J Mater Sci: Mater Med (2014) 25:2573–2578 DOI 10.1007/s10856-014-5264-7
A comparative study of oxygen diffusion in tissue engineering scaffolds T. Fiedler • I. V. Belova • G. E. Murch • G. Poologasundarampillai • J. R. Jones • J. A. Roether • A. R. Boccaccini
Received: 16 March 2014 / Accepted: 19 June 2014 / Published online: 14 July 2014 Ó Springer Science+Business Media New York 2014
Abstract Tissue engineering scaffolds are designed to support tissue self-healing within physiological environments by promoting the attachment, growth and differentiation of relevant cells. Newly formed tissue must be supplied with sufficient levels of oxygen to prevent necrosis. Oxygen diffusion is the major transport mechanism before vascularization is completed and oxygen is predominantly supplied via blood vessels. The present study compares different designs for scaffolds in the context of their oxygen diffusion ability. In all cases, oxygen diffusion is confined to the scaffold pores that are assumed to be completely occupied by newly formed tissue. The solid phase of the scaffolds acts as diffusion barrier that locally inhibits oxygen diffusion, i.e. no oxygen passes through the scaffold material. As a result, the oxygen diffusivity is determined by the scaffold porosity and pore architecture. Lattice Monte Carlo simulations are performed to compare the normalized oxygen diffusivities in scaffolds obtained by the foam replication (FR) method, robocasting and sol–gel T. Fiedler (&) I. V. Belova G. E. Murch School of Engineering, The University of Newcastle, Callaghan NSW 2287, Australia e-mail: [email protected] G. Poologasundarampillai J. R. Jones Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK J. A. Roether Department of Materials Science and Engineering, Institute of Polymer Materials, University of Erlangen-Nuremberg, 91058 Erlangen, Germany A. R. Boccaccini Department of Materials Science and Engineering, Institute of Biomaterials, University of Erlangen-Nuremberg, 91058 Erlangen, Germany
foaming. Scaffolds made by the FR method were found to have the highest oxygen diffusivity due to their high porosity and interconnected pores. These structures enable the best oxygen supply for newly formed tissue among the scaffold types considered according to the present numerical predictions.
1 Introduction Over the past 60 years significant research has been conducted focusing on improved materials with enhanced biocompatibility. The result of impressive research efforts worldwide is the development of so-called third-generation biomaterials that are slowly resorbed by the body whilst at the same time stimulating tissue regrowth [1]. Perhaps the most promising use of these advanced biomaterials is in tissue engineering scaffolds within the discipline of regenerative medicine. Indeed the design of scaffolds that can provide the greatest chance of a successful tissue or organ repair is an area of extensive continuous research [2, 3]. In general terms the suitability of a scaffold for application in tissue engineering is governed by its composition (and resulting bioactivity), scaffold porosity, pore size, degradation rate and its mechanical properties [4]. The present study focuses on a further important criterion, namely oxygen diffusivity, which is related to the pore structure of the scaffolds and has been investigated only to a limited extend so far. It is well-known that the transport of oxygen, nutrients, waste and biomolecules in tissue engineering scaffolds is essential for the function and growth of new tissue [2, 5]. In addition, waste products need to be removed. Failure to do so will trigger necrosis and ultimately cause the failure of the tissue engineering approach. The main transport mechanism
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of oxygen within tissue engineering scaffolds is diffusion. In a comprehensive study involving experimental measurements of oxygen diffusion in cylindrical polycaprolactone (PCL) scaffolds, two stages of the diffusion process were differentiated [5]. It was found that initial diffusion was controlled by pore tortuosity whereas diffusion at a later stage was governed by the scaffold porosity. Overall, the scaffold porosity was identified to be the dominating factor. Further geometric features that affect the mobility of nutrients, waste and biomolecules in tissue engineering scaffolds are pore size and permeability [6]. In addition, scaffold degradation (resorption) alters the aforementioned parameters over time. Kang et al. [7] conducted experimental measurements combined with numerical simulation on a simplified geometry to study tissue formation in scaffolds. They described a decrease of the oxygen diffusivity with increasing tissue formation, i.e. newly formed tissue decreases the mobility of oxygen within the scaffold. They suggest the use of a time-dependent diffusivity to consider this phenomenon in numerical modelling. The present investigation focuses on the final stage of oxygen diffusion where tissue has completely penetrated the scaffold but prior to vascularization and neglecting a significant effect of the growth of blood vessels during tissue growth, as would be relevant in bone for example. As a result, a lower bound for oxygen diffusivity is obtained. Croll et al. [8] used a homogenized model to simulate oxygen diffusion and cell growth. A qualitative comparison between simulation and in vivo experiments showed good agreement. One of the main conclusions of their study [8] was that localized cell seeding in the proximity of blood vessels is beneficial for tissue formation by minimizing necrosis. Vascularization has been correctly identified as an essential prerequisite for successful tissue regeneration on samples in bone tissue engineering [9, 10]. Chung et al. [11] developed a mathematical model for cell growth in (non-vascular) cartilage tissue engineering scaffolds. Their simulation incorporated cell growth and cell diffusion. In contradiction to a previous study [8] they concluded that uniform seeding is a beneficial strategy that increases the cell growth rate. Shanbhag et al. [12] investigated cell diffusion inside an inverted colloidal crystal (ICC) geometry using Brownian dynamics and Monte Carlo simulations. The regular geometry of the material was approximated using a simplified model structure made of intersecting spheres. For small particles (small nutrients or oxygen) they found a 70 % reduction of the relative diffusivity. In addition, the diffusivity was found to decrease linearly with increasing particle size. The present study uses Lattice Monte Carlo (LMC) analysis to determine the effective diffusivity in different types of scaffolds which are being widely investigated in tissue engineering for various tissues (see Fig. 1). LMC is a versatile finite difference method that has already been
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successfully applied towards the simulation of mass and thermal diffusion in composite materials and cellular structures similar to tissue engineering scaffolds [13–15]. Effective diffusivities are obtained and compared for 45S5 bioglass-PCL robocast structures [16], bioactive glass 70S30C (70 mol% SiO2, 30 mol% CaO) sol–gel foam (SGF) [17, 18] and titania scaffolds produced via the foam replication (FR) method [19]. Driven by the complex and stochastic scaffold geometries, the numerical models used are derived from micro-computed tomography (lCT) data.
