[The use of electronic computers and methods of linear programming for the choice of optimal conditions in radioteletherapy].
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Computers↗
Biomedical subjects
L Ia Klepper
Publications and source records attributed to L Ia Klepper.
[Mathematical models of dose fractionation based on LQ function. (population-tissue models)].
A mathematical model was developed to calculate the probability of tumor tissue sterilization. It is assumed that tumor tissue contains normal and radio-resistant tumor cells and the survival of both types of tumor cells can be described by LQ functions. A package of programmes was created to solve the extreme problems in the determination of the parameters of LQ functions and the relative count of radio-resistant cells in the volume of tumor tissue. A programme complex was devised to solve practical tasks in radiological care. The series of tasks, which illustrate various aspects of determination of the parameters of the mathematical model by using clinical data and calculating the probability of tumor tissue radiation sterilization.
Carcinoma, Squamous Cell↗
[Choice of optimal centering points of radiation beams in planning radiotherapy in malignant tumors].
A programmed complex has been developed to determine the optimum radiation protocols which include the optimum positions of intersection centers of central axes of radiation beams, the optimum directions of radiation, the optimum time of exposure. Analyzing the optimum radiation protocols has shown that variations in the positions of intersection centers of radiation beams play a crucial role in the targeted formation of the optimum dose fields. To choose the optimum radiation protocols for central lung cancer is a challenge whose solution depends on the initial position of intersection centers of radiation beams, which give rise to iterative solution of emergency problems. An effective radiation protocol has been chosen among its varieties by making a multicriteria assessment of gross characteristics of dose fields in the lung tissue.
Algorithms↗
[Nonuniform dose distributions in normal body organs and tissues in the radiotherapy of malignant tumors].
A mathematical model has been developed to evaluate the nonuniform impact of tissue radiation exposure in an equal dose (or an effective dose). The equal dose (or effective dose) is that of the uniform tissue radiation, which is equivalent to the nonuniform distribution of a dose. The paper presents a mathematical analysis of the model and studies its properties. The factor that can be regarded as a measure for systemic reparative tissue capacity against radiation exposure is identified.
Humans↗
[Interactive determination of the parameters of mathematical models for planning radiotherapy of malignant tumors. I. Mathematical models for calculating dose tolerance, adequate doses and the likelihood of development of radiation complications in normal organs and tissues].
Mathematical models for calculating tolerance doses, adequate doses and the likelihood of radiation complications in the body's normal tissues are considered. To determine the parameters of these models that describe the outcomes of radiation exposure of complicated biological systems, a method of local adjustment of the parameters of the models has been developed, which will be described in parts 2 and 3 of the proposed paper. In part 1 (the present paper), particular emphasis is laid on the inclusion of an important parameter, such as a volume, into Ellis and LQ models. A mathematical model is presented for calculating the likelihood of a radiation complication in the tissue, which is the basis for deriving a formula to calculate an adequate uniform tissue radiation dose that is equivalent to the nonuniform tissue distribution of a dose in terms of the likelihood of radiation complications.
Humans↗
[The interactive determination of the mathematical model parameters for the planning of the radiation therapy of malignant tumors. 2. A method of adjusting the mathematical model parameters for calculating the tolerance doses and probabilities of the occurrence of radiation complications in body organs and tissues].
To enhance the accuracy of calculation of tolerance doses, adequate doses and the likelihood of radiation complications in normal organs and tissues, a method has been developed for local model parameter adjustment (LMPA) by using mathematical models. It includes the analysis of the structure of a mathematical model, the systematization of clinical data and their goal-oriented use for model adjustment. The necessity of developing a new research line (LMPA) is determined by the complexity of the irradiated organism as a system and by the attempts to take into account the impact of the system on the parameters of mathematical models. LMPA can be considered to generalize determination of the parameters of mathematical models or their directed (interactive) determination. The strategy of using LMPA, which is based on the preset radiation treatment protocol and its respective dosage distributions in normal organs and tissues, is described. The efficiency of LMPA is shown to depend on the volume and relevance of clinical data that the radiological therapist has at his disposal.
Computer Simulation↗
[Interactive determination of the parameters of mathematical models in planning radiotherapy of malignant tumors. 3. Method of local adjustment of the parameters of mathematical models (examples of application)].
