Assessing bone healing in mandibular segmental repair : a simulation study

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1 The University of Toledo The University of Toledo Digital Repository Theses and Dissertations 2016 Assessing bone healing in mandibular segmental repair : a simulation study Bahram Raad University of Toledo Follow this and additional works at: Recommended Citation Raad, Bahram, "Assessing bone healing in mandibular segmental repair : a simulation study" (2016). Theses and Dissertations This Thesis is brought to you for free and open access by The University of Toledo Digital Repository. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of The University of Toledo Digital Repository. For more information, please see the repository's About page.

2 A Thesis Entitled Assessing Bone Healing in Mandibular Segmental Repair: A Simulation Study By Bahram Raad Submitted to the Graduate Faculty as partial fulfillment for the requirements of the Master of Science Degree in Mechanical Engineering Dr. Mohammad Elahinia, Committee Chair Dr. Mehdi Pourazady, Committee Member Dr. Lesley Berhan, Committee Member Dr. Amanda Bryant-Friedrich, Dean College of Graduate Studies The University of Toledo May 2016

3 Copyright 2016, Bahram Raad This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author.

4 An Abstract of Assessing Bone Healing in Mandibular Segmental Repair: A Simulation Study by Bahram Raad Submitted to the Graduate Faculty as partial fulfillment of the requirements for the Master of Science Degree in Mechanical Engineering The University of Toledo May 2016 Mandibular defects may result from trauma, tumor resection, or inflammation. The goals for mandibular reconstruction surgeries are to retrieve mandible functions, applications, and appearance. To this end, surgeons use a combination of bone grafts and metallic implants. Implants mechanical properties are drastically different from the surrounding bone. So, the density and stress distribution in the mandible changes after the surgery. In addition, the long-term abnormal stress/strain distribution may lead to graft failure due to bone resorption as a result of stress shielding and hardware failure due to stress concentrations. During the healing period of six to nine months, it is important to achieve complete immobilization and changing mandibular micro-motion down to the level of µm while chewing. After this period, it is desired that bone retrieve its normal density distribution as the success of the treatment. Although current stiff fixation hardware iii

5 accomplishes the immobilization during the healing period, over the long-term, the immobilized and stress-shielded engrafted bone tends to resorb. On the other hand, screw loosening or/and hardware fracturing is observed as the stress concentration at certain hardware locations. The first stage of this research is to investigate the problems encountered following a mandible reconstructive surgery. In this respect, we designed a finite element model of a healthy mandible, which includes cancellous and cortical bone, the periodontal ligament and teeth. Using this model, we studied a healthy adult mandible under maximum bite force for stress, strain, reaction force distribution, and bone density distribution. Stress distribution of the healthy mandible was then used as the criteria to show the problems of the current standard of care. For mandibular segmental reconstruction surgery, the current standard of care includes the use of Surgical Grade 5 titanium also known as Ti-6Al-4V hardware and a single/double fibula barrel vascularized bone graft. Our model which is designed for this study includes double barrel fibular bone graft containing a section of the mandible, metallic fixation hardware and screws. We found out that the stiffness mismatch between the bone and the fixation hardware causes stress concentration at the fixation hardware and screws and stress shielding on the bone graft and the host mandible. To improve the long-term outcome of using metallic implants, it is essential to recreate the normal density distribution and the stress pattern to achieve a faster bone healing period. To this end, we investigated the use of porous superelastic nitinol (NiTi) as a substitute for the currently used high stiffness titanium hardware. While nitinol has a iv

6 lower stiffness than titanium, it is possible to add porosity to reduce its stiffness, even more, to be closer to the stiffness of cortical bone. The ultimate goal is to design a fixation hardware that has proper stiffness for immobilization during remodeling the normal bone density distribution. Using an FE model of devices fabricated from titanium and nitinol, we have found that using porous superelastic nitinol hardware with conventional geometries leads to the recreation of normal density distribution, stress-strain trajectories, and finally better treatment outcome. v

7 To my kind wife

8 Acknowledgments Foremost, I would like to express my great gratitude to my advisor Professor Mohammad Elahinia for the continuous support of my study and research at the Dynamic and Smart Systems Laboratory; for his patience, motivation, enthusiasm and immense knowledge. He had a great influence on me, both as an individual and a researcher, and my sincere regards will be always upon him Besides, I would like to express my appreciation towards the members of my committee, Dr. Pourazady and Dr. Berhan for all their helpful and constructive suggestions and sharply logical comments of my work. I would also like to express my thanks to the faculty and staff of the M.I.M.E. department. I would like to thank my family, whom I miss so much, my parents and sister for their spiritual support and their long-distance love. I would finally like to thank my kind wife, Shiva RaissiCharnakani, without her unconditional support and sacrifices I would not have been able to complete this dissertation. Her love and encouragement has supported me throughout my graduate studies, and I thank her for all that he has done. vii

