NSF Proposal Project Discription
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NSF Proposal Project Discription

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Proposal to National Science Foundation co-authored by Ian Nieves and James Earthman. It describes using FEA simulation and advanced computer-assisted fabrication techniques to develop materials......

Proposal to National Science Foundation co-authored by Ian Nieves and James Earthman. It describes using FEA simulation and advanced computer-assisted fabrication techniques to develop materials for bone regeneration.

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  • 1. Introduction Each year millions of Americans suffer from a variety of debilitating bone-degenerative ailments such as osteoporosis and bone cancer [1]. In addition to the immediate physical discomfort and impairment, such afflictions also result in lost wages, high medical expenses and death. Particularly vulnerable are the elderly, wherein skeletal deterioration and invasive treatments frequently lead to more severe medical complications and accompany high rates of morbidity. Congenital conditions in which skeletal degeneration is a major complication, such as sickle-cell anemia which currently afflicts approximately 65,000 Americans, disproportionately afflict minorities of African, Latin American and Middle Eastern extraction [2,3]. The attendant costs and suffering of bone degeneration is expected to increase dramatically over the next century in tandem with expected increases in the number of senior citizens and minorities. Per annum treatment costs for osteoporosis alone already exceed $30 billion [4]. The treatments currently used to rehabilitate skeletal injuries and degeneration all suffer from significant drawbacks. Most commonly, injured bones are replaced with a prosthetic made of titanium, cobalt and/or chromium and secured to adjacent bones with adhesives [5]. Injured hip joints are replaced by polyethylene-coated metallic cup and ball joints secured to the femur and to the inside of the patient’s acetabulum. Adhesives in vivo degrade over time and require further invasive procedures to maintain. Wear debris between components of hip replacements frequently provokes an immune response that leads to re-absorption of the surrounding bone [6]. Tissue obtained through bone harvesting is plagued by its own set of problems. Autograph-based reconstruction is limited by the available quantity of the patient’s own bone [7]. Cadaver- harvested bone is often brittle, subject to immune rejection and can serve as a vector for pathogens such as cytomegalovirus or HIV. Similar limitations and risks apply to allographs and zenographs [8]. Much research therefore focuses on developing materials and procedures whereby normal skeletal function is restored through in situ regeneration of the patient’s own bone. In situ, directed osteogenesis reduces the need for follow-up invasive procedures and eliminates the risks associated with the introduction of foreign tissue. Such a methodology requires the development of bio-active materials which serve as both prosthetics during convalescence and as promoters of new bone growth. Furthermore, these materials should be biodegradable, thus facilitating their eventual replacement by new bone growth and thereby eliminating the need for follow-up surgery. Additionally, these materials should be producible by a comparatively inexpensive fabrication process that can be easily tailored to the medical needs of individual patients. Among the most promising candidates for bone-regenerative prosthetics are polylactide-co-glycolide (PLGA) and hydroxyapatite (HAP) that gradually degrade in vivo as new tissue grows into the region of implantation. Computer-aided design and fabrication techniques have been used by Calvert and colleagues to produce prototype free-form scaffolds (FFS) bundles composed of PLGA-HAP that have displayed excellent bio-conductive and bio-inductive abilities [9,10]. The steps involved in producing and implanting FFS bundle implants is shown schematically in Fig. 1. In their research, Calvert and co-workers seeded the component layers of several scaffolds by soaking them in solutions containing bone marrow cells with concentrations in excess of 1 x 108cells/ml [11]. The layers thus treated exhibited extensive cell proliferation and substantial bone matrix synthesis. The goal of the proposed work is to develop dynamic finite element 1
  • 2. Fig. 1 Steps in the design, fabrication and implantation of free-form scaffold (FFS) bundled layer implants for healing large-scale bone defects in the mandible. X-ray computer tomography (CT) data are used to design layers that are then fabricated by numerically controlled machining and seeded with the patient’s cells, growth factors, and possibly other agents prior to implantation. The primary goal of the proposed work is to develop and use dynamic finite element models to better understand and simulate the mechanical behavior of FFS materials. models to better understand and simulate the mechanical behavior of FFS structures. This research will lead to FEA tools that can be incorporated into the computer-aided design of the layers for optimized mechanical biocompatibility. FFS assemblies grouped together with surgical sutures (bundles) also exhibited the capacity to induce extensive vascularization during animal studies. In one study, seeded and unseeded bundles were implanted within a rabbit rectus abdominis adjacent and superficially to the right and left deep inferior epigastric bundles, respectively. After 12 weeks had elapsed, both bundles were explanted and assayed to determine the extent of cell induction and vascularization. The controls were shown to be biologically inactive, while the seeded bundle exhibited extensive cell proliferation and displayed new HAP depositions of 3+/-1%. Histologic sectioning revealed that the layers comprising the seeded bundle had undergone fusion, while those of the control remained disconnected. The central regions of the seeded layers also exhibited extensive penetration by capillaries from the nearby vascular bundles, while those of the controls were devoid of vascularization. Crucial for promoting new bone growth, vascularization establishes 2
