Математическое моделирование хронобиологических изменений среднего артериального давления у различных возрастных групп

Выполняется статистическая обработка данных систематического измерения среднею артериального давления для пациентов различного возраста. Для решения задачи анализа и прогнозирования среднего артериального давления предлагается использовать процедуру 9-точечного сглаживания. Выявляются общие закономерности процесса и их особенности, характерные для различных возрастных групп. Предлагаются алгоритмы долгосрочного и краткосрочного прогнозирования среднего артериального давления и проводится анализ качества прогноза.

The Prediction of the Mean Arterial Pressure

The finding of the regularities in the dynamics of the arterial pressure is the basic question for its prediction. Some regularities are known and studied. Other ones are not so evident and known; the special experiments have to be carried out and significant information has to be gathered to find them. The twenty-four-hour monitoring of the mean arterial pressure (MAP) for the patients of the different ages was performed to study its temporal structure. The measurements were taken every half hour during a day and every hour at night. In this paper the measurements data of the MAP for the 4 patients, namely the 24 and 34 years old young men, 54 years old man and 57 years old woman are studied. The statistical data manipulation of the MAP based on the creation of the 9-point smoothed mean allowed finding some regularities of its dynamics. The smoothed value of MAP at the every point j is defined as weighted sum of the 9 successive measurements with the center at the current point. An analysis of the smoothed values showed that the dynamics of MAP has the cyclic nature with the period of 24 hours, the minimum occurs at 3-5 a.m. However there are two local maximums that occur at day time. Time interval between them is 5-7 hours. The dynamics of MAP for elder age group is considerably less regular than that for the younger patients. It is exhibited in the saltatory variation of maximums, more significant fluctuations of the time in- terval between maximums, high dispersion of MAP during the declining phase, duration of its phase, more saltatory behaviour of MAP in the rise and declining phases. The regular dynamics of MAP for the young patients lets to perform the long-term predictions some days and more ahead on the basis of the parameters choice of the periodic approximating function according to the first measurements. The comparison of the smoothed and predictable values of MAP indicated that the long-term prediction for the young patients is characterized by high accuracy on the most of cases. The extrapolation error is less than 3 points for the MAP of 24 years old patient in 92 points from 138 (67%), and this for the 34-years old patient is at 54%. However the probability of the relatively accurate prediction for the elder patients significantly decreases (14% for 54 years old man and 19% for the 57 years old woman). The regularities of MAP dynamics of such patients are not so evident and for the long-term prediction the additional study has to be conducted. For the short-term prediction (some hours ahead) of MAP for the elder patients in the conditions of the limited possibilities to find the regularities of the long process development, it is proposed to use the algorithms of the filtration and extrapolation on the basis of the stochastic process model. The proposed method of prediction can be considered as the development of the cosi-nor method. The deterministic base of the used model is presented by periodic function Pj = A cos(atj + Here pj - true value of MAP, tj - time of measurement j, со =-(I/hour),

- initial phase, determined by the time of the measurement beginning. However the unpredictable process behaviour is taken into account by stochastic component, introduced to the model. Moreover it is supposed that the measurements of MAP were obtained in the presence of additive random noise. The estimate of the predictable values is obtained on the basis of the extended Kalman filter for the proposed model. The comparison of the smoothed and predicted values of MAP indicated that the stochastic model for the short-term prediction of the MAP for the elder patients provides the significant accuracy increase compared to the prediction on the basis of the deterministic model. The prediction on the basis of the proposed algorithm is characterized by the error that in the half of the cases does not exceed the 3 points.