The University of Sydney Slide 1web.aeromech.usyd.edu.au/AMME5981/Course_Documents/files...The University of Sydney Slide 3 Simulation Types – There is more to finite element analysis

The University of Sydney Slide 1


SIMULATION DRIVEN BIOMEDICAL DESIGN

Presented by

Dr Paul Wong

AMME4981/9981

Semester 1, 2016

Lecture 4


Simulation Types

– There is more to finite element

analysis than “static structural”

– If the physics can be discretised,

there can be a computational

solution


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


MODAL ANALYSES

For natural frequencies (resonance)


– 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/

https://xkcd.com/228/


Tacoma Narrows Bridge


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


Osseointegration: Experimental Setup

– Changing the curing time of the silicone to mimic different levels of osseointegration


Osseointegration: In Vitro and In Vivo


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.


– 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


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


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


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)


COUPLED ANALYSES

For interdependent physics


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


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


Load Transfer: FSI during Pulsatile Blood Flow

Incompressible

fluid flow model

Structural

model

Transfer

shear stress


FSI of Valve in Blood Vessels


FSI during Pulsatile Breathing


Inhalation and Deposition in the Lung


Inhalation and Deposition in the Lung


VERIFICATION AND SAFETY


– 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

http://www.fda.gov/downloads/MedicalDevices/DeviceRegulationandGuidance/GuidanceDocuments/UCM381813.pdf


Computational Modelling for Regulatory Submissions


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


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


Current Flows from Cochlear Implants


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


Orthopaedic Implant Failure Modes

Mode I

(Tension, opening)

Mode II

(In-Plane Shear, Sliding)

Mode III

(Out-Of-Plane Shear,

Tearing)


– 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


– 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


Mode I Fracture in a Dental Bridge


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


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


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”…


GROUP PROJECTS


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)