## 4 Search Results for Spine Biotensegrity Models
### Spine Biotensegrity Models  
Three variations of spine biotensegrity models (SB1, SB2, and SB3) are successfully established by using the proposed form-finding strategies. Figure 15 illustrates the configuration and nodal numbers. The larger nodes represent the modification through approach two. In any model, nodes of all cells excluding the nodes at top and base are considered for modification during approach two. Table A1 in Appendix A shows the nodal coordinates for the spine biotensegrity models. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{11}{c}{**Modification of Nodal Coordinates (mm) in Y-Direction for Cases A1-H1**} \\ \hline \multicolumn{11}{c}{**Case**} & \multicolumn{11}{c}{**Nodes**} & \multicolumn{11}{c}{**Case**} & \multicolumn{11}{c}{**Nodes**} & \multicolumn{11}{c}{**} \\ \cline{2-11}  & **6** & **20** & **15** & **12** & **13** & **14** & **5** & **4** & **19** & **6** & **20** & **15** & **12** & **13** & **14** & **5** & **4** & **19** \\ \hline
**A1** & \(-\)10 & \(-\)5 & \(-\)7 & 3 & \(-\)3 & \(-\)7 & 0 & 0 & 0 & **E1** & 0 & \(-\)5 & \(-\)7 & 4 & \(-\)3 & \(-\)7 & \(-\)10 & 0 & 0 \\
**B1** & 0 & \(-\)5 & \(-\)7 & 3 & \(-\)3 & \(-\)7 & \(-\)10 & 0 & 0 & **F1** & 0 & \(-\)5 & \(-\)7 & 4 & \(-\)3 & \(-\)7 & \(-\)10 & 0 & 2 \\
**C1** & 0 & \(-\)5 & \(-\)7 & 3 & \(-\)3 & \(-\)7 & \(-\)15 & 0 & 0 & **G1** & 0 & \(-\)5 & \(-\)7 & 4 & 0 & \(-\)7 & \(-\)10 & 0 & 2 \\
**D1** & 0 & \(-\)5 & \(-\)7 & 3 & \(-\)3 & \(-\)7 & \(-\)10 & \(-\)5 & 0 & **H1** & 0 & \(-\)5 & \(-\)7 & 4 & 0 & \(-\)7 & \(-\)10 & 0 & 7 \\ \hline \multicolumn{11}{c}{**Axial Force (N) for Case 30505050 and Cases A1-H1**} \\ \hline \multicolumn{11}{c}{**Cable**} & \multicolumn{11}{c}{**30505050**} & \multicolumn{11}{c}{**A1**} & \multicolumn{11}{c}{**B1**} & \multicolumn{11}{c}{**C1**} & \multicolumn{11}{c}{**D1**} & \multicolumn{11}{c}{**E1**} & \multicolumn{11}{c}{**F1**} & \multicolumn{11}{c}{**G1**} & \multicolumn{11}{c}{**H1**} \\ \hline
40 & \(-\)7.73 & 1.65 & 3.94 & 10.00 & 10.00 & 5.00 & 10.00 & 5.00 & 6.07 & \\
42 & 10.00 & \(-\)2.74 & 0.11 & 1.58 & \(-\  
The determined coefficients \(\beta_{i}\) are \(-1399.907\), \(-2490.990\), \(-131.972\) in SB1, \(786.626\), \(-2855.643\), \(462.793\) in SB2 and \(-1368.241\), \(1188.504\), \(74.294\) in SB3. The above sets of coefficients beta \(\beta_{i}\) (\(i\) = 1, 2, 3), are used to calculate the vector of axial forces (see Equation (10) that satisfy the inequality constraint represented by Equations (12) and (13). It is emphasized that the solution obtained for the self-equilibrated configuration for SB1, SB2, and SB3 represents one possible configuration with close resemblance to the geometry of the human spine. The self-equilibrated configuration could be further refined through solution of constrained optimization problem using maximum stiffness, minimum weight or other suitable criteria as objective functions. In the process of determination of coefficients \(\beta_{i}\)*, the combinations of coefficients \(\beta_{1}\)*, \(\beta_{2}\)* and \(\beta_{3}\)* that lead to tension in struts or compression in cables are rejected. Non-acceptance of the trial values of coefficients \(\beta_{i}\)*(\(i\) = 1,2,3) obtained from solution of problem defined by Equation (11) is always due to non-satisfaction of Equation (12) (the existence of slackened cables) within the trial configuration of spine biotensegrity models. The proposed form-finding strategy using approach one and two yields updated trial configurations of spine biotensegrity models to reduce slackened cables and to maintain closely the geometrical characteristics of the spine. Approach two eliminates inconsistent cables and further refines the configuration. It is found that, although modification of nodal coordinates in some cases can reduce slackened cables, increment in the degree of slackness in other slackened cables and the generation of new slackened cables are observed.