  • 3. conduits for nutrient supply and waste removal and facilitates leukocyte access. A section of an explanted layer showing vascularization is shown in Fig. 2. While the bone-regenerative capacity of FFS bundles has been established, little information exists regarding their mechanical behavior. In performing their bone-regenerative function, these materials would be subjected to a variety of static and dynamic stresses stemming from routine muscle-skeletal exertions, interstitial fluid pressure and other facets of the in vivo environment [12]. The resulting stresses and strains experienced by these materials would affect both their structural integrity and bone-regenerative ability. Particularly useful for therapy is the development of FFS bundles whose bone-regenerative activities are a function of imparted stress levels [13]. Crucial for this is a thorough assessment of their capacity to withstand, transmit and distribute dynamic stresses and strains arising from ambulatory movements and other exertions. Numerous studies have identified dynamic stresses as the principal agents responsible for skeletal adaptation. Animal studies of leg bones subjected to dynamic stresses similar to those arising during normal gait reveal extensive restructuring of the endo-cortical regions [14]. Neonatal studies assign culpability for infant temporary brittle bone disease to dynamic stress deficits resulting from inhibited fetal movements in utero [15]. The Mechanostat theory of skeletal adaptation, which was formulated using the results of such studies, reliably predicts routine bone maintenance (modeling) and bone adaptation to lethargy or to overexertion (remodeling) as functions of both dynamic stress rates and intensities [16]. Despite the exhaustively documented role of dynamic stresses in promoting bone growth, most efforts have concentrated on scaffold material performance under quasi-static stresses. Optimizing reconstructive materials for withstanding and transmitting dynamic stresses is pivotal in maximizing their bone regenerative abilities and the bulk of the proposed work will therefore be focused toward achieving this objective. Importance will be assigned to optimizing the FFS bundle mechanical response. Several studies have shown that osteogenesis increases nonlinearly with increasing strain rate [17]. Additionally, animal models of distraction osteogenesis have shown that high strain magnitudes are effective in inducing the synthesis of collagen–HAP formations aligned in the direction of the Fig. 2 Transmission electron micrograph of vascularized FFS scaffold. 3
  • 4. allied stress [18]. Other studies implicate the strain parameters associated with dynamic stresses, as opposed to the stresses themselves, as the causative agents in remodeling the endo-cortical architecture [19,20]. By moderating these stresses and strains through energy dissipative processes, FFS bundles optimized for performance under physiological stress magnitudes and strain rates therefore hold the promise of materials specifically tailored to stimulate optimum bone regeneration during normal physical activities and trauma. Before these materials are employed as bone-regenerative prosthetics it is critical to optimize their mechanical characteristics to both maximize their bone-regenerative abilities and to minimize the risks of fatigue and catastrophic failure. Effecting such optimization should enable physicians to design FFS bundles with bone-regenerative properties tailored to specific clinical situations and which exhibit reliable, predictable mechanical behavior. Pivotal to both efforts is the development of simulation methodologies whereby key facets of FFS bundles such as cell architecture and desired mechanical properties can be reliably designed, assessed and incorporated into usable, reliable implants. Finite element analysis (FEA) has been used by the researchers and others to simulate the mechanical response of materials with a wide range of cell architectures and microstructures, including implants [21-26]. This technique has also been used to better understand the details of bone maintenance and adaptive restructuring as predicted by the Mechanostat theory of skeletal adaptation [27]. When performed with powerful computational software, FEA gives highly detailed, accurate predictions of in situ stresses and strains. These predictions can in turn facilitate the design of materials that exhibit specific structural changes in response to physiological loading conditions. The proposed study will therefore elucidate the mechanical response of FFS bundles to dynamic stresses through FEA, which is thought to be crucial for the development of optimized, medically useful bone-regenerative materials. The proposed research will therefore concentrate on developing simulations wherein dynamic loading is affected in such a way as to both re- enforce structural integrity while accentuating