrils reached 5.1%, whereas with continuous GAG depletion it reached only 1%. Here, strains of those fibrils that were deposited during culture in the radial direction of the construct are shown as the representative strain in the collagen fibril network (Fig. 7d). The strain in the fibrils deposited in other directions showed similar trends (data not shown). Study 3
Our FEM calculations showed that compared with the control case (shown in Fig. 7a), continuous depletion of GAG content in the first 2 weeks or first 4 weeks of culture initially decreased the Young’s modulus at day 28 and then increased the Young’s modulus of the construct by 75% and 81% at day 42, respectively (Fig. 8a). Our model suggests that the influence of GAG depletion from day 14 to 28 on
FIG. 6. Finite element method (FEM) results for Young’s modulus compared to those measured in the experiments by Mauck et al.9 (a) and those measured in the experiments by Bian et al.12 (b).
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FIG. 7. FEM results (a) and experimental measurements by Bian et al.12 (b) for Young’s modulus, and FEM calculation for osmotic swelling pressure (c) and representative strain in the collagen network during culture (d). GAG and collagen contents were taken from the experimental data of Bian et al.12
FIG. 8. Young’s modulus (a) and osmotic swelling pressure (b) during culture calculated in FEM simulations, where GAG depletion only changed the rate of GAG deposition rate and it did not change the total GAG and collagen content before or after the depletion period.
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enhancing the Young’s modulus at day 42 (297 kPa) compared with the control case (281 kPa) was not substantial. The changes of the Young’s modulus corresponded to those of the osmotic swelling pressure (Fig. 8b). Discussion
The present study introduces an approach to simulate TE cartilage development over time, which uses synthesized GAG and collagen contents as input parameters. Using this approach, which results in realistic tissue development (study 1), we showed that by modulating the deposition ratio of GAG versus collagen over time, the mechanical properties of TE cartilage constructs can be improved (study 2), in agreement with experimental data.12 In these experiments, however, GAG depletion from day 14 to 28 increases the total collagen content, whereas continuous depletion of GAG for 4 weeks of culture decreases the collagen content. The present numerical model allows selective adjustment of the deposition ratio between GAG and collagen, while ensuring that total GAG and collagen contents at day 42 of culture are identical between simulations. Our model suggests that indeed the stiffness of TE cartilage constructs improves as a consequence of the changes in matrix deposition rate, independent of the total matrix content (study 3). Consistent with previous findings in the literature, it is worth mentioning that reasonably both our and Nagel and Kelly’s33 studies share a conclusion that cartilage TE construct with enhanced compressive stiffness may be achieved by finding cues to further elevate internal osmotic swelling pressure of the constructs. Importantly, the computational approach exposes the underlying mechanism that explains this observation. Our model suggests that it is mainly associated with the interplay between osmotic swelling pressure and the strain field in the collagen network. When collagen deposition is first allowed in the TE constructs while the GAG deposition is delayed, less swelling occurs in the first period of culture. Therefore, the strain in the collagen fibrils remains low and more homogeneous than when the tissue swells gradually over time. When GAG is produced in the second stage of the culture, the collective fibers are more effective in resisting the internal osmotic swelling pressure. This results in less total swelling of the construct. As a consequence, the same amount of GAG is located in a smaller volume and therefore the resulting osmotic swelling pressure is higher. The osmotic pressure correlates closely with the effective tissue stiffness (Figs. 7a, c and 8). Consistent with previous findings in the literature,33 these results suggest that cartilage TE construct with enhanced compressive stiffness may be achieved by finding cues to further elevate internal osmotic swelling pressure of the constructs. The differences in collagen content depending on the duration of CABC treatment have been speculated to result from inhibiting effects of CABC on the beneficial effects of transforming growth factor (TGF)-b. However, an alternative explanation is proposed here. Our model suggests that when GAGs are depleted for the 4 initial weeks of culture, the strain in the collagen fibers remains low (studies 2 and 3). It is known that collagen is more susceptible to enzymatic degradation at strains below 4%.34–36 Therefore, synthesized collagen may have been degraded under
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low strain conditions that persist when CABC treatment is prolonged. The composition-based approach to account for temporal effects of the transient deposition of GAG and collagen during TE culture is promising, because it uses measurable collagen and GAG amounts over time as direct input. Also, the computed increase in tissue stiffness over time is in good agreement with the reference TE experiments, except for one single data point.12 In addition, the total increase in volume concurred with the experimental data [19% (Bian et al.12) vs. 16% (simulations) after 6 weeks of culture]. Although a good match between model predictions and most experimental data is obtained, after 42 days of culture with TGF-b supplementation, samples were stiffer in the experiments12 than that our model predicted. One explanation may be that the distribution of ECM in these constructs has changed from one in which islands of matrix are separated by scaffold material into one in which these islands coalesce. This is likely to occur after long-term culture and with TGF-b supplementation, which is known to produce more equally distributed matrix in TE constructs.37 Nonlinear effects caused by such changes in internal matrix distribution have been discussed elsewhere17,38,39 and are outside the scope of the present study. While the general agreements between the numerical predictions and the experimental measurements enforce the confidence in the present approach, refinement of the model and further quantitative validation is possible. For instance, mechanical properties of collagen and GAGs and their swelling behavior are chosen identical to those of mature cartilage,20–21 which may not be the case in immature constructs. Other examples of effects that were not yet accounted for, but have been included in former models and may be incorporated in the future, are effects of growth factors or nutrients,38 mechanical loading,18 and ECM diffusion.39 Because there is no evidence of collagen fiber reorganization in cartilage TE constructs during free swelling culture,31 in the present study collagen fibers were assumed to remain randomly oriented. When addressing loaded TE constructs where substantial collagen reorganization may occur, collagen remodeling algorithms28,40 may provide useful insights. In conclusion, the present article introduces a promising numerical approach to simulate TE cartilage development. This model is adopted to evaluate and explain the experimental observation that temporal GAG depletion during culture may result in stiffening of the ultimate TE cartilage construct.12 This insight in the effect of matrix synthesis rates on construct stiffness may help improving culturing regimes for TE cartilage, and the present model may be considered a valuable tool for designing optimized cartilage TE experiments. This is another step toward developing TE cartilage with native mechanical properties. Acknowledgment
This study was supported with funding from the Dutch Technology Foundation STW (VIDI-07970). Disclosure Statement
No competing financial interests exist.
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Address correspondence to: Corrinus C. van Donkelaar, PhD Orthopaedic Biomechanics Department of Biomedical Engineering Eindhoven University of Technology PO Box 513 Eindhoven 5600 MB The Netherlands E-mail: [email protected] Received: June 9, 2013 Accepted: December 4, 2013 Online Publication Date: April 14, 2014
