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1

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The in-vitro engineering of tissue requires an artificial environment that can promote the desired

evolution of cellular processes. Many processes influence cell proliferation and differentiation,

though the strain environment maybe the most important as it dictates the path by which the

mechano-sensitive systems lead cell evolution [McMahon et al., 2008]. As a cell-seeded scaffold is

often strained in-vitro [Ignatius et al., 2005], the amount of strain imparted onto the cells dictates

the level of tissue growth. To achieve engineered tissue suitable for in-vivo implantation, the tissue

needs to demonstrate homogenous mechanical and architectural properties so that the rate of cell

proliferation and differentiation, as governed by the forces imparted by the local strain environment,

occur at equal magnitudes throughout the entire scaffold [Hollister et al., 2002; McMahon et al.,

2008; et al., et al., 2005].

A Collagen-glycosaminoglycan (CG) scaffold, a construct biologically suited to promoting tissue

growth [Chang and Yannas, 1992; Chamberlain et al., 1998; et al., 2004; Yannas et al.,

1989; Yannas 2001], has already been described mechanically from classic experimental

measurements [Harley et al.,2007; Harley et al.,2008; Lee et al.,2001]. However, apparent

mechanical properties do not provide an appreciation of microscale or regional strain environments

important to mechano-sensitive cell systems (see Figure 1). It is important to note that Figure 1

illustrates a varying pore morphology along the longitudinal axis (z-axis). Though this Scanning

Electron Microscope (SEM) image clearly depicts a regional variance in architecture, and has been

mentioned in previous investigations [Harley et al., 2007], there is no quantitative data to explain

the influence on cell activity. Consequently, in an attempt to quantify microscale deformations,

Stops et al. (2008) used microscale Finite Element (FE) modelling to show how a strained CG

scaffold imparts a large range of strains onto the seeded cells. Though this recent study helped

demonstrate the influence of macroscopic scaffold strain on the microscale strain environment, the

implementation of an idealised geometry did not allow an insight into regional differences. Ideally,

scaffold-specific geometry should be characterised from high resolution imaging [Hollister et al.,

2002]. In accord with this proposal, Sandino et al. (2008) used µComputed Tomography (µCT)

imaging to construct a representative model of a calcium-phosphate scaffold. The effect of the

internal architecture on the resulting mechanical deformations and fluid dynamics were found to

vary according to the morphology of the material. Significantly, Sandino et al. (2008) suggested

that any non-uniformity in the scaffold architecture will create localised areas of high strain, stress

and/or fluid flow, that in-turn will create localised hotspots of mechanical stimuli imparted onto the

cells

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2

Though many previous µFE (FE analysis at microscale resolution) models of scaffolds have

sampled small regions of interest [Sandino et al., 2008; Lacroix et al., 2006], large-scale µFE

modelling (consisting of many millions of elements) has been used successfully in other domains,

particularly in the study of trabecular and cancellous bone [Harrison et al., 2008; Jacobs et al.,

1999]. By representing a large proportion of the structure, or even the entire assembly if

computational capacity allows, large-scale µFE affords a comparison of regional variances in one

single analysis. Thus large-scale µFE modelling eliminates many of the typical prediction errors

seen when scaling up from small representative models. Furthermore, by using maximum

resolution voxel element representation (one voxel element models one CT-image pixel), local

microstructural features can be accurately represented in terms of both architectural and mechanical

detail [Homminga et al.,2001; Ladd and Kinney, 1998].

Previously, CT-imaging of a CG scaffold was impractical due to the relative resolution

requirements: a CG scaffold has a ver et al., 2004]) and

requires a very high resolution to capture the geometry. Yet now, with the timely advent of

technology, the determination of microscopic strains can be made using large-scale FE modelling.

Hence, the aim of this investigation was twofold. First, using a large-scale 3D mesh constructed

from CT-images, an FE analysis was performed to determine the salient microstructural features

that influence the region-specific variances within a CG scaffold. Second, by exploring the key

factors that influence the microscale mechano-sensitive cell systems, a CG scaffold was examined

with respect to the potential to grow homogeneous tissue suitable for in-vivo implantation.

3

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In this section, the methodology is divided into two sub-sections: 2.1) the development of 3D

microscale geometries of the scaffold and the procedures employed to assess the architectural

features of the CG scaffold and, 2.2) the mechanical conditions applied to the FE mesh to realise

accurate micro-mechanics for multi-scale mechanical assessment.