morphological features thought to underlay bio- conductive and bio-inductive abilities. These simulations will then be used to fabricate FFS layers that possess the same geometries as the models through three-dimensional printing techniques. Dynamic and static mechanical testing will be performed on both the individual layers and on FFS bundles comprised of these layers in order to verify that the properties indicated by the simulations are possessed by the fabricated materials and to provide further insights for structural refinement. Comparisons will be made between the mechanical behavior of FFS bundles and corresponding monolithic FFS materials in order to elucidate and enhance properties unique to the multi-layered materials. Modeling and testing will also be performed on samples subjected to a liquid saline environment for prolonged periods in order to establish the effects of interstitial fluid pressure and in vivo degradation on FFS structural integrity and morphology. The proposed study will focus initial efforts on developing a better understanding of FFS mechanical behavior in the mandibular-facial environment. FFS bundles tailored to promote temporo-mandibular joint and condyle repair offer enormous promise for alleviating the often extreme discomfort that debilitates the 30 million Americans currently suffering from damage to the temporo-mandibular joint (TMJ) [28]. The development of such materials would also greatly benefit the burgeoning number of children and adolescents who suffer fractures to the mandible and condyle, currently the largest group of pediatric skeletal injuries [29]. This initial effort would draw from both the work of our laboratory on the time-dependent behavior of complex 4
  • 5. materials and its accomplishments in tissue engineering for the oral-facial regions [30]. The experience acquired through both efforts will be used to accurately simulate the dynamic stresses conditions anticipated to confront these materials when used in face and jaw reconstruction. This effort is also anticipated to result in expertise and methodologies required to optimally adapt these materials for bone regeneration throughout the body. a b c d Fig. 3 Schematic of the 3D Printing method for fabricating the proposed FFS scaffold bundles depicting (a) binder injection, (b) powder deposition, (c) powder compaction, and (d) piston retraction. Materials and Methods I. Three-Dimensional Printing Three-dimensional printing will be used to produce the FFS materials under investigation. This technique is versatile in that a variety of intricate biologically active medical devices, including controlled dosage delivery agents and FFS layers, are produced directly from computer aided design tools [31,32]. The scaffold will be first designed with modeling software and then fabricated through sequential layer deposition and bonding. As shown in Fig. 3, layer production involves deposition of powders of the precursor material in a cavity formed by a retracted piston [33]. The geometry specific to the layer is produced through jet deposition of the binder. Upon completion of a layer, the piston will be retracted by a length equal to the thickness of the next layer and the previous steps will be repeated. Following their fabrication, the layers will be bound together with surgical sutures. The inherent versatility of simulation control combined with facets of the fabrication process establishes 3D printing as a particularly suitable processing method for the proposed modeling. Moreover, this technique has proven its ability to produce intricate surface textures and extensive interconnected porosity, both of which facilitate integration of the prosthetic with adjacent bone [34]. Porosity in particular has been shown to promote intercellular contact and is therefore thought to be crucial for cell differentiation [35]. In general, the size of reproducible detail will only be limited by the size of the particles used in the fabrication. Thus, the direct simulation-to-fabrication methodology of 3D printing ensures accurate reproduction of model features, while the powder-bonding methodology eliminates the involved chemical syntheses, 5
  • 6. bonding and/or molding steps used by competing processes such as computer-facilitated micro- injection and sequential lamination [36,37]. II. Ceramic/Polymer Scaffolds for Skeletal Reconstruction The proposed study will employ composite FFS layers composed of 10 µm diameter hydroxyapatite (HAP) particles imbedded in a poly-lactide co-glycolide (PLGA) matrix [38]. PLGA is thought to impart to the layers the toughness and damping properties supplied to bone by collagen, while the HAP enhances both rigidity and bio-compatibility [35,39]. The matrix possesses an open-cellular structure with pore sizes in the 150 – 250 _m range, thus mimicking the structure of higher-density trabecular bone [40]. This porosity is thought to promote cell induction and differentiation by limiting the outer surface area available for cell attachment and by facilitating cell transport throughout the matrix. The FFS layers will be left separate during fabrication and subsequently grouped together with surgical sutures, producing FFS bundles. This approach has been shown to facilitate access to the scaffold interior by osteoblasts and marrow cells in vitro. The inherent sliding between layers can also provide for energy dissipation to further dampen dynamic stresses associated with normal function as well as trauma. III. Simulation Software Patran/Nastran (P/N) and Dytran/Nastran (D/N) are finite element modeling software packages produced