Hydraulic permeability of multilayered collagen gel scaffolds under plastic compression-induced unidirectional fluid flow

Acta Biomaterialia 9 (2013) 4673–4680

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Hydraulic permeability of multilayered collagen gel scaffolds under plastic compression-induced unidirectional fluid flow Vahid Serpooshan a, Thomas M. Quinn b, Naser Muja a, Showan N. Nazhat a,⇑ a b

Department of Mining and Materials Engineering, McGill University, MH Wong Building, 3610 University Street, Montreal, Quebec, Canada H3A 0C5 Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, Quebec, Canada H3A 0C5

a r t i c l e

i n f o

Article history: Received 22 December 2011 Received in revised form 1 August 2012 Accepted 20 August 2012 Available online 1 September 2012 Keywords: Microstructure Hydraulic permeability Ultrafiltration Collagen lamella Darcy’s law

a b s t r a c t Under conditions of free fluid flow, highly hydrated fibrillar collagen gels expel fluid and undergo gravity driven consolidation (self-compression; SC). This process can be accelerated by the application of a compressive stress (plastic compression; PC) in order to generate dense collagen scaffolds for tissue engineering. To define the microstructural evolution of collagen gels under PC, this study applied a two-layer micromechanical model that was previously developed to measure hydraulic permeability (k) under SC. Radially confined PC resulted in unidirectional fluid flow through the gel and the formation of a dense lamella at the fluid expulsion boundary which was confirmed by confocal microscopy of collagen immunoreactivity. Gel mass loss due to PC and subsequent SC were measured and applied to Darcy’s law to calculate the thickness of the lamella and hydrated layer, as well as their relative permeabilities. Increasing PC level resulted in a significant increase in mass loss fraction and lamellar thickness, while the thickness of the hydrated layer dramatically decreased. Permeability of lamella also decreased from 1.8  1015 to 1.0  1015 m2 in response to an increase in PC level. Ongoing SC, following PC, resulted in a uniform decrease in mass loss and k with increasing PC level and as a function SC time. Experimental k data were in close agreement with those estimated by the Happel model. Calculation of average k values for various two-layer microstructures indicated that they each approached 1015–1014 m2 at equilibrium. In summary, the two-layer micromechanical model can be used to define the microstructure and permeability of multi-layered biomimetic scaffolds generated by PC. Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

1. Introduction Control of the three-dimensional (3-D) fibrillar microstructure of collagen gel scaffolds is required for tissue engineering and biocompatible delivery systems [1–4]. However, in vitro reconstituted, highly hydrated collagen gels are characterized by a dominant volume fraction of unbound fluid [5,6]. Therefore, the hydraulic permeability (k) of these porous structures can significantly influence the mechanical properties (biphasic or poroviscoelastic theory) [7–9] and mass transfer characteristics (convection and diffusion of oxygen, nutrients and other macromolecules) [10,11] of constructs. A similar role of k has been reported for the control of interstitial fluid flow in tissues such as cartilage and bone [8,12,13]. Several experimental methods have been developed to assess the k (conductivity) of tissues and scaffold structures. For example, incorporation of the sedimentation velocity of physically entangled macromolecules in an aqueous solution during ultracentrifugation

⇑ Corresponding author. Tel.: +1 514 398 5524; fax: +1 514 398 4492. E-mail address: [email protected] (S.N. Nazhat).

into Darcy’s law has been used to measure the k of the sediment [10,14,15]. However, this approach is limited by the dilute concentration of macromolecules in aqueous solutions, scattered sedimentation velocity, reswelling of the sedimented polymer, and unaccounted buoyant and frictional forces [15,16]. Alternatively, the average k of hydrated scaffolds and tissues has been measured by incorporation of experimental creep deformation data of constructs, under confined compression, into a model for one-dimensional creep [17–19]. However, accurate evaluation of creep deformation in highly hydrated scaffolds is difficult due to their unstable physical structure [17,20,21]. Furthermore, the application of a pressure gradient to a porous construct and measurement of the resulting fluid flow velocity through the construct has been employed to measure k through Darcy’s law [22–24]. Yet, pressureinduced deformation and significant microstructural changes within highly hydrated constructs can cause substantial variations in the measured k [9,25]. This phenomenon is analogous to concentration polarization and cake layer (gel) formation during ultrafiltration of macromolecular solutions using permeable filters. In these experiments, fluid flow through the membrane can be described using Darcy’s law [26,27]. By applying the boundary conditions existing within the cake layer during ultrafiltration, the

