Project 2 TMJ TJR Group 4

BIOE/ME C117 Project II - Group 4
Total Temporomandibular Joint Replacement
Leo Brossollet, Kristy Ip, Lulu Li, Josephine Wu
March 17, 2016
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Contents
1 Executive Summary 1
2 Introduction 1
3 Analysis of Load-Bearing Requirements 2
4 Stress Analysis of the Biomet Microﬁxation System 2
4.1 Overview of Failure Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . 2
4.2 Reasonable Failure Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.2.1 Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.2.2 Fatigue-Mediated Fracture . . . . . . . . . . . . . . . . . . . . . . . . 3
4.3 Loads and boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.4 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4.5 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.5.1 Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.5.2 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.5.3 Discussion of Wear . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.5.4 Discussion of Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.6 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.7 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5 Case Study 7
6 Discussion of Future Designs 8
7 Conclusion 8
A Relevant Equations 9
B Found or Assumed Material Properties 9
C Image J measurements 10
D Published Matlab Files and Code 10
List of Figures
1 Biomet Microﬁxation Device, adapted from [3] . . . . . . . . . . . . . . . . . 1
2 Normal and overload cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Measurements used to approximate geometry, adapted from [4] . . . . . . . . 10
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List of Tables
1 Summary of Key Outcomes from Stress Analysis Rows 1-2: Geometry and
Loading, Row 3: Yielding, Rows 4-6: Total Life Fatigue, Row 7: Defect
Tolerant Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
iii

1 Executive Summary
Total temporomandibular joint (TMJ) replacement is a last resort treatment for pro-
gressive TMJ disorders. TMJ replacement presents unique challenges, as the joint is bi-
condylar, small, and anatomically complex. Of three major devices available for TMJ
replacement, we chose to perform a stress analysis of the Biomet Microfixation system,
examining yield, fatigue, wear, and corrosion as potential modes of failure. It was con-
cluded that while the device is safe from purely mechanically failure, it is highly susceptible
to mechanically-induced biological failure such as inflammatory responses from wear and
corrosion debris.
2 Introduction
Temporomandibular joint (TMJ) disorders are uniquely difficult to treat due to the
small size and anatomical complexity of the joint [1]. The TMJ is a bicondylar joint, where
mechanical changes on one side affect the other [2]. Patients with TMJ disorders tend
to initially opt for non-surgical treatments, but because of the progressive nature of the
condition, about 1% of patients may eventually choose surgical treatments [1].
The most extreme and invasive of surgical options is total joint arthroplasty, or TMJ
replacement, and has success rates ranging from 30-100% [2]. The prosthesis includes a
temporal component, which replaces the glenoid fossa and interpositional disk to function
as an articular bearing. The device also has a mandibular component, which replaces the
condyle as a counter-bearing [1].
Figure 1: Biomet Microfixation Device,
adapted from [3]
The Biomet Microfixation TMJ im-
plant is one of three major systems avail-
able for TMJ replacement, and it is the
device we will be analyzing [Figure 1]. It
can be used for either unilateral or bilateral
joint reconstruction. The temporal compo-
nent of the system, also known as the fossa
prosthesis, is fixed to the base of the skull.
Made entirely of ultra high molecular weight
polyethylene (UHMWPE), the fossa pros-
thesis is about 25mm across and available
in small, medium, or large sizes [3, 4]. The
mandibular component of the system, also
known as the condylar prosthesis, is fixed
to the ramus. The component is primarily
made of cobalt-chrome (CoCr) alloy and its
underside is coated with a titanium plasma spray. The Biomet mandibular component is
45, 50, or 55mm long, paired with standard, offset, or narrow styles. Both the fossa and
condylar components are fixed with titanium screws [3].
In this report, we examine the load-bearing requirements of TMJ replacement sys-
tems, review relevant literature on failure modes, perform a stress analysis of the Biomet
Microfixation TMJ TJR system, and conclude with a discussion of implications for future
1

