GSC 2003 - Bone Adaptation as a Cellular Automata 1/22

Bone Adaptation as a Cellular Automata Optimization Process

Andrés Tovar John E. Renaud

University of Notre DameDepartment of Aerospace and Mechanical Engineering

Graduate Student Conference AME 2003October 24, 2003 – Notre Dame, IN

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Content

• Bone Adaptation

• Cellular Automata

• Structural Optimization

• Proposed Algorithm

• Final Remarks

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Bone Structure

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[University of Washington]

Bone Structure

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Bone Cells

Osteclasts > Resorb bone Osteblasts > Make bone

Osteocytes > Sensors Lining cells > Inactive osteoblasts

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Osteogenesis and Modeling

• OsteogenesisFormation of new soft bone tissue or cartilage

• ModelingReshaping of the bone by independent action of osteblasts and osteoclasts

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Remodeling

• RemodelingReshaping of the bone by coupled action of osteblasts and osteoclasts

[Martin & Burr, 1989]

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Remodeling

• RemodelingReshaping of the bone by coupled action of osteblasts and osteoclasts

[American Society for Bone and Mineral Research]

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Cellular Automata

What makes them attractive?

1) An overall global behavior can be computed by local rules.

1) Inherent massive parallel algorithm.

What are the challenges?

1) Given a CA rule, what are its properties?

2) Given the evolution of a system, what is the CA rule?

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Cellular Automata

Neighborhoods

Neumann Moore Expanded Moore

Local rule

C(k+1) = f(c(k),c1(k),...,cN(k))

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Cellular Automata

if c(k)==1 & sumNei==0 c(k+1)=0;if c(k)==0 & (sumNei==1 | sumNei==4) c(k+1)=1;else c(k+1)=0;end

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Game of Life

if c(k)==0 & sumNei==3 c(k+1) = 1;elseif c(k)==1 & (sumNei==2 | sumNei==3) c(k+1)=1;else c(k+1)=0;end % if

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Game of Bone

if c(k) < 0.50 c(k+1) = c(k) - eps; if (sumEne > avgEne) | (sumDen > avgDen) c(k+1) = c(k+1) + eps; end

elseif c(k) > 0.50 c(k+1) = c(k) + eps; if ((sumEne < avgEne) | (sumDen < avgDen)) c(k+1) = c(k) - eps; end

else c(k+1) = c(k);

end

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Game of Bone

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Game of Bone

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Structural Optimization

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Structural Optimization

[O. Sigmund, 2001]

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Structural Optimization

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Proposed Algorithm

1) Definition of the design domain

2) FEA to obtain compliance

3) Derivation of a CA rule

4) Apply CA rule for several iterations

5) Go to step 2

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Derivation of a CA rule

[Hajela and Kim, 2001]

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Final Remarks

1) CA models seems to be suitable to represent biological process.

2) Structural Optimization will lead the derivation of the CA rules.

3) This modeling process can be extended to any type of structure.

4) Is it really a new kind of science?

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Thanks

Time for some questions

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Bone Structure

Level Size RangeCortical

StructureTrabecular Structure

0 > 3 mm Solid Porous

1 0.1 – 0.3 mm Osteons Trabeculae

2 1 – 20 m Lamellae, cement lines

3 0.06 – 0.4 m Collagen-mineral composite