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 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. 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 200-500 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 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 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 To my kind wife… 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 Table of Contents
Abstract ...... iii Acknowledgments ...... vii Table of Contents ...... viii
1. Chapter one: Introduction ...... 1 1.1. Mandibular segmental defects surgery ...... 1 1.2. The principal risk for a mandibular implant failure ...... 3 1.3. Advantages of porous Nitinol fixation hardware ...... 6 1.3.1. Low stiffness ...... 7 1.3.2. Implant Integration...... 8 1.3.3. Superelastic behavior ...... 10 1.3.4. Energy absorption ...... 11 1.4. Additive Manufacturing of the Nitinol ...... 11 1.5. Objective of study ...... 13 1.5.1. The use of stiffness-matched Nitinol fixation hardware ...... 13 1.6. Publications ...... 14 2. Chapter Two: Modeling and Material Properties ...... 16 2.1. Finite element modeling...... 16 2.2. Material properties ...... 20 2.3. Model meshing ...... 21 2.4. Constraints, loadings and model validation ...... 22 3. Chapter Three: Bone Remodeling Algorithm ...... 24 3.1. Bone remodeling literature review ...... 24 3.2. Simulation of the bone remodeling behavior using User Material Subroutine...... 26 3.3. Algorithm validation...... 29 4. Chapter Four: Results and Discussion ...... 32 4.1. Effects on the bone remodeling ...... 32 4.2. Von Mises stress distribution ...... 36
viii 4.3. Normal mandibular masticatory loading ...... 37 4.3.1. Displacement distribution ...... 37 4.3.2. Compression/tension stress distribution ...... 37 5. Chapter Five: Conclusion ...... 39 References ...... 42
ix 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 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 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 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 (17.6-31.2 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 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 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.
1.3. 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 1.3.1. 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 17.6-31.2 GPa [46].
Table 1-1 Stiffness of mandible. Unit: GPa [30]
Mandible Cortical bone Cancellous bone
Symphysis 18.9-22.3 2.3-3.6
Parasymphysis 17.6-23.5 1.5-2.6
Angle 21.3-25.7 2.5-4.5
Ramus 20.8-28.7 2.8-3.5
Condyle 21.9-26.4 1.8-2.6
Coronoid 25.6-31.2 2.6-3.3
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 1.3.2. 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 50-500 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 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 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].
1.3.3. 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 Figure 1-4 Superelastic behavior of bone and Nitinol [5].
1.3.4. 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].
1.4. 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 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 20-100 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 F2063-05) [60]. It is
probable to fabricate patient-specific implants with desired material/mechanical properties
12 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.
1.5. 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.
1.5.1. 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 mandible (17.6-31.2 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 long- term 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.
1.6. 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 Intelligent Systems. 2016. 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 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 Figure 2-2 CT-scan images in top-bottom direction
Figure 2-3 Separating Teeth, Cortical, and Cancellous
17 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 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 Figure 2-5 The components of the reconstructed mandible bone using a metallic fixation hardware [5].
2.2. 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
EX EY EZ XY YZ XZ GXY GYZ GXZ Cortical Symphysis 23,000.0 15,000.0 10,000.0 0.3 0.3 0.3 6,200 3,600 4,800 regions 20,000.0 12,000.0 11,000.0 0.3 0.3 0.3 6,000 5,300 4,800 Angle regions Rest of the 17,000.0 8,200.0 6,900.0 0.315 0.325 0.31 4,600 2,900 2,800 mandible Cancellous Bone 960.0 390.0 320.0 0.3 0.3 0.3 170 130 90 Teeth 17,600.0 17,600.0 17,600.0 0.25 0.25 0.25
20 Periodontal 2.7 2.7 2.7 0.45 0.45 0.45 Ligament Porous Nitinol 20,000.0 20,000.0 20,000.0 0.3 0.3 0.3 Ti-6Al-4V 112,000.0 112,000.0 112,000.0 0.3 0.3 0.3 Cortical fibular graft 26,800.0 26,800.0 26,800.0 0.3 0.3 0.3 Cancellous fibular 1,650.0 1,650.0 1,650.0 0.3 0.3 0.3 graft
2.3. 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 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].
