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Introduction

Each year millions of Americans suffer from a variety of debilitating bone-degenerativeailments such as osteoporosis and bone cancer [1]. In addition to the immediate physicaldiscomfort and impairment, such afflictions also result in lost wages, high medical expenses anddeath. Particularly vulnerable are the elderly, wherein skeletal deterioration and invasivetreatments frequently lead to more severe medical complications and accompany high rates ofmorbidity. Congenital conditions in which skeletal degeneration is a major complication, such assickle-cell anemia which currently afflicts approximately 65,000 Americans, disproportionatelyafflict minorities of African, Latin American and Middle Eastern extraction [2,3]. The attendantcosts and suffering of bone degeneration is expected to increase dramatically over the nextcentury in tandem with expected increases in the number of senior citizens and minorities. Perannum treatment costs for osteoporosis alone already exceed $30 billion [4].

The treatments currently used to rehabilitate skeletal injuries and degeneration all sufferfrom significant drawbacks. Most commonly, injured bones are replaced with a prosthetic madeof titanium, cobalt and/or chromium and secured to adjacent bones with adhesives [5]. Injuredhip joints are replaced by polyethylene-coated metallic cup and ball joints secured to the femurand to the inside of the patient’s acetabulum. Adhesives in vivo degrade over time and requirefurther invasive procedures to maintain. Wear debris between components of hip replacementsfrequently 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-basedreconstruction 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 forpathogens such as cytomegalovirus or HIV. Similar limitations and risks apply to allographs andzenographs [8].

Much research therefore focuses on developing materials and procedures whereby normalskeletal 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 risksassociated with the introduction of foreign tissue. Such a methodology requires the developmentof bio-active materials which serve as both prosthetics during convalescence and as promoters ofnew bone growth. Furthermore, these materials should be biodegradable, thus facilitating theireventual replacement by new bone growth and thereby eliminating the need for follow-upsurgery. Additionally, these materials should be producible by a comparatively inexpensivefabrication process that can be easily tailored to the medical needs of individual patients. Amongthe 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 theregion of implantation.

Computer-aided design and fabrication techniques have been used by Calvert andcolleagues to produce prototype free-form scaffolds (FFS) bundles composed of PLGA-HAPthat have displayed excellent bio-conductive and bio-inductive abilities [9,10]. The stepsinvolved in producing and implanting FFS bundle implants is shown schematically in Fig. 1. Intheir research, Calvert and co-workers seeded the component layers of several scaffolds bysoaking them in solutions containing bone marrow cells with concentrations in excess of 1 x108cells/ml [11]. The layers thus treated exhibited extensive cell proliferation and substantialbone matrix synthesis. The goal of the proposed work is to develop dynamic finite element

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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-raycomputer tomography (CT) data are used to design layers that are then fabricated bynumerically controlled machining and seeded with the patient’s cells, growth factors,and possibly other agents prior to implantation. The primary goal of the proposed workis to develop and use dynamic finite element models to better understand and simulatethe mechanical behavior of FFS materials.

models to better understand and simulate the mechanical behavior of FFS structures. Thisresearch will lead to FEA tools that can be incorporated into the computer-aided design of thelayers for optimized mechanical biocompatibility.

FFS assemblies grouped together with surgical sutures (bundles) also exhibited thecapacity to induce extensive vascularization during animal studies. In one study, seeded andunseeded bundles were implanted within a rabbit rectus abdominis adjacent and superficially tothe right and left deep inferior epigastric bundles, respectively. After 12 weeks had elapsed, bothbundles 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 extensivecell proliferation and displayed new HAP depositions of 3+/-1%. Histologic sectioning revealedthat the layers comprising the seeded bundle had undergone fusion, while those of the controlremained disconnected. The central regions of the seeded layers also exhibited extensivepenetration by capillaries from the nearby vascular bundles, while those of the controls weredevoid of vascularization. Crucial for promoting new bone growth, vascularization establishes

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conduits for nutrient supply and waste removal and facilitates leukocyte access. A section of anexplanted layer showing vascularization is shown in Fig. 2.