2 Methodology In the context of the current study, oxygen diffusion in tissue engineering scaffolds is addressed. To this end, lCT data of three different types of conventional scaffolds is converted into LMC calculation models. The considered scaffolds are robocast PCL-bioglass composites (RC) [16], SGF scaffolds [17], and scaffolds obtained by the FR method [18]. Owing to different manufacturing techniques these materials exhibit significantly different porosities and pore architecture. The corresponding values of porosity for the tested samples are 41.7–46.4 % (RC), 75.6 % (SGF) and 89.7–91.2 % (FR). In LMC simulations, the effective diffusivity is calculated as a percentage of the ‘solid’ tissue diffusivity. This means that pure tissue (in the absence of a scaffold) has a normalized diffusivity D = 100 %. The presence of a scaffold will impede the motion of oxygen molecules (i.e. it acts as a local barrier) decreasing this diffusivity. In order to obtain the absolute value of diffusivities, normalized diffusivities are multiplied by the oxygen diffusivity of the corresponding tissue. The approach selected presumes that oxygen diffuses exclusively within the newly formed tissue (e.g. gray phase in Fig. 2). The oxygen diffusion coefficient in tissue is governed by its water content [20]. Examples are the oxygen diffusivities in muscle D = 1.7 9 10-9 m2/s, lung D = 2.21 9 10-9 m2/s, brain D = 1.62 9 10-9 m2/s or blood D = 2.10 9 10-9 m2/s [21, 22]. In comparison, the oxygen diffusivity of scaffolds materials is several orders of magnitudes lower. For example, the oxygen diffusivity in Ti-20Mo is below 10-14 m2/s [23] and PCL is commonly used as an oxygen barrier [24]. It should be mentioned here that sol–gel scaffolds have nano-porous struts that permit some oxygen diffusion; however, this effect is not considered in the numerical modelling approach. As a result, oxygen diffusion inside the tissue will govern the ability of the scaffolds to provide oxygen to newly formed tissue. This assumption had already been made in a previous study on oxygen diffusion in tissue engineering scaffolds [7].
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Fig. 1 Micro-computed tomography reconstructions of scaffolds produced by a robocasting (RC) technique, b sol–gel foaming (SGF) method and c foam replication (FR) technique
Fig. 2 Decomposition in scaffold and tissue phases
For the determination of the effective diffusivities, LMC simulation is applied. This numerical method has already been successfully used in the simulation of mass transfer [11], the determination of effective thermal conductivities and mass diffusivities, transient thermal analyses, and moving boundary problems [12, 13]. LMC analysis is a phenomenological approach to diffusion simulation. Probing particles are randomly injected into a lattice model and allowed to explore their environment on random walks. The lattice models can be generated using lCT data. For RC, SGF and FR scaffolds two, one and three lCT data sets were available, respectively. The lCT data was stored as pixel images that represent layers of the material. By combining these layers, a three-dimensional voxel model of the scaffolds was obtained. Voxels have a primitive cubic topology, i.e. each voxel has six neighbors. As a result, probing particles have six possible jump directions, one of which is randomly chosen for each jump attempt. The probing particles do not interact, i.e. the presence of further particles does not affect the motion of each particle. As discussed earlier, oxygen diffusion is assumed to be limited to the tissue and the scaffold material acts as a barrier. As a consequence, only probing particles within the tissue phase are able to move. The tissue phase is identified by segmentation of the lCT data. Each voxel has been
assigned a grey level that corresponds to the X-ray attenuation within its volume. As a result, scaffold voxels exhibit light gray levels whereas pore (tissue) voxels appear darker. Accordingly, a threshold grey level can be assigned that separates both phases. A particle located within the tissue space can only move into a neighboring tissue voxel. In this case, the jump attempt always succeeds. Jump attempts aimed into the scaffold phase are rejected and the particle remains on its current location. After each jump attempt (successful or unsuccessful) the simulation time tLMC is incremented. The final simulation time tLMC must be chosen large enough so that the probing particles can explore a representative fraction of the scaffold geometry. Within the current simulations, an average displacement R = l/2 where l is the side length of the scaffold was considered sufficient to satisfy this condition. Using the Einstein diffusion equation (1) and the mean square displacement \R2[ of a large population of probing particles, the effective diffusivity D in d-dimensions can be calculated: D¼
\R2 [ 2d tLMC
ð1Þ
By considering only directional components of \R2[ a possible anisotropy of the diffusion coefficient can be
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In the following, results for the diffusion simulation of three different types of tissue engineering scaffolds are given: robocast (RC), SGF, and FR. Figure 3 shows the oxygen diffusivities for brain, muscle and lung tissue. As discussed above, the simulation model presumes that the tissue has completely penetrated the pore space of the scaffolds. Lung tissue has the highest intrinsic diffusivity thus exhibiting higher values for each scaffold (square markers). Overall, the oxygen diffusivity varies between 0.39 9 10-9 m2/s and 1.83 9 10-9 m2/s. It should be noted that the selected tissues, for which relevant data in the literature is available, are not necessarily related to the application of bioactive glass scaffolds used as model systems for this study (which are relevant in the context of bone regeneration). In order to better compare the performance of the various scaffold designs the diffusivities have been normalized in Fig. 4. In general, the diffusivity increases with volume fraction of the tissue. Robocast scaffolds exhibit the lowest porosity 41.7–46.4 % thus having low normalized diffusivities. Minimum and maximum directional diffusivities are indicated by cross markers. It can be seen that oxygen diffusion in the tissue phase of RC scaffolds exhibits a weak anisotropy. Sol–gel foam scaffolds have a significantly higher porosity of 75.6 %. However, its normalized diffusivity only slightly exceeds the value of the RC scaffolds. A likely explanation is the limited connectivity of neighboring pores through relatively small orifices (see Fig. 1b). Interconnects had a modal diameter of 96 lm [25]. Scaffolds
