**1. Introduction**

The history of the development of radiobiological models began immediately after the discovery of X-rays and is rapidly continuing at present time, overcoming an increasing number of restrictions. The practical application of biological radio models is a typical clinical practice when treating oncological diseases.

Owing to the development of radiobiological models, it has become possible to mathematically describe the biological phenomena that occur in the body under the influence of ionizing radiation. They allow for predicting the event that causes ionizing radiation in a particular cell. The practical application of radiobiological models makes it possible to calculate radiation doses and the number of fractions, compare the biological effect of irradiation under different dose fractionation regimes, and present physical quantities in the form of clinical indicators. Radiation therapy (RT) is characterized by physical and mathematical values, which are expressed by specific numerical values (dose per fraction, total radiation dose, number of RT sessions, time interval between RT sessions, etc.). But when developing and optimizing radiation treatment plans, doctors and physicists use clinical indicators (biologically effective dose, linear-quadratic equivalent dose for 2 Gy fractions, tumor control probability, normal tissue complication probability, etc.) [1, 2].

Such radiobiological models as NSD, KRE, and TDF are considered out-of-date and can be useful only for the prevention of radiation complications, but they are not effective for the destruction of malignant tumors. Also, they cannot be used to calculate the biological effect on parenchymal tissues (lungs, nervous tissue, intestines, liver, kidneys, etc.).

To date, the LQ model is the most commonly used model in clinical practice [3], but it also has limitations being a simplified model of cell damage, and it should be used with caution considering the assessment of the possible risks of complications from the dose and irradiated volume, based on the QUANTEC findings in the conditions of modern medical imaging, optimization of dosimetric planning of exposure, and new approaches to conducting RT sessions. Today, there are modifications of the LQ model [4–6], which allow calculating tolerant doses, as well as the probability of occurrence of radiation complications in tissues as a function of the volume of exposure, and single and total dose.

To achieve the main goal of radiation therapy (tumor eradication, alleviation of the patient's condition), it is necessary to deliver a dose of radiation, which is sufficient to destroy the tumor, to the volume of radiation exposure [7]. This occurs at the cost of acceptable toxicity of normal tissue, which is associated with radiation complications. The rapid development and improvement of RT planning technologies significantly affect the reduction of the negative consequences of the influence of radiation on healthy tissues and organs at risk without worsening the results of the treatment of cancers. But even with the use of the best planning technologies on modern radiotherapy equipment in accordance with high standards of treatment, for many sites, there is a high frequency of relapses and mortality from the underlying disease. A key role in this belongs to an increase in the duration of the general course of RT [8–12].

The problem of estimation of the negative impact of interruptions in radiation treatment and the ways of their compensation is regularly raised at the training courses by the International Atomic Energy Agency (IAEA) in cooperation with the Government of Russian Federation through the State Research Centre—Burnasyan Federal Medical Biophysical Centre of Federal Medical Biological Agency and the Association of Medical Physicists of Russia (AMPR). At the same time, at the present stage, it is proposed to rely on the linear-quadratic radiobiological model (LQM) theory, which has a long and complex history [13–15].

The practical application of the LQM in many institutions is an integral part of the clinical practice of cancer therapy. However, calculations related to the estimation of radiation doses when the radiation treatment schedule changes during the course of RT lead to a significant increase in the working time of medical physicists and radiation oncologists and also require special training of qualified specialists capable of conducting them.

Introducing LQM into practice for estimation of radiation doses taking into account the loss of the biological effect when modifying radiation treatment regimens, specialists face the above-mentioned difficulties. Therefore, to solve the identified issues, we have proposed the Web application that allows us to optimize the processes associated with the estimation of radiation doses when modifying the radiation treatment schedule for patients.

The aim of our study was to optimize calculations related to the estimation of radiation doses when the radiation treatment schedule changes by simulating such changes in special software created on the basis of the theory of a linear-quadratic radiobiological model.
