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# Dimensional Study of an Interference Fit Allograft

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DIMENSIONAL STUDY OF AN IN TERFERENCE FIT ALLOGRAFT By NATHAN A. MAUNTLER A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2006

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Copyright 2006 by Nathan A. Mauntler

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This thesis is dedicated to my mother, Marg aret Mauntler: the most selfless, dedicated, and loving person I know. Thank you for your love, your support, your faith, and all those cookies you sent from Ohio.

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iv ACKNOWLEDGMENTS I would first like to thank my graduate committee Tony L. Schmitz (chair), W. Gregory Sawyer, and John C. Ziegert for their guidance, their support, and their patience. I would like to thank the me mbers of the Tribology Labor atory and the Machine Tool Research Center at the University of Flor ida: Jerry Bourne, Dave Burris, Matt Hamilton, Luis Alvarez, Alison Dunn, Pam and Dan Dickrell, Vince Lee, Nick Argibay, Chris Martens, Kevin Powell, Scott Payne, G. Sc ott Duncan, Raul Zapata, Lee Kumanchik, Kevin Cheng, and Lonny Houck. I am very grateful for their friendship, their comradeship, their help, and their shenanigans. I wish to thank Becky Bassett, Earl Jones, Roy Clark, Jason Bootle, and the rest of the staff at Regeneration Technologies, Inc. for their generous support and access to their facilities. Finally, I would lik e to acknowledge the generos ity and kindness of the donors who make the fine work at Rege neration Technologies possible.

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v TABLE OF CONTENTS page ACKNOWLEDGMENTS.................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES...........................................................................................................ix ABSTRACT....................................................................................................................... xi 1 INTRODUCTION AND PROBLEM STATEMENT..................................................1 Dimensional Measurements and Mechanical Testing..................................................2 Modeling....................................................................................................................... 2 2 REVIEW OF THE LITERATURE..............................................................................6 The Structure and Mechanical Properties of Bone.......................................................6 Classifications of Developed Bone.......................................................................6 Mechanical Properties of Cortical Femoral and Tibial Bone Material.................7 Mechanical Properties of Cancellous Material......................................................8 Analytical Interference Fit Models...............................................................................9 Stress, Pressure, and Pull-apart Force Predictions................................................9 Limitations of the Analytical Model...................................................................11 Finite Element Analysis of Bone................................................................................11 3 THE CORNERSTONE ASR ALL OGRAFT MANUFACTURING PROCESS..16 Cutting Blanks For Machining...................................................................................16 Preparation for Assembly...........................................................................................17 Assembly and Finishing Cuts.....................................................................................17 BioCleanse Sterilization Process............................................................................18 Lyophilization Process................................................................................................18 4 EQUIPMENT AND PROCEDURES.........................................................................23 Dimensional Measurements........................................................................................23 Probe Tip Qualification.......................................................................................23 Measuring the Allograft Stack-ups and Parts......................................................24 Cortical-cancellous stack-ups.......................................................................25

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vi Loose cortical plates.....................................................................................27 Cortical pins.................................................................................................28 Pull-apart Tests...........................................................................................................30 Sample preparation..............................................................................................30 Pull-apart test procedure......................................................................................31 Finite Element Analysis..............................................................................................31 Analytical Model and M onte Carlo Simulation..........................................................32 5 RESULTS AND DISCUSSION.................................................................................42 Dimensional Measurements........................................................................................42 Interference Pins..................................................................................................42 Measurement repeatability...........................................................................43 Taper characterization..................................................................................43 Collet clamping effects.................................................................................44 Pin manufacturing repeatability...................................................................45 Cortical Plate Holes.............................................................................................45 Hole diameter measur ement repeatability....................................................45 Effects of the RTI machining fixture...........................................................45 Straightness error..........................................................................................46 Diametric variation between the two plate holes.........................................46 Diametric variation between plates..............................................................46 Manufacturing process repeatability............................................................47 Diametric Interference.........................................................................................47 Mechanical Pull-apart Tests.......................................................................................48 Finite Element Analysis..............................................................................................49 Monte Carlo Simulation.............................................................................................50 6 CONCLUSIONS........................................................................................................70 APPENDIX  MONTE CARLO SIMULATION MATLAB code...................................72 LIST OF REFERENCES...................................................................................................75 BIOGRAPHICAL SKETCH.............................................................................................78

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vii LIST OF TABLES Table page 2-1 A survey of the elastic propert ies of cortical bone compiled by..............................14 2-2 A study of RTI donor cortical bone strength............................................................14 2-3 Bone elastic material properties used in fi nite element studies...............................15 2-4 Bone elastic material properties used in study of an inter-vertebral fusion degeneration.............................................................................................................15 4-1 Input parameters for the Monte Carlo analysis........................................................41 5-1 Average pin diameters in mm by do nor over the RTI manufacturing step..............52 5-2 Pin measurement repeatability.................................................................................52 5-3 Average single-pin diameter range values in mm by donor and manufacturing process......................................................................................................................53 5-4 Average pin straightness error values in mm...........................................................54 5-5 Diametric differences in mm between the chamfered and non-chamfered pin ends........................................................................................................................... 54 5-6 Average collet clamping effect in mm.....................................................................55 5-7 Variation of pin diameter s in mm across a single donor..........................................56 5-8 Average cortical plate hole diam eters (mm) by donor and manufacturing process......................................................................................................................56 5-9 Ten repeated measurements of one cortical plate hole.............................................57 5-10 Effects of the RTI machin ing fixture on hole diameter...........................................57 5-11 Ten repeated measurements of a cor tical plate hole diameter (mm) while clamped in the RTI machining fixture.....................................................................58 5-12 Average straightness error (mm) of cortical plate holes by donor and manufacturing cycle.................................................................................................58

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viii 5-13 Average diametric difference between hole 1 and hole 2.................................59 5-14 Average diametric difference in mm betw een the holes of the two cortical plates of a single allograft...................................................................................................59 5-15 Average diameter variation in mm over a single plate.............................................60 5-16 Range of hole diameter va lues in mm over a single donor......................................61 5-17 Average predicted diametric interfer ence in mm for each manufacturing cycle.....62 5-18 Pull-apart test results................................................................................................63 5-19 Pullapart test results for grafts where the interference fit failed............................64 5-20 Finite element analysis inputs..................................................................................66 5-21 Finite element outputs..............................................................................................66 5-22 Monte Carlo simulation inputs.................................................................................67 5-23 Multi-parameter Monte Carl o simulation overall results.........................................67 5-24 Monte Carlo simulation results for single parameter variations..............................69

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ix LIST OF FIGURES Figure page 1-1 The Cornerstone ASR cortical-cancellous allograft...............................................4 1-2 Allograft failure by pull-apart....................................................................................4 1-3 Stress cracking in an allograft plate...........................................................................5 2-1 An analytical model of an inte rference fit between two cylinders...........................15 3-1 Cancellous blocks, corti cal pins, and cortical plates are harvested from specific areas of the femur and tibia......................................................................................20 3-2 Orientation of the cortic al bone pieces with respect to anatomical bone material directions..................................................................................................................20 3-3 Lathe tooling for turn ing the cortical pins................................................................21 3-4 The chamfered end of a cortical pin.........................................................................21 3-5 Assembling and grooving fixture.............................................................................22 3-6 Custom tool for inserting interference pins into holes re amed in allograft..............22 4-1 Brown and Sharpe MicroVal PFx coordinate measuring machine..........................34 4-2 Probe tip geometry used in this study......................................................................34 4-3 Allograft parts as receiv ed from RTI for one donor.................................................35 4-4 RTI indexing wheel and assembling/grooving fixtures...........................................35 4-5 Stack-up measurement. Inset shows hole naming convention.................................36 4-6 Stack-up coordinate system alignment features.......................................................36 4-7 Measurement of the cortical plates while stacked in the machining fixture............36 4-8 Definition of straightness error................................................................................37 4-9 One corner of each loose plate wa s removed to preserve orientation......................37

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x 4-10 Loose cortical plates were cl amped directly to the CMM table...............................37 4-11 Cortical plate coordinate system alignment features................................................38 4-12 Cortical pins were measured while clamped in a 5-C collet and manual collet holder........................................................................................................................3 8 4-13 Pins were clamped in the coll et with 6.2 mm of length exposed.............................38 4-14 Cortical pin coordinate system alignment features..................................................39 4-15 Measurement locations for one side of the cortical pin...........................................39 4-16 Cortical pin meas urement procedure. ......................................................................40 4-17 Pull-apart test setup..................................................................................................40 4-18 The ANSYS model and mesh used in the finite element analysis...........................41 5-1 Diameter range over a single pin..............................................................................53 5-2 Comparison of average diam eters of the two pin ends............................................54 5-3 Pin diameter variati on over a single donor...............................................................55 5-4 Diameter variation over th e 8 holes of a single plate...............................................60 5-5 Hole diameter variation over al l the plates from a given donor...............................61 5-6 Pull-apart test resu lt trends where the inte rference fit failed...................................65 5-7 Trial 3 von Mises stress distribution........................................................................66 5-8 Trial 3 pin contact pressure distribution...................................................................67 5-9 Monte Carlo simulation results................................................................................68

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xi Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science DIMENSIONAL STUDY OF AN IN TERFERENCE FIT ALLOGRAFT By Nathan A. Mauntler August 2006 Chair: Tony L. Schmitz Major Department: Mechanic al and Aerospace Engineering The Cornerstone ASR cortical-cancellous allograft made by Regeneration Technologies, Inc. (RTI) of Alachua, Florida, is an implant used in cervical spinal fusion surgeries. Making use of two cortical bone plates for structur al support surrounding a cancellous bone block for grow th conduction, the graft is he ld together by two cortical interference pins. The success of the interferen ce fit depends on the manufacturing tolerances of the components as well as th e quality of the donor bone used to produce the graft. In this study, the diameters of interference pins and cortical pl ate holes required to produce thirty allografts are measured on a c oordinate measuring machine at four critical points in the manufacturing cycle: after mach ining, after chemical sterilization, after freeze-drying (lyophilization), and after re-hyd ration. A statistical distribution of the interference fit component dimensions is obtained. Lyophilization is found to have the largest effect on the component dimensions, cau sing an average decrease of 21 m in the predicted interference, which should nominally be between 25 and 38 m.

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xii Thirty separate allografts are manufacture d by RTI to investigate the occurrence of pull-apart failure and cracking in the allografts. Of the thirty grafts, seventeen (57%) showed signs of cracking on one or both of the cortical plates Four (13%) of the grafts failed manual pull-apart tests following lyophilization and pr ior to hydration. Following a thirty second hydration, the graf ts were epoxied to aluminum plates and pulled apart on a mechanical tensile testing machine. For twenty of the grafts, one plate was removed from the interference fit at an aver age pull-apart force of 83.4 N. For the remaining ten grafts, the epoxy failed prior to interfer ence fit failure. Of the seven grafts that were separated and showed no signs of cracking, the averag e pull-apart force was found to be 100.6 N. Any relationship between the predicted diam etric interference value and the pull-apart force was obscured by the small sample size of undamaged grafts and variations in material property. A finite element analysis of the interference fit is created to attempt to model the scenario observed in the mechanical testing. The model predicts a pull-apart force of 93 N and a maximum von Mises stress of 35 MPa. Additionally, the model shows no evidence of a stress c oncentration at the edge of the contact. Finally, a Monte Carlo simulation based on an isotropic analytical model of the interference fit is de veloped. In this simulation, the input parameters are varied by random values within one standard deviati on of the mean. The Monte Carlo simulation indicates that diametric interference is the larg est factor affecting th e interference fit. The simulation accurately predicts the rate of occurrence of pull-apart and material failures at 13% and 57%, respectively.

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1 CHAPTER 1 INTRODUCTION AND PROBLEM STATEMENT This thesis describes an investigation of an interference-fit allograft used in spinal fusion surgeries. Spinal fusion is the join ing of two vertebrae in order to treat degenerative disk disease or otherwise remove pressure from the sp inal cord. Fusion is accomplished by inserting a graft between the tw o vertebrae. This graft serves both as a structural support and a medium through whic h the two bones can grow together and eventually fuse. Grafts made from hum an cadaver bone are known as allografts. One such allograft is the Cornerst one ASR cortical-cancellous block manufactured by Regeneration T echnologies, Inc. (RTI) for use in cervical spine fusion surgeries (Figure 1-1). This graft is assembled from a cancellous bone block sandwiched between two cortical bone plates held together by two interf erence-fit pins. The cortical plates provide structural strength while th e cancellous block provides a medium for new bone growth. By manufacturing the graft from separate cortical and cancellous pieces, more efficient use can be made of the bone donor material. Also, the use of an interference connection for the assembly enables an all-bone construction. Drawbacks to an interference fit connecti on include the possibility of pull-apart failure and cracking. Pull-apart failure occurs when the strength of the interference fit is insufficient to hold the graft together under te nsile loads (Figure 1-2) Pull-apart failure can occur as a result of inade quate radial interference (the pi n is insufficiently larger than the plate holes) or as a result of the compone nts having too much mechanical compliance. Cracking occurs when the stresses caused by th e interference fit are large enough to cause

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2 material failure in the bone. As opposed to pul l-apart failure, cracki ng is the result the radial interference or material stiffness being too large. The purpose of this study is to examine the quality of the ASR interference fit connection in the light of the various RTI ma nufacturing processes in order to identify the most probably failure source. To this end, dimensional measurements of the pins and cortical plate holes and mechanical pull-ap art tests are performe d to characterize the accuracy of the RTI machining process and th e effects of various chemical, dehydration, and re-hydration treatments. Mech anical testing is used to measure the force required to separate the interference fit. Finally, a finite element analysis of the graft and a Monte Carlo simulation are performed to predict interference fit failures. Dimensional Measurements and Mechanical Testing In the dimensional study, the diameters of pins and cortical plate holes are measured at various points throughout the ma nufacturing process. The parts required to produce six grafts from each of ten donors ar e provided by RTI. Half of these grafts follow the normal manufacturing cycle/assembly steps in order to later measure the force required to separate the interference fit. Th e remaining pieces are not assembled so that dimensional measurements may be performe d. Pin and hole diameter measurements are recorded after each of the follo wing manufacturing processes: Machining The chemical steriliza tion process BioCleanse Freeze-drying, or lyophilization Hydration for thirty seconds. Modeling The data obtained from the dimensional m easurements are then used along with published material properties to create a finite element model of the interference fit. This

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3 three-dimensional orthotropic model is used to simulate the stresses and pressures present in the allograft as well as the pull-apart force. The finite element model is in turn used to validate and improve an isotropic analytical model which was used in a Monte Carlo simulation, a computational technique wher e the model inputs are randomly selected from pre-selected distributions and used to compute the output over many iterations. The results of the Monte Carlo simulation is a stat istical distribution of the output parameters (e.g. stress, pressure, and pullapart force). Finally, the stre sses and pull-apart forces predicted by the finite element model and Monte Carlo analysis are compared to the failures observed in the actual allografts.

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4 Figure 1-1. The Cornerstone ASR cortical-cancellous allograft Figure 1-2. Allograft failure by pull-apart.

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5 Figure 1-3. Stress cracking in an allograft plate.

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6 CHAPTER 2 REVIEW OF THE LITERATURE To make predictions regarding the eff ectiveness of the a llograft interference connections, it is necessary to have an unders tanding of the mechanical behavior of bone from an engineering standpoint. Once the physic al properties of bone are identified, they can be applied to mechanical models which si mulate the conditions of the interference fit. The following sections provide a review of pub lications relevant to the study of bone as an engineering material and its application to specific mech anical scenarios. A discussion of relevant analytical and finite element modeling tec hniques is also included. The Structure and Mechanical Properties of Bone Bone is a composite material comprise d of an inorganic phase, primarily hydroxyapatite (Ca10(PO)4)6(OH)2) crystals, embedded in an organic matrix, primarily collagen.[1] At the micrometer level, these co llagen fibrils and embedded hydroxyapatite crystals bundle to form fibers.[2] The organization of these bone fibers above the micrometer level depends on the development and function of the bone area of interest.[3] Classifications of Developed Bone The macrostructure of mature bone can be categorized as cortical or cancellous. Slow-forming cortical, or compact, bone is ma de up of organized layers, or lamellae, which form in nominally para llel cylindrical patterns.[2] The directionality of these lamellae causes cortical bone to have anisotropic properties. Strictly speaking, the elastic properties of cortical bone are orthotropic. However, little e rror is introduced by modeling cortical bone material from long bones as transversely isotropic in nature.[4] In

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7 long bones such as the femur and tibia, cortic al bone forms in the central shaft, or diaphyis.[6] In contrast, cancellous, or trabecular, mate rial is made up of a porous matrix of bony struts, called trabeculae, packed with mineral and marrow deposits.[1,2] In general, the bulk properties of cancellous bone are func tions of the density and directionality of this matrix.[3] In long bones, cancellous material pr imarily forms on the ends (epiphyses) of the bones, but can also be found under the can cellous surface of th e shaft close to the epiphyses.[3,5] The transition within a bone from cancel lous to cortical material can be gradual and microstructural an alysis is often necessary to distinguish between the two.[2] Assigning values to the material properties of bone material, whether cortical or cancellous, is not trivial. Factors that can aff ect the elastic and strength properties include mineral content, trabecular density, the t ype of bone, the harvest location on the donor bone, and the scale at which measurements are taken.[1-3,6-11] To try to address these issues, a wide variety of methods have b een used to investigate bone mechanics. Buckling tests, tension tests, compression tests, bending tests, indentation methods, acoustic methods, and x-ray computed tomography have all been used to measure the elastic and failure properties of cortical and cancellous bone.[3,12-15] For the sake of relevance and to limit the discussion to a reas onable length, the follo wing subsections are limited to a discussion of huma n femoral and tibial bone only. Mechanical Properties of Cortical Fe moral and Tibial Bone Material Table 2-1 contains da ta compiled by Cowin[1] and Currey[3] from mechanical and ultrasound studies of the elastic prop erties of cortical bone material.[16-19] Data from Reilly and Burstein suggests that cortical bone can behave differently in tension than in compression.[16-17] Standard deviations, where applicab le, are in parentheses. Note that

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8 two of these studies assume transversely is otropic material symmetry while the other two account for orthotropic material properties. Here, the 1 direction corresponds to the radial bone direction, the 2 direction corresponds to the circumferential bone direction, and the 3 direction corresponds to the radial bone direction. It should be noted that the values for Poissons ratio greater than 0.5 reported by Reilly and Burstein are physically impossible. Table 2-2 contains a collection of material strength information for cortical bone under a variety of loading conditions and phys ical treatments relevant to this study.[5] This data is of particular in terest since it repres ents RTI donor material for use in spinal allografts. Note that the standard deviation of the failure stress is between 12% and 25% of the mean value. This gives some indicati on of the substantial variation in material properties that can be present from sample to sample for bone material. For comparison, Reilly and Burstein report the tensile streng th of bone as 53 MPa in the circumferential direction and 133 MPa in the l ongitudinal direction and the co mpressive strength of bone as bone 131 MPa in the circumferential di rection and 205 MPa in the longitudinal direction.[16] Mechanical Properties of Cancellous Material While cancellous bone is, strictly speaking, or thotropic, for practi cal purposes it is becoming common to model cancellous bone as isotropic.[6,20] While values for the elastic modulus of trabeculae are on par with those of cortical bone,[3] Youngs modulus values for bulk cancellous material is substan tially smaller. Rice et al. suggest that both Youngs modulus and the cancellous bone streng th are dependent on the apparent density of the material to the second power.[21] The same study reported values all less than 500 MPa for the bulk Youngs modulus of human cancellous bone. Since the modulus values

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9 for bulk cancellous bone are so much smaller th an those of cortical bone, the effect of cancellous bone is neglected in the following analyses. Analytical Interference Fit Models Once the mechanical properties of bone material are understood, they can be incorporated into specific mechanical models. The classic analytical model of an interference fit connection is the hollow, th ick-walled cylinder representation shown in Figure 2-1.[22] In this model, a hollow cylinder 1 of nominal outer radius R is forced into another hollow cylinder 2 wh ose inner radius is some amount smaller than R. To accommodate the radial interference, both cyli nders must deform such that the outer radius of cylinder 1 decreases by some amount 1 while the inner radius of cylinder 2 increases by some amount 2. The deformations 1 and 2 must add up to the radial mismatch Stress, Pressure, and Pull-apart Force Predictions The two-dimensional state of stress at the boundary of either cylinder can be described in terms of the pressure p at the interface and the three radii as in Eq. (2-1) through Eq. (2-4). In these equations 1t and 2t represent the tangential stresses of cylinders 1 and 2 while 1r and 2r represent the radial stress es in cylinders 1 and 2. The sign convention is such that positive stress es are tensile and negative stresses are compressive. If the two cylinders are not both infinitely long, a stre ss concentration will exist at the edges of the contact. For this reason, the st ress concentration factor Kt is included in the radial stress equations. A stre ss concentration factor of 2 is a reasonable upper bound value.[22] (2-1) 1tp # R2ri2$R2ri2# % PAGE 22 10 (2-2) (2-3) (2-4) The von Mises equivalent stress v at the interface of either cylinder can be calculated as shown in Eq. (2-5), where 1 and 2 represent the two-dimensional principal stresses. Substituting Eq. (2-1) th rough Eq. (2-4) into Eq. (2-5), the von Mises stresses for cylinder 1 in Eq. (2-6) and cy linder 2 in Eq.(2-7) can be found. Since in this study the pin (cylinder 1) is solid, ri is assigned a value of zero. The calculated von Mises stresses can then be directly compar ed to the failure strength of the cylinder materials. (2-5) (2-6) (2-7) Thick-walled cylinder elastic theory can be used to calculate the pressure p at the press-fit interface as in Eq. (2-8), where E represents Youngs modulus and # represents Poissons ratio. The force require d to separate the interference fit can be found from Eq. (2-9) where Ac represents the area in contact, Lc represents the length of the contact and represents the static coefficient of friction between the inner pin and outer plate. If Eq. 2tp ro2R2$ ro2R2# % 1rKt # p % 2rKt # p % v 12" 1 2 % #" 2 2 $v1pKt2Kt # 1$ % v2pKt2Kt ro2R2$ro2R2# & ' ( ) + %$ ro2R2$ro2R2# & ' ( ) + 2$ %

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11 (2-1) through Eq. (2-9) are assumed to pr ovide a reasonable repr esentation of an interference fit, the force required to separate a cortical plate from tw o cortical pins could be estimated by multiplying the force F in Eq. (2-9) by a factor of two. The integral in equation 2-9 is to account for the fact that th e stress concentration f actor is not constant along the length of the contact, desi gnated here as the x-direction. (2-8) (2-9) Limitations of the Analytical Model The analytical model has three primary limitations. First, the assumption is made that the material properties of both the pin and plate are isotropic in nature. Secondly, this model cannot account for the effect a second pin in close proximity would have on the stress state. Finally, the mode l cannot account for plate geometry that is not cylindrical. Finite Element Analysis of Bone Due to the limitations of analytical models finite element analysis has become a common method of modeling bone behavior. Th e following paragraphs discuss several application of the finite element met hod to various scenarios involving bone. The choice of a finite element model de pends on the geometric and mechanical complexity of the scenario being modeled. Often, three-dimensional models are necessary, but under certain circumstances, si mplifying assumptions can be applied to reduce the computational requirements. Pl ane strain, plane stress conditions, or p R E1 1 1 #./% R E2 ro2R2$ro2R2# 2$& ' ( ) + % \$ Fx Ktx ()p % Ac () %0 % 1 2 3 d x Ktx ()p % 2 4 % R % Lc %./%0 % 1 2 3 d

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12 axisymmetric conditions can justify the use of two-dimensional models. Twoor threedimensional models can also be simplified when loads, boundary conditions, and material properties are symmetric about a given axis. When modeling the reconstruc tion of mandibles, Nagasao et al. and Tie et al. used computed tomography (CT) scans to create solid models with accurate information regarding the location and thickness of cortic al and cancellous bone.[23-25] Nagasao et al. used 10-node tetrahedral elements for the enti re model while Tie et al used four-node tetrahedral elements to model the cancellous inner mandible and membrane shell elements to model the thin cortical shell. Both studies assumed isotropic material properties; see Table 2-3. Similarly, Barker et al. used CT scans to create a three-dimensional model of a human metacarpal.[26] Additionally, bone density information from the CT scans was used to predict calcium and potassium conten t. Power laws developed by Lotz et al. and Dalstra et al. were then used to create isotropic and orthotropic material models.[12,13] The solid models were meshed using hexahedral and pentahedral elements without mid-side nodes. Wang and Dumas used 8-node brick elements with isotropic material properties for both cortical and cancellous spinal bone when modeling an inter-vertebral fusion scenario.[27] This study investigated the likely vari ation in material properties from bone to bone by using a range of values for both Youngs modulus and Poissons ratio (Table 2.4). When studying stress concentration create d by surgically drilled holes in canine tibia, Zapata used a two-dimensional axisymetric model.[28] Transversely isotropic

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13 material properties were used to model the cortical tibial bone while isotropic material properties were used to model woven bone growing where the hole was drilled. The model was meshed using quadrilateral elements. In this study, we will apply a three-dimens ional model solid model of one cortical plate and two cortical pins. The model is meshed with 20-node orthotropic hexahedral elements. Transversely isotropic material pr operties are used for bot h the cortical plate and the cortical pins.