2.1 Architectural Analysis

Image-Thresholding Procedure

From an SEM study, the major load-bearing structures were found to be significantly larger than

2). Consequently, given that the microstructure between multiple CG scaffold

et al., 2004], a single CG scaffold was µCT imaged at a

. The CG scaffold was manufactured using a

lyophilisation process at a freezing drying temperature of -40°C and dehydrothermal treatment

(DHT) crosslinked at 105°C for 24 hours in a large stainless ste et

al., 2004]. From a resolution study, where a series of FE meshes

with sub-micron resolution (0.29- ) meshes (SKYSCAN, Belgium), the mesh

was corroborated; the load-bearing microstructure was sufficiently captured to accurately predict

stress fields (sub-micron data not presented here). With an in-house code, the µCT data was

thresholded and segmented to form a 3D interconnecting structure in the form of a voxel element

mesh (one µCT pixel equalled one voxel element, with dimensions of ).

As Figure 1 clearly shows - -

, named according to the surface of the construct (the two surfaces are exposed to different

cooling regimes: the pan-side cools from conduction through the pan, while the air-side cools via

convection), this investigation characterised two sections of a CG scaffold in order to quantify this

regional effect. Accordingly, the Transverse (TRV) model corresponded to a region taken from the

intermediate mid-region of the scaffold in the transverse plane, whereas the Longitudinal (LGD)

model described the architecture of the air-side, the pan-side and the mid-region by detailing the

scaffold along the longitudinal z-axis (Figure 3).

Assessment of Volume Fraction and Relative Density

The two FE models were defined by a solid volume (selected pixels) to non-solid volume (non-

selected pixels) fraction for a scaffold level and a regional level (Table 1); scaffold-level refers to a

scale level equivalent to ~millimetres, whereas regional level refers to ~250micrometres. However,

the calculation of the scaffold volume fraction assumes the chosen greyscale values above a

4

threshold value to be solid. In reality, each individual pixel has a unique greyscale value, or in

other terms, each pixel has a unique density. This partial volume effect has also been observed

when CT scanning bone [Homminga et al., 2001]. Consequently, to quantify the effect of these

pixel densities on the volume fraction calculation, and to identify if localised regions of densities

occur within the scaffold, the greyscale values were normalised relative to the base constituent of

the scaffold, e.g. collagen.

A solid sample of bovine collagen, extracted at source, was freeze dried at a temperature of -40°C

for 24 hours to remove the water content. Subsequently, the sample was µCT imaged at the same

scan settings of the aforementioned CG scaffold (SCANCO, Switzerland). With a purpose written

Matlab® code, was determined from the µCT-images.

Subsequently, the greyscale values of the scaffold mesh were normalised with respect to the mean

collagen pixel greyscale value. This described the relative density of each individual voxel element

in the scaffold mesh, thus allowing a true scaffold density to be calculated. Furthermore, regional

properties were also evaluated in two forms: 1) regional volume fractions (the scaffold volume as a

fraction of the total volume scanned), and 2) regional relative densities (the product of the volume

fraction and the corresponding voxel densities). The two forms of regional properties can be

interpreted such that, the volume fraction defines the space in which a cell can occupy, while the

relative density is associated with the specific rate of synthesis and scaffold degradation [Pek et al.,

2004].

Pore Geometry Assessment

To further explore the admissible space available for cells, 3D pore geometry was examined. A

purpose written algorithm was used to identify pore geometries by determining the equatorial and

polar boundaries of the non-solid space(s) at multiple angles rotated around the principal axes. The

unique intersections of these equatorial and polar centroids denote the centre of the scaffold pores.

The pore geometry was characterised in the form of an ellipsoidal volume, whereby

12

2

2

2

2

2

c

z

b

y

a

x

(1)

where a and b are the equatorial radii (along the x and y axes) and c is the polar radius (along the z-

axis). Note if all three radii are equal, the body is a sphere. Average pore sizes for a region were

used to define the mean, maximum and minimum values reported in Table 1. In addition to this 3D

ellipsoid method, a linear intercept length analysis [ et al. (2005)], was used to measure the

mean 2D pore sizes from multiple plane sections. Briefly, by identifying the frequency that a series

5

of parallel lines intercepted a pore, a best-fit ellipse was constructed to represent the average pore

cross-section.

2.2 Mechanical Analysis

FE Model Formulation

As the two FE models (TRV and LGD) were of the order of 6-8 million 8-noded voxel elements, it

was essential to minimize the computational requirement in line with the capabilities and time

restraints of the resources available to this investigation. Consequently, the following

methodologies were designed to increase computational efficiency.

FEEBE/linear (verified by Harrison et al., 2008), an in-house small strain FE solver was

implemented to solve the deformation of the scaffold mesh. The solver FEEBE/linear affords an

element-by-element solution that reduces the computational RAM requirements by solving from

one stiffness matrix. A single stiffness matrix was possible as every element is equal in shape and

volume, thus assuming identical stiffness functions. Furthermore, this solver demonstrates an

excellent scalability when multi-processors are employed.