and marketed by MSC Software Corporation in Santa Ana, CA [41]. Each consists of pre-processing software that is used to construct geometries and meshes and to apply material properties and boundary conditions, the processing software, Nastran, and post- processing software for saving and displaying the results. Patran uses implicit codes that simulate linear static loading cases and will be used to model facets of periosteal thickening thought to result from persistent muscle-applied stresses. By contrast, Dytran employs explicit codes that simulate nonlinear dynamic loading situations and will therefore be employed in simulating masticulation, locomotion, blunt trauma and fluidic interactions. The versatility of P/N and D/N makes both software packages ideally suited for simulating the behaviors of complex three-dimensional structures. Both contain numerous tools and commands which can be used to construct a wide variety of models with varying geometries and physical properties. Dytran in particular possesses Contact options that computationally link discrete solids and/or surfaces to one another, thereby permitting simulation of such events as inter-surface sliding, collisions and the penetration of one solid by another. Specific interaction characteristics can be specified by the Penalty and Kinematic methods, which define permissible penetration depths or disallow penetration by treating all contacts as rigid walls, respectively, and by friction coefficient entries. Failure of interacting solids is defined by the Adaptive Contact option, which removes failed elements. Additional flexibility is granted by the GAP option, which permits the coupling of interactions between spatially separated elements. The various Contact options should facilitate the accurate modeling of mechanical interactions between FFS bundles and adjacent anatomical structures such as bones and muscles. The Self Contact Option even allows the simulation of physical contact between separate portions of the same solid and can therefore be employed to simulate energy dissipation by friction at the interface of FFS layers. While Lagrangian Solids will be used to construct the FFS bundles and anatomical features, Euler Elements will be used to model interstitial fluid effects. Still other options common to both Patran and Dytran permit the comprehensive analysis of hydrostatic and 6
  • 7. principal stresses, the magnitudes of which have been shown to correlate with the extents of endo-cortical remodeling. The capacity of Dytran to dynamically model implant mechanical performance has previously been demonstrated in analyses of in situ denture behavior [42]. The robust analysis software used with both pre-processing packages allows the researcher to generate results depicting the various stress and strain parameters (Von Mises, principal, axial, shear, etc.) required for predicting mechanical behavior. Additionally, Dytran possesses a Time History (TH) Results function that generates graphs of the magnitudes of the various forces arising on surfaces linked through a Contact or Coupling option, as well as of the progressive distance between the closest points on these surfaces. This function permits the graphing of a series of Master-Slave Contacts, thereby facilitating the analysis of energy transferred from the in vivo medium through the constituent layers of a FFS bundle. Together with the Contact Surface visualization option, TH will be employed to determine the amount of energy transferred from an initial physiological exertion or impact trauma through successive FFS layers and to access the amount of interlayer sliding and intra-layer straining produced. The analysis of inter-surface sliding is thought to be pivotal in optimizing FFS bundle bio-inductive properties since experimental studies reveal that small extents of implant-bone sliding promote bone in-growth, while large sliding magnitudes inhibit it [43]. IV. Material Model The proposed material model will employ DYMAT 24, which models an isotropic, elastic-plastic material with failure through piecewise plasticity [44]. This model is ideal for materials whose stress-strain response is too complex to be modeled by a bilinear representation. A stress-strain table will be used to describe a piecewise linear approximation of the stress-strain curve for the material under investigation. Individual iterations of the stress will be determined from the equivalent strain through interpolation from the stress-strain table: s = [(si - si-1)(e - ei-1)/(ei - ei-1)] + s i-1 (1) where si and ei are the stresses and strains specified by the table. This model is particularly useful for the proposed dynamic simulations since it allows the user to explicitly use dynamic stresses with the Cowper – Symonds rate enhancement formula: . sd/sy = 1 + ( e/D)1/P (2) . where sd is the dynamic stress, sy is the static yield stress, e is the strain rate, and D and P are constants. These constants as well as † stress-strain table required for Eq. (1) will be the determined from mechanical test data for a range of strain rates that correspond to masticulatory function. † VI. Model Validation Four Point Bend Tests FFS bundles and corresponding monolithic scaffold blocks will be tested under four-point bending conditions to validate model predictions of behavior. Three replicate samples of each FFS layer configuration under investigation will be tested. The sample dimensions will be 3 x 3 7