with ICC geometry exhibit a similar topology. A value of the effective diffusivity taken from [12] indicates an even lower diffusivity for ICC scaffolds. The highest diffusivity is found in the tissue phase of FR scaffolds. Due to the high scaffold porosity of 89.7–91.2 % and the good connectivity of pores, diffusivities reach up to 82.9 %. For vascularization the absolute size of interconnection is another important parameter. The channel width of the inter-cell connections is 700 lm in the RC, 96 lm in the SGF and approximately 300 lm in the FR scaffolds. The channel width of the SGF structure is expected to rapidly increase after a partial degradation of the scaffold has occurred, whereas the interconnectivity of the RC and FR structure will remain approximately constant. The dependence of the normalized diffusivity D on the tissue volume fraction U can be expressed using the simple relation D = U2. The corresponding function is plotted in Fig. 4 as a full line. The oxygen diffusivity D of scaffolds is closely related to their oxygen permeability P, an alternative parameter that is commonly used in a biological context [26]. In contrast to the diffusivity, the permeability does not account for the concentration gradient but instead uses the concentration difference to calculate flux J (i.e. J = -Ddc/dx = -PDc). However, both diffusion and permeability closely depend on the structure’s porosity and tortuosity. Thus, structures with high diffusivities such as scaffolds manufactured using the FR method also exhibit high oxygen permeability. As a result, oxygen can be better supplied to tissue formed inside the scaffold and away from the structure’s surface. This allows the formation and function of new tissue and prevents necrosis. It should be pointed out that as scaffolds are designed to degrade as tissue grows in, a future refining of the model should include the erosion of the scaffold walls to simulate degradation and to predict oxygen diffusion under such dynamic conditions.
Fig. 3 Oxygen diffusivities in different types of tissue that have penetrated the scaffold pore space
Fig. 4 Normalised diffusivity in tissue engineering scaffolds represented in Fig. 1
tested. In the results section, diffusivity values are given for the average diffusivity and the minimum and maximum directional diffusivities.
3 Results
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It is of interest to attempt to correlate the diffusivity and structural parameters of tissue engineering scaffolds. To this end, the ImageJ [27] plugin BoneJ [28] was used to calculate the connection density dC, the mean strut thickness t and the mean pore size s. The results are presented in Table 1 together with the coefficients of variation (CoVt,s) for strut thickness and pore size respectively. As already discussed above, it can be seen that the tissue volume fraction U has a significant impact on the diffusivity (see Fig. 4). The connection density dc describes the number of trabeculae per unit volume. Due to the more closed geometry of SGF scaffolds this parameter is not defined for this scaffold type. A higher connectivity may improve the diffusivity of the structure; however, this hypothesis cannot be confirmed by the limited data available. The mean strut thickness t and pore size s are obtained by growing spheres at each point within either the scaffold or pore space and determining the maximum size that fits within the corresponding phase. Even so, the absolute value of the pore size has limited impact on diffusion (unless convection becomes significant). Its coefficient of variation allows a quantification of pore size uniformity. The simplified example in Fig. 5 shows channels with a similar average pore size s. Model a has a constant diameter s that allows for fast diffusion whereas Model b has a thin bottleneck that will strongly decrease diffusion. Clearly the average absolute pore size is unsuitable for capturing this important difference between these structures. However, the coefficient of variation CoVs of both structures varies strongly. The corresponding value for Model a is about zero; whereas a high value Table 1 Diffusivities and structural parameters of tissue engineering scaffolds Structure RC SGF FR
D [–]
U [–]
dC [mm-3]
t [mm]
CoVt [–]
s [mm]
CoVs [–]
0.29
0.46
11.0
0.34
0.15
0.27
0.27
0.24
0.41
10.1
0.35
0.15
0.27
0.29
0.41 0.80
0.76 0.90
– 32.3
0.25 0.091
0.44 0.30
0.74 0.48
0.41 0.20
0.83
0.91
30.1
0.097
0.29
0.51
0.18
(approximately 0.58) is obtained for Model b where the sphere diameter decreases rapidly as one approaches the bottleneck. As a result, a small value of CoVs is a likely indication of a uniform pore size that is beneficial for diffusion as it indicates the absence of bottlenecks. This is reflected in low values of CoVs for the FR structures whereas the small orifices of the SGF cause a relatively large CoVs. The present paper focused exclusively on the oxygen diffusivity in tissue engineering scaffolds. However, the multi-functional nature of these structures must be considered. As an example, scaffolds must exhibit a sufficient mechanical strength to support tissue regeneration. Even though FR scaffolds exhibit the maximum oxygen diffusivity, their high porosity and micro-cracks limit their strength to *0.3 MPa making them the mechanically weakest structure among the scaffolds investigated, meaning that they should be reinforced with other phases, e.g. biopolymers [29]. In comparison, SGF structures have a compressive strength of 2.4 MPa [25] and preliminary tests on the RC scaffolds indicate a strength above 6 MPa.