designs.
3 Analysis of Load-Bearing Requirements
The prosthesis must restore two primary functions of the joint: speech and mastication.
For both actions, the joint must have at least 50% of healthy translational and rotational
kinematics. There should be medial-lateral and anterior-posterior translation, and sagittal
and transverse plane rotation of the jaw. The TMJ is subjected to primarily compressive
and also shear loads under cyclic loading. Due to incongruent anatomy of the joint, the
contact area is quite small and experiences large stresses during loading [1]. In mastication,
incisors transfer the most force to the TMJ (60-90%), whereas molars transfer the least
(5-70%) [1, 5]. A TMJ replacement should be able to sustain 800N of compressive loads
and 200N of shear loads for 400,000 cycles per year. As many patients who undergo TMJ
replacement are in their 30s, the device should have a lifetime of at least 20 years [1].
This project examines possible failure mechanisms under normal loading conditions in the
Biomet TMJ replacement system.
4 Stress Analysis of the Biomet Microfixation System
4.1 Overview of Failure Mechanisms
Failure of TMJ total joint replacement (TJR) devices typically manifests as pain around
the joint space or a decrease in jaw mobility. Of the three devices on the market today,
there is not a significant depth of literature concerning the underlying mechanical failure
modes. It is reasonable to conclude that most TMJ TJR devices on the market today do
not fail due to yielding, fracture, or bending, but from wear, corrosion, infection, and other
biological responses. These latter failures are difficult to predict quantitatively.
In a study of 442 Biomet implants in 228 patients, removals of devices or revision
surgeries were prompted only by infection or bone formation around the joint space that
limited opening of the jaw [6]. While this was only a 3-year follow-up, other studies indicate
that revision surgeries with longer follow-up periods were caused by similar bone formation
[7, 8]. A 2007 follow-up of patients with custom TMJ Concepts devices revealed that
85% reported an increase in quality of life at 10 years [9]. The overall clinical success
and lack of revision surgery would suggest that these devices do not undergo mechanical
failure within 10 years. Another study looked at six patients that presented with symptoms
associated with fibrous capsule formation around the joint. Only one case of six presented
with inflammatory reactions in surrounding tissue, and none featured foreign body particles
in tissue surrounding the joint space [4]. In a study of 28 failed retrieved Christensen
implants, wear characteristics were observed and discussed, but the failure criteria and
modes were not explicitly defined [10]. As there is not a consensus in medical literature
suggesting preference for a specific failure mode, we will examine the Biomet Microfixation
device for failure in yield, fatigue, wear, and corrosion.
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4.2 Reasonable Failure Criterion
4.2.1 Yield
UHMWPE and CoCr are both ductile materials, as they yield before fracture. As
yielding causes plastic deformation in both materials, yielding in either could change the
geometry of the TJR system and result in significant discomfort or pain. Therefore we treat
yielding of either the UHMWPE or CoCr as failure. However, UHMWPE has a lower elastic
modulus and compressive strength, therefore we use a von Mises yielding criterion for the
UHMWPE to evaluate safety against yielding in the system. As yielding would precede fast
fracture from a single load cycle in this system, we next consider fatigue-mediated fracture.
4.2.2 Fatigue-Mediated Fracture
A total-life philosophy of fatigue and Miner’s rule are used to determine damage in-
curred in the device with daily use. Additionally, a defect-tolerant, crack-propagation
scheme is used to evaluate device susceptibility to crack growth and fast fracture. Al-
though susceptibility to failure by wear is difficult to quantify, we recognize and discuss
qualitative factors that affect wear mechanisms, including the Hertz contact stresses and
frictional forces at the contact surface that may liberate debris. Likewise, corrosion resis-
tance is assessed in terms of material properties of the components, device construction,
and implementation. Material properties for UHMWPE and CoCr are listed in 2.
4.3 Loads and boundary conditions
Two loading conditions are considered in the stress analyses: maximum bite force
(MBF, 800N) and chewing (mastication, 20-400N, 2000 cycles/day for 20 years) [1, 2]. The
resultant contact forces on the TMJ can be estimated to be at most 70% of the magnitude of
molar forces; load transfer ratios differ along the mandible and vary based on the dentition
and anatomy of each patient [1]. The joint reaction force is further simplified to be a point
load applied orthogonally to the articular surface, equal in both bearing surfaces. The
articular surfaces of the CoCr and UHMWPE are assumed to carry no bending moments,
though these may occur during eccentric loading or translation.
Grinding, gnashing, and clenching of the teeth (bruxism) represent dynamic and static
loading conditions that introduce significant shear stresses in the teeth, which may transfer
to the bone-implant interface and cause micromotion and implant loosening [11]. Stress
analyses of bruxism, condylar sliding, and traumatic impact are more complex than can
reasonably be approached in this project.
4.4 Geometry
The following analyses are performed assuming a convex CoCr condylar component
(radius = 5 mm) articulating upon a fixed, concave UHMWPE fossa component (radius =
6.5 mm). These dimensions were estimated by measuring images of a representative device
with SolidWorks and ImageJ [4] (see appendix C). Though simplification to a concave
spheroid is inaccurate (the UHMWPE fossa must permit translation), it is sufficient for
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this analysis. Furthermore, we altered the geometry and performed several fatigue analyses
to test the effect of varying thicknesses and radii of curvature. No analyses were performed
on any fixation element of the device in either the fossa or mandibular components, nor
on the Ti-alloy screws, as these geometries are hard to approximate and failure in fixation
elements was not seen clinically.
4.5 Analysis
4.5.1 Yield
Principal stresses in the articular surface of the UHMWPE are calculated from point
loads in MBF and mastication. Equations for Hertz contact theory were obtained [12] and
applied using a MATLAB script (Appendix D). Principal stresses are then used to calculate
the effective von Mises stress at three points in the UHMWPE: directly beneath the point
load, a distance of a away from the point load on the surface, and a distance of 0.51a
beneath the point load, where a is the radius of contact of the two surfaces. The maximum
von Mises stress between these points in the UHMWPE are compared to the compressive
yield strength of UHMWPE.
4.5.2 Fatigue
Device damage sustained in a single day’s use was calculated using Miner’s rule as-
suming 1800 cycles/day under typical masticatory loads in the TMJ (20-400 N) and 200
cycles/day under atypical conditions (20-800 N) [1, 2]. These forces are used to calculate
Hertz contact and effective von Mises stresses in the UHMWPE as described for yield.
Maximum differences in the von Mises stresses in both loading cases are taken as stress
amplitudes. Cycles to failure in UHMWPE at each stress amplitude are calculated from
a linear approximation to an S-N plot for UHMWPE, adapted from Basquin’s equation in
spite of compressive mean stress [13].
Figure 2: Normal and overload cycles
Additionally, a defect-tolerant fatigue
model will evaluate the UHMWPE compo-
nent’s susceptibility to fracture by cyclic
loading of a pre-existing crack, based on
both stress amplitudes used in the total-life
model. Initial crack length was chosen as 1
mm, based on what could be reasonably de-
tected in manufacturer inspection. Critical
stress intensity factor of 1.7 MPa
√
m, geo-
metric coefficient for single edge-notched ge-
ometry, 1.12, and the stress amplitude cor-
responding to typical mastication are used
to calculate critical crack length (ac = 127.3
mm) [13]. Paris equation constants for
UHMWPE are obtained from experimen-
tal values for 65 kGy remelted UHMWPE
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loaded sinusoidally at frequency of 3 Hz [14]. Cycles to failure under these conditions are
predicted by integrating the Paris equation over the initial and critical crack lengths.
4.5.3 Discussion of Wear
Fatigue may contribute to failure by wear, as wear particles are frequently liberated
as a result from fatigue crack propagation from subsurface defects resulting from shear
stress. Wear may be generated by friction forces resulting from translation of the convex
CoCr component against the UHMWPE, and cyclic loading of subsurface cracks to cause
delamination. Likewise, frictional forces may slough off asperities from the surface of the
UHMWPE and generate wear, and surrounding bone or metal debris may result in third
body wear. Wear rate studies are usually performed by the device manufacturer and dis-
closed to the FDA as preclinical testing. A Summary of Safety and Effectiveness document
for a similar TMJ replacement listed 0.010 mm
million cycles
of penetration and 0.39 mm3
million cycles
of volumetric wear [15].
Ultimately, wear particles may trigger an immune reaction in the surrounding tissue,
which can lead to revision surgery if the patient experiences pain or discomfort. Wear
particles can also elicit an immune response which results in bone resorption and implant
loosening [1]. Frictional force can be estimated as the product of compressive force and the
coefficient of friction between CoCr and UHMWPE (max ≈ 800 ∗ 0.094 = 75 N), though
further quantitative analysis of wear is beyond the scope of this project [16].
4.5.4 Discussion of Corrosion
Given the complex and changing conditions in vivo, it is important to consider corro-
sion as a possible mechanism for failure. From the surgery for device implantation, there
will be an inflammatory response which triggers production of hydrogen peroxide, proteins,
and cytokines. Subsequently, the device will continue to be exposed to biofilms, proteins,
and joint fluids. These biological factors contribute to changes in the pH of the environ-
ment surrounding the implant, and ultimately accelerate corrosion processes of the TMJ
prosthesis [17].
In the Biomet Microfixation prosthesis, the condylar surface is at greatest risk for cor-
rosion [10]. The condylar component is primarily made of CoCr but coated with Ti, which
has better corrosion resistance, but presents risk for galvanic corrosion [17]. Manufacturers
should minimize rough surfaces, which are at risk for delamination, which are at risk for
corrsion. Once corrosion begins to roughen the surface of a device, it leaves the implant
susceptible to further corrosion [10].
There is evidence of pitting corrosion and deposited corrosion products in retrieved
failed TMJ implants. Most often, there was a loss of the Ti coating on the condylar head,
and underneath, scratches, surface breakdown, and surface cracking [10]. In the absence
of infection, corrosion products were usually the cause of local pain or swelling in patients.
Release of metal ions into tissue also induced cytotoxic responses such as decreased enzyme
activity, carcinogenicity, mutagenicity, skeletal and nervous system disorders. In addition to
biological failure, corrosion weakened the devices, thereby limiting lifespan and accelerating
mechanical failure mechanisms [17].
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Table 1: Summary of Key Outcomes from Stress Analysis Rows 1-2: Geometry and Load-
ing, Row 3: Yielding, Rows 4-6: Total Life Fatigue, Row 7: Defect Tolerant Fatigue
Case 1 Case 2 Case 3 Case 4 Case 5
Normal Cycle Forces, Overload Cycle Forces [N]
20-400,
20-800
20-400,
20-800
20-400,
20-800
20-400,
20-800
20-400,
20-800
Radius of Condyle, Radius of Fossa,
Thickness of Fossa [mm]
5, 6.5, 11 5, 10, 11 5, ∞, 11 5, 6.5, 5 5, 10, 5
Magnitude of Maximum von Mises Stress [MPa],
Factor of Safety
4.79, 4.38 8.03, 2.62 12.7, 1.65 6.79, 3.09 11.38, 1.84
Stress amplitude:
Normal, Overload [MPa]
2.40, 3.39 4.02, 5.68 6.39, 9.02 3.41, 4.8 5.7, 8.04
Estimated Years until
Crack Initiation at 2000/day
10% Overload 12962 2245 147 4427 331
100% Overload 5777 632 25 1469 64
Damage at 20 years of 10% Overload 0.0015 0.0089 0.1364 0.0045 0.061
Critical Flaw Size [mm],
Years to Fast Fracture with Initial Flaw 0.5 mm
126,
3.9e11
45,
1.5e11
18,
6e10
63,
2.1e11
22,
7.5e10
4.6 Results
Results for yield and fatigue analysis are in Table 1. Case 1 corresponds to the geometry
and load conditions described in this report thus far. Cases 2-5 are exploratory alterations
of geometry and load conditions in order to account for error in these assumptions. These
cases can be viewed as variations in the conformity of the articulating joint.
Effective von Mises stresses were calculated in the UHMWPE component as described
above using Hertz contact theory. Maximum von Mises stress and factor of safety against
yield, assuming an engineering compressive yield strength of UHMWPE of 21 MPa [13], are
in row 3. The minimum factor of safety for MBF is thus 4.38 for the described loading and
the prosthesis will not yield during use. Additionally, the CoCr condyle, with engineering
compressive yield strenght exceeding 655 MPa, will not yield [18]. As conformity decreases,
maximum effective von Mises stress increases as the contact area decreases.
Damage calculations to determine failure by fatigue in the total-life model are rep-
resented in Table Y1, and were obtained using Miner’s rule. Damage accumulated from
20 years of 90% typical and 10% atypical cyclic loading was 0.0015. Miner’s rule predicts
failure when damage, a dimensionless number, reaches 1. By these calculations, no flaws
will initiate and propagate in the UHMWPE within the expected lifetime of the device.
Similarly, evaluation of CoCr susceptibility to flaw initiation under the total-life fatigue
model was ignored because flaws are expected to form in UHMWPE before CoCr.
Number of cycles to failure was obtained by integrating the Paris equation with respect
to crack length over initial and critical lengths in mm. This was found to be 2.88e17 cycles,
or 3.94e11 years, which far exceeds the expected number of cycles experienced in a device’s
lifetime. Additionally, the stress intensity range ∆ K calculated for the typical mastication
case is 0.1067 MPa
√
m, which appears below experimental threshold values for fatigue
crack propogation in the Paris regime. At the stress amplitudes expected in the TMJ, the
prosthesis will not propagate a crack of initial length visible to the naked eye to critical
length; fast fracture will not occur, and the device is expected not to fail by fatigue fracture.
6