While the bone-regenerative capacity of FFS bundles has been established, littleinformation exists regarding their mechanical behavior. In performing their bone-regenerativefunction, these materials would be subjected to a variety of static and dynamic stresses stemmingfrom routine muscle-skeletal exertions, interstitial fluid pressure and other facets of the in vivoenvironment [12]. The resulting stresses and strains experienced by these materials would affectboth their structural integrity and bone-regenerative ability. Particularly useful for therapy is thedevelopment of FFS bundles whose bone-regenerative activities are a function of imparted stresslevels [13]. Crucial for this is a thorough assessment of their capacity to withstand, transmit anddistribute dynamic stresses and strains arising from ambulatory movements and other exertions.Numerous studies have identified dynamic stresses as the principal agents responsible forskeletal adaptation. Animal studies of leg bones subjected to dynamic stresses similar to thosearising during normal gait reveal extensive restructuring of the endo-cortical regions [14].Neonatal studies assign culpability for infant temporary brittle bone disease to dynamic stressdeficits resulting from inhibited fetal movements in utero [15]. The Mechanostat theory ofskeletal adaptation, which was formulated using the results of such studies, reliably predictsroutine bone maintenance (modeling) and bone adaptation to lethargy or to overexertion(remodeling) as functions of both dynamic stress rates and intensities [16]. Despite theexhaustively documented role of dynamic stresses in promoting bone growth, most efforts haveconcentrated on scaffold material performance under quasi-static stresses. Optimizingreconstructive materials for withstanding and transmitting dynamic stresses is pivotal inmaximizing their bone regenerative abilities and the bulk of the proposed work will therefore befocused toward achieving this objective.

Importance will be assigned to optimizing the FFS bundle mechanical response. Severalstudies have shown that osteogenesis increases nonlinearly with increasing strain rate [17].Additionally, animal models of distraction osteogenesis have shown that high strain magnitudesare effective in inducing the synthesis of collagen–HAP formations aligned in the direction of the

Fig. 2 Transmission electron micrograph of vascularized FFS scaffold.

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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-corticalarchitecture [19,20]. By moderating these stresses and strains through energy dissipativeprocesses, FFS bundles optimized for performance under physiological stress magnitudes andstrain rates therefore hold the promise of materials specifically tailored to stimulate optimumbone regeneration during normal physical activities and trauma.

Before these materials are employed as bone-regenerative prosthetics it is critical tooptimize their mechanical characteristics to both maximize their bone-regenerative abilities andto minimize the risks of fatigue and catastrophic failure. Effecting such optimization shouldenable physicians to design FFS bundles with bone-regenerative properties tailored to specificclinical situations and which exhibit reliable, predictable mechanical behavior. Pivotal to bothefforts is the development of simulation methodologies whereby key facets of FFS bundles suchas cell architecture and desired mechanical properties can be reliably designed, assessed andincorporated into usable, reliable implants.

Finite element analysis (FEA) has been used by the researchers and others to simulate themechanical 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 ofbone maintenance and adaptive restructuring as predicted by the Mechanostat theory of skeletaladaptation [27]. When performed with powerful computational software, FEA gives highlydetailed, accurate predictions of in situ stresses and strains. These predictions can in turnfacilitate the design of materials that exhibit specific structural changes in response tophysiological loading conditions.

