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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