4.7 Limitations
UHMWPE and CoCr components of the device were considered to be linear, elastic,
homogeneous, and isotropic materials for simplicity of calculations. However, UHMWPE is
a viscoelastic material and thus experiences time- and temperature-dependent mechanical
behavior. Sustained load or deformation were not considered in the stress analyses, and
potentially would have provided examples of stress relaxation or creep. Bruxism, especially
during sleep, has been studied in finite element analyses with viscoelastic consideration of
the UHMWPE [11]. These considerations were omitted in this study to simplify calculations
and because patients who habitually exhibit this type of behavior are often not selected for
TMJ TJR procedures [15]. Additional complexity in evaluation of fatigue behavior of the
UHMWPE was omitted; though considered ductile, UHMWPE is sensitive to peak stress
intensity factor and behaves more similarly to a brittle material at the advancing crack tip.
Joint reaction forces in the TMJ were estimated from bite forces, which are easily
obtained and found in literature. A previous attempt to calculate joint reaction forces in
the TMJ utilized a static force analysis including muscle forces from the masseter, pterygoid,
and temporalis groups [19]. This approach was not feasible due to the numerous attachment
points of the muscles and their respective lines of action, and was abandoned in favor
of estimating with bite force [1]. Ultimately, this simplified method for calculating joint
reaction forces at the articular surface of the TMJ prosthesis insufficiently captures the
complex mechanics of the jaw. The transfer of loads in the oral cavity (by the teeth, muscles,
and mandible) to the TMJ vary widely with patient anatomy and loading conditions, but
were simplified here with generalized values and ratios from the textbook.
The stress analysis was calculated by hand using these simplified conditions and as-
sumptions. An FEA analysis would provide more accurate results, and also analyze stresses
and moments in other regions of the prosthesis and bone. One failure mode neglected in
this analysis is fracture, yield, and fatigue in the Ti screws; the effect of stress concentra-
tors in the device such as screws could have been characterized by FEA as well. Additional
failure modes such as dislocation, stress shielding, and loosening from micromotion were
unexamined. Effect of varied placement of the device was not considered either.
5 Case Study
One of the most well-known recalled TMJ implants was the Proplast-Teflon interpo-
sitional jaw implant (a.k.a. IPI), widely used in the 1980s and early 1990s. Proplast is a
composite made of carbon and polytetrafluoroethylene, initially used in orthopedic femoral
and total hip surgeries [1]. Teflon (PTFE) was selected for its known biocompatibility.
While the initial assessment of the implant had high success rates, many follow-up studies
showed patients experiencing chronic inflammatory responses. The FDA issued a recall and
re-examination of the Proplast-Teflon implant in December 1990[20]. Since the recall, TMJ
implants have been reclassified as Class III devices in the FDA, and many follow-up case
studies have been done to further examine the cause of failure of the Vitek implant [1].
In a long-term analysis published in 1993, many of the Vitek Proplast-Teflon TMJ
implants were removed from patients who received the implant between 1983 and 1987.
Removal surgeries indicated that all joints and the implant exhibited abnormalities. Micro-
7