4 Conclusions The present paper addressed the simulation of oxygen diffusion in tissue engineering scaffolds. As a result, the effective oxygen diffusivities in the tissue of selected scaffold structures were determined. Three different scaffold types (manufactured by robocasting, SGF and FR method) were considered. The diffusivity D was found to increase with the tissue volume fraction U. This dependence can be approximated using the simple parabolic function D = U2. Accordingly, high porosity scaffolds such as structures obtained by the FR method are beneficial for improved oxygen diffusion. High oxygen diffusivity supports the growth and function of tissue and contributes towards avoiding cell necrosis. In addition, the coefficient of variation of the pore sizes in a scaffold (calculated using ImageJ/BoneJ software) was identified as a likely parameter that influences the effective diffusivity. A low coefficient is a strong indicator of a pore network with uniform
Fig. 5 Uniformity of pore size
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cross sections without diffusion ‘‘bottlenecks’’ and thus a higher diffusivity for any given porosity. Certainly, other characteristics need to be considered for an ideal scaffold, including mechanical properties. For example, while FR scaffolds exhibit the highest oxygen diffusivity (as found in this numerical study) they are also the weakest of the three scaffold types investigated which may limit their application. Further improvement of the model are planned, for example incorporating the scaffold degradation kinetics to assess how it affects oxygen diffusion and to consider the study of oxygen diffusion on partially filled scaffolds to mimic closely the time-dependent slow growth of tissue along the scaffold wall. Acknowledgments The authors Dr Fiedler, Prof. Murch and Prof. Boccaccini want to acknowledge financial support by the Australian Research Council (ARC) in the framework of the Discovery Project DP130101377.
References 1. Hench LL, Polak JM. Third-generation biomedical materials. Science. 2002;295:1014–7. 2. Hutmacher DW, Schantz JT, Lam CXF, Tan KC, Lim TC. State of the art and future directions of scaffold-based bone engineering from a biomaterials perspective. J Tissue Eng Regen Med. 2007;1:245–60. 3. Ratner BD, Hoffman AS, Schoen FJ, Lemons JE. Biomaterials science: an introduction to materials in medicine. Amsterdam: Academic Press; 2004. 4. Rezwan K, Chen QZ, Blaker JJ, Boccaccini AR. Biodegradable and bioactive porous polymer/inorganic composite scaffolds for bone tissue engineering. Biomaterials. 2006;27:3413–31. 5. Karande TS. Effect of scaffold architecture on diffusion of oxygen in tissue engineering constructs. Ph.D. thesis, The University of Texas at Austin; 2007. 6. Karande TS, Ong JL, Agrawal CM. Diffusion in musculoskeletal tissue engineering scaffolds: design issues related to porosity, permeability, architecture, and nutrient mixing. Ann Biomed Eng. 2004;32:1728–43. 7. Kang TY, Kang HW, Hwang CM, Leel SJ, Park J, Yoo JJ, et al. The realistic prediction of oxygen transport in a tissue-engineered scaffold by introducing time-varying effective diffusion coefficients. Acta Biomater. 2011;7:3345–53. 8. Croll TI, Gentz S, Mueller K, Davidson M, O’Connor AJ, Stevens GW, et al. Modelling oxygen diffusion and cell growth in a porous, vascularizing scaffold for soft tissue engineering applications. Chem Eng Sci. 2005;60:4924–34. 9. Santos MI, Reis RL. Vascularization in bone tissue engineering: physiology, current strategies, major hurdles and future challenges. Macromol Biosci. 2010;10:12–27.