  • 8. x 60 mm. Each specimen will be subjected to a four-point bending test, using a custom built cyclic loading machine at a loading frequency that is within a range consistent with masticultory loading rates. Specimens will be submerged in 0.9% saline (Ringer’s solution) at a constant temperature of 37° C during the testing. The data will be used to calculate the flexural modulus of elasticity and the loss coefficient, h, value of damping capacity [45-48]. The loss coefficient is given by E h= d (3) 2pEi where Ed is the energy dissipated and Ei is the input energy. For cyclic loading conditions, the loss coefficient can be readily determined from h = tanf (4) where f is the phase angle difference for stress and strain. The loss coefficient will be used to gage how well the specimens moderate the transmission of dynamic stresses into the surrounding bone. In particular, comparisons between the layered FFS samples and corresponding monolithic samples will reveal the how interlayer sliding effects this dissipation. Compression Testing FFS and monolithic block specimens will be tested under compression loading conditions under a range of strain rates that are consistent with normal masticulatory function. Elastic modulus and yield strength will be determined from these tests both in air and in saline (Ringer’s) solution. The compression samples will be in the form of cubes (10x10x10 mm). Compressive percussion probe measurements will also be made to determine the damping capacity according to Eq. (3) under these loading conditions. The small size of the probe will allow for percussion of individual layers on end in addition to percussion normal to the layers. End-on percussion will be used to measure damping associated with direct shear forces on the interfaces between the layers. The results for all of the above experiments will be compared with numerical predictions for validation and refinement of the finite element models. VI. Modeling, Testing and Characterization Equipment All modeling with be performed using a dedicated Dell Dimension 8300 Series Workstation with a Pentium 4 Processor, 2GB of memory, and operating at 800MHz. For more extensive models, supercomputer facilities available at UC Irvine will be accessed as needed. Mechanical testing will be performed with either a MTS 918 servo-hydraulic mechanical testing machine or an Inston 3367 tabletop test system, both of which are in the UCI Department of Chemical Engineering and Materials Science. These devices are equipped to perform static tension and compression and bending tests and can be readily modified for dynamic testing. Additionally, we will use the Periometer percussion probe system for measuring the damping capacity of the FFS samples under simulated masticulatory loading conditions. This system, developed at UC Irvine and Newport Coast Oral-Facial Institute in Newport Beach, has been used to measure the damping characteristics of a range of dental implant materials [48]. All experimental tests duplicating interstitial fluid effects on FFS bundles will be performed with liquid saline (Ringer’s solution) using immersion equipment that exists in our laboratories. Geometric and compositional characterization of FFS bundles will be performed with a Phillips XL 30 scanning electron microscope equipped with an EDAX energy dispersive 8
  • 9. spectroscopy (EDS) system. In particular, the samples will be inspected for that might alter the mechanical properties both before and after mechanical testing. The compositional uniformity of the samples will also be evaluated using EDS. Research Goals I. Overall Plan The objectives of the proposed research are threefold: 1. Comprehensively model and elucidate the stresses and strains imparted to FFS bundles under mandibular-facial conditions (see Appendix I). 2. Use the information obtained in (1) to construct simulations of FFS bundles that contain layers possessing improved mechanical properties and osteo-conductive and inductive geometries. 3. Fabricate and test FFS bundles expected to exhibit improved mechanical performance and bone regenerative abilities based on the finite element results. 4. Refine FEA models based on test results and SEM examinations of untested and tested samples. In addressing these tasks, the proposed work will employ MSC software operated on high capacity computers to create highly detailed, realistic simulations of the FFS bundles subject to compressive, tensile, bending and sheer forces imparted by muscles, impacts and interstitial fluid. Overall, the simulations will be used to improve the understanding of loading responses to in vivo stresses by addressing the following questions (among others) vital to their roles as bone regenerators: A) How do FFS bundles deform under normal physiological conditions and how much energy dissipation (damping) occurs during a normal loading cycle? B) How do the FFS bundles respond to impact trauma? Would this response alter scaffold integrity and bone-regenerating capacity? C) How does the layered structure of FFS bundles dampen dynamic loading compared to monolithic samples with identical densities and porosities? How much damping can be attributed to the sliding of the layers across each other? How do interfacial agents, such as stem cells, affect this sliding behavior? How does interlayer sliding affect the stress amplitude and distribution in the surrounding bone? Answering these questions is critical for future design of FFS bundles with sufficient strength and superior bone regenerative capabilities. We will use 3D printing to fabricate FFS bundles from simulations produced during (2) to achieve objective (3). Mechanical testing will then be employed to verify that the scaffolds possess the improved mechanical properties indicated by the simulations. Care will be taken to assure that bone-regenerative properties are retained during structural modification. Objectives (2) and (3) are anticipated to be accomplished by re-iterative processes wherein FFS mechanical properties are refined and enhanced through further simulation, testing and comparison. This 9