motion of tissues surrounding the implant caused foreign-body giant-cell reactions. Excess
loading caused the fragmentation of the implant in situ, which manifested as pain and de-
creased function for the patients. These fragmentations are directly linked to the progressive
bone degeneration 1-2 years after implantation [21].
Another follow-up case study, published in 2003, evaluated the Vitek Proplast-Teflon
TMJ implant in 32 patients in the United States [22]. Each patient was assessed for pain,
response to sensory stimuli, quality of life, and autoimmunity. The case study found that
there was a high correlation between myofascial pain and fibromyalgia. From patients’ blood
samples, abnormal percentages of T-lymphocytes were found, suggesting their compromised
immune system have been compromised.
The failure to predict biomechanical stresses in the body caused the failure of the
Vitek Proplast-Teflon implant. Despite biocompatibility, PTFE tends to disintegrate in
load-bearing joints and wear poorly. Despite the initial warnings from DuPont, supplier of
Teflon, Vitek manufactured the device [23]. Due to early pre-market approval, the necessary
long term studies were never performed, leading to the eventual recall of the device [23].
6 Discussion of Future Designs
Preliminary tissue-engineered models for a TMJ disk consist of a polymer scaffold
seeded with chondrocytes and cultured with select growth factors to optimize cartilage
tissue growth [24]. Poly-L-lactic acid (PLLA) non-woven meshes have been identified as
a viable scaffolding material and a spinning method has been optimized for incorpora-
tion of cells [25]. Transforming growth-factor-beta-1 was found to stimulate collagen and
glycosaminoglycan production, which improves tissue mechanics [26]. Tissue engineering
allows the regeneration of cartilage that is otherwise unable to self-repair, thus eliminating
the need for TMJ reconstruction in patients with deficient disks.
Similar to tissue engineering, 3D printing introduces a new degree of tailorability, which
is beneficial to a joint as complex as the TMJ. In 2012, a 3D-printed jaw was successfully
implanted into a 83-year-old patient. The implant, made of Ti powder with a bioceramic
coating, was constructed in thousands of thin layers and then melted together. The proce-
dure lasted one fifth of the time of a standard replacement surgery [27]. Customized fit to
a patient’s unique anatomy reduces the risk of chronic inflammation. Further experimenta-
tion and investigation is required to assess the performance and biocompatibility of these
future designs.
7 Conclusion
Stress analysis on the TMJ total joint replacement indicates that the predominant
modes of failure occur in the form of biological reactions. These occur due to unpredictable
loading and sub-optimal placement of the implant. To correct these issues, future designs
are aim to increase tailorability to patient-specific anatomy.
8

A Relevant Equations
Von Mises Effective Stress
σeffV.M. =
1
√
2
(σ1 − σ2)2 + (σ2 − σ3)2 + (σ3 − σ1)2 (1)
Factor of Safety Against Yielding
XV.M. =
σyield
σeffV.M.
(2)
Critical Stress Intensity
(
KIC
1.12∆σ
)2 1
pi
= acrit ⇐⇒ KIC = 1.12∆σ
√
acritπ (3)
Miner’s Rule damage in one block consisting of k different stress amplitudes
D =
k
i=1
ni
Nf,i
(4)
Basquin Equation
σa = σf (Nf )b
(5)
Kurtz’s Approximation of the Basquin Equation for UHMWPE [13]
σa = 26.3 − 2.38log(Nf ) (6)
Paris Law
da
dN
= C(∆K)m
= C(1.12∆σ
√
π)m
(7)
Paris Law Integrated Form
N =
1
C(1.12∆σ
√
π)m
2
m − 2
[a
(1−m
2
)
crit − a
(1−m
2
)
i ] (8)
B Found or Assumed Material Properties
Table 2: Material Properties
Material
Elastic
Modulus
Poisson
Ratio
Yield
Strength
Coeffecient
of Friction
UHMWPE 1000 [MPa] 0.3 21 [MPa][13]
0.094 [16]
Cobalt Chrome 210*10ˆ3 [MPa] 0.3 655 [MPa][18]
9