2.4. 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 507.4 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 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 −0.32 + 1.37 + 0.65 +0.27 + 1.14 + 0.54 Deep −0.81i + 1.12j − 0.53k +0.67i + 0.93j − 0.44k Medial Pterygoid +1.09i + 1.76j + 0.82k −0.78i + 1.26j + 0.59k Temporalis Anterior −0.19i + 1.27j + 0.05k +0.15i + 1.01j + 0.04k Middle −1.07i + 4.08j − 2.43k +1.08i + 4.14j − 2.46k Posterior −0.72i + 1.61j − 2.95k +0.48i + 1.07j − 1.95k
23 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 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 post- operative 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 3.2. Simulation of the bone remodeling behavior using User Material Subroutine
Wolff’s law was improved later by Beaupre [79, 80] in 1990. 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:
= ( − ) 0 < ≤ (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 is the ideal bone density. Young’s modulus is also related to density via:
= ^ (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 3-1.
26 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 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 node-
based 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 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
Orientation of the forces Magnitude of the forces (N)
Muscle Incisive Canine Molar X Y Z R L R L R L
Superficial +0.41 +0.207 -0.885 76.2 76.2 87.6 110.4 106.6 38.1 masseter 9
Deep -0.358 +0.546 -0.758 21.2 21.2 37.5 47.3 45.7 16.3 masseter
29 Anterior +0.04 +0.149 -0.988 12.6 12.6 85.3 22.1 102.7 80.6 temporalis 4
Middle -0.500 +0.221 -0.837 5.7 5.7 45.9 19.1 57.4 50.7 temporalis
Posterior -0.855 +0.208 -0.474 3.0 3.0 31.8 19.7 40.8 40.8 temporalis
Medial +0.37 -0.486 -0.791 136.3 136.3 96.1 82.2 169.6 82.2 pterygoid 2
Lateral +0.75 -0.630 +0.174 61.9 61.9 28.7 62.1 33.5 23.9 pterygoid 7
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 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 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 Figure 4-1 Healthy Mandible Density Distribution
Figure 4-2 Mandible with Ti-6Al-4V Fixation Hardware
33 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 Healthy Mandible Mandible with Ti Fixation % Ti Mandible with NiTi Fixation Region [g/cm3] Hardware [g/cm3] Error Hardware [g/cm3]
A 1.74 1.71 1.7 1.71
B 1.42 1.42 0.0 1.42
C 1.67 1.59 4.7 1.59
D 1.67 1.41 15.5 1.52
E 1.42 1.32 7.0 1.34
F 1.74 1.71 1.7 1.71
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 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 0.911 and 0.845 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 23.79 MPa, the coronoid process on the balancing side has the stress of
17.65 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 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.
4.3.1. 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. [102-107] 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
4.3.2. 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 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 5. Chapter Five: Conclusion
Mandibular segmental defects commonly occur following treatment for benign tumor, trauma, and infections. The goal of mandibular reconstruction surgery is to repair the defect and restore chewing, swallowing, and speaking, as well as aesthetic form. The current standard of care for mandibular reconstruction is the use of Ti-6Al-4V fixation hardware and fibular graft, either single barrel or double barrel. One of the major problems associated with using permanent Ti-6Al-
4V fixation hardware is stress shielding on the grafted bone and stress concentration on the fixation
devices caused by the very stiff Ti-6Al-4V hardware. It should be noted that the high stiffness
hardware is essential to provide the required immobilization during the bone healing period, and
the healed graft/host junction is thereafter significantly stress-shielded.
The aim of this study was to find a solution to overcome the problems associated with
currently used fixation hardware to reach to a density distribution more similar to that of the normal
mandible. Long-term stress concentration at the fixation hardware and screws may put them at risk
for hardware failure or screw pullout. On the other hand, reduced stress on the grafted bone will
cause it to resorb, and it may finally fail completely. We wish to find a way to increase the stress
on the grafted bone and decrease the stress on the fixation hardware in order to minimize the risk
of failure caused by stress shielding. To do so, we first studied the behavior of a normal mandible
for stress and displacement trajectories under the maximum unilateral chewing at right M1. The
results for stress distribution of normal mandible will be used to be compared with the reconstructed
mandible.