The proposed study will therefore elucidate the mechanical response of FFS bundles todynamic stresses through FEA, which is thought to be crucial for the development of optimized,medically useful bone-regenerative materials. The proposed research will therefore concentrateon 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 FFSlayers that possess the same geometries as the models through three-dimensional printingtechniques. Dynamic and static mechanical testing will be performed on both the individuallayers and on FFS bundles comprised of these layers in order to verify that the propertiesindicated by the simulations are possessed by the fabricated materials and to provide furtherinsights for structural refinement. Comparisons will be made between the mechanical behaviorof FFS bundles and corresponding monolithic FFS materials in order to elucidate and enhanceproperties unique to the multi-layered materials. Modeling and testing will also be performed onsamples subjected to a liquid saline environment for prolonged periods in order to establish theeffects of interstitial fluid pressure and in vivo degradation on FFS structural integrity andmorphology.

The proposed study will focus initial efforts on developing a better understanding of FFSmechanical behavior in the mandibular-facial environment. FFS bundles tailored to promotetemporo-mandibular joint and condyle repair offer enormous promise for alleviating the oftenextreme discomfort that debilitates the 30 million Americans currently suffering from damage tothe temporo-mandibular joint (TMJ) [28]. The development of such materials would also greatlybenefit the burgeoning number of children and adolescents who suffer fractures to the mandibleand condyle, currently the largest group of pediatric skeletal injuries [29]. This initial effortwould draw from both the work of our laboratory on the time-dependent behavior of complex

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materials and its accomplishments in tissue engineering for the oral-facial regions [30]. Theexperience acquired through both efforts will be used to accurately simulate the dynamic stressesconditions anticipated to confront these materials when used in face and jaw reconstruction. Thiseffort is also anticipated to result in expertise and methodologies required to optimally adaptthese materials for bone regeneration throughout the body.

Fig. 3 Schematic of the 3D Printing method for fabricating the proposed FFS scaffoldbundles depicting (a) binder injection, (b) powder deposition, (c) powder compaction,and (d) piston retraction.

Materials and Methods

I. Three-Dimensional PrintingThree-dimensional printing will be used to produce the FFS materials under

investigation. This technique is versatile in that a variety of intricate biologically active medicaldevices, including controlled dosage delivery agents and FFS layers, are produced directly fromcomputer aided design tools [31,32]. The scaffold will be first designed with modeling softwareand then fabricated through sequential layer deposition and bonding. As shown in Fig. 3, layerproduction involves deposition of powders of the precursor material in a cavity formed by aretracted piston [33]. The geometry specific to the layer is produced through jet deposition of thebinder. Upon completion of a layer, the piston will be retracted by a length equal to the thicknessof the next layer and the previous steps will be repeated. Following their fabrication, the layerswill be bound together with surgical sutures.

The inherent versatility of simulation control combined with facets of the fabricationprocess establishes 3D printing as a particularly suitable processing method for the proposedmodeling. Moreover, this technique has proven its ability to produce intricate surface texturesand extensive interconnected porosity, both of which facilitate integration of the prosthetic withadjacent bone [34]. Porosity in particular has been shown to promote intercellular contact and istherefore thought to be crucial for cell differentiation [35]. In general, the size of reproducibledetail will only be limited by the size of the particles used in the fabrication. Thus, the directsimulation-to-fabrication methodology of 3D printing ensures accurate reproduction of modelfeatures, while the powder-bonding methodology eliminates the involved chemical syntheses,

a

cb

d

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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 ReconstructionThe 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 boneby collagen, while the HAP enhances both rigidity and bio-compatibility [35,39]. The matrixpossesses an open-cellular structure with pore sizes in the 150 – 250 _m range, thus mimickingthe structure of higher-density trabecular bone [40]. This porosity is thought to promote cellinduction and differentiation by limiting the outer surface area available for cell attachment andby facilitating cell transport throughout the matrix.

The FFS layers will be left separate during fabrication and subsequently grouped togetherwith surgical sutures, producing FFS bundles. This approach has been shown to facilitate accessto the scaffold interior by osteoblasts and marrow cells in vitro. The inherent sliding betweenlayers can also provide for energy dissipation to further dampen dynamic stresses associated withnormal function as well as trauma.

