Introduction 2001 2004 1998 2000 2002 1998 2002 2002 2004 1991 1995 2004 2005 2004 Methods and materials Patients For our research purposes the patients were designated on the basis of selective criteria. The inclusion criteria were established sick sinus syndrome and pacemaker implantation lasting more than 6 months. The exclusion criteria were left ventricle dysfunction, clinical significant valvular disease and other pathological structural heart changes. The patients with other than sinus rhythm, AV block under 110 beat/min during stimulation or bad image quality from echocardiography examination were also excluded. Our research finally involved thirteen patients with the sick sinus syndrome (eight males and five females with the average age 73 years, ranging 59–82 years). These patients with permanent dual-chamber pacemaker implantation were taken to echocardiography examination. Study protocol The numerical model of cardiovascular system was used to calculate the myocardial energetic parameters such as the stroke work index and the myocardial oxygen consumption for three types of pacing. 2 \documentclass[12pt]{minimal}
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\begin{document}$$ {\text{work}} = {\text{blood volume change}} \times {\text{pressure change}}{\text{.}} $$\end{document} http://www.lidco-ir.co.uk/html/clinical/nhp.asp 1 1 \documentclass[12pt]{minimal}
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$$ {\text{LVSWI}} = 0.0136 \cdot {\left( {{\text{MAP}} - {\text{PAOP}}} \right)} \cdot {\text{SV}}/{\text{BSA}} $$\end{document} 2 2 2 1992 2 \documentclass[12pt]{minimal}
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$$ {\text{BSA}} = 0,007184 \cdot {\text{BW}}^{{0.425}} \cdot {\text{BH}}^{{0.725}} $$\end{document} 2 2 1990 2 2 3 \documentclass[12pt]{minimal}
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$$ {\text{MVO}}_{2} = a \times {\text{PVA}} + b $$\end{document} a b 2 4 \documentclass[12pt]{minimal}
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$$ {\text{PVA}} = {\text{EW}} + {\text{PE}} $$\end{document} 1 5 \documentclass[12pt]{minimal}
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$$ \begin{aligned}{} & {\text{EW}} = {\left( {p_{{{\text{peakS}}}} - p_{{{\text{ED}}}} } \right)} \cdot {\left( {V_{{{\text{ED}}}} - V_{{{\text{ES}}}} } \right)} \\ & {\text{PE}} = {\left( {p_{{{\text{peakS}}}} - p_{{{\text{ED}}}} } \right)} \cdot {\left( {V_{{{\text{ES}}}} - V_{{\text{o}}} } \right)} \\ \end{aligned} $$\end{document} Fig. 1 Ventricular pressure–volume loops  5 p peakS p pED V ED 3 V ES 3 V o 3 1 1983 1984 Medical Ethical Committees of the University Hospital Královské Vinohrady, Prague, approved the study protocol and the informed consent was obtained from all patients. Mathematical model 2 Fig. 2 Scheme of the human cardiovascular system applied to heart workload calculations  The system is approximated by twenty-four compartments, which are characterized by elasticity, resistivity and transfer of the relevant chemical components. The pulsating heart consists of the following compartments: RA—Right Atrium, RV—Right Ventricle, LA—Left Atrium, LV—Left Ventricle. The pulmonary circuit includes compartments representing the pulmonary artery (PA), arteries (Paa), capillaries (Pc), postcapillary venules (Pvv), and pulmonary veins (PV). Systemic circuit connects the aorta (Ao), systemic arteries (Saa), capillaries (Sc), head arteries (HA), capillaries (Hc), and head veins (HV). In addition, the systemic circuit includes the coronary circulation with coronary arteries (CA), capillaries (Cc), veins (CV), shunt (CS), and also the bronchial circulation with bronchial arteries (BA), left bronchial veins (BVL), capillaries (BRc), and right bronchial veins (BVR). The compartments of the pulmonary and systemic blood circulation are connected in series with the four pulsating heart compartments. The suggested model describes the one-dimensional flow of incompressible blood through the network of elastic blood vessels. The heart compartments are considered to be made of anisotropic and viscoelastic incompressible material. 1977 Discussion and conclusions All experimental results obtained with the investigated patients and simulated values resulting from the applied numerical model were elaborated by the following statistical analysis. We use the null hypothesis to demonstrate the agreement or discrepancy between the values of the myocardial energetic parameters (stroke work index, myocardial oxygen consumption) obtained by the numerical simulation for the three pacing modes. f 3 P P Fig. 3 Stroke work index calculated by the numerical model of cardiovascular and respiratory system  4 P P Fig. 4 Myocardial oxygen consumption calculated by the numerical model of cardiovascular system in various pacemaker modes  P 1995 1998 P 2004 P P The insufficient number of the designated subjects gives the limitation of our research study because very strict exclusion criteria exist for the concomitant disease. Many pacemaker patients were not eligible for echocardiography examination because they had hypertension, left ventricle dysfunction or valvular disease. We conclude that mathematical modelling of the cardiovascular system is a recommended method for the estimation of the myocardial energy demand in patients with heart diseases.