  • 10. methodology will lead to the fabrication of FFS bundles possessing both maximum allowable strengths and optimum geometries for bone regeneration. The overall research plan is shown in Table 1. The investigative steps comprising the research plan are scheduled to proceed according to the sequence given in the timetable in Table 2. The plan consists of several sup-optimization, or enhancement, steps designed to direct the efficient production of maximally optimized FFS bundles. Furthermore, each step involves the creation of a candidate FFS group through the creation of geometric representations of their cell architectures using the pre-processing software. The strongest members of this group will be identified through FEA, wherein the cellular response to stresses arising from routine maxillo-facial exertions will be assessed. Architectures thus selected will be incorporated into FFS layers fabricated through three- dimensional printing. Static and dynamic mechanical testing will then be employed to verify that these materials possess the properties predicted by FEA, to select the best members of this group and to identify failures mechanism in order to direct the next phase in materials enhancement. This phase will also begin with the creation of a group of simulated cell architectures, in this case produced from the materials selected in phase (1). The mechanical and SEM results obtained previously will be used to design architectures that have been re-enforced with respect to the mechanisms that have been identified as governing failure. Once again, mechanical testing will be employed to verify material properties and, this time, to select optimized FFS-bundles for future animal and clinical studies. Table 2. Research Plan Research Plan Optimization. Table 1. for FFS-Bundle Data from in vivo FFS Bundles Simulation of in vivo FFS Bundles Simulation with Optimized Properties Fabrication of FFS Bundles Mechanical Testing Optimized FFS Bundles Table 2. Timeline for the Proposed Research 10
  • 11. Objective Time _ Year 1 ][ Year 2 ][ Year 3 Design and selection of FEA pilot model 6 Months group (PMG) from current FFS bundles Fabrication and testing of FFS bundles produced from PGM, selection of strongest ___ 18 Months ____ scaffolds (StFFS) Design and simulation of enhanced FFS’s 24 Months (EFFS) with enhanced mechanical ____ properties Fabrication and mechanical testing of FFS 24 Months bundles produced from EFFS models Final Progress Report and Publications 2 Months - II. Modeling FFS Bundles A better understanding of the mechanics of FFS bundles is anticipated to provide the information to accomplish goals (2) and (3). As shown in Fig. 4, in vivo FFS-bundles are anticipated to experience a variety of stresses arising from muscular contractions, interstitial fluid pressure, tissue growth and other biological activity. These stresses in turn produce motions of the separate layers relative to each other and induce straining in the individual layers. Such straining is thought to both alter FFS mechanical properties and to affect bio-compatibility by changing the surface morphology and pore conformation. Compression Tension Shear 1 2 1) Tension -compression from asymmetrical muscle contraction. FFS Layer Suture 2) Shear from symmetrical contraction. Contracted Muscle Flaccid Muscle Fig. 4 Examples of stresses Force Exerted by Muscle Force Imparted to Bundle experienced in vivo by FFS bundles : 11
  • 12. The proposed models will represent the FFS cell geometry as a semi-regular polyhedral open-cellular lattice. The seminal work of Ko and Knipschild identified strut bending in this type of lattice as the predominant mechanism governing deformation in cellular materials [49,50]. A model devised later by Gibson and Ashby represents open cell geometry as a network of staggered cubes, thereby deriving the mechanical response from struts bending to align themselves with applied stresses [40]. Work by Warren and Kranik also ties mechanical behavior to strut bending, but employs tetrahedral and tetrakaidecahedral cell geometries [51,52]. As with these earlier efforts, a polygonal geometry will be adopted in which strut bending predominates over strut stretching. FFS cell architecture will be modeled with selected members of the regular and semi-regular polyhedral groups and those whose behavior most closely matches that of the FFS selected. The strut geometry itself will be modeled with an hourglass shape, as opposed to simple columns, with dimensions derived from experimental data. Structural parameters such as the cell length, strut dimensions and surface detail can be changed in accordance with the experimental findings. Summary I. Immediate Benefits of Activity FFS-bundles composed of PLGA and HAP offer promise for bone regeneration in patients suffering from traumas and progressive skeletal degeneration. Extensive in vitro and animal studies have established that these materials promote osteoblast and marrow cell conduction and simulate the synthesis of both collagen and HAP. Since FFS-Bundles are composed of biocompatible and bio-reabsorbable materials, they are also promising candidates for therapies wherein bone growth gradually replaces the original implants. The fabrication process whereby these materials