Abstract
The Gompertz model is the long-time well-known mathematical model of exponential expression among mortality models in the literature that are used to describe mortality and survival data of a population. The death rate of the “probacent” model developed by the author based on animal experiments, clinical applications and mathematical reasoning was applied to predict age-specific death rates in the US elderly population, 2001, and to express a relationship among dose rate, duration of exposure and mortality probability in total body irradiation in humans. The results of both studies revealed a remarkable agreement between “probacent”-formula-predicted and published-reported values of death rates in the US elderly population or mortality probabilities in total body irradiation in humans (p - value > 0.995 in χ² test in each study). In this study, both the Gompertz and “probacent” models are applied to the Sacher’s comprehensive experimental data on survival times of mice daily exposed to various doses of total body irradiation until death occurs with an assumption that each of both models is applicable to the data. The purpose of this study is to construct general formulas expressing relationship between dose rate and survival time in total body irradiation in mice. In addition, it is attempted to test which model better fits the reported data. The results of the comparative study revealed that the “probacent” model not only fit the Sacher’s reported data but also remarkably better fit the reported data than the Gompertz model. The “probacent” model might be hopefully helpful in research in human tolerance to low dose rates for long durations of exposure in total body irradiation, and further in research in a variety of biomedical phenomena.
Highlights
The death rate of the “probacent” model developed by the author based on animal experiments, clinical applications and mathematical reasoning was applied to predict age-specific death rates in the US elderly population, 2001, and to express a relationship among dose rate, duration of exposure and mortality probability in total body irradiation in humans
The results of both studies revealed a remarkable agreement between “probacent”-formula-predicted and published-reported values of death rates in the US elderly population or mortality probabilities in total body irradiation in humans (p-value > 0.995 in χ2 test in each study). Both the Gompertz and “probacent” models are applied to the Sacher’s comprehensive experimental data on survival times of mice daily exposed to various doses of total body irradiation until death occurs with an assumption that each of both models is applicable to the data
The “probacent” model of death rate equation is applied to the Sacher’s experimental data on dose rates versus mean after-survival times (MAS) in mice daily irradiated during the duration of life [37]
Summary
The Gompertz model (1825) is the long-time well-known mathematical model of exponential expression among mortality models in the literature that are used to describe mortality and survival data of a population [1,2,3].The ordinary procedure in biomedical survival data analysis is to apply the non-parametric life table method or nowadays, especially the non-parametric KaplanMeier product-limit method [1,4,5,6,7,8].The most commonly used methods of parametric estimation for distributions of survival times are the fittings of exponential, lognormal, Weibull, gamma and Gompertz function of survival time.1.1. On the basis of experimental observations on animals, clinical applications and mathematical reasoning, the author developed a general mathematical model of “probacent”-probability equation that may be applicable as a general approximation method to possibly calculate the probability of safe survival in humans and other living organisms exposed to any harmful or adverse circumstances in overcoming the risk, and further to predict degrees of risk and/or mortality probability in terms of percent probability. In this way, the “probacent” model might make useful predictions of probable outcomes in a variety of biomedical phenomena in protecting exposed subjects [9,10,11,12]. The model of “probacent”-probability equation expressed by Eq. was constructed from experimental studies on animals to express survival probability in mice exposed to g-force in terms of magnitude of acceleration and exposure time [9,13]; and to express a relationship among intensity of stimulus or environmental agent (such as drug [9,10,14], heat [15], pH [16], and electroshock [15,17]), duration of exposure and biological response in animals
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