C Image J measurements
Figure 3: Measurements used to approximate geometry, adapted from [4]
D Published Matlab Files and Code
10

1
Table of Contents
Fatigue Analysis Total Life ME C117 TMJ TJR ...................................................................... 1
Initiate radii of curvature ...................................................................................................... 1
Normal loading condition ..................................................................................................... 1
Second Loading Condition .................................................................................................... 2
Calculate factor of Safety Against Yielding ............................................................................. 3
Plot two separate loading cycles. ........................................................................................... 3
Calculate damage per loading block ....................................................................................... 4
Plot approximation for S-N curve. ......................................................................................... 5
Assume all cycles are worst case ........................................................................................... 6
Initialize constants for crack propagation constants ................................................................... 7
Other Cases ........................................................................................................................ 8
Fatigue Analysis Total Life ME C117 TMJ TJR
clear all; close all; clc;
Initiate radii of curvature
cocrcurve = 0.005; % [m] Curvature Radius of CoCr Condyle
polycurve = 0.0065; % [m] Curvature Radius of UHMWPE Bearing Surface
tpoly = 11; % [mm] thickness of fossa
Normal loading condition
display('CONTACT STRESS CALCULATIONS------------------------------------')
n1 = 1800;
Fmax1 = 400; %N
Fmin1 = 20; %N
display(' ')
display('--------------------Normal Cycle Stresses--------------------')
display(' ')
%Call function, get min and max stress in UHMWPE
[maxstate1, r_max1] = Hertzcase1(tpoly,cocrcurve,polycurve,Fmax1);
maxstate1 = 1/1000*maxstate1; %turns maxstate from kPa to MPa
%maxstate comes out in the form of principal stresses of three different
%points. Each row gives the principal stress state of three critical
%points. Using these outputs we then calculate the vonmises stress at each
%of these three points.
VMmax1 = zeros(3,1);
for i = 1:1:3
VMmax1(i) = 1/sqrt(2)*sqrt(...
(maxstate1(i,1)-maxstate1(i,2))^2+...
(maxstate1(i,3)-maxstate1(i,1))^2);
end

2
VMmax1;
%repeat for the minimum force loading.
[minstate1, r_min1] = Hertzcase1(tpoly,cocrcurve,polycurve,Fmin1); %[kPa,m]
minstate1 = 1/1000*minstate1 ;%turns minstate from kPa to MPa
VMmin1 = zeros(3,1);
for i = 1:1:3
VMmin1(i) = 1/sqrt(2)*sqrt(...
(minstate1(i,1)-minstate1(i,2))^2+...
(minstate1(i,2)-minstate1(i,3))^2+...
(minstate1(i,3)-minstate1(i,1))^2);
end
VMmin1;
%find stress amplitudes at three different points.
stressamps1 = VMmax1-VMmin1;
display(' ')
display('Stress amplitudes [MPa] at points a, b, and c in the contact region are:'
display(' ')
display(num2str(stressamps1'))
display(' ')
CONTACT STRESS CALCULATIONS------------------------------------
--------------------Normal Cycle Stresses--------------------
Stress amplitudes [MPa] at points a, b, and c in the contact region are:
0.75106 2.4034 0.83256
Second Loading Condition
n2 = 200;
Fmax2 = 800; %N
Fmin2 = 20; %N
display('--------------------Overload Cycle Stresses--------------------')
display(' ')
[maxstate2, r_max2] = Hertzcase1(tpoly,cocrcurve,polycurve,Fmax2);
maxstate2 = 1/1000*maxstate2; %turns maxstate from kPa to MPa
VMmax2 = zeros(3,1);
for i = 1:1:3
VMmax2(i) = 1/sqrt(2)*sqrt(...
(maxstate2(i,3)-maxstate2(i,1))^2);
end
VMmax2;
%Minimum force loading is the same as above.
minstate2 = minstate1;

3
VMmin2 = VMmin1;
stressamps2 = VMmax2-VMmin2;
display('Stress amplitudes [MPa] at a, b & c in the contact region are:')
display(' ')
display(num2str(stressamps2'))
display(' ')
% The maximum nominal stresses and stress amplitudes for both loading
% cycles occur at point B, which is beneath the surface of impact. This
% concurs with Hertzian contact stress theory. Now we proceed using these
% amplitudes for the two loading cycles to construct a loading block.
--------------------Overload Cycle Stresses--------------------
Stress amplitudes [MPa] at a, b & c in the contact region are:
1.0601 3.3925 1.1752
Calculate factor of Safety Against Yielding
display('YIELDING--------------------------------------------------------')
display(' ')
yieldstress = 21; %[MPa]
maxVMstress = max([VMmax1; VMmax2]);
FOS = yieldstress/maxVMstress;
display('Factor of safety againsty yielding in the UHMWPE is ')
display(' ')
display(num2str(FOS))
display(' ')
YIELDING--------------------------------------------------------
Factor of safety againsty yielding in the UHMWPE is
4.3802
Plot two separate loading cycles.
%Store the stressamplitudes of different loading cycles more conveniently.
amp1 = stressamps1(2);
amp2 = stressamps2(2);
%find the mean stress of the loading cycles
center1 = (VMmax1(2)+VMmin1(2))/2;
center2 = (VMmax2(2)+VMmin2(2))/2;
t = 0:0.01:1;
figure()
plot(t,-amp1/2*cos(2*pi*t+pi)-center1,'-c')
hold on
plot(t,-center1*ones(size(t)),'c')