are produced also facilitates the inexpensive tailoring of FFS- Bundles to the medical needs of individual patients. The proposed project will work to realize the therapeutic potential of FFS bundles by optimizing their mechanical and bio-inductive properties for facial and jaw restoration. Modeling their mechanical response to in vivo mandibular-facial conditions is anticipated to provide the information that with both lead to a comprehensive understanding of their bone-regenerative behavior and, ultimately, to facilitate the production and use these materials in the repair of a wide range of skeletal pathologies and injuries throughout the body. II. Intellectual Merits of Activity The proposed work will seek to optimize the mechanical performance of FFS bundles in accordance with the postulates of the Mechanostat theory of skeletal re-modeling. This work therefore offers the prospect of elucidating and refining the details of this theory and of tailoring these particulars to specific regions of the skeleton Optimizing FFS bundles for bone regeneration is anticipated to clarity the role of static loading in re-modeling. Although both copious experimental evidence and the Mechanostat theory assign priority to dynamic stresses, several studies also indicate that static stresses participate in periosteal re-modeling [14]. This evidence, however, is contradictory, with many studies asserting that static loading inhibits re-modeling, while others claim it promotes periosteal thickening. The modeling work and the subsequent clinical trials of optimized FFS bundles should therefore elucidate the possible contribution of static stresses to bone re- modeling. 12
  • 13. The work assessing the influence of interstitial fluid effects on FFS bundle performance is anticipated to elucidate the contributions of this medium to bone re-modeling. While the well- established correlation of bone thickening with hydrostatic stress magnitude establishes the importance of interstitial fluid action for re-modeling, its precise role in this process remains uncertain [53,54]. Optimizing FFS bundles with respect to interstitial fluid stresses should help to clarify this medium’s contribution to skeletal re-modeling. This work will also address the role of fatigue in stimulating re-modeling. While it is generally accepted that such damage is detrimental to skeletal integrity, much evidence implies that a modicum of damage also enhances skeletal function by inducing beneficial re-modeling [55,56]. FFS bundle optimization will necessarily entail addressing fatigue’s role in re-modeling. III. Broader Impacts of Activity FFS bundles offer great promise for alleviating the often extreme discomfort that debilitates the 30 million Americans currently suffering from damage to the temporo-mandibular joint (TMJ) architecture. The incorporation of numerical modeling in computer-aided materials design and fabrication should be particularly useful for producing implant materials based on patient CT data and near-net shaped processing techniques. Optimizing the mechanical and bone regenerative abilities of FFS bundles is anticipated to advance the design of a wide variety of skeletal and dental implant materials. As various functional parameters are modeled and tested and the FFS bundle bone regenerative abilities optimized, values for the re-modeling threshold stresses for regions of the mandible and other facial skeletal features are expected to be determined. These results may facilitate the construction of clinical “profiles” wherein threshold values specific to selected patients and pathologies are specified. Such information would tailor FFS bundles to treat specific medical conditions and could facilitate the treatment of numerous other pathologies and traumas. FFS bundle optimization may also facilitate the development of so-called “smart” materials. Much materials research aims to produce synthetic or bioengineered analogues to natural materials that can “re-model” themselves in accordance with functional needs [57,58]. Understanding the effects of FFS bundle optimization on bone remodeling should also facilitate the development of such “smart” materials that incorporate living cells between the bundled layers. The proposed research will also provide educational opportunities at the undergraduate as well as graduate levels for training students in the use of numerical modeling techniques for the design and computer-based fabrication of complex material structures. In particular, the proposed work would allow the PI to incorporate content on numerical modeling for optimized near-net shape materials processing in the introductory course E54 “Principles of Materials Science and Engineering,” a required course for engineering majors at UC Irvine. This course is taught using the problem-based learning approach and would therefore be ideally suited for this incorporation. In addition, students of underrepresented groups will participate including Ian Nieves who has completed his coursework and passed his preliminary exam in the Ph.D. degree program in Materials Science and Engineering at UC Irvine. IV. Appendix—Modeling FFS Bundles for Facial-Mandibular Applications This project will initially focus on optimizing FFS bundles for the treatment of selected jaw and dental-related pathologies. As with the previous animal studies, tailoring these materials to such functions will begin with devising implantation schemes wherein their ability to promote 13
