TSINGHUA SCIENCE AND TECHNOLOGY ISSN 1007-0214 03/38 pp20-23 Volume 14, Number S1, June 2009

On Modeling Bio-Scaffolds: Structural and Fluid Transport Characterization Based on 3-D Imaging Data

HU Zhigang1, NOTARBERARDINO Bruno2, BAKER Matthew3, TABOR Gavin3, HAO Liang3, TURNER Irene3, YANG Lincoln4,**

1. Henan University of Science and Technology, Luoyang, Henan 471003, China;

2. School of Engineering, Computing and Mathematics, University of Exeter, Exeter EX4 4QF, United Kingdom; 3. Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, United Kingdom;

4. Shanghai Gaitech Scientific Instruments Co., Ltd., Shanghai 200030, China

Abstract: Bio-scaffolds which are most commonly open celled porous structures are increasingly used for

tissue engineering and regenerative medicine. A number of studies have shown that the bulk properties of

such irregular structures are poorly modeled using idealized unit cell approaches. The paper therefore uses

novel image based meshing techniques to explore both fluid flow and bulk structural properties of a bone

scaffold, as accurate modeling of bio-scaffolds with non-uniform cellular structures is very important for the

development of optimal scaffolds for tissue engineering application. In this study, a porous hydroxyapa-

tite/tricalcium phosphate (HA/TCP) bone scaffold has been scanned in a Micro-CT scanner, and converted

into a volumetric mesh using image processing software developed by the authors. The resulting mesh was

then exported to commercial FEA and CFD solvers for analysis. Initial FEA and CFD studies have shown

promising results and have highlighted the importance of accurate modeling to understand how microstruc-

tures influence the mechanical property of the scaffold, and to analyze flow regimes through the sample.

The work highlights the potential use of image based meshing for the ad hoc characterization of scaffolds as

well as for assisting in the design of scaffolds with tailored strength, stiffness, and transport properties.

Key words: bio-scaffolds; material characterization; finite element; computational fluid dynamics; dynamics

microstructures

Introduction

Recent development of high resolution imaging mo-dalities such as Micro-CT allows realistic porous struc-tures to be straightforwardly and accurately scanned with sub-micron image resolutions possible on some commercially available systems. Combined with novel meshing techniques, these imaging techniques allow for robust and rapid conversion of the 3-D scan data into finite element and finite volume meshes which can straightforwardly be used to characterize

the response[1]. In addition, various image processing tools allow for interesting sensitivity analyses to be carried out helping to elucidate relationships between key architectural parameters such as rib thickness and bulk properties. A number of studies will demonstrate the ease with which fidelic models of the complex micro-architectures of bio-scaffolds can be generated.

1 Data Acquisition

A porous hydroxyapatite/tricalcium phosphate (HA/ TCP) bone scaffold manufactured at the University of Bath[2], shown in Fig. 1, was studied. The manufactur-ing process consists broadly of coating a poly-ethylene

Received: 2008-11-09; revised: 2009-03-24

** To whom correspondence should be addressed. E-mail: service@gaitech.net; Tel: 86-13371892277

HU Zhigang et al：On Modeling Bio-Scaffolds: Structural and Fluid Transport …

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open celled foam in hydroxy-apatite and sintering the foam using the dipping method[3].

Fig. 1 Porous hydroxyapatite/tricalcium phosphate (HA/TCP) bone scaffold

3-D image scanning was performed using the Sky-Scan1174 compact Micro-CT. This scan utilizes an X-ray source with adjustable voltage and a range of filters for versatile adaptation to different object densities. A sensitive 1.3 megapixel X-ray camera allows scanning of the whole sample volume in several minutes. Vari-able magnification (6-30 µm pixel size) is combined with object positioning for easy selection of the object part to be scanned. For the specific case a magnifica-tion of 18 µm and an exposure time of 4350 ms have been selected. 50 kV and 800 µA were imposed re-spectively for the Voltage and the Current. The flat-field correction option was used and the average frames considered for the scanning process was equal to 5. A 7.5 mm aluminium filter was introduced to re-duce the maximum absorption value registered by the camera.

2 Image Segmentation and Mesh Generation

Resultant image files were imported into ScanIP[4] and thresholded for values from 18 to 255 to create the re-spective masks. Re-sampled at a resolution of 0.036 mm × 0.036 mm × 0.036 mm the models were rescaled to preserve the original size. The relative density com-puted is ∅ =24.7 %. An image of the model generated in ScanIP is presented in Fig. 2.

The model was imported into +ScanFE[5] and a mesh of both HA and the void domains inside the struts was generated. The voids were used to measure the internal

porosity related to the manufacturing process (Fig. 3) and the HA mesh was used to establish bulk stiffness and to explore the influence of the microstructure on the strength of the structure[6]. There are a number of major advantages in the +ScanFE approach used for mesh generation including: image based accuracy; fi-nite element and finite volume compatible meshes; and perfectly conforming cell/element interfaces at domain interfaces. For a review of image based meshing tech-niques the reader is referred to Ref. [7].

