Cardiac assist by intrathoracic and abdominal pressure variations: a mathematical study

Estimation of respiratory volumes from the photoplethysmographic signal. Part 2: A model study

A Windkessel model has been constructed with the aim of investigating the respiratory-volume dependence of the photoplethysmographic (PPG) signal. Experimental studies show a correlation between respiratory volume and the peak-to-peak value of the respiratory-induced intensity variations (RIIV) in the PPG signal. The model compartments are organised in two closed chambers, representing the thorax and the abdomen, and in a peripheral part not directly influenced by respiration. Cardiac pulse and respiration are created by continuous adjustment of the pressures in the affected compartments. Together with the criteria for heart and venous valves, the model is based on a set of 17 differential equations. These equations are solved for varying thoracic and abdominal pressures corresponding to different respiratory volumes. Furthermore, a sensitivity analysis is performed to evaluate the properties of the model. The PPG signals are created as a combination of peripheral blood flow and pressure. From these signals, the respiratory synchronous parts are extracted and analysed. To study some important limitations of the model, respiratory type and rate are varied. From the simulations, it is possible to verify our earlier experimental results concerning the relationship between respiratory volume and the peak-to-peak value of the RIIV signal. An expected decrease in the amplitude of the respiratory signal with increased respiratory rate is also found, which is due to the lowpass characteristics of the vessel system. Variations in the relationship between thoracic and abdominal respiration also affect the RIIV signal. The simulations explain and verify what has been found previously in experimental studies.

Theoretical analysis of the relationship between the ratio of ventricular systolic elastance to diastolic stiffness and stroke volume

The maintenance of adequate blood circulation requires a sufficient ventricular contractility; in addition, to eject blood, the ventricles must first receive a sufficient volume, requiring a low diastolic stiffness. A simplified cardiovascular model was used to derive formulae for stroke volume (SV) as a function of atrial pressure and the ratio of ventricular end-systolic elastance to end-diastolic stiffness. A more complex cardiovascular model was used to assess the ability of the expressions to predict stroke volume under various steady-state conditions. The predicted SV correlated linearly with the model SV over a wide range of diastolic stiffnesses and systolic elastance. The formulae predict that with fixed right atrial pressure the SV is proportional to the ratio of end-systolic elastance to end-diastolic stiffness (GR) for the right ventricle, but relatively insensitive to the ratio (GL) for the left ventricle provided that GL is greater than GR. Model simulations confirmed this. When the right atrial pressure was not fixed increases in GR with fixed GL reduced the right atrial pressure with little change in SV. Similarly, varying GL with fixed GR produced little change in SV. The ratios highlight the importance of diastole to cardiac function.

Manipulation of external pressure as a method to assist the failing heart

The development and state of the art in circulatory assistance using external pressure variations is reviewed. All of these techniques use the principle that by cyclic external pressure waves properly timed to the cardiac cycle, hemodynamic energy can be noninvasively transmitted to assist the circulation. Cyclic pressure waves to the lower body require that the high pressure phase occurs in diastole in order to augment cardiac output or coronary flow. In contrast, pressure waves to the chest would optimally augment cardiac output if they begin at the onset of ventricular systole. Manipulation of lung pressure by synchronized ventilation may be also utilized to augment cardiac output. The above methods are discussed in detail in the manuscript with special emphasis on the pathophysiology and mechanisms of cardiac assistance.

Circulatory assistance by intrathoracic pressure variations: optimization and mechanisms studied by a mathematical model in relation to experimental data

The hemodynamic effects of phasic variations in intrathoracic pressure (ITP) timed to the cardiac cycle were predicted by a mathematical model and were compared with data from canine experimental studies. The model was used to predict the hemodynamic effects of changing the onset of the ITP rise relative to the start of cardiac systole, as well as the hemodynamic effects of changes in the duration and amplitude of the ITP rise. The predictions of the model were compared with hemodynamic data from seven anesthetized dogs. Cardiac function was depressed with large doses of verapamil and propranolol, and the hearts were atrioventricular sequentially paced at a rate of 72 beats/min. Phasic ITP variations were generated by a perithoracic vest and were electronically timed to the cardiac cycle. The model predicted, and the experimental data confirmed, that phasic intrathoracic pressure variations generated by vest inflation, timed to the cardiac cycle, can augment both peak and mean aortic flow. The following predictions of the model were also confirmed by the experimental data: 1) Maximum flow augmentation occurs when the onset of the ITP rise is simultaneous with the onset of left ventricular isovolumic contraction, and the ITP rise has a duration of 400 msec. 2) The magnitude of the flow augmentation is a function of the amplitude of the ITP rise. The experimental data showed that there was little further flow augmentation when the ITP rise was greater than 30-40 mm Hg. 3) The magnitude of flow augmentation was inversely proportional to the peak left ventricular elastance (Emax). The best fit between the measured and predicted flow augmentations was obtained for an assumed Emax of 0.5 mm Hg/ml, while Emax measurements in three dogs, using a volume conductance catheter and transient vena caval occlusion, yielded values of 0.4-1.6 mm Hg/ml. Thus, both the mathematical model and canine experiments showed that relatively low-amplitude ITP variations, rising synchronously with the onset of cardiac systole and having an optimal duration, assist the failing heart by augmentation of aortic flow. The degree of cardiac assistance decreases if the ITP variations do not rise synchronously with the onset of systole, or if their duration is not optimal. Thus, properly applied ITP variations may be used as an efficient, noninvasive method to temporarily assist the failing heart.

Model studies of the effects of the thoracic pressure on the circulation

Two models of the cardiovascular system subjected to changes in intrathoracic pressure (ITP) are used to simulate the response to normal and positive pressure ventilation and the Mueller maneuver. The first model, based on our earlier model for cardiopulmonary resuscitation and cardiac assist by ITP variations, is based on lumped parameter representation of the cardiovascular system with two ventricles which function based on the time-varying elastance concept using their transmural pressures as the load. The ITP is assumed to be equally distributed in the thoracic cavity and equally affecting all cardiovascular structures within the