A CG scaffold seeded with cells in-vitro, typically exhibit a dimension range of 10-15mm in

diameter and a thickness of approximately 3-4mm [Harley et al., 2007; Jaasma et al., 2008;

Jungreuthmayer et al., 2009a; et al., 2005; Schulz Torres et al.,2000]. Consequently, if the

required. Due to this impracticality, dimensions of approximately 1.5 x 1.5 x 3.9mm were chosen

for the LGD mesh and 3 x 3 x 1.5mm for the TRV mesh. In light of this, symmetric boundary

conditions, in accordance with periodic unit cells [Böhm, 2004], were applied to the model to

realise the representation of a larger structure, albeit periodic in nature. Specifically, 4 faces,

consisting of 2 pairs of parallel faces, were applied a symmetric condition such that, on the two

sides of the boundary, the same physical processes existed. Thus, the unit cell modelled a system

that was of a structure repeating in the transverse plane.

As with many other highly porous materials, the mechanical properties of the substance within each

CT voxel are not easily measured [Scheiner et al., 2009]. Consequently, given the mean voxel

density (0.055 from the CT images described in section 2.1) indicated voxel-level porosity (the

voxel volumes are partially filled), a voxel-density calibration procedure was developed in order to

provide voxel-level properties. Thus, as previous investigations have indicated the validity of

cellular solid mechanics for representing constructs with a relative density below 0.15 [Li et al.,

6

2003; Warren and Kraynik, 1997] and our voxels have a relative density of 0.055, the Gibson and

Ashby equation [Gibson, 2005] was employed. The voxel modulus Ev was related to the known

material modulus Em of a strut by,

m

s

vV EE

2

(2)

where Em = 5.28MPa [Harley et al., 2007] and 0550.s

v . Thus, EV was calculated to be

16.32kPa. This method enabled a relationship between an experimentally measured mechanical

property (the strut modulus) [Harley et al., 2007], and the representative voxels at this given scale-

level. Note, an homogeneous elastic modulus was assigned to all of the elements.

Mechanical Assessment

To investigate the apparent mechanics of the two FE models, a 1% compressive uniaxial strain in

the z-axis (see Figure 3 for axis conventions) was applied. This afforded a comparison between the

mid-region, as simulated by the TRV model, and the entire construct, as represented by the LGD

model. Additionally, an elastic modulus was calculated for each principal direction (Table 2).

Micro-mechanical Elastic Stability

The stress strain relationship of a CG scaffold under uniaxial compression can be described in

terms of three regimes: a linear elastic regime in which bending of the internal struts occur; a stress

plateau wherein a progressive collapse of the struts results from elastic buckling; and densification,

which corresponds to the subsequent impacting of the struts against one another [Gibson, 2005;

Harley et al., 2007]. Note the earliest indication of strut buckling occurs at the elastic buckling

stress. At this point of scaffold strain, a critical magnitude of microscopic stress exists within the

interconnecting strut-structure that defines the initiation of elastic buckling. Consequently, the

apparent elastic buckling stress of the entire scaffold, calculated to be 13.56Pa, was determined

using the offset method (0.2%) from the initial linear portion of the stress-strain curve [data

extracted from Harley et al. 2007]. Accordingly, at an apparent scaffold strain of 5.6%, the voxel-

level stresses were used as a criterion for microstructural failure.

- -architecture of the load-bearing structures within the scaffold (see

Figure 4), a critical elastic stress magnitude, cr, was defined in accord with plate mechanics

[Bulson, 1970] such that,

7

2

2

2

112 b

t

-

Ekcr

(3)

where k is a dimensionless buckling coefficient, t is the thickness, b is the height, while E and v are

aterial, respectively. The thickness and the height

inputs were assumed from previously published data, with t=3.9µm and b=137.4µm [Freyman et

al., 2001; Harley et al., 2007; Harley et al., 2007b] as these considered the thinnest and longest

dimensions, i.e. a worse-case scenario for buckling, E was equal to the strut modulus of 5.28MPa

[Harley et al., 2007

- and subjected to a uniform compression, k=0.43 [Bulson,

1970]. Thus, the critical elastic stress magnitude was calculated to be 1.78kPa. Consequently, cr

was implemented as a threshold value so that a critical volume fraction could be determined for

each FE model. Hence, the critical volume fraction defines the portion of the scaffold that has

approached the elastic collapse regime at the scaffold elastic buckling strain of 5.6% compression.

Note cr was implemented as performance criterion for comparative purposes only.