9 Table of Contents Abstract... iii Acknowledgments... vii Table of Contents... viii 1. Chapter one: Introduction Mandibular segmental defects surgery The principal risk for a mandibular implant failure Advantages of porous Nitinol fixation hardware Low stiffness Implant Integration Superelastic behavior Energy absorption Additive Manufacturing of the Nitinol Objective of study The use of stiffness-matched Nitinol fixation hardware Publications Chapter Two: Modeling and Material Properties Finite element modeling Material properties Model meshing Constraints, loadings and model validation Chapter Three: Bone Remodeling Algorithm Bone remodeling literature review Simulation of the bone remodeling behavior using User Material Subroutine Algorithm validation Chapter Four: Results and Discussion Effects on the bone remodeling Von Mises stress distribution viii

10 4.3. Normal mandibular masticatory loading Displacement distribution Compression/tension stress distribution Chapter Five: Conclusion... 3 References... ix

11 Chapter One Introduction 1.1. Mandibular segmental defects surgery Tumor resection, infection, trauma or chronic inflammation can lead to mandibular bone defects. The bone defects can be the reason of loss of speech and swallowing, airway obstruction, deformity, and impairment of mastication [1] if left untreated. The goal of mandibular reconstruction surgeries is to restore normal function and appearance of the mandible, including bone continuity, normal density distribution and stable dentition [2]. Almost none of the current reconstructive methods meet all of the requirements for full functional restoration [3, 4]. Based on each patient s needs, the surgeon should select a particular method knowing that each method has its cons and pros. However, the most prevalent method for doing a reconstruction surgery is to use one or more surgical grade 5 Titanium (Ti-6Al-4V) fixation hardware and a fibula vascularized bone graft [5-8] which is demonstrated in figure 1-1. The purpose of using fixation hardware is to stack up the junction between the newly grafted bone and the host mandible bone and to make them to fuse and heal together faster. The reason for using the barrel grafts is to provide the mandibular continuity, support chewing, and the proper floor for dental implant following the reconstruction surgery. As shown in figure 1-1, to attach the upper barrel to the superior border of the host mandible and provide the sufficient stability, mandibular reconstruction with a double barrel fibular graft often requires two additional mini-plates [9, 10]. 1

12 Figure 1-1 CT scan image after mandibular reconstruction showing a double bone graft and surgical grade 5 Titanium hardware [9]. Mandibular segmental defects can occur in different locations of the mandible and also different lengths. For smaller defects, the iliac crest is a good alternative for harvesting bone graft (e.g., <6 cm). Iliac crest grafts can supply proper mandibular height to support dental implants [11]. For larger defects, the fibula is a common site for bone graft harvesting (e.g., >6 cm) because it provides enough length while its removal causes minimal donor site morbidity [2, 11]. However the maximum fibular length is approximately 24 cm, it should be mentioned that the using of a very long segment of it would make a knee or ankle joint more unstable [9] [12]. The main disadvantage of the fibula graft is the lack of providing sufficient height and width for reliable dental implantation and the loss of mandibular contour [9, 13]. In addition, the graft provides less depth that results in more applied torque on the dental implant post [14]. The limited height can be compensated by using a double barrel fibula graft created by cutting a fibula into two segments (see figure 1-2) while preserving the blood supply, and then folding the 2

13 segments on top of each other [9]. It should be mentioned that microvascular surgery is needed to join the blood vessels that supply the bone, to blood vessels near the defect. Figure 1-2 Fibula Graft as A) single barrel, B) double barrel [15] 1.2. The principal risk for a mandibular implant failure The current standard of care for mandibular reconstruction surgery is the use of Ti- 6Al-4V (surgical grade 5 titanium) fixation hardware and autogenous graft. While the fixation hardware supplies required proper immobilization for the bone segments to heal following reconstructive surgery [5], they rarely allow normal stress-strain trajectories to recur along the mandible when healing occurs; the reason is the stress concentration/shielding caused by high stiffness of the titanium hardware [16]. Although hardware removal which should happen after bone healing would reduce stress concentrations/shielding, as well as the risk of infection, in most cases the Ti-6Al-4V hardware is not extracted because it could be associated with the loss of normal mandible contour and may disrupt the vascular supply of the underlying bone graft [17]. An optimal 3

14 reconstruction method should be developed to both restore the normal mandible mechanical properties once the bone is healed and provide immobilization during the healing period. If the titanium hardware and screws are left in the mandible after the bone has healed, it results in stress shielding due to its high stiffness (E=112 GPa) in comparison with the surrounding host mandible bone ( GPa). The stiffness mismatch causes an abnormal load sharing between the fixation hardware, barrel grafts and the host mandible. As a result, it may cause stress concentration on the screws and hardware and stress shielding from the surrounding bone. The mandible generally undergoes two major types of loading, bite forces, and muscle forces. The temporalis, masseter, and pterygoid muscles are the three most important muscles, which work together to open/close the mandible and provide positioning assistance even when the mandible is at rest. The quantity of muscle force depends on many factors including bite loading conditions (balanced/unbalanced loading, unilateral or bilateral loading, clenching, or grinding), and the teeth which are involved [18, 19]. Eventually, stress shielding on the surrounding bone may cause the grafted bone weakening, implant failure and dental implant loosening [20, 21]. The reason is that bone alters its internal structure (such as density) and external contour in response to mechanical forces based on the bone remodeling process. Bone remodeling is a physiological process that balances new bone absorption and bone resorption in response to variation in local mechanical stimuli to optimize load bearing function. The process will continue following mandibular reconstruction surgery until stress and strain levels return to normal [22]. Strain-adaptive bone remodeling theory can predict the amount of bone loss [23]. For the 4

