MAW Thesis


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Thesis presented by Matthew Wettergreen on April 16th, 2008 as the final requirement for the degree of Doctor of Philosophy

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  • MAW Thesis

    1. 1. The Effect of Material Organization on the Architectural Properties of Porous Architectures Matthew A. Wettergreen Committee: Michael A.K. Liebschner, Chair Antonios G. Mikos Mateo Pasquali Eser Yuksel
    2. 2. Overview <ul><li>Background </li></ul><ul><li>Objective </li></ul><ul><li>Hypothesis </li></ul><ul><li>Specific Aims </li></ul><ul><li>Highlighted Research </li></ul><ul><li>Summary </li></ul>
    3. 3. Bone Anatomy / Physiology <ul><li>Bone exists on 5 levels: whole bone, architecture, tissue, lamellar, and ultrastructural level </li></ul><ul><li>Bone growth is mechanically mediated and most simply explained by Frost’s Mechanostat Theory </li></ul>
    4. 4. Pauwel’s Hypothesis of Tissue Differentiation Bone Growth Theories Perren’s Interfragmentary Strain Theory
    5. 5. Typical Micro-Architecture of the Human Skeleton Vertebral Trabecular Bone Femoral Trabecular Bone
    6. 6. PPF PLGA PCL PGA Scaffolds Structure ≠ Bone Morphology Interconnectivity Anisotropy Density Density Permeability Porosity Porosity Trabecular Spacing Pore Size Trabecular Thickness Scaffold Properties Trab. Bone Properties
    7. 7. Material vs. Architectural Properties <ul><li>Material Properties </li></ul><ul><ul><li>Density </li></ul></ul><ul><ul><li>Poisson’s Ratio </li></ul></ul><ul><ul><li>Elastic modulus </li></ul></ul><ul><ul><li>Stiffness </li></ul></ul><ul><li>Architectural Properties </li></ul><ul><ul><li>Structural Stiffness </li></ul></ul><ul><ul><li>Strength </li></ul></ul><ul><ul><li>Structural Modulus </li></ul></ul><ul><ul><li>Ultimate stress </li></ul></ul><ul><ul><li>Porosity </li></ul></ul>
    8. 8. Motivation <ul><li>Scaffold design is currently untenable for defects in mechano-active or load-bearing anatomical sites </li></ul><ul><li>Mechanically mediated parameters are essential for the long-term success of scaffold integration </li></ul><ul><li>Treatment options favor bone growth but not bone quality </li></ul>
    9. 9. Objective <ul><li>Explore parameters that can affect the degree and quality of bone growth into orthopaedic tissue engineered scaffolds and apply derived relationships to the specific design potentials of computer-aided tissue engineering (CATE) for orthopaedic applications. </li></ul>
    10. 10. Hypothesis <ul><li>Material spatial organization significantly influences the architectural properties of a scaffold at multiple structural levels, specifically its surface mechanical environment, apparent biomechanical properties, and fluid flow properties </li></ul>
    11. 11. Specific Aims <ul><li>Specific Aim 1 – Modulation of (+) space </li></ul><ul><ul><li>Investigate the relationships between material organization and architectural properties for regular, symmetric solids </li></ul></ul><ul><ul><li>Validate computational results and develop correlative models </li></ul></ul><ul><li>Specific Aim 2 – Modulation of (-) space </li></ul><ul><ul><li>Investigate the relationships between material organization and architectural properties for particulate leached random solids </li></ul></ul><ul><ul><li>Develop predictive models between architecture and permeability </li></ul></ul><ul><li>Specific Aim 3 – Apply derived relationships in SA1/2 to the design potentials of Computer Aided Tissue Engineering (CATE) </li></ul><ul><ul><li>Modulate (+) space in the design of orthopaedic tissue engineered scaffolds </li></ul></ul><ul><ul><li>Modulate (-) space in the design of orthopaedic tissue engineered scaffolds </li></ul></ul>
    12. 12. Specific Aim 1 <ul><li>Determine the effect of material organization on the architectural properties of solids based on Platonic and Archimedean solids </li></ul><ul><li>Validate computational results with experimental testing of rapid prototyped architectures </li></ul><ul><li>Investigate correlations between geometric parameters and architectural properties </li></ul>