Fig. 2 (HA/TCP) bone scaffold 3-D reconstruction from Micro-CT data in ScanIP (Simpleware) of 3-D scan

Fig. 3 Mask of the internal pores segmented in ScanIP; the pores not belonging to the mask are con-nect to the outside in the previous and following slices

3 Characterization

An optimized scaffold design must incorporate the ele-ments of both biological and mechanical characteristics of the studied system[8,9]. Both the flow characteristics and the mechanical behaviour of these microstructures

Tsinghua Science and Technology, June 2009, 14(S1): 20-23 22

are of fundamental importance. The fluid dynamics is necessary for the nutrient transfer and cell migration. The mechanical environment involves the loading re-quirements as well as the spatial localization of cell types to promote cell-cell signaling; scaffolds engi-neered for this environment may be successful at trans-ferring mechanical loads. Failure to incorporate both of these design criteria into the entire structure will in-hibit the success and longevity of treatment.

3.1 Structural characterization

3.1.1 Computational model The segmented volume was automatically meshed us-ing +ScanFE and a model consisting of 4 464 293 lin-ear tetrahedral elements and 992 000 nodes was gener-ated. The meshing scheme was automated and robust with no need for correcting for pathological or poor quality elements. 3.1.2 Boundary conditions and loads The model was fixed on the bottom surface in the di-rection of the applied displacement (free breathing) and a displacement equal to 0.084 mm was applied on the top surface. The displacement has been applied in the direction normal to the top surface of the model. All the nodes of this surface have been constrained in the direction of the applied displacement and let free to move in the other two directions (free breathing). The displacement has been calculated in order to get an ef-fective engineering strain of ε = 1%. The mechanical properties considered for the model consist in a Young’s Modulus E = 40 GPa and a Poisson’s ratio ν = 0.45 and the structure has been assumed com-pletely elastic. The finite element analysis was run us-ing Abaqus/Standard[10] within the framework of the small displacement theory. 3.1.3 Results The response to the static displacement was of interest in order to understand how the microscructure influ-ences the mechanical property of the scaffold. The ef-fective Young’s Modulus of the structure computed E*= 0.49 GPa is over eighty times lower than the Young’s modulus of the parent Hydroxyapatite (40 GPa). Although the effective density of the scaf-fold is only slightly less than a quarter that of uniform HA, this is not an unexpected result as the relationship between effective density and the Young’s modulus is highly non-linear[11]. The stress distribution calculated

in Abaqus (Figs. 4a, 4b) shows that the bigger amount of the stress is localized where the coating of HA around the ribs of the original polyurethane foam is thinner.

(a) Before compression

(b) After compression

Fig. 4 Stress-strain distribution calculated in Abaqus/ Standard before and after compression

3.2 Flow characterization

3.2.1 Computational model The negative of the segmented volume was automati-cally meshed using +ScanFE and a model consisting of 26 481 770 tetrahedral cells was produced. 3.2.2 Boundary conditions and loads The commercial CFD code Fluent[12] was used to cre-ate contours of velocity magnitude through the sample, as shown in Fig. 5a indicating distinct pathways of mainstream velocity. Initial computational studies were run using water at a range of Reynolds numbers from Re=0.4 to Re=2.0. Pressure drop per unit length was calculated as a function of the Reynolds number as shown in Fig. 5b. 3.2.3 Results Initial CFD studies have shown promising results and have highlighted the importance of CFD in analyzing

HU Zhigang et al：On Modeling Bio-Scaffolds: Structural and Fluid Transport …

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flow regimes through the sample.

(a) Map distribution

(1-e is the packing density or volume fraction)

(b) Graph Fig. 5 Pressure drop per unit length as a function of the Reynolds number

4 Conclusions

The work being carried out highlights the potential use of image based meshing techniques for the ad hoc characterization of scaffolds as well as for assisting in the design of scaffolds with tailored strength, stiffness, and transport properties. What is important to under-line is the ease with which such numerical studies can now be carried out due to advances in image based meshing algorithms, computational hardware, and im-proved imaging techniques. Indeed all the computa-tional analyses presented were carried out on desktop (DELL) personal computers.

References

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[5] +ScanFE. Simpleware Ltd, Innovation Centre, Rennes Drive, EX4 4RN, UK, http://www.simpleware.com.

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[7] Young P G, Beresford-West T B H, Coward S R L, Notar-berardino B, Walker B, Aziz A. An efficient approach to converting 3-D image data into highly accurate computa-tional models. Philosophical Transactions of the Royal So-ciety A, 2008, 366: 3155-3173.

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[10] Abaqus/Standard. SIMULIA, Rising Sun Mills, 166 Valley Street, Providence, RI, 02909, USA, http://www.simulia. com.

[11] Gibson L J, Ashby M F. Cellular Solids: Structure and Properties. Cambridge University Press, Cambridge, UK, 1997.

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