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J Mater Sci: Mater Med (2014) 25:2573–2578 10. Gorustovich AA, Roether JA, Boccaccini AR. Effect of bioactive glasses on angiogenesis: in-vitro and in-vivo evidence. A review. Tissue Eng Part B. 2010;16:199–207. 11. Chung CA, Yang CW, Chen CW. Analysis of cell growth and diffusion in a scaffold for cartilage tissue engineering. Biotechnol Bioeng. 2006;94:1138–46. 12. Shanbhag S, Lee JW, Kotov N. Diffusion in three-dimensionally ordered scaffolds with inverted colloidal crystal geometry. Biomaterials. 2005;26:5581–5. 13. Fiedler T, Murch GE, Belova IV. Solving complex thermal and mass transport problems with the Lattice Monte Carlo method. Cairns, QLD; 2010. p. 1476–81. 14. Veyhl C, Fiedler T, Andersen O, Meinert J, Bernthaler T, Belova IV, et al. On the thermal conductivity of sintered metallic fibre structures. Int J Heat Mass Transf. 2012;55:2440–8. 15. Fiedler T, Belova IV, Murch GE. Theoretical and Lattice Monte Carlo analyses on thermal conduction in cellular metals. Comput Mater Sci. 2010;50:503–9. 16. Eqtesadi S, Motealleh A, Miranda P, Pajares A, Lemos A, Ferreira JMF. Robocasting of 45S5 bioactive glass scaffolds for bone tissue engineering. J Eur Ceram Soc. 2014;34:107–18. 17. Midha S, Kim TB, van den Bergh W, Lee PD, Jones JR, Mitchell CA. Preconditioned 70S30C bioactive glass foams promote osteogenesis in vivo. Acta Biomater. 2013;9:9169–82. 18. Jones JR. Review of bioactive glass: from Hench to hybrids. Acta Biomater. 2013;9:4457–86. 19. Novak S, Druce J, Chen QZ, Boccaccini AR. TiO2 foams with poly(D, L-lactic acid) (PDLLA) and PDLLA/Bioglass coatings for bone tissue engineering scaffolds. J Mater Sci. 2009;44:1442–8. 20. Longmuir IS, Bourke A. The measurement of the diffusion of oxygen through respiring tissue. Biochem J. 1960;76(2):225–9. 21. Zaritzky NE, Bevilacqua AE. Oxygen diffusion in meat tissues. Int J Heat Mass Transf. 1988;31:923–30. 22. Evans NTS, Naylor PFD, Quinton TH. The diffusion coefficient of oxygen in respiring kidney and tumour tissue. Respir Physiol. 1981;43:179–88. 23. Nogueira RA, Grandini CR. Oxygen diffusion in Ti-20Mo alloys, used as biomaterial, measured by mechanical spectroscopy. Defect Diffus Forum. 2012;326–328:702–7. 24. Cava D, Gimenez E, Gavara R, Lagaron JM. Comparative performance and barrier properties of biodegradable thermoplastics and nanobiocomposites versus pet for food packaging applications. J Plast Film Sheeting. 2006;22:265–74. 25. Jones JR, Ehrenfried LM, Hench LL. Optimising bioactive glass scaffolds for bone tissue engineering. Biomaterials. 2006;27: 964–73. 26. German RM. Particle packing characteristics. Princeton: Metal Powder Industries Federation; 1989. 27. Schneider CA, Rasband WS, Eliceiri KW. NIH Image to ImageJ: 25 years of image analysis. Nat Methods. 2012;9:671–5. 28. Doube M, Kłosowski MM, Arganda-Carreras I, Cordelie´res F, Dougherty RP, Jackson J, et al. BoneJ: free and extensible bone image analysis in ImageJ. Bone. 2010;47:1076–9. 29. Fiedler T, Fisher M, Roether JA, Belova IV, Samtleben T, Bernthaler T, et al. Strengthening mechanism of PDLLA coated titania foam. Mech Mater. 2014;69:35–40.
A comparative study of oxygen diffusion in tissue engineering scaffolds T. Fiedler • I. V. Belova • G. E. Murch • G. Poologasundarampillai • J. R. Jones • J. A. Roether • A. R. Boccaccini
Received: 16 March 2014 / Accepted: 19 June 2014 / Published online: 14 July 2014 Ó Springer Science+Business Media New York 2014
Abstract Tissue engineering scaffolds are designed to support tissue self-healing within physiological environments by promoting the attachment, growth and differentiation of relevant cells. Newly formed tissue must be supplied with sufficient levels of oxygen to prevent necrosis. Oxygen diffusion is the major transport mechanism before vascularization is completed and oxygen is predominantly supplied via blood vessels. The present study compares different designs for scaffolds in the context of their oxygen diffusion ability. In all cases, oxygen diffusion is confined to the scaffold pores that are assumed to be completely occupied by newly formed tissue. The solid phase of the scaffolds acts as diffusion barrier that locally inhibits oxygen diffusion, i.e. no oxygen passes through the scaffold material. As a result, the oxygen diffusivity is determined by the scaffold porosity and pore architecture. Lattice Monte Carlo simulations are performed to compare the normalized oxygen diffusivities in scaffolds obtained by the foam replication (FR) method, robocasting and sol–gel T. Fiedler (&) I. V. Belova G. E. Murch School of Engineering, The University of Newcastle, Callaghan NSW 2287, Australia e-mail: [email protected] G. Poologasundarampillai J. R. Jones Department of Materials, Imperial College London, South Kensington Campus, London SW7 2AZ, UK J. A. Roether Department of Materials Science and Engineering, Institute of Polymer Materials, University of Erlangen-Nuremberg, 91058 Erlangen, Germany A. R. Boccaccini Department of Materials Science and Engineering, Institute of Biomaterials, University of Erlangen-Nuremberg, 91058 Erlangen, Germany
foaming. Scaffolds made by the FR method were found to have the highest oxygen diffusivity due to their high porosity and interconnected pores. These structures enable the best oxygen supply for newly formed tissue among the scaffold types considered according to the present numerical predictions.
