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Table 1 Factor form and curvature radius by planes for the fibrosarcoma Sa-37 tumor

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

Planes Form factor (FF) Curvature Radius Rc (in mm)
Rc-L1 Rc-L2 Rc-L3
xy πab/2p 2 ab b 2/a a 2/b -
xz πac/2p 2 ac c 2/a - a 2/c
yz πbc/2p 2 bc - c 2/b b 2/c
  1. a (a = L1/2), b (b = L2/2) and c (c = L3/2) are the semi-axes of triaxial (or scalene) ellipsoid tumor on their respective planes. pab, pac and pbc are the ellipse perimeters on planes xy, xz and yz, respectively. Rc-L1 is the curvature radius in the point A, Rc-L2 in the point B and Rc-L3 in the point C, as shown in Fig. 1a. It is important to point that the general expression for ellipse curvature radius on each plane is not given because the points of the closed curve do not experimentally measure
  2. \( {p}_{a b}=\pi \left( a+ b\right)\left[1+\frac{1}{4}{\left(\frac{a- b}{a+ b}\right)}^2+\frac{1}{64}{\left(\frac{a- b}{a+ b}\right)}^4+\frac{1}{256}{\left(\frac{a- b}{a+ b}\right)}^6\right] \)
  3. \( {p}_{a c}=\pi \left( a+ c\right)\left[1+\frac{1}{4}{\left(\frac{a- c}{a+ c}\right)}^2+\frac{1}{64}{\left(\frac{a- c}{a+ c}\right)}^4+\frac{1}{256}{\left(\frac{a- c}{a+ c}\right)}^6\right] \)
  4. \( {p}_{b c}=\pi \left( b+ c\right)\left[1+\frac{1}{4}{\left(\frac{b- c}{b+ c}\right)}^2+\frac{1}{64}{\left(\frac{b- c}{b+ c}\right)}^4+\frac{1}{256}{\left(\frac{b- c}{b+ c}\right)}^6\right] \)