4
plot(t,-amp2/2*cos(2*pi*t+pi)-center2,'-k')
plot(t,-center2*ones(size(t)),'k')
xlabel('Number of cycles')
ylabel('Stress [MPa]')
title('Superimposed Plot of Two Loading Cycles')
legend1 = legend(['F = 20-400 N, for 1800 cycles, amp = ' num2str(amp1) ' MPa'],..
['Mean of First Cycle = ' num2str(-center1) ' MPa'],...
['F = 20-800 N, for 200 cycles, amp = ' num2str(amp2) ' MPa'],...
['Mean of Second Cycle = ' num2str(-center2) ' MPa']);
set(legend1,...
'Position',[0.339282711599545 0.8025310879018 0.352053679868847 0.109641132047
hold off
Calculate damage per loading block
display('TOTAL LIFE PHILOSOPHY-------------------------------------------')
display(' ')
% Calculate cycles to fail for both stress amplitudes
N1 = 10^((amp1-26.3)/-2.38);
N2 = 10^((amp2-26.3)/-2.38);
% Calculate damage per cycle and damage per block
d1 = 1800/N1;
d2 = 200/N2;
dblock = d1+d2;

5
% Damage at 20 years
d20years = dblock*365*20;
% Calculate blocks (days) to fail
days = 1/dblock;
years = days/365;
display('--------------------90% Normal, 10% Overload--------------------')
display(' ')
display('For a daily loading block of 2000 cycles a day, with 1800 at')
display('20-400 N and 200 at 20-800 N the days to crack initiation is: ')
display(' ')
display([num2str(round(days)) ' days, which corresponds to: '])
display(' ')
display([num2str(round(years)) ' years of loading.'])
display(' ')
if years>20
display('Crack initiation is not predicted at the 20 year mark.')
else
display('Crack initiation is predicted to occur by the 20 year mark.')
end
display(' ')
TOTAL LIFE PHILOSOPHY-------------------------------------------
--------------------90% Normal, 10% Overload--------------------
For a daily loading block of 2000 cycles a day, with 1800 at
20-400 N and 200 at 20-800 N the days to crack initiation is:
4731159 days, which corresponds to:
12962 years of loading.
Crack initiation is not predicted at the 20 year mark.
Plot approximation for S-N curve.
%approximation for S-N curve was taken from "UHMWPE Biomaterials Handbook"
%by Steven M. Kurtz. Full citation is in bibliography
N = logspace(0,12);
S = 26.3-2.38*log10(N);
Srunout = 26.3-2.38*log10(10^7);
Srunouty = Srunout*ones(size(N));
figure()
semilogx(N,S,'g',N,Srunouty,'m')
hold on
plot(N1,amp1,'sk','MarkerSize',10,'MarkerFaceColor','k')
plot(N2,amp2,'sc','MarkerSize',10,'MarkerFaceColor','c')
ylim([0,30])
legend2 = legend('S-N Relation [Kurtz, 2016]','Endurance Limit',...
'Fatigue life for first loading cycle','Fatigue life for second loading cycle'

6
set(legend2,...
'Position',[0.485581906264082 0.7487183317985 0.376904010815683 0.146449226378
xlabel('N [cycles]')
ylabel('Stress Amplitude [MPa]')
title('S-N approximations for UHMWPE')
Assume all cycles are worst case
display('--------------------0% Normal, 100% Overload--------------------')
display(' ')
Ntotal = N2;
baddays = N2/2000;
badyears = baddays/365;
display('100% Overload')
display(' ')
display('For a daily loading of 2000 cycles a day at 20-800 N,')
display('the number of days to crack initiation is: ')
display(' ')
display([num2str(round(baddays)) ' days'])
display(' ')
display('which corresponds to: ')
display(' ')
display([num2str(round(badyears)) ' years of loading.'])
display(' ')
if badyears>20
display('Crack initiation is not predicted in the device lifetime.')

7
else
display('Crack initiation is predicted to occur by the 20 year mark')
end
display(' ')
--------------------0% Normal, 100% Overload--------------------
100% Overload
For a daily loading of 2000 cycles a day at 20-800 N,
the number of days to crack initiation is:
2108557 days
which corresponds to:
Crack initiation is not predicted in the device lifetime.
Initialize constants for crack propagation con-
stants
display('DEFECT TOLERANT PHILOSOPHY--------------------------------------')
display(' ')
ai = .5; % [mm]
m = 5.81;
c = 3.6*10^-4;
Kc = 1.7;
amp = amp1; %use amplitude from the overload cycle for a worst case eval.
ac = (1/pi)*(Kc/(1.12*amp))^2; % [m]
acrit = ac*1000; % [mm]
display('Critical Crack Length [mm] = ')
display(' ')
display(num2str(acrit))
display(' ')
%calculate N to fast fracture
N = (2/(m-2))*(1/(c*1.12*amp*sqrt(pi)))^m*(ac^(1-m/2)-ai^(1-m/2));%[cycles]
%Convert to years
yearsprop = N/(2000*365);
display('Years until crack reaches critical length = ')
display(' ')
display(num2str(yearsprop))
display(' ')
DEFECT TOLERANT PHILOSOPHY--------------------------------------
Critical Crack Length [mm] =

8
126.9585
Years until crack reaches critical length =
394721969501.4122
Other Cases
% fatigueanalysis is just a function that runs the above script for given
% radii of curvature of CoCr and UHMWPE.
i = 1;
case2=[0.005,0.01,11];
case3=[0.005,10^200,11];
case4=[0.005,0.0065,5];
case5=[0.005,0.01,5];
cases = {case2, case3, case4, case5};
fatigueanalysis(cases{i})
i = i+1;
1.2576 4.0243 1.394
1.7751 5.6804 1.9677
YIELDING--------------------------------------------------------
2.6159
--------------------90% Normal, 10% Overload--------------------

9
--------------------0% Normal, 100% Overload--------------------
100% Overload
230505 days
45.2834
150382382858.7352

10
i = i+1;
1.9963 6.3881 2.2129
2.8178 9.017 3.1236
YIELDING--------------------------------------------------------
1.6479
--------------------90% Normal, 10% Overload--------------------

11
--------------------0% Normal, 100% Overload--------------------
100% Overload
9135 days
17.9707
60193815295.0555