1742-7061/$ - see front matter Ó 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.actbio.2012.08.031

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hydraulic resistance of the cake layer can be measured [9,26]. It is noteworthy that the formation of a dense collagen region during confined compression of collagen gels has been shown to locally increase the compressive stiffness and hydraulic resistance of hydrated gels, as well as diminish the fluid flow through the construct [9,28]. Previously, we reported a micromechanical model to describe fluid flow and k of hydrated collagen gels during radially confined self-compression (SC) [29]. Confined SC resulted in a unidirectional fluid flow through the gel, which transformed the highly hydrated gel without structural competence into a considerably dense lamella at the fluid expulsion boundary (FEB) (44-fold increase in solid volume fraction, r) with a significantly reduced k (100- to 1000-fold). Thereupon, as revealed by confocal and electron microscopy, a two-layer model, consisting of an upper highly hydrated collagen layer with a dense lamella at the bottom, was developed. The initial boundary conditions, along with the mass loss fraction data obtained from confined SC of collagen gels, were applied to Darcy’s law, to measure the k of the lamella. Since the two-layer model is best applied to measure the k of hydrated gels with uniform fibrillar structure, further development of this model is necessary in order to analyse more complex boundary conditions, such as the presence of a heterogeneous structure or an external stress through the application of plastic compression (PC). PC is a rapid method for generating extracellular matrix (ECM)-like dense collagen scaffolds for tissue engineering through fluid expulsion via the application of compressive stress on collagen gels. Therefore, a modified form of the two-layer model was employed to define the permeability of different collagen gel microstructures, produced by applying increasing levels of PC, followed by SC. Using this model, the microstructure and permeability of multi-layered scaffolds generated by PC can be defined. Such analysis would enable the development of a novel approach to measure the k of biomimetic collagen gels, developed as scaffolds and tissue equivalents. The modelling also allows for the precise control of the physical and mechanical properties in hydrated biomimetic scaffolds, and in the creation of bulkier (e.g. layered or rolled) heterogeneous structures.

gen gels were allowed to undergo SC at room temperature in a closed chamber maintained at 100% relative humidity (Fig. 1B). Confined SC allowed unidirectional fluid flow out of the gel, parallel to the direction of the driving force for flow (gravity, x direction in Fig. 1). The initial weight of the hydrated collagen gel was recorded (Mettler Toledo AL204, Canada) before and after PC and also monitored over time during SC up to 50 min, until equilibrium was reached. Thereupon, the mass loss fraction k(t) (the fraction of gel mass lost divided by the initial mass at casting) was measured for each gel specimen. The collagen volume fractions of highly hydrated collagen gel (rb) and lamella (rc) were determined as described previously [29], and found to be 0.0016 ± 0.0001 and 0.0708 ± 0.0043, respectively. A minimum of four replicate specimens were tested for all experimental conditions. Statistical analysis was performed using Student’s t-test to determine p-values at a significance level of 0.05. 2.3. Microscopic characterization of collagen gel microstructure undergoing plastic and self-compression Confocal laser scanning microscopy (CLSM; Carl Zeiss, LSM5 Exciter, Canada) was used to further investigate gel microstructure following either PC or SC. Gel specimen preparation for collagen fibril immunostaining was performed as described previously [29]. Briefly, after either 0 or 20 min of SC, collagen gels were fixed using a 4% formalin fixative and incubated overnight in phosphate-buffered saline (PBS) containing rabbit anti-rat collagen type I antibody (ab24133, 1 lg ml1, Abcam, USA). Gel specimens were then transferred to PBS containing 1 lg ml1 goat anti-rabbit polyclonal antibodies conjugated to Alexa488 (Invitrogen Inc, USA) for 2 h. Using a 20 objective, Z-stacks of fluorescent immunoreactivity towards collagen type I throughout the thickness of each specimen were acquired at 1 airy unit using a slice interval thickness of 15 lm. Maximum intensity projections and orthogonal images of collagen scaffolds were generated using NIH ImageJ v. 1.43. 2.4. Modelling of gel mechanics during plastic and self-compression