15 case of Ti-6Al-4V fixation hardware, the high stiffness hardware reduces the load previously exposed on the grafted bone and those areas would remodel in response, both externally in the form of reduced thickness, and internally in the form of increased porosity. These resorption effects cause the bones to become weaker and more fragile. Additionally, the increased stress on the hardware and screws may eventually result in hardware failure and/or screw pullout [24]. Resorption resulting from stress shielding and/or the damage resulting from abnormal stress concentrations can contribute to the failure of an implant [25-27]. To overcome problems associated with stress shielding and/or stress concentrations, stiffness and the geometry should be optimized in the design of an implant. The geometry factors which affect the stress distribution on the bones surrounding the implant along the reconstructed mandible are as follows: the area of bone-graft interface, the radius of the graft, and the contour of any external components used to heal a mandibular defect [28, 29]. The effect of geometry changing also can be seen in other implants such as femur and hip. Most hip implants have distal stress concentration, leaving little stress in the proximal region of the femur. The increased density of bone in the distal region reduces axial stem displacement, and the reduced density of bone in the proximal region would make this area weaker and more fragile. To overcome this problem associated with abnormal stress distribution, a shorter stem is designed to reduce shear stress along the implant-host bone interface, and a proximal plate is also added to distribute the load over an entire cross-section of the femur [23]. The second method to overcome the stress shielding and/or stress concentration is to optimize the stiffness. One potential method to reduce stiffness of the implant is making 5

16 the implant porous, either distributed porosity or surface porosity which can only result in minor reduction in the stiffness [30], and the main purpose of adding surface porosity is to ease the bone ingrowth which would enhance osseointegration and anchorage in surrounding bone [31, 32]. On the other hand, an implant with distributed porosity has significantly less stiffness [33]. The level of stiffness can be altered and optimized by controlling the pore size, pore distribution and pore shape strategically during the design of the implant [34]. It is worth mentioning that an increase in porosity decreases the static and fatigue strength of an implant Advantages of porous Nitinol fixation hardware Generally, titanium alloys attach more quickly to the bone in comparison with cobalt-chromium alloys in long-term biomechanical use [35-37]. Surgical Grade 5 Titanium (Ti-6Al-4V) is a biocompatible Titanium based alloy that has numerous applications in the medical industry [38], and it has low density, high strength, high biocompatibility and a passive oxide biofilm at the surface of implants which resists corrosion after implantation [39]. Nickel-Titanium (Nitinol, NiTi) is an alloy that is currently used in medical applications such as orthodontic wire and stents. However, there is little clinical data on its use in bone immobilization fixation hardware. Nitinol offers the properties of shape memory, superelasticity, high damping capacity, wear resistance, and fatigue resistance [40-45]. Porous Nitinol could be specifically used for mandibular fixation hardware because it additionally offers lower stiffness, stronger bone-implant integration, superelasticity behavior and energy absorption. 6

17 Low stiffness The relatively low stiffness of nitinol has many applications in regenerative medicine such as bone implants. Nitinol s stiffness is tunable applying different levels of porosity through geometric design both at the microscopic and the macroscopic level [46]. It is important not to have stiffness mismatch between the host bone and the fixation hardware. As a result, the implant failure risk due to the stress shielding is minimized. As shown in Table 1-1, the stiffness of the mandible is changing locally, and it is in the range of GPa [46]. Table 1-1 Stiffness of mandible. Unit: GPa [30] Mandible Cortical bone Cancellous bone Symphysis Parasymphysis Angle Ramus Condyle Coronoid Based on the desired level of stiffness, the stiffness of Nitinol can be reduced even further by applying a specific level of porosity into the implant during alloying or during implant design. 7

18 Implant Integration Porosity not only could reduce the stiffness, but it also can improve the bone-implant incorporation [47]. The main purpose of making a metallic implant porous, specifically a solid nitinol implant, is to reduce the stiffness further. It is seen that vascular and cellular activities, and thereby blood clot formation, would increase within the porous Nitinol implant in comparison with solid Nitinol implants. Interconnecting pores within the implant would provide more space for bone ingrowth, more surfaces for bone-implant integration, and interlocking between the implant and surrounding bone [48]. The optimal pore size for bone tissue ingrowth under load bearing conditions is µm [49]. One important factor which affects bone ingrowth within the porous Nitinol implant is osseointegration and bone apposition. It can be defined as the formation of a direct interface between an implant and bone, without intervening with any soft tissue. An in vivo study has been done on a porous Nitinol and a dense Ti-6Al-4V implant in mature sheep lumbar spine for 3, 6, and 12 months. The results show that osseointegration of porous nitinol is better than Ti-6Al-4V over the recovery time [50]. Another study also has been done on the porous Nitinol implant into the femurs of rabbits for 15 weeks, to investigate whether any fibrous tissue would appear at the interface between implants and bone. The results confirm the excellent osseointegration of porous Nitinol implant (See figure 1-3). 8

