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for a=0.003:0.0005:1; b=0.002:0.0005:0.9; c=0.001:0.0005:0.8;d=0.0005:0.0005:0.7;

E1=a* E_Bone;

E2=b* E_Bone;

E3=c* E_Bone;

E4=d* E_Bone;

G1=a* G_Bone;

G2=b* G_Bone;

G3=c* G_Bone;

G4=d* G_Bone;

%% Integration for cortical bone parts

Integ_Bone = (Bone_Length -2.0*(Half_Gap+Callus_ext))/(G_Bone*J_Bone) ; % Integration for bone part

%% Integration for fracture gap

Flex= @(z) 1.0/( G1* J_Bone + G1*J_Callus );

Integ_Gap1=quadv(Flex, Fract_Left, F1) ;

Flex= @(z) 1.0/( G2* J_Bone + G2*J_Callus );

Integ_Gap2=quadv(Flex, F1, F2) ;

Flex= @(z) 1.0/( G3* J_Bone + G3*J_Callus );

Integ_Gap3=quadv(Flex, F2, F3) ;

Flex= @(z) 1.0/( G4* J_Bone + G4*J_Callus );

Integ_Gap4=quadv(Flex, F3, F4) ;

Integ_GapL=Integ_Gap1+Integ_Gap2+Integ_Gap3+Integ_Gap4;

Integ_Gap=2*Integ_GapL;

%% integration for callus part ( excluding gap)

Flex= @(z) 1.0/( G_Bone*J_Bone + G1*J1 );

Integ_Left = quadv(Flex, Callus_Left, Fract_Left ) ;

Integ_Right= quadv(Flex, Fract_Right, Callus_Right ) ;

%% integration for whole bone

Integ_Whole = Integ_Bone+Integ_Gap +Integ_Left +Integ_Right ;

%% Integration for intact cortical bone

Integ_Intact = Bone_Length/(G_Bone*J_Bone) ; % Integration for whole bone

%% Non-dimensional torsional stiffness

T_Stiff= Integ_Intact/Integ_Whole ;

sprintf('The Non-dimensional torsional stiffness = %f ', T_Stiff)

end