Less than full circumferential fusion of a tibial nonunion is sufficient to achieve mechanically valid fusion - Proof of concept using a finite element modeling approach

Table 1 Optimisation algorithm in pseudo code

Optimisation algorithm
1:	initialize the algorithm:
2:	compute the worst case scenario
3:	set the material parameters of each nonunion area mesh cell to soft tissue
4:	compute the von Mises stress for the tibia
5:	search for the maximum stress value
6:	define max:=maximum stress value
7:	compute the initial scenario
8:	set the material parameters of each nonunion area mesh cell to cortical bone
9:	compute the von Mises stress for the tibia
10:	define the stress threshold
11:	define the stop_criterion
12:	repeat
13:	if von Mises stress of nonunion area mesh cell < threshold x max
14:	set material parameter of each nonunion area mesh cell from cortical bone to soft tissue

Beginning in a state of complete union fracture area mesh cells with von Mises stress < threshold x max are identified. The material parameters for these cells are set from cortical bone to soft tissue. After one cycle over all fracture area mesh cells, the new material parameters are used as starting point for the next optimization run.