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14 Table 2-1. A survey of the elastic prop erties of cortical bone compiled by. Yoon and Katz (1976) [17] Knets et al. (1977) [18] Ashman et al. (1984) [19] CompressionTension Symmetry applied Transversely Isotropic Transversely Isotropic Transversely IsotropicOrthotropicOrthotropic Bone typeFemurFemurFemurTibiaFemur Testing method MechanicalMechanicalUltrasoundMechanicalUltrasound E1 (GPa)11.5 (1.01)12.8 (3.0)18.86.9112.0 E2 (GPa)11.5 (1.01)12.8 (3.0)18.88.5113.4 E3 (GPa)18.2 (0.85)17.7 (3.6)27.418.420.0 G12 (GPa)3.63.67.172.414.53 G13 (GPa)3.3 (0.42)3.3 (0.42)8.713.565.61 G23 (GPa)3.3 (0.42)3.3 (0.42)8.714.916.23 12 0.63 (0.20)0.53 (0.25)0.3120.490.376 13 0.38 (0.15)0.41 (0.15)0.1930.120.222 v23 0.38 (0.15)0.41 (0.15)0.1930.140.235 v21 0.63 (0.20)0.53 (0.25)0.3120.630.422 v31 0.38 (0.15)0.41 (0.15)0.2810.320.371 v32 0.38 (0.15)0.41 (0.15)0.2810.310.35[1,3]Reilly and Burstein (1975) [16] Table 2-2. A study of RTI donor cortical bone strength. MeanSt. Dev.MeanSt. Dev.MeanSt. Dev. Physiologic20424.584.716.2295.0 Freeze dried (FD)30375.960.315.031.810.1 FD + Reconstituted16919.697.013.824.75.3 BioCleanse20336.1--29.24.6[5]Axial CompressionTransverse ShearTransverse Tension Treatment

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15 Figure 2-1. An analytical model of an interference fit between two cylinders. Table 2-3. Bone elastic material proper ties used in finite element studies. Young's modulus (GPa)Poisson's ratio Cortical bone150.33 Cancellous bone1.50.3 [23-25] Table 2-4. Bone elastic materi al properties used in study of an inter-vertebral fusion degeneration

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16 CHAPTER 3 THE CORNERSTONE ASR ALLOGRAFT MANUFACTURING PROCESS The ASR cervical spinal allograft is produced using femoral or tibial bone from a single donor. Donor material is processed from whole limbs which are received frozen. After removing the soft tissue, the bones ar e cut into blanks, machined to shape, assembled, cleaned, and freeze dried as discusse d in the following sections. Each of the following sections occurs in a single machining episode to prevent the intermixing of donor material. Cutting Blanks For Machining The bones are cut into blanks using a stainl ess steel band saw. Cortical blanks are taken from the shaft (diaphysis) of the bones while cancellous blanks are cut from the heads (Figure 3-1). Blanks for cortical plat es are harvested from the stronger central portion of the shaft. The cortical region of the donor bone has a fi nite thickness, so the cortical blanks must be cut in a specific or ientation with respect to the lay of the bone (Figure 3-2). Cancellous blanks are chosen from the denses t regions of cancellous bone. All blanks are cut oversized to accommodate final machini ng. Cortical pin bla nks are cut 25 mm long and 3-4 mm wide. Cortical plate blanks ar e cut 12.5-13 mm long and to a width of the operators discretion. Cortical pin and plate blank thicknesses are driven by the thickness of the bone raw material. Cancellous blanks are cut to 11.3 mm by 11.3 mm by 4.5 mm.

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17 Preparation for Assembly Cortical pin blanks are turned down to pi ns on an OmniTurn GT-Jr CNC lathe. The pins are first turned using conventional too ling, then reamed by a tubular tool with a sharpened inner edge to a nominal diameter of 2 mm (Figure 3-3). The reaming tool is produced by drilling a hole through a conve ntional reamer. When turning the pins, isopropyl alcohol is used as a cutting fluid. Th e turned pin is then parted from the blank, leaving a chamfer on one end (Figure 3-4). The length of the parted pin is approximately 17.5 mm. After the pins have been machined, th ey are immersed in alcohol, removed and left to dry for 15 minutes. They are then wei ghed to ensure that they meet minimum bone density requirements. The pins are finally so rted into groups with diameters in a 0.013 mm (0.0005 in) range. Cortical plate blanks are squared on a Fadal 904-1L CNC mill. Blanks are first faced and squared on three sides in one clamp pallet, then faced and squared on the other three sides in a second clamp pallet. Like th e cortical pins, the plates are checked for minimum mass requirements. Cancellous blanks are dimineralized in 0.5 N HCL for 3-5 minutes, then submerged in water for 8-10 minutes. No further machin ing is required for the cancellous blanks. Assembly and Finishing Cuts Cortical plates and cancellous blocks are clamped in the assembling and grooving fixture (Figure 3-5). Six of these fixtures are then bolted into an indexing wheel. Two holes are drilled and reamed through the cor tical-cancellous stack-ups. The diameter of the reamer is designated to be 0.025-0.038 mm (0.0010-0.0015 in) smaller than the pins which will be used for that graft. Isopropyl alcohol is used as a cutting fluid while reaming the holes.

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18 Pins are inserted chamfered end first into the reamed holes using a custom tool (Figure 3-6). The side clamps of the machini ng fixture are then removed and the sides of the allograft are grooved. Th e interference fit assembly is then removed from the assembly and grooving fixture and loaded into the profiling fixture for final radius cuts. Allografts are then inspected and frozen. BioCleanse Sterilization Process BioCleanse is a chemical treatment th at kills viral, fungal, and bacterial contaminants without adversely aff ecting the bone material properties.[30] Normally, a BioCleanse cycle is completed with allogr afts from a single donor. However, due to cost considerations, all donor material for this study was processed in a single BioCleanse batch. RTI offers BioCleanse  in two different recipes depending on whether or not the donor material contains so ft tissue. The more chemically aggressive hard-tissue-only recipe was used for this st udy since it was assumed to be more likely to adversely affect the material and dimensi onal properties of the allografts. Normally allografts are visually inspected, package d, and stored frozen after completing the BioCleanse cycle. However, for this study, loos e cortical plates and cortical pins were packaged in sealed plastic pouches and sent to the University of Florida for additional dimensional measurements (see Chapter 4). Lyophilization Process Lyophilization is a freeze drying process perf ormed on allografts so that they may be stored at room temperature for extended periods. The allografts and allograft parts from donors 1-6 underwent lyophilization in one cycle while the material from donors 710 were run in a separate cycle.

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19 After lyophilization, a llografts are visually inspec ted for cracks and manually inspected for pull-apart failures. Since the pull-apart tests are pe rformed by hand, the applied force is unknown. The allografts are then repackaged and the packages sterilized for distribution.

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20 Figure 3-1. Cancellous blocks, cortical pins, and cortical plates are harvested from specific areas of the femur and tibia. Bone images from http://www.ana.cuhk.edu.hk/3dana/main.htm [29 ] Figure 3-2. Orientation of the cortical bone pieces with respect to anatomical bone material directions.

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21 Figure 3-3. Lathe tooling for turning the cortical pins. Figure 3-4. The chamfered end of a cortical pin.

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22 Figure 3-5. Assembling a nd grooving fixture. Figure 3-6. Custom tool for inse rting interference pins into holes reamed in allograft.

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23 CHAPTER 4 EQUIPMENT AND PROCEDURES This chapter discusses the procedures us ed in this study, including measurement techniques, analytical and finite el ement models, and mechanical testing. Dimensional Measurements Measurements of the allograft stack-ups and components were carried out on a Brown and Sharpe MicroVal PFx three-axis coordinate measuring machine (Figure 41) using a Renishaw MIP touch-trigger pr obe. This coordinate measuring machine (CMM) is operated via PC-DMIS CAD++ software and is certified to be accurate to 12 m over its work volume according to Am erican National Standard ASME B89.4.12001b.[31] The CMM could be operated in either ma nual mode or direct computer control (DCC) mode. In manual mode, the CMM was co ntrolled by the operator using a joystick. In DCC mode, the CMM was commanded by th e machine controller. In this study, the manual operation mode was used to locate part s and define the part coordinate frame. DCC mode was used to refine the alignment and take measurements. Probe Tip Qualification Two types of stylus probe tips were used in this study. A 20 mm long tip was used to measure the loose cortical plates and pi ns while a 27 mm long tip was used to measure the stack-ups held in the RTI assembly and grooving fixture. Both tips were composed of a 1 mm diameter ruby ball fixed to a carbide shank and steel body (F igure 4-2). Points were recorded by moving the CMM axes until the ruby ball ca me into contact with the

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24 part being measured. This cause d the probe tip to swivel w ithin the probe housing until a switch registered the contact. A contact force of 0.1 N was required to register probe tip contact. To ensure accurate measurements, the probe tips must be calib rated periodically. For this study, probe tips were calibrated if: The CMM controller had been turned off after the most recent calibration. The PC-DMIS software had been closed after the most recent calibration. The tip had not been calibrated for th e current donor and measurement type. The tip was qualified by taking 24 points abou t a spherical artifact. The diameter of this construct was then compared to th e known 19.050 mm diameter of the artifact. Additionally, the standard de viation of the 24 radius values was calculated. The calibration was considered acceptable if the co nstructed diameter was accurate to better than 3 m. A standard deviation of the radii of less than 2 m was considered acceptable for the 20 mm long tip while a standard devi ation of less than 4 m was considered acceptable for the 27 mm long tip. Measuring the Allogra ft Stack-ups and Parts Dimensional measurements of the allograf t pin and hole diameters were taken at four points during the manufacturing cycle: just prior to pin insertion, after BioCleanse, after lyophili zation, and after a 30 sec ond hydration by immersion in water. A discussion of the RTI manufactur ing procedure can be found in Chapter 3. Grafts from ten donors were followed th rough the manufacturing process. Each donor set consisted of the part s required to make six all ograft assemblies (Figure 4-3). The parts were first received prior to pin insertion with co rtical plates and cancellous blocks still clamped in the RTI indexing wheel (Figure 4-4). At this time the holes in the

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25 top cortical plate were measur ed. Half of the cortical-cancellous stack-ups were then removed so that individual co rtical plates could be measured. The remaining three stackups were left in their respective machining fixt ures and returned to RTI for final assembly and machining. This was done so that half the parts could be passed through the RTI manufacturing process for further measurements and half could be assembled for failure testing. During this first measurement cycle, the tw elve cortical pins per donor were also measured and sorted according to size. Six pins were selected to be inserted into three allografts including the two largest and two sm allest pins. These extreme diameter pins were deliberately mismatched with the extrem e diameter holes in order to try to increase the likelihood of fracture and pull-apart failures. The thr ee assembled grafts per donor were then assembled, machined and treated as per RTI specifications with BioCleanse and lyophilization. The remaining six pins along with the cortic al plates that were removed from the RTI assembling and grooving fixtures were then re-measured after each remaining portion of the manufacturing sequence. The can cellous blocks were assumed to have no effect on the performance of the graft (see Chapter 2). For this reason, the cancellous blocks that were removed from the machining fixtures were discarded. Cortical-cancellous stack-ups As noted, the six cortical-cancellous stack -ups per donor were measured while still clamped in the RTI machining fixture prior to pin insertion. Each stack-up was assigned a label ASM X-Y where the prefix ASM de signated the parts as an assembly, X was the position of the graft in the RTI indexing wheel (1-6), and Y was the donor number (110). Due to the limited length of the probe ti p, only the topmost cortical plate could be

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26 measured in the fixture. The two holes were designated as hole 1 and hole 2 as shown in Figure 4-5. The indexing wheel was received from RTI sealed in a plastic container containing water to keep the bone material in a mo ist environment. The bone pieces were not immersed in the water, however. Individual fixtures containi ng the grafts were removed from the plastic container and indexing wheel one at a time to be meas ured. First, the reamed holes were cleaned with water and compressed 1,1,1,2 te trafluorethane dust remover in an effort to remove machined bone chips. The assembling and groo ving fixtures were then bolted into an aluminum adapter which was then bolted to the CMM table for measurement as shown in Figure 4-5. The CMM software coordinate system was th en aligned to the fixture as shown in Figure 4-6. First, a plane was created from fi ve points on the top f ace of the support arm. This plane was defined as the z-plane into which all two-dimensiona l features would be projected. Next, a line was created from two poi nts taken from left to right along the front face of the support arm to define the x-direction. A four-point circle was then taken inside of hole 1 the center of which defined the xand y-direction zero. Finally, a single point was taken on the top face of the front clamp. This point, which was at the same level as the top of the stack-up, defined the z-direction zero. This se quence was completed first in the CMM manual operation mode and then in DCC mode. The y-direction vector was constructed in the PC-DMIS software as th e cross product of the z-direction and the xdirection

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27 Once the coordinate system was aligned to the graf t, hole 1 and hole 2 were measured. Four ten-point circles were taken at 0.5 mm intervals along the axis of each hole (Figure 4-7). The diameter of each hole wa s defined as the average diameter of the four circles. Additionally, th e straightness of each hole was calculated. To do this, the best-fit line through the centers of the four circles in the hole was determined. The straightness of the hole was then defined as the farthest dist ance of any given center from the best-fit line (Figure 4-8). Loose cortical plates The holes of the cortical plates were assigned a name by the convention PL X-YZ. Here, the prefix PL designated the part as a plate. The X numeral was filled by a 1 or a 2 to designate the plat e as the top or bottom plate in the fixture, respectively. The Y numeral indicated the posit ion of the graft in the inde xing wheel (1-6) and the Z numeral referred to the donor number (1-10) The hole designations described in the cortical-cancellous stack-up section we re carried over to the loose plates. Once a plate was removed from the machin ing fixture, one corner was removed with a razor blade as shown in Figure 4-9. This was done to keep track of the plate orientation throughout the remaining measurem ent cycles. The plate was then cleaned with water and compressed 1,1,1,2 tetrafluorethane to remove any remaining bone chips and excess water. It should be noted that no cleaning was performed on the parts after lyophilization and subsequent hydration. Exce ss water was wiped from the re-hydrated parts using a lint free tissue. The loose cortical plates were then clam ped to the CMM table as shown in Figure 4-10. The CMM coordinate system was aligned to the part as shown in Figure 4-11. Note that the removed corner is hidden by the cl amp. First, a plane was constructed from six

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28 points taken on the top face of the plate. This plane defined the z-plane into which all two-dimensional features were projected. Next two circles were constructed from four points each in hole 1 and hole 2. A line from hole 1 to hole 2 was then constructed which defined the negative y direction. The xand ydirection zero coordina tes were shifted to the center of hole 1. Finally, a six-point pl ane was measured on the CMM table around the plate which defined the z-direction zero va lue. The x-direction was calculated as the cross product of the y-directi on and z-direction. These featur es were measured first in manual operation mode and then in DCC mode to improve accuracy. As with the clamped stack-ups, four 10-poi nt circles were m easured at 0.5 mm intervals in each of the plate holes. The diameter of each hole and the hole straightness were then calculated as described fo r the cortical-cancellous stack-ups. Cortical pins Cortical pins were received in a heat-s ealed plastic bag. Once this bag was opened, the pins were coated with isopropyl alc ohol then allowed to dry for 30 minutes. Individual pins were measured while cl amped in a 5C collet (Figure 4-12). Only the portions of the pin which would be in contact with the cortical plates were measured. Pins were therefore inserted into the collet such that 6.2 mm of pin length was exposed (Figure 4-13). This allowed 1 mm cl earance from the portion of the pin to be measured to the top of the collet. As with the other part types, the first step in the measurement process was to align the CMM coordinate system to the pin (Figur e 4-14). First, a plane was constructed from five points on the top flat surface of the manual collet holder to which the z-plane was leveled. Next, a four-point circle was m easured around the pin, the center of which defined the xand y-coordinate zero values Finally, a single point was taken on the top

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29 surface of the pin which defined the zcoordinate zero. Due to the nominally axisymmetric shape of the pin, the xand ydirections were not explicitly defined. As with other part types, this alignment was performed first in manual operation mode then in DCC mode. The non-chamfered end of the pin was measur ed first using eight 10-point circles at 0.5 mm intervals along the length of the pin shaft (Figure 4-15). The pin was then removed from the collet, re-c lamped with the chamfered e nd exposed, and measured in the same fashion. Finally, the non-chamfered end was re-measured. The first measurement of the non-chamfered end was not used in determining the dimensions of the pin. The pin diameter was calculated as the av erage of the 16 diameter values taken from both ends of the pin (Figure 4-16). The straightness error of either end was determined by constructing a best-fit line thr ough the centers of the eight circles, then calculating the maximum center deviation from that line. The pin straightness error was defined as the larger straight ness error from the two ends. Unlike the cortical plates, which were de signated according to their location in the machining fixture, cortical pins could not be given a designation until after they were measured and paired to an allograft, whethe r or not that graft would later be assembled. Pins were named according to the convention PN X-Y-Z. Here, the X numeral designated whether the pin was to be inserted into hole 1 or hole 2 of its corresponding graft. The Y numeral designa ted the station of the indexi ng wheel containing the stackup into which the pin would be inserted. Again, this designation carried over even if that

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30 graft was in stations 4-6 and would not be assembled. Finally, the Z  place holder indicated which donor the pin came from. Pull-apart Tests The quality of the interference fit of the assembled allografts was experimentally investigated by measuring the force required to separate a cortical plate from its two interference pins. These tests were carried out using an MT S Q-Test 5 Load Frame with Testworks 4 software. The load frame was f itted with a 5 kN load cell and mechanical grips as in Figure 4-17. The grafts to be tested were fixed wi th epoxy to grooved aluminum blocks which were clamped in the mechanical grips. This was done to avoid the need to clamp the cortical plates and thereby affect the inte rference connection. The 3.2 mm (1/8 in.) grooves in the aluminum blocks prevented the pins from being glued to the aluminum or the cortical plates. Prior to any mechanical testing, the grafts were tested by hand as done in the RTI production environment. To do this, each cor tical plate was held between the thumb and index finger of one hand and tension was applie d. If any resistance was met, tension was ceased. Grafts that separated with no appr eciable resistance were reassembled and retested as described in the following sections. Sample preparation The aluminum blocks were first filed to remove any residual epoxy from previous tests, then roughened with 60 grit sand paper to improve the ability of the epoxy to bond. The blocks were sonicated in acetone and me thanol, rinsed with water, and blown dry with compressed air.

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PAGE 44

32 to the average of all pin diameters from the dimensional study. The diameter of the holes was made equal to the pin diameter minus the average predicted interference value from the dimensional study. Twenty-node brick elemen ts were used to populate the pin and the plate. To simulate the interference fit, contact and target elements were created at the pinplate interfaces. A two-step load scenario was used to study the interference fit. First, a static study was used to model the stresses in the assemb led allograft. Von Mises equivalent stress values and contact pressures observed after th is load step. Next, a relative motion of 100 m was applied to one end of both pins to in duce slippage. The pull-apart force was then found by summing the z-direction forces of all of the contact elements. Analytical Model and Monte Carlo Simulation An analytical interference fit model form ed the basis for a Monte Carlo simulation used to predict the rate of pull-apart failure of the assembled grafts. The analytical model applied in this simulation was discussed in Chapter 2. This model assumes isotropic material properties and a cylindrical geometry of both pin and plate. The purpose of the Monte Carlo simulation wa s to serve as a tool for predicting the frequency of interference fit failures, either by insufficien t pull-apart force or yielding. Additionally, the simulation was used to comp are the relative influence of the different model parameters. The Monte Carlo simulati on was written in Matlab (see Appendix). To estimate the frequency of failure, each input parameter in Table 4-1 was assigned a mean value and standard deviation. Mean values and sta ndard deviations of geometric variables were taken from the resu lts of the dimensional study. Values for the elastic constants were obtained from the lite rature (Chapter 2). The stress concentration

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33 factor Kt and the effective plate outer radius were obtained by comparison with the finite element model (see Chapter 5). The Monte Carlo simulation was then used to generate histograms which predicted the number of occurrences of both negative pul l-apart forces and V on Mises stress values above the failure stress. This was done by sele cting values for each of the variables in Table 4-1 randomly within one standard devi ation of their mean value. Forces and stresses were then calculated according to the analytical model discussed in Chapter 2. Von Mises stress was only calculated when th e interference was greater than zero. This process was repeated 250,000 times to generate a distri bution of outputs. The relative influence of individual variables could then be tested by setting the standard deviation values for all variables, except the variable of interest, to zero. The resultant standard deviation of the pull-apart force distributio n could then be compared to similar simulations for other variables to determine the most influence factors on the interference fit.

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34 Figure 4-1. Brown and Sharpe MicroVal PFx coordinate measuring machine. Figure 4-2. Probe tip geomet ry used in this study.