19 Figure 1-3 Histological morphology of porous Nitinol at A) interface between implant and bone, and B) inner pores of the implant [51]. (Green: new mature bone, bright yellow: Achromycin, orange: osteoid tissue) Another important factor affecting implant integration is bone apposition which is defined as the bone tissue capacity to set itself to the surface material. It is an indicator for implant biocompatibility that leads to strength of the tissue implant interface. Textured and porous nitinol has shown more bone apposition due to more contact points and more 9

20 surface area [52]. An in vivo experiment has shown that bone apposition is much greater for porous Nitinol compared to currently used Ti-6Al-4V implants which are implanted in mature sheep lumbar spine for 3,6, and 12 months [50]. Additionally, the superelasticity and pore interconnectivity of porous Nitinol give the implant pump-like and capillary-like properties which cause the implant to absorb more fluid required for bone ingrowth from the surrounding area [53-55]. It should be pointed out that the material s wettability affects the fluid velocity within the interconnecting pores. Capillary force and wettability of the porous Nitinol implants act together to allow bone penetration through the pores into the internal area of the implant [56] Superelastic behavior Nitinol has a unique superelastic behavior similar to bone which differentiates it from all other materials. Superelasticity means that the material can be deformed more than the normal elastic behavior of materials, but this large deformation can still be recovered after unloading [57]. Figure 1-4 shows the superelastic behavior of bone and porous Nitinol. 10

21 Figure 1-4 Superelastic behavior of bone and Nitinol [5] Energy absorption Porous Nitinol provides a high damping capacity for use in energy absorbing structures due to a combination of its superelasticity and well-adjusted porosity. Nitinol implants can provide protection against the propagation of shock waves if it is subjected to shock loading. Absorbed energy would increase as the porosity increase within the implant. It is shown the amount of energy absorption of porous NiTi is more than Ti and Ti-6Al-4V of a certain amount of stress [58] Additive Manufacturing of the Nitinol Our group has established methodologies for fabricating and designing nitinol and titanium parts using a 3D Systems (Rock Hill, SC) Selective Laser Melting method (SLM) 3D printer. We have found that the additive manufacturing technology (AM) could result in better part performance in comparison with the other standard fabrication technologies in which the reactive properties, functional, and structural of nitinol are highly degraded 11

22 and influenced. Most of the recent nitinol applications have simple contours (e.g. bar, rod, tube, wire, sheet) because stress-induced martensite, burr formation, work hardening and spring back effects can make sharp machining difficult and can account for important tool wear. While conventional hot isostatic pressing, metal injection molding, and sintering have been used to fabricate porously, and dense nitinol made implants, an adequate technology for creating patient-specific implants with predefined and precise mechanical properties is AM. A chamber filled with Argon is required to minimize oxidation in an AM process of this alloy. As shown in Figure 1-5, the AM processes create 3D parts right from CAD data by adding material in successive layers. The powder material is accommodated by a roller in µm layers. Figure 1-5 Powder based additive manufacturing of Nitinol devices [59]. It is shown that Selective Laser Melting fabricated non-porous and porous nitinol parts created using pre-alloyed powders show homogeneous and high strength properties. In addition, additively manufactured parts are proved to have proper low impurity concentrations and meet the medical devices requirements (ASTM F ) [60]. It is probable to fabricate patient-specific implants with desired material/mechanical properties 12

23 through additive manufacturing. One of the applications of additively manufactured parts is the biomedical fixation hardware which is required for immobilization of bone grafts in a mandibular reconstruction surgery Objective of study One of the goals of this research is to investigate the current standard of care for mandibular defects reconstruction surgery. To this end, we started to study the mechanical and biomechanical behavior (displacement, strain, stress, and density) of a healthy mandible as the baseline of the simulations. Based on finite element simulations we assessed and contrasted the remodeled mandible bones for the following cases: 1) Healthy Mandible, 2) a reconstructed mandible using a double barrel graft and Ti-6Al-4V fixation hardware, and finally, 3) a reconstructed mandible using a double barrel fibular graft and Nitinol fixation hardware. It is worth mentioning that the segmental defect is designed to be in the M1-3 regions The use of stiffness-matched Nitinol fixation hardware One of the methods for improving the surgery outcome is using a fixation hardware with consonant stiffness to that of cortical bone. Solid NiTi is now getting used in the clinics for intravascular stent devices and orthodontic braces, so it is an adequate choice to be considered as the substitution of the currently used metallic fixation hardware (Ti-6Al- 4V). Solid NiTi has the stiffness of 38.5 GPa while the stiffness of Ti-6Al-4V is 112 GPa. To better scale the stiffness of the metallic fixation hardware with cortical bone of the 13