Representative-Cell Loading

Previous research has shown two main modes of cell attachment for in-vitro culture: cells spread

along the surface of the scaffold struts, or cells bridge multiple struts [Stops et al., 2008]. In fact,

~76% of the cells seeded in a CG scaffold bridge multiple struts, while ~24% of the seeded cells

spread over strut surfaces. To quantify cell strain resulting from scaffold loading, two post-solution

analyses were undertaken. Firstly, to assess strain on cells that bridge multiple struts, pairs of

displacement throughout the scaffold deformation (~120million pairs of nodes were monitored in

each mesh). Subsequently, cell strain was calculated from the change in length between each pair

of nodes. This procedure was much like the application of 2D bar elements with zero stiffness.

Secondly, to assess the loads imparted onto ~24% of the cells that remain spread over the surface,

principal strains on the surface of the scaffold struts were assessed.

8

í λ­«´¬­

Volume Fraction and Relative Density

The volume fraction and the relative density measurements of the two meshes compared well with

previously published data [Harley et al., 2007; Nehrer et al., 1997 et al., 2005].

Specifically, the TRV model volume fraction exhibited a value of 0.12, while the LGD model

demonstrated 0.16 (Table 1); Nehrer et al. (1997) measured a volume fraction of 0.13-0.17. While

the mean relative densities of 0.0059 and 0.0096 (Table 1), for the TRV and the LGD models

respectively, compare well with the value of 0.0058 measured by Harley et al. (2007). However, on

a regional basis, there appeared to be a substantial variation, up to 10% difference in some cases,

between the pan-side and the air-side (Figure 5a). At ~1mm below the air-side region (regions 7-8

in Figure 5a), the volume fraction was highest, while at approximately 1mm above the pan-side

region (region 3 in Figure 5a), the volume fraction was the lowest. This trend continues when

examined in terms of relative density: the TRV model and the LGD model have similar mean

relative densities (Table 1), but the highest relative density occurs in the regions proximal to the air-

side (regions 8 and 9 in Figure 5b), while the lowest relative density was found just above the pan-

side (region 3 in Figure 5b) in the in LGD model.

Pore Architecture

The mean pore sizes corresponded well with previous data for this type of CG scaffold [Harley et

al., 2007; Brien et al., 2005]. Specifically, with a mean pore sizes (TRV)

(LGD) et

al. (2005) et al. (2005), a

s measured for the transverse region, which concurs with the

ly observed in a CG

scaffold [Harley et al., 2007]. However, it is important to note that these particular CG scaffolds

measured by Harley et al. (2007) had much higher densities than the ones modelled in this

investigation. Yet as the maximum density measured in this investigation is comparable with the

average relative density in the aforesaid study (0.0103 from Table 1, compared to 0.012 from

Harley et al. 2007), it is likely that the occurrence of these large holes is density dependent.

Apparent Mechanics

The elastic moduli of ~135Pa (TRV) and ~392Pa (LGD) compared well with that of previously

data: ~206Pa [Harley et al., 2007], ~40Pa (140 et al., 2001], ~500Pa

[Haugh et al., 2008]. As seen from Table 2, the variation observed between the three principal

9

elastic moduli is consistent for both models, i.e. Ex and Ey are approximately 60% of Ez. Thus, CG

scaffold anisotropy is consistent.

The principal stress distribution and the displacements within the LGD model is shown to be much

more heterogeneous than the TRV model (Figure 6 and 7). The stress contours demonstrate distinct

stress concentrations within the LGD model, whereas the TRV model displays much less variance

(Figure 6). Also, the displacement magnitudes (Figure 7) show the LGD model to experience a

pronounced magnitude variance, as shown by the displacement range. Furthermore, not only are

the stress magnitudes much more widely spread in the LGD model, but the mean principal stress of

-156.53 ±228.71Pa is a significantly (p<0.001) higher magnitude of compression than the -58.19

±120.21Pa calculated for the TRV model (for an apparent compressive strain of 5.6%).

Micro-mechanical Elastic Stability

The critical volume fraction that exceeded the critical elas cr (for an apparent compressive

strain of 5.6%) differed for the two FE models (Figure 9). Approximately 0.2% of the total LGD

model experienced an elastic stress above 1.78kPa, whereas the TRV model had 0.02% of its total

solid part exceeding the critical elastic value.

high stress: the region that experienced the highest percentage of stress magnitudes above the

critical elastic stress value was the pan-side (1.64% of solid above cr); the second highest

percentage was the air-side region (0.75% above cr); and the third highest region was ~1mm below

the air-side region (0.46% above cr). Consequently, the potential for elastic instability varied in a

regional-level basis within the LGD model.

Inferred Cell Loading

The cell strains for an apparent scaffold compressive strain of 1%, were found to be normally

distributed, for both the surface cells and the strut-bridging cells in both of the two FE models.