III. Simulation SoftwarePatran/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]. Eachconsists of pre-processing software that is used to construct geometries and meshes and to applymaterial properties and boundary conditions, the processing software, Nastran, and post-processing software for saving and displaying the results. Patran uses implicit codes that simulatelinear static loading cases and will be used to model facets of periosteal thickening thought toresult from persistent muscle-applied stresses. By contrast, Dytran employs explicit codes thatsimulate nonlinear dynamic loading situations and will therefore be employed in simulatingmasticulation, locomotion, blunt trauma and fluidic interactions.

The versatility of P/N and D/N makes both software packages ideally suited forsimulating the behaviors of complex three-dimensional structures. Both contain numerous toolsand commands which can be used to construct a wide variety of models with varying geometriesand physical properties. Dytran in particular possesses Contact options that computationally linkdiscrete solids and/or surfaces to one another, thereby permitting simulation of such events asinter-surface sliding, collisions and the penetration of one solid by another. Specific interactioncharacteristics can be specified by the Penalty and Kinematic methods, which define permissiblepenetration 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 AdaptiveContact option, which removes failed elements. Additional flexibility is granted by the GAPoption, which permits the coupling of interactions between spatially separated elements. Thevarious Contact options should facilitate the accurate modeling of mechanical interactionsbetween FFS bundles and adjacent anatomical structures such as bones and muscles. The SelfContact Option even allows the simulation of physical contact between separate portions of thesame solid and can therefore be employed to simulate energy dissipation by friction at theinterface of FFS layers. While Lagrangian Solids will be used to construct the FFS bundles andanatomical features, Euler Elements will be used to model interstitial fluid effects. Still otheroptions common to both Patran and Dytran permit the comprehensive analysis of hydrostatic and

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principal stresses, the magnitudes of which have been shown to correlate with the extents ofendo-cortical remodeling. The capacity of Dytran to dynamically model implant mechanicalperformance has previously been demonstrated in analyses of in situ denture behavior [42].

The robust analysis software used with both pre-processing packages allows theresearcher to generate results depicting the various stress and strain parameters (Von Mises,principal, axial, shear, etc.) required for predicting mechanical behavior. Additionally, Dytranpossesses a Time History (TH) Results function that generates graphs of the magnitudes of thevarious forces arising on surfaces linked through a Contact or Coupling option, as well as of theprogressive distance between the closest points on these surfaces. This function permits thegraphing of a series of Master-Slave Contacts, thereby facilitating the analysis of energytransferred from the in vivo medium through the constituent layers of a FFS bundle. Togetherwith the Contact Surface visualization option, TH will be employed to determine the amount ofenergy transferred from an initial physiological exertion or impact trauma through successiveFFS layers and to access the amount of interlayer sliding and intra-layer straining produced. Theanalysis of inter-surface sliding is thought to be pivotal in optimizing FFS bundle bio-inductiveproperties since experimental studies reveal that small extents of implant-bone sliding promotebone in-growth, while large sliding magnitudes inhibit it [43].

IV. Material ModelThe proposed material model will employ DYMAT 24, which models an isotropic, elastic-plasticmaterial with failure through piecewise plasticity [44]. This model is ideal for materials whosestress-strain response is too complex to be modeled by a bilinear representation. A stress-straintable will be used to describe a piecewise linear approximation of the stress-strain curve for thematerial under investigation. Individual iterations of the stress will be determined from theequivalent 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 toexplicitly 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 the stress-strain table required for Eq. (1) will bedetermined from mechanical test data for a range of strain rates that correspond to masticulatoryfunction.