1 Introduction Over the past 60 years significant research has been conducted focusing on improved materials with enhanced biocompatibility. The result of impressive research efforts worldwide is the development of so-called third-generation biomaterials that are slowly resorbed by the body whilst at the same time stimulating tissue regrowth [1]. Perhaps the most promising use of these advanced biomaterials is in tissue engineering scaffolds within the discipline of regenerative medicine. Indeed the design of scaffolds that can provide the greatest chance of a successful tissue or organ repair is an area of extensive continuous research [2, 3]. In general terms the suitability of a scaffold for application in tissue engineering is governed by its composition (and resulting bioactivity), scaffold porosity, pore size, degradation rate and its mechanical properties [4]. The present study focuses on a further important criterion, namely oxygen diffusivity, which is related to the pore structure of the scaffolds and has been investigated only to a limited extend so far. It is well-known that the transport of oxygen, nutrients, waste and biomolecules in tissue engineering scaffolds is essential for the function and growth of new tissue [2, 5]. In addition, waste products need to be removed. Failure to do so will trigger necrosis and ultimately cause the failure of the tissue engineering approach. The main transport mechanism
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of oxygen within tissue engineering scaffolds is diffusion. In a comprehensive study involving experimental measurements of oxygen diffusion in cylindrical polycaprolactone (PCL) scaffolds, two stages of the diffusion process were differentiated [5]. It was found that initial diffusion was controlled by pore tortuosity whereas diffusion at a later stage was governed by the scaffold porosity. Overall, the scaffold porosity was identified to be the dominating factor. Further geometric features that affect the mobility of nutrients, waste and biomolecules in tissue engineering scaffolds are pore size and permeability [6]. In addition, scaffold degradation (resorption) alters the aforementioned parameters over time. Kang et al. [7] conducted experimental measurements combined with numerical simulation on a simplified geometry to study tissue formation in scaffolds. They described a decrease of the oxygen diffusivity with increasing tissue formation, i.e. newly formed tissue decreases the mobility of oxygen within the scaffold. They suggest the use of a time-dependent diffusivity to consider this phenomenon in numerical modelling. The present investigation focuses on the final stage of oxygen diffusion where tissue has completely penetrated the scaffold but prior to vascularization and neglecting a significant effect of the growth of blood vessels during tissue growth, as would be relevant in bone for example. As a result, a lower bound for oxygen diffusivity is obtained. Croll et al. [8] used a homogenized model to simulate oxygen diffusion and cell growth. A qualitative comparison between simulation and in vivo experiments showed good agreement. One of the main conclusions of their study [8] was that localized cell seeding in the proximity of blood vessels is beneficial for tissue formation by minimizing necrosis. Vascularization has been correctly identified as an essential prerequisite for successful tissue regeneration on samples in bone tissue engineering [9, 10]. Chung et al. [11] developed a mathematical model for cell growth in (non-vascular) cartilage tissue engineering scaffolds. Their simulation incorporated cell growth and cell diffusion. In contradiction to a previous study [8] they concluded that uniform seeding is a beneficial strategy that increases the cell growth rate. Shanbhag et al. [12] investigated cell diffusion inside an inverted colloidal crystal (ICC) geometry using Brownian dynamics and Monte Carlo simulations. The regular geometry of the material was approximated using a simplified model structure made of intersecting spheres. For small particles (small nutrients or oxygen) they found a 70 % reduction of the relative diffusivity. In addition, the diffusivity was found to decrease linearly with increasing particle size. The present study uses Lattice Monte Carlo (LMC) analysis to determine the effective diffusivity in different types of scaffolds which are being widely investigated in tissue engineering for various tissues (see Fig. 1). LMC is a versatile finite difference method that has already been
123
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successfully applied towards the simulation of mass and thermal diffusion in composite materials and cellular structures similar to tissue engineering scaffolds [13–15]. Effective diffusivities are obtained and compared for 45S5 bioglass-PCL robocast structures [16], bioactive glass 70S30C (70 mol% SiO2, 30 mol% CaO) sol–gel foam (SGF) [17, 18] and titania scaffolds produced via the foam replication (FR) method [19]. Driven by the complex and stochastic scaffold geometries, the numerical models used are derived from micro-computed tomography (lCT) data.
2 Methodology In the context of the current study, oxygen diffusion in tissue engineering scaffolds is addressed. To this end, lCT data of three different types of conventional scaffolds is converted into LMC calculation models. The considered scaffolds are robocast PCL-bioglass composites (RC) [16], SGF scaffolds [17], and scaffolds obtained by the FR method [18]. Owing to different manufacturing techniques these materials exhibit significantly different porosities and pore architecture. The corresponding values of porosity for the tested samples are 41.7–46.4 % (RC), 75.6 % (SGF) and 89.7–91.2 % (FR). In LMC simulations, the effective diffusivity is calculated as a percentage of the ‘solid’ tissue diffusivity. This means that pure tissue (in the absence of a scaffold) has a normalized diffusivity D = 100 %. The presence of a scaffold will impede the motion of oxygen molecules (i.e. it acts as a local barrier) decreasing this diffusivity. In order to obtain the absolute value of diffusivities, normalized diffusivities are multiplied by the oxygen diffusivity of the corresponding tissue. The approach selected presumes that oxygen diffuses exclusively within the newly formed tissue (e.g. gray phase in Fig. 2). The oxygen diffusion coefficient in tissue is governed by its water content [20]. Examples are the oxygen diffusivities in muscle D = 1.7 9 10-9 m2/s, lung D = 2.21 9 10-9 m2/s, brain D = 1.62 9 10-9 m2/s or blood D = 2.10 9 10-9 m2/s [21, 22]. In comparison, the oxygen diffusivity of scaffolds materials is several orders of magnitudes lower. For example, the oxygen diffusivity in Ti-20Mo is below 10-14 m2/s [23] and PCL is commonly used as an oxygen barrier [24]. It should be mentioned here that sol–gel scaffolds have nano-porous struts that permit some oxygen diffusion; however, this effect is not considered in the numerical modelling approach. As a result, oxygen diffusion inside the tissue will govern the ability of the scaffolds to provide oxygen to newly formed tissue. This assumption had already been made in a previous study on oxygen diffusion in tissue engineering scaffolds [7].