From Figure 10, the attachment type greatly influenced the strain on the cells. Namely, the strut-

bridging cells underwent much larger strains with much more variety than the surface cells (Figure

10a and 10b). In terms of mean cell strain, the surface cells experienced a strain very close to zero;

-4.17x10-7% and -2.06x10-6% for the TRV and the LGD model respectively, while the mean strain

on the strut-bridging cells was much higher with values of -0.176% and -0.155%, for the TRV and

the LGD respectively.

10

While there was a minimal disparity between the TRV and the LGD models in strain on the surface

cells (Figure 10a), the two FE models did produce different strain levels in the strut-bridging cells

(Figure 10b). Although the TRV and the LGD models imparted similar mean strains, -0.176% and

-0.155%, the range of strains were very different: the TRV model exerted a range of -16 to 15%,

while the LGD model range was much larger, -35 to 28%.

11

ì Ü·­½«­­·±²

This investigation employed a multi-scale methodology to assess the salient architectural and

mechanical features of a CG scaffold. From µCT characterisation, the unique implementation of

large-scale FE analysis (models had in excess of 6-7 million elements) allowed the mechanical

response of the CG scaffold to be realised via symmetric boundary conditions. The accumulation of

these procedures allowed localised micro-mechanics to be evaluated, e.g. cell-level strains and

macro-mechanical properties, so that an understanding of how regional level characteristics within a

CG scaffold may influence the function of the seeded cells.

Procedural Limitations

Unlike studies that have modelled small regions of interest [Lacroix et al., 2006; Sandino et al.,

2008], the work herein modelled a substantial volume and to provided a region-to-region account of

mechanics. However, the use of 6µm FE meshes meant that some of the sub-micron microstructure

was omitted. Although sub-micron meshes are available, they do not permit modelled volumes in

excess of 100 x 100 x 100µm dimensions due to current computational and imaging capabilities.

Furthermore, from Figure 2, it is evident that the major components responsible for structural

integrity can be captured from resolutions above micron level. Furthermore, recent work by

Jungreuthmayer et al. (2009a) and Jungreuthmayer et al. (2009b) corroborated the current

resolution (6 ) by accurately modelling fluid dynamics in a CG scaffold. Thus, w

resolution may have omitted the very thin struts seen in Figure 2, these thin struts can be considered

relatively un-influential to the overall mechanics. Therefore, given that the major load-bearing

structures were successfully represented, i.e. pore size and strut spacing, which in turn meant that

the structures to which the cells attached were represented, and the many metrics that matched

previous data,

investigation.

In reality, an in-vitro CG scaffold is submersed in an aqueous medium. Consequently, in a cyclical

strain environment, fluid movement could deform the microstructure of a porous material; this

fluid-solid interaction was not modelled herein. However, previous studies have shown interstitial

fluid flow within porous materials to have a minimal influence on apparent modulus when the

<5%) [Dawson et al., 2008]. Furthermore, as the lowest flow rates are

typically observed at the strut surfaces of porous materials [Porter et al.,2005, the influence of the

inertial forces on mechanical deformation can be expected to be minimal [Comiti et al., 2000].

Consequently, the simulation of low apparent strains justifies a solid mechanics approach for

12

modelling a CG scaffold; the low apparent strains also justifies the use of small strain kinematics as

there was no significant volume of the material that underwent large local strains.

4.1 Analysis of Results

The apparent elastic moduli calculated for the two FE models compared favourably with

experimental data [Freyman et al., 2002; Harley et al., 2007; Haugh et al., 2008]. Yet, the two FE

models demonstrated a slight disparity: the LGD model modulus was approximately twice that of

the TRV model (Table 2). This difference may have arisen from the differing architectural features

of the two meshes: the overall volume fraction for the LGD model was ~30% higher than the TRV

model (Table 1). Interestingly, the deformation patterns of the LGD model clearly shows the mid-

region (which corresponds to the same region from which the TRV model was sampled) to be

highly compliant, as seen by the large displacement magnitudes (Figure 7). In fact, the majority of

the deformation occurs within this region, which suggests the mid-region is much more compliant

than the rest of the scaffold. The architecture, and therefore the mechanical response, of the

microstructure from the pan-side up to the air-side is highly varied (Figure 1).