    13. 13. Research Design <ul><li>Hypothesis – Diverse architectural properties can be obtained through modulation of material organization </li></ul><ul><li>Methodology </li></ul><ul><ul><li>Generate models of regular architectures and computationally determine the architectural properties </li></ul></ul><ul><ul><li>Measure the mechanical properties of rapid prototyped models of the architectures </li></ul></ul><ul><ul><li>Develop a correlative model between geometric parameters and mechanical and architectural properties using regression models </li></ul></ul>
    14. 14. <ul><li>Platonic and Archimedean solids exhibit regularity and symmetry </li></ul><ul><li>Multiple occurrences of these architectures arising naturally </li></ul>Architecture Selection
    15. 15. Generation of Polyhedra <ul><li>Ball and stick models of four architectures generated with CAD </li></ul><ul><ul><li>Hexahedron (H) </li></ul></ul><ul><ul><li>Truncated Hexahedron (TH) </li></ul></ul><ul><ul><li>Rhombitruncated Cuboctahedron (RC) </li></ul></ul><ul><ul><li>Truncated Octahedron (TO) </li></ul></ul><ul><li>Same bounding box for all shapes </li></ul><ul><li>5 porosities: 50, 60, 70, 80, 90% </li></ul>
    16. 16. Results – Geometric Comparison
    17. 17. Results - FEA <ul><li>H is the strongest shape across all porosities </li></ul><ul><li>TO is the weakest shape at 50% and is the 2 nd strongest every subsequent porosity </li></ul><ul><li>H deforms via cell wall stretching deformation </li></ul><ul><li>TH and RC have similar deformation mechanisms (n ~2.25), edge bending </li></ul>1 Gibson, L.J. and M.F. Ashby, Cellular Solids: Structure and Properties . 1999, New York: Pergamon Press. 357. 1
    18. 18. Stress Distribution <ul><li>Across porosities, 16.5% of the stress values for the H lie in the tensile range </li></ul><ul><li>Compressive peak shifts towards higher stress values with decrease in porosity </li></ul><ul><li>TH is nearly equally loaded in tension and compression with 41% of the total elements in tension </li></ul><ul><li>H exhibits the highest stress peak in the compressive region </li></ul>
    19. 19. Verification of FEA <ul><li>Truncated Octahedron was the strongest shape at 80% porosity </li></ul><ul><li>Ductility, plastic region increases with increasing porosity </li></ul><ul><li>Densification of polyhedra seen at higher porosities </li></ul><ul><li>FEA under predicted Modulus, mean (±stdev) error between experimental and FEA modulus was 0.05 </li></ul>
    20. 20. Energy Absorption Efficiency (EAE) <ul><li>EAE a measure of defect tolerance, the area under the curve of rectangle, akin to the energy absorption of a perfect plastic material </li></ul><ul><li>EAE for H decreased with an increase in ρ </li></ul><ul><li>Remaining architectures showed constant or slightly increase with an increase in ρ </li></ul><ul><li>Stiffness and strength linearly related across a four-fold difference </li></ul>
    21. 21. Geometric Modeling Scaled Modulus Best Model, r 2 = 0.8335 Stiffness Best Model, r 2 = 0.9625 Strength Best Model, r 2 = 0.9502 Strain at Fracture Best Model, r 2 = 0.8596 EAE Best Model, r 2 = 0.845
    22. 22. Conclusions Specific Aim 1 <ul><li>Due to beam overlapping, high beam numbered architectures exhibit a parabolic surface area relationship with respect to porosity </li></ul><ul><li>At low porosities, small pores do not contribute to the overall modulus of the architectures and a stress backbone is responsible for the modulus </li></ul><ul><li>Optimal material organizations vary with volume fraction </li></ul><ul><ul><li>Equal modulus values can be obtained with volumetric discrepancies of up to 10% </li></ul></ul><ul><li>Constant EAE can exist over a 300MPa stiffness range and with strengths ranged 0.1-1.5 MPa </li></ul><ul><li>Morphological parameters more heavily control the deformation, strength and plastic properties of an architecture when subjected to large deformations </li></ul><ul><ul><li>For small deformations and/or high loads, a stronger shape such as the Hexahedron would be desired. </li></ul></ul><ul><ul><li>For large deformations and/or small loads, a complex architecture is beneficial due to its favorable ductility and extended plastic region </li></ul></ul><ul><li>Linear multivariate regression shows highest correlation with geometric parameters and EAE and strength </li></ul>