24 mandible ( GPa) [46], the stiffness of NiTi could be reduced even more through applying the porosity during SLM or topologically while implant design. Not only does this biocompatible biomaterial provide lower stiffness, but it also develops the impact attenuation possibility due to its superelastic behavior [61]. In this thesis we investigate using of stiffness matched porous NiTi fixation hardware as a substitute for conventional Ti-6Al-4V metallic hardware. We expect to have the stress transferred from the metallic fixation hardware to the fibula grafted bone as the patient attempts to have the full function (e.g., chewing). Hence, the nitinol fixation hardware and screws will have reduced stress concentration. We hypothesize that applying more force on the grafted bone will facilitate its strengthening and remodeling which may result in fewer resorption of the bone, a longterm reconstruction surgery that is less prone to failure, and normal chewing muscle power. In this research, we analyze and compare stress, strain and density distribution using finite element analysis, after a reconstruction surgery for the case of using high stiffness Ti-6Al- 4V fixation hardware and porous NiTi fixation hardware Publications B. Raad, N. S. Moghaddam and M. Elahinia, Improving bone healing in mandibular segmental repair by replacing Titanium fixation hardware with porous superelastic Nitinol Under Publication B. Raad, N. S. Moghaddam and M. Elahinia, A Comparison Between Porous NiTi and Ti-6Al-4V Fixation Hardware on Bone Remodeling After a Reconstruction Surgery ASME 2016 Conference on Smart Materials, Adaptive Structures, and 14

25 Intelligent Systems VirginiaTech, Blacksburg, American Society of Mechanical Engineers B. Raad, N. S. Moghaddam and M. Elahinia, Porous NiTi vs. Ti-6Al-4V Fixation Hardware Effect on Bone Remodeling After a Reconstruction Surgery RAPID 2016, Orlando, Florida B. Raad, N. S. Moghaddam and M. Elahinia, The Effect of NiTi Superelastic Fixation Hardware on Bone Remodeling SPIE Smart Structures/NDE 2016 Conference, Nevada B. Raad, N. S. Moghaddam and M. Elahinia, The Effect of Fixation Hardware Stiffness on the Mandibular Bone Remodeling During the Healing Period 10th World Biomaterials Congress, Montréal, Canada 15

26 Chapter Two Modeling and Material Properties 2.1. Finite element modeling We have created a computer-aided model of a normal mandible from CT scan data. The components of a normal mandible based on high-resolution patient s 3D CT-scan data. Different steps of this process which was created in Materialise Mimics (Materialise, Plymouth, MI) are shown below: Figure 2-1 CT-scan images in posterior-anterior direction 16

27 Figure 2-2 CT-scan images in top-bottom direction Figure 2-3 Separating Teeth, Cortical, and Cancellous 17

28 Figure 2-4 Final 3D Model To locate periodontal ligament, separate CT data is observed. In order to model and simulate a common mandibular reconstruction surgery, a segmental defect (in this case, left segment bearing M1-3) with 40 mm resected location from the normal mandible. Other necessary components for simulating the mandibular reconstruction surgery such as the metallic fixation hardware, screws, and the fibula graft, are all modeled in SolidWorks [62]. Dimensions of the lower fixation hardware are 1.5 mm 78 mm 4 mm and it has nine threaded holes [10]. The fixation hardware is usually deformed in the operating room by the surgeon to match the outer shape of the grafted bone and the inferior border of the mandible. The hardware is bent virtually to model the procedure. In the lower metallic fixation hardware, one of the screws is designed to be placed in each of the remaining host mandible segments and two screws on the fibula graft bone. Bicortical screws are used to fasten the large inferior fixation hardware to the bone (i.e., screws should be long enough 18

29 to pass the both lingual and buccal cortices of the bone) [10]. The diameter of the threaded screws is 1.4 mm, and the height of each of the single barrel grafts is 20 mm with 14 mm width. Two more mini pieces of hardware are required to fix the upper barrel graft; this can be seen in figure 2-5. Each mini-hardware is bent slightly to fit tightly onto both the mandible and grafted bone contour. All of the designed holes on the metallic fixation hardware are not useful for the surgery; the surgeon usually uses some of the holes along the mini-hardware and hardware for screw insertion. Three threaded holes are designed in each mini-hardware with dimensions of 1 mm 18 mm 2.8 mm. Only one screw is required to fix the upper fixation mini-hardware to the remaining host mandible, and one is needed to attach it to the fibula grafted bone. Unicortical screws are used to fasten the mini-hardware these screws are that only pass through the buccal cortex of the bone, with the diameter of 1.4 mm [10]. Two single barrel grafts are placed at the top of each other to create a double barrel graft and to best mimic the contour of the mandible; this almost always happens during surgery [10]. The double barrel graft has a height of 38 mm [12] (See figure 2-5). To simulate the case of using porous NiTi fixation hardware as a substitution for Ti-6Al-4V hardware, the effective porosity of the material is applied. 19

30 Figure 2-5 The components of the reconstructed mandible bone using a metallic fixation hardware [5] Material properties Table 2-1 summarizes the material properties of the model components [63-65]. The superelastic behavior of Nitinol was modeled using an Abaqus UMAT developed at Texas A&M University [66]. Cortical and cancellous bone were modeled as anisotropic material, and the other components were assumed as linear elastic. Table 2-1 Material Properties Cortical Symphysis regions Angle regions Rest of the mandible EX EY EZ υxy υyz υxz GXY GYZ GXZ 23, , , ,200 3,600 4,800 20, , , ,000 5,300 4,800 17, , , ,600 2,900 2,800 Cancellous Bone Teeth 17, , ,