Interesting, the identification of plate-like microstructure proves to be a novel finding. Unlike

previous studies that define struts as cylindrical columns [Freyman et al., 2001; Harley et al.,

2007b], the 3D illustration in Figure 4 clearly illustrates plate-like features. Note, previous studies

have typically implemented a 2D analysis of pore structure, whereas this study used a 3D

examination. The cooling regimes, exposed to the CG scaffold during fabrication, may be the cause

of these plate-like structures: the air-side undergoes cooling via convection while the pan-side cools

by conduction. As convection cools considerably faster than conduction, the temperature transfer

imparts a distinct preference toward convective release, which in this case is toward the upper

surface, and so solidification occurs in a directional manner. These plate-like features may help to

explain the anisotropy of the apparent moduli (Table 2) and in previous publications [Harley ey al.,

2007]. Considering the in-plane direction of the plates followed the x-z or y-z plane(s) (see Figure 4

for example), it is of no surprise that the scaffold elastic modulus was higher in the z direction.

Though the plate orientation was not quantified by direct measurement, it is highly feasible that

these direction-dependent features are significant contributors to the apparent moduli. While

beyond the scope here, further work may wish to examine the influence of these plates on fluid flow

as it is likely any directional variance will influence the effectiveness of nutrient and cell dispersion.

Defining a critical elastic buckling criterion for materials with irregular microstructure can be a

complex and formidable task. Consequently, a critical stress magnitude, cr, defined from plate

13

buckling mechanics, was implanted as a threshold for elastic instability. From the fraction of the

scaffold above the critical elastic stress magnitude, the critical volume fraction, the LGD model

proved prone to microstructural buckling compared to the TRV model (Figure 9). In fact, the

potential for buckling, as interpreted by the critical volume fraction, is an order of magnitude

greater in the LGD model. Interestingly, a regional-level variance indicated a heightened potential

for elastic buckling in the periphery (the air-side and the pan-side of the LGD model). The

architectural features of the peripheries are clearly distinct: the air-side region has elongated

elliptical pores (Figure 1a), the intermediate mid-region has relatively equiaxed spherical pores

(Figure 1b) and the pan-side has an irregular network of struts (Figure 1c). Hence, the elongated

elliptical pores and the irregular strut network of the air-side and the pan-side, respectively, are less

conducive to stress dissipation than the intermediate mid-region (the spherical pores of the mid-

region dissipate stress evenly via bending, compression and tension, while conversely the columns

or plates of the air-side axially compress causing localised hotspots at strut junctions, and the

irregular network within the pan-side has disconnected and incoherent struts causing high stress

localisations).

The regional architecture also influenced the predicted cell strains (Figure 10): the LGD model

imparted a maximum strain over two times higher than the TRV model for surface cells, while also

imparting a maximum strain again almost two times higher than the TRV model for strut-bridging

cells. These cell strains compare well with CG scaffold data [Isaksson et al., 2006; Lacroix et al.,

2006; Stops et al., 2008]. For example, Lacroix et al. (2006) also found surfaces strains to be close

to zero, while Stops et al. (2008) predicted a similarly large range of cell strains for cells bridging

struts (-26% to 49%). As with the conclusions made by Stops et al. (2008), two distinct

mechanisms influence cell strain: the strain on cells elongated along single struts are dependent on

scaffold surface strain, while secondly, the strain on cells bridging across struts are dictated by a

hinge-like re-arrangement of the scaffold microstructure. Thus, the strut-bridging cells are hugely

sensitive to the cell length to pore size ratio and it is therefore likely that any changes to the pore

dimensions will greatly affect cell strain. Importantly, the strut bridging cells represent 76% of the

seeded cells in a CG scaffold [Stops et al., 2008], and so the strain on these cells are arguably the

most representative of a cell population. So, it is important to note that the mean strains on the strut

bridging cells undergwent 1/10th of the apparent scaffold strain. Furthermore, the typically range of

strains experienced by these cells demonstrates -1.24 to 0.89% for the TRV model and -1.40 to

1.09% for the LGD model for 1% compression of the scaffold 95%

interval calculated from the mean and the standard deviation). Thus, the LGD model imparted a

larger maximum strain and a larger range of strains on the cell population that the TRV model.

14

Finally, the LGD model demonstrated different volume fractions and different relative densities

compared to the TRV model (Table 1). While the relative densities of the TRV model concurred

with previous experiments, the LGD model had a relative density some 50% higher [Harley et al.,

2007]. This disparity may arise due to localised hotspots of high density within the LGD model.