VI. Model ValidationFour Point Bend TestsFFS bundles and corresponding monolithic scaffold blocks will be tested under four-pointbending conditions to validate model predictions of behavior. Three replicate samples of eachFFS layer configuration under investigation will be tested. The sample dimensions will be 3 x 3

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x 60 mm. Each specimen will be subjected to a four-point bending test, using a custom builtcyclic loading machine at a loading frequency that is within a range consistent with masticultoryloading rates. Specimens will be submerged in 0.9% saline (Ringer’s solution) at a constanttemperature of 37° C during the testing. The data will be used to calculate the flexural modulusof elasticity and the loss coefficient, h, value of damping capacity [45-48]. The loss coefficient isgiven by

i

d

E

E

ph

2= (3)

where Ed is the energy dissipated and Ei is the input energy. For cyclic loading conditions, theloss 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 togage how well the specimens moderate the transmission of dynamic stresses into the surroundingbone. In particular, comparisons between the layered FFS samples and correspondingmonolithic samples will reveal the how interlayer sliding effects this dissipation.Compression TestingFFS and monolithic block specimens will be tested under compression loading conditions undera range of strain rates that are consistent with normal masticulatory function. Elastic modulusand 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). Compressivepercussion probe measurements will also be made to determine the damping capacity accordingto Eq. (3) under these loading conditions. The small size of the probe will allow for percussion ofindividual layers on end in addition to percussion normal to the layers. End-on percussion willbe used to measure damping associated with direct shear forces on the interfaces between thelayers.

The results for all of the above experiments will be compared with numerical predictionsfor validation and refinement of the finite element models.

VI. Modeling, Testing and Characterization EquipmentAll 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 moreextensive models, supercomputer facilities available at UC Irvine will be accessed as needed.

Mechanical testing will be performed with either a MTS 918 servo-hydraulic mechanicaltesting machine or an Inston 3367 tabletop test system, both of which are in the UCI Departmentof Chemical Engineering and Materials Science. These devices are equipped to perform statictension 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 dampingcapacity 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 beenused to measure the damping characteristics of a range of dental implant materials [48]. Allexperimental tests duplicating interstitial fluid effects on FFS bundles will be performed withliquid saline (Ringer’s solution) using immersion equipment that exists in our laboratories.

Geometric and compositional characterization of FFS bundles will be performed with aPhillips XL 30 scanning electron microscope equipped with an EDAX energy dispersive

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spectroscopy (EDS) system. In particular, the samples will be inspected for that might alter themechanical properties both before and after mechanical testing. The compositional uniformity ofthe samples will also be evaluated using EDS.

Research Goals

I. Overall PlanThe objectives of the proposed research are threefold:

1. Comprehensively model and elucidate the stresses and strains imparted to FFS bundlesunder mandibular-facial conditions (see Appendix I).

2. Use the information obtained in (1) to construct simulations of FFS bundles that containlayers possessing improved mechanical properties and osteo-conductive and inductivegeometries.

3. Fabricate and test FFS bundles expected to exhibit improved mechanical performanceand bone regenerative abilities based on the finite element results.

4. Refine FEA models based on test results and SEM examinations of untested and testedsamples.

In addressing these tasks, the proposed work will employ MSC software operated on highcapacity computers to create highly detailed, realistic simulations of the FFS bundles subject tocompressive, tensile, bending and sheer forces imparted by muscles, impacts and interstitialfluid. Overall, the simulations will be used to improve the understanding of loading responses toin vivo stresses by addressing the following questions (among others) vital to their roles as boneregenerators:

A) How do FFS bundles deform under normal physiological conditions and how muchenergy dissipation (damping) occurs during a normal loading cycle?

B) How do the FFS bundles respond to impact trauma? Would this response alter scaffoldintegrity and bone-regenerating capacity?

C) How does the layered structure of FFS bundles dampen dynamic loading compared tomonolithic samples with identical densities and porosities? How much damping can beattributed to the sliding of the layers across each other? How do interfacial agents, suchas stem cells, affect this sliding behavior? How does interlayer sliding affect the stressamplitude and distribution in the surrounding bone?

