Skip to main content

Table 3 Mean ± mean standard error of the parameters and criteria for model assessment using in fitting of fibrosarcoma Sa-37 tumor growth data with modified models of Gompertz (Eq. 2), Logistic (Eq. 1) and Kolmogorov-Johnson-Mehl-Avrami (mKJMA) (Eq. 6) from t ≥ 8 days

From: Is cancer a pure growth curve or does it follow a kinetics of dynamical structural transformation?

  Modified equations on normalized data
Gompertz Logistic mKJMA
X1 ± SD (0.473 ± 0.053) days−1 0.953 ± 0.031 (0.083 ± 0.008) days−1
X 2 ± SD (0.233 ± 0.031) days−1 (0.425 ± 0.043) days−1 3.409 ± 0.529
X3 ± SD - - 1.509 ± 0.366
r2 ± SD 0.991 ± 0.005 0.982 ± 0.011 0.991 ± 0.006
r 2 a ± SD 0.990 ± 0.007 0.979 ± 0.013 0.990 ± 0.007
SE ± SD 0.030 ± 0.009 0.044 ± 0.013 0.030 ± 0.009
SSE ± SD 0.009 ± 0.006 0.019 ± 0.010 0.009 ± 0.006
PRESS ± SD 0.0008 ± 0.0005 0.0015 ± 0.0008 0.0007 ± 0.0005
MPRESS1 ± SD 0.0011 ± 0.0007 0.0022 ± 0.0014 0.0010 ± 0.0007
MPRESS2 ± SD 0.0012 ± 0.0008 0.0024 ± 0.0016 0.0012 ± 0.0007
MPRESS3 ± SD 0.0014 ± 0.0009 0.0026 ± 0.0018 0.0013 ± 0.0009
Ko (days−1) - - 0.109 ± 0.014
Ea (J/mol) - - 706.97 ± 393.15
RT (J/mol) - - 2 568.85
  1. X1 and X 2 variables signify the parameters α and β in the modified Gompertz equation whereas these two variables symbolize the parameters K* and r* in the modified Logistic equation, respectively. X1 X 2 and X3 represent K, n and λ in Modified KJMA equation, respectively. RT is the thermal energy calculated. SE: Standard error of the estimate. SSE sum of squares of errors. r 2 a : adjusted r2. PRESS Predicted residual error sum of squares and MPRESS Multiple predicted residual sum error of squares. SD Standard deviation. Ko is the pre-exponential factor. Ea is the activation energy (activation enthalpy) of tumor cell nucleation. r 2 is the goodness-of-fit. Details of SE, SSE, r 2, r 2 a , PRESS and MPRESS are given in [2, 14]