The next step in our study is to simulate the current methods for mandibular reconstruction,
either the use of Ti-6Al-4V fixation devices and single barrel graft, or the same reconstruction using
39 double barrel graft. The FEA results showed that reconstruction using a double fibular barrel graft
helped recreate more normal stress-strain trajectories in the reconstructed mandible compared to a
single fibular barrel graft. It is shown that using a single fibular barrel graft removes stress from a
large portion of the mandible (i.e., the region between the top of the graft and occlusion surface).
Stress shielding can be observed in both cases, but the use of double barrel graft is more preferable
since it creates more normal stress distribution. It is helpful to find a reconstruction method to both
provide sufficient immobilization following the surgery as well as recreate normal stress distribution along the reconstructed mandible once the bone is healed. To this point, we are not aware of any attempts to optimize the geometry and/or stiffness of fixation devices to overcome the aforementioned problems.
We suggest the use of stiffness matched Nitinol hardware in order to minimize stress shielding caused by stiffness mismatching between the Ti-6Al-4V and bone. In order to match the stiffness of Nitinol with the surrounding bone, it is necessary to incorporate porosity into the implant to further reduce its stiffness. We expect to see more von Mises stress on the grafted bone and adjacent remaining mandible, less stress concentration on the fixation devices (e.g., fixation hardware and screws), while keeping an eye on the maximum gap distance at the aforementioned interfaces in order not to exceed 200-400 micron which is required for bone healing. The FEA results confirm the expectation from the suggested device. The increased load on the grafted bone, especially at the bottom regions, would drive remodeling of the cortical graft, especially by fusing the region between two fibula barrel grafts which will result in a single outer cortical shell around the graft that is better capable of carrying the normal load, especially after dental implantation. This would also increase the possibility of chewing power restoration as the reconstructed bone strengthened. Finally, the overall long-term stability of the reconstruction would be assured. We did both experimental and simulation studies in order to predict the level of porosity required for a
40 desired level of stiffness. In our study, we showed a porosity of 53% achieved a stiffness of 20
GPa, which is similar to that of cortical mandible bone.
It is useful to find another method to look at new geometries and a new range of stiffness- matching material properties to overcome the limitations associated with the previously suggested method, including not being able to restore chewing power completely. We suggest that a two stage mechanism which separates bone healing from bone restoration and regeneration may be more effective. The new mechanism utilizes a releasable Ti-6Al-4V bone fixation device and a wire- frame apparatus, the Bone Bandaid. The high stiffness fixation hardware will provide sufficient fixation of grafted bone during the healing period. The device is equipped with a releasable mechanism which allows it to unlock bone fixation in an outpatient procedure once the bone has healed. The unlocking of the immobilization hardware allows the wire frame apparatus to play the important role in redirecting the stress-strain distribution along the reconstructed mandible. The redirected stress-strain trajectory will facilitate bone remodeling of the graft, restoration of chewing power, and the stability of dental implants. Our FEA results for stage I show that the stress concentration on the grafted bone is increased and the stress concentration on the fixation devices is reduced. The results for stage II demonstrate that stress-strain trajectories along the grafted bone and mandible are more similar to a normal mandible.
41 References
1. SCHMITZ, J.P. and J.O. Hollinger, The critical size defect as an experimental
model for craniomandibulofacial nonunions. Clinical orthopaedics and related
research, 1986. 205: p. 299-308.
2. Schrag, C., et al., Complete rehabilitation of the mandible following segmental
resection.
Journal of surgical oncology, 2006. 94(6): p. 538-545.
3. Abukawa, H., et al., Reconstruction of mandibular defects with autologous
tissue- engineered bone. Journal of oral and maxillofacial surgery, 2004.
62(5): p. 601-606.
4. Abbas, A., Reconstruction skeleton for the lower human jaw using
CAD/CAM/CAE.
Journal of King Saud University-Engineering Sciences, 2012. 24(2): p. 159-164.
5. Shayesteh Moghaddam, N., et al., Enhancement of Bone Implants by
Substituting Nitonol for Titanium (TI-6AL-4V): A Modeling Comparison, in
ASME 2014 Conference on Smart Materials, Adaptive Structures and Intelligent
Systems. 2014: Newport, Rhoad Island.
6. Mataee, M.G., M.T. Andani, and M. Elahinia, Adaptive ankle–foot orthoses
based on superelasticity of shape memory alloys. Journal of Intelligent
Material Systems and Structures, 2014: p. 1045389X14544145.