Answering these questions is critical for future design of FFS bundles with sufficient strengthand 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 scaffoldspossess the improved mechanical properties indicated by the simulations. Care will be taken toassure that bone-regenerative properties are retained during structural modification. Objectives(2) and (3) are anticipated to be accomplished by re-iterative processes wherein FFS mechanicalproperties are refined and enhanced through further simulation, testing and comparison. This

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methodology will lead to the fabrication of FFS bundles possessing both maximum allowablestrengths and optimum geometries for bone regeneration. The overall research plan is shown inTable 1.

The investigative steps comprising the research plan are scheduled to proceed accordingto 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 FFSbundles. Furthermore, each step involves the creation of a candidate FFS group through thecreation of geometric representations of their cell architectures using the pre-processingsoftware. The strongest members of this group will be identified through FEA, wherein thecellular 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 thatthese materials possess the properties predicted by FEA, to select the best members of this groupand 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 caseproduced from the materials selected in phase (1). The mechanical and SEM results obtainedpreviously will be used to design architectures that have been re-enforced with respect to themechanisms that have been identified as governing failure. Once again, mechanical testing willbe employed to verify material properties and, this time, to select optimized FFS-bundles forfuture animal and clinical studies.

Table 1. Research PlanTable 2. Research Plan for FFS-Bundle Optimization.

Data from in vivo FFS BundlesData from in vivo FFS Bundles

Optimized FFS BundlesOptimized FFS Bundles

Simulation of in vivo FFS BundlesSimulation of in vivo FFS Bundles

Simulation with Optimized PropertiesSimulation with Optimized Properties

Fabrication of FFS BundlesFabrication of FFS Bundles

Mechanical TestingMechanical Testing

Table 2. Timeline for the Proposed Research

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2 Months -Final Progress Report and Publications

24 Months ____Fabrication and mechanical testing of FFS bundles produced from EFFS models

24 Months____Design and simulation of enhanced FFS’s(EFFS) with enhanced mechanical

properties

18 Months___Fabrication and testing of FFS bundles produced from PGM, selection of strongest

scaffolds (StFFS)

6 Months_Design and selection of FEA pilot model group (PMG) from current FFS bundles

Time

Year 1 ][ Year 2 ][ Year 3

Objective

2 Months -Final Progress Report and Publications

24 Months ____Fabrication and mechanical testing of FFS bundles produced from EFFS models

24 Months____Design and simulation of enhanced FFS’s(EFFS) with enhanced mechanical

properties

18 Months___Fabrication and testing of FFS bundles produced from PGM, selection of strongest

scaffolds (StFFS)

6 Months_Design and selection of FEA pilot model group (PMG) from current FFS bundles

Time

Year 1 ][ Year 2 ][ Year 3

Objective

II. Modeling FFS BundlesA 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 areanticipated to experience a variety of stresses arising from muscular contractions, interstitialfluid pressure, tissue growth and other biological activity. These stresses in turn produce motionsof the separate layers relative to each other and induce straining in the individual layers. Suchstraining is thought to both alter FFS mechanical properties and to affect bio-compatibility bychanging the surface morphology and pore conformation.

Compression Tension

Shear

1) Tension -compression from asymmetrical muscle contraction.

2) Shear from symmetrical contraction.

Fig. 4 Examples of stresses experienced in vivo by FFS bundles :

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FFS Layer

Suture

Contracted Muscle

Flaccid Muscle

Force Exerted by Muscle

Force Imparted to Bundle

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The proposed models will represent the FFS cell geometry as a semi-regular polyhedralopen-cellular lattice. The seminal work of Ko and Knipschild identified strut bending in this typeof lattice as the predominant mechanism governing deformation in cellular materials [49,50]. Amodel devised later by Gibson and Ashby represents open cell geometry as a network ofstaggered cubes, thereby deriving the mechanical response from struts bending to alignthemselves with applied stresses [40]. Work by Warren and Kranik also ties mechanical behaviorto strut bending, but employs tetrahedral and tetrakaidecahedral cell geometries [51,52]. As withthese earlier efforts, a polygonal geometry will be adopted in which strut bending predominatesover strut stretching. FFS cell architecture will be modeled with selected members of the regularand semi-regular polyhedral groups and those whose behavior most closely matches that of theFFS selected. The strut geometry itself will be modeled with an hourglass shape, as opposed tosimple columns, with dimensions derived from experimental data. Structural parameters such asthe cell length, strut dimensions and surface detail can be changed in accordance with theexperimental findings.

