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

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


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