To increase the accuracy of calculation of tolerance doses of the likelihood of radiation-induced complications in normal organs and tissues by using mathematical models, the author has developed a method for local mathematical model parameter adjustment (LMMPA) which included analysis of the structure of a mathematical model, systematization of clinical information and its goal-oriented use to determine the parameters of a model. The necessity of developing the LMMPA method stemmed from the complexity of the body exposed to radiation a system and from the quest for taking into account the impact of the system on the values of mathematical models. LMMPA may be regarded as the extension of determination of the parameters of mathematical models or as the interactive determination of their parameters that describing radiation exposures of complex biological systems. Different aspects of using of LMMPA are indicated how to apply it to the determination of tolerance doses for connective tissue, lung tissue, and the brain by using the Ellis and LQ models. The extended LMMPA is shown how to determine the parameters of a mathematical models for calculation of the likelihood of radiation-induced complications in the lung tissue.
Brain↗
[Method of calculating the equivalent tumor dose as a function as to irradiated tumor tissue volume].
Based on the assumption that tumor tissue consists of normal and radiation-resistant, that the survival of both types of tumor cells may be described by LQ functions and that the count of radiation-resistant cells is in proportion to that of tumor cells, the author has developed a method for calculating the equivalent tumor dose as a function as to irradiated tumor tissue volume for the fixed value of a single dose in the session of radiation. The developed formalism may be used to test the hypothesis that the count of clonogenic and radiation-resistant cells is in proportion to the baseline number of the cells in the tumor tissue.
Adenocarcinoma↗
[Probability of tissue cell death, integral cellularity and likelihood of radiation-induced tissue complications].
The paper describes a mathematical model for determining the likelihood of radiation-induced complications in the tissue as a function of the number of surviving cells. It is suggested the irradiated tissue cannot be regarded as a structureless point set of cells and that there are repairable and nonrepairable spatial configurations formed by surviving tissue cells. The probability of none tissue radiation complications may be considered is that of formation of a repairable structure from the surviving tissue cells. The paper shows why the radiation effect of radiation may be coupled (graded) in units of integral cellularity. Recurrent equations have been derived for calculating the number of repairable structures in relation to the conditions of tissue radiation. The values of a number of repairable structures as a function of an area and single dose of radiation are calculated as an example.
Cell Death↗
[Approximate methods for calculation of the likelihood of radiation-induced complications. 1. ACLRC method. 2. CERC method].
The paper deals with the method of approximate calculation of the likelihood of radiation complication (ACLRC) in normal organs and tissues when the volume of information is insufficient to determine all the parameters of a mathematical model. How to use the approximate method of LRC in the heart is exemplified. A method for approximate calculation of equivalent radiation conditions (CERC) in the focus of a lesion is offered, which allows the preset analytical (or graphic) description of the relationship of resorption likelihood (RL) to SOD for the fixed volume of a lesion focus to be transferred to the description of this relationship for other volumes.
Humans↗
[Approximate methods for calculating the probability of radiation complications. The PKLQ method].
A method of approximate calculation of the probability of resorption of a lesion focus by means of three mathematical models: the Poisson model, the Klepper model, and the LQ-model (the PKLQ method) is described. The method is based on a procedure for reducing SOD to the preset scope of a lesion focus. It is suggested that radio-sensitive (RS) cells predominate in the focus of lesion; radio-resistant cells are available in small quantities or their radiobiological properties differ from RS cells.
Poisson Distribution↗
[Approximate methods for calculation of the likelihood of radiation complications. The generalized PKLQ method (GPKLQM)].
Search for rational schedules of radiation therapy for malignant tumors is a topical problem of modern radiology. It cannot be solved without prognostic estimates of radiation affecting tumor and normal organs and tissues. The aim of the study was to develop mathematical models to be used for approximate evaluation of radiation affecting a tumor focus and normal organs and tissues. This paper provides a theoretical rationale for the generalized PKLQ (GPKLQ) method for a random count of tumor tissue radio-resistant cells, which is based on the view of the effective count of radio-sensitive cells (the effective volume of a damage focus).