42 7. Hadi, A., et al. Modeling and Experiment of a Flexible Module Actuated by
Shape Memory Alloy Wire. in ASME 2014 Conference on Smart Materials,
Adaptive Structures and Intelligent Systems. 2014. American Society of
Mechanical Engineers.
8. Elahinia, M., et al. Site-specific Material Properties And The Additive
Manufacturing Of Nitinol Musculoskeletal Implants. in TISSUE
ENGINEERING PART A. 2014. MARY ANN LIEBERT, INC 140
HUGUENOT STREET, 3RD FL, NEW ROCHELLE, NY 10801 USA.
9. Bähr, W., P. Stoll, and R. Wächter, Use of the “double barrel” free
vascularized fibula in mandibular reconstruction. Journal of oral and
maxillofacial surgery, 1998. 56(1): p. 38- 44.
10. Lovald, S.T., J.D. Wagner, and B. Baack, Biomechanical optimization of bone
plates used in rigid fixation of mandibular fractures. Journal of oral and
maxillofacial surgery, 2009. 67(5): p. 973-985.
11. Dinh, P., et al. Reconstruction of osteomyelitis defects. in Seminars in plastic
surgery. 2009. Thieme Medical Publishers.
12. He, Y., et al., Double-barrel fibula vascularized free flap with dental
rehabilitation for mandibular reconstruction. Journal of Oral and
Maxillofacial Surgery, 2011. 69(10): p. 2663-2669.
13. Bidabadi, M., A.H.A. Natanzi, and S.A. Mostafavi, Thermophoresis effect on
volatile particle concentration in micro-organic dust flame. Powder
Technology, 2012. 217: p. 69-76.
14. Lee, J., et al., Concomitant reconstruction of mandibular basal and alveolar
bone with a free fibular flap. International journal of oral and maxillofacial
43 surgery, 2004. 33(2): p. 150-156.
15. Goh, B.T., et al., Mandibular reconstruction in adults: a review. International
journal of oral and maxillofacial surgery, 2008. 37(7): p. 597-605.
16. Kennady, M.C., et al., Histomorphometric evaluation of stress shielding in
mandibular continuity defects treated with rigid fixation plates and bone grafts.
International journal of oral and maxillofacial surgery, 1989. 18(3): p. 170-174.
17. Boyd, T.G., et al., CASE REPORT Removal of Exposed Titanium Reconstruction
Plate After Mandibular Reconstruction With a Free Fibula Osteocutaneous Flap
With Large Surgical Pin Cutters: A Case Report and Literature Review. Eplasty,
2012. 12.
18. Tanaka, E. and J. Koolstra, Biomechanics of the temporomandibular joint.
Journal of dental research, 2008. 87(11): p. 989-991.
19. Kavanagh, E., et al., Use of finite element analysis in presurgical planning:
treatment of mandibular fractures. Irish journal of medical science, 2008.
177(4): p. 325-331.
20. Keller, E.E., D. Tolman, and S. Eckert, Endosseous implant and autogenous
bone graft reconstruction of mandibular discontinuity: a 12-year longitudinal
study of 31 patients. International journal of oral & Maxillofacial Implants,
1997. 13(6): p. 767-780.
21. Yarlagadda, P.K., M. Chandrasekharan, and J.Y.M. Shyan, Recent advances
and current developments in tissue scaffolding. Bio-medical materials and
engineering, 2005. 15(3): p. 159-177.
22. Print Ready 3D Model Lower Jaw Bone Human, The 3D Studio, Burbank, CA.
April 2014. 44 23. Van Rietbergen, B., et al., The mechanism of bone remodeling and resorption
around press-fitted THA stems. Journal of biomechanics, 1993. 26(4): p. 369-
382.
24. Nagasao, T., et al., A comparison of stresses in implantation for grafted and
plate-and- screw mandible reconstruction. Oral Surgery, Oral Medicine, Oral
Pathology, Oral Radiology, and Endodontology, 2010. 109(3): p. 346-356.
25. Joshi, M.G., et al., Analysis of a femoral hip prosthesis designed to
reduce stress shielding. Journal of biomechanics, 2000. 33(12): p. 1655-
1662.