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35 Figure 4-3. Allograft parts as received from RTI for one donor. Cortical-cancellous stackups 1-3 as marked above were assemble d into allografts. Stack-ups 4-6 were removed from the assembling and grooving fixture for further measurement. Figure 4-4. RTI indexing wheel and assembli ng/grooving fixtures. Only the top cortical plate could be measured in this fixt ure due to probe tip length limitations.

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36 Figure 4-5. Stack-up measurement. In set shows hole naming convention. Figure 4-6. Stack-up coordinate system alignment features. Figure 4-7. Measurement of the cortical plates while stacked in the machining fixture.

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37 Figure 4-8. Definition of straightness error. Figure 4-9. One corner of each loose plat e was removed to preserve orientation. Figure 4-10. Loose cortical plates were clamped directly to the CMM table.

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38 Figure 4-11. Cortical plate coordi nate system alignment features. Figure 4-12. Cortical pins were measured while clamped in a 5-C collet and manual collet holder. Figure 4-13. Pins were clamped in the collet with 6.2 mm of length exposed.

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39 Figure 4-14. Cortical pin coordina te system alignment features. Figure 4-15. Measurement locations fo r one side of the cortical pin.

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40 Figure 4-16. Cortical pin measurement pr ocedure. 1. Measure non-chamfered end. 2. Measure chamfered end. 3. Measure non-ch amfered end again to investigate effects of collet clamping. Figure 4-17. Pull-apart test setup.

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41 Figure 4-18. The ANSYS model and mesh us ed in the finite element analysis. Table 4-1. Input parameters fo r the Monte Carlo analysis ParameterSymbol Radial Interference Young's Modulus (Pin)Ei Young's Modulus (Plate)Eo Poisson's Ratio (Pin)i Poisson's Ratio (Plate)o Interface Radiusb Effective Plate Radiusc Stress ConcentrationKt Length of ContactL Friction Coefficientf

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42 CHAPTER 5 RESULTS AND DISCUSSION The following sections contain the results of the dimensional measurements, pullapart tests, finite element analyses, and M onte Carlo simulation. Additionally, results are presented for the friction testing that was pe rformed in support of the finite element and Monte Carlo models. Dimensional Measurements As was discussed in previous chapters, dimensional measurements were completed both to understand the accuracy and consistency of the RT I manufacturing process as well as to use in predictive models of the interference fit. To this end, results are presented first for the pins and plate holes se parately, then for the combined interference of the allograft components. Interference Pins Average diameter values by donor are shown in Table 5-1. Note that the diameters from the first, second, and third donors have substantially larger diameters than those pins from the other seven donors. A tool chan ge was performed on the lathe used to turn the pins between the times when donors 3 and 4 were processed. Also note that while the diameter values stay relatively constant after BioCleanse, lyoph ilization causes the pin diameters to drop by an average of 50 m. Subsequent hydration of the pins for 30 s results in an average diametric recovery of 11 m. Also included in Table 5-1 are the average diameter values measured with calipers by the RTI machinist for each donor. Since thes e diameter values represent the bin to

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43 which the pins were assigned, and thereby dete rmine the reamer sized used in drilling the plate holes, their accuracy is of some im portance. The RTI-measured average diameter values deviate by anywhere from 1 m to 12 m from the diameters measured asmachined using the Brown and Sharpe CMM. Recall from Chapter 3 that reamer sizes are available in 0.0005 in (12.7 m) increments. Measurement repeatability Before further comments can be made on the measurement results for the pin diameters, it is first necessary to quantify the reliability of the CMM measurements. To that end, the results of ten re peated measurements of a singl e pin are shown in Table 5-2. Between each repetition, the pin is removed and re-fixtured in the collet. Over the ten measurements, the measured pin diameter varies over a 6 m range with a standard deviation of 2 m. Taper characterization RTI manufacturing drawings call out a maximum taper of 0.0005 in (12.7 m) over the length of a pin. In this st udy, the taper of the pins is inve stigated in three ways. First, the range of diameter values over the sixtee n circles measured on each pin is recorded (Figure 5-1). Average single-pin diameter range values are tabulated by donor and manufacturing process in Tabl e 5-3. It should be noted av erage values for donor 3 are consistently out of specification. However, after lyophilization and re-hydration, only one of the pins from donor three was ac tually out of specification at 15 m of variation. The average value for donor 3 was skewed due to th e fact that two pins were lost during the BioCleanse cycle. Also note that the av erage single-pin diameter range for each process stays relatively constant but is slightly hi gher after lyophilizati on. Eight of fifty-

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44 seven loose pins that completed the manufact uring process had a taper of greater than 12.7 m. Next, pin straightness error, as defined in Chapter 4, is calculated as the deviation of circle center locations from a best fit lin e through all measured circles (Figure 4-8). Average pin straightness error values for each donor and manufacturing process are recorded in Table 5-4. Note that the average st raightness error stays c onsistent to within 4 m for each donor. Finally, a comparison between the diamet ers of the chamfered and non-chamfered ends of each pin (Figure 5-2) is made in orde r to ensure that one end of the pin is not systematically larger than the other. The average diametric difference between the two ends of each pin are recorded for each donor and manufacturing cycl e in Table 5-5. Here, the diametric difference is defined as the average diameter of the non-chamfered end minus the average diameter of the chamfered end. Table 5-5 indicates that while one end may be larger than another for a given pin or even for the pins from a given donor, this difference is small compared to the repeatability of pin measurements show n in Table 5-2. More significant from a manufacturing standpoint, neither end is consistently larger or smaller than the other as one might expect from turning a cantilevered beam (see Chapter 3). Collet clamping effects One item of concern when fixing the pins for measurement on the CMM was that the collet was plastically compressing the bone material. To investigat e the possibility of permanent deformation, the non-chamfered e nd of each pin was measured twice. The average difference of the second diameter measurement minus the first, the clamping

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45 effect, is catalogued for each donor in Ta ble 5-6. The collet clamping effect, while generally 0-2 m, is most notable prior to lyophiliz ation for larger diameter pins. Pin manufacturing repeatability For each donor, the range of diameters for the six pins not inserted into allografts was calculated as shown in Figure 5-3. This was done to gain some understanding of the repeatability of each stage in the manufacturi ng process. The pin diameter variation for each donor at each manufacturing cycle is shown in Table 5-7. It should be noted that the average single-donor diameter variation decreases after BioCleanse and increases dramatically afte r lyophilization. Cortical Plate Holes Average cortical plate hole diameters for each donor and manufacturing step are shown in Table 5-8 along with the correspondin g reamer diameter used by RTI. Like the pin diameters, the plate hole diameters fall dramatically, here by an average of 29 m, after lyophilization. However, unlike the cortical pins, 30 se conds of immersion in water only recovers an average of 3 m of diameter. Hole diameter measurement repeatability As with the cortical pins, ten repeat meas urements were taken of a single cortical plate hole. The results of these repeat meas urements are shown in Table 5-9. Over the 10 measurements, a standard deviation of 0.005 mm from the mean value is observed. Effects of the RTI machining fixture As was discussed in Chapter 4, the corti cal plates are measured both in the RTI machining fixture and clamped to the CMM table to determine whether any diametric change occurs. Table 5-10 shows the aver age discrepancy between the two sets of measurements. The loose plates are on average 6 m larger than the plates measured in

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46 the machining fixture with a standard deviati on of 7 m. This relativ ely large variance in the effect of the fixture may be due to variati ons in the cortical plat e exterior dimensions. Since the front and side clamps of the machini ng fixture are tightened to be flush with the fixture body, rather than to a set force, the amount of stress and strain that a plate is subjected to could vary significantly if the plate was oversized or undersized. Accompanying Table 5-10 are the results of a ten repeated measurements of a cortical plate hole clamped in a machining fixt ure (Table 5-11). Note that the range and standard deviation of the values ar e comparable to those in Table 5-9. Straightness error Table 5-12 shows the average straightness error values of the cortical plate holes sorted by donor and manufacturing cycle. Av erage straightness error values for the cortical pin holes range from 2 m to 10 m and do not vary more than 4 m over the various stages of the manufacturing process. These results are similar to those seen for the cortical pins. Diametric variation between the two plate holes Table 5-13 shows the average diametric vari ation between the tw o holes of a given cortical plate. Here, the diam etric variation is defined as the diameter of hole 2 minus the diameter of hole 1. Tabl e 5-13 indicates that, on average, hole 1 is 2-3 m larger than hole 2, though with a standard deviation of 3-5 m, regardless of the manufacturing cycle. Diametric variation between plates Table 5-14 shows the average diametric va riation between the holes of the two cortical plates of a given allograft. Here, diametric variation is defined as the average diameter from plate 2 minus the average di ameter from plate 1. Table 5-14 indicates

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47 that once the plates complete the manufacturi ng process, little diffe rence exists between the diameters of the two plates. Manufacturing process repeatability As with the cortical pins, it is desirable not just to know the accuracy of the hole diameter values, but also their precision. The quality and repeatabilit y of the drilled and reamed holes are characterized in two ways. First, the single-plat e range of diameter values is calculated as shown in Figure 54. Table 5-15 shows the average values of the single-plate diameter range for each donor a nd manufacturing cycle. On average, the diameters of the holes of a given plate vary by 10-11 m. Additionally, the range of hol e diameters over a single donor is calculated as shown in Figure 5-5. The results of these calculati ons are shown in Table 5-16, which indicates significant diametric variation from hole to hole. At the end of the manufacturing process, the twelve cortical plate holes associated with a given donor will vary by an average of 17 m. Diametric Interference Table 5-17 shows the average predicted diam etric interference between the cortical pins and the cortical plate holes for each donor and each manufacturing process. Here, the predicted diametric interference is defined as the calculated diametric difference between the pins and plate holes that were not formed into allografts. Recall from Chapter 3 that RTI specifies a machined diametric inte rference of 0.0010-0.0015 in. (25-38 m). Table 5-17 indicates that with the exception of donor 9, the average interference values after machining are within acceptable limits. The pr edicted interference dr ops by an average of 21 m after lyophilization and recovers by an average of 7 m afte r thirty seconds of immersion in water. Donor 9 is of particular note since the predicte d interference values

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48 become negative after lyophili zation. Also note that the standard deviation of the interference values are a much larger percentage of the aver age values afte r lyophilization and rehydration than after machining and BioCleanse. Mechanical Pull-apart Tests Table 5-18 shows the results for the m echanical pull-apart tests including occurrences of manual pull-apar t failures, the plate that failed, which epoxy was used and the load at which failure occured. As discusse d in Chapter 4, the allografts were first tested manually for pull-apart failure after lyophilization a nd before hydration. Out of the thirty grafts considered in this study, 4 (13%) failed during manual testing and 17 (57%) exhibited visible cracking in one or both cortical plates. N one of the grafts that failed the manual pull-apart test were made from sets of pins and plates de liberately matched to have poor interference. All of the cracks were in the long itudinal bone direction and ran from the pin to the edge of the plate. Of the 30 assembled allografts, 20 were pul led apart during mechanical testing. For the remaining 10 grafts, the epoxy holding the gr aft to the aluminum blocks failed before the interference fit. Results for the 20 grafts that were pulled apar t are listed in Table 519. The average pull-apart force was found to be 83.4 N with a standard deviation of 25.9 N. The average pull-apart force of the graf ts with no cracks was found to be 100.6 N with a standard deviation of 28.5 N. The average pu ll-apart force of the grafts what exhibited cracks was found to be 74.1 N with a standard deviation of 19.8 N. Also included in Table 5-19 are the pred icted interference va lues for each graft after machining and adjusted by the average process effect for each donor after lyophilization and hydration. Here, the pred icted interference after machining is

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49 calculated as the difference between the aver age pin diameter and average hole diameter for each graft. Figure 5-6 shows the pull-apart force plotted against donor number and the predicted interference values. Unexpectedly, Figure 5-6 indicates little or no correlation between the predicted diametric interference a nd the pull-apart force. This could indicate that over the small sample size (the seven grafts that were pulled apar t that did not exhibit cracking) variations in mate rial properties play a larg er role than dimensional interference. It is also possible that the poor corr espondence between predicted interference and pull-apart for ce reflects a difference in th e effects of lyophilization and hydration on the assembled graft as oppos ed to the measured loose parts. Finite Element Analysis The finite element analysis described in Chapter 4 was completed three times with three separate sets of material property a nd geometric inputs (Table 5-20). Here, the subscript r refers to the radial bone direction, the s ubscript c refers to the circumferential bone direction, and the subs cript l refers to the longitudinal bone direction. The von Mises stress and pull-apart force results from each trial are shown in Table 5-21. For the first trial, the ma terial properties were taken from [16] while the pin diameter and diametric interference were taken from the measurement results after hydration. The second trial used the same materi al properties as the first trial but used geometric values associated w ith the lyophilized state. The th ird trial used a pin diameter and interference equal to thos e of the second trial, but us ed mechanical properties reduced by roughly one standard deviation from th e values used in the first two trials. Of the three trials, the third tria l (reduced modulus a nd interference values ) shows the closest agreement to the experimental data.

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50 The von Mises stress distribution and contact pressure plot for the third trial are shown in Figures 5-7 and 5-8, respectively. No t surprisingly, the highest stresses are located at the contact and betw een the two pins. Somewhat mo re surprising is the absence of a defined stress concentration at the edge of the edge of the contact where the pins overlap the holes. Monte Carlo Simulation The Monte Carlo simulation inputs are s hown in Table 5-22. Interference values and pin diameter values are taken from the measured results afte r lyophilization. Mean Youngs modulus values are the same as the radial and circumferential values from the finite element model. The Youngs modulus sta ndard deviation, as well as the Poissons ratio mean and standard deviat ion values, are selected from.[16] According to the finite element analysis results, a st ress concentration factor of 1 was used. Finally, the effective plate outer radius was adjusted until the simulation results best matched the finite element results. The output statistical distributions from the multi-parameter Monte Carlo simulation are shown in Table 5-23 and Figure 59. Note that the mean pull-apart force is within the range of results obs erved in the mechanical tes ting while the pull-apart force standard deviation is dramatically higher. Th is suggests that the M onte Carlo analysis is overstating the variation in the actual force and stress levels. The model indicates a pull-apart failure (F < 0) rate of 13%. Recall from the mechanical testing that the pul l-apart failure rate was also found to be 13%. Assuming a failure stress of 25 MPa (the ultimat e tensile strength reported by Bianchi [5]), the simulation predicts a von Mises stress failure rate in the cortical plates of 84%. If the tensile failure stress is assumed to be 53 MPa (as reported by Reilly and Burstein [16]), the

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51 simulation predicts that 57% of the grafts will fail. Recall from the mechanical testing that the 57% of the allografts we re found to have cracks in them. Table 5-24 shows the results of the si ngle-parameter variation simulation. The simulation indicates that the diametric inte rference, coefficient of friction, and plate Youngs modulus are the most influential para meters on the pull-apart force. Also, the simulation indicates that diametric inte rference, plate Youngs modulus, and bone Poissons ratio are the most influential fact ors on the von Mises stress in the cortical plate. Note that the prediction that diametric interference is the most influential factor in the quality of the interference fit is not supported by the pull-apart data.

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52 Table 5-1. Average pin diameters in mm by donor over the RTI manufacturing step. DonorRTI MeasuredMachined BioCleanse LyophilizationRehydrated 12.0142.0132.0141.9581.975 22.0142.0212.0241.9651.994 32.0102.0122.0141.9651.965 41.9761.9701.9751.9301.937 51.9801.9751.9771.9301.939 61.9801.9681.9731.9261.931 71.9781.9671.9731.9371.945 81.9751.9701.9761.9341.945 91.9751.9621.9701.9031.918 101.9701.9681.9741.9211.926 Max 2.0142.0212.0241.9651.994 Min 1.9701.9621.9701.9031.918 Range 0.0440.0590.0540.0610.076 St. Dev. 0.0180.0230.0210.0200.024 Average 1.9871.9831.9871.9371.948 Table 5-2. Pin measurement repeatability. Pin Diameter (mm) 11.955 21.954 31.955 41.953 51.953 61.953 71.953 81.952 91.951 101.957 Max 1.957 Min 1.951 Range 0.006 St. Dev 0.002 Average 1.954 Trial

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53 Figure 5-1. Diameter range over a single pin. Di ameter variation graphically exaggerated for clarity. Table 5-3. Average single-pin diameter range values in mm by donor and manufacturing process. Donor Machined BioCleanse LyophilizationRehydrated 1 0.010 0.014 0.017 0.013 2 0.009 0.010 0.010 0.010 3 0.014 0.016 0.016 0.010 4 0.010 0.012 0.015 0.013 5 0.006 0.006 0.006 0.006 6 0.005 0.006 0.004 0.006 7 0.008 0.006 0.007 0.006 8 0.007 0.007 0.007 0.007 9 0.011 0.008 0.009 0.009 10 0.012 0.008 0.006 0.005 Max 0.014 0.016 0.017 0.013 Min 0.005 0.006 0.004 0.005 St. Dev. 0.003 0.004 0.005 0.003 Average 0.009 0.009 0.010 0.009

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54 Table 5-4. Average pin straig htness error values in mm. DonorMachined BioCleanse LyophilizationRehydrated 10.0070.0110.0080.008 20.0050.0060.0060.005 30.0050.0080.0060.007 40.0060.0080.0090.010 50.0030.0030.0030.005 60.0040.0040.0030.004 70.0030.0040.0040.003 80.0050.0050.0050.005 90.0040.0030.0050.005 100.0030.0040.0040.003 Max 0.0070.0110.0090.010 Min 0.0030.0030.0030.003 St. Dev. 0.0010.0030.0020.002 Average 0.0040.0060.0050.006 Figure 5-2. Comparison of average diameters of the two pin ends. Table 5-5. Diametric differences in mm be tween the chamfered and non-chamfered pin ends. DonorMachined BioCleanse LyophilizationRehydrated 10.0030.0050.0070.004 2-0.002-0.002-0.0010.000 30.0020.0030.0050.001 40.0000.0010.0030.001 50.000-0.0010.0010.000 60.000-0.001-0.001-0.002 70.0000.0000.000-0.001 80.000-0.0020.001-0.002 90.0010.0000.000-0.001 100.001-0.0010.001-0.001 Max 0.0030.0050.0070.004 Min -0.002-0.002-0.001-0.002 St. Dev. 0.0010.0020.0030.002 Average 0.0000.0000.0010.000

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55 Table 5-6. Average collet clamping effect in mm. DonorMachined BioCleanse LyophilizationRehydrated 1-0.005-0.0050.000-0.002 2-0.004-0.0030.000-0.001 3-0.0030.0020.002-0.001 4-0.001-0.0020.0000.001 5-0.002-0.0020.0010.000 6-0.001-0.0010.0000.000 7-0.001-0.0010.0000.000 80.000-0.0010.000-0.002 9-0.002-0.0010.0000.001 10-0.001-0.0010.0010.000 Max 0.0000.0020.0020.001 Min -0.005-0.0050.000-0.002 Range 0.0040.0060.0020.003 St. Dev. 0.0010.0020.0010.001 Average -0.002-0.0010.0000.000 Figure 5-3. Pin diameter vari ation over a single donor

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56 Table 5-7. Variation of pin diamet ers in mm across a single donor. DonorMachined BioCleanse LyophilizationRehydrated 10.0080.0100.0240.028 20.0140.0080.0190.012 30.0080.0080.0180.022 40.0110.0070.0180.019 50.0120.0040.0080.011 60.0080.0030.0100.008 70.0150.0070.0170.017 80.0160.0070.0170.015 90.0220.0110.0360.027 100.0080.0090.0150.014 Max 0.0220.0110.0360.028 Min 0.0080.0030.0080.008 Range 0.0140.0080.0280.020 St. Dev. 0.0050.0020.0080.007 Average 0.0120.0070.0180.017 Table 5-8. Average cortical plate hole di ameters (mm) by donor and manufacturing process. Dono r RTI ReamerMachined BioCleanse LyophilizationRehydrated 11.9811.9681.9831.9521.951 21.9761.9781.9821.9531.961 31.9761.9841.9821.9621.961 41.9431.9371.9471.9181.915 51.9431.9271.9461.9131.918 61.9381.9381.9391.9071.913 71.9431.9321.9381.9091.915 81.9411.9411.9491.9231.922 91.9381.9441.9441.9101.914 101.9301.9301.9411.9101.925 Max 1.9811.9841.9831.9621.961 Min 1.9301.9271.9381.9071.913 Range 0.0510.0570.0450.0550.048 St. Dev. 0.0190.0210.0190.0210.020 Average 1.9511.9481.9551.9261.929

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57 Table 5-9. Ten repeated measuremen ts of one cortical plate hole. TrialHole Diameter (mm) 11.915 21.921 31.923 41.926 51.927 61.928 71.929 81.930 91.931 101.931 Max 1.931 Min 1.915 Range 0.016 St. Dev. 0.005 Average 1.926 Table 5-10. Effects of the RTI m achining fixture on hole diameter. In Mach. Fixt.Loose PlatesDiscrepancy (mm)(mm)(mm) 11.9641.9780.014 21.9711.9780.006 31.9691.9820.013 41.9341.932-0.002 51.9321.9330.002 61.9291.9370.008 71.9331.925-0.008 81.9331.9430.010 91.9371.9440.007 101.9261.9360.010 Max0.014 Min-0.008 Range0.022 Std Dev0.007 Mean0.006 Donor # Average "Plate 1" Hole Diameter

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58 Table 5-11. Ten repeated measurements of a cortical plate hole diameter (mm) while clamped in the RTI machining fixture. Trial Hole Diameter 1 1.924 2 1.925 3 1.928 4 1.934 5 1.936 6 1.933 7 1.936 8 1.935 9 1.933 10 1.934 Max 1.936 Min 1.924 Range 0.012 St. Dev. 0.004 Average 1.932 Table 5-12. Average straightness error (mm) of cortical plate holes by donor and manufacturing cycle. DonorMachined BioCleanse LyophilizationRehydrated 10.0030.0030.0030.007 20.0040.0020.0020.002 30.0050.0060.0060.008 40.0060.0060.0060.007 50.0090.0100.0060.006 60.0020.0060.0080.003 70.0030.0050.0040.006 80.0040.0040.0030.004 90.0020.0020.0030.002 100.0050.0030.0050.003 Max 0.0090.0100.0080.008 Min 0.0020.0020.0020.002 Range 0.0070.0080.0060.005 St. Dev. 0.0020.0030.0020.002 Average 0.0040.0050.0050.005

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59 Table 5-13. Average diametric differe nce between hole 1 and hole 2 DonorMachined BioCleanse LyophilizationRehydrated 1-0.0020.0000.0030.002 2-0.003-0.002-0.003-0.003 3-0.001-0.001-0.0020.001 4-0.013-0.009-0.009-0.009 50.007-0.013-0.002-0.005 60.000-0.004-0.005-0.003 7-0.002-0.004-0.002-0.002 80.0020.0010.0030.002 90.0000.0000.000-0.001 10-0.0030.0000.0010.000 Max 0.0070.0010.0030.002 Min -0.013-0.013-0.009-0.009 Range 0.0210.0140.0120.010 St. Dev. 0.0050.0050.0040.003 Average -0.002-0.003-0.002-0.002 Table 5-14. Average diametric difference in mm between the holes of the two cortical plates of a single allograft. DonorMachined BioCleanse LyophilizationRehydrated 1-0.0200.0050.0010.003 20.0010.0030.0040.003 30.0030.0050.0060.003 40.0020.0080.0120.005 5-0.0130.0160.0120.005 60.002-0.002-0.0020.000 70.014-0.006-0.009-0.005 8-0.0030.0020.0030.002 90.000-0.0010.0010.000 10-0.011-0.006-0.006-0.005 Max 0.0140.0160.0120.005 Min -0.020-0.006-0.009-0.005 Range 0.0350.0220.0210.010 St. Dev. 0.0100.0070.0070.003 Average -0.0030.0030.0020.001