Humans↗
[A summarized method for calculating the possibility of resorption of a focal lesion as a function of its volume and irradiation dose].
The mathematical model of calculation of equivalent conditions of irradiation (CECI) can be used in those cases, when it is impossible to divide clearly the tumor cells into radiation sensitive (RS) and radiation resistant (RR) and when the spectrum of radio-biological properties of tumor cells can be regarded as quasi-continuous.
Humans↗
[Formation of optimum dose fields in contact radiation therapy of malignant tumors].
The definition of the homogeneity of a dose field in the contact radiation therapy for malignant tumors is introduced. The mathematical interpretation of problems in the formation of optimum dose fields, to which the maximum homogeneity of a dose field at the site of lesion corresponds, is presented. It is shown that the problems in the formation of optimum dose fields may be divided into two subsets in relation to whether the sources of radiation are located at the site of lesion or adjacent to the latter (application techniques of radiation). An analytical method for solving a problem in the formation of an optimal dose field in the ring circle by means of one ring source of radiation (the first type of problems). The investigation was conducted with the support of the Russian Fund of Fundamental Investigations (RFFI 01-01-00137).
Dose-Response Relationship, Radiation↗
[Shaping-up of optimal dose fields in a stretch by means of dot-type and linear sources of irradiation (theoretical aspects)].
Shaping-up of a dose field in a stretch by means of dot-type and linear irradiation sources is mathematically interpreted. A criterion of an optimal dose field is formulated for the contact radiotherapy applicable to malignant tumors, which is based on homogeneity of such therapy. The task of forming an optimal dose field in a stretch by the dot-type and linear irradiation sources is insoluble on the basis of analytical methods. The task properties were investigated and an iterative method designed to solve it was elaborated on the basis of such properties.
Brachytherapy↗
[A method of the interactive visual optimization of the therapeutic dose field in contact radiation therapy of malignant tumors (theoretical aspects of the problem)].
The mathematical and interpretation tasks of a directed shaping of dose fields in the contrast radiation therapy of malignant tumors are defined on the basis of the dose-field homogeneity parameter. A schematic iterative algorithm of how to solve the tasks is described. A method for the visual optimization of such field is elaborated; it is based on preset limits to the dose field in the lesion focus and in the healthy organs and tissues. The dose field is shaped by an applicator with multiple terminal fixed positions of irradiation sources--the effect is achieved due to variability of their exposure duration.
Dose-Response Relationship, Radiation↗
[The mathematical modeling of the optimal dose fields in radiation therapy of malignant tumors. Part 1 (Distance radiotherapy)].
The specificity of mathematical modeling of optimal dose fields in radiation therapy of malignant tumors is under consideration. The permissible dose field is set now for irradiated body as a system of linear limitations to the doses at control spots (CS) distributed in the lesion focus and in the healthy organs and tissues. It is for the first time that an issue related with choosing an adequate number and method of CS distribution, based on uniform continuity of the dose field, is addressed in the paper. An iterative procedure of building the local CS networks is suggested. The method of linear programming (LP) can be used to select an optimal irradiation plan. A method of serial input of limitations, which cuts both the LP task scope and its computer-aided solution, is described.
Algorithms↗
[Mathematical modeling of optimal dose fields in radiotherapy of malignant tumors. Part 2 (Contact methods of radiotherapy)].
The principles of mathematical modeling of optimal dose fields in contact radiotherapy (RT) of malignant tumors are investigated. The point dose additivity provides for presetting the permissible dose field in an irradiated organism as a system of linear limitations to doses in the control points (CP) distributed in the lesion focus and in healthy organs and tissues. It was shown as impossible to shape a dose field by linear limitations to doses in CP in using the RT contact methods with the irradiation sources being implanted into lesion focus. A mathematic interpretation was suggested for the task (with its solution by an iterative algorithm) of forming an optimal dose field in the lesion focus with implanted irradiation sources, which is based on maximizing the factor of dose-field homogeneity. It was further demonstrated that linear limitations, if added to the dose in healthy organs and tissues, make the task even more complicated if not insoluble. Finally, it is suggested to use the method of shaping an effective dose field by the iterative method with interactive visual optimization of the dose field.
Algorithms↗