31 Periodontal Ligament Porous Nitinol 20, , , Ti-6Al-4V 112, , , Cortical fibular graft 26, , , Cancellous graft fibular 1, , , Model meshing All the mandible components were meshed in Hypermesh (Hyperwork, MI, USA) with 4-node tetrahedral elements (C3D4). The proper number of the element are reported in Table 2-2 based on the mesh convergence analysis of each component. Table 2-2 The number of C3D4 elements for the model components based on convergence analysis. Model Component Element Type Total No. Resected mandible 3D, Solid, Tetrahedral, Deformable 218,328 Teeth (13 Total) 3D, Solid, Tetrahedral, Deformable 65,179 Ligaments (13 Total) 3D, Solid, Tetrahedral, Deformable 21,053 Top Graft 3D, Solid, Tetrahedral, Deformable 42,065 Lower Graft 3D, Solid, Tetrahedral, Deformable 45,037 Fixation hardware(s) 3D, Solid, Tetrahedral, Deformable 58,327 Screws (10 Total) 3D, Solid, Tetrahedral, Deformable 67,027 Then all meshed parts were assembled, and the possible interactions between fixation-host mandible, fixation-grafts, host mandible-grafts and constraints between screws-fixation, screws-host mandible, screws-graft, teeth-ligaments and host mandible- 21

32 ligaments were simulated [10]. Finally, all muscle forces related to the highest bite force during chewing (i.e., a 526N bite force on the right first molar tooth) were extracted from Korioth et al. [67]. Since the reconstruction surgery causes a reduction in chewing power, all the muscle force values were assumed to be of 60% of Korioth et al. values and applied to the model [10]. More details on the model development and boundary conditions are presented in previous studies [10, 64, 68] Constraints, loadings and model validation To restrain condylar movements in all three directions, we restrained 24 nodes on the outer cortical surface of each condyle [67]. In order to simulate the peak bite force, seven nodes of bite contact on the buccal cusps of the lower right first molar are constrained from moving in all three directions [10]. The force on the bite contact obtained from the experiment presented by Korioth et al. group was compared with our simulation results (Note: all the material properties, boundary conditions muscle forces and directions of our studies are taken from the study by Korioth et al.). For the experiment, the bite force at the right first molar tooth is 526 N. Our simulation results show the bite force of which is obtained by the summation of nodes reaction forces at the first molar tooth. The bite force which is obtained here shows an 3% discrepancy with the model presented by Korioth et al. (i.e., bite force is equal to 526 N) [67]. This discrepancy may be due to mandibular shape differences, the existence of periodontal ligament in our model, minor differences in the muscle attachment sites, and differences in the selection of the seven nodes. All muscle forces are distributed homogeneously across the area of attachment [69-71]. The area of attachment is approximated based on anatomical data for the mandible [9]. Muscle forces 22

33 are assumed to be 60% of the average value recorded for a normal mandible after mandibular reconstruction [10]. Since all of the muscles are restored to [72] their normal location following mandibular reconstruction surgery, small amounts [73] of the muscles would overlie the graft in some cases. Table 2-3 The muscle forces and muscle directions during peak-centric occlusal (chewing) force [74]. (The X vector is directed from right to left and is normal to the sagittal plane. The Y vector is directed from superior to inferior and is normal to the occlusal Muscle Group Working Side Balancing Side Masseter Superficial Deep 0.32i j k +0.27i j k 0.81i j 0.53k +0.67i j 0.44k Medial Pterygoid +1.09i j k 0.78i j k Temporalis Anterior Middle Posterior 0.19i j k +0.15i j k 1.07i j 2.43k +1.08i j 2.46k 0.72i j 2.95k +0.48i j 1.95k 23

34 3. Chapter Three: Bone Remodeling Algorithm 3.1. Bone remodeling literature review It was Wolff who first suggested that there is a relationship between bone structures and applied loads [75]. The bone acts as if it has some sensors that can measure the internal load and activate the bone cells to make the bone grow or resorb. This phenomenon is called bone remodeling, which is mainly associated with density which is an internal issue and/or geometric changes which is an external phenomena. There might be a stimulus for bone remodeling, which begins with bone resorption and then followed by bone formation [76, 77]. Numerous investigators have put forward quantitative numerical models for the prediction of bone remodeling. For example, Frost [78] proposed the 3-way Rule for external remodeling, taking into account a bone s end load and its local surface strain. He was able to use his theory to explain some of the known principal adaptations of lamellar bone, including trabecular thickening and straightening of bone to minimize bending stresses. A stress-based time-dependent theory for bone modeling and remodeling was presented by Beaupre et al. [79] who used it to determine the distribution of bone density within the proximal femur under an assumed normal loading history [80]. Huiskes et al. [81] used the strain energy density as a mechanical stimulus in their remodeling model and employed it in conjunction with the finite element method to consider the relationship between stress shielding and bone resorption in the placement of hip implants. The problem of stress-shielding induced by the prosthesis and the resulting bone resorption was also studied by McNamara et al. [82] who adopted a damage-based approach developed by 24