Given that this LGD relative density is comparable to the density measured for larger pore size CG

scaffolds [Harley et al., 2007], it is likely that these hotspots are a product of the fabrication

process. The volume fractions of 0.12 and 0.16, TRV and LGD respectively, did however both

concur with experimental data of 0.13-0.17 [Nehrer et al., 1997]. Importantly, these two descriptors

define two cell characteristics: cell movement and fluid flow patterns, as defined by the local

volume fraction, and cell synthesis and scaffold degradation rates, as defined by the local relative

densities. From the results, it appears that within either the air-side or the pan-side, cell movement

and fluid flow may be highest as these two areas demonstrated the lowest volume fraction (regions

1-4 and 10 in Figure 5a). Conversely, the mid-region appears to have the highest relative densities

(regions 6-9 in Figure 5b), thus suggesting relatively slow synthesis and degradation rates. The

impact of these regional variances on localised tissue growth is unknown. However, on a scaffold-

level, previous investigations have demonstrated that scaffold volume fraction can influence cell

infiltration: the larger the pore size (lower volume fraction) the more the cells disperse throughout

the scaffold due the increased fluid movement [Byrne et al., 2008; Tierney et al., 2008]; though

interestingly without fluid influences, and when contact guidance is measured (cell motility along

scaffold struts), cells migrate less in larger pores (151µm to 96µm) [Harley et al., 2008]. Similarly,

biosynthesis and degradation rates have also been shown to vary according to scaffold properties,

such as cross-link densities and stiffness, which in part is related to relative density [Chevallay et

al., 2000; Lee et al., 2001; Petite et al., 1994; Powell et al., 2006; Vickers et al., 2006; Weadcock et

al., 1996]. Thus, it is likely the regional variances do impact on cell activity and tissue growth.

Further work should look to explore and quantify the influence of these CG scaffold characteristics

on tissue growth patterns.

15

ë ÝÑÒÝÔËÍ×ÑÒÍ

This investigation has examined the salient mechanical and architectural characteristics of a CG

scaffold. The findings suggest that a regional-level environment exists within a CG scaffold. For

example, the intermediate region (TRV) exhibited a lower structural modulus (~40%), a lower

volume fraction (~30%), a lower relative density (~38%) but a larger average pore size (~25%),

compared to the entire scaffold (LGD). Regional level cell strain also occurred: the entire scaffold

(LGD) imparted a higher maximum strain (~200%) and a much more diverse range of strains than

the intermediate region alone (TRV). Yet, to what extent these regional variances influence

localised tissue growth is uncertain and future studies may wish to explore this avenue further by

sampling specific regions of interest. However, we can speculate that the regional architectural and

mechanical characteristics will influence cell differentiation and proliferation rates. While the

mechanical stimuli imparted onto the cells via the micro-mechanical deformation of the scaffold

will vary from region to region, it is also likely that the architectural variances will impact on fluid

flow. Without an in-depth analysis of cell activity within each region, the potential for

homogeneous tissue grown from a CG scaffold cannot be fully appreciated.

This study has provided a platform for future studies to generate idealised computational models

based on the geometric and mechanical descriptors found herein. Furthermore, this investigation

offers current in-vitro mechanical stimulation protocols a better understanding of micro-mechanical,

or cell-level, deformation magnitudes. As the intermediate mid-region demonstrated the most

homogeneous environment, future in-vitro procedures may wish to either adjust the manufacturing

process to deliver an entire construct in line with the intermediate mid-region, or alternatively,

isolate the intermediate mid-region for cell culture.

Acknowledgements

Funding for this work was provided by the Programme for Research in Third Level Institutions

(PRTLI), administered by the Higher Education Authority (HEA) and a SFI Foundation Ireland

on the SGI Altix high performance computer at NUI, Galway under an academic license from Intel

Fortran, Inc. Furthermore, the authors wish to acknowledge the SFI/HEA Irish Centre for High-

End Computing (ICHEC) for the provision of computational facilities and support.

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Figure 1. A CG scaffold has regional architectural characteristics due to the manufacturing technique. The aboveSEM images highlight the three significant regions referred to throughout this investigation with a) the air-side layer, b)the intermediate mid-region and c) the pan-side region. All images were taken from a dry CG Scaffold samplefabricated at a freeze drying temperature of -40oc.

Figure 2. An SEM study was undertaken to highlight the micro-structural dimensions of a CG scaffold. Aboveshows a sequential series of zoomed-in images taken from the intermediate region of the scaffold. Selections of strutthicknesses are indicated within images b, c and d. Also, tellipse for images b and c; note a typical cell scaled to fit image d was too large to fit within the image dimensions.

Figure 3. Two unit cell FE models were constructed so that the architectural variances observed between the air-sideand the pan-side of a CG scaffold could be examined. Accordingly, the TRV model corresponded to a region takenfrom the intermediate mid-region in the transverse plane (x-y), whereas the LGD model represented the architecture ofboth the air- and pan-side by detailing the scaffold along the entire longitudinal axis (z). Note all the subsequent FEanalyses follow the same axis conventions stated here and represent a uniaxial compressive strain in the z direction.

Figure 4. Two sections extracted from the LGD model displaying te-like configuration of the microstructureas signified by the highlighted surfaces.