2. Materials and methods 2.1. Collagen gel preparation Collagen gel scaffolds were prepared by adding 0.8 ml of 10 Dulbecco’s modified Eagle’s medium to 3.2 ml of rat-tail type I collagen dissolved in acetic acid (2.10 mg ml1, First Link Ltd., UK). This solution was neutralized by initially introducing 70 ll of 5 M NaOH followed by the sequential addition of 0.5 ll of 1 M NaOH until physiological pH (7.4) was attained. Thereafter, 0.9 ml of the solution was pipetted into impermeable circular moulds (16 mm in diameter) and left for 30 min in an incubator to set at 37 °C. 2.2. Determination of mass loss following radially confined plastic and self-compression of collagen gels Cast collagen gels underwent radially confined PC by applying different static stresses of 0, 340, 690 and 1022 N m–2 (referred to as PC0, PC1, PC2 and PC3 respectively) for 2 min (Fig. 1A). Highly hydrated collagen gels were transferred to a saturated porous support consisting of (bottom to top) absorbent paper blot layers, stainless steel mesh and a polymer mesh. The wet substrate was maintained at the level of a water bath to allow for fluid flow. As shown in Fig. 1A, an impermeable polystyrene tube was used to laterally support the gel, inhibiting radial fluid flow. Post-PC, colla-

In concert with our previous study [29], a number of assumptions were made here in order to describe collagen gel PC using the two-layer model. A highly hydrated collagen gel without structural competence (zero stiffness) was assumed. Furthermore, the stiffness of the lamella was assumed to be high enough to prevent flow-induced deformation [15,26,30], i.e. the k of lamella was uniform [15,26]. Therefore, by applying a radially confined compressive stress, the gel undergoes compression (Fig. 1A), while the highly hydrated gel loses water and consolidates against FEB. The static compressive load and gravitational force are driving forces for!downstream fluid flow. This fluid loss results in a fluid velocity of U through the lamella. The cast gel was assumed to have uniform fibrillar density. Hence, the osmotic pressure gradient within each layer was zero. Accordingly, a two-layer model was developed to describe the PC of collagen gel, by modifying Darcy’s law to define the fluid flow through both the highly hydrated gel and the lamella, !

U¼

k

l

!

rðp þ qgxÞ

ð1Þ

where l is the fluid viscosity, p is the fluid pressure, q is the fluid density, g is the acceleration due to gravity and x defines the upwards vertical direction. By applying the existing boundary conditions under confined PC (Fig. 1A), we found:

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Fig. 1. Schematic representation of the experimental methods to study PC and SC of collagen gels. (A) Top panel; collagen gel PC was performed under radial confined conditions using an impermeable polystyrene tube over a wet porous substrate. A static load was applied on top of the gel for 2 min. Bottom panel: formation of a two-layer structure with a dense lamella (cake) at the FEB. (B) Top panel: the sequence of collagen gel SC due to gravity g over a wet porous substrate post-PC. Bottom panel: in the equilibrium state, only the lamella (cake layer) exists. (C) The conceptualization of collagen gel PC (left) and SC (right) in a two-layer model. PC involves compressive pressure-induced (PPC) and gravity-driven (g) fluid flow, and SC involves g-driven flow, through the surface at x = 0, where the gel is supported by a rigid porous substrate (the coordinate x represents the upwards vertical direction). The gel is initially cast at the relatively low solid volume fraction rb, then collapses into a lamella at x = 0 as fluid drains into a saturated cloth below the rigid porous support. The lamella has a time-dependent thickness c(t), a solid volume fraction rc and hydraulic permeability kc. The thickness of the upper highly hydrated gel layer is represented by b(t). At x = c + b, the fluid pressure has boundary conditions of p = Patm + PPC and p = Patm during PC and SC, respectively. At x = 0, fluid pressure p = Patm during both PC and SC (due to negligible flow resistance within the saturated cloth).