13
i = i+1;
1.0643 3.4058 1.1798
1.5023 4.8074 1.6653
YIELDING--------------------------------------------------------
3.091
--------------------90% Normal, 10% Overload--------------------
--------------------0% Normal, 100% Overload--------------------
100% Overload
536367 days

14
63.2217
208012183088.887

15
1.7821 5.7027 1.9755
2.5155 8.0496 2.7885
YIELDING--------------------------------------------------------
1.846
--------------------90% Normal, 10% Overload--------------------

16
--------------------0% Normal, 100% Overload--------------------
100% Overload
23292 days
22.5499
75459288807.5621

1
% Lulu Li 23459552 December 2014
% Hertz contact stress
% N/mm; MPa
% tm - thickness of CoCr in m
% tp - thickness of UHMWPE in m
% Rff - radius of curvature - femoral frontal
% Rfs - radius of curvature - femoral sagittal
% Rtf - radius of curvature - tibial frontal
% Rts - radius of curvature - tibial sagittal
function [SigmaH1, contrad1] = Hertzcase1(tp,Rff,Rtf,Force)
% ------- Constants ---------
Ep = 1e3; % Elastic modulus of UHMWPE [MPa]
Em = 210e3; % Elastic modulus of CoCr [MPa]
P1 = Force; % [N]
Rfs = Rff; %spherical assumed. [m]
Rts = Rtf; %spherical assumed. [m]
% ----- Stresses ------
SigmaH1 = zeros(3,3); % SigmaH1(1,:) = principle stresses for A
% ----- Calculate Hertz contact stresses at contact point -----
[S,contrad1] = modHertz(P1,Rff,Rfs,-Rtf,-Rts,0,tp,Em,Ep,0.3); % contrad is the a v
Taumax = (1/3)*-S(3);
% Principle stresses for point A
SigmaH1(1,1) = S(1);
SigmaH1(1,2) = S(2);
SigmaH1(1,3) = S(3);
% Principle stresses for point B
SigmaH1(2,1) = (2*Taumax)+S(3);
SigmaH1(2,2) = S(3);
SigmaH1(2,3) = (2*Taumax)+S(3);
% Principle stresses for point C
SigmaH1(3,1) = (1/3)*(1-2*0.3)*-S(3);
SigmaH1(3,2) = (1/3)*(1-2*0.3)*S(3);
SigmaH1(3,3) = 0;
end
Published with MATLAB® R2014a

1
% Lulu Li 23459552 December 2014
function[S,a]=modHertz(P,R1,R1p,R2,R2p,psi,tp,E1,E2,v)
% P - applied load
% R1 - radius of curvature of metal - frontal, Rtf
% R1p - radius of curvature of metal - sagittal, Rts
% R2 - radius of curvature of polyethylene - frontal, Rff
% R2p - radius of curvature of polyethylene - sagittal, Rfs
% tp - thickness of plastic, tp
% E1 - elastic modulus of metal, Em
% E2 - elastic modulus of polyethylene, Ep
% v - Poisson's ratio - 0.3
% Gives Sz, Sy, and Sx at the point of contact; gives a, radius of contact
% - but the area of contact is not circular!
n1=(1-v^2)/E1;
n2=(1-v^2)/E2;
BplusA=0.5*(1/R1+1/R1p+1/R2+1/R2p);
BminusA=0.5*((1/R1-1/R1p)^2+(1/R2-1/R2p)^2+2*(1/R1-1/R1p)*(1/R2-1/R2p)*cos(2*psi))
Kappa=-0.87*(BminusA/BplusA)+0.92;
Beta=-0.48*(BminusA/BplusA)+0.96;
D=Beta*(3*P*(n1+n2)/(4*BplusA))^(1/3);
C=D/Kappa;
Sz=-1.5*P/(pi*C*D)*(-4.140/tp^2+4.960/tp+0.5656);
Sx=2*v*Sz+(1-2*v)*Sz*(D/(C+D));
Sy=Sx;
S=[Sx Sy Sz];
a=sqrt(C*D);
end
Published with MATLAB® R2014a

References
[1] Pruitt L, Chakravartula A. Mechanics of biomaterials. Cambridge: Cambridge Univer-
sity Press; 2011.
[2] Huang H, Su K, Fuh L, Chen M, Wu J, Tsai M et al. Biomechanical analysis of a
temporomandibular joint condylar prosthesis during various clenching tasks. Journal
of Cranio-Maxillofacial Surgery [Internet]. 2015 [cited 16 March 2016];43(7):1194-1201.
Available from: http://www.sciencedirect.com/science/article/pii/S1010518215001201
[3] [Internet]. Biomet.com. 2016 [cited 16 March 2016]. Available from: Biomet website
(link abbreviated)
[4] Westermark A, Leiggener C, Aagaard E, Lindskog S. Histological ﬁnd-
ings in soft tissues around temporomandibular joint prostheses after up
to eight years of function. International Journal of Oral and Maxillofacial
Surgery [Internet]. 2011 [cited 16 March 2016];40(1):18-25. Available from:
http://www.sciencedirect.com/science/article/pii/S0901502710004029
[5] Smith D, McLachlan K, McCall W. A Numerical Model of Temporomandibular Joint
Loading. Journal of Dental Research [Internet]. 1986;65(8):1046-1052. Available from:
http://jdr.sagepub.com/content/65/8/1046.full.pdf
[6] Giannakopoulos H, Sinn D, Quinn P. Biomet Microﬁxation Temporo-
mandibular Joint Replacement System: A 3-Year Follow-Up Study of Pa-
tients Treated During 1995 to 2005. Journal of Oral and Maxillofacial
[7] Pinto L, Wolford L, Buschang P, Bernardi F, Gon¸calves J, Cassano D. Maxillo-
mandibular counter-clockwise rotation and mandibular advancement with TMJ
Concepts R total joint prostheses. International Journal of Oral and Maxillofa-
cial Surgery [Internet]. 2009 [cited 16 March 2016];38(4):326-331. Available from:
http://www.sciencedirect.com/science/article/pii/S0901502708004189?np=y
[8] Guarda-Nardini L, Manfredini D, Olivo M, Ferronato G. Long-Term Symptoms Onset
and Heterotopic Bone Formation around a Total Temporomandibular Joint Prosthe-
sis: a Case Report. JOMR [Internet]. 2014 [cited 16 March 2016];5(1). Available from:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4007372/
[9] Mercuri L, Edibam N, Giobbie-Hurder A. Fourteen-Year Follow-Up of a Patient-Fitted
Total Temporomandibular Joint Reconstruction System. Journal of Oral and Maxillo-
facial Surgery [Internet]. 2007 [cited 16 March 2016];65(6):1140-1148. Available from:
[10] Kerwell S, Alfaro M, Pourzal R, Lundberg H, Liao Y, Sukotjo C et al.
Examination of failed retrieved temporomandibular joint (TMJ) implants. Acta
Biomaterialia [Internet]. 2016 [cited March 16 2016];32:324-335. Available from:
30

