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Lyman-Kutcher-Burman Model (NTCP)
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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
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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:

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

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Factor $t$ of the LKB Model
Equation

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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.

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Effective Dose in the LKB Model
Equation

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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.

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Data Model LKB
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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

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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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