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60 Figure 5-4. Diameter variation over the 8 holes of a single plate. Table 5-15. Average diameter varia tion in mm over a single plate. DonorMachined BioCleanse LyophilizationRehydrated 10.0180.0110.0100.010 20.0070.0090.0110.010 30.0110.0120.0130.015 40.0150.0160.0160.016 50.0200.0250.0160.016 60.0030.0090.0120.005 70.0070.0090.0110.010 80.0090.0080.0080.008 90.0030.0030.0040.004 100.0090.0070.0070.006 Max 0.0200.0250.0160.016 Min 0.0030.0030.0040.004 Range 0.0170.0230.0130.012 St. Dev. 0.0060.0060.0040.004 Average 0.0100.0110.0110.010

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61 Figure 5-5. Hole diameter variation over all the plat es from a given donor. Table 5-16. Range of hole diameter values in mm over a single donor. DonorMachined BioCleanse LyophilizationRehydrated 10.0190.0160.0190.013 20.0160.0170.0140.025 30.0200.0220.0230.022 40.0510.0390.0410.037 50.0860.0630.0310.022 60.0050.0160.0230.008 70.0440.0370.0470.018 80.0120.0090.0100.007 90.0050.0050.0070.008 100.0320.0110.0150.011 Max 0.0860.0630.0470.037 Min 0.0050.0050.0070.007 Range 0.0820.0570.0400.030 St. Dev. 0.0250.0180.0130.010 Average 0.0290.0240.0230.017

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62 Table 5-17. Average predicted diametric in terference in mm for each manufacturing cycle. DonorMachinedBioCleanseLyophilizationRehydrated 10.0450.0310.0070.024 20.0430.0420.0120.033 30.0280.0320.0020.004 40.0330.0280.0120.021 50.0480.0300.0170.021 60.0300.0340.0190.019 70.0350.0360.0280.030 80.0290.0260.0110.024 90.0190.026-0.0060.004 100.0370.0320.0110.001 Max0.0480.0420.0280.033 Min0.0190.026-0.0060.001 Range0.0290.0160.0340.032 Std Dev0.0090.0050.0090.011 Average0.0350.0320.0110.018

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63 Table 5-18. Pull-apar t test results GraftManual Pull-apart S eparated PlateEpoxy Peak Load (N)Comments 1-1 NoNAQuick-setting82.5 Epoxy failed 2-1 NoNAQuick-setting55.8 Epoxy failed 3-1 NoNAQuick-setting68.6 Plate broke and separated 1-2 NoNAQuick-setting152.3 Epoxy failed 2-2 NoTopQuick-setting69.1 Interference fit failed, opposite plate cracked 3-2 YesNAQuick-setting15.3 Epoxy failed, both plates cracked 1-3 NoTopQuick-setting73.5 Interference fit failed 2-3 NoNAQuick-setting62.2 Epoxy failed 3-3 NoBottomQuick-setting96.7 Interference fit failed 1-4 NoTopQuick-setting93.6 Interference fit failed, opposite plate cracked 2-4 NoTopQuick-setting82.4 Interference fit failed 3-4 YesBottomQuick-setting61.9 Interference fit failed, removed plate cracked 1-5 NoNAQuick-setting114.6 Epoxy failed, one plate cracked 2-5 NoNAQuick-setting67.2 Epoxy failed, one plate cracked 3-5 NoNAQuick-setting71.7 Epoxy failed, one plate cracked 1-6 NoNAQuick-setting64.7 Epoxy failed, one plate cracked 2-6 NoTopQuick-setting67.6 Interference fit failed, both plates cracked 3-6 YesTopMetal/Concrete57.8 Interference fit failed, removed plate cracked 1-7 NoNAMetal/Concrete99.5 Epoxy failed 2-7 NoBottomMetal/Concrete71.1 Interference fit failed, both plates cracked 3-7 NoBottomMetal/Concrete94.2 Interference fit failed, opposite plate cracked 1-8 NoTopMetal/Concrete118.3 Interference fit failed, removed plate cracked 2-8 NoTopMetal/Concrete130.9 Interference fit failed 3-8 NoTopMetal/Concrete101.7 Interference fit failed 1-9 NoTopMetal/Concrete146.3 Interference fit failed 2-9 NoBottomMetal/Concrete72.5 Interference fit failed 3-9 NoTopMetal/Concrete92.4 Interference fit failed, both plates cracked 1-10 NoBottomMetal/Concrete67.0 Interference fit failed, both plates cracked 2-10 NoTopMetal/Concrete52.2Interference fit failed, both plates cracked 3-10 YesTopMetal/Concrete49.6 Interference fit failed, both plates cracked, opposite plate removed as from manual test

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64 Table 5-19. Pullapart test results for gr afts where the inte rference fit failed. Graft Manual Pull-apart Predicted Interference (mm) Interference Adjusted for Lyophilization (mm) Predicted Interference Adjusted for Hydration (mm) Peak Load (N) 3-1No0.0650.0270.04568.6 2-2No0.0460.0150.03669.1 1-3No0.0590.0340.03573.5 3-3No0.0840.0590.06096.7 1-4No0.0310.0110.02093.6 2-4No0.0440.0240.03382.4 3-4Yes0.0370.0170.02661.9 2-6No0.0350.0230.02367.6 3-6Yes0.0420.0300.03057.8 2-7No0.0270.0200.02271.1 3-7No0.0420.0350.03794.2 1-8No0.0370.0200.032118.3 2-8No0.0440.0270.039130.9 3-8No0.0300.0130.025101.7 1-9No0.0370.0120.022146.3 2-9No0.0280.0030.01372.5 3-9No0.015-0.010-0.01092.4 1-10No0.0380.0110.00267.0 2-10No0.0520.0250.01652.2 3-10Yes0.0440.0170.00849.6 Max146.3 Min49.6 Std Dev25.9 Quick-set Epoxy Avg76.7 Metal Epoxy Avg87.8 Total Avg83.4

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65 Figure 5-6. Pull-apart test result trends where th e interference fit failed. 1) Test results by donor 2) Histogram of the pul l-apart forces 3) Pull-a part force vs. predicted interference after machining. 4) Pull-a part force vs. pred icted interference adjusted for lyophilization. 5) Pull-apart force vs. predicted interference adjusted for 30 s hydration. 6) Pull-ap art force vs. predicted interference adjusted for 30 s hydration: grafts without cracking only.

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66 Table 5-20. Finite element analysis inputs. Trial123 Er12.012.09.0 Ec12.012.09.0 El18.018.014.0 Grc3.33.32.9 Grl3.33.32.9 Gcl3.33.32.9 !rc0.500.500.5 !rl0.400.400.4 !cl0.250.250.25 0.290.290.29 Pin D 1.9481.9361.936 Diametric Interference ( mm ) 0.0180.0110.011 Table 5-21. Finite element outputs !vm(max)Ff (Mpa)(N) 180.6216.0 245.0120.3 334.693.9 Trial Figure 5-7. Trial 3 von Mi ses stress distribution

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67 Figure 5-8. Trial 3 pin cont act pressure distribution Table 5-22. Monte Carl o simulation inputs ParameterMean ValueStandard Deviation Diametric interference ( m)119 Pin Young's modulus (GPa)91 Plate Young's modulus (GPa)91 Pin Poisson's ratio0.410.15 Plate Poisson's ratio0.410.15 Pin diameter (mm)1.9370.021 Plate outer radius (mm)1.20 Stress concentration factor10 Contact length (mm)7.00.3 Coefficient of friction0.30.15 Table 5-23. Multi-parameter Monte Carlo simulation overall results. Mean ValueStandard Deviation Pull-apart force (N)133141 Von Mises stress (pin) (MPa)137 Von Mises stress (plate) (MPa)6539

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68 1 2 3 Figure 5-9. Monte Carlo simulation results. 1) Pull-apart force. 2) Von Mises stress in the plate. 3) Von Mises stress in the pin.

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69 Table 5-24. Monte Carlo simulation results for single parameter variations Individual parameters St. Dev. F (N) S t. Dev. Pin vm (MPa) S t. Dev. Plt vm (MPa) Diametric interference 109738 Coefficient of friction66<10 Plate Young's modulus1315 Pin diameter611 Contact length61<1 Pin Poisson's ratio4<12 Plate Poisson's ratio4<12

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70 CHAPTER 6 CONCLUSIONS The diameters of 57 cortical pins from 10 donors were measured. Over a single pin, the average diameter variation was found to be 9 m with a standard deviation of 3 m. The average range of pin diameters over si ngle donors was found to be 12 m after machining, 7 m after BioCleanse, 18 m af ter lyophilization, and 17 m after a thirty second hydration. The hole diameters of 60 cortical plat es from 10 donors were measured. The average diameter variation over a single plat e was found to be 10-11 m. Over a single donor, the average range of hole diameters wa s found to be 29 m after machining, 24 m after BioCleanse, 23 m after lyophili zation, and 17 m after a thirty second hydration. Lyophilization was found to have the larges t effect on feature size. Cortical pin diameters decreased by an average of 50 m af ter lyophilization while cortical plate hole diameters decreased by an average of 29 m. Thirty seconds of immersion in water caused the pins to regain an av erage of 11 m of diameter and the plate holes to regain an average of 3 m of diameter. Twenty assembled allografts were pulled ap art with a mechanical tensile tester. The average force required to se parate the interference f it was 83.4 N with a standard deviation of 25.9 N. Of the allografts without cracked cortical plates, the average pullapart force was 100.6 N with a standard devi ation of 28.5 N. Of th e allografts with

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71 cracked cortical plates, the average pullapart force was found to be 74.1 N with a standard deviation of 19.8 N. 13% of the assembled allografts faile d a manual pull-apart test. 57% of the assembled allografts showed signs of cracking. The sample size of allografts that were not cracked and were successfully pulled apart is too small to derive a correlation between the predicted diametric interference and the pull-apart force. Furthermore, any such co rrelation may be obscured by variations in donor material properties. A finite element model was created to model the interference fit. Average geometric conditions from after lyophilization were used while material properties were drawn from the litera ture. The maximum von Mises stress in the graft was found to be between 34.6 MPa and 80.6 MPa. The pull-apart force required to separate the graft was found to be between 94 N and 216 N. An analytical model of the interferen ce fit was used to create a Monte Carlo simulation. A Monte Carlo simulation predicted diametric interference, the coefficient of friction, and the plate modulus to be the most influential factors on the interf erence fit pull-apart force. The simulation predicted diam etric interference and elastic properties to be the most influential factors affecting th e state of stress in the cortical plates. The Monte Carlo simulation accurately re flected the frequency of occurrence of pull-apart and cracking failure s at 13% and 57%, respectivel y. The simulation predicted the average pull-apart force to be 133 N w ith a standard deviation of 141 N and the average von Mises stress in the plate to be 65 MPa with a standard deviation of 39 MPa.

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72 APPENDIX APPENDIX  MONTE CARLO SIMULATION MATLAB CODE clear all close all clc n = 25e4; % number of Monte Carlo iterations % Define variables mean_delta1 = 11e-6; % diametral interference (m) std_delta1 = 9e-6; delta1 = mean_delta1 + std_delta1*randn(n, 1); delta = delta1/2; % radial interference (m) mean_Ei = 9E9; % pin modulus (N/m^2) std_Ei = 1e9; Ei = mean_Ei + std_Ei*randn(n, 1); mean_Eo = 9E9; % plate modulus (N/m^2) std_Eo = 1e9; Eo = mean_Eo + std_Eo*randn(n, 1); mean_mui = 0.41; % pin Poisson's ratio std_mui = 0.15; mui = mean_mui + std_mui*randn(n, 1); mean_muo = 0.41; % plate Poisson's ratio std_muo = 0.15; muo = mean_muo + std_muo*randn(n, 1); mean_b1 = 1.937e-3; % pin outer diameter (m) std_b1 = 0.021e-3; b1 = mean_b1 + std_b1*randn(n, 1); b = b1/2; % pin outer radius mean_c = 1.2e-3; % plate outer radius (m) std_c = 0; c = mean_c + std_c*randn(n, 1); mean_Kt = 1; % stress concentration factor std_Kt = 0; Kt = mean_Kt + std_Kt*randn(n, 1); mean_L = 7e-3; % axial contact length between pin and plate (m) std_L = 0.3e-3; % Note: doubled L to account for 2 pins

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73 L = mean_L + std_L*randn(n, 1); mean_cof = 0.3; % coefficient of friction std_cof = 0.15; cof = mean_cof + std_cof*randn(n, 1); sigma_fail = 25e6; % Failure stress of bone %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Determine pressure, p (N/m^2) C = b./Eo.*((c.^2 + b.^2)./(c.^2 b.^2) muo) + b./Ei.*(1 mui); p = delta./C; % Calculate stresses sigma_r_i = -Kt.*p; % pin radial stress (N/m^2) sigma_t_i = -p; % pin tangential stress (N/m^2) sigma_r_o = -Kt.*p; % plate radial stress (N/m^2) sigma_t_o = p.*(c.^2 + b.^2)./(c.^2 b.^2); % plate tangential stress (N/m^2) % pull apart force (N) F = -2*pi*L.*b.*sigma_r_i.*cof; % Find all force values greater than zero Pos_Force = find(F>0); % Calculate the von Mises stress only for instances where F>0 sigma_p_i = (sigma_r_i(Pos_Force).^2 sigma_r_i(Pos_Force).*sigma_t_i(Pos_Force) + sigma_t_i(Pos_Force).^2).^0.5; % pin sigma_p_o = (sigma_r_o(Pos_Force).^2 sigma_r_o(Pos_Force).*sigma_t_o(Pos_Force) + sigma_t_o(Pos_Force).^2).^0.5; % plate %Calculate some statistical parameters Fmean = mean(F) Fstd = std(F) PercFLessZero = length(find(F<0))/n*100 Sigmapin = mean(sigma_p_i) StdSigmapin = std(sigma_p_i) PercSMoreFail2 = length(find(sigma_p_i>sigma_fail))/length(Pos_Force)*100 Sigmaplate = mean(sigma_p_o) StdSigmaplate = std(sigma_p_o) PercSMoreFail = length(find(sigma_p_o>sigma_fail))/length(Pos_Force)*100 bins = 10000; figure(1) hist(sigma_p_i/1e6, bins) xlabel( '\sigma (MPa)' ) ylabel( 'Number of occurrences' ) title( 'von Mises stress (pin)' )

PAGE 86

74 set(gcf, 'color' 'white' ) xlim([0 70]) figure(2) hist(sigma_p_o/1e6, bins) xlabel( '\sigma (MPa)' ) ylabel( 'Number of occurrences' ) title( 'von Mises stress (plate)' ) set(gcf, 'color' 'white' ) xlim([0 250]) figure(3) hist(F, bins) xlabel( 'F (N)' ) ylabel( 'Number of occurrences' ) title( 'Force to pull apart' ) xlim([-200,600]) set(gcf, 'color' 'white' )

PAGE 87

75 LIST OF REFERENCES 1. Cowin, S. (1989). Bone Mechanics CRC Press, Inc., Boca Raton, FL. 2. Rho, J., L. Kuhn-Spearing, P. Zioupos ( 1998). Mechanical properties and the hierarchical structure of bone. Medical Engineering and Physics 20(2): 92-102. 3. Currey, J. (2002). Bones: Structure and Mechanics. Princeton University Press, Princeton, NJ. 4. Huiskes, R. (1982). On the modeling of long bones in structural analyses. Journal of Biomechanics 15(1): 65-69. 5. Bianchi, J. (1999). Design and Mechanical Behavior of the MD Series of Bone dowels University of Florida, Gaines ville, FL. Doctor of Philosophy. 6. Choi, K., J. Kuhn, M. Ciarelli, S. Goldst ein (1990). The elastic moduli of human subchondral, trabecular, and co rtical bone tissue and the si ze depencency of cortical bone modulus. Journal of Biomechanics 23(11): 1103-1113. 7. Zioupos, P., J. Currey (1998). Changes in th e stiffness, strength, and toughness of human cortical bone with age. Bone 22(1): 57-66. 8. Akkus, O., F. Adar, M. Schaffler (2004). Age related changes in physiochemical properties of mineral crystals are related to impared mechanical function of cortical bone. Bone 34(3): 443-453. 9. Bensamoun, S., M. Tho, S. Luu, J. Gherb ezza, J. de Belleval (2004). Spatial distribution of acoustic and elastic properties of human femoral cortical bone. Journal of Biomechanics 37(4): 503-510. 10. Dunham, C., S. Takaki, J. Johnson, C. Dunning (2005). Mechanical properties of cancellous bone of the distal humerus. Clinical Biomechanics 20(8): 834-838. 11. Hoc, T., L. Henry, M. Verdier, D. Aubry, L. Sedel, A. Meunier (2006). Effect of microstructure on the mechanical prop erties of haversian cortical bone. Bone 38(4) 466-474. 12. Lotz, J., T. Gerhart, W. Hayes (1990). Mechanical properties of trabecular bone from the proximal femur  a quantitative CT study. Journal of Computer Assisted Tomography 14(1) 107-114.

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76 13. Dalstra, M., R. Huiskes, A. Odgaar d, L. Vanerning (1993). Mechanical and textural properties of pelvic trabecular bone. Journal of Biomechanics 26(4-5): 523-535. 14. Rho, J., M. Roy, T. Tsui, G. Pharr (1999). Elastic properties of microstructural components of human bone tissue as measured by nanoindentation. Journal of Biomedical Materials Research 45(1): 48-54. 15. Bensamoun, S., J. Gherbezza, J. de Belleval, M. Tho (2004). Transmission scanning acoustic imaging of human co rtical bone and relation with the microstructure. Clinical Biomechanics 19(6): 639-647. 16. Reilly, D. and A. Burstein (1975). The elastic modulus and ultimate properties of compact bone tissue. Journal of Biomechanics 8: 393. 17. Yoon, H. and J. Katz (1976). Ultrasonic wave propagation in human cortical bone II: Measurements of elastic pr operties and micro-hardness. Journal of Biomechanis 9: 459. 18. Knets, I. and A. Malmeisters (1977). Deformability and strength of human compact bone tissue. Proceedings of the Euromech Colloquium on Mechanics of Biological Solids. 133. Ed. G. Brankov. Bulg arian Academy of Sciences, Sofia, Bulgaria. 19. Ashman, R., S. Cowin, W. Van Buskirk, J. Rice (1984). A continuous wave technique for the measurement of the elastic properties of cortical bone. Journal of Biomechanics 17: 349-361. 20. Kabel, J., B. van Rietbergen, M. Dalstra, A. Odgaard, R. Huiskes (1999). The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone. Journal of Biomechanics 32(7): 673-680. 21. Rice, J., S. Cowin, J. Bowman (1988). O n the dependency of the elasticity and strength of cancellous bo ne on apparent density. Journal of Biomechanics 21(2): 155-178. 22. Shigley, J. and C. Mischke (2001). Mechanical Engineering Design McGraw-Hill, New York, New York. 23. Nagasao, T., M. Kobayashi, Y. Tsuchiya, T. Kaneko, T. Nakajima (2002). Finite element analysis of the stresses ar ound endosseous implants in various reconstructed mandibular models. Journal of Cranio-Maxillofacial Surgery 30(3): 170-177. 24. Nagasao, T., M. Kobayashi, Y. Tsuchiya, T. Kaneko, T. Nakajima (2002). Finite element analysis of the stresses around fixt ures in various reco nstructed mandibular models  Part II (effect of horizontal load). Journal of Crani o-Maxillofacial Surgery 31(3): 168-175.

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77 25. Tie, Y., D. Wang, C. Wang, C. Zhang ( 2006). Three-dimensional finite-element analysis investigating the biomechan ical effects of human mandibular reconstruction with au togenous bone grafts. Journal of Cranio-Maxifillofacial Surgery  Article in press. 26. Barker, D., D. Netherway, J. Krishnan, T. Hearn (2005). Validation of a finite element model of the human metacarpal. Medical Engineering & Physics 27(2): 103-113. 27. Wang, X., G. Dumas (2005). Evaluation of effects of selected factors on intervertebral fusion  a simulation study. Medical Engineering & Physics 27 (3): 197207. 28. Zapata, J. (2001). Reduction of stress con centration around a surgically drilled hole in cortical bone. University of Florida, Gainesville, FL. Master of Science. 29. Yew, D. Virtual anatomy http://www.ana.cuhk.edu.hk/3dana/main.htm Last accessed July 2, 2006. 30. Mroz, T., E. Lin, M. Summit, J. Bianchi, J. Keesling, M. Roberts, C. Vangsness, J. Wang (2006). Biomechanical analysis of a llograft bone treated with a novel tissue sterilization process. The Spine Journal 6: 34-39. 31. American National Standard ASME B89.4.1-2001b. New York, NY.

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78 BIOGRAPHICAL SKETCH Nate Mauntler was born on April 10, 1981, th e second of four sons of John and Margaret Mauntler. He graduated from Tr oy High School in Troy, Ohio, in June of 1999. Mr. Mauntler then left Ohio to pursue a B achelor of Science de gree in mechanical engineering at the University of Florida, which was completed in May of 2004. Since that time, Mr. Mauntler has been continuing his e ducation at the University of Florida in pursuit of a masters degree in mechanical engi neering. This thesis was written in partial fulfillment of this degree. Upon graduation, Mr Mauntler will stay on at the University of Florida Tribology Laboratory and Machine To ol Research Center to pursue a doctoral degree.

## Material Information

Title: Dimensional Study of an Interference Fit Allograft
Physical Description: Mixed Material

## Record Information

Source Institution: University of Florida
Holding Location: University of Florida
System ID: UFE0015875:00001

## Material Information

Title: Dimensional Study of an Interference Fit Allograft
Physical Description: Mixed Material

## Record Information

Source Institution: University of Florida
Holding Location: University of Florida
System ID: UFE0015875:00001

Full Text

DIMENSIONAL STUDY OF AN INTERFERENCE FIT ALLOGRAFT

By

NATHAN A. MAUNTLER

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA

2006

by

Nathan A. Mauntler

This thesis is dedicated to my mother, Margaret Mauntler: the most selfless, dedicated,
those cookies you sent from Ohio.

ACKNOWLEDGMENTS

I would first like to thank my graduate committee Tony L. Schmitz (chair), W.

Gregory Sawyer, and John C. Ziegert for their guidance, their support, and their patience.

