The University of Sydney Slide 1web.aeromech.usyd.edu.au/AMME5981/Course_Documents/files...The...
Transcript of The University of Sydney Slide 1web.aeromech.usyd.edu.au/AMME5981/Course_Documents/files...The...
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The University of Sydney Slide 1
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The University of Sydney Slide 2
SIMULATION DRIVEN BIOMEDICAL DESIGN
Presented by
Dr Paul Wong
AMME4981/9981
Semester 1, 2016
Lecture 4
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The University of Sydney Slide 3
Simulation Types
– There is more to finite element
analysis than “static structural”
– If the physics can be discretised,
there can be a computational
solution
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The University of Sydney Slide 4
Multiphysics Modelling and Types of Analysis
Physics DOF(s) - Typical Analysis Type
Structural Displacement Static, transient, modal
Thermal Temperature Static, transient
Incompressible fluid flow Velocity Steady-state, transient
Acoustic Acoustic pressure Frequency-domain
ElectromagneticsElectric potential,
magnetic vector potential
Static, frequency-
domain, transient
Diffusion ConcentrationSteady-state, frequency-
domain
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The University of Sydney Slide 5
MODAL ANALYSES
For natural frequencies (resonance)
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The University of Sydney Slide 6
– Used to study vibrational excitation
– Function of geometry and material property only
– Determining natural frequencies allows for some interesting applications
Modal Analyses
https://xkcd.com/228/
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The University of Sydney Slide 7
Tacoma Narrows Bridge
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The University of Sydney Slide 8
Modal Analyses in Biomedical Engineering
– Modal analyses enable measurement of osseointegration
– Natural frequency analysis of osseointegration for transfemoral implants
Shao et al., Annals of Biomedical Engineering 35:817-824, 2007
– Varying levels of osseointegration result in different interfacial conditions, resulting in changes to the natural frequency
– Experimentally determine the resonant characteristics of the implant
Small mechanical excitation
Measure vibration response
FFT(spectral analysis)
Determine modal
frequency
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The University of Sydney Slide 9
Osseointegration: Experimental Setup
– Changing the curing time of the silicone to mimic different levels of osseointegration
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The University of Sydney Slide 10
Osseointegration: In Vitro and In Vivo
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The University of Sydney Slide 11
Osseointegration: Results and Conclusions
– In vitro: Longer curing times higher natural frequency
– In vivo: Longer healing times higher natural frequency
– Higher natural frequency because of the increase in stiffness/stability of the interface between “bone” and implant.
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The University of Sydney Slide 12
– Relationship between the stiffness (i.e. Young’s Modulus) and natural frequency
– Use this relationship to determine osseointegration in models
Osseointegration: In Silico
Host Bone
Implant
Interfacial layer with
Young’s modulus
between 0.1 and 0.7
MPa
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The University of Sydney Slide 13
Peri-Implant Layer
E1=0.05 – 0.6GPa
E2=16GPa
E3=0.6GPa
– Peri-implant region (up to 1mm from screw thread) is defined in the model
– Some damage occurs during implant insertion, resulting in changes to mechanical properties
– Healing and bone remodelling in this area determine osseointegration
The Peri-Implant Region
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The University of Sydney Slide 14
Bone Remodelling Loop for Dental Implants
Fully clampedSectional plane
Lateral incisor
Canine
Dental implant
2nd molar
1st molar
2nd pre-molardental crown
1st pre-molar
Fully clampedSectional plane
Buccal
side
Lingual
side
z
yx
k = k + 1
FE model
Based on CT scans
Initial: k=0
Static FEA
Strain Energy
Density (k)
)(
)(
)()( )1( k
k
kk t
)()()1( kkk
Calculate density change
Update modulus
Dynamic FEA
Resonance
Frequency
Update density
Cortical
Cancellous15.2349.2 cancellousE
2493.23 corticalE
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The University of Sydney Slide 15
Osseointegration: In Silico Results
– One month loop intervals
– Interface stabilises after 4 months
measured by increase in resonant
frequency
– Validation with experimental
results
0
1000
2000
3000
4000
5000
6000
7000
8000
Re
so
na
nc
e f
req
ue
nc
y (
Hz)
This study Glauser et al. [40] De Smet et al’s [54]*
month 1 month 12
Non-invasive measurement tools
Natural frequency
5500
6500
7500
8500
9500
10500
11500
0 4 8 12 16 20 24 28 32 36 40 44 48
Number of month
Na
tura
l fr
eq
ue
nc
y (
Hz)
1st natural frequency
2nd natural frequency
3rd natural frequency
Reso
nan
ce f
req
uen
cy (
Hz)
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The University of Sydney Slide 16
COUPLED ANALYSES
For interdependent physics
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The University of Sydney Slide 17
Coupled Analysis
– Solving for more than one set of
DOFs
– Two methods
– Load Transfer
– Direct Coupling
– Most commonly:
– Thermal-structural
– Fluid-structural interactions (FSI)
– Thermal-electric
– Off-the-shelf solutions are
commonplace
– In many cases, in-house code is used
for highly specific applications
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The University of Sydney Slide 18
Transient Analyses
– Transient (time-dependent) solvers are required for many biomedical applications