i. within the highly hydrated layer (c < x < b + c), U = 0 and p + qgx is constant (Eq. (1)); therefore: p þ qgx ¼ constant ¼ Patm þ P pc þ qgðc þ bÞ ii. at the interface between the two layers (x = c): p(c) = Patm + PPC + qgb; and iii. at the bottom surface of the gel x = 0: p(0) = Patm

the solid volume fractions of the lamella and highly hydrated gel layers, respectively. In this study, by insertion of k values measured after application of each PC level into Eqs. (3), corresponding c and b values were determined. Moreover, introducing Eqs. (3) into Eq. (2) provides a relationship between U and k: !

U :^ıx ¼  where Patm is the atmospheric pressure, PPC is the static compressive pressure applied by PC (340, 690 and 1022 N m2 for PC1, PC2 and PC3, respectively), and c and b are the thicknesses of the lamella and the highly hydrated gel layer, respectively. By applying the boundary conditions at x = 0 and x = c to Eq. (1), within the lamella ! kc qgðc þ bÞ þ Ppc U ¼ ^lx l c

  kc qg ð1  abÞ  ð1  aÞk kc PPC ð1  abÞ 1  k k la lb0 a

ð4Þ

Therefore, a governing equation for mass loss fraction during PC can be written as

  dk kc qgð1  abÞ ð1  abÞ  ð1  aÞk kc PPC ð1  abÞ2 1 þ ¼ dt k lb0 að1  aÞ lb20 að1  aÞ k

ð5Þ

ð3Þ

Integration of Eq. (5) over a time interval from t to t + Dt gives rise to an expression for k of the lamella during PC (K PC c ) as a function of k and other experimentally accessible parameters: " !   PC ð1  abÞð1 þ qPgb Þ  ð1  aÞkðtÞ lb0 a 1 P PC PC 0 ln Kc ¼ 1þ PC Dt qg 1  a qgb0 ð1  abÞð1 þ qPgb Þ  ð1  aÞkðt þ DtÞ 0  1 ½kðt þ DtÞ  kðtÞ ð6Þ  1  ab

where kðtÞ ¼ 1  bb0  bc0 qqc ; b0 is the gel thickness at casting b ((3.76 ± 0.19)  103 m, when c = 0), and a  rrbc and b  qqc are two b new constants, with qc and qb the densities of the lamella and highly hydrated gel layers, respectively. In addition, rc and rb are

Accordingly, by inserting experimental k values, measured after applying PC, into Eq. (6), K PC c was measured. Post-PC, the progress of collagen gel consolidation due to subsequent SC was modelled by incorporating the following new boundary conditions to our previously derived model [29]. A two-layer structure consisting of a highly hydrated gel layer and a lamella already existed prior to the onset of SC. Therefore, the final mass loss

ð2Þ

where ^lx represents a unit vector in the x direction. Taking into account fluid continuity during PC, and conservation of collagen within the compressing gel [29], c and b can be expressed in terms of mass loss fraction k(t)

b0 ak 1  ab b0 b¼ ½ð1  abÞ  k 1  ab

c¼

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fraction due to PC was used as the starting k(t) values in Eq. (7). Moreover, by inserting k values measured at different time intervals during SC into Eqs. (3), c(t) and b(t) values for each gel specimen were determined. K SC c ¼







lb0 a 1 ð1  abÞ  ð1  aÞkðtÞ 1 ln  ½kðt þ DtÞ  kðtÞ ð1  abÞ  ð1  aÞkðt þ DtÞ 1  ab D t qg 1  a



