S.I. Shchukin, Y.E. Kirpichenko, A.V. Kobelev, D.P. Timokhin

Nowadays noninvasive instrumental methods are to be used in medicine. There is an opportunity to study cardiac electrical activity in conjunction with hemodynamics when a method of tetrapolar frequency-division of rheocardiographic and electrocardiographic signals is used. Addition to the traditional transthoracic rheocariographic technique precadiac rheographic signals processing allows to analyze not only comprehensive indicators of hemodynamics, but also all the processes of individual sites of heart (valves, ventricles, cardiac apex).Thus, the precardiac rheocardiogram technique can be considered as an additional tool for ultrasound or even as an independent procedure for heart functionality determination. In precardiac rheography method development it is essential to solve several tasks, one of them is modelling of the distribution of electric potentials in the precardiac area (direct problem) and the other one is the determination of model parameters by means of these distributions (inverse problem). Thereby, solving direct and inverse problems in the precardiac rheocardiography (preRCG) and calculating parameters of the heart model, we can estimate the location of the heart and also determine its biomechanical parameters, such as stroke volume, heart-rate etc. The essence of precardiac rheography technique is that for measurement purposes 4 electrodes usually have to be applied to the body surface. Two electrodes (usually called current electrodes) are used to pass a constant alternating current with a high frequency (60 - 100 kHz) and very low amplitude (1 mA). The current is imperceptible to the patient and does not cause any physiological reactions. The other two electrodes (usually called measuring electrodes) are placed between the current electrodes and they measure the voltage which is caused by the current flowing through the body segment. This voltage corresponds to the impedance of the body segment and changes in blood volume variations. On this basis the blood flow can be measured and analyzed. In modeling for solving direct and inverse problems in the precardiac rheography method we use several biological tissue models. In this paper horizontally poly-layered, spherical and bispherical models are analyzed. Under the poly-layer model we consider tissue compound, which contains muscle tissue (ρmuscle = 5 Ohm-m), pulmonary tissue (ρpulm = 8 Ohm-m), myocardium (ρmyo = 5 Ohm-m, hmyo = 0.02 m), bone tissue (ρbone = 10 Ohm-m) and blood (iblood = 1.0-1.5 Ohm-m, semi-infinite layer). The major mathematical modeling of the preRCG involves calculation of direct and inverse problems. In the direct problem governing equations in the preRCG field are derivable from Laplace's Equation (electrostatic approximation for low frequency). Direct problem solution allows us to recognize physiological mechanism of the heart functionality, determine optimal electrode system parameters in hemodynamic parameters determination tasks. For biomechanical heart parameters evaluation we suppose inverse problem solution by using apparent resistivity concept and iterative algorithms. A preliminary result of hemodynamic parameters calculation by using precardiac rheography technique is presented in this paper. This result is in close agreement with values calculated by using invasive methods. It makes possible to determine and monitor parameters of the heart pump-function in real-time mode.