A new formula for calculating normal tissue complication probability

Area of Science:

• Radiation Oncology
• Biophysics
• Medical Physics

Background:

• Quantitative modeling of biological effects is crucial for effective treatment planning.
• Accurate calculation of normal tissue complication probability (NTCP) is essential to minimize treatment toxicity.
• Existing models, like the Lyman-Kutcher-Burman (LKB) formula, can be complex for direct application.

Purpose of the Study:

• To develop a simplified equivalent function to the Lyman formula for calculating NTCP.
• To facilitate the integration of quantitative biological modeling into radiotherapy treatment planning.
• To introduce a new NTCP model based on equivalent uniform dose (EUD).

Main Methods:

• Approximation of the Lyman-Kutcher-Burman (LKB) formula using three parameters (n, m, TD50) as a function of equivalent uniform dose (EUD).
• Mathematical derivation and definition of new formula parameters in terms of LKB model parameters.
• Recalibration of parameters to existing tolerance data using the proposed formula.

Main Results:

• A new sigmoidal NTCP formula was developed, symmetrical about TD50, with minimal differences (<0.1%) compared to the LKB model.
• The derived parameters (n, m, TD50) are mathematically robust and provide a superior fit to recalibrated tolerance data.
• The new model demonstrates comparable or improved fitting of brain data versus the LKB model.

Conclusions:

• A new formula representing NTCP as a function of EUD has been successfully developed.
• The derived parameters are mathematically sound and offer enhanced data fitting capabilities.
• This simplified model is potentially useful for treatment planning and shows strong performance with brain data.