ð7Þ Measured kc values were imported into the Happel model [31] to predict collagen fibril hydraulic radius (a) for each gel specimen. Estimates of a were compared to scanning electron microscopy measurements in order to verify the conformity between the theory and experimental technique. 3. Results 3.1. Collagen gel mass loss due to plastic compression and subsequent self-compression Collagen gel mass loss due to radially confined PC and subsequent SC were measured and applied to Darcy’s law in order to measure the thickness of the lamella and hydrated gel layer, as well as their relative permeabilities. Application of 340 (PC1), 690 (PC2) or 1022 Nm–2 (PC3) compressive stress to highly hydrated collagen gels for 2 min resulted in a mass loss fraction of 0.69 ± 0.04, 0.82 ± 0.03 or 0.88 ± 0.02, respectively. Thereupon, collagen gels underwent confined SC, resulting in a continuous mass loss until reaching an equilibrium state (Fig. 2A). This was achieved after 40–50 min in PC0, 35–40 min in PC1, and 20–25 min in PC2 and PC3. The total k value obtained by SC was reduced in response to increased PC level. However, the final overall mass loss fractions calculated by summation of the k values of PC and SC for each gel specimen were approximately the same for all specimens, at 0.97 ± 0.01, 0.94 ± 0.04, 0.93 ± 0.05 and 0.93 ± 0.02%, for PC0, PC1, PC2 and PC3, respectively. 3.2. Microscopic characterization of collagen gel microstructure following PC and SC To study the microstructural changes following PC and SC, CLSM was carried out to detect immunoreactivity towards collagen type I throughout the gel thickness after confined PC (time 0 of SC, Fig. 3A) and after 20 min of confined SC (Fig. 3B). For direct comparison of collagen immunoreactivity between the two specimens, the fluorescence intensity in Fig. 3A and B was normalized according to that in Fig. 3A. Representative cross-sectional images (y  z

plane) of gel specimens, together with orthogonal images of the x  y and x  z planes, are shown for each sample. Applying PC resulted in the formation of a lamella exhibiting an increased amount of collagen immunoreactivity, indicative of higher fibrillar density at the FEB (Fig. 3A). Further SC of the PC2 specimen for 20 min resulted in an increase in lamellar thickness, while the thickness of the highly hydrated layer significantly decreased. The thickness of the lamella in the PC2 gel specimen pre- and post-SC was measured as 6.5–7.0  105 and 8.5–9.0  105 m, respectively. 3.3. Two-layer model of plastic and self-compression – k measurement The mass loss fractions of gel specimens measured after PC were applied to Eqs. (3) to measure b and c, as a function of PC stress. As shown in Fig. 4A, b values reduced dramatically with an increase in PC stress from 3.76  103 m in PC0 to 3.65  104 m in PC3. A significant increase in c values occurred from PC0 to PC3 by increasing PC level. In order to determine the effect of PC on lamellar permeability kc, k values obtained by the application of different levels of PC, together with physical parameters described previously [29], were inserted into Eq. (6) (Fig. 4B). An increase in the PC level resulted in a significant increase in k, while k decreased from (1.8 ± 0.3)  1015 to (1.0 ± 0.1)  1015 m2. As shown in Fig. 2A, measurements of gel mass loss were performed at 10 time points over the course of SC, which defined nine time intervals within which b, c and k of the lamella could be measured. However, since the gel specimens had already lost different fractions of water due to PC, they reached equilibrium at different time points during SC. Therefore, k measurements were performed until equilibrium was attained for each specimen. Incorporation of k values (Fig. 2A) into Eqs. (3) provided b and c values as functions of time during SC (Fig. 5A). Progress in SC was associated with a significant reduction in b and a considerable increase in c values. All gel specimens exhibited approximately matching b values (8.0–14.0  105 m) and c values (8.0–8.3  105 m) after equilibrium was achieved. In order to determine lamellar permeability during SC, k(t) values of confined SC were introduced into Eq. (7). In this case, k(t = 0) was equal to the mass loss fraction resulting from each PC level. As shown in Fig. 5B, over the course of SC, the k of PC0 initially increased from 4.3  1015 to 1.19  1014 m2, followed by a decline until equilibrium was reached after 40 min. At each time interval during SC, an increase in PC level resulted in a decrease in k. Permeability of compressed gels continuously decreased until the equilibrium state was achieved. The mean k values, calculated for each gel specimen over the time period of SC, were (8.2 ± 2.3)  1015, (7.3 ± 4.1)  1015, (6.8 ± 4.8)  1015 and (5.7 ± 5.5)  1015 m2 for PC0, PC1, PC2 and PC3, respectively. These values were applied to the Happel equation to predict the collagen fibril bundle diameter within the lamella in each gel specimen. The Happel model predicted that collagen fibril bundles in these gels exhibited hydraulic radius a values ranging from 10 to 55 nm, which corresponded with our previous finding [32], where a histogram of collagen bundle diameters within PC0–PC3 gel specimens indicated distributions of bundle diameters with the most frequent diameter in the range of 25– 50 nm. 4. Discussion

Fig. 2. Gel mass loss fraction determined during radially confined SC of collagen gels that previously underwent different levels of confined PC for 2 min (PC0–PC3). Solid lines indicate the best fit to the data.