26. Nagels, J., M. Stokdijk, and P.M. Rozing, Stress shielding and bone resorption
in shoulder arthroplasty. Journal of shoulder and elbow surgery, 2003. 12(1): p.
35-39.
27. Bahraminasab, M., et al., Aseptic loosening of femoral components–A review of
current and future trends in materials used. Materials & Design, 2012. 42: p.
459-470.
28. Sutradhar, A., et al., Topological optimization for designing patient-specific
large craniofacial segmental bone replacements. Proceedings of the
National Academy of Sciences, 2010. 107(30): p. 13222-13227.
29. Tie, Y., et al., Three-dimensional finite-element analysis investigating the
biomechanical effects of human mandibular reconstruction with autogenous
bone grafts. Journal of Cranio-Maxilofacial Surgery, 2006. 34(5): p. 290-298.
30. Greiner, C., S.M. Oppenheimer, and D.C. Dunand, High strength, low
stiffness, porous NiTi with superelastic properties. Acta Biomaterialia, 2005.
1(6): p. 705-716.
45 31. Kienapfel, H., et al., Implant fixation by bone ingrowth. Journal of arthroplasty,
1999.
14(3): p. 355-368.
32. Urban, R.M., et al., The Bone-Implant Interface of Femoral Stems with Non-
Circumferential Porous Coating. A Study of Specimens Retrieved at Autopsy*.
Journal of Bone And Joint Surgery, 1996. 78(7): p. 1068-81.
33. Wen, C., et al., Processing and mechanical properties of autogenous titanium
implant materials. Journal of Materials Science: Materials in Medicine, 2002.
13(4): p. 397-401.
34. Elahinia, M.H., et al., Manufacturing and processing of NiTi implants: A review.
Progress in Materials Science, 2012. 57(5): p. 911-946.
35. Jinno, T., et al., Osseointegration of surface‐blasted implants made of titanium
alloy and cobalt–chromium alloy in a rabbit intramedullary model. Journal of
biomedical materials research, 1998. 42(1): p. 20-29.
36. Andani, M.T. and M. Elahinia, A rate dependent tension–torsion constitutive
model for superelastic nitinol under non-proportional loading; a departure
from von Mises equivalency. Smart Materials and Structures, 2014. 23(1): p.
015012.
37. Andani, M.T., A. Alipour, and M. Elahinia, Coupled rate-dependent superelastic
behavior of shape memory alloy bars induced by combined axial-torsional
loading: a semi-analytic modeling. Journal of Intelligent Material Systems and
Structures, 2013: p. 1045389X13488251.
38. Elias, C., et al., Biomedical applications of titanium and its alloys. Jom, 2008.
60(3): p. 46- 49. 46 39. De Peppo, G., et al., Free-form-fabricated commercially pure Ti and
Ti6Al4V porous scaffolds support the growth of human embryonic stem
cell-derived mesodermal progenitors. The Scientific World Journal, 2012.
2012.
40. Reece, P.L., Progress in Smart Materials and Structures. 2007: Nova Publishers.
41. Mehrabi, R., et al., Microplane modeling of shape memory alloy tubes under
tension, torsion, and proportional tension–torsion loading. Journal of
Intelligent Material Systems and Structures, 2014: p. 1045389X14522532.
42. Elahinia, M., M.T. Andani, and C. Haberland, Shape memory and superelastic
alloys. High Temperature Materials and Mechanisms, 2014: p. 355.
43. Andani, M.T., M. Elahinia, and R. Rahmanian. Effect of loading rate on the
superelastic behavior of smas under multi-axial loading conditions; analytical
modeling and experiment. in SPIE Smart Structures and Materials+
Nondestructive Evaluation and Health Monitoring. 2013. International Society
for Optics and Photonics.
44. Andani, M.T. and M. Elahinia, Modeling and Simulation of SMA Medical
Devices Undergoing complex Thermo-mechanical Loadings. Journal of
Materials Engineering and Performance, 2014. 23(7): p. 2574-2583.
45. Andani, M.T., et al. Modeling of a Shape Memory Alloy Circular Bar Under
Combined Axial-Torsional Loading. in ASME 2012 Conference on Smart
Materials, Adaptive Structures and Intelligent Systems. 2012. American
Society of Mechanical Engineers.
