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Table 2 Theoretical and measured values of the perimeter scaling factor ξ for small neighbourhood sizes, needed for calculating the effective J value in the CPM

From: The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics

  2D 3D
neigh. neigh. ξ , estimated ξ , numer. % error neigh. ξ , estimated ξ , numer. % error
number radius using Eq. 29 determined   radius using Eq. 33 determined  
1 1 0.67 1 50.00 1 0.79 1 27.32
2 $\sqrt {2}$ 1.89 3 59.10 $\sqrt {2}$ 3.14 5 59.15
3 2 5.33 5 -6.25 $\sqrt {3}$ 7.07 9 27.32
4 $\sqrt {5}$ 7.45 11 47.58 2 12.57 11 -12.46
5 $2\sqrt {2}$ 15.08 15 -0.56 $\sqrt {5}$ 19.64 23 17.14
6 3 18.00 18 0 $\sqrt {6}$ 28.27 39 37.93
7 $\sqrt {10}$ 21.08 26 23.33 $2\sqrt {2}$ 50.27 47 -6.50
8 $\sqrt {13}$ 31.25 36 15.21 3 63.62 70 10.03
12 $2\sqrt {5}$ 59.63 68 14.04 $\sqrt {13}$ 132.73 134 0.96
20 $2\sqrt {10}$ 168.66 173 2.58 $\sqrt {22}$ 380.13 410 7.86
100 $3\sqrt {29}$ 2811.06 2850 1.39 $\sqrt {118}$ 1.09·104 11127 1.75
1000 $\sqrt {3365}$ 130133 130181 0.037 $3\sqrt {133}$ 1.13·106 1127539 0.20