Lyman-Kutcher-Burman Model (NTCP)
Image
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:
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Probability of Complications with LKB Model
Equation
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
$NTCP=\displaystyle\frac{1}{\sqrt{2\pi}}\int_{-\infty}^t e^{-u^2/2}du$ |
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Factor $t$ of the LKB Model
Equation
The probability of failure of an organ is estimated based on the deviation of the effective dose calculated for the healthy tissue
$ t =\displaystyle\frac{ D_{eff} - TD_{50} }{ mTD_{50} }$ |
The
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Approximation of the NTCP Function in the LKB Model
Equation
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:
$NTCP=\displaystyle\frac{1}{1+e^{-1.5976t-0.07056t^3}}$ |
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Effective Dose in the LKB Model
Equation
The dose is calculated by considering the fraction of the
Thus, the effective dose is:
$D_{eff}=\left(\sum_iv_iD_i^{1/n}\right)^n$ |
where
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Data Model LKB
Description
The typical data of the LKB model are the exponent
Organo | N | M | TD50
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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
Parótida | 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.
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Lyman-Kutcher-Burman Simulator (NTCP)
Storyboard
The NTCP according to the LKB model is diagrammed for different
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