A new formula for calculating normal tissue complication probability

Abstract

Purpose: To facilitate the use of quantitative modeling of biological effects in treatment planning by introducing a simpler function equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP).

Methods: We first provide an approximation of the Lyman-Kutcher-Burman (LKB) formula using three parameters (n, m, TD₅₀) as a function of equivalent uniform dose (EUD). The parameters for the new formula are defined in terms of the Lyman model’s m and TD₅₀. Conversely, m and TD₅₀ are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter n remains unchanged from its role in the Lyman model.

Results: The new formula, which exhibits a sigmoidal shape, demonstrates symmetry about TD₅₀, akin to the LKB model. The difference in NTCP between the two formulas is less than 0.1%. The parameters (n, m, TD₅₀) are preserved through rigorous mathematical deduction and have been recalibrated to the tolerance data of Emani et al. using the proposed formula. This new model provides a better fit to these data than the model by Burman et al., which was fitted “by eye” rather than using statisticalmethods.

Conclusion: We have developed a formula that represents NTCP as a function of EUD, which proves to be potentially useful. The parameters derived in this study are mathematically robust and offer a superior fit to the data compared to previous efforts. Additionally, the new model fits brain data as well as, if not better than, the LKB model.

Keywords

Normal tissue complications / LKB model / Equivalent uniform dose

References

[1] DenRB, DickerAP. IMRT, IGRT, SBRT: Advances in Treatment Planning and Delivery of Radiotherapy. Int J Radiat Oncol Biol Phys. 2012;83(1):e3-e3.

[2] WolbarstAB, ChinLM, SvenssonGK. Optimization of radiation therapy: integral-response of a model biological system. Int J Radiat Oncol Biol Phys. 1982;8(10):1761-1769.

[3] LymanJT. Complication probability as assessed from dose-volume histograms. Radiat Res Suppl. 1985;8:S13-S19.

[4] KutcherGJ, BurmanC. Calculation of complication probability factors for non-uniform normal tissue irradiation: the effective volume method. Int J Radiat Oncol Biol Phys. 1989;16(6):1623-1630.

[5] EmamiB, LymanJ, BrownA, et al. Tolerance of normal tissue to therapeutic irradiation. Int J Radiat Oncol Biol Phys. 1991;21(1):109-122.

[6] SchultheissTE, OrtonCG, PeckRA. Models in radiotherapy: volume effects. Med Phys. 1983;10(4):410-415.

[7] KällmanP, AgrenA, BrahmeA. Tumour and normal tissue responses to fractionated non-uniform dose delivery. Int J Radiat Biol. 1992;62(2):249-262.

[8] KhanAJ, KirkMC, MehtaPS, et al. A dosimetric comparison of threedimensional conformal, intensity-modulated radiation therapy, and MammoSite partial-breast irradiation. Brachytherapy. 2006;5(3):183-188.

[9] UematsuM, ShiodaA, TaharaK, et al. Focal, high dose, and fractionated modified stereotactic radiation therapy for lung carcinoma patients: a preliminary experience. Cancer. 1998;82(6):1062-1070.

[10] HernandoML, MarksLB, BentelGC, et al. Radiation-induced pulmonary toxicity: a dose-volume histogram analysis in 201 patients with lung cancer. Int J Radiat Oncol Biol Phys. 2001;51(3):650-659.

[11] LeeTF, TingHM, ChaoPJ, et al. Model Parameters Estimating on Lyman-Kutcher-Burman Normal Tissue Complication Probability for Xerostomia on Head and Neck Cancer. Int J Med Heal Biomed Bioeng Pharm Eng. 2012;6:319-322.

[12] KehwarTS. Analytical approach to estimate normal tissue complication probability using best fit of normal tissue tolerance doses into the NTCP equation of the linear quadratic model. J Cancer Res Ther. 2005;1(3):168-179.

[13] NiemierkoA. Reporting and analyzing dose distributions: a concept of equivalent uniform dose. Med Phys. 1997;24(1):103-110.

[14] NiemierkoA, Goitein M. Modeling of normal tissue response to radiation: the critical volume model. Int J Radiat Oncol Biol Phys. 1993;25(1):135-145.

[15] GayHA, Niemierko A. A free programfor calculating EUD-basedNTCP and TCP in external beam radiotherapy. Phys Med. 2007;23(3-4):115-125.

[16] BurmanC, Kutcher GJ, EmamiB, GoiteinM. Fitting of normal tissue tolerance data to an analytic function. Int J Radiat Oncol Biol Phys. 1991;21:123–135.

[17] LymanJT. Complication probability as assessed from dose-volume histograms. Radiat Res Suppl. 1985;8:S13-S19.

[18] ParkC, PapiezL, ZhangS, Story M, TimmermanRD. Universal survival curve and single fraction equivalent dose: useful tools in understanding potency of ablative radiotherapy. Int J Radiat Oncol Biol Phys. 2008;70(3):847-852.

RIGHTS & PERMISSIONS

2024 The Author(s). Precision Radiation Oncology published by John Wiley & Sons Australia, Ltd on behalf of Shandong Cancer Hospital & Institute.