Model Based Sensitivity Analysis of Arterial Pressure Response to Hemodialysis Induced Hypovolemia

Abstract

The role of hemodynamic and regulatory factors in the arterial pressure response to hemodialysis induced hypovolemia was investigated by means of a computer model of the cardiovascular system, including the main short-term pressure regulatory mechanisms. The model mimics the arterial and venous systemic circulation, Starling's law and inotropic heart regulation, arterial and cardiopulmonary baroreflex controls of resistance, and capacitance vessels. All of the model parameters have a clear physiologic meaning: 10 represent the systemic circulation, 4 describe cardiac pump performance, and 3 characterize baroreflex regulation. Sensitivity analysis is performed to determine the effect of each parameter on the pressure response to mild hypovolemia (a 10% blood volume reduction after 4 hours). The results demonstrate that circulatory parameters, such as resistances and compliances, have no relevant effect upon the pressure response. Conversely, regulation of venous capacity seems to play a pivotal role in sustaining arterial pressure during hemodialysis induced hypovolemia. Regulation of systemic peripheral resistance exerts a compensatory action only as long as the blood volume reduction is < 5%, but it is inadequate to compensate for a larger blood volume reduction when venous capacity regulation is absent. A paradoxical arterial pressure increase during hypovolemia can be referred to a prevalence of cardiopulmonary afferences in the regulatory process.

Mathematical Modeling of Thermal and Circulatory Effects During Hemodialysis

“…in which V iu is the unstressed volume of compartment i . Arterial pressure ( p a ) was in accordance with other studies (1,25,27) considered as mean arterial pressure (MAP).…”

“…When the CV system is stressed by the loss of circulatory BV, as occurs during HD + UF, venous capacity can actively be constricted. This mechanism compensates for changes in circulatory BV due to an increase in vasomotor tone (27). In particular, splanchnic and cutaneous vessels have a variable blood storage function.…”

“…Because the hemodynamic response under study involves much slower dynamics than the HR period, the pulsating nature of the cardiac pump can be averaged out and the heart can be modeled as a continuous pump. Then, the CV model's CO Q co,cv is expressed by relationship 13 (27): in which Q sat is the saturation level, p ra is the right atrial pressure, p ras is the pressure for null CO (no flow through the heart), and p ran is a sensitivity parameter that determines the sensitivity of CO to right atrial pressure (27). The inotropic effect of the heart is taken into account by a sigmoid function of the HR, which modulates the saturation level ( Q sat ) of the cardiac curve (27): …”

“…Efferent regulations were modeled by sigmoid functions suitable for obtaining linear behavior for small pressure perturbations and the typical saturation effects for large perturbations (27): …”

Sympathetic Activity, Vascular Capacitance, and Long-Term Regulation of Arterial Pressure

“…What conclusions did these investigators draw about the development of renin-dependent hypertension based on their model? First, “It is not necessary to assume that blood volume is increased.” Second, “cardiac output is enhanced by adrenergic activity…and supported by increased venous return from contracted peripheral capacitance vessels.” Other attempts to explain disordered arterial pressure regulation with the use of circulatory models also have emphasized the potentially important role of changes in venous compliance or capacitance66, 67. Thus there is theoretical support for the notion that a sympathetically mediated reduction in vascular capacitance occurs in angiotensin-dependent hypertension.…”