35 Prendergast and Taylor [83]. Bone resorption is a major problem in prosthetic implantation as it causes looseness at the bone-implant interface, thus undermining the integrity of the implant system [82, 84]. While stress-shielding (under load) is commonly regarded as a reason for bone resorption, high stresses (overload) at the interface has also been suggested as a contributing factor. According to the damage-repair theory, high loading can cause continuum damage in the bone. At the same time, since bone is an organic structure, it can repair the damage itself to some extent. However, if we have a high loading that the self-repair mechanism cannot keep pace with the increasing damage, overload resorption will occur. Huiskes and Nunamaker [85] reported bone absorption around orthopedic implants was associated with high peak stresses at the interface in the immediate postoperative stage. Quirynen et al. [86], in studying the performance of a certain dental implant system, concluded that increased marginal bone loss was associated with occlusal overloading. A numerical analysis of bone adaptation around an oral implant due to overload stress was recently carried out by Crupi et al. [87] using a modified version of the remodeling theory developed by Beaupre et al. [79]. Other suggested effects of overloading include the accumulation of damage that can cause fatigue failures of bones [88]. Jianying et al. [89] have proposed an alternative mathematical model for bone remodeling which can account for bone resorption due to both underload and overload. It is based on the theory proposed by Weinans et al. [90] who model bones as continuous materials and use the strain energy density as the stimulus for bone remodeling. It preserves most of the features of the original model for bone growth and underload resorption and thus allows comparison to be made readily between the new and old models. 25

36 3.2. Simulation of the bone remodeling behavior using User Material Subroutine Wolff s law was improved later by Beaupre [79, 80] in According to this theory, changes in bone density are a function of the mechanical stimulus. The local mechanical load can be measured from local strain and stress tensors in the bone. The rate of density change is defined as: = B( K) 0 < ρ ρ (3-1) Where B is a constant, U is the strain energy density (SED) and K is the reference SED, so U/ρ is the daily mechanical stimulus, and ρ is the ideal bone density. Young s modulus is also related to density via: E = Cρ^r (3-2) Where C is a constant [91], and in this paper r=2 [90]. Garijo et al. [92] have analyzed and verified the stability and convergence of this model numerically. For the reconstructed mandible with NiTi fixation hardware, two different UMATs were designed to be used in this process; one for modeling the superelastic behavior of the NiTi and the other one to simulate the bone remodeling algorithm. These two UMATs were linked together through a FORTRAN code and were called during the numerical simulation automatically by the FORTRAN program. The process is shown in the figure

37 Figure 3-1 Remodeling flow chart for a) Healthy and reconstructed mandible with Titanium b) reconstructed mandible with Nitinol The remodeling process used in our study is based on the theory proposed by Beaupre [79, 80] whose research extracted diagrams to compare three different bone behaviors during the remodeling process. Firstly, where the rate of bone remodeling is negative that causes bone resorption, dead zone where the remodeling rate is not significantly affected by the changes in the stress stimulus and finally where the bone remodeling has positive rate and more load causes higher remodeling rate. There are many 27

38 studies done on the spine, proximal femur, and hips or modeling mandibular issues such as dental implants [93-97] and orthodontic tooth movements [98, 99] using Beaupre model. Chen et al. have compared two different numerical approaches of element-based and nodebased using finite element tools [100] by applying Beaupre model (using a UMAT), on a simple model. They had also validated their subroutine with experimental CT data [101]. The subroutine that is being used in our simulations has also been applied to a similar simple model with the same dimensions, boundary conditions, loadings and meshing that had been used in Chen's study to validate the code. As a result, there was a good quantitative agreement between the density distribution of our and Chen's paper. In this paper, the density distribution and remodeling process of the mandible bone are being numerically simulated with two different fixation hardware of two distinct materials, having different levels of porosity. Finite Element Analysis applied using ABAQUS (Dassault Systèmes, Waltham, MA) with a user material subroutine (UMAT) to simulate the remodeling behavior. The simulations are divided into 100-time steps and at each time step, bone remodeling algorithm is embedded in the FE analysis to simulate bone behavior. In the mentioned subroutine, material properties are a function of density and these properties are evaluated by the estimation of the local density of the bone. The stimulus is obtained by strain and stresses; the rate of density change and density are stored into two solution-dependent state variables to be used in the next iteration [79]. 28

39 3.3. Algorithm validation To validate the bone remodeling algorithm, we replicated exact loadings and boundary conditions used in the J. Reina et al. [96] paper to repeat the results. To this end, the mandible was divided into seven different sections with its own kind of loading. Figure 3-2 Insertions of the different portions of mastication muscles and condyles support with closed mouth Table 3-1 Orientation of the forces exerted by the muscles on the left side and magnitude of forces in both sides, in the following cases: symmetrical incisive bite, canine bite with the right side, and mastication with right molars Muscle Orientation of the forces X Y Z Magnitude of the forces (N) Incisive Canine Molar R L R L R L Superficial masseter Deep masseter