    23. 23. Specific Aim 2 <ul><ul><li>Quantify the effect of pore void organization on the fluid flow properties of particulate leached systems with defined pore architectures </li></ul></ul><ul><ul><li>Model the effect of geometric parameters on architectural properties </li></ul></ul>
    24. 24. Research Design <ul><li>Hypothesis – Diverse values can be obtained for structural and fluid flow properties as a result of material organization </li></ul><ul><li>Methodology: </li></ul><ul><ul><li>Generate porogens with novel architecture </li></ul></ul><ul><ul><li>Create and measure flow properties of porous solids </li></ul></ul><ul><ul><li>Apply current fluid flow models using geometric parameters to back determine permeability </li></ul></ul>
    25. 25. RP Evaluation / Porogen Creation <ul><li>Calibration model to evaluate machine resolution printed with a series of holes and pillars </li></ul><ul><ul><li>Holes were undercompensated </li></ul></ul><ul><ul><li>Pillars were printed as designed </li></ul></ul><ul><li>Porogens generated using CAD based on simple 2D shapes extruded into the z-direction. </li></ul><ul><li>Porogen volumes were matched to sieved NaCl particles </li></ul>
    26. 26. Soft Lithography * Poly(dimethylsiloxane) # Poly(propylene fumarate) di-ethyl fumarate Glass PDMS Mold PPF-DEF # Place in Vacuum Metal Clamp Remove PDMS Microparticles Microparticle Platform Degassed PDMS Microparticle Platform Let cure 24 Hours, peel away PDMS 2) Pour PDMS platform <ul><ul><li>Degass PDMS* </li></ul></ul>Silicon Master Negative
    27. 27. Morphological Analysis <ul><li>Dimensional measurement of steps leading to production of final microparticles </li></ul><ul><li>All architectures smaller than designed </li></ul><ul><li>Similar material shrinkage measured for all architectures </li></ul><ul><ul><li>Compensation mechanism could account for modification </li></ul></ul>
    28. 28. Porous Scaffold Evaluation <ul><li>Scaffolds evaluated with constant head permeameter </li></ul><ul><li>standard curve of fluid flow through the scaffold was constructed </li></ul><ul><li>Three measurements taken for each sample </li></ul><ul><li>SEM and uCT applied for each scaffold to determine morphological parameters of pore volumes </li></ul>Porogen Dimensions Measured from Imaging 0 200 400 600 800 1000 Arm Length Leg Width Leg Length Dimension (um) Designed SEM uCT
    29. 29. <ul><li>Capillary Models </li></ul><ul><ul><li>Simple model accounts for n channels of uniform length and diameter </li></ul></ul><ul><ul><li>Complex model accounts for variation in pore diameter and length </li></ul></ul><ul><li>Hydraulic Radius </li></ul><ul><ul><li>Application of capillary based models </li></ul></ul><ul><ul><li>Hydraulic radius is ratio of volume to surface area of global solid </li></ul></ul><ul><ul><li>Works well for packed solids </li></ul></ul><ul><li>Drag Models </li></ul><ul><ul><li>Opposite of Capillary model </li></ul></ul><ul><ul><li>Capillaries are obstructions to flow </li></ul></ul><ul><ul><li>Permeability is dependent upon flow rate </li></ul></ul><ul><li>Phenomenological Models </li></ul><ul><ul><li>Permeation factor, K (m/s) is exponentially related to parameters </li></ul></ul><ul><ul><li>Includes empirically calculated parameters </li></ul></ul>Permeability Models