Figure 5. The regional characteristics of the CG scaffold from the LGD model mesh are defined here in terms of a)the volume fraction and b) the density relative to pure collagen. The vertical axes denote the region from which thedata expresses; the corresponding region number refers to the region in the vertical axis of the model from which thedata expresses; note region 1 relates to the most pan-side region, while region 10 refers to the most air-side region.Note the images adjacent to the vertical axes depict the corresponding regions within the CG scaffold (i.e. the air -sidecorresponds to region 10: volume fraction = 0.1539; relative density = 0.0096).

Figure 6. The maximum principal stresses (Pa) are depicted for a) the TRV model and, b) the LGD model for anapparent uniaxial compressive strain of 1% along the z axis.

Figure 7. The total displacement magnitudes, i.e. square root(ux2 + uy

2 + uz2), (µm) experienced for a) the TRV

model and b) the LGD model for an apparent uniaxial compressive strain of 1% in the z axis (the maximumdisplacement corresponds to the respective 1% strain). Note, for an homogeneous, isotropic solid material, thedisplacement contours would display horizontal iso-bands.

Figure 8. The peak principal stress distributions are depicted as a fraction of the scaffold solid for both the TRVmodel and the LGD model for an apparent uniaxial compressive strain of 5.6% in the z axis. A comparison of themeans showed a significant (p<0.001) difference between the LGD and the TRV model respectively.

Figure 9. The number of voxels that exceed the pre-defined critical stress magnitude of 1.78kPa is depicted as a) theregional volume fraction in the TRV model and b) the regional volume fraction in the LGD model. For both models,an apparent uniaxial compressive strain of 5.6% along the z axis was applied. The vertical axis numbers (1-10)correspond to the contiguous regions in the adjacent image, i.e. region 1 relates to the most pan-side region and region10 refers to the most air-side region.

Figure 10. The inferred cells strains are depicted here as boxplots for a) the cells cross-bridging multiple struts and,b) the cells spread along a single strut surface. Both the TRV and the LGD model were given an apparent uniaxialcompressive strain of 1% strain along the z axis. Note the above boxplots are for illustrative purposes only as themaximum and minimum values depicted by the whiskers of the boxplots are the statistical maximum and minimumvalues, not the actual maximum and minimum values quoted within the text. The dots represent the statistical outliers,as defined by a z score equal to or above to 5 standard deviationsas this would have resulted in a scale with illegible boxplot dimensions.

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We thank the reviewers for raising important questions regarding the work from this manuscript. In thefollowing we attempt to deal with the concerns of the reviewers and in the process of doing so, webelieve that the clarifications and justifications that have been added to the manuscript nowstrengthen the paper. We have responded to each question individually with commentary and a smallsummary of the changes made to the manuscript, and where possible, indicated the location of thesechanges.

In particular, we would note the significant effort made to accommodate what appeared to us to bediffering views of the two reviewers in relation to the written style: Reviewer#1 praised the languagestyle while Reviewer#2 suggested the wording was too verbose; we hope we have managed toaccommodate both opinions.

Note, all commentary by the authors is in red arial font.

place). W the manuscript with the revisions highlighted in red to helpthe reviewer locate the changes.

Reviewer #1: This paper is about making finite element models oftissue engineering scaffolds. The work involved constructing twomodels of parts of a CG scaffold. Results include analysis ofporosity, scaffold shape factors (e.g. struts, plates etc), elasticmodulus and strains experienced by cells attached in different ways.

This is a significant achievement given the size of the meshinvolved and the practical difficulties in measuring the abovequantities. I have only a few comments:

1) They say there was significant variation in porosity: actually Iwas surprised that the variation was so small, around 10%. Anywayit's good that they can visualise and quantify the regionaldifferences in porosity which occur due to processing methods.We agree that 10% may seem relatively small, but we have attempted to use the volume fraction asone method in a system of methods to describe the scaffold. We believe that this level of detail isvital in contributing towards the understanding of the scaffold as a whole.

2) The criterion for elastic buckling is simplistic and the authorsadmit this and discuss it. It's probably better just to say that youare recording the %age of the material which exceeds a certainstress, arbitrarily chosen but possibly related to the stress atwhich failure by buckling occurs.

We agree that this is a criterion based on a simplified value, but we chose this buckling criterion toadd a functional, or a - Following much considerationand discussion, we decided to keep the buckling criteria description within the methods section as webelieve that it deserves a reasonable description of how we came to the critical stress magnitude (itwould have been too long for the discussion section). We believe this description in the methodssections enables the reader to appreciate that the critical stress magnitude is based on reasonablelogic, though simplified input values. We do feel that this criterion does enable the reader to betterappreciate the value of the stress magnitudes within the scaffold and so believe it should receivesome attention within the methods section.

3) As regards the strain experienced by the cells, I don't

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