Mathematical model of the transfer of lead from peripheral blood into the organs and muscle tissue of sheep (Ovis aries)

To obtain livestock products that meet sanitary and hygienic standards for lead, it is necessary to establish the permissible limits of its daily intake by animals from the ration. In this work, based on the model we have developed, the parameters of lead transport between peripheral blood, organs and muscle tissue were determined for the first time, depending on the daily concentration of the metal in the ration and the duration of its entry into the body. Our aim was to develop and parametrize a chamber model of the transfer of lead from peripheral blood to the organs and muscle tissue of sheep during chronic dietary intake. The experiments were carried out on 27 Romanov sheep. The age of the animals is 1-1.5 years, body weight is 33.5±0.7 kg. Sheep were kept in boxes of 4-5 heads in the vivarium of the All-Russian Research Institute of Physiology, Biochemistry and Nutrition (BIFIP, Kaluga region, Borovsk). Feeding was carried out twice a day with free access to water. The animals were divided into four groups: group I (control) - 4 sheep, group II - 5 sheep, groups III and IV - 9 sheep each. The concentration of lead in the ration for group II was 5 mg•kg-1 (1 MPL), for group III - 25 mg•kg-1 (5 MPL), for group IV - 150 mg•kg-1 (30 MPL). Lead nitrate Pb(NO3)2 was added to compound feed once a day. The daily intake of metal for group II was 10 mg/head, group III - 50 mg/head, group IV - 300 mg/head, or 0.3, 1.5 and 9 mg•kg-1 body weight. Blood samples were taken before feeding from the jugular vein before the experiment, on days 30, 60 and 90. During the study period, animals were slaughtered, 1 sheep before the experiment, on days 30 and 60 1 sheep from group II and 3 sheep from groups III and IV; on day 90 - 3 sheep from each group. The patterns of distribution and accumulation of lead in the organs and tissues of sheep were analyzed using a mathematical model in which the liver, kidneys, spleen, lungs, heart and muscle tissue are represented as separate chambers physiologically interconnected by transport communications. Changes in the constants of the rate of transfer of lead from peripheral blood into different organs and muscle tissue of sheep, depending on the metal content in the ration and the duration of its intake, were established. The parameters characterizing the ratio of the constants of the rate of transfer of lead from the blood into the organs and back (from the organs into the blood) are determined. It is shown that the values of the parameters for the liver and kidneys as compared to other organs and tissues (spleen, lungs, heart and muscle tissue) are 10 and 100 times lower, respectively. Comparative analysis of experimental data and calculations on the model is carried out. The degree of coincidence of the results shows that the chamber model satisfactorily describes the transfer of lead from the peripheral blood into the organs and muscle tissue of sheep. The developed mathematical model is recommended for assessing and predicting the safety of sheep products.