The 3-D microstructure of highly hydrated collagen gels is a determinant of mass transport and mechanical properties of the scaffold, as well as cellular function and cell–scaffold interactions [7,8,10,11,33]. Furthermore, porosity, pore size and distribution,

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Fig. 3. CLSM of collagen immunoreactivity in PC collagen scaffolds following 20 min of radially confined SC. (A) 3-D image stack of a collagen gel specimen post-PC (PC2, 690 N m–2 for 2 min), prior to the initiation of SC. (B) A representative PC2 gel scaffold after 20 min of SC. The fluorescence intensity of collagen immunoreactivity (green) in (A) and (B) was normalized according to the intensity used in (A) for the aim of the comparison between the different conditions. Applying the initial PC resulted in formation of a lamella of a higher collagen density at the bottom surface of the gel y  z plane), as represented by the green wavy structure representing the cake layer in the orthogonal views of the x  y and x  z planes. Note also the presence of foci of collagen immunoreactivity dispersed throughout the bulk layer in (A). Self-compression further increased the thickness of the cake layer and diminished the hydrated collagen layer, as indicated by expansion of the lamella and a reduction in the area containing green foci of collagen immunoreactivity. The square image in each panel shows the topography of the compressed collagen gel at the FEB, revealing an embossment of the polymer mesh pattern (used as substrate during plastic and self-compression).

Fig. 4. (A) Highly hydrated collagen layer thickness (b, left axis) and dense collagen lamellar thickness (c, right axis) within plastic compressed collagen gels as a function of the applied compressive stress. b and c were measured by inserting the mass loss fraction due to PC into Eqs. (3) presented in the two-layer model. Increasing the compression level resulted in a decrease and a significant increase in b and c, respectively. (B) Mass loss fraction (k, left axis) and measured hydraulic permeability of the dense collagen lamella (kc, right axis) as a function of the applied compressive stress. Increasing the compression level resulted in a significant decrease in kc, as well as an increase in the mass loss fraction due to compression. Solid lines indicate the best fit to the data.

interconnectivity and pore orientation affect scaffold hydraulic permeability (k). k is the ability of a porous structure to transfer fluid through its interstices under an applied pressure which drives fluid flow. Therefore the poroviscoelastic characteristic of scaffolds – stiffness, mass transport and, consequently, cell–cell and cell– scaffold interactions – are each potentially influenced by k [10– 12]. In addition, highly hydrated collagen gels are mechanically

Fig. 5. (A) Time progression in the thickness of the highly hydrated collagen layer (b(t), left axis, black lines) and the dense collagen lamella (c(t), right axis, grey lines) within different collagen gel specimens undergoing radially confined SC. b and c were measured by incorporation of the mass loss fraction data during SC into Eqs. (3) presented in the two-layer model. Initiation and progression of SC resulted in significant decrease in b and increase in c. (B). Measured hydraulic permeability of lamella (kc) as a function of time during SC until reaching the equilibrium. Confined SC of collagen gels resulted in a uniform decrease in kc (except in PC0, where an initial increase in kc was followed by a decrease at longer time points). Gel specimens that underwent greater levels of plastic compression (Fig. 4) exhibited lower k values at each time interval.

unstable as they are characterized by more than 0.99 mass fraction fluid and, when left in an unconfined space (e.g. not surrounded by fluid), undergo a gravity-driven consolidation process (SC). The time-dependent gravity-driven SC and PC (the application of an external load) of highly hydrated collagen gels have recently been

