Proposals of models for new formulations of the current complication-free cure (P+) and uncomplicated tumor control probability (UTCP) concepts, and total normal tissue complication probability of late complications

Abstract

This study proposes phenomenological models for total normal tissue complication probability (TNTCP) and NTCP0. NTCP0 is a new acronym for reformulating the current complication-free cure (P+) and uncomplicated tumor control probability (UTCP) concepts, and TNTCP will reformulate the current NTCP involving multiple organs at risks. The current probabilistic concepts are incoherently formulated with mathematical operations of tumor control probability (TCP) and normal tissue complication probability (NTCP) that are associated with different stochastic processes and random variables. NTCP0 is equal to NTCP₀ (normal tissue non-complication probability) that is calculated as the ratio of a number of patients of a population without late complications and a total of them. As a cumulative distribution function (CDF) of late complications, TNTCP = sum(NTCP_i), where NTCP_i is the NTCP of the i^th late complication. TNTCP is also a new acronym, and the probabilistic complement of NTCP0, then NTCP0 = 100% − TNTCP. The NTCP0/TNTCP (D(d)) proposing models are based on the relationship between the NTCP0/TNTCP and total dose (D = n×d; where d = dose per fraction, and n = number of fractions). TNTCP(D) model will be correlated with LKB model (the normal CDF) that is an increasing function; and NTCP0(D) model with a decreasing function, which additionally will define clear limits of three possible regions for NTCP0: 0 and 100% deterministic, and a stochastic. These models are function D, which is widely used for characterizing radiation therapies.

Keywords:

• TCP
• NTCP
• complication-free cure
• uncomplicated TCP
• cumulative distribution function
• LKB

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Terman Frometa-Castillo

Terman Frometa-Castillo, Medical physicist of the Oncology Hospital of Santiago de Cuba. Founder and leader of the statistical models project (SMp) that develops probabilistic phenomenological/mechanistic models and computational simulators.

Anil Pyakuryal

Anil Pyakuryal, PhD, is an Adjunct Professorial Lecturer of Mathematics and Statistics at American University, and an Adjunct Instructor of Physics and Engineering at the University of District of Columbia.

Amadeo Wals-Zurita

Amadeo Wals-Zurita, MD, is a specialist in Radiation Oncology with experience in Lung Cancer, Head and Neck Cancer Lymphomas Brain cancer. Member of SEOR (Spanish Radiation Oncology Society), Member of the SAC (Andalusian Cancer Society), Professor at UNIA (Universidad Internacional de Andalucia).

Asghar Mesbahi

Asghar Mesbahi, PhD, is a Professor of Medical Physic (PhD) and Senior Radiation Therapy Physicist at Shahid Madani Hospital (Radiation Oncology Department), and has been working in medical physics sector since 2004 with focus on radiation therapy physics and dosimetry.