[11] Abe S, Kawano F, Kohge K, Kawaoka T, Ueda K, Hattori-Hara E et al. Stress analysis
in human temporomandibular joint affected by anterior disc displacement during pro-
longed clenching. J Oral Rehabil [Internet]. 2013 [cited March 16 2016];40(4):239-246.
Available from: http://www.ncbi.nlm.nih.gov/pubmed/23398635
[12] Bartel D, Bicknell V, Wright T. The effect of conformity, thickness, and material on
stresses in ultra-high molecular weight components for total joint replacement. The Jour-
nal of Bone and Joint Surgery [Internet]. 2016 [cited 16 March 2016];68-A(7). Available
from: http://jbjs.org/content/jbjsam/68/7/1041.full.pdf
[13] Kurtz S. UHMWPE biomaterials handbook. Amsterdam ; London: Academic Press;
2009. 694-700. https://books.google.com/books?isbn=0323354351
[14] Sirimamilla A, Furmanski J, Rimnac C. Peak stress intensity factor gov-
erns crack propagation velocity in crosslinked ultrahigh-molecular-weight
polyethylene. Journal of Biomedical Materials Research Part B: Applied Bio-
materials [Internet]. 2012 [cited 16 March 2016];:n/a-n/a. Available from:
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3825479/
[15] P980052 Summary of Safety and Effectiveness [Inter-
net]. FDA.gov. 2016 [cited 16 March 2016]. Available from:
http://www.accessdata.fda.gov/cdrh docs/pdf/P980052b.pdf
[16] Kutz M. Handbook of Materials Selection [Internet]. Google Books. 2016 [cited 16
March 2016]. Available from: https://books.google.com/books?isbn=0471359246
[17] Royhman D, Radhakrishnan R, Yuan J, Mathew M, Mercuri L, Sukotjo C. An
electrochemical investigation of TMJ implant metal alloys in an artificial joint
fluid environment: The influence of pH variation. Journal of Cranio-Maxillofacial
[18] ASTM F75 CoCr Alloy [Internet]. Arcam.com. 2016 [cited 16 March 2016]. Avail-
able from: http://www.arcam.com/wp-content/uploads/Arcam-ASTM-F75-Cobalt-
Chrome.pdf
[19] Ackland D, Moskaljuk A, Hart C, Vee Sin Lee P, Dimitroulis G. Prosthesis Load-
ing After Temporomandibular Joint Replacement Surgery: A Musculoskeletal Mod-
eling Study. Journal of Biomechanical Engineering [Internet]. 2015 [cited 16 March
2016];137(4):041001. Available from: http://www.ncbi.nlm.nih.gov/pubmed/25565306
[20] Burlington B, Gundaker W. Important Information About TMJ Im-
plants [Internet]. Fda.gov. 2016 [cited 16 March 2016]. Available from:
http://www.fda.gov/MedicalDevices/Safety/AlertsandNotices/PublicHealth
Notifications/ucm243871.htm
[21] Feinerman D, Piecuch J. Long-term retrospective analysis of twenty-three Proplast R -
Teflon R temporomandibular joint interpositional implants. International Journal of
31

Oral and Maxillofacial Surgery [Internet]. 1993 [cited 16 March 2016];22(1):11-16. Avail-
able from: http://www.sciencedirect.com/science/article/pii/S0901502705803480
[22] Ta L, Phero J, Pillemer S, Hale-Donze H, McCartney-Francis N, Kingman A et al. Clin-
ical evaluation of patients with temporomandibular joint implants. Journal of Oral and
Maxillofacial Surgery [Internet]. 2002 [cited 16 March 2016];60(12):1389-1399. Available
from: http://www.sciencedirect.com/science/article/pii/S027823910200633X
[23] Anguiano v. EI DuPont De Nemours and Co., Inc., 808 F. Supp. 719
(D. Ariz. 1992) [Internet]. Justia Law. 2016 [cited 16 March 2016]. Available
from: http://law.justia.com/cases/federal/district-courts/FSupp/808/719/1478400/
http://law.justia.com/cases/federal/district-courts/FSupp/808/719/1478400/
[24] Naujoks C, Meyer U, Wiesmann H, Jäsche-Meyer J, Hohoff A, Depprich R et
al. Principles of cartilage tissue engineering in TMJ reconstruction. Head & Face
Medicine [Internet]. 2008 [cited 16 March 2016];4(1):3. Available from: http://head-
face-med.biomedcentral.com/articles/10.1186/1746-160X-4-3
[25] Allen K, Athanasiou K. Tissue Engineering of the TMJ Disc: A Review. Tissue En-
gineering [Internet]. 2006 [cited 16 March 2016];0(0):060509063358001. Available from:
http://online.liebertpub.com/doi/pdf/10.1089/ten.2006.12.1183
[26] Allen K, Athanasiou K. Scaffold and Growth Factor Selection in Temporomandibular
Joint Disc Engineering. Journal of Dental Research [Internet]. 2008 [cited 16 March
2016];87(2):180-185. Available from: http://jdr.sagepub.com/content/87/2/180.long
http://jdr.sagepub.com/content/87/2/180.long
[27] Transplant jaw made by 3D printer claimed as first - BBC News [Internet]. BBC News.
2016 [cited 16 March 2016]. Available from: http://www.bbc.com/news/technology-
16907104 http://www.bbc.com/news/technology-16907104
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