  • 14. Lateral Pterygoid Muscle FFS Condyle Bundle Deep Part of Masseter Muscle Masseteric Artery Fig. 8 Situation of FFS bundle for TMJ-related condyle repair. bone regeneration is utilized to stimulate the repair of specific damage. Once the implantation site is selected, geometrical facsimiles of relevant anatomical features such as muscles, ligaments, bones and key facets of the interstitial fluid medium will be produced using the pre- possessing software. Contact and other Boundary Condition (BC) options will be used to specify FFS bundle attachment to the surrounding medium and stresses typical of those produced in the selected region through masticultion will be applied. For example, in the TMJ disfunction-related implantation scheme depicted in Fig. 8, a FFS bundle has been placed superficially to the masseter artery and proximate to the condyle in order to promote self-vascularization and to stimulate the repair of the latter. Accordingly, Dytran pre-processing software will be used to reproduce condylar and messeter muscle geometry and that of the FFS bundles themselves possessing the desired detail from a combination of Shell and Sold Lagrangian elements. The Master-Slave BC scheme will be used to couple the displacements of all three structures to one- another and the Self Contact BC employed to model the interactions among the FFS layers themselves. In all such cases, the Penalty Method will be employed to specify the degree of solid/solid and/or surface/surface penetration allowed and the Adaptive Contact protocols would define collision-induced element failure. The physical link between the FFS bundles and the messeter and condyle would be simulated through shard nodes at the implant-anatomical interfaces [59]. While Lagrangian solids would comprise the representations of the various anatomical structure and the FFS bundles, Euler elements would be used to model interstitial fluid action. Forces originating directly from the masseter muscle, as well as those produced thusly and conducted to the implant via the condyle, would then be applied to the FFS bundle. Both sets of forces would have approximately 11N peak loads as well as loading rates consistent with those reported in the literature, with the characteristics of the condyle-conducted forces modified by the mechanical properties of this bone tissue [60]. Forces transmitted by the 14
  • 15. interstitial fluid would augment those originating from the messeter. The post-processing will produce detailed representations of the principal, hydrostatic and shear stress concentrations as well as the displacements in both the FFS bundles and the surrounding anatomy. Of particular interest will be the stresses and strains experienced within the cellular scaffold network, since stress shielding effects in orthopedic implants have been correlated with bone ingrowth and strain-induced changes in morphology may change details of cell architecture that stimulate osteogenesis. Condlye stress intensities adjacent to the implant will also be assessed since these could potentially induce remodeling irrespective of FFS bundle action. Previous finite element- based insights into dynamic TMJ properties and jaw mechanics demonstrate the feasibility of modeling this implantation scheme [61-63]. Previous NSF Support The Role of Impurities in Superplastic Flow and Cavitation (DMR-9810422; $405,001; 8/1/98-7/31/01, PI: F. A. Mohamed, Co-PI: J. C. Earthman) The objectives of the present program are: (i) to investigate the correspondence between the effect ofimpurities on creep behavior and that of impurities on the contribution of boundary sliding to the total strain at small elongations (20-30%); and (ii) to assess the extent of impurity segregation at boundaries during superplastic deformation. Accomplishments. Two studies were conducted on two grades Pb-62% Sn (high purity grade and a grade doped with Cd) and two grades of Zn-22% Al (the first grade was doped with 1300 ppm Cu and the second grade doped with 1400 ppm Fe) to provide information that can be used to examine whether a particular impurity influences both superplastic deformation and boundary sliding behavior in superplastic alloys in a parallel manner. The results of these studies indicate a correspondence between the effect of impurities on boundary sliding and the effect of impurities on defamation behavior. Indirect support for the occurrence of impurity segregation at boundaries in Zn-22% Al was also uncovered and presented within the framework of a theoretical model. Development of Human Resources. Three graduate students (Kimberly Duong, Ali Yousefiani, and Yuwei Xun) joined the program as Research Assistants. Ali Yousefiani completed his Ph.D. dissertation on cavitation and he is now working as a technical staff member at the Boeing Company, Huntington Beach, CA. Kimberly Duong, who has a physical disability, completed her Ph.D. dissertation that focused on effects of impurity level on boundary sliding behavior. She is now working in a failure analysis company in Santa Ana, CA. • Publications (Total of 15 publications resulted, 4 are listed below) 1. A Yousefiani, J. C. Earthman, and F. A. Mohamed, “Formation of Cavity Stringers During Superplastic Deformation,” Acta Materialia, 46, 3557-3570 (1998). 2 . K. Duong and F. A. Mohamed,” Effect of Cd on Boundary Sliding Behavior inPb-62% Sn,” Philosophical Magazine A, 80, 2721, (2000). 3. A Yousefiani, F. A. Mohamed, and J. C. Earthman, “Multiaxial Creep Rupture in Annealed and Overheated 7075 Al,” Metallurgical and Materials Transactions A, 31A, 2807-2822 (2000). 4. T. J. Ginter, P. K. Chaudhury, and F. A. Mohamed,” An Investigation of Harper-Dorn Creep at Large Strains,” Acta Materialia, 49, 263 (2001). 15