I would like to thank the members of the Tribology Laboratory and the Machine Tool

Research Center at the University of Florida: Jerry Bourne, Dave Burris, Matt Hamilton,

Luis Alvarez, Alison Dunn, Pam and Dan Dickrell, Vince Lee, Nick Argibay, Chris

Martens, Kevin Powell, Scott Payne, G. Scott Duncan, Raul Zapata, Lee Kumanchik,

Kevin Cheng, and Lonny Houck. I am very grateful for their friendship, their

comradeship, their help, and their shenanigans.

I wish to thank Becky Bassett, Earl Jones, Roy Clark, Jason Bootle, and the rest of

the staff at Regeneration Technologies, Inc. for their generous support and access to their

facilities. Finally, I would like to acknowledge the generosity and kindness of the donors

who make the fine work at Regeneration Technologies possible.

A C K N O W L E D G M E N T S ................................................................................................. iv

LIST OF TABLES .................. .................. ................. ............ .............. .. vii

LIST OF FIGURES ......... ............................... ........ ............ ix

A B ST R A C T .............................................. xi

1 INTRODUCTION AND PROBLEM STATEMENT............... ..................1

Dimensional Measurements and Mechanical Testing ...............................................2
M modeling .................................................................................... . 2

2 REVIEW OF THE LITERATURE ........................................ ......................... 6

The Structure and M echanical Properties of Bone.....................................................6
Classifications of Developed Bone .......................... .................................... 6
Mechanical Properties of Cortical Femoral and Tibial Bone Material ...............7
Mechanical Properties of Cancellous Material..........................................8
A nalytical Interference Fit M odels..................................... ............................ ........ 9
Stress, Pressure, and Pull-apart Force Predictions ............................................. 9
Limitations of the Analytical M odel ........................................... .................11
Finite E lem ent A analysis of B one......................................................................... ..... 11

3 THE CORNERSTONETM ASR ALLOGRAFT MANUFACTURING PROCESS ..16

C cutting B lanks F or M achining ........................................................ .....................16
P reparation for A ssem bly ............................................ ......................................... 17
A ssem bly and Finishing Cuts ........................................................ .............. 17
BioCleanseTM Sterilization Process ........................................ ........................ 18
Lyophilization Process......... ...... ........................ ......... ...... .. .... .. ........ .... 18

4 EQUIPM ENT AND PROCEDURES..................................... ........................ 23

Dimensional Measurements ......... ............... ...... ............... 23
Probe Tip Q qualification ........... .......... ....................... ....... ............... 23
Measuring the Allograft Stack-ups and Parts.............. .... .................24
Cortical-cancellous stack-ups.................................... ....................... 25

Loose cortical plates ............... ...................................... 27
C o rtic a l p in s ........................................................................................... 2 8
P ull-apart T ests ......... ................................................................................ .. 30
Sam ple preparation ...... .. ..... ..... .. ...... .... ........ ...... .. ..... ................ 30
Pull-apart test procedure ............... ............... .................... 31
Finite Elem ent A analysis ............................. ............................. 31
Analytical Model and Monte Carlo Simulation .............................................. 32

5 RESULTS AND DISCU SSION ........................................... .......................... 42

Dimensional Measurements............................ ......... ...... ............... 42
Interference Pins ........... .................. ........................ ................. 42
M easurem ent repeatability ........................................ ....................... 43
Taper characterization ....................................................... ............... 43
C ollet clam ping effects........................................... .......................... 44
Pin m manufacturing repeatability ....................................... ............... 45
Cortical Plate H oles .......... .... ........ ........ .. .................. .. .......... 45
Hole diameter measurement repeatability ....................... ..................45
Effects of the RTI machining fixture ............... .................................... 45
Straightness error.................. ...................... .............. .... ........... 46
Diametric variation between the two plate holes ......................................46
Diametric variation between plates.................. ........................... ....46
M manufacturing process repeatability ................................. ................ 47
Diametric Interference ......... ............... ....... ............... 47
M echanical Pull-apart Tests ............................................... ............................ 48
Finite E lem ent A nalysis.......................................... .................... ............... 49
M onte C arlo Sim ulation ..................................................................... ..................50

6 C O N C L U SIO N S ............................................................................. .......... ..... 7 0

APPENDIX MONTE CARLO SIMULATION MATLAB code...............................72

L IST O F R E F E R E N C E S ........................................................................ .....................75

B IO G R A PH IC A L SK E TCH ..................................................................... ..................78

LIST OF TABLES

Table p

2-1 A survey of the elastic properties of cortical bone compiled by............................ 14

2-2 A study of RTI donor cortical bone strength..................................... ..................14

2-3 Bone elastic material properties used in finite element studies. ...........................15

2-4 Bone elastic material properties used in study of an inter-vertebral fusion
d eg en e ratio n ....................................................... ................ 1 5

4-1 Input parameters for the M onte Carlo analysis ................................ ............... 41

5-1 Average pin diameters in mm by donor over the RTI manufacturing step .............52

5-2 Pin m easurem ent repeatability. ........................................ .......................... 52

5-3 Average single-pin diameter range values in mm by donor and manufacturing
p ro c e s s ........................................................................... 5 3

5-4 Average pin straightness error values in mm. ................... ........................ 54

5-5 Diametric differences in mm between the chamfered and non-chamfered pin
e n d s ............................................................................. 5 4

5-6 Average collet clamping effect in mm. ....................................... ............... 55

5-7 Variation of pin diameters in mm across a single donor................. ............. ...56

5-8 Average cortical plate hole diameters (mm) by donor and manufacturing
p ro c e s s ........................................................................... 5 6

5-9 Ten repeated measurements of one cortical plate hole..........................................57

5-10 Effects of the RTI machining fixture on hole diameter. ........................................57

5-11 Ten repeated measurements of a cortical plate hole diameter (mm) while
clamped in the RTI machining fixture. ........................................ ............... 58

5-12 Average straightness error (mm) of cortical plate holes by donor and
m manufacturing cycle. ..................................... ... .. ....... .... ............ 58

5-13 Average diametric difference between hole "1" and hole "2" ..............................59

5-14 Average diametric difference in mm between the holes of the two cortical plates
of a single allograft .................. ..................................... .. ........ .... 59

5-15 Average diameter variation in mm over a single plate......................................60

5-16 Range of hole diameter values in mm over a single donor. ............. ..................61

5-17 Average predicted diametric interference in mm for each manufacturing cycle.....62

5-18 P u ll-ap art test resu lts ........................................................................ .................. 63

5-19 Pull- apart test results for grafts where the interference fit failed..........................64

5-20 Finite elem ent analysis inputs. ............................................................................ 66

5-2 1 F inite elem ent outputs ...................................................................... .................. 66

5-22 M onte Carlo simulation inputs ...................................................... ..................67

5-23 Multi-parameter Monte Carlo simulation overall results .......................................67

5-24 Monte Carlo simulation results for single parameter variations ...........................69

LIST OF FIGURES

Figure page

1-1 The CornerstoneTM ASR cortical-cancellous allograft.............................................4

1-2 Allograft failure by pull-apart. ............................................................................. 4

1-3 Stress cracking in an allograft plate. ........................................ ....... ............... 5

2-1 An analytical model of an interference fit between two cylinders...........................15

3-1 Cancellous blocks, cortical pins, and cortical plates are harvested from specific
areas of the fem ur and tibia ......................................................................... ... ... 20

3-2 Orientation of the cortical bone pieces with respect to anatomical bone material
direction s. ......................................................... ................ 2 0

3-3 Lathe tooling for turning the cortical pins.................................... ............... 21

3-4 The chamfered end of a cortical pin. ......................... ..................................... 21

3-5 Assembling and grooving fixture. ........................................ ......................... 22

3-6 Custom tool for inserting interference pins into holes reamed in allograft..............22

4-1 Brown and Sharpe MicroVal PFx coordinate measuring machine........................34

4-2 Probe tip geometry used in this study. ........................................ ............... 34

4-3 Allograft parts as received from RTI for one donor...............................................35

4-4 RTI indexing wheel and assembling/grooving fixtures .......................................35

4-5 Stack-up measurement. Inset shows hole naming convention................................36

4-6 Stack-up coordinate system alignment features..................................................... 36

4-7 Measurement of the cortical plates while stacked in the machining fixture. ...........36

4-8 D definition of straightness error. ........................................ ......................... 37

4-9 One corner of each loose plate was removed to preserve orientation....................37

4-10 Loose cortical plates were clamped directly to the CMM table.............................37

4-11 Cortical plate coordinate system alignment features................... .............. 38

4-12 Cortical pins were measured while clamped in a 5-C collet and manual collet
holder...................... ..... .... .......... ........................................... 38

4-13 Pins were clamped in the collet with 6.2 mm of length exposed...........................38

4-14 Cortical pin coordinate system alignment features. ............................................39

4-15 Measurement locations for one side of the cortical pin. ........................................39

4-16 Cortical pin measurement procedure. ........................................... ............... 40

4-17 Pull-apart test setup. ...... ........................... ............................................ 40

4-18 The ANSYS model and mesh used in the finite element analysis.........................41

5-1 D iam eter range over a single pin........................................ .......................... 53

5-2 Comparison of average diameters of the two pin ends. .........................................54

5-3 Pin diam eter variation over a single donor................................... ............... 55

5-4 Diameter variation over the 8 holes of a single plate........................ ...............60

5-5 Hole diameter variation over all the plates from a given donor.............................61

5-6 Pull-apart test result trends where the interference fit failed. .................................65

5-7 Trial 3 von M ises stress distribution ............................................. ............... 66

5-8 Trial 3 pin contact pressure distribution ......................................... .............67

5-9 M onte Carlo simulation results. ........................................ ......................... 68

Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

DIMENSIONAL STUDY OF AN INTERFERENCE FIT ALLOGRAFT

By

Nathan A. Mauntler

August 2006

Chair: Tony L. Schmitz
Major Department: Mechanical and Aerospace Engineering

The CornerstoneTM ASR cortical-cancellous allograft made by Regeneration

Technologies, Inc. (RTI) of Alachua, Florida, is an implant used in cervical spinal fusion

surgeries. Making use of two cortical bone plates for structural support surrounding a

cancellous bone block for growth conduction, the graft is held together by two cortical

interference pins. The success of the interference fit depends on the manufacturing

tolerances of the components as well as the quality of the donor bone used to produce the

graft.

In this study, the diameters of interference pins and cortical plate holes required to

produce thirty allografts are measured on a coordinate measuring machine at four critical

points in the manufacturing cycle: after machining, after chemical sterilization, after

freeze-drying lyophilizationn), and after re-hydration. A statistical distribution of the

interference fit component dimensions is obtained. Lyophilization is found to have the

largest effect on the component dimensions, causing an average decrease of 21 ptm in the

predicted interference, which should nominally be between 25 and 38 pm.

Thirty separate allografts are manufactured by RTI to investigate the occurrence of

pull-apart failure and cracking in the allografts. Of the thirty grafts, seventeen (57%)

showed signs of cracking on one or both of the cortical plates. Four (13%) of the grafts

failed manual pull-apart tests following lyophilization and prior to hydration. Following a

thirty second hydration, the grafts were epoxied to aluminum plates and pulled apart on a

mechanical tensile testing machine. For twenty of the grafts, one plate was removed from

the interference fit at an average pull-apart force of 83.4 N. For the remaining ten grafts,

the epoxy failed prior to interference fit failure. Of the seven grafts that were separated

and showed no signs of cracking, the average pull-apart force was found to be 100.6 N.

Any relationship between the predicted diametric interference value and the pull-apart

force was obscured by the small sample size of undamaged grafts and variations in

material property.

A finite element analysis of the interference fit is created to attempt to model the

scenario observed in the mechanical testing. The model predicts a pull-apart force of 93

N and a maximum von Mises stress of 35 MPa. Additionally, the model shows no

evidence of a stress concentration at the edge of the contact.

Finally, a Monte Carlo simulation based on an isotropic analytical model of the

interference fit is developed. In this simulation, the input parameters are varied by

random values within one standard deviation of the mean. The Monte Carlo simulation

indicates that diametric interference is the largest factor affecting the interference fit. The

simulation accurately predicts the rate of occurrence of pull-apart and material failures at

13% and 57%, respectively.

CHAPTER 1
INTRODUCTION AND PROBLEM STATEMENT

This thesis describes an investigation of an interference-fit allograft used in spinal

fusion surgeries. Spinal fusion is the joining of two vertebrae in order to treat

degenerative disk disease or otherwise remove pressure from the spinal cord. Fusion is

accomplished by inserting a graft between the two vertebrae. This graft serves both as a

structural support and a medium through which the two bones can grow together and

eventually fuse. Grafts made from human cadaver bone are known as allografts.

One such allograft is the CornerstoneTM ASR cortical-cancellous block

manufactured by Regeneration Technologies, Inc. (RTI) for use in cervical spine fusion

surgeries (Figure 1-1). This graft is assembled from a cancellous bone block sandwiched

between two cortical bone plates held together by two interference-fit pins. The cortical

plates provide structural strength while the cancellous block provides a medium for new

bone growth. By manufacturing the graft from separate cortical and cancellous pieces,

more efficient use can be made of the bone donor material. Also, the use of an

interference connection for the assembly enables an all-bone construction.

Drawbacks to an interference fit connection include the possibility of pull-apart

failure and cracking. Pull-apart failure occurs when the strength of the interference fit is

insufficient to hold the graft together under tensile loads (Figure 1-2). Pull-apart failure

can occur as a result of inadequate radial interference (the pin is insufficiently larger than

the plate holes) or as a result of the components having too much mechanical compliance.

Cracking occurs when the stresses caused by the interference fit are large enough to cause

material failure in the bone. As opposed to pull-apart failure, cracking is the result the

radial interference or material stiffness being too large.

The purpose of this study is to examine the quality of the ASR interference fit

connection in the light of the various RTI manufacturing processes in order to identify the

most probably failure source. To this end, dimensional measurements of the pins and

cortical plate holes and mechanical pull-apart tests are performed to characterize the

accuracy of the RTI machining process and the effects of various chemical, dehydration,

and re-hydration treatments. Mechanical testing is used to measure the force required to

separate the interference fit. Finally, a finite element analysis of the graft and a Monte

Carlo simulation are performed to predict interference fit failures.

Dimensional Measurements and Mechanical Testing

In the dimensional study, the diameters of pins and cortical plate holes are

measured at various points throughout the manufacturing process. The parts required to

produce six grafts from each of ten donors are provided by RTI. Half of these grafts

follow the normal manufacturing cycle/assembly steps in order to later measure the force

required to separate the interference fit. The remaining pieces are not assembled so that

dimensional measurements may be performed. Pin and hole diameter measurements are

recorded after each of the following manufacturing processes:

* Machining
* The chemical sterilization process BioCleanseTM
* Freeze-drying, or lyophilization
* Hydration for thirty seconds.

Modeling

The data obtained from the dimensional measurements are then used along with

published material properties to create a finite element model of the interference fit. This

three-dimensional orthotropic model is used to simulate the stresses and pressures present

in the allograft as well as the pull-apart force. The finite element model is in turn used to

validate and improve an isotropic analytical model which was used in a Monte Carlo

simulation, a computational technique where the model inputs are randomly selected

from pre-selected distributions and used to compute the output over many iterations. The

results of the Monte Carlo simulation is a statistical distribution of the output parameters

(e.g. stress, pressure, and pull-apart force). Finally, the stresses and pull-apart forces

predicted by the finite element model and Monte Carlo analysis are compared to the

failures observed in the actual allografts.

cancellous block

Figure 1-1. The CornerstoneTM ASR cortical-cancellous allograft

Figure 1-2. Allograft failure by pull-apart.

5

crack

Figure 1-3. Stress cracking in an allograft plate.

CHAPTER 2
REVIEW OF THE LITERATURE

To make predictions regarding the effectiveness of the allograft interference

connections, it is necessary to have an understanding of the mechanical behavior of bone

from an engineering standpoint. Once the physical properties of bone are identified, they

can be applied to mechanical models which simulate the conditions of the interference fit.

The following sections provide a review of publications relevant to the study of bone as

an engineering material and its application to specific mechanical scenarios. A discussion

of relevant analytical and finite element modeling techniques is also included.

The Structure and Mechanical Properties of Bone

Bone is a composite material comprised of an inorganic phase, primarily

hydroxyapatite (Calo(PO)4)6(OH)2) crystals, embedded in an organic matrix, primarily

collagen.[1l At the micrometer level, these collagen fibrils and embedded hydroxyapatite

crystals bundle to form fibers.[2] The organization of these bone fibers above the

micrometer level depends on the development and function of the bone area of interest.[3]

Classifications of Developed Bone

The macrostructure of mature bone can be categorized as cortical or cancellous.

Slow-forming cortical, or compact, bone is made up of organized layers, or lamellae,

which form in nominally parallel cylindrical patterns.[2] The directionality of these

lamellae causes cortical bone to have anisotropic properties. Strictly speaking, the elastic

properties of cortical bone are orthotropic. However, little error is introduced by

modeling cortical bone material from long bones as transversely isotropic in nature.[4] In

long bones such as the femur and tibia, cortical bone forms in the central shaft, or

diaphyis.[6]

In contrast, cancellous, or trabecular, material is made up of a porous matrix of

bony struts, called trabeculae, packed with mineral and marrow deposits.[1,2] In general,

the bulk properties of cancellous bone are functions of the density and directionality of

this matrix.[3] In long bones, cancellous material primarily forms on the ends epiphysess)

of the bones, but can also be found under the cancellous surface of the shaft close to the

epiphyses.[3,5] The transition within a bone from cancellous to cortical material can be

gradual and microstructural analysis is often necessary to distinguish between the two.12]

Assigning values to the material properties of bone material, whether cortical or

cancellous, is not trivial. Factors that can affect the elastic and strength properties include

mineral content, trabecular density, the type of bone, the harvest location on the donor

bone, and the scale at which measurements are taken.[1-3'6-11] To try to address these

issues, a wide variety of methods have been used to investigate bone mechanics.

Buckling tests, tension tests, compression tests, bending tests, indentation methods,

acoustic methods, and x-ray computed tomography have all been used to measure the

elastic and failure properties of cortical and cancellous bone.13,12-15] For the sake of

relevance and to limit the discussion to a reasonable length, the following subsections are

limited to a discussion of human femoral and tibial bone only.

Mechanical Properties of Cortical Femoral and Tibial Bone Material

Table 2-1 contains data compiled by Cowin1il and Currey[3] from mechanical and

ultrasound studies of the elastic properties of cortical bone material.[16-19] Data from

Reilly and Burstein suggests that cortical bone can behave differently in tension than in

compression.[16-17] Standard deviations, where applicable, are in parentheses. Note that

two of these studies assume transversely isotropic material symmetry while the other two

account for orthotropic material properties. Here, the "1" direction corresponds to the

radial bone direction, the "2" direction corresponds to the circumferential bone direction,

and the "3" direction corresponds to the radial bone direction. It should be noted that the

values for Poisson's ratio greater than 0.5 reported by Reilly and Burstein are physically

impossible.

Table 2-2 contains a collection of material strength information for cortical bone

under a variety of loading conditions and physical treatments relevant to this study.[5]

This data is of particular interest since it represents RTI donor material for use in spinal

allografts. Note that the standard deviation of the failure stress is between 12% and 25%

of the mean value. This gives some indication of the substantial variation in material

properties that can be present from sample to sample for bone material. For comparison,

Reilly and Burstein report the tensile strength of bone as 53 MPa in the circumferential

direction and 133 MPa in the longitudinal direction and the compressive strength of bone

as bone 131 MPa in the circumferential direction and 205 MPa in the longitudinal

direction.[16]

Mechanical Properties of Cancellous Material

While cancellous bone is, strictly speaking, orthotropic, for practical purposes it is

becoming common to model cancellous bone as isotropic.[6'20] While values for the

elastic modulus of trabeculae are on par with those of cortical bone, 3] Young's modulus

values for bulk cancellous material is substantially smaller. Rice et al. suggest that both

Young's modulus and the cancellous bone strength are dependent on the apparent density

of the material to the second power.[21] The same study reported values all less than 500

MPa for the bulk Young's modulus of human cancellous bone. Since the modulus values

for bulk cancellous bone are so much smaller than those of cortical bone, the effect of

cancellous bone is neglected in the following analyses.

Analytical Interference Fit Models

Once the mechanical properties of bone material are understood, they can be

incorporated into specific mechanical models. The classic analytical model of an

interference fit connection is the hollow, thick-walled cylinder representation shown in

Figure 2-1.[22] In this model, a hollow cylinder "1" of nominal outer radius R is forced

into another hollow cylinder "2" whose inner radius is some amount 5 smaller than R. To

accommodate the radial interference, both cylinders must deform such that the outer

radius of cylinder "1" decreases by some amount 61 while the inner radius of cylinder

"2" increases by some amount 62. The deformations 61 and 62 must add up to the radial

mismatch 6.

Stress, Pressure, and Pull-apart Force Predictions

The two-dimensional state of stress at the boundary of either cylinder can be

described in terms of the pressure p at the interface and the three radii as in Eq. (2-1)

through Eq. (2-4). In these equations alt and o2t represent the tangential stresses of

cylinders 1 and 2 while olr and o2r represent the radial stresses in cylinders 1 and 2. The

sign convention is such that positive stresses are tensile and negative stresses are

compressive. If the two cylinders are not both infinitely long, a stress concentration will

exist at the edges of the contact. For this reason, the stress concentration factor Kt is

included in the radial stress equations. A stress concentration factor of 2 is a reasonable

upper bound value.[22]

R2 +ri
lt = -p- (2-1)
R2 .2
R -n

2 2
ro + R
2t = p-- (2-2)
2 2
ro R

rlr= -Kt.p (2-3)

c2r= -Kt.p (2-4)

The von Mises equivalent stress ov at the interface of either cylinder can be

calculated as shown in Eq. (2-5), where ol and c2 represent the two-dimensional

principal stresses. Substituting Eq. (2-1) through Eq. (2-4) into Eq. (2-5), the von Mises

stresses for cylinder "1" in Eq. (2-6) and cylinder "2" in Eq.(2-7) can be found. Since in

this study the pin (cylinder "1") is solid, ri is assigned a value of zero. The calculated von

Mises stresses can then be directly compared to the failure strength of the cylinder

materials.

S= 4c2 2 (2-5)
ov= 01 01- 12+G2

ovl = p.-Kt2 Kt + 1 (2-6)

v22 21 2 +R2
= p.Kt2 ro + R ro + R) (2-7)
ro2 R2) ro2 -R2)

Thick-walled cylinder elastic theory can be used to calculate the pressure p at the

press-fit interface as in Eq. (2-8), where E represents Young's modulus and v represents

Poisson's ratio. The force required to separate the interference fit can be found from Eq.

(2-9) where Ac represents the area in contact, Lc represents the length of the contact and

t represents the static coefficient of friction between the inner pin and outer plate. If Eq.

(2-1) through Eq. (2-9) are assumed to provide a reasonable representation of an

interference fit, the force required to separate a cortical plate from two cortical pins could

be estimated by multiplying the force F in Eq. (2-9) by a factor of two. The integral in

equation 2-9 is to account for the fact that the stress concentration factor is not constant

along the length of the contact, designated here as the x-direction.