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Fig. 1 Micro-computed tomography reconstructions of scaffolds produced by a robocasting (RC) technique, b sol–gel foaming (SGF) method and c foam replication (FR) technique
Fig. 2 Decomposition in scaffold and tissue phases
For the determination of the effective diffusivities, LMC simulation is applied. This numerical method has already been successfully used in the simulation of mass transfer [11], the determination of effective thermal conductivities and mass diffusivities, transient thermal analyses, and moving boundary problems [12, 13]. LMC analysis is a phenomenological approach to diffusion simulation. Probing particles are randomly injected into a lattice model and allowed to explore their environment on random walks. The lattice models can be generated using lCT data. For RC, SGF and FR scaffolds two, one and three lCT data sets were available, respectively. The lCT data was stored as pixel images that represent layers of the material. By combining these layers, a three-dimensional voxel model of the scaffolds was obtained. Voxels have a primitive cubic topology, i.e. each voxel has six neighbors. As a result, probing particles have six possible jump directions, one of which is randomly chosen for each jump attempt. The probing particles do not interact, i.e. the presence of further particles does not affect the motion of each particle. As discussed earlier, oxygen diffusion is assumed to be limited to the tissue and the scaffold material acts as a barrier. As a consequence, only probing particles within the tissue phase are able to move. The tissue phase is identified by segmentation of the lCT data. Each voxel has been
assigned a grey level that corresponds to the X-ray attenuation within its volume. As a result, scaffold voxels exhibit light gray levels whereas pore (tissue) voxels appear darker. Accordingly, a threshold grey level can be assigned that separates both phases. A particle located within the tissue space can only move into a neighboring tissue voxel. In this case, the jump attempt always succeeds. Jump attempts aimed into the scaffold phase are rejected and the particle remains on its current location. After each jump attempt (successful or unsuccessful) the simulation time tLMC is incremented. The final simulation time tLMC must be chosen large enough so that the probing particles can explore a representative fraction of the scaffold geometry. Within the current simulations, an average displacement R = l/2 where l is the side length of the scaffold was considered sufficient to satisfy this condition. Using the Einstein diffusion equation (1) and the mean square displacement \R2[ of a large population of probing particles, the effective diffusivity D in d-dimensions can be calculated: D¼
\R2 [ 2d tLMC
ð1Þ
By considering only directional components of \R2[ a possible anisotropy of the diffusion coefficient can be
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In the following, results for the diffusion simulation of three different types of tissue engineering scaffolds are given: robocast (RC), SGF, and FR. Figure 3 shows the oxygen diffusivities for brain, muscle and lung tissue. As discussed above, the simulation model presumes that the tissue has completely penetrated the pore space of the scaffolds. Lung tissue has the highest intrinsic diffusivity thus exhibiting higher values for each scaffold (square markers). Overall, the oxygen diffusivity varies between 0.39 9 10-9 m2/s and 1.83 9 10-9 m2/s. It should be noted that the selected tissues, for which relevant data in the literature is available, are not necessarily related to the application of bioactive glass scaffolds used as model systems for this study (which are relevant in the context of bone regeneration). In order to better compare the performance of the various scaffold designs the diffusivities have been normalized in Fig. 4. In general, the diffusivity increases with volume fraction of the tissue. Robocast scaffolds exhibit the lowest porosity 41.7–46.4 % thus having low normalized diffusivities. Minimum and maximum directional diffusivities are indicated by cross markers. It can be seen that oxygen diffusion in the tissue phase of RC scaffolds exhibits a weak anisotropy. Sol–gel foam scaffolds have a significantly higher porosity of 75.6 %. However, its normalized diffusivity only slightly exceeds the value of the RC scaffolds. A likely explanation is the limited connectivity of neighboring pores through relatively small orifices (see Fig. 1b). Interconnects had a modal diameter of 96 lm [25]. Scaffolds
with ICC geometry exhibit a similar topology. A value of the effective diffusivity taken from [12] indicates an even lower diffusivity for ICC scaffolds. The highest diffusivity is found in the tissue phase of FR scaffolds. Due to the high scaffold porosity of 89.7–91.2 % and the good connectivity of pores, diffusivities reach up to 82.9 %. For vascularization the absolute size of interconnection is another important parameter. The channel width of the inter-cell connections is 700 lm in the RC, 96 lm in the SGF and approximately 300 lm in the FR scaffolds. The channel width of the SGF structure is expected to rapidly increase after a partial degradation of the scaffold has occurred, whereas the interconnectivity of the RC and FR structure will remain approximately constant. The dependence of the normalized diffusivity D on the tissue volume fraction U can be expressed using the simple relation D = U2. The corresponding function is plotted in Fig. 4 as a full line. The oxygen diffusivity D of scaffolds is closely related to their oxygen permeability P, an alternative parameter that is commonly used in a biological context [26]. In contrast to the diffusivity, the permeability does not account for the concentration gradient but instead uses the concentration difference to calculate flux J (i.e. J = -Ddc/dx = -PDc). However, both diffusion and permeability closely depend on the structure’s porosity and tortuosity. Thus, structures with high diffusivities such as scaffolds manufactured using the FR method also exhibit high oxygen permeability. As a result, oxygen can be better supplied to tissue formed inside the scaffold and away from the structure’s surface. This allows the formation and function of new tissue and prevents necrosis. It should be pointed out that as scaffolds are designed to degrade as tissue grows in, a future refining of the model should include the erosion of the scaffold walls to simulate degradation and to predict oxygen diffusion under such dynamic conditions.