40 Anterior temporalis Middle temporalis Posterior temporalis Medial pterygoid Lateral pterygoid Figure 3-3 shows three different sections of the mandible with their corresponding density distribution of the bone. Some CT images were taken from the actual mandible at the same sections by J. Reina et al. and are shown below. The similarity between our numerical results and the CTs is quite noticeable. It must be remembered that the geometry of these regions could not be measured exactly and was approximated. 30

41 Figure 3-3 Up: distribution of bone obtained in the reference simulation (a) incisive region, (b) premolar region, (c) region of the first molar. Down: CT images from the same points of the mandible. 31

42 4. Chapter Four: Results and Discussion 4.1. Effects on the bone remodeling We have established a comprehensive FE model to simulate using of stiffness matched porous Nitinol and stiff Titanium as the fixation hardware for reconstruction surgery. To investigate the outcome of using stiffness matched porous NiTi over traditional fixation hardware, the density distribution has been studied over the mandible and grafted bone through finite element analysis. Figure 4-1, 4-2 and 4-3 show the contours of density distribution on the healthy mandible bone under maximum biting and muscle forces; we could consider this contour as the baseline. Density distribution contours of the reconstructed mandible with stiff Titanium and superelastic porous Nitinol fixation hardware are presented in the figures 4-2 and 4-3. In these figures, the most focused region of the mandible is the grafts, after the healing period, where we need to have similar density distribution to the healthy mandible. As the baseline, density is represented in the range of 800 g/cm3 for the cancellous bone to 1800g/cm3 for cortical bone, based on CT scan images. The change in bone density with assigned mechanical parameters are displayed after 100-time steps. Results are shown both on the surface of the whole mandible. It is worth mentioning again that the density distribution of maximum chewing forces for the healthy mandible is chosen as the baseline. 32

43 Figure 4-1 Healthy Mandible Density Distribution Figure 4-2 Mandible with Ti-6Al-4V Fixation Hardware 33

44 Figure 4-3 Mandible with NiTi Fixation Hardware Figure 4-4 has divided the cortical layer of the mandible into six different regions to make a comparison between different three cases. It is worth mentioning that regions D and E are where the reconstruction surgery is applied, and it is expected to see the main difference in these regions. Figure 4-4 Different density regions 34

45 Region Healthy Mandible [g/cm3] Mandible with Ti Fixation Hardware [g/cm3] % Ti Error Mandible with NiTi Fixation Hardware [g/cm3] A B C D E F Table 4-1 comparison between numerical values of average density for the three cases Our results show that changes in density distribution occur in both cases of mandibular reconstruction. However, a more normal density distribution occurs along the mandible when using NiTi fixation hardware. The faster pace of bone remodeling, improvement in bone healing, and the long-term health of the reconstructed mandible are some of the consequences of using NiTi instead of Titanium. Table 4-1 is comparing the bone density distribution of the cortical layer after applying the bone remodeling algorithm quantitatively. We could find out from the table 35

46 that using superelastic Nitinol fixation hardware has an error of 8.9% while using Titanium fixation hardware causes and 15.5% of deviation from the baseline in the worst case scenario. In other words, the average density in the mandible with NiTi fixation hardware has more conformity with the normal mandible than the Ti-6Al-4V fixation hardware by the factors of and respectively. The error would be defined as: Error = 100 (4-1) 4.2. Von Mises stress distribution Figure 4-5 shows the Von Mises stress during unilateral mastication at the right M1 in the healthy adult mandible. The maximum stress regions happen on the right first molar tooth which is MPa, the coronoid process on the balancing side has the stress of MPa, the stress in the buccal alveolar ridge of the cortical mandible in the right molar area is equal to 16.9 MPa, and 12 MPa is the stress level at the neck of condylar process on the balancing side. It should be mentioned that on the periodontal ligament the maximum stress is 1.4 MPa. Figure 4-5 von Mises stress distribution for unilateral chewing at the right M1 of a normal mandible; A) buccal view, B) lingual view. Unit: MPa 36

47 4.3. Normal mandibular masticatory loading The results of our analyzes show displacement, Von Mises stress, and compression stress during normal mastication at the right M1 after mandibular defect reconstruction surgery Displacement distribution Figure 4-6 shows displacement contours: a) before loading, and b) after loading unilaterally. To show the results more clearly deformation is magnified 30 times since the displacement is small with a maximum of 0.48 mm. [ ] The displacement around the condyles and the local bite contact regions are very close to zero. It could be noticed that the regions of the non-working side such as balancing side, undergo higher deformation, so the highest stress is seen to be along the inferior corpus region and at the angle. Figure 4-6 The displacement distribution for the mandible during normal chewing at right M1: A) before chewing, and B) after chewing. Unit: Millimeter Compression/tension stress distribution Figure 4-7 demonstrates tension and compression contours as a result of normal chewing at the right molar M1. The areas under tension and compression are respectively 37

48 demonstrated in brown and white. Compression and tension are defined as hydrostatic pressure or the third invariant of the element stresses. As demonstrated in the figure, the buccal surface of the working side and the lingual surface of the balancing side corpus demonstrate compressive stress. Figure 4-7 The areas under compression and tension of a mandible for unilateral chewing at the right M1: A) buccal side, B) lingual side. (White and brown colors represent areas under compression and tension, respectively.) 38