46. Andani, M.T., et al., Metals for bone implants. Part 1. Powder metallurgy and
implant rendering. Acta biomaterialia, 2014.
47 47. Williams, D.F., On the mechanisms of biocompatibility. Biomaterials, 2008.
29(20): p. 2941-2953.
48. Wazen, R.M., et al., Initial evaluation of bone ingrowth into a novel porous
titanium coating. Journal of Biomedical Materials Research Part B: Applied
Biomaterials, 2010. 94(1): p. 64-71.
49. Kujala, S., et al., Effect of porosity on the osteointegration and bone
ingrowth of a weight-bearing nickel–titanium bone graft substitute.
Biomaterials, 2003. 24(25): p. 4691-4697.
50. Assad, M., et al., Porous titanium‐nickel for intervertebral fusion in a sheep
model: Part
1. Histomorphometric and radiological analysis1. Journal of Biomedical
Materials Research Part B: Applied Biomaterials, 2003. 64(2): p. 107-120.
51. Zhu, S., et al., Effect of porous NiTi alloy on bone formation: A comparative
investigation with bulk NiTi alloy for 15 weeks in vivo. Materials Science and
Engineering: C, 2008. 28(8): p. 1271-1275.
52. Assad, M., et al., Porous titanium‐nickel for intervertebral fusion in a sheep
model: Part
1. Histomorphometric and radiological analysis1. Journal of Biomedical
Materials Research Part B-Applied Biomaterials, 2003. 64(2): p. 107-120.
53. Zhu, S., et al., Effect of porous NiTi alloy on bone formation: A comparative
investigation with bulk NiTi alloy for 15 weeks in< i> vivo. Materials
Science & Engineering. C: Materials for Biological Applications, 2008. 28(8): p.
1271-1275.
54. Li, Y.-H., et al., The influence of porosity on corrosion characteristics of porous 48 NiTi alloy in simulated body fluid. Materials Letters, 2002. 57(2): p. 448-451.
55. Li, B.-Y., L.-J. Rong, and Y.-Y. Li, Stress–strain behavior of porous Ni–Ti
shape memory intermetallics synthesized from powder sintering. Intermetallics,
2000. 8(5): p. 643-646.
56. Hernandez, R., et al., Characteristics of porous nickel-titanium alloys for
medical applications. Bio-Medical Materials and Engineering, 2002.
12(1): p. 37-45.
57. Liu, X., et al., Relationship between osseointegration and superelastic
biomechanics in porous NiTi scaffolds. Biomaterials, 2011. 32(2): p. 330-338.
58. Köhl, M., et al., Characterization of porous, net-shaped NiTi alloy regarding its
damping and energy-absorbing capacity. Materials Science and Engineering: A,
2011. 528(6): p. 2454-2462.
59. Haberland, C., et al. Visions, concepts and strategies for smart Nitinol
actuators and complex Nitinol structures produced by Additive
Manufacturing. in ASME 2013 Conference on Smart Materials, Adaptive
Structures and Intelligent Systems. 2013. American Society of Mechanical
Engineers.
60. Haberland, C., et al., On the development of high quality NiTi shape memory
and pseudoelastic parts by additive manufacturing. Smart Materials and
Structures, 2014. 23(10): p. 104002.
61. Walker, J.M., Additive Manufacturing towards the Realization of Porous and
Stiffness- tailored NiTi Implants. 2014, University of Toledo.
62. Shayesteh Moghaddam, N., et al. Three dimensional printing of stiffness-tuned,
nitinol skeletal fixation hardware with an example of mandibular segmental
49 defect repair. in Procedia CIRP. 2015.
63. Andani, M.T., et al., Metals for bone implants. Part 1. Powder metallurgy and
implant rendering. Acta biomaterialia, 2014. 10(10): p. 4058-4070.
64. Nagasao, T., J. Miyamoto, and H. Kawana, Biomechanical evaluation of
implant placement in the reconstructed mandible. The International
journal of oral & maxillofacial implants, 2008. 24(6): p. 999-1005.
65. Shetty, P.P., et al., A finite element analysis for a comparative evaluation of
stress with two commonly used esthetic posts. European journal of dentistry,
2013. 7(4): p. 419.
66. Lagoudas, D.C., Shape memory alloys: modeling and engineering
applications. 2008: Springer.