6
p RR ro 2 + (2-8)
--.( vl) + -_ + v2
El E2 r2 -2 I
ro -R R

F= Kdx=x) p (Ac)dx= Kt(x).p.(2..R.Lc)d (2-9)

Limitations of the Analytical Model

The analytical model has three primary limitations. First, the assumption is made

that the material properties of both the pin and plate are isotropic in nature. Secondly, this

model cannot account for the effect a second pin in close proximity would have on the

stress state. Finally, the model cannot account for plate geometry that is not cylindrical.

Finite Element Analysis of Bone

Due to the limitations of analytical models, finite element analysis has become a

common method of modeling bone behavior. The following paragraphs discuss several

application of the finite element method to various scenarios involving bone.

The choice of a finite element model depends on the geometric and mechanical

complexity of the scenario being modeled. Often, three-dimensional models are

necessary, but under certain circumstances, simplifying assumptions can be applied to

reduce the computational requirements. Plane strain, plane stress conditions, or

axisymmetric conditions can justify the use of two-dimensional models. Two- or three-

dimensional models can also be simplified when loads, boundary conditions, and material

properties are symmetric about a given axis.

When modeling the reconstruction of mandibles, Nagasao et al. and Tie et al. used

computed tomography (CT) scans to create solid models with accurate information

regarding the location and thickness of cortical and cancellous bone.123-251 Nagasao et al.

used 10-node tetrahedral elements for the entire model while Tie et al used four-node

tetrahedral elements to model the cancellous inner mandible and membrane shell

elements to model the thin cortical shell. Both studies assumed isotropic material

properties; see Table 2-3.

Similarly, Barker et al. used CT scans to create a three-dimensional model of a

human metacarpal.1261 Additionally, bone density information from the CT scans was

used to predict calcium and potassium content. Power laws developed by Lotz et al. and

Dalstra et al. were then used to create isotropic and orthotropic material models.[12,13] The

solid models were meshed using hexahedral and pentahedral elements without mid-side

nodes.

Wang and Dumas used 8-node brick elements with isotropic material properties for

both cortical and cancellous spinal bone when modeling an inter-vertebral fusion

scenario.[27] This study investigated the likely variation in material properties from bone

to bone by using a range of values for both Young's modulus and Poisson's ratio (Table

2.4).

When studying stress concentration created by surgically drilled holes in canine

tibia, Zapata used a two-dimensional axisymetric model.[28] Transversely isotropic

13

material properties were used to model the cortical tibial bone while isotropic material

properties were used to model woven bone growing where the hole was drilled. The

model was meshed using quadrilateral elements.

In this study, we will apply a three-dimensional model solid model of one cortical

plate and two cortical pins. The model is meshed with 20-node orthotropic hexahedral

elements. Transversely isotropic material properties are used for both the cortical plate

and the cortical pins.

Table 2-1. A survey of the elastic properties of cortical bone compiled by.

Reilly and Burstein (1975) [16]

Symmetry
applied
Bone type
Testing
method
E1 (GPa)
E2 (GPa)
E3 (GPa)
G12 (GPa)
G13 (GPa)
G23 (GPa)
v12
v13
v23
v21
v31
v32
[1,3]

Compression
Transversely
Isotropic
Femur

Mechanical
11.5(1.01)
11.5(1.01)
18.2 (0.85)
3.6
3.3 (0.42)
3.3 (0.42)
0.63 (0.20)
0.38 (0.15)
0.38 (0.15)
0.63 (0.20)
0.38 (0.15)
0.38 (0.15)

Tension
Transversely
Isotropic
Femur

Mechanical
12.8(3.0)
12.8(3.0)
17.7 (3.6)
3.6
3.3 (0.42)
3.3 (0.42)
0.53 (0.25)
0.41 (0.15)
0.41 (0.15)
0.53 (0.25)
0.41 (0.15)
0.41 (0.15)

Yoon and Katz
(1976) [17]

Transversely
Isotropic
Femur

Ultrasound
18.8
18.8
27.4
7.17
8.71
8.71
0.312
0.193
0.193
0.312
0.281
0.281

Knets et al.
(1977) [18]

Ashman et al.
(1984) [19]

Orthotropic Orthotropic
Tibia Femur

Mechanical
6.91
8.51
18.4
2.41
3.56
4.91
0.49
0.12
0.14
0.63
0.32
0.31

Ultrasound
12.0
13.4
20.0
4.53
5.61
6.23
0.376
0.222
0.235
0.422
0.371
0.35

Table 2-2. A study of RTI donor cortical bone strength.

Axial Compression
Mean St. Dev.

Transverse Shear
Mean St. Dev.

Transverse Tension
Mean St. Dev.

Physiologic
Freeze dried (FD)
FD + Reconstituted
BioCleanseTM
[5]

Treatment

24.5
75.9
19.6
36.1

84.7
60.3
97.0

16.2
15.0
13.8

29
31.8
24.7
29.2

I

'V.

Figure 2-1. An analytical model of an interference fit between two cylinders.

Table 2-3. Bone elastic material properties used in finite element studies.
I Young's modulus (GPa) Poisson's ratio
Cortical bone 15 0.33
Cancellous bone 1.5 0.3
[23-25]

Table 2-4. Bone elastic material properties used in study of an inter-vertebral fusion
degeneration

. I .

I '. ,

CHAPTER 3
THE CORNERSTONETM ASR ALLOGRAFT MANUFACTURING PROCESS

The ASR cervical spinal allograft is produced using femoral or tibial bone from a

single donor. Donor material is processed from whole limbs which are received frozen.

After removing the soft tissue, the bones are cut into blanks, machined to shape,

assembled, cleaned, and freeze dried as discussed in the following sections. Each of the

following sections occurs in a single machining episode to prevent the intermixing of

donor material.

Cutting Blanks For Machining

The bones are cut into blanks using a stainless steel band saw. Cortical blanks are

taken from the shaft diaphysiss) of the bones while cancellous blanks are cut from the

heads (Figure 3-1). Blanks for cortical plates are harvested from the stronger central

portion of the shaft.

The cortical region of the donor bone has a finite thickness, so the cortical blanks

must be cut in a specific orientation with respect to the lay of the bone (Figure 3-2).

Cancellous blanks are chosen from the densest regions of cancellous bone. All blanks are

cut oversized to accommodate final machining. Cortical pin blanks are cut 25 mm long

and 3-4 mm wide. Cortical plate blanks are cut 12.5-13 mm long and to a width of the

operator's discretion. Cortical pin and plate blank thicknesses are driven by the thickness

of the bone raw material. Cancellous blanks are cut to 11.3 mm by 11.3 mm by 4.5 mm.

Preparation for Assembly

Cortical pin blanks are turned down to pins on an OmniTurn GT-Jr CNC lathe. The

pins are first turned using conventional tooling, then reamedd" by a tubular tool with a

sharpened inner edge to a nominal diameter of 2 mm (Figure 3-3). The reaming tool is

produced by drilling a hole through a conventional reamer. When turning the pins,

isopropyl alcohol is used as a cutting fluid. The turned pin is then parted from the blank,

leaving a chamfer on one end (Figure 3-4). The length of the parted pin is approximately

17.5 mm. After the pins have been machined, they are immersed in alcohol, removed and

left to dry for 15 minutes. They are then weighed to ensure that they meet minimum bone

density requirements. The pins are finally sorted into groups with diameters in a 0.013

mm (0.0005 in) range.

Cortical plate blanks are squared on a Fadal 904-1L CNC mill. Blanks are first

faced and squared on three sides in one clamp pallet, then faced and squared on the other

three sides in a second clamp pallet. Like the cortical pins, the plates are checked for

minimum mass requirements.

Cancellous blanks are dimineralized in 0.5 N HCL for 3-5 minutes, then submerged

in water for 8-10 minutes. No further machining is required for the cancellous blanks.

Assembly and Finishing Cuts

Cortical plates and cancellous blocks are clamped in the assembling and grooving

fixture (Figure 3-5). Six of these fixtures are then bolted into an indexing wheel. Two

holes are drilled and reamed through the cortical-cancellous stack-ups. The diameter of

the reamer is designated to be 0.025-0.038 mm (0.0010-0.0015 in) smaller than the pins

which will be used for that graft. Isopropyl alcohol is used as a cutting fluid while

reaming the holes.

Pins are inserted chamfered end first into the reamed holes using a custom tool

(Figure 3-6). The side clamps of the machining fixture are then removed and the sides of

the allograft are grooved. The interference fit assembly is then removed from the

assembly and grooving fixture and loaded into the profiling fixture for final radius cuts.

Allografts are then inspected and frozen.

BioCleanseTM Sterilization Process

BioCleanseTM is a chemical treatment that kills viral, fungal, and bacterial

contaminants without adversely affecting the bone material properties.[30] Normally, a

BioCleanseTM cycle is completed with allografts from a single donor. However, due to

cost considerations, all donor material for this study was processed in a single

BioCleanseTM batch. RTI offers BioCleanseTM in two different recipes depending on

whether or not the donor material contains soft tissue. The more chemically aggressive

hard-tissue-only recipe was used for this study since it was assumed to be more likely to

adversely affect the material and dimensional properties of the allografts. Normally

allografts are visually inspected, packaged, and stored frozen after completing the

BioCleanseTM cycle. However, for this study, loose cortical plates and cortical pins were

packaged in sealed plastic pouches and sent to the University of Florida for additional

dimensional measurements (see Chapter 4).

Lyophilization Process

Lyophilization is a freeze drying process performed on allografts so that they may

be stored at room temperature for extended periods. The allografts and allograft parts

from donors 1-6 underwent lyophilization in one cycle while the material from donors 7-

10 were run in a separate cycle.

19

After lyophilization, allografts are visually inspected for cracks and manually

inspected for pull-apart failures. Since the pull-apart tests are performed by hand, the

applied force is unknown. The allografts are then repackaged and the packages sterilized

for distribution.

cancellous blocks

cortical pins

cortical plates

cortical pins

cancellous blocks

femur

diaphysis
(shaft)

tibia

Figure 3-1. Cancellous blocks, cortical pins, and cortical plates are harvested from
specific areas of the femur and tibia. Bone images from
http://www.ana.cuhk.edu.hk/3dana/main.htm [29]

cortical pin blank

turned pin

cortical bone
raw material

cortical plate blank

squared and
drilled plate

final plate
as in graft

Figure 3-2. Orientation of the cortical bone pieces with respect to anatomical bone
material directions.

final pin
as in graft

r
a

Figure 3-3. Lathe tooling for turning the cortical pins.

chamfered end

Figure 3-4. The chamfered end of a cortical pin.

Figure 3-5. Assembling and grooving fixture.

Translates to
1 push pin into
hole
insert pin here
Figure 3-6. Custom tool for inserting interference pins into holes reamed in allograft.

CHAPTER 4
EQUIPMENT AND PROCEDURES

This chapter discusses the procedures used in this study, including measurement

techniques, analytical and finite element models, and mechanical testing.

Dimensional Measurements

Measurements of the allograft stack-ups and components were carried out on a

Brown and Sharpe MicroValTM PFx three-axis coordinate measuring machine (Figure 4-

1) using a Renishaw MIP touch-trigger probe. This coordinate measuring machine

(CMM) is operated via PC-DMIS CAD++ software and is certified to be accurate to 12

[tm over its work volume according to American National Standard ASME B89.4.1-

2001b.[31]

The CMM could be operated in either manual mode or direct computer control

(DCC) mode. In manual mode, the CMM was controlled by the operator using a joystick.

In DCC mode, the CMM was commanded by the machine controller. In this study, the

manual operation mode was used to locate parts and define the part coordinate frame.

DCC mode was used to refine the alignment and take measurements.

Probe Tip Qualification

Two types of stylus probe tips were used in this study. A 20 mm long tip was used

to measure the loose cortical plates and pins while a 27 mm long tip was used to measure

the stack-ups held in the RTI assembly and grooving fixture. Both tips were composed of

a 1 mm diameter ruby ball fixed to a carbide shank and steel body (Figure 4-2). Points

were recorded by moving the CMM axes until the ruby ball came into contact with the

part being measured. This caused the probe tip to swivel within the probe housing until a

switch registered the contact. A contact force of 0.1 N was required to register probe tip

contact.

To ensure accurate measurements, the probe tips must be calibrated periodically.

For this study, probe tips were calibrated if:

* The CMM controller had been turned off after the most recent calibration.

* The PC-DMIS software had been closed after the most recent calibration.

* The tip had not been calibrated for the current donor and measurement type.

The tip was qualified by taking 24 points about a spherical artifact. The diameter of

this construct was then compared to the known 19.050 mm diameter of the artifact.

Additionally, the standard deviation of the 24 radius values was calculated. The

calibration was considered acceptable if the constructed diameter was accurate to better

than 3 am. A standard deviation of the radii of less than 2 am was considered acceptable

for the 20 mm long tip while a standard deviation of less than 4 am was considered

acceptable for the 27 mm long tip.

Measuring the Allograft Stack-ups and Parts

Dimensional measurements of the allograft pin and hole diameters were taken at

four points during the manufacturing cycle: just prior to pin insertion, after

BioCleanseTM, after lyophilization, and after a 30 second hydration by immersion in

water. A discussion of the RTI manufacturing procedure can be found in Chapter 3.

Grafts from ten donors were followed through the manufacturing process. Each

donor set consisted of the parts required to make six allograft assemblies (Figure 4-3).

The parts were first received prior to pin insertion with cortical plates and cancellous

blocks still clamped in the RTI indexing wheel (Figure 4-4). At this time the holes in the

top cortical plate were measured. Half of the cortical-cancellous stack-ups were then

removed so that individual cortical plates could be measured. The remaining three stack-

ups were left in their respective machining fixtures and returned to RTI for final assembly

and machining. This was done so that half the parts could be passed through the RTI

manufacturing process for further measurements and half could be assembled for failure

testing.

During this first measurement cycle, the twelve cortical pins per donor were also

measured and sorted according to size. Six pins were selected to be inserted into three

allografts including the two largest and two smallest pins. These extreme diameter pins

were deliberately mismatched with the extreme diameter holes in order to try to increase

the likelihood of fracture and pull-apart failures. The three assembled grafts per donor

were then assembled, machined and treated as per RTI specifications with BioCleanseTM

and lyophilization.

The remaining six pins along with the cortical plates that were removed from the

RTI assembling and grooving fixtures were then re-measured after each remaining

portion of the manufacturing sequence. The cancellous blocks were assumed to have no

effect on the performance of the graft (see Chapter 2). For this reason, the cancellous

blocks that were removed from the machining fixtures were discarded.

Cortical-cancellous stack-ups

As noted, the six cortical-cancellous stack-ups per donor were measured while still

clamped in the RTI machining fixture prior to pin insertion. Each stack-up was assigned a

label "ASM X-Y" where the prefix "ASM" designated the parts as an assembly, X was

the position of the graft in the RTI indexing wheel (1-6), and Y was the donor number (1-

10). Due to the limited length of the probe tip, only the topmost cortical plate could be

measured in the fixture. The two holes were designated as "hole 1" and "hole 2" as

shown in Figure 4-5.

The indexing wheel was received from RTI sealed in a plastic container containing

water to keep the bone material in a moist environment. The bone pieces were not

immersed in the water, however.

Individual fixtures containing the grafts were removed from the plastic container

and indexing wheel one at a time to be measured. First, the reamed holes were cleaned

with water and compressed 1,1,1,2 tetrafluorethane dust remover in an effort to remove

machined bone chips. The assembling and grooving fixtures were then bolted into an

aluminum adapter which was then bolted to the CMM table for measurement as shown in

Figure 4-5.

The CMM software coordinate system was then aligned to the fixture as shown in

Figure 4-6. First, a plane was created from five points on the top face of the support arm.

This plane was defined as the z-plane into which all two-dimensional features would be

projected. Next, a line was created from two points taken from left to right along the front

face of the support arm to define the x-direction. A four-point circle was then taken inside

of hole 1 the center of which defined the x- and y-direction zero. Finally, a single point

was taken on the top face of the front clamp. This point, which was at the same level as

the top of the stack-up, defined the z-direction zero. This sequence was completed first in

the CMM manual operation mode and then in DCC mode. The y-direction vector was

constructed in the PC-DMIS software as the cross product of the z-direction and the x-

direction

Once the coordinate system was aligned to the graft, hole 1 and hole 2 were

measured. Four ten-point circles were taken at 0.5 mm intervals along the axis of each

hole (Figure 4-7). The diameter of each hole was defined as the average diameter of the

four circles. Additionally, the straightness of each hole was calculated. To do this, the

best-fit line through the centers of the four circles in the hole was determined. The

straightness of the hole was then defined as the farthest distance of any given center from

the best-fit line (Figure 4-8).

Loose cortical plates

The holes of the cortical plates were assigned a name by the convention "PL X-Y-

Z". Here, the prefix "PL" designated the part as a plate. The "X" numeral was filled by a

1 or a 2 to designate the plate as the top or bottom plate in the fixture, respectively. The

"Y" numeral indicated the position of the graft in the indexing wheel (1-6) and the "Z"

numeral referred to the donor number (1-10). The hole designations described in the

cortical-cancellous stack-up section were carried over to the loose plates.

Once a plate was removed from the machining fixture, one corer was removed

with a razor blade as shown in Figure 4-9. This was done to keep track of the plate

orientation throughout the remaining measurement cycles. The plate was then cleaned

with water and compressed 1,1,1,2 tetrafluorethane to remove any remaining bone chips

and excess water. It should be noted that no cleaning was performed on the parts after

lyophilization and subsequent hydration. Excess water was wiped from the re-hydrated

parts using a lint free tissue.

The loose cortical plates were then clamped to the CMM table as shown in Figure

4-10. The CMM coordinate system was aligned to the part as shown in Figure 4-11. Note

that the removed corner is hidden by the clamp. First, a plane was constructed from six

points taken on the top face of the plate. This plane defined the z-plane into which all

two-dimensional features were projected. Next, two circles were constructed from four

points each in hole 1 and hole 2. A line from hole 1 to hole 2 was then constructed which

defined the negative y direction. The x- and y-direction zero coordinates were shifted to

the center of hole 1. Finally, a six-point plane was measured on the CMM table around

the plate which defined the z-direction zero value. The x-direction was calculated as the

cross product of the y-direction and z-direction. These features were measured first in

manual operation mode and then in DCC mode to improve accuracy.

As with the clamped stack-ups, four 10-point circles were measured at 0.5 mm

intervals in each of the plate holes. The diameter of each hole and the hole straightness

were then calculated as described for the cortical-cancellous stack-ups.

Cortical pins

Cortical pins were received in a heat-sealed plastic bag. Once this bag was opened,

the pins were coated with isopropyl alcohol then allowed to dry for 30 minutes.

Individual pins were measured while clamped in a 5C collet (Figure 4-12).

Only the portions of the pin which would be in contact with the cortical plates were

measured. Pins were therefore inserted into the collet such that 6.2 mm of pin length was

exposed (Figure 4-13). This allowed 1 mm clearance from the portion of the pin to be

measured to the top of the collet.

As with the other part types, the first step in the measurement process was to align

the CMM coordinate system to the pin (Figure 4-14). First, a plane was constructed from

five points on the top flat surface of the manual collet holder to which the z-plane was

leveled. Next, a four-point circle was measured around the pin, the center of which

defined the x- and y-coordinate zero values. Finally, a single point was taken on the top

surface of the pin which defined the z-coordinate zero. Due to the nominally

axisymmetric shape of the pin, the x- and y-directions were not explicitly defined. As

with other part types, this alignment was performed first in manual operation mode then

in DCC mode.

The non-chamfered end of the pin was measured first using eight 10-point circles at

0.5 mm intervals along the length of the pin shaft (Figure 4-15). The pin was then

removed from the collet, re-clamped with the chamfered end exposed, and measured in

the same fashion. Finally, the non-chamfered end was re-measured. The first

measurement of the non-chamfered end was not used in determining the dimensions of

the pin.

The pin diameter was calculated as the average of the 16 diameter values taken

from both ends of the pin (Figure 4-16). The straightness error of either end was

determined by constructing a best-fit line through the centers of the eight circles, then

calculating the maximum center deviation from that line. The pin straightness error was

defined as the larger straightness error from the two ends.

Unlike the cortical plates, which were designated according to their location in the

machining fixture, cortical pins could not be given a designation until after they were

measured and paired to an allograft, whether or not that graft would later be assembled.

Pins were named according to the convention "PN X-Y-Z". Here, the "X" numeral

designated whether the pin was to be inserted into hole 1 or hole 2 of its corresponding

graft. The "Y" numeral designated the station of the indexing wheel containing the stack-

up into which the pin would be inserted. Again, this designation carried over even if that

graft was in stations 4-6 and would not be assembled. Finally, the "Z" place holder

indicated which donor the pin came from.

Pull-apart Tests

The quality of the interference fit of the assembled allografts was experimentally

investigated by measuring the force required to separate a cortical plate from its two

interference pins. These tests were carried out using an MTS Q-Test 5 Load Frame with

Testworks 4 software. The load frame was fitted with a 5 kN load cell and mechanical

grips as in Figure 4-17.

The grafts to be tested were fixed with epoxy to grooved aluminum blocks which

were clamped in the mechanical grips. This was done to avoid the need to clamp the

cortical plates and thereby affect the interference connection. The 3.2 mm (1/8 in.)

grooves in the aluminum blocks prevented the pins from being glued to the aluminum or

the cortical plates.

Prior to any mechanical testing, the grafts were tested by hand as done in the RTI

production environment. To do this, each cortical plate was held between the thumb and

index finger of one hand and tension was applied. If any resistance was met, tension was

ceased. Grafts that separated with no appreciable resistance were reassembled and

retested as described in the following sections.

Sample preparation

The aluminum blocks were first filed to remove any residual epoxy from previous

tests, then roughened with 60 grit sand paper to improve the ability of the epoxy to bond.

The blocks were sonicated in acetone and methanol, rinsed with water, and blown dry

with compressed air.

The grafts were then epoxied to the aluminum blocks. A quick-setting epoxy was

used for donors 1-6. X of the Y tests for these donors resulted in the failure of the epoxy

bond rather than the interference fit. For that reason, a metal and concrete epoxy was

used for donors 7-10. After a five minute curing period, the bond was reinforced by

applying more epoxy to the sides of the cortical plates. The epoxy was then allowed to

cure for 24 hours. Just prior to tensile testing, the grafts were immersed in water for 30

seconds as per RTI specifications.

Pull-apart test procedure

The allograft and aluminum block assembly was fixed in the load frame grips. A

ground parallel block was used to help align the assembly to the tensile direction of the

load frame. The lower grip was tightened on the lower aluminum block first. While the

keep the load on the graft as close to zero as possible.

When the allograft-aluminum assembly was fixed in the grips, the tensile load was

increased at a nominal rate of 20 N/s until the crosshead had moved by 3.5 mm,

indicating that the graft had separated or broken free from an aluminum block. During the

tests, load, crosshead position, and time were recorded by the MTS software. The peak

force in the load cycle was taken to be the pull-apart force.