    30. 30. Permeability and Modeling <ul><li>Permeability of the scaffolds using Y shape architecture was at least 6 times higher than NaCl scaffold </li></ul><ul><li>Permeability of asterisk shape were at least 15 times more permeable than the NaCl scaffold </li></ul><ul><li>Large variability existed across all the samples </li></ul><ul><li>Straight Capillary Model most closely predicted the permeability of the NaCl scaffold but was a poor predictor of y-shape samples </li></ul><ul><li>Drag Theory underpredicted by the largest error </li></ul><ul><li>Phenomenological Model overpredicted but overall error was smallest for the porous architectures </li></ul>
    31. 31. Conclusions Specific Aim 2 <ul><li>Permeability can be modulated through pore volume manipulation </li></ul><ul><ul><li>Magnitude in difference can be witnessed with varied architecture </li></ul></ul><ul><ul><li>Error matches previous studies; similar specimens may exhibit orders of magnitude difference in results </li></ul></ul><ul><li>Improved modeling can be accomplished by taking into account architectural parameters (phenomenological) </li></ul><ul><ul><li>Current theoretical models do not take into account complex geometry, may need to use reverse engineering to develop predictive models through curve fitting </li></ul></ul><ul><li>Soft Lithography process created microparticles built repeatably with conservation of architecture </li></ul><ul><ul><li>Average of 98.6% reclamation for architectures </li></ul></ul><ul><ul><li>Average 56.3% deviation from designed architecture </li></ul></ul><ul><ul><li>Decreased shape matching with increased complexity </li></ul></ul><ul><li>Lithography process is material independent providing versatility based upon design considerations </li></ul><ul><li>SEGUE INTO DRUG RELEASE STUDY </li></ul>
    32. 32. Specific Aim recap <ul><li>Where are we now and what does the drug release have to do with it? </li></ul>
    33. 33. Design of Drug Release Vehicle - Methods <ul><li>Drug laden PMMA constructs created with NaCl porogens with 2.5 wt% doxorubicin in four volumetric ratios: 0, 20, 33 and 47 percent volume </li></ul><ul><li>Doxorubicin release kinetics measured over 28 days at 37C via absorbance with visible spec </li></ul><ul><li>At end of study scaffolds scanned using micro-computed tomography (μCT) and contoured for morphological measurements </li></ul><ul><li>Hydraulic permeability measured via constant head permeameter </li></ul><ul><li>U87 MG human multiforme glioma cells were used to determine the bioactivity and cytopathic effect of the doxorubicin released from the PMMA. </li></ul><ul><li>Porogen laden bone cement injected into bone cores and measured with μCT </li></ul>
    34. 34. Sustained Drug Release <ul><li>Statistical significance seen with all but 20% porous sample </li></ul><ul><li>Two phase release response in all scaffolds </li></ul><ul><li>Variability in data endemic to randomly porous solids </li></ul>
    35. 35. Surface Area Contribution to Release <ul><li>Porosity values lower than expected for 20 and 33 % porous samples </li></ul><ul><li>Difference in release between 0 % and 20 % accounted for by similar porosity and surface areas </li></ul><ul><li>Interconnectivity seen only with 47 % volumetric porosity </li></ul><ul><ul><li>Embedded porogens remain at lower porosities </li></ul></ul>
    36. 36. Permeability <ul><li>High variability exists in arrangement of pore structure </li></ul><ul><li>Statistical significance seen between 47% porosity and all other porosity values (p<.05) </li></ul><ul><li>47% porosity sample within same magnitude of permeability of bone </li></ul>
    37. 37. Bioactivity <ul><li>Doxorubicin maintained bioactivity and was cytopathic during the 5 day study </li></ul><ul><li>A separate test at the end of the 28 day demonstrated maintenance of bioactivity of the doxorubicin </li></ul><ul><li>Doxorubicin alone at 4.31  M left only 14.2 (SD = 2.96%) cells remaining in the wells, while at 21.6 uM, only 9.31 (SD = 0.377%) were resident. </li></ul><ul><li>PMMA hemispheres laden with doxorubicin demonstrated a mean of 17.6 (SD = 4.22%) remained. </li></ul>
