Bone structure adaptation as a cellular automaton optimization process

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Bone structure adaptation as a cellular automaton
optimization process

• Andrés Tovar, Glen L. Niebur, Mihir Sen and John
  E. Renaud
• Department of Aerospace and Mechanical
  Engineering
• University of Notre Dame, Indiana
• Brian Sanders
• Air Force Research Laboratory
• Wright-Patterson AFB, Ohio
• Presentation at General Motors Corporation
• Detroit, Michigan
• 6 May 2004

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Meyer and Culmann, 1867 Wolff, 1892
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Cellular Automata (CAs) Biological dynamics
Finite Element Method (FEM) Bone static models
Hybrid Cellular Automata (HCA) Bone adaptation
dynamic model
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Content

• 1. Bone Adaptation
• 2. Cellular Automata (CAs)
• 3. The Hybrid Cellular Automaton (HCA) method
• Local Control Rule
• Performance
• 4. Examples
• 5. Final remarks

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1. Bone Adaptation
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100mm
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Frost, 1964, 1969
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10mm
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Skerry et al., 1989 Cowin et al., 1991 Lanyon,
1993 Klein-Nulend et al., 1995
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Mullender et al. 1994, Mullender and Huiskes,
1995
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Ott, 2001
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2. Cellular Automata
0.1mm
The average density of osteocytes is 12,000
20,000 cells/mm3 Frost, 1960 Bodyne, 1972
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2. Cellular Automata
CAs are dynamical systems that are discrete in
space and time and operate on a uniform, regular
lattice.
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CAs are characterized by local interactions.
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CAs have been used to simulate physical and
biological phenomena since their creation by von
Neumann in 1940s.
Wolfram, 2002
Conway, 1970
Tovar, 2003
Chopard and Droz, 1998
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3. Hybrid Cellular Automaton Model
Mechanical set point
Mechanical signal
U
U
Hajela and Kim, 2001 Abdalla and Gürdal, 2002

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3. Hybrid Cellular Automaton Model
FEM
U
U
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3. Hybrid Cellular Automaton Model
FEM
U
U
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3. Hybrid Cellular Automaton Model
FEM
U
U
no
yes
?
End
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3.1 Local control strategy
a) Two-position control
b) Proportional control
c) Integral control
d) Derivative control
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3.1 Local control strategyTwo-position control
t21 U6.7170 M0.539
c.f. Sauter, 1992
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3.1 Local control strategyProportional control
t23 U6.3265 M0.581
c.f. Martin et al., 1998
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3.1 Local control strategyProportional-Integral
control
t16 U6.4576 M0.568
c.f. Hazelwood et al., 2001
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3.1 Local control strategyProportional-Derivative
control
t23 U6.2938 M0.585
c.f. Fyhrie and Schaffler, 1995
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3.1 Local control strategy Proportional-Integral-
Derivative control
t15 U6.4338 M0.569
c.f. Davidson et al., 2004
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3.2 PerformanceInitial design
M 1.0
M 0.5
t21 U6.4502 M0.568
t15 U6.4338 M0.569
M 0.0
M 0.5
t21 U6.4668 M0.568
t17 U6.4350 M0.568
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3.2 PerformanceNeighborhood
t16 U6.8073 M0.529
t15 U6.4338 M0.569
t13 U6.3511 M0.574
t16 U6.2062 M0.592
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3.2 PerformanceBoundary conditions
t15 U6.4338 M0.569
t13 U6.3905 M0.584
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3.2 PerformanceSize of the Design Domain
10x10
60x60
30x30
t18 U5.9944 M0.598
t20 U6.8146 M0.540
t15 U6.4338 M0.569
120x120
90x90
t17 U7.1222 M0.526
t16 U6.9805 M0.533
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3.2 PerformanceTarget mechanical stimulus U
U0 0.005
U U0/5
U U0
t15 U6.4338 M0.569
t6 U4.4033 M0.920
U 5U0
U 10U0
t19 U13.1251 M0.274
t18 U18.5379 M0.193
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3.2 PerformanceThe trade-off curve
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3.2 PerformanceThe trade-off curve
Sigmund, 2001
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4. ExamplesStructures in cantilever
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4. ExamplesStructures in cantilever
t10 U10.3091 M0.483
t18 U11.0233 M0.551
t10 U12.9910 M0.189
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5. ExamplesTrabecular bone (one-load case)
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5. ExamplesTrabecular bone (two-load case)
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6. Final Remarks

• HCA CA FEM, using local control rules.
• HCA models are suitable to simulate biological
  structural optimization process.
• HCA local control rules need to be tuned
  according to biological evidence.
• Time effects, like mineralization of bone tissue,
  can be included in the model.
• A probabilistic HCA model can be implemented to
  simulate non-deterministic process in bone
  remodeling.
• The time scales are still a concern for HCA model.

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Thanks