Summary

I. Immediate Benefits of ActivityFFS-bundles composed of PLGA and HAP offer promise for bone regeneration in

patients suffering from traumas and progressive skeletal degeneration. Extensive in vitro andanimal studies have established that these materials promote osteoblast and marrow cellconduction and simulate the synthesis of both collagen and HAP. Since FFS-Bundles arecomposed of biocompatible and bio-reabsorbable materials, they are also promising candidatesfor therapies wherein bone growth gradually replaces the original implants. The fabricationprocess 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 byoptimizing their mechanical and bio-inductive properties for facial and jaw restoration. Modelingtheir mechanical response to in vivo mandibular-facial conditions is anticipated to provide theinformation that with both lead to a comprehensive understanding of their bone-regenerativebehavior and, ultimately, to facilitate the production and use these materials in the repair of awide range of skeletal pathologies and injuries throughout the body.

II. Intellectual Merits of ActivityThe 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 worktherefore offers the prospect of elucidating and refining the details of this theory and of tailoringthese particulars to specific regions of the skeleton

Optimizing FFS bundles for bone regeneration is anticipated to clarity the role of staticloading in re-modeling. Although both copious experimental evidence and the Mechanostattheory assign priority to dynamic stresses, several studies also indicate that static stressesparticipate in periosteal re-modeling [14]. This evidence, however, is contradictory, with manystudies asserting that static loading inhibits re-modeling, while others claim it promotesperiosteal thickening. The modeling work and the subsequent clinical trials of optimized FFSbundles should therefore elucidate the possible contribution of static stresses to bone re-modeling.

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The work assessing the influence of interstitial fluid effects on FFS bundle performanceis 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 theimportance of interstitial fluid action for re-modeling, its precise role in this process remainsuncertain [53,54]. Optimizing FFS bundles with respect to interstitial fluid stresses should helpto clarify this medium’s contribution to skeletal re-modeling.

This work will also address the role of fatigue in stimulating re-modeling. While it isgenerally accepted that such damage is detrimental to skeletal integrity, much evidence impliesthat 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 ActivityFFS bundles offer great promise for alleviating the often extreme discomfort that

debilitates the 30 million Americans currently suffering from damage to the temporo-mandibularjoint (TMJ) architecture. The incorporation of numerical modeling in computer-aided materialsdesign and fabrication should be particularly useful for producing implant materials based onpatient CT data and near-net shaped processing techniques. Optimizing the mechanical and boneregenerative abilities of FFS bundles is anticipated to advance the design of a wide variety ofskeletal and dental implant materials. As various functional parameters are modeled and testedand the FFS bundle bone regenerative abilities optimized, values for the re-modeling thresholdstresses for regions of the mandible and other facial skeletal features are expected to bedetermined. These results may facilitate the construction of clinical “profiles” wherein thresholdvalues specific to selected patients and pathologies are specified. Such information would tailorFFS bundles to treat specific medical conditions and could facilitate the treatment of numerousother 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 tonatural 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 facilitatethe development of such “smart” materials that incorporate living cells between the bundledlayers.

The proposed research will also provide educational opportunities at the undergraduate aswell as graduate levels for training students in the use of numerical modeling techniques for thedesign and computer-based fabrication of complex material structures. In particular, theproposed work would allow the PI to incorporate content on numerical modeling for optimizednear-net shape materials processing in the introductory course E54 “Principles of MaterialsScience and Engineering,” a required course for engineering majors at UC Irvine. This course istaught using the problem-based learning approach and would therefore be ideally suited for thisincorporation. In addition, students of underrepresented groups will participate including IanNieves who has completed his coursework and passed his preliminary exam in the Ph.D. degreeprogram in Materials Science and Engineering at UC Irvine.

