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Title: Applied Biomedical Engineering


1
Applied Biomedical Engineering AMME4981 Lecture
5 Finite Element Modelling
Course Web
http//www.aeromech.usyd.edu.au/people/academic/qi
ngli/AMME4981.htm
2
Contents
  • Multiphysical modelling in biomedical
    engineering
  • Prosthetic failure (Fracture and Fatigue)
  • Ansys Workbench

3
FE Multiphysical Modelling
  • Static analysis stress, strain, displacement
  • Dynamic analysis Frequency, mode shape
  • Acoustic analysis Sound pressure
  • Thermal analysis Temperature, heat flux
  • Fluid analysis Velocity, shear stress
  • Electrical analysis Electrical field
    intensity
  • Magnetic analysis magnetic flux, magnetic
    potential
  • Coupled analyses Thermal-Structural,
    Fluid-Structural,
  • Electrical-magnetic, etc

4
I. Dynamic Analysis Osseointegration Study
Natural Frequency Analysis of Osseointegration
for Trans-Femoral Implant
Shao et al, Annals of Biomedical Engineering
35817824, 2007
5
Mechanism
  • Hypothesis
  • Different osseointegration degree leads to
    different interfacial condition, thereby
    different natural frequency. Different silicone
    rubber interfaces with the curing time are used
    to simulate (mimic) osseointegration process.
  • Method
  • Use the resonant characteristics of the implant
    system to determine the changes in stability as a
    reflection of boundary condition of the implant.
    With a small mechanical excitation,
  • Vibration responses of the trans-femoral implant
    to a small mechanical excitation are measured
    using an accelerometer
  • The vibration signal will be analyzed using Fast
    Fourier Transform (FFT) software to obtain the
    fundamental natural frequency of the implant
    system.
  • Result
  • In-vitro study was conducted using different
    silicone rubbers to simulate the interface
    condition. The result showed that a high NF
    corresponded to a high elastic modulus of the
    interface material between the implant and bone.

6
Apparatus in-vitro and in-vivo
In-Vitro Apparatus
In-vivo Apparatus
Curing time of silicon rubber
Real osseointegration measurement
Shao et al, Annals of Biomedical Engineering
35817824, 2007
7
Result Natural Freq vs Remodelling Time
The longer the curing time, the higher the
natural frequency, thereby the better the
osseointegration and more stable prosthetic
outcome
The longer the healing time, the higher the
natural frequency, thereby the better the
osseointegration and more stable prosthetic
outcome
8
Result Freq vs Interfacial Youngs Modulus
The longer the curing time, the higher the
interfacial Youngs modulus, the higher the
natural frequency, thereby the better the
osseointegration and more stable prosthetic
outcome
Modelling Scheme
Blood layer with a Youngs modulus between 0.1
and 0.7MPa
Implant
Host Bone
9
Osseointegration in Dental Implants
Peri-Implant Layer E10.05 0.6GPa
E216GPa
E30.6GPa
A peri-implant interfacial area, up to 1 mm
external to the implant thread, was carefully
modelled with the aim of differentiating the
anatomical region that was damaged by implant
placement and whose mechanical properties changed
during the integration process. In fact, tissue
damage phenomena because of the mechanical
drilling process are unavoidable and there is
strong evidence of bone tissue activity in the
healing phase after the implant placement,
resulting in new bone deposition and structural
rearrangement.
10
Dynamic Result for Dental Implant
Relation between 1st natural frequency vs
interfacial Youngs modulus better
osseointegration
Osseointegration
Boen remodelling
Youngs Modulus vs healing Time
11
II. Fluid Flow Pulse Blood Flowing in Artery
CFD-Structural Coupled Problem
Ansys From Leap Australia
12
Biomedical Example Particle Flow in Lung
Ansys From Leap Australia
13
Biomedical Example Air Flow in Pulse
Flow-Structural coupling problem
Ansys From Leap Australia
14
Biomedical Example Valve Sheldon
15
III. Electromagnetic modelling
Specific Absorption Rate (SAR)
FEA model
Temperature Change
Electromagnetic radiation effect of mobile phone
on possible consequences of on health.
16
Modelling Adaptive Meshing
Dense Mesh
Modeller Ansys Workbench
17
IV. Dynamic-Flow-Electrical Cochlear Mechanics
Middle Ear
Inner Ear
External Ear
  • External Ear (E) comprises the pinna and
    acoustic meatus. It funnels sound vibrations to
    the middle ear.
  • Middle Ear (M) comprises three tiny bones
    (ossicles) malleus, incus and stapes. Its
    function is to transform air-born vibrations
    impinging on the tympanic membrane into
    oscillations of the fluid filling the inner ear.
  • Inner Ear (I) - Cochlear

18
The Middle Ear as a Mechanical Transformer
The middle ear is a full-fledged mechanical
energy transformer. The three ossicles (malleus,
incus and stapes) work like a lever system that
increases the force transmitted from the tympanic
membrane to the stapes by decreasing the ratio of
their oscillation amplitudes. The footplate of
stapes acts like a small piston on the cochlear
fluid through a membraneous connection that seals
the oval window of the cochlea. The buckling
motion of the tympanic membrane decreases the
velocity two-fold an increases the force
two-fold, changing the impedance ratio four-fold.
Thanks to the large surface ratio between
tympanic membrane and oval window (about 35) and
the ossicle system lever gain (about 1.32), the
forward impedance gain is about 30 dB. Filtering
effects due to resonances of the middle ear
cavity and mechanical parameters of the ossicle
system produce a peak between 1 and 2 kHz.
19
Basilar Membrane as a Thin Elastic Fibers
The basilar membrane is internally formed by thin
elastic fibers tensed across the cochlear duct.
The fibers are short and closely packed in the
basal region, i.e. close to the stapes, and
become longer and sparse proceeding towards the
apex of the cochlea, where the basilar membrane
ends in a foramen that joins the two partions of
the spiral canal (see Anatomy). Being under
tension, the fibers can vibrate like the strings
of a musical instrument. Traveling waves peak at
frequency-dependent locations, higher frequencies
peaking closer to more basal location. Peak
position is an exponential function of input
frequency because of the exponentially graded
stiffness of the basilar membrane. Part of the
stiffness change is due to the increasing width
of the membrane and part to its decreasing
thickness.
20
Cochlear Hydrodynamics 2D Modelling
Fluid



