The Windkessel model revisited: A qualitative analysis of the circulatory system

Роль Гидродинамических Параметров В Формировании Низкочастотных Колебаний Артериального Давления У Человека

“…1). The suggested model represents a system of equations, which describe the flow of viscous fluid through elastic reservoirs, the so-called Windkessel model [17]. The equations enable to calculate a number of parameters in vascular reservoir i: blood pressure ( Single-chamber pump: …”

Windkessel Model in the Qualitative Analysis of the Circulatory System of Smokers

“…The difference between the variation in left and right ventricular compliance is in the maximum value Cd, which corresponds to C VIdiastole y C VDdiastole . The maximum ventricular compliances obtained by Tsanas and Goulermas [5] were 0.0145 L/mmHg for C VIdiastole and 0,03436 L/mmHg for C VDdiastole.. In order to adjust the model, certain considerations and approaches were necessary due to the lack of more precise data, the patient specific factors, except age, take Boolean values, but this error is small enough.…”

“…3) seeks to identify the effect of smoking on the model parameters, taking as inputs patient specific factors and the usual pressure measurements, and as outputs estimate the CO and the arterial pressure. In order to establish appropriate relationships between patient specific factors (inputs) with six unknow model parameters (Rsa, Rpa, Csa, Cpa, C VIdiastole y C VDdiastole ) and estimate their actual values, the polynomial coefficients used in the model shown in table 2 and obtained by Tsanas and Goulermas [5] from the following equation: Parameter i = a 0,i + a 1,i *age + a 2,i *sex + a 3,i *smoking + a 4,i *fitness + a 5,i *drug 1 + a 6,i *drug 2 + a 7,i *drug 3. The time step size ΔT was set to be 0,01 times the period (T).…”

“…For simplicity, the heart rate F was adjusted to depend only on age with a linear relationship (imposed in the model through the period T = 1/F), we have used the average of the measured frequency by age of patients in the database studied, obtaining a T=0.00001*age+0.0141. The ratio between the systolic time for each period pulse is assumed constant, systolic time= 0.353T [5].…”

“…However, its complexity makes its application for the entire body impossible [2], although attempts have been made to combine it with the Windkessel model (WM) [3] in order to achieve an accurate circulatory representation and to reduce the complexity of applications related to blood pressure, flow and heart load [4]. The proposed model is based on the work by Tsanas and Goulermas [5], which suggest a variation of the WM without solving the resulting equations; a closed loop approach that offers a functional view of the complicated cardiovascular system in terms of providing the estimated blood pressure in various parts of this system. Moreover, it simply relates measurements in patients, smoking and the use of drugs with the parameters of the Windkessel theory, and allows to obtain the values of systemic arterial compliances and resistances, and to evaluate changes that occur in them according to the characteristics and habits of each patient.…”