67. Korioth, T.W., D.P. Romilly, and A.G. Hannam, Three‐dimensional finite
element stress analysis of the dentate human mandible. American Journal of
Physical Anthropology, 1992. 88(1): p. 69-96.
68. Shayesteh Moghaddam, N., et al., Improving bone implant success by using
nitinol as a substitute for titanium: A modeling comparison, in ASME 2014
Smart Materials, Adaptive Structures and Intelligent Systems. 2014: Newport,
Rhode Island.
69. Bidabadi, M., et al., Modeling flame propagation of micron-sized iron dust
particles in media with spatially discrete sources. Fire Safety Journal, 2014.
69: p. 111-116.
50 70. Bidabadi, M., et al., Modeling quenching distance and flame propagation speed
through an iron dust cloud with spatially random distribution of particles.
Journal of Loss Prevention in the Process Industries, 2016. 43: p. 138-146.
71. Bidabadi, M., et al., Modelling of combustion of a magnesium dust cloud in
heterogeneous media. Combustion, Explosion, and Shock Waves, 2014. 50(6):
p. 658- 663.
72. Shirani, M., et al. A Modified Microplane Model Using Transformation
Surfaces to Consider Loading History on Phase Transition in Shape Memory
Alloys. in ASME 2014 Conference on Smart Materials, Adaptive Structures
and Intelligent Systems. 2014. American Society of Mechanical Engineers.
73. Ahmadi, A., A Micromechanical-based Computational Framework for Modeling
the Mechanical Properties of the Metallic Parts Fabricated by Selective Laser
Melting. 2016, University of Toledo.
74. Van Eijden, T., J. Korfage, and P. Brugman, Architecture of the human
jaw‐closing and jaw‐opening muscles. The anatomical record, 1997. 248(3): p.
464-474.
75. Wolff, J., The law of bone remodelling. 2012: Springer Science & Business Media.
76. Burr, D.B., et al., Bone remodeling in response to in vivo fatigue microdamage.
Journal of biomechanics, 1985. 18(3): p. 189-200.
77. Frost, H., Presence of microscopic cracks in vivo in bone. Henry Ford Hosp
Med Bull, 1960. 8(2): p. 35.
78. Frost, H., Skeletal structural adaptations to mechanical usage (SATMU): 1.
Redefining Wolff's law: the bone modeling problem. The Anatomical Record,
1990. 226(4): p. 403- 413. 51 79. Beaupré, G., T. Orr, and D. Carter, An approach for time‐dependent bone
modeling and remodeling—theoretical development. Journal of Orthopaedic
Research, 1990. 8(5): p. 651-661.
80. Beaupré, G., T. Orr, and D. Carter, An approach for time‐dependent bone
modeling and remodeling—application: A preliminary remodeling simulation.
Journal of Orthopaedic Research, 1990. 8(5): p. 662-670.
81. Huiskes, R., et al., Adaptive bone-remodeling theory applied to
prosthetic-design analysis. Journal of biomechanics, 1987. 20(11-12): p.
1135-1150.
82. McNamara, B.P., D. Taylor, and P.J. Prendergast, Computer prediction of
adaptive bone remodelling around noncemented femoral prostheses: the
relationship between
damage-based and strain-based algorithms. Medical engineering & physics, 1997.
19(5): p. 454-463.
83. Prendergast, P. and D. Taylor, Prediction of bone adaptation using
damage accumulation. Journal of biomechanics, 1994. 27(8): p.
1067-1076.
84. Huiskes, R., et al., Adaptive bone-remodeling theory applied to
prosthetic-design analysis. Journal of biomechanics, 1987. 20(11): p.
1135-1150.
85. Huiskes, R. and D. Nunamaker, Local stresses and bone adaption around
orthopedic implants. Calcified tissue international, 1984. 36(1): p. S110-
S117.
86. Quirynen, M., I. Naert, and D. Van Steenberghe, Fixture design and overload
52 influence marginal bone loss and future success in the Brånemark® system.
Clinical oral implants research, 1992. 3(3): p. 104-111.
87. Crupi, V., et al., Numerical analysis of bone adaptation around an oral
implant due to overload stress. Proceedings of the Institution of Mechanical
Engineers, Part H: Journal of Engineering in Medicine, 2004. 218(6): p. 407-
415Frost, H.M., Wolff's Law and bone's structural adaptations to
mechanical usage: an overview for clinicians. The Angle Orthodontist, 1994.
