The Lyman-Kutcher-Burman model seeks to estimate the probability of complications in healthy tissue (NTCP) by delivering a probability curve according to the dose:

(ID 2715)

The estimation of the probability of complications in the Lyman Kutcher Burman Model (LKB) assuming that the probability of failure can be represented as a gauseana around dose D50. For this reason the NTCP value is estimated by integrating the gauseana to the value of t:

$NTCP=\displaystyle\frac{1}{\sqrt{2\pi}}\int_{-\infty}^t e^{-u^2/2}du$

(ID 4699)

The probability of failure of an organ is estimated based on the deviation of the effective dose calculated for the healthy tissue D_{eff} and the dose under which there is a 50% probability of failure TD50:

$ t =\displaystyle\frac{ D_{eff} - TD_{50} }{ mTD_{50} }$

The m factor defines the slope of the NTCP curve and assumes values around 0.40.

(ID 4846)

The integral of the Gaussian can be approximated by the expression

$\displaystyle\frac{1}{\sqrt{2\pi}}\displaystyle\int_{-\infty}^t du\,e^{-u^2/2}=\displaystyle\frac{1}{1+e^{-0.07056 t^3 - .5976 t}}$

so it is necessary that in the first approximation the NTCP is:

$NTCP=\displaystyle\frac{1}{1+e^{-1.5976t-0.07056t^3}}$

(ID 4700)

The dose is calculated by considering the fraction of the v_i volumes of the different i elements in which the patient's body is subdivided (voxels).

Thus, the effective dose is:

$D_{eff}=\left(\sum_iv_iD_i^{1/n}\right)^n$

where n is a factor that fits and its value is around the unit.

(ID 4708)

The typical data of the LKB model are the exponent n, the slope factor m and the dose in which 50% of the cases will have complications TD50:

Organo | N | M | TD50
Eur-lex.europa.eu eur-lex.europa.eu
Joint and jaw | 0.07 | 0.1 | 72
Femoral head and neck | 0.25 | 0.12 | 65
Thoracic box | 0.1 | 0.21 | 68
Equine Tail | 0.03 | 0,12 | 75
Brain | 0.25 | 0.15 | 60
Brain, brain stem | 0.16 | 0.14 | 65
Colon | 0.17 | 0.11 | 55
Heart | 0.35 | 0.1 | 48
Laryngeal-laryngeal edema | 0.11 | 0.075 | 80
Esophagus | 0.06 | 0,11 | 68
Stomach | 0.15 | 0.14 | 65
Liver | 0.32 | 0.15 | 40
Small Intestine | 0.15 | 0.16 | 55
Lens | 0.3 | 0.27 | 18
Spinal cord | 0.05 | 0.175 | 66.5
Cartilage necrosis of the larynx | 0.08 | 0.17 | 70
Optic nerve | 0.25 | 0.14 | 65
Ear, Acute Serous Otitis | 0,01 | 0.15 | 40
Ear, chronic otitis | 0.01 | 0.095 | 65
Par tida | 0.7 | 0,18 | 46
Leather | 0.1 | 0.12 | 70
Brachial plexus | 0.03 | 0.12 | 75
Lungs (both combined) | 0.87 | 0.18 | 24.5
Optical chiasm | 0.25 | 0.14 | 65
Rectum | 0.12 | 0,15 | 80
Retina | 0.2 | 0,19 | 65
Kidney | 0.7 | 0.1 | 28
Thyroid | 0.22 | 0.26 | 80
Bladder | 0.5 | 0.11 | 80

From Burman C, Kutcher G J, Emami B and Goitein M 1991 Fitting of normal tissue tolerance data to an analytic function Int. J. Radiat. Oncol. Biol. Phys.

(ID 8816)

The NTCP according to the LKB model is diagrammed for different n, m and TD50.

(ID 8817)