Poster: Tailoring the Mechanical Environment of Scaffolds with Computer Aided Design and Rapid Prototyping, 10/2004

INTRODUCTION Porous scaffolds are successful in stimulating tissue growth but contain variable local properties which are not optimal. Stress profiles depend on volume fraction and vary wildly, presenting regions unsuitable for cellular functions. Repeatable, patterned architectures allow for a tailored mechanical environment. A library of architectures was evaluated which could be used for scaffold design in an assembled manner. Three groups were evaluated, random scaffold models, regular architectures taken from the literature, and natural architectures taken from the Platonic and Archimedean solids. We demonstrate the effect of material arrangement on the resulting apparent properties and the stress distributions. We further illustrate that architectures with mechanical integrity do not have optimal stress distributions. METHODS: Computer Aided Design Tailoring The Mechanical Environment Of Scaffolds With Computer Aided Design And Rapid Prototyping

Computer algorithm to simulate particulate leaching scaffold design (Figure 1)

Pore sizes of 225µm, 400µm, and 605µm were used in repeated simulations

Volumetric porosity was varied from 50 to 80% for each pore size

METHODS: Finite Element Analysis Figure 7. Finite element analysis procedure for architectures. Left, single architecture, fixed in translation in y-direction and displaced from the top. Middle, boundary conditions applied to the unit block in the y-direction. Right, contour plot of elemental maximum principal stress within the architecture. Acknowledgements Thanks to Jeremy Lemoine. This work supported by the Texas ATP Grant Program. References 1.Wilson, C et al. J Biomed Mater Res 68A: 123-132, 2004. 2.Chu TM et al. J. Mat. Sci 12: 471-478, 2001. 3.Yang, S et al. Tissue Eng 8(1): 1-11 (2002) 4.Leong KFet al. Biomaterials. 2003 Jun;24(13):2363-78

Various architectures were meshed using ABAQUS/CAE (Abaqus, Inc., Pawtuckett, RI) with greater than 20,000 elements (Figure 7) based upon a previous convergence study (Figure 8)

Single step, linear, elastic finite element analysis performed using ABAQUS Standard (Abaqus, Inc., Pawtuckett, RI)

Boundary conditions were unconfined uniaxial compression with a prescribed displacement of 1%

All scaffolds were assigned isotropic material properties with a Young’s modulus (E) of 2GPa and a Poisson’s Ratio (v) of 0.3

Apparent (structural) Modulus was calculated in each case

Tissue engineering scaffolds from particulate leaching, literature designs, and Platonic and Archimedean solids were generated with volumetric porosity which was varied from 50-90%. All scaffolds were designed with the same global bounding box. DISCUSSION RESULTS: Random Porous Solids Figure 8. Architectures were meshed at varying densities to determine convergence of reaction force. Reaction force was calculated from the nodal displacement of the top face. Figure 11. Histogram of elemental stress distributions of random porous solids. With decreasing material, stress distribution shifted towards zero stress. At 80% porosity for all pore sizes there were numerous unconnected regions which contributed to the high number of unstressed elements. The peak of each 80% architecture is cut off for display purposes. The peak values are .32, .32, and .18 respectively. Successful scaffold design requires balancing mechanical strength with pore interconnectivity and a viable surface environment. Random porous scaffolds exhibit the desired mechanical properties, but with the caveat of poor interconnectivity. Regular architectures may promote better mass transfer, but sacrifice mechanical properties. Additionally, stress concentrations may be too high to sustain viable cells in certain architectures. Surface smoothing, as demonstrated in the hexahedron, can reduce peaks in stress concentrations. Our study provides a basis for the use of multiple parameters in choosing the optimal tissue engineering scaffold. Figure 9. Modulus of random porous solids. Three pore volumes were evaluated: 605, 400, and 225 um pores, corresponding to standard sodium chloride (NaCl) particle sizes used in porogen leaching processes. Figure 10. Peak stresses in random porous solids. There was no trend observed in the peak stresses of the surveyed architectures. Vales were similar for all pore architectures save the 80% porosity where the smallest pore size exhibited a higher stress peak. RESULTS: Regular Architectures Figure 16. Results of finite element analysis on fiber extruded architectures. Modulus values are magnitudes lower than the results observed for all other architectures. The in plane stiffness of the architectures is weak due to their arrangement. The stress profiles for the architectures illustrate a shift from positive and negative stress values towards zero with closer grouping of the archtiectures through smaller rotational packing. Computer Generated Random Architectures

Architectures designed for generation via rapid prototyping processes

Volumetric porosities range from 50 to 90% porous

Designs based on unit cell repeating architectures (Figures 2 and 3) and fiber extrusion methods (Figure 4)

Literature Scaffold Designs Platonic and Archimedean Solids

Architectures exhibit regularity and symmetry along 3 axis

Space filling models were converted to wireframes (Figure 5)

Four natural architectures selected based upon the number of struts and the interconnectivity of the struts (Figure 6)

Volumetric porosities were varied between 50 and 90%

Wettergreen, M A; Bucklen, B S Mikos, A G; Liebschner, M A K Department of Bioengineering, Rice University, Houston, TX Figure 3. Architecture 1 taken from Wilson, C et al. J Biomed Mater Res 68A: 123-132, 2004. Approximated as a hexahedron with sharp corners. Figure 2. Architecture 2 taken from Chu TM et al. J. Mat. Sci 12: 471-478, 2001. Approximated as a cube with superimposed hollow sphere. Figure 4. Architectures 3-5 taken from Leong KFet al. Biomaterials. 2003 Jun;24(13):2363-78. Approximated as crosshatched parallepipeds. 36 degree offset 60 degree offset 90 degree offset Figure 6. Platonic and Archimedean solids. Left to right, Hexahedron, Rhombitruncated Cuboctahedron, Truncated Hexahedron, Truncated Octahedron. Figure 5. Space filling model converted to wireframe approximation Figure 1. Random porous solid with 225 um pore size at 80% porosity. Figure 12. Modulus of regular, symmetric architectures. Architecture 1 has the highest modulus throughout the porosities. Architecture 2 is eclipsed by the hexahedron at the higher porosities. At 90%, the modulus of the hexahedron is 2.66 times greater than architecture 2. Figure 13. Histogram of elemental stress for the hexahedron. There are two observable peaks for each porosity, the first below -20MPa and the second slightly greater than zero. The second peak moves towards zero with decreasing material volume. Figure 14. Histogram of elemental stress for architecture 1 (hexahedron with sharp corners). There are two exhibited peaks for each porosity, the first less than -20MPa and the second slightly greater than zero. As material volume decreases, more elements take on the higher stress value while also moving to zero stress. Figure 15. Histogram of elemental stress for architecture 2 (cube with hollow sphere). There is a ranged stress distribution demonstrated at all porosities combined with two peaks at around zero and -20 MPa. As material volume decreases, the high stress value in compression is minimized while a shift towards low level tension values also occurs.