64(3): p. 175-188.
88. Li, J., et al., A mathematical model for simulating the bone remodeling
process under mechanical stimulus. dental materials, 2007. 23(9): p. 1073-
1078.
89. Weinans, H., R. Huiskes, and H. Grootenboer, The behavior of adaptive bone-
remodeling simulation models. Journal of biomechanics, 1992. 25(12): p. 1425-
1441.
90. Rice, J., S. Cowin, and J. Bowman, On the dependence of the elasticity and
strength of cancellous bone on apparent density. Journal of biomechanics, 1988.
21(2): p. 155-168.
91. Garijo, N., et al., Numerical stability and convergence analysis of bone
remodeling model. Computer Methods in Applied Mechanics and Engineering,
2014. 271: p. 253- 268.
92. Chou, H.-Y., J.J. Jagodnik, and S. Müftü, Predictions of bone remodeling
around dental implant systems. Journal of Biomechanics, 2008. 41(6): p. 1365-
1373.
93. Hasan, I., et al., Computational simulation of internal bone remodelling 53 around dental implants: a sensitivity analysis. Computer methods in
biomechanics and biomedical engineering, 2012. 15(8): p. 807-814.
94. Lin, D., et al., Dental implant induced bone remodeling and associated algorithms.
Journal of the Mechanical Behavior of Biomedical Materials, 2009. 2(5): p. 410-
432.
95. Reina, J., et al., Numerical estimation of bone density and elastic constants
distribution in a human mandible. Journal of Biomechanics, 2007. 40(4): p.
828-836.
96. Wang, C., G. Fu, and F. Deng, Difference of natural teeth and implant-
supported restoration: A comparison of bone remodeling simulations. Journal
of Dental Sciences, 2015.
97. Bourauel, C., D. Vollmer, and A. Jäger, Application of bone remodeling
theories in the simulation of orthodontic tooth movements. Journal of
Orofacial Orthopedics/Fortschritte der Kieferorthopädie, 2000. 61(4): p. 266-
279.
98. Duerig, T., A. Pelton, and D. Stöckel, An overview of nitinol medical applications.
Materials Science and Engineering: A, 1999. 273: p. 149-160.
99. Chen, G., et al., Comparison of two numerical approaches for bone remodelling.
Medical engineering & physics, 2007. 29(1): p. 134-139.
100. Chen, G., et al., A new approach for assigning bone material properties from
CT images into finite element models. Journal of biomechanics, 2010. 43(5): p.
1011-1015.
101. Shahrokhabadi, S. and A. Ahmadi, Method of Fundamental Solution (MFS)
coupled with Particle Swarm Optimization (PSO) to determine optimal phreatic
54 line in unconfined seepage problem. Sci. Iranica. Trans. A, Civil Eng, 2013. 20:
p. 1327.
102. Shahrokhabadi, S., V. Khoshfahm, and H.N. Rafsanjani, Hybrid of natural
element method (NEM) with genetic algorithm (GA) to find critical slip
surface. Alexandria Engineering Journal, 2014. 53(2): p. 373-383.
103. Shahrokhabadi, S. and M. Toufigh, The solution of unconfined seepage
problem using Natural Element Method (NEM) coupled with Genetic
Algorithm (GA). Applied Mathematical Modelling, 2013. 37(5): p. 2775-2786.
104. Shahrokhabadi, S., M. Toufigh, and R. Gholizadeh. Application of Natural
Element Method in Solving Seepage Problem. in Geoenvironmental Engineering
and Geotechnics: Progress in Modeling and Applications. 2010. ASCE.
105. Shahrokhabadi, S., F. Vahedifard, and E. Ghazanfari. Modeling flow regime in
shale using isogeometric analysis. in Shale Energy Engineering 2014: Technical
Challenges, Environmental Issues, and Public Policy. 2014. ASCE.
55 106. Shahrokhabadi, S., F. Vahedifard, and S. Yarahmadian, Integration of Thiele
Continued Fractions and the method of fundamental solutions for solving
unconfined seepage problems. Computers & Mathematics with Applications,
2016. 71(7): p. 1479-1490.
56