– Pulsatile flow
– Slow processes like diffusion, deposition
– Body kinematics
– Transient solutions can be obtained by two methods
– Implicit: enables larger time-steps, but implicit expression needs iterations
– Explicit: smaller time-steps to prevent drift, but explicit expression for solution is easier to solve
𝜕𝑢
𝜕𝑡= lim
∆𝑡→0
𝑢 𝑡 + ∆𝑡, 𝑥 𝑡 , 𝑝 𝑡 − 𝑢(𝑡, 𝑥 𝑡 , 𝑝 𝑡 )
∆𝑡
𝑑𝑢
𝑑𝑡= lim
∆𝑡→0
𝑢 𝑡 + ∆𝑡, 𝑥 𝑡 + ∆𝑡 , 𝑝 𝑡 + ∆𝑡 − 𝑢(𝑡, 𝑥 𝑡 , 𝑝 𝑡 )
∆𝑡
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The University of Sydney Slide 19
Load Transfer: FSI during Pulsatile Blood Flow
Incompressible
fluid flow model
Structural
model
Transfer
shear stress
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The University of Sydney Slide 20
FSI of Valve in Blood Vessels
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The University of Sydney Slide 21
FSI during Pulsatile Breathing
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The University of Sydney Slide 22
Inhalation and Deposition in the Lung
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The University of Sydney Slide 23
Inhalation and Deposition in the Lung
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The University of Sydney Slide 24
VERIFICATION AND SAFETY
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The University of Sydney Slide 25
– Any device that interacts with the body must be approved by regulatory authorities prior to sale
– Currently, most submissions include evidence on efficacy and safety from in vitro and in vivo studies
– The FDA recently released draft guidance on the reporting of in silico studies as a complementary source of evidence, with the goal of reducing dependency on existing (and costly) sources
Computational Modelling for Regulatory Submissions
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The University of Sydney Slide 26
Computational Modelling for Regulatory Submissions
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The University of Sydney Slide 27
Simulation-based Verification of Electromagnetic Devices
– FEA can be used to verify electromagnetic compatibility and safety of devices
– Communications devices emit radiation at radio frequencies (RF)
Specific Absorption Rate SAR = නsample
𝜎(𝑟) 𝐸(𝑟) 2
𝜌(𝑟)
FE model Temp. ChangeSAR
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The University of Sydney Slide 28
Verification of Cochlear Implant Stimulation
– Electrode array inserted into
cochlea
– Bypass hair cells by electrically
stimulating cochlear nerve fibres
directly
– External Microphone Signal
Processing Electrode Array
– Limited understanding in vivo
justifies the development of
computational models
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The University of Sydney Slide 29
Current Flows from Cochlear Implants
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The University of Sydney Slide 30
Verification of Stimulation Limits for Neuroprostheses
– Modelling electric field effects
on electrochemistry
– Safe stimulation avoids or limits
irreversible reactions
– Frequency-dependent
behaviour
– Time-dependent analyses
– Non-linear boundary conditions
to model reaction kinetics
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The University of Sydney Slide 31
Orthopaedic Implant Failure Modes
Mode I
(Tension, opening)
Mode II
(In-Plane Shear, Sliding)
Mode III
(Out-Of-Plane Shear,
Tearing)
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The University of Sydney Slide 32
– Griffith’s Crack Theory is based on strain energy release rate (G).
– Irwin’s modification utilises stress intensity factor (K).
– Geometric correction factor (Y)depending on geometry.
Fracture Mechanics Theory
a WW
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The University of Sydney Slide 33
– Crack insertion and propagation based on stress values
Fracture of Dental Bridges
FE Modelling of Bridge Fracture (Li et al., 2006) Cracking Simulation in Dental Bridges (Li et al., 2006)
2 unit cantilever bridge 4 unit fixed bridge
– Discontinuous shape functions (XFEM), or discrete element method enables modelling of cracks
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The University of Sydney Slide 34
Mode I Fracture in a Dental Bridge
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The University of Sydney Slide 35
Implant Failure by Fatigue
– Cyclic loading
– Gait cycle (knee and hip
replacements).
– Bending, torsion and
compression of spine (spinal
fusion, spinal disc prostheses).
– S-N curve data is required
– Static and dynamic loading is
tested
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The University of Sydney Slide 36
Fatigue Criteria
Goodman Theory
Soderberg Theory
Gerber Theory
– Se is the endurance limit, Su is ultimate tensile strength, Sy is yield strength
– Safety factors with respect to the endurance limit are determined for different designs
Senalp et al, Materials and Design 28 (2007) 1577–1583
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The University of Sydney Slide 37
What Did We Learn?
– The use of computational methods
in biomedical engineering is
favourable in:
– Research
– Product development
– These methods add value because
they provide answers that are not
easily measured in vivo
– Importance of understanding
underlying biological phenomena
– There is more to FEA than “static
structural”…
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The University of Sydney Slide 38
GROUP PROJECTS
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The University of Sydney Slide 39
Group Projects
3D Printing
– Induction scheduled for Tuesday,
5th April
– Each group can claim up to $150
for 3D printing
Mechanical Testing
– Safety paperwork required prior
to lab induction
– Need lab coat, safety shoes, and
safety glasses (available)