Finite Element Analysis

A finite element model of the interference fit was created to both predict allograft

failures and validate/improve the isotropic model used in the Monte Carlo simulation.

ANSYS 10 software was used to create the solid model and mesh as well as to

complete the analysis (Figure 4-18). To simplify the model, the 11 mm radius on the top

of the graft was neglected. The diameter of the pin in this model was given a value equal

to the average of all pin diameters from the dimensional study. The diameter of the holes

was made equal to the pin diameter minus the average predicted interference value from

the dimensional study. Twenty-node brick elements were used to populate the pin and the

plate. To simulate the interference fit, contact and target elements were created at the pin-

plate interfaces.

A two-step load scenario was used to study the interference fit. First, a static study

was used to model the stresses in the assembled allograft. Von Mises equivalent stress

values and contact pressures observed after this load step. Next, a relative motion of 100

[tm was applied to one end of both pins to induce slippage. The pull-apart force was then

found by summing the z-direction forces of all of the contact elements.

Analytical Model and Monte Carlo Simulation

An analytical interference fit model formed the basis for a Monte Carlo simulation

used to predict the rate of pull-apart failure of the assembled grafts. The analytical model

applied in this simulation was discussed in Chapter 2. This model assumes isotropic

material properties and a cylindrical geometry of both pin and plate.

The purpose of the Monte Carlo simulation was to serve as a tool for predicting the

frequency of interference fit failures, either by insufficient pull-apart force or yielding.

Additionally, the simulation was used to compare the relative influence of the different

model parameters. The Monte Carlo simulation was written in Matlab (see Appendix).

To estimate the frequency of failure, each input parameter in Table 4-1 was

assigned a mean value and standard deviation. Mean values and standard deviations of

geometric variables were taken from the results of the dimensional study. Values for the

elastic constants were obtained from the literature (Chapter 2). The stress concentration

factor Kt and the effective plate outer radius were obtained by comparison with the finite

element model (see Chapter 5).

The Monte Carlo simulation was then used to generate histograms which predicted

the number of occurrences of both negative pull-apart forces and Von Mises stress values

above the failure stress. This was done by selecting values for each of the variables in

Table 4-1 randomly within one standard deviation of their mean value. Forces and

stresses were then calculated according to the analytical model discussed in Chapter 2.

Von Mises stress was only calculated when the interference was greater than zero. This

process was repeated 250,000 times to generate a distribution of outputs.

The relative influence of individual variables could then be tested by setting the

standard deviation values for all variables, except the variable of interest, to zero. The

resultant standard deviation of the pull-apart force distribution could then be compared to

similar simulations for other variables to determine the most influence factors on the

interference fit.

Figure 4-1. Brown and Sharpe MicroVal PFx coordinate measuring machine.

steel base

carbide shank
tip
Length

Figure 4-2. Probe tip geometry used in this

inserted
into
allog rafts

retained
for further
measurements

cortical-cancellous stack-ups
in indexing wheel

loose cortical pins

Figure 4-3. Allograft parts as received from RTI for one donor. Cortical-cancellous stack-
ups 1-3 as marked above were assembled into allografts. Stack-ups 4-6 were
removed from the assembling and grooving fixture for further measurement.

machining fixture

indexing

Figure 4-4. RTI indexing wheel and assembling/grooving fixtures. Only the top cortical
plate could be measured in this fixture due to probe tip length limitations.

smallest

largest

n

Figure 4-5. Stack-up measurement. Inset shows hole naming convention.

Figure 4-6. Stack-up coordinate system alignment features.

hole"2" hole"1"

10 hits per circle

Figure 4-7. Measurement of the cortical plates while stacked in the machining fixture.

best fit line

error

Figure 4-8. Definition of straightness error.

Figure 4-9. One corner of each loose plate was removed to preserve orientation.

Figure 4-10. Loose cortical plates were clamped directly to the CMM table.

z-plane

Figure 4-11. Cortical plate coordinate system alignment features.

Figure 4-12. Cortical pins were measured while clamped in a 5-C collet and manual
collet holder.

Figure 4-13. Pins were clamped in the collet with 6.2 mm of length exposed.

Figure 4-14. Cortical pin coordinate system alignment features.

Figure 4-15. Measurement locations for one side of the cortical pin.

1.

t
1.7 mm

1.7 mm

t\
pin diameter
chamfered end

=average

Figure 4-16. Cortical pin measurement procedure. 1. Measure non-chamfered end. 2.
Measure chamfered end. 3. Measure non-chamfered end again to investigate
effects of collet clamping.

grip

allograft

aluminum block

Figure 4-17. Pull-apart test setup.

cortical plate

pins

plane of symmetry/
Figure 4-18. The ANSYS model and mesh used in the finite element analysis.

Table 4-1. Input parameters for the Monte Carlo analysis
Parameter Symbol
Young's Modulus (Pin) Ei
Young's Modulus (Plate) Eo
Poisson's Ratio (Pin) pi
Poisson's Ratio (Plate) po
Stress Concentration Kt
Length of Contact L
Friction Coefficient pf

specify 20
nodes on each edge

CHAPTER 5
RESULTS AND DISCUSSION

The following sections contain the results of the dimensional measurements, pull-

apart tests, finite element analyses, and Monte Carlo simulation. Additionally, results are

presented for the friction testing that was performed in support of the finite element and

Monte Carlo models.

Dimensional Measurements

As was discussed in previous chapters, dimensional measurements were completed

both to understand the accuracy and consistency of the RTI manufacturing process as

well as to use in predictive models of the interference fit. To this end, results are

presented first for the pins and plate holes separately, then for the combined interference

of the allograft components.

Interference Pins

Average diameter values by donor are shown in Table 5-1. Note that the diameters

from the first, second, and third donors have substantially larger diameters than those

pins from the other seven donors. A tool change was performed on the lathe used to turn

the pins between the times when donors 3 and 4 were processed. Also note that while the

diameter values stay relatively constant after BioCleanseTM, lyophilization causes the pin

diameters to drop by an average of 50 im. Subsequent hydration of the pins for 30 s

results in an average diametric recovery of 11 im.

Also included in Table 5-1 are the average diameter values measured with calipers

by the RTI machinist for each donor. Since these diameter values represent the 'bin' to

which the pins were assigned, and thereby determine the reamer sized used in drilling the

plate holes, their accuracy is of some importance. The RTI-measured average diameter

values deviate by anywhere from 1 tm to 12 tm from the diameters measured as-

machined using the Brown and Sharpe CMM. Recall from Chapter 3 that reamer sizes

are available in 0.0005 in (12.7 [im) increments.

Measurement repeatability

Before further comments can be made on the measurement results for the pin

diameters, it is first necessary to quantify the reliability of the CMM measurements. To

that end, the results of ten repeated measurements of a single pin are shown in Table 5-2.

Between each repetition, the pin is removed and re-fixtured in the collet. Over the ten

measurements, the measured pin diameter varies over a 6 .im range with a standard

deviation of 2 rim.

Taper characterization

RTI manufacturing drawings call out a maximum taper of 0.0005 in (12.7 im) over

the length of a pin. In this study, the taper of the pins is investigated in three ways. First,

the range of diameter values over the sixteen circles measured on each pin is recorded

(Figure 5-1). Average single-pin diameter range values are tabulated by donor and

manufacturing process in Table 5-3. It should be noted average values for donor 3 are

consistently out of specification. However, after lyophilization and re-hydration, only one

of the pins from donor three was actually out of specification at 15 .im of variation. The

average value for donor 3 was skewed due to the fact that two pins were lost during the

BioCleanseTM cycle. Also note that the average single-pin diameter range for each

process stays relatively constant, but is slightly higher after lyophilization. Eight of fifty-

seven loose pins that completed the manufacturing process had a "taper" of greater than

12.7 rm.

Next, pin straightness error, as defined in Chapter 4, is calculated as the deviation

of circle center locations from a best fit line through all measured circles (Figure 4-8).

Average pin straightness error values for each donor and manufacturing process are

recorded in Table 5-4. Note that the average straightness error stays consistent to within 4

lm for each donor.

Finally, a comparison between the diameters of the chamfered and non-chamfered

ends of each pin (Figure 5-2) is made in order to ensure that one end of the pin is not

systematically larger than the other. The average diametric difference between the two

ends of each pin are recorded for each donor and manufacturing cycle in Table 5-5. Here,

the diametric difference is defined as the average diameter of the non-chamfered end

minus the average diameter of the chamfered end.

Table 5-5 indicates that while one end may be larger than another for a given pin or

even for the pins from a given donor, this difference is small compared to the

repeatability of pin measurements shown in Table 5-2. More significant from a

manufacturing standpoint, neither end is consistently larger or smaller than the other as

one might expect from turning a cantilevered beam (see Chapter 3).

Collet clamping effects

One item of concern when fixing the pins for measurement on the CMM was that

the collet was plastically compressing the bone material. To investigate the possibility of

permanent deformation, the non-chamfered end of each pin was measured twice. The

average difference of the second diameter measurement minus the first, the "clamping

effect", is catalogued for each donor in Table 5-6. The collet clamping effect, while

generally 0-2 rim, is most notable prior to lyophilization for larger diameter pins.

Pin manufacturing repeatability

For each donor, the range of diameters for the six pins not inserted into allografts

was calculated as shown in Figure 5-3. This was done to gain some understanding of the

repeatability of each stage in the manufacturing process. The pin diameter variation for

each donor at each manufacturing cycle is shown in Table 5-7. It should be noted that the

average single-donor diameter variation decreases after BioCleanseTM and increases

dramatically after lyophilization.

Cortical Plate Holes

Average cortical plate hole diameters for each donor and manufacturing step are

shown in Table 5-8 along with the corresponding reamer diameter used by RTI. Like the

pin diameters, the plate hole diameters fall dramatically, here by an average of 29 [am,

after lyophilization. However, unlike the cortical pins, 30 seconds of immersion in water

only recovers an average of 3 [tm of diameter.

Hole diameter measurement repeatability

As with the cortical pins, ten repeat measurements were taken of a single cortical

plate hole. The results of these repeat measurements are shown in Table 5-9. Over the 10

measurements, a standard deviation of 0.005 mm from the mean value is observed.

Effects of the RTI machining fixture

As was discussed in Chapter 4, the cortical plates are measured both in the RTI

machining fixture and clamped to the CMM table to determine whether any diametric

change occurs. Table 5-10 shows the average discrepancy between the two sets of

measurements. The loose plates are on average 6 am larger than the plates measured in

the machining fixture with a standard deviation of 7 am. This relatively large variance in

the effect of the fixture may be due to variations in the cortical plate exterior dimensions.

Since the front and side clamps of the machining fixture are tightened to be flush with the

fixture body, rather than to a set force, the amount of stress and strain that a plate is

subjected to could vary significantly if the plate was oversized or undersized.

Accompanying Table 5-10 are the results of a ten repeated measurements of a

cortical plate hole clamped in a machining fixture (Table 5-11). Note that the range and

standard deviation of the values are comparable to those in Table 5-9.

Straightness error

Table 5-12 shows the average straightness error values of the cortical plate holes

sorted by donor and manufacturing cycle. Average straightness error values for the

cortical pin holes range from 2 [am to 10 [am and do not vary more than 4 [am over the

various stages of the manufacturing process. These results are similar to those seen for

the cortical pins.

Diametric variation between the two plate holes

Table 5-13 shows the average diametric variation between the two holes of a given

cortical plate. Here, the diametric variation is defined as the diameter of hole "2" minus

the diameter of hole "1". Table 5-13 indicates that, on average, hole "1" is 2-3 [am larger

than hole "2", though with a standard deviation of 3-5 [am, regardless of the

manufacturing cycle.

Diametric variation between plates

Table 5-14 shows the average diametric variation between the holes of the two

cortical plates of a given allograft. Here, diametric variation is defined as the average

diameter from plate "2" minus the average diameter from plate "1". Table 5-14 indicates

that once the plates complete the manufacturing process, little difference exists between

the diameters of the two plates.

Manufacturing process repeatability

As with the cortical pins, it is desirable not just to know the accuracy of the hole

diameter values, but also their precision. The quality and repeatability of the drilled and

reamed holes are characterized in two ways. First, the single-plate range of diameter

values is calculated as shown in Figure 5-4. Table 5-15 shows the average values of the

single-plate diameter range for each donor and manufacturing cycle. On average, the

diameters of the holes of a given plate vary by 10-11 tm.

Additionally, the range of hole diameters over a single donor is calculated as shown

in Figure 5-5. The results of these calculations are shown in Table 5-16, which indicates

significant diametric variation from hole to hole. At the end of the manufacturing

process, the twelve cortical plate holes associated with a given donor will vary by an

average of 17 [tm.

Diametric Interference

Table 5-17 shows the average predicted diametric interference between the cortical

pins and the cortical plate holes for each donor and each manufacturing process. Here, the

predicted diametric interference is defined as the calculated diametric difference between

the pins and plate holes that were not formed into allografts. Recall from Chapter 3 that

RTI specifies a machined diametric interference of 0.0010-0.0015 in. (25-38 [tm). Table

5-17 indicates that with the exception of donor 9, the average interference values after

machining are within acceptable limits. The predicted interference drops by an average of

21 jam after lyophilization and recovers by an average of 7 jam after thirty seconds of

immersion in water. Donor 9 is of particular note since the predicted interference values

become negative after lyophilization. Also note that the standard deviation of the

interference values are a much larger percentage of the average values after lyophilization

and rehydration than after machining and BioCleanseTM.

Mechanical Pull-apart Tests

Table 5-18 shows the results for the mechanical pull-apart tests including

occurrences of manual pull-apart failures, the plate that failed, which epoxy was used and

the load at which failure occurred. As discussed in Chapter 4, the allografts were first

tested manually for pull-apart failure after lyophilization and before hydration. Out of the

thirty grafts considered in this study, 4 (13%) failed during manual testing and 17 (57%)

exhibited visible cracking in one or both cortical plates. None of the grafts that failed the

manual pull-apart test were made from sets of pins and plates deliberately matched to

have poor interference. All of the cracks were in the longitudinal bone direction and ran

from the pin to the edge of the plate.

Of the 30 assembled allografts, 20 were pulled apart during mechanical testing. For

the remaining 10 grafts, the epoxy holding the graft to the aluminum blocks failed before

the interference fit. Results for the 20 grafts that were pulled apart are listed in Table 5-

19. The average pull-apart force was found to be 83.4 N with a standard deviation of 25.9

N. The average pull-apart force of the grafts with no cracks was found to be 100.6 N with

a standard deviation of 28.5 N. The average pull-apart force of the grafts what exhibited

cracks was found to be 74.1 N with a standard deviation of 19.8 N.

Also included in Table 5-19 are the predicted interference values for each graft

after machining and adjusted by the average process effect for each donor after

lyophilization and hydration. Here, the predicted interference after machining is

calculated as the difference between the average pin diameter and average hole diameter

for each graft.

Figure 5-6 shows the pull-apart force plotted against donor number and the

predicted interference values. Unexpectedly, Figure 5-6 indicates little or no correlation

between the predicted diametric interference and the pull-apart force. This could indicate

that over the small sample size (the seven grafts that were pulled apart that did not exhibit

cracking) variations in material properties play a larger role than dimensional

interference. It is also possible that the poor correspondence between predicted

interference and pull-apart force reflects a difference in the effects of lyophilization and

hydration on the assembled graft as opposed to the measured loose parts.

Finite Element Analysis

The finite element analysis described in Chapter 4 was completed three times with

three separate sets of material property and geometric inputs (Table 5-20). Here, the

subscript "r" refers to the radial bone direction, the subscript "c" refers to the

circumferential bone direction, and the subscript "1" refers to the longitudinal bone

direction. The von Mises stress and pull-apart force results from each trial are shown in

Table 5-21. For the first trial, the material properties were taken from [16] while the pin

diameter and diametric interference were taken from the measurement results after

hydration. The second trial used the same material properties as the first trial but used

geometric values associated with the lyophilized state. The third trial used a pin diameter

and interference equal to those of the second trial, but used mechanical properties

reduced by roughly one standard deviation from the values used in the first two trials. Of

the three trials, the third trial (reduced modulus and interference values) shows the closest

agreement to the experimental data.

The von Mises stress distribution and contact pressure plot for the third trial are

shown in Figures 5-7 and 5-8, respectively. Not surprisingly, the highest stresses are

located at the contact and between the two pins. Somewhat more surprising is the absence

of a defined stress concentration at the edge of the edge of the contact where the pins

overlap the holes.

Monte Carlo Simulation

The Monte Carlo simulation inputs are shown in Table 5-22. Interference values

and pin diameter values are taken from the measured results after lyophilization. Mean

Young's modulus values are the same as the radial and circumferential values from the

finite element model. The Young's modulus standard deviation, as well as the Poisson's

ratio mean and standard deviation values, are selected from.[161 According to the finite

element analysis results, a stress concentration factor of 1 was used. Finally, the effective

plate outer radius was adjusted until the simulation results best matched the finite element

results.

The output statistical distributions from the multi-parameter Monte Carlo

simulation are shown in Table 5-23 and Figure 5-9. Note that the mean pull-apart force is

within the range of results observed in the mechanical testing while the pull-apart force

standard deviation is dramatically higher. This suggests that the Monte Carlo analysis is

overstating the variation in the actual force and stress levels.

The model indicates a pull-apart failure (F < 0) rate of 13%. Recall from the

mechanical testing that the pull-apart failure rate was also found to be 13%. Assuming a

failure stress of 25 MPa (the ultimate tensile strength reported by Bianchi [5]), the

simulation predicts a von Mises stress failure rate in the cortical plates of 84%. If the

tensile failure stress is assumed to be 53 MPa (as reported by Reilly and Burstein [16]), the

simulation predicts that 57% of the grafts will fail. Recall from the mechanical testing

that the 57% of the allografts were found to have cracks in them.

Table 5-24 shows the results of the single-parameter variation simulation. The

simulation indicates that the diametric interference, coefficient of friction, and plate

Young's modulus are the most influential parameters on the pull-apart force. Also, the

simulation indicates that diametric interference, plate Young's modulus, and bone

Poisson's ratio are the most influential factors on the von Mises stress in the cortical

plate. Note that the prediction that diametric interference is the most influential factor in

the quality of the interference fit is not supported by the pull-apart data.

Table 5-1. Average pin diameters in mm by donor over the RTI manufacturing step.
Donor RTI Measured Machined BioCleanseTM Lyophilization Rehydrated
1 2.014 2.013 2.014 1.958 1.975
2 2.014 2.021 2.024 1.965 1.994
3 2.010 2.012 2.014 1.965 1.965
4 1.976 1.970 1.975 1.930 1.937
5 1.980 1.975 1.977 1.930 1.939
6 1.980 1.968 1.973 1.926 1.931
7 1.978 1.967 1.973 1.937 1.945
8 1.975 1.970 1.976 1.934 1.945
9 1.975 1.962 1.970 1.903 1.918
10 1.970 1.968 1.974 1.921 1.926
Max 2.014 2.021 2.024 1.965 1.994
Min 1.970 1.962 1.970 1.903 1.918
Range 0.044 0.059 0.054 0.061 0.076
St. Dev. 0.018 0.023 0.021 0.020 0.024
Average 1.987 1.983 1.987 1.937 1.948

Table 5-2. Pin measurement repeatability.
Pin Diameter
Trial (mm)
1 1.955
2 1.954
3 1.955
4 1.953
5 1.953
6 1.953
7 1.953
8 1.952
9 1.951
10 1.957
Max 1.957
Min 1.951
Range 0.006
St. Dev 0.002
Average 1.954

i

pin diameter I nge

lrgeyet diameter smallest diameter

Figure 5-1. Diameter range over a single pin. Diameter variation graphically exaggerated
for clarity.

Table 5-3. Average single-pin diameter range values in mm by donor and manufacturing

process.
Donor Machined

1
2
3
4
5
6
7
8
9
10
Max
Min
St. Dev.
Average

0.010
0.009
0.014
0.010
0.006
0.005
0.008
0.007
0.011
0.012
0.014
0.005
0.003
0.009

BioCleanseTM

0.014
0.010
0.016
0.012
0.006
0.006
0.006
0.007
0.008
0.008
0.016
0.006
0.004
0.009

Lyophilization
0.017
0.010
0.016
0.015
0.006
0.004
0.007
0.007
0.009
0.006
0.017
0.004
0.005
0.010

Rehydrated
0.013
0.010
0.010
0.013
0.006
0.006
0.006
0.007
0.009
0.005
0.013
0.005
0.003
0.009

-_--- largest diameter circle

-- smaest diameter circle
- smallest diameter circle

Table 5-4.
Donor
1
2
3
4
5
6
7
8
9
10
Max
Min
St. Dev.
Average

Average pin straightness error values in mm.
Machined BioCleanseTM Lyophilization
0.007 0.011 0.008
0.005 0.006 0.006
0.005 0.008 0.006
0.006 0.008 0.009
0.003 0.003 0.003
0.004 0.004 0.003
0.003 0.004 0.004
0.005 0.005 0.005
0.004 0.003 0.005
0.003 0.004 0.004
0.007 0.011 0.009
0.003 0.003 0.003
0.001 0.003 0.002
0.004 0.006 0.005

Rehydrated
0.008
0.005
0.007
0.010
0.005
0.004
0.003
0.005
0.005
0.003
0.010
0.003
0.002
0.006

S average of 8 circle diameters = non-cha mfered end diamnreter

S average of 8 circle diameters = chamfered end diameter

Figure 5-2. Comparison of average diameters of the two pin ends.

