1/22GSC Bone Adaptation as a Cellular Automata Bone Adaptation as a Cellular Automata Optimization Process Andrés TovarJohn E. Renaud University of Notre Dame Department of Aerospace and Mechanical Engineering Graduate Student Conference AME 2003 October 24, 2003 – Notre Dame, IN

2/22GSC Bone Adaptation as a Cellular Automata Content Bone Adaptation Cellular Automata Structural Optimization Proposed Algorithm Final Remarks

3/22GSC Bone Adaptation as a Cellular Automata Bone Structure

4/22GSC Bone Adaptation as a Cellular Automata [University of Washington] Bone Structure

5/22GSC Bone Adaptation as a Cellular Automata Bone Cells Osteclasts > Resorb bone Osteblasts > Make bone Osteocytes > Sensors Lining cells > Inactive osteoblasts

6/22GSC Bone Adaptation as a Cellular Automata Osteogenesis and Modeling Osteogenesis Formation of new soft bone tissue or cartilage Modeling Reshaping of the bone by independent action of osteblasts and osteoclasts

7/22GSC Bone Adaptation as a Cellular Automata Remodeling Reshaping of the bone by coupled action of osteblasts and osteoclasts [Martin & Burr, 1989]

8/22GSC Bone Adaptation as a Cellular Automata Remodeling Reshaping of the bone by coupled action of osteblasts and osteoclasts [American Society for Bone and Mineral Research]

9/22GSC Bone Adaptation as a Cellular Automata 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?

10/22GSC Bone Adaptation as a Cellular Automata Cellular Automata Neighborhoods Neumann Moore Expanded Moore Local rule C(k+1) = f(c(k),c1(k),...,cN(k))

11/22GSC Bone Adaptation as a Cellular Automata 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

12/22GSC Bone Adaptation as a Cellular Automata 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

13/22GSC Bone Adaptation as a Cellular Automata 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

14/22GSC Bone Adaptation as a Cellular Automata Game of Bone

15/22GSC Bone Adaptation as a Cellular Automata Game of Bone

16/22GSC Bone Adaptation as a Cellular Automata Structural Optimization

17/22GSC Bone Adaptation as a Cellular Automata Structural Optimization [O. Sigmund, 2001]

18/22GSC Bone Adaptation as a Cellular Automata Structural Optimization

19/22GSC Bone Adaptation as a Cellular Automata 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

20/22GSC Bone Adaptation as a Cellular Automata Derivation of a CA rule [Hajela and Kim, 2001]

21/22GSC Bone Adaptation as a Cellular Automata 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?

22/22GSC Bone Adaptation as a Cellular Automata Thanks Time for some questions

23/22GSC Bone Adaptation as a Cellular Automata Bone Structure LevelSize Range Cortical Structure Trabecular Structure 0> 3 mmSolidPorous 10.1 – 0.3 mmOsteonsTrabeculae 2 1 – 20  m Lamellae, cement lines – 0.4  m Collagen-mineral composite