Аннотация.

Работа посвящена проблеме математического моделирования лечебно-диагностического процесса. Предложен подход к построению модели процесса в классе управляемых стохастических процессов с памятью. Модель основывается на двух постулатах: моделирование в классе стохастических процессов и прецедентный характер «управления» в медицине. Концептуальная основа модели имеет ясную содержательную интерпретацию для специалистов-медиков.

Ключевые слова:

лечебно-диагностический процесс, генерализация медицинских данных, математическая модель, стохастический управляемый процесс с памятью, Марковский процесс.

Стр. 60-72.

V.L. Malykh, Ya.I. Guliev

"Mathematical model of clinical processes implemented in the class of stohastic markov control processes with memory"

The work is devoted to problem of mathematical modeling of the diagnostic and treatment process. There is a whole arsenal of methods designed for the processing of experimental data and building models of dynamic objects (processes). But the problem of mathematical modeling of the diagnostic and treatment process is still not resolved. Difficulties associate with the medicine area itself. The dimensions of control process (medical treatments) and of observable characteristics of the patient state (medical symptoms and indicators) are very big. These dimensions create a barrier for formalization and construction of dynamic model of clinical process based on experimental data. We propose an approach to the construction of abstract mathematical model of clinical process in the class of stochastic Markov processes with memory. The model is based on two postulates. Implementation of model in the class of stochastic processes; according to Ross Ashby’s system classification complex systems and processes should have stochastic nature. Usage of precedents is the next basis of the approach. Medicine is very conservative, active actions (control) are selected on the basis of already known precedents that have been proven effective (evidence based medicine). The conceptual basis of the model has a clear, meaningful interpretation for medical professionals.

Keywords: clinical process, generalization of medical data, mathematical model, stochastic control process with memory, Markov process

Полная версия статьи в формате pdf.

REFERENCES

1. Malykh V.L., Guliev Y.I. (2013). Modeling of medical-diagnostic process in a class of controlled stochastic processes with memory. Vrach i informatsionniye tekhnologii, (2), 6-15.
2. Nazarenko G.I., Polubentseva E.I. Upravlenie kachestvom meditsinskoy pomoschi [Medical services quality management]. Moscow, Meditsina, 2000.
3. Nazarenko G.I., Osipov G.S. Osnovyi teorii meditsinskikh tehnologicheskikh protsessov [Fundamentals of the theory of medical technological processes]. Moscow, Fizmatlit, 2005.
4. Informational letter of the Ministry of health and social development of Russia N 14-3/10/2-11668, 2011.   URL: http://www.minzdravsoc.ru/docs/mzsr/spa/112
5. Malykh V.L., Guliev Y.I. (2009). Precedents in medical information systems. Programmniye produkty i sistemy,  2(86), 19-27.
6. Bukreev V.G., Kolesnikova A.E., Yankovskaya A.E. Vyiavlenie zakonomernostey vo vremennykh ryadakh v zadachakh raspoznavaniya sostoyaniy dinamicheskikh ob'ektov [Revealing of regularities in time series in problems of recognition of the states of dynamic objects]. Tomsk, Izdatelstvo Tomskogo politehnicheskogo universiteta, 2010.
7. Belov A.K. Filosofiya estestvennoy prirody [The philosophy of nature]. Moscow, Izdatelstvo «Sputnik+», 2011. 355 p.
8. Gelfand I.M., Rosenfeld B.I., Shifrin M.A. Ocherki o sovmestnoy rabote matematikov i vrachey [Essays on Collaboration of Mathematicians and Physicians]. Moscow, Editorial URSS, 2005. 320 p.
9. Malykh V.L., Guliev Y.I., Krylov A.I., Ryumina E.V. (2009). Problems of automation of calculation of direct material expenditures in medicine. Precedent-based architecture of materials accounting. Audit i finansoviy analiz, (2), 465-471.
10. Thomas J. Handler, M.D., Barry R. Hieb, M.D. Gartner's 2007 Criteria for the Enterprise CPR URL: http://rsept.wikispaces.com...