Fig. 3 Oxygen diffusivities in different types of tissue that have penetrated the scaffold pore space
Fig. 4 Normalised diffusivity in tissue engineering scaffolds represented in Fig. 1
tested. In the results section, diffusivity values are given for the average diffusivity and the minimum and maximum directional diffusivities.
3 Results
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It is of interest to attempt to correlate the diffusivity and structural parameters of tissue engineering scaffolds. To this end, the ImageJ [27] plugin BoneJ [28] was used to calculate the connection density dC, the mean strut thickness t and the mean pore size s. The results are presented in Table 1 together with the coefficients of variation (CoVt,s) for strut thickness and pore size respectively. As already discussed above, it can be seen that the tissue volume fraction U has a significant impact on the diffusivity (see Fig. 4). The connection density dc describes the number of trabeculae per unit volume. Due to the more closed geometry of SGF scaffolds this parameter is not defined for this scaffold type. A higher connectivity may improve the diffusivity of the structure; however, this hypothesis cannot be confirmed by the limited data available. The mean strut thickness t and pore size s are obtained by growing spheres at each point within either the scaffold or pore space and determining the maximum size that fits within the corresponding phase. Even so, the absolute value of the pore size has limited impact on diffusion (unless convection becomes significant). Its coefficient of variation allows a quantification of pore size uniformity. The simplified example in Fig. 5 shows channels with a similar average pore size s. Model a has a constant diameter s that allows for fast diffusion whereas Model b has a thin bottleneck that will strongly decrease diffusion. Clearly the average absolute pore size is unsuitable for capturing this important difference between these structures. However, the coefficient of variation CoVs of both structures varies strongly. The corresponding value for Model a is about zero; whereas a high value Table 1 Diffusivities and structural parameters of tissue engineering scaffolds Structure RC SGF FR
D [–]
U [–]
dC [mm-3]
t [mm]
CoVt [–]
s [mm]
CoVs [–]
0.29
0.46
11.0
0.34
0.15
0.27
0.27
0.24
0.41
10.1
0.35
0.15
0.27
0.29
0.41 0.80
0.76 0.90
– 32.3
0.25 0.091
0.44 0.30
0.74 0.48
0.41 0.20
0.83
0.91
30.1
0.097
0.29
0.51
0.18
(approximately 0.58) is obtained for Model b where the sphere diameter decreases rapidly as one approaches the bottleneck. As a result, a small value of CoVs is a likely indication of a uniform pore size that is beneficial for diffusion as it indicates the absence of bottlenecks. This is reflected in low values of CoVs for the FR structures whereas the small orifices of the SGF cause a relatively large CoVs. The present paper focused exclusively on the oxygen diffusivity in tissue engineering scaffolds. However, the multi-functional nature of these structures must be considered. As an example, scaffolds must exhibit a sufficient mechanical strength to support tissue regeneration. Even though FR scaffolds exhibit the maximum oxygen diffusivity, their high porosity and micro-cracks limit their strength to *0.3 MPa making them the mechanically weakest structure among the scaffolds investigated, meaning that they should be reinforced with other phases, e.g. biopolymers [29]. In comparison, SGF structures have a compressive strength of 2.4 MPa [25] and preliminary tests on the RC scaffolds indicate a strength above 6 MPa.
4 Conclusions The present paper addressed the simulation of oxygen diffusion in tissue engineering scaffolds. As a result, the effective oxygen diffusivities in the tissue of selected scaffold structures were determined. Three different scaffold types (manufactured by robocasting, SGF and FR method) were considered. The diffusivity D was found to increase with the tissue volume fraction U. This dependence can be approximated using the simple parabolic function D = U2. Accordingly, high porosity scaffolds such as structures obtained by the FR method are beneficial for improved oxygen diffusion. High oxygen diffusivity supports the growth and function of tissue and contributes towards avoiding cell necrosis. In addition, the coefficient of variation of the pore sizes in a scaffold (calculated using ImageJ/BoneJ software) was identified as a likely parameter that influences the effective diffusivity. A low coefficient is a strong indicator of a pore network with uniform
Fig. 5 Uniformity of pore size
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cross sections without diffusion ‘‘bottlenecks’’ and thus a higher diffusivity for any given porosity. Certainly, other characteristics need to be considered for an ideal scaffold, including mechanical properties. For example, while FR scaffolds exhibit the highest oxygen diffusivity (as found in this numerical study) they are also the weakest of the three scaffold types investigated which may limit their application. Further improvement of the model are planned, for example incorporating the scaffold degradation kinetics to assess how it affects oxygen diffusion and to consider the study of oxygen diffusion on partially filled scaffolds to mimic closely the time-dependent slow growth of tissue along the scaffold wall. Acknowledgments The authors Dr Fiedler, Prof. Murch and Prof. Boccaccini want to acknowledge financial support by the Australian Research Council (ARC) in the framework of the Discovery Project DP130101377.
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