Table 5-5. Diametric differences in mm between the chamfered and non-chamfered pin
ends.
Donor Machined BioCleanseTM Lyophilization Rehydrated
1 0.003 0.005 0.007 0.004
2 -0.002 -0.002 -0.001 0.000
3 0.002 0.003 0.005 0.001
4 0.000 0.001 0.003 0.001
5 0.000 -0.001 0.001 0.000
6 0.000 -0.001 -0.001 -0.002
7 0.000 0.000 0.000 -0.001
8 0.000 -0.002 0.001 -0.002
9 0.001 0.000 0.000 -0.001
10 0.001 -0.001 0.001 -0.001
Max 0.003 0.005 0.007 0.004
Min -0.002 -0.002 -0.001 -0.002
St. Dev. 0.001 0.002 0.003 0.002
Average 0.000 0.000 0.001 0.000

---I

I

Table 5-6.
Donor
1
2
3
4
5
6
7
8
9
10
Max
Min
Range
St. Dev.
Average

D2

03

D4

Diameter Range Over 1 Donor = Max(D 1:D6) Min(D1:D6)
Figure 5-3. Pin diameter variation over a single donor

Average collet clamping effect in mm.
Machined BioCleanseTM Lyophilization
-0.005 -0.005 0.000
-0.004 -0.003 0.000
-0.003 0.002 0.002
-0.001 -0.002 0.000
-0.002 -0.002 0.001
-0.001 -0.001 0.000
-0.001 -0.001 0.000
0.000 -0.001 0.000
-0.002 -0.001 0.000
-0.001 -0.001 0.001
0.000 0.002 0.002
-0.005 -0.005 0.000
0.004 0.006 0.002
0.001 0.002 0.001
-0.002 -0.001 0.000

D1

Re hydrated
-0.002
-0.001
-0.001
0.001
0.000
0.000
0.000
-0.002
0.001
0.000
0.001
-0.002
0.003
0.001
0.000

D5

D6

I

I

I

I

I

Table 5-7. Variation of pin diameters in mm across a single donor.
Donor Machined BioCleanseTM Lyophilization Rehydrated
1 0.008 0.010 0.024 0.028
2 0.014 0.008 0.019 0.012
3 0.008 0.008 0.018 0.022
4 0.011 0.007 0.018 0.019
5 0.012 0.004 0.008 0.011
6 0.008 0.003 0.010 0.008
7 0.015 0.007 0.017 0.017
8 0.016 0.007 0.017 0.015
9 0.022 0.011 0.036 0.027
10 0.008 0.009 0.015 0.014
Max 0.022 0.011 0.036 0.028
Min 0.008 0.003 0.008 0.008
Range 0.014 0.008 0.028 0.020
St. Dev. 0.005 0.002 0.008 0.007
Average 0.012 0.007 0.018 0.017

Table 5-8. Average cortical
process.
Donor RTI Reamer
1 1.981
2 1.976
3 1.976
4 1.943
5 1.943
6 1.938
7 1.943
8 1.941
9 1.938
10 1.930
Max 1.981
Min 1.930
Range 0.051
St. Dev. 0.019
Average 1.951

plate hole diameters (mm) by donor and manufacturing

Machined
1.968
1.978
1.984
1.937
1.927
1.938
1.932
1.941
1.944
1.930
1.984
1.927
0.057
0.021
1.948

BioCleanseTM
1.983
1.982
1.982
1.947
1.946
1.939
1.938
1.949
1.944
1.941
1.983
1.938
0.045
0.019
1.955

Lyophilization
1.952
1.953
1.962
1.918
1.913
1.907
1.909
1.923
1.910
1.910
1.962
1.907
0.055
0.021
1.926

Rehyd rated
1.951
1.961
1.961
1.915
1.918
1.913
1.915
1.922
1.914
1.925
1.961
1.913
0.048
0.020
1.929

I

I

I

I

I

Table 5-9. Ten repeated measurements of one cortical plate hole.
Trial Hole Diameter (mm)
1 1.915
2 1.921
3 1.923
4 1.926
5 1.927
6 1.928
7 1.929
8 1.930
9 1.931
10 1.931

Max
Min
Range
St. Dev.

Average

1.931
1.915
0.016
0.005

1.926

Table 5-10. Effects of the RTI machining fixture on hole diameter.
I [ Average "Plate 1" Hole Diameter

Donor#

In Mach. Fixt.
(mm)

Loose Plates
(mm)

Discrepancy
(mm)

1 1.964 1.978 0.014
2 1.971 1.978 0.006
3 1.969 1.982 0.013
4 1.934 1.932 -0.002
5 1.932 1.933 0.002
6 1.929 1.937 0.008
7 1.933 1.925 -0.008
8 1.933 1.943 0.010
9 1.937 1.944 0.007
10 1.926 1.936 0.010
Max 0.014
Min -0.008
Range 0.022
Std Dev 0.007
Mean 0.006

Table 5-11. Ten repeated measurements of a cortical plate hole diameter (mm) while
clamped in the RTI machining fixture.
Hole
Trial Diameter
1 1.924
2 1.925
3 1.928
4 1.934
5 1.936
6 1.933
7 1.936
8 1.935
9 1.933
10 1.934
Max 1.936
Min 1.924
Range 0.012
St. Dev. 0.004
Average 1.932

Table 5-12. Average straightness error (mm) of cortical plate holes by donor and
manufacturing cycle.
Donor Machined BioCleanseTM Lyophilization Rehydrated
1 0.003 0.003 0.003 0.007
2 0.004 0.002 0.002 0.002
3 0.005 0.006 0.006 0.008
4 0.006 0.006 0.006 0.007
5 0.009 0.010 0.006 0.006
6 0.002 0.006 0.008 0.003
7 0.003 0.005 0.004 0.006
8 0.004 0.004 0.003 0.004
9 0.002 0.002 0.003 0.002
10 0.005 0.003 0.005 0.003
Max 0.009 0.010 0.008 0.008
Min 0.002 0.002 0.002 0.002
Range 0.007 0.008 0.006 0.005
St. Dev. 0.002 0.003 0.002 0.002
Average 0.004 0.005 0.005 0.005

Table 5-13. Average diametric difference between hole "1" and hole "2"
Donor Machined BioCleanseTM Lyophilization Rehydrated
1 -0.002 0.000 0.003 0.002
2 -0.003 -0.002 -0.003 -0.003
3 -0.001 -0.001 -0.002 0.001
4 -0.013 -0.009 -0.009 -0.009
5 0.007 -0.013 -0.002 -0.005
6 0.000 -0.004 -0.005 -0.003
7 -0.002 -0.004 -0.002 -0.002
8 0.002 0.001 0.003 0.002
9 0.000 0.000 0.000 -0.001
10 -0.003 0.000 0.001 0.000
Max 0.007 0.001 0.003 0.002
Min -0.013 -0.013 -0.009 -0.009
Range 0.021 0.014 0.012 0.010
St. Dev. 0.005 0.005 0.004 0.003
Average -0.002 -0.003 -0.002 -0.002

Table 5-14. Average diametric difference in mm between the holes of the two cortical
plates of a single allograft.
Donor Machined BioCleanseTM Lyophilization Rehydrated
1 -0.020 0.005 0.001 0.003
2 0.001 0.003 0.004 0.003
3 0.003 0.005 0.006 0.003
4 0.002 0.008 0.012 0.005
5 -0.013 0.016 0.012 0.005
6 0.002 -0.002 -0.002 0.000
7 0.014 -0.006 -0.009 -0.005
8 -0.003 0.002 0.003 0.002
9 0.000 -0.001 0.001 0.000
10 -0.011 -0.006 -0.006 -0.005
Max 0.014 0.016 0.012 0.005
Min -0.020 -0.006 -0.009 -0.005
Range 0.035 0.022 0.021 0.010
St. Dev. 0.010 0.007 0.007 0.003
Average -0.003 0.003 0.002 0.001

Dl DS

Diameter Range Over 1 Plate = Max(D1:DB) MinD1 :D8)

Figure 5-4. Diameter variation over the 8 holes of a single plate.

Table 5-15. Average diameter variation in mm over a single plate.
Donor Machined BioCleanseTM Lyophilization Rehydrated
1 0.018 0.011 0.010 0.010
2 0.007 0.009 0.011 0.010
3 0.011 0.012 0.013 0.015
4 0.015 0.016 0.016 0.016
5 0.020 0.025 0.016 0.016
6 0.003 0.009 0.012 0.005
7 0.007 0.009 0.011 0.010
8 0.009 0.008 0.008 0.008
9 0.003 0.003 0.004 0.004
10 0.009 0.007 0.007 0.006
Max 0.020 0.025 0.016 0.016
Min 0.003 0.003 0.004 0.004
Range 0.017 0.023 0.013 0.012
St. Dev. 0.006 0.006 0.004 0.004
Average 0.010 0.011 0.011 0.010

D10
D9

Diameter Range Over 1 Donor = Max(D1:D12) Min(D1:D12)

Figure 5-5. Hole diameter variation over all the plates from a given donor.

Table 5-16. Range of hole diameter values in mm over a single donor.

Donor Machined BioCleanseTM Lyophilization Rehydrated
1 0.019 0.016 0.019 0.013
2 0.016 0.017 0.014 0.025
3 0.020 0.022 0.023 0.022
4 0.051 0.039 0.041 0.037
5 0.086 0.063 0.031 0.022
6 0.005 0.016 0.023 0.008
7 0.044 0.037 0.047 0.018
8 0.012 0.009 0.010 0.007
9 0.005 0.005 0.007 0.008
10 0.032 0.011 0.015 0.011

Max
Min
Range
St. Dev.

Average

0.086
0.005
0.082
0.025

0.029

0.063
0.005
0.057
0.018
0.024

0.047
0.007
0.040
0.013
0.023

0.037
0.007
0.030
0.010
0.017

D12
D11

Table 5-17. Average predicted diametric interference in mm for each manufacturing
cycle.
Donor Machined BioCleanse Lyophilization Rehydrated
1 0.045 0.031 0.007 0.024
2 0.043 0.042 0.012 0.033
3 0.028 0.032 0.002 0.004
4 0.033 0.028 0.012 0.021
5 0.048 0.030 0.017 0.021
6 0.030 0.034 0.019 0.019
7 0.035 0.036 0.028 0.030
8 0.029 0.026 0.011 0.024
9 0.019 0.026 -0.006 0.004
10 0.037 0.032 0.011 0.001
Max 0.048 0.042 0.028 0.033
Min 0.019 0.026 -0.006 0.001
Range 0.029 0.016 0.034 0.032
Std Dev 0.009 0.005 0.009 0.011
Average 0.035 0.032 0.011 0.018

Table 5-18. Pull-apart test results

Graft Manual Pull-apart

Separated
Plate

Epoxy

(N)

1-1 No NA Quick-setting 82.5 Epoxy failed
2-1 No NA Quick-setting 55.8 Epoxy failed
3-1 No NA Quick-setting 68.6 Plate broke and separated
1-2 No NA Quick-setting 152.3 Epoxy failed
Interference fit failed, opposite
No Top Quick-setting 69.1 plate cracked
Epoxy failed, both plates
3-2Yes NA Quick-setting 15.3 cracked
1-3 No Top Quick-setting 73.5 Interference fit failed
2-3 No NA Quick-setting 62.2 Eox failed
3-3 No Bottom Quick-setting 96.7 Interference fit failed
1-4 Interference fit failed, opposite
No Top Quick-setting 93.6 plate cracked
2-4 No Top Quick-setting 82.4 Interference fit failed
4 Interference fit failed, removed
Yes Bottom Quick-setting 61.9 plate cracked
1-5
No NA Quick-setting 114.6 Epoxy failed, one plate cracked

2-5
No NA Quick-setting 67.2 Epoxy failed, one plate cracked

3-5 No NA Quick-setting 71.7 Epoxy failed, one plate cracked
1-6
No NA Quick-setting 64.7 Epoxy failed, one plate cracked
Interference fit failed, both
No Top Quick-setting 67.6 plates cracked
Interference fit failed, removed
Yes Top Metal/Concrete 57.8 plate cracked
1-7 No NA Metal/Concrete 99.5 Epoxy failed
Interference fit failed, both
No Bottom Metal/Concrete 71.1 plates cracked
Interference fit failed, opposite
No Bottom Metal/Concrete 94.2 plate cracked
1-8 Interference fit failed, removed
No Top Metal/Concrete 118.3 plate cracked
2-8 No Top Metal/Concrete 130.9 Interference fit failed
3-8 No Top Metal/Concrete 101.7 Interference fit failed
1-9 No Top Metal/Concrete 146.3 Interference fit failed
2-9 No Bottom Metal/Concrete 72.5 Interference fit failed
Interference fit failed, both
3-9
No Top Metal/Concrete 92.4 plates cracked
Interference fit failed, both
SNo Bottom Metal/Concrete 67.0 plates cracked
Interference fit failed, both
No Top Metal/Concrete 52.2 plates cracked

Interference fit failed, both
3-10 plates cracked, opposite plate
Yes Top Metal/Concrete 49.6 removed as from manual test

Table 5-19. Pull- apart test results for grafts where the interference fit failed.

Predicted
Manual Interference
Graft Pull-apart (mm)

Interference
Lyophilization
(mm)

Predicted Interference
(mm)

(N)

3-1 No 0.065 0.027 0.045 68.6
2-2 No 0.046 0.015 0.036 69.1
1-3 No 0.059 0.034 0.035 73.5
3-3 No 0.084 0.059 0.060 96.7
1-4 No 0.031 0.011 0.020 93.6
2-4 No 0.044 0.024 0.033 82.4
3-4 Yes 0.037 0.017 0.026 61.9
2-6 No 0.035 0.023 0.023 67.6
3-6 Yes 0.042 0.030 0.030 57.8
2-7 No 0.027 0.020 0.022 71.1
3-7 No 0.042 0.035 0.037 94.2
1-8 No 0.037 0.020 0.032 118.3
2-8 No 0.044 0.027 0.039 130.9
3-8 No 0.030 0.013 0.025 101.7
1-9 No 0.037 0.012 0.022 146.3
2-9 No 0.028 0.003 0.013 72.5
3-9 No 0.015 -0.010 -0.010 92.4
1-10 No 0.038 0.011 0.002 67.0
2-10 No 0.052 0.025 0.016 52.2
3-10 Yes 0.044 0.017 0.008 49.6

Max

146.3

Min 49.6
Std Dev 25.9
Quick-set Epoxy Avg 76.7
Metal Epoxy Avg 87.8
Total Avg 83.4

1 2
0-

0 --

n
1 1-

I
i u 0 -1:

3 o 4

Ss3 0 p i D Mr
a U

n [ D

S1 ci V; na D a 0 00 Cs BO E 009 5ce 3 an 00 C;I a0 Oa O 01 OB co.D
I 0

Predicted interference after machining (mm) Predicted interference adjusted for lyophilization (mm)

-0 ra0

I0

Ired Predicted inte ference ,xdjksted fro h ydration (mm,
Figure 5-6. Pull-apart test result trends where the interference fit failed. 1) Test results by

adjusted for Iyophilization. 5) Pull-apart force vs. predicted interference
adjusted for 30 s hydration. 6) Pull-apart force vs. predicted interference
adjusted for 30 s hydration: rafts without cracking only.
^redid-ed interference adjusted For Iiydra inn (mmn Preded i nterferiance .id jured [or h,.driation (mmn

Table 5-20. Finite element analysis inputs.
Trial 1 2 3
Er 12.0 12.0 9.0
E, 12.0 12.0 9.0
El 18.0 18.0 14.0
Grc 3.3 3.3 2.9
Gri 3.3 3.3 2.9
G,! 3.3 3.3 2.9
Vrc 0.50 0.50 0.5
Vri 0.40 0.40 0.4
S vi 0.25 0.25 0.25
L 0.29 0.29 0.29
Pin D 1.948 1.936 1.936
Diametric
Interference 0.018 0.011 0.011
(mm)

Table 5-21. Finite element outputs
Trial avm(max) Ff
(Mpa) (N)
1 80.6 216.0
2 45.0 120.3
3 34.6 93.9

Figure 5-7. Trial 3 von Mises stress distribution

Figure 5-8. Trial 3 pin contact pressure distnl

Table 5-22. Monte Carlo simulation inputs
Parameter Mean Value

Diametric interference (pm)
Pin Young's modulus (GPa)
Plate Young's modulus (GPa)
Pin Poisson's ratio
Plate Poisson's ratio
Pin diameter (mm)
Stress concentration factor
Contact length (mm)
Coefficient of friction

11
9
9
0.41
0.41
1.937
1.2
1
7.0
0.3

Standard Deviation
9
1
1
0.15
0.15
0.021
0
0
0.3
0.15

Table 5-23. Multi-parameter Monte Carlo simulation overall results.
Mean Value Standard Deviation
Pull-apart force (N) 133 141
Von Mises stress (pin) (MPa) 13 7
Von Mises stress (plate) (MPa) 65 39

ZZ

Force to pull apart

-200 -100 0 100 200 300 400 500 600
F (N)

von Mises stress (plate)

0 50 100 150 200 250
o (MPa)

von Mises stress (pin)
1n1 -

3 40 50 60 70
a (MPa)

Figure 5-9. Monte Carlo simulation results. 1) Pull-apart force. 2) Von Mises stress in the

plate. 3) Von Mises stress in the pin.

Table 5-24. Monte Carlo simulation results for single parameter variations
St. Dev. Pin avm St. Dev. Pit avm
Individual parameters St. Dev. F (N) (MPa) (MPa)
Diametric interference 109 7 38
Coefficient of friction 66 <1 0
Plate Young's modulus 13 1 5
Pin diameter 6 1 1
Contact length 6 1 <1
Pin Poisson's ratio 4 <1 2
Plate Poisson's ratio 4 <1 2

CHAPTER 6
CONCLUSIONS

The diameters of 57 cortical pins from 10 donors were measured. Over a single pin,

the average diameter variation was found to be 9 tm with a standard deviation of 3 am.

The average range of pin diameters over single donors was found to be 12 am after

machining, 7 am after BioCleanseTM, 18 am after lyophilization, and 17 am after a thirty

second hydration.

The hole diameters of 60 cortical plates from 10 donors were measured. The

average diameter variation over a single plate was found to be 10-11 am. Over a single

donor, the average range of hole diameters was found to be 29 am after machining, 24

atm after BioCleanseTM, 23 atm after lyophilization, and 17 atm after a thirty second

hydration.

Lyophilization was found to have the largest effect on feature size. Cortical pin

diameters decreased by an average of 50 am after lyophilization while cortical plate hole

diameters decreased by an average of 29 am. Thirty seconds of immersion in water

caused the pins to regain an average of 11 am of diameter and the plate holes to regain an

average of 3 am of diameter.

Twenty assembled allografts were pulled apart with a mechanical tensile tester. The

average force required to separate the interference fit was 83.4 N with a standard

deviation of 25.9 N. Of the allografts without cracked cortical plates, the average pull-

apart force was 100.6 N with a standard deviation of 28.5 N. Of the allografts with

cracked cortical plates, the average pull-apart force was found to be 74.1 N with a

standard deviation of 19.8 N.

13% of the assembled allografts failed a manual pull-apart test. 57% of the

assembled allografts showed signs of cracking.

The sample size of allografts that were not cracked and were successfully pulled

apart is too small to derive a correlation between the predicted diametric interference and

the pull-apart force. Furthermore, any such correlation may be obscured by variations in

donor material properties.

A finite element model was created to model the interference fit. Average

geometric conditions from after lyophilization were used while material properties were

drawn from the literature. The maximum von Mises stress in the graft was found to be

between 34.6 MPa and 80.6 MPa. The pull-apart force required to separate the graft was

found to be between 94 N and 216 N.

An analytical model of the interference fit was used to create a Monte Carlo

simulation. A Monte Carlo simulation predicted diametric interference, the coefficient of

friction, and the plate modulus to be the most influential factors on the interference fit

pull-apart force. The simulation predicted diametric interference and elastic properties to

be the most influential factors affecting the state of stress in the cortical plates.

The Monte Carlo simulation accurately reflected the frequency of occurrence of

pull-apart and cracking failures at 13% and 57%, respectively. The simulation predicted

the average pull-apart force to be 133 N with a standard deviation of 141 N and the

average von Mises stress in the plate to be 65 MPa with a standard deviation of 39 MPa.

APPENDIX
APPENDIX MONTE CARLO SIMULATION MATLAB CODE

clear all
close all
clc

n = 25e4;

% Define variables
mean deltal = lle-6;
std deltal = 9e-6;
deltal = mean deltal
delta = deltal/2;

mean Ei = 9E9;
std Ei = le9;
Ei = mean Ei + std E:

mean Eo = 9E9;
std Eo = le9;
Eo = mean Eo + std E(

% number of Monte Carlo iterations

% diametral interference (m)

+ std deltal*randn(n, 1);

% pin modulus (N/m^2)

i*randn(n, 1);

% plate modulus (N/m^2)

o*randn(n, 1);

mean mui = 0.41; % pin Poisson's ratio
std mui = 0.15;
mui = mean mui + std mui*randn(n, 1);

mean muo = 0.41; % plate Poisson's ratio
std muo = 0.15;
muo = mean muo + std muo*randn(n, 1);

mean bl = 1.937e-3; % pin
std bl = 0.021e-3;
bl = mean bl + std bl*randn(n, 1);
b = bl/2; % pi

outer diameter

mean c = 1.2e-3; % plate outer radius (m)
std c = 0;
c = mean c + std c*randn(n, 1);

mean Kt = 1; % stress concentration factor
std Kt = 0;
Kt = mean Kt + std Kt*randn(n, 1);

axial contact length between pin and plate (m)
% Note: doubled L to account for 2 pins

mean L = 7e-3;
std L = 0.3e-3;

L = mean L + std L*randn(n, 1);

mean cof = 0.3; % coefficient of friction
std cof = 0.15;
cof = mean cof + std cof*randn(n, 1);

Failure stress of bone

Determine pressure, p (N/m^2)
= b./Eo.*((c.^2 + b.^2)./(c.^2 b.^2)
= delta./C;

% Calculate stresses
sigma r i = -Kt.*p;
sigma t i = -p;
sigma r o = -Kt.*p;
sigma t o = p.*(c.^2
stress (N/m^2)

muo) + b./Ei.*(l mui);

% pin tangential stress (N/m^2)
+ b.^2)./(c.^2 b.^2); % plate tangential

% pull apart force (N)
F = -2*pi*L.*b.*sigma r i.*cof;

% Find all force values greater than zero
Pos Force = find(F>0);

% Calculate the von Mises stress only for instances where F>0
sigma p i = (sigma r i(Pos Force).^2 -
sigma r i(Pos Force).*sigma t i(Pos Force) +
sigma t i(Pos Force).^2).^0.5;% pin
sigma p o = (sigma r o(Pos Force).^2 -
sigma r o(Pos Force).*sigma t o(Pos Force) +
sigma t o(Pos Force).^2).^0.5;% plate

%Calculate some statistical parameters
Fmean = mean(F)
Fstd = std(F)
PercFLessZero = length(find(F<0))/n*100
Sigmapin = mean(sigma p i)
StdSigmapin = std(sigma p i)
PercSMoreFail2 =
length(find(sigma p i>sigma fail))/length(Pos Force)*100
Sigmaplate = mean(sigma p o)
StdSigmaplate = std(sigma p o)
PercSMoreFail =
length(find(sigma p o>sigma fail))/length(Pos Force)*100

bins = 10000;
figure (1)
hist(sigma p i/le6, bins)
xlabel('\sigma (MPa)')
ylabel('Number of occurrences')
title('von Mises stress (pin)')

sigma fail

25e6;

set(gcf, 'color', 'white')
xlim([0 70])

figure(2)
hist(sigma p o/le6, bins)
xlabel('\sigma (MPa) ')
ylabel('Number of occurrences')
title('von Mises stress (plate)')
set(gcf, 'color', 'white')
xlim([0 250])

figure (3)
hist(F, bins)
xlabel('F (N)')
ylabel('Number of occurrences')
title('Force to pull apart')
xlim([-200,600])
set(gcf, 'color', 'white')

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BIOGRAPHICAL SKETCH

Nate Mauntler was born on April 10, 1981, the second of four sons of John and

Margaret Mauntler. He graduated from Troy High School in Troy, Ohio, in June of 1999.

Mr. Mauntler then left Ohio to pursue a Bachelor of Science degree in mechanical

engineering at the University of Florida, which was completed in May of 2004. Since that

time, Mr. Mauntler has been continuing his education at the University of Florida in

pursuit of a master's degree in mechanical engineering. This thesis was written in partial

fulfillment of this degree. Upon graduation, Mr. Mauntler will stay on at the University

of Florida Tribology Laboratory and Machine Tool Research Center to pursue a doctoral

degree.