A longitudinal section of the uncoiled cochlea is
represented with vertical dimension expanded by
about 3 times. A traveling wave elicited by a 3
kHz tone is shown as a solid red line displacing
the basilar membrane (unbroken black line) from
its resting position (the wave amplitude is
magnified about 106 times for clarity) Arrows
around wave peaks indicate the direction of local
fluid flow. The fluid mass affects the dynamics
of the basilar membrane, loading its different
parts by amounts that depend upon the local wave
length. Notice the progressive shortening of the
wave length up to a critical point beyond which
both the basilar membrane and the fluid keep at
rest. The inset shows a cross section of the
spiral canal, showing that the basilar membrane
is laterally clamped across the duct and supports
the organ of Corti, that hosts two types of
sensory hair cells inner hair cells, that
transmit signals to the acoustic nerve, and outer
hair cells that provide mechanical amplification
to the basilar membrane motion

21
In Cochlear Hari Cells
Sounded
Static
The animation at left visualizes the activation
of an IHC by the fluid viscous drag applied to
its stereocilia by the oscillation of the
tectorial membrane. Outer hair cells are the
target of abundant efferent innervation and
possess a unique type of motility. They convert
receptor potentials into cell length changes at
acoustic frequencies. The animation at right
visualizes the activation of the outer hair cell
motor driven by the motion of the tectorial
membrane into which the tips of the tallest
stereocilia are inserted. A second class of
sensory receptors, the outer hair cells couple
visco-elastically the reticular lamina to the
basilar membrane through their supporting
Deiters' cells.
22
V. Fracture Modelling
Mode I (Tension, opening)
Mode II (In-Plane Shear, Sliding)
Mode III (Out-Of-Plane Shear, Tearing)
23
Fracture Mechanics Griffith Theory
  • Griffith's Crack Theory strain energy release
    rate
  • For the simple case of a thin rectangular plate
    with a crack perpendicular to the load Griffiths
    theory becomes
  •   
  •                           
  • where G is the strain energy release rate, s is
    the applied stress, a is half the crack length,
    and E is the Youngs modulus. The strain energy
    release rate can otherwise be understood as the
    rate at which energy is absorbed by growth of the
    crack.
  • However, we also have that
  •                              
  • If G Gc, this is the criterion for which the
    crack will begin to propagate. ?f is the critical
    stress for failure of material

24
Fracture Mechanics Irwin's Theory
  • Irwin's modified Griffith crack theory fracture
    toughness

Eventually a modification of Griffiths theory
emerged from this work a term called stress
intensity replaced strain energy release rate and
a term called fracture toughness replaced surface
energy. Both of these terms are simply related to
the energy terms that Griffith used
Plane stress
Plane strain
where KI is the stress intensity, Kc the fracture
toughness, and ? is Poissons ratio. ? It is
important to recognise the fact that fracture
parameter Kc has different values when measured
under plane stress and plane strain ? Fracture
occurs when KI Kc. For the special case of
plane strain deformation, Kc becomes KIc and is
considered a material property. ? The subscript
I arises because of the different ways of loading
a material to enable a crack to propagate. It
refers to loading via Mode I - the most common
form of loading
25
Stress Intensity Geometric Effect
  • Dimensionless
  • We must note that the expression for stress
    intensity KI will be different for geometries
    other than the center cracked plate.
    Consequently, it is necessary to introduce a
    dimensionless correction factor, Y, in order to
    characterise the geometry. We thus have
  •                                  
  • where Y is a function of the crack length and
    width of sheet given by
  •                                            

W
26
VI. Fatigue Analysis
Ensure the hip prostheses against static, dynamic
and fatigue failure.
Material Fatigue Experiment
How to conduct fatigue analysis Step 1. Conduct
static analyses under body load. Step 2. Conduct
dynamic analyses were performed under walking
load. Step 3. Fatigue behavior of stem shapes was
predicted using ANSYS Workbench for given
material fatigue data (S-N curve).
Senalp et al, Materials and Design 28 (2007)
15771583
27
VI. Fatigue Modelling
Mean stress
Alternating stress
Goodman
Solderberg
2
Gerber
Su Endurance limit Sy Yield Strength
Senalp et al, Materials and Design 28 (2007)
15771583
28
VI. Fatigue Result
Under Static Load
Under Dynamic Load
Senalp et al, Materials and Design 28 (2007)
15771583
29
VII. Ansys Workbench A Design Tool
Download tutorial material from
http//www.aeromech.usyd.edu.au/people/academic/qi
ngli/AMME4981.htm
  • Design Modeler Evaluation Guide A Quick
    Tutorial
  • static Analysis
  • Modal Analysis

30
Summary
  • FE Multiphysics Modelling
  • Prosthetic Failure (Fracture and Fatigue)
  • Ansys Workbench
  • Task in Week 5
  • Read two papers of
  • Shao et al, Annals of Biomedical Engineering,
    35817824, 2007
  • Senalp et al, Materials and Design 2815771583,
    2007
  • Attempt Ansys modelling in classic GUI and/or
    Workbench
  • Group discussion of project on modelling
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