    38. 38. Results <ul><li>Drug release vehicle combining a clinically available acrylic cement and chemotherapeutic drug for the application of secondary spinal tumor control and prevention for use in load bearing applications </li></ul><ul><li>Statistical results showed a two-tailed approach and that porosities greater than 47% double the effective drug release </li></ul><ul><li>Permeability of the 47% porosity samples were statistically significant with respect to the remainder of the samples </li></ul><ul><li>Bioactivity of the samples was conserved throughout the duration of the experiment demonstrating 1-4% more cells remaining than doxorubicin alone </li></ul><ul><li>Injectable, biodegradable porogens require less volumetric porosity to increase the surface area with regards to drug release </li></ul><ul><li>Demonstrated release of the doxorubicin from the composite cements we show is consistent with other studies that used doxorubicin in similar conditions </li></ul>
    39. 39. Computer Aided Tissue Engineering Wettergreen et al. ABME 2005 Investment Casting of mold with biomaterial
    40. 40. Computer Aided Tissue Engineering
    41. 41. <ul><li>QCT powerful for obtaining information about bone </li></ul><ul><ul><li>Spatial distribution of bone mineral density </li></ul></ul><ul><ul><li>Attainable resolution of 1.0 mm </li></ul></ul><ul><ul><li>Image density related to BMD via phantoms </li></ul></ul><ul><li>Extraction to geometric three-dimensional model is routine via numerous programs (i.e. Analyze, IDL) </li></ul><ul><ul><li>Reconstruction: raw projection data converted to 3-D data </li></ul></ul><ul><ul><li>Segmentation: surface geometry generated </li></ul></ul><ul><ul><li>Volume creation: volume data created from 3-D profiles and data </li></ul></ul>CATE - Tissue Imaging
    42. 42. CATE - Tissue Modeling <ul><li>Library generation via CAD </li></ul><ul><ul><li>Architecture generation </li></ul></ul><ul><ul><li>3x3x3 mm 3 volume </li></ul></ul><ul><ul><li>Feature size > 200 um </li></ul></ul><ul><li>Finite element analysis (FEA) of architecture </li></ul><ul><ul><li>Characterization for internal and apparent material properties </li></ul></ul><ul><ul><li>Force, stiffness, and stress-strain relations </li></ul></ul><ul><ul><li>Quantification of structural organization is material independent </li></ul></ul>
    43. 43. <ul><li>Methodology of assigning primitive properties to tissue regions </li></ul><ul><li>Bone contains complex geometry with mechanical properties that vary spatially and anatomically </li></ul><ul><ul><li>Two continuous phases (bone matrix and interstitial fluid) are responsible for the global mechanical properties </li></ul></ul><ul><ul><li>Interior properties of bone (or other) can be determined through imaging modalities </li></ul></ul><ul><li>Computer aided tissue engineering for a defect site utilizes this theory </li></ul><ul><ul><li>Complete load transfer utilizing an engineered scaffold to mimic the variants with respect to direction. </li></ul></ul>Biomimetic Design Theory
    44. 44. Unit Cube Library <ul><li>12 shapes, 80 % porosity </li></ul><ul><li>6 polyhedral derived, 6 space filling </li></ul>8
    45. 45. Library Characterization <ul><li>Simulated linear uni-axial displacement to 1.0% strain in confined and unconfined compression </li></ul><ul><li>Isotropic material properties, E = 2000 GPa, v = 0.3 </li></ul><ul><li>Convergence study to determine proper seeding density </li></ul>C
    46. 46. Analysis of Stress Profiles <ul><li>Dissimilar architectures may have similar profiles, converse is true also </li></ul><ul><li>Specific architectural elements may be highlighted through viewing profiles </li></ul><ul><li>Decreasing porosity shifts loading profile away from tensile to compressive </li></ul><ul><li>Decreasing porosity results in higher compressive stress values </li></ul>
    47. 47. Implant Design and Manufacturing <ul><li>Library assembly requires marriage of mechanical properties and biological considerations </li></ul><ul><li>Assembly progresses in parallel and series based on regional properties </li></ul><ul><li>Shape matching and load transfer requires interface between parts </li></ul><ul><li>Boolean processes completes global contours </li></ul><ul><li>Conversion of final file for rapid prototyping processes </li></ul>