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developed as poroviscoelastic responses of scaffolds to the applied compressive loads. These methods generate a fluid expulsion within the fibrillar porous structure and produce dense, ECM-like scaffolds within minutes [34,35]. Fluid expulsion is dictated by the extent and duration of loading, where the application of standard PC (1 kN m2 for 300 s) results in equilibrated gels with >40-fold increase in solid volume fraction (collagen fibrillar density), attributable to an approximately 0.98 mass fraction in fluid loss. Upon removal of load post-standard PC, these equilibrated dense gels do not undergo further self-compression, even when in an unconfined space. In addition to improving the mechanical properties of collagen gels, PC has been reported to maintain and improve the viability, proliferation and differentiation of various cell types within compressed scaffolds [36–39] as these gels mimic the native ECM collagen fibrillar density and its microenvironment. However, upon application of lower extents (e.g. 340 or 690 kN m2) or shorter durations (e.g. 120 s) of loading, only partial compression occurs and the gels undergo further self-compression when maintained in an unconfined space. On the other hand, further self-compression does not take place if the partially compressed gels are immediately transferred to culture medium. Previously, we applied partial compression (through the application of 340, 690 or 1022 kN m2 for 120 s) to generate collagen gels with different solid volume fractions and used the Happel model to theoretically calculate k [32,33]. The Happel model describes the relationship between the k of a random array of long cylindrical fibres and the geometry, and is particularly useful in fibrillar materials, as in the case of collagen gels [31]. Studies have demonstrated that the extent of cellular responses (e.g. proliferation and cell-mediated collagen gel contraction [32,33], as well as cell differentiation [33]) to collagen gels with different k values (theoretically calculated through the Happel model) may be correlated. We therefore hypothesized that k may be used as a 3-D parameter to characterize the microstructural properties of collagen gels. However, the Happel model can only be applied on a macroscopic scale with a number of assumptions, including a uniform fibrillar density and the random orientation of fibres, which may deviate from the microstructure of plastic compressed collagen gel scaffolds. In order to investigate the microstructural processes involved in SC of collagen gels, we previously introduced a two-layer model to describe the microstructural evolution, gravity-driven fluid flow and hydraulic permeability of highly hydrated collagen gels during radially confined SC [29]. It was assumed that the collagen gel microstructure was initially homogeneous and that no external force was applied to the gel. The formation of a dense cake layer at the fluid leaving the surface of hydrated collagen gels during plastic compression was also reported recently, where the fluid flux was analyzed in two stages using Darcy’s law [9]. In the current work, more general boundary conditions were applied to Darcy’s law in order to measure: (i) the k of the collagen gel when an external compressive stress was applied; and (ii) the k of plastically compressed gels with a non-uniform microstructure during SC. In analogy to the formation of a cake layer at the surface of an ultrafiltration membrane [27,40], PC and SC of highly hydrated collagen gels resulted in the formation of a lamella due to accumulation of collagen fibrils at the FEB of the collagen gel [29,34]. The application of increasing levels of confined PC resulted in increases in k (0.69, 0.82 and 0.88 for PC1, PC2 and PC3, respectively). These were considerably lower than the k values measured previously for the application of the same levels of PC under unconfined conditions (0.88, 0.91 and 0.93 for PC1, PC2 and PC3, respectively) [33]. This can be attributed to hindered fluid flow under radially confined PC. Furthermore, increasing the PC level from PC0 to PC3 decreased both the rate (1.8-fold) and the total (2-fold) mass loss fraction obtained during the following SC.