IV. Appendix—Modeling FFS Bundles for Facial-Mandibular ApplicationsThis 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 materialsto such functions will begin with devising implantation schemes wherein their ability to promote

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Deep Part of Masseter Muscle

Lateral Pterygoid MuscleCondyle

Masseteric Artery

FFS FFS BundleBundle

Fig. 8 Situation of FFS bundle for TMJ-related condyle repair.

bone regeneration is utilized to stimulate the repair of specific damage. Once the implantationsite 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 specifyFFS bundle attachment to the surrounding medium and stresses typical of those produced in theselected region through masticultion will be applied. For example, in the TMJ disfunction-relatedimplantation scheme depicted in Fig. 8, a FFS bundle has been placed superficially to themasseter artery and proximate to the condyle in order to promote self-vascularization and tostimulate the repair of the latter. Accordingly, Dytran pre-processing software will be used toreproduce condylar and messeter muscle geometry and that of the FFS bundles themselvespossessing the desired detail from a combination of Shell and Sold Lagrangian elements. TheMaster-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 layersthemselves. In all such cases, the Penalty Method will be employed to specify the degree ofsolid/solid and/or surface/surface penetration allowed and the Adaptive Contact protocols woulddefine collision-induced element failure. The physical link between the FFS bundles and themesseter and condyle would be simulated through shard nodes at the implant-anatomicalinterfaces [59]. While Lagrangian solids would comprise the representations of the variousanatomical structure and the FFS bundles, Euler elements would be used to model interstitialfluid action. Forces originating directly from the masseter muscle, as well as those producedthusly 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 consistentwith those reported in the literature, with the characteristics of the condyle-conducted forcesmodified by the mechanical properties of this bone tissue [60]. Forces transmitted by the

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interstitial fluid would augment those originating from the messeter. The post-processing willproduce detailed representations of the principal, hydrostatic and shear stress concentrations aswell as the displacements in both the FFS bundles and the surrounding anatomy. Of particularinterest will be the stresses and strains experienced within the cellular scaffold network, sincestress shielding effects in orthopedic implants have been correlated with bone ingrowth andstrain-induced changes in morphology may change details of cell architecture that stimulateosteogenesis. Condlye stress intensities adjacent to the implant will also be assessed since thesecould potentially induce remodeling irrespective of FFS bundle action. Previous finite element-based insights into dynamic TMJ properties and jaw mechanics demonstrate the feasibility ofmodeling 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 theeffect ofimpurities on creep behavior and that of impurities on the contribution of boundarysliding to the total strain at small elongations (20-30%); and (ii) to assess the extent of impuritysegregation at boundaries during superplastic deformation.Accomplishments. Two studies were conducted on two grades Pb-62% Sn (high purity gradeand a grade doped with Cd) and two grades of Zn-22% Al (the first grade was doped with 1300ppm Cu and the second grade doped with 1400 ppm Fe) to provide information that can be usedto examine whether a particular impurity influences both superplastic deformation and boundarysliding behavior in superplastic alloys in a parallel manner. The results of these studies indicate acorrespondence between the effect of impurities on boundary sliding and the effect of impuritieson defamation behavior. Indirect support for the occurrence of impurity segregation atboundaries in Zn-22% Al was also uncovered and presented within the framework of atheoretical 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 BoeingCompany, Huntington Beach, CA. Kimberly Duong, who has a physical disability, completedher Ph.D. dissertation that focused on effects of impurity level on boundary sliding behavior. Sheis 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 DuringSuperplastic 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 Annealedand 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 Creepat Large Strains,” Acta Materialia, 49, 263 (2001).