    48. 48. Implant Assembly <ul><li>Scaffold assembled based upon stiffness values derived from density </li></ul><ul><li>Four characterized architectures used in assembly and printed using Patternmaster, 3D Printer </li></ul>
    49. 49. Results <ul><li>Highlighted the creation of a unit library of architectures that can be used to assemble a complex scaffold of individual characterized microstructures </li></ul><ul><ul><li>Allows for tailoring of mechanical stability and connectivity </li></ul></ul><ul><ul><li>Regularity of architectures promotes mass transfer </li></ul></ul><ul><li>Mechanical properties vary by a magnitude as a function of architecture </li></ul><ul><li>Inclusion of common interface promotes union between mechanically dissimilar architectures </li></ul><ul><li>Stress profiles highlight importance of specific architectural features on modulus </li></ul><ul><li>Library may be assembled into global scaffold using defect information as input </li></ul>
    50. 50. Creation of Interface Library <ul><li>20 sections from 10 T-9 human vertebral bodies scanned at 30 µm isotropic resolution </li></ul><ul><li>Bone viewed at three architectural levels </li></ul><ul><li>Repeated patterns were translated into tissue primitives </li></ul><ul><li>In most cases, closed 3-D versions did not exist, but were included in closed form for space-filling and regularity purposes </li></ul>
    51. 55. Scaffold Fabrication from Density Data <ul><li>Modulus Map determined a 3 x 3 x 3 mm subvolume of bone </li></ul><ul><li>Interfaces generated through the application of interface volume and area matching algorithm </li></ul>
    52. 56. Conclusions Specific Aim 3 <ul><li>Principles of CATE can be used to modulate permeability of a random solid for drug delivery </li></ul><ul><li>Mechanical properties may be adjusted to near bone levels while still delivering drug to defect site </li></ul><ul><li>Unit cube libraries can be used to design specific architectural properties or modulus values that vary by an order of magnitude at same porosity </li></ul><ul><li>Bone architecture derived tissue primitive libraries can be assembled into structure that matches the native porosity and sitffness properties of bone </li></ul><ul><li>An interface library can be used to augment or highlight disparate architectures and mechanical properties </li></ul>
    53. 57. Summary <ul><li>Density is the strongest factor in controlling modulus, though optimal material arrangement can result in similar modulus values even with volumetric discrepancies of up to 10%. </li></ul><ul><li>Morphological parameters played a larger role in the plastic deformation and post yield behavior of an architecture when subjected to large deformations </li></ul><ul><li>Architectures with geometric complexity become more ductile with increased porosity and are more defect tolerant </li></ul><ul><li>Permeability may be controlled through pore volume architecture modulation with a range of an order of magnitude </li></ul><ul><li>Phenomenological models can closely predict the permeabilities of architectures with empirically determined pore volume values </li></ul><ul><li>The guiding principles of CATE may be applied to scaffolds with mechanical design demands that also release chemotherapeutic drug </li></ul><ul><li>Tissue primitive and tissue primitive interface libraries may be created with tailorable architectural properties to replace tissue defects in well characterized environments </li></ul>
    54. 58. Acknowledgements <ul><li>Advisor: Dr. Liebschner </li></ul><ul><li>Committee Members: Dr. Mikos, Dr. Pasquali, Dr. Yuksel </li></ul><ul><li>Members of the CEBL and Mikos lab at Rice </li></ul><ul><li>Dr. Wei Sun, Bobby Chang, Lauren Shor of the CATE lab at Drexel University </li></ul>