While the collagen volume fraction within the lamella (rc) was assumed to be constant for all gel specimens in this study, an approximately uniform reduction in kc was observed with increasing PC level and as a function of time during SC. Moreover, comparison of kc values measured after application of PC and during SC demonstrated a significant increase (10-fold) in kc for each compressed gel specimen upon removal of the compressive stress. These findings may be due to the pressure-induced deformation of the lamella as a consequence of the application of an increasing level of compressive stress, which in turn increases the fluid flow resistance [26,30]. Previously, both theoretical models and experimental investigations have revealed the generation of large localized compressive strains within diverse tissues in vivo [41,42]. For example, similar strain-dependent permeability behaviour has been reported for cartilage and the nucleus pulposus of intervertebral spinal discs when under compression [30,41]. Moreover, the spatial changes in fibrillar organization within the lamellae in PC0–PC3 gel specimens may contribute to variations in k [34,43,44]. An in-depth microstructural evaluation of the lamellae formed within different compressed gel specimens may explain this k reduction. The accuracy of the model to calculate lamellar thickness can be verified by comparison with the CLSM micrographs (Fig. 3). There was an agreement between the c measurement in the PC2 gel specimen ((7.1 ± 0.3)  105 m), as calculated by the two-layer model, and the actual thickness of the lamella measured from the micrograph in Fig. 3A (6.5–7.0  105 m). This concurrence also existed 20 min post-SC of PC2 gel specimens (8.0–8.3  105 m calculated by the model in Fig. 5A vs. 8.5–9.0  105 m measured via confocal imaging in Fig. 3B).

Fig. 6. Average hydraulic permeability of two-layer structure of collagen gels, calculated using Eq. (8) and plotted (in logarithmic scale) as a function of the compressive stress applied in confined plastic compression (A), and as a function of time during confined self-compression of collagen gels (B). The inset in (A) also demonstrates the kave variation on a linear scale. An increase in the plastic compression level resulted in a dramatic decrease in k after PC or during SC.

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By incorporating rb (0.0016 ± 0.0001) and collagen fibril radius a (10–55 nm) into the Happel model [31], the permeability of highly hydrated collagen layer (kb) can be calculated at (8.446 ± 0.011)  1013 m2, which is 100-fold greater than the mean kc values measured within the lamella of each gel specimen. Thus, the lamella, which is characterized by significantly restricted permeability values in comparison to the highly hydrated layer, plays a dominant role in different scaffold properties, such as mass transport and stiffness [9,26,29]. For a collagen gel consisting of a highly hydrated gel layer and a lamella, in a series configuration, the average permeability (kave) of the construct [45] can be written as

bþc b c ¼ þ K av e kb kc

ð8Þ

whereby the kave of collagen gel specimens after PC and during SC can be determined (Fig. 6). Collagen gels with increased level of PC exhibited significantly reduced kave after PC (Fig. 6A) and during SC (Fig. 6B). Overall, the range of k values measured here for different collagen gel microstructures were in agreement with previously measured k values in hydrated collagen gels (e.g. 1014–1012, 1015–1014 and 1013–1011 m2 [22,33]). It is noteworthy that in Fig. 6B the kave of non-compressed and compressed collagen gel specimens approached a similar equilibrium range (1–10  1015 m2), which can be considered as the equilibrium permeability characteristic of these scaffolds. A similar trend was observed for b and c values as a function of time during SC, where an ultimate stable microstructure was achieved for all gel specimens at equilibrium state b and c values in the range of 8.0–15.0  105 and 8.0–8.3  105 m, respectively). According to these results, PC and SC of highly hydrated collagen gels can provide a means to fabricate collagen scaffolds with defined microstructures and hydraulic permeability values to serve in diverse biomedical applications.

5. Conclusion In this study, fluid flow mechanics and microstructural processes involved in one-dimensional PC and subsequent SC of highly hydrated collagen gel scaffolds were analysed to determine hydraulic permeability of scaffolds using Darcy’s law. In parallel to tissue behaviour in vivo and in vitro, strain-dependent permeability values were obtained for hydrated collagen gels under compression. The results indicated the ability of controlled PC and SC to generate multi-layered collagen gel scaffolds with defined microstructures and permeability values with implications for diverse biomedical applications. Acknowledgements This work was supported by the Canadian Natural Sciences and Engineering Research Council, the Canada Foundation for Innovation: Leaders Opportunity Funds, Quebec MDEIE and McGill University Faculty of Engineering Gerald Hatch Faculty Fellowship. V.S. is a recipient of a McGill Engineering Doctoral Award, Hatch Faculty scholarship and McGill Provost Award.

Appendix A. Figures with essential color discrimination Certain figures in this article, particularly Figs. 1 and 3, are difficult to interpret in black and white. The full color images can be found in the on-line version, at http://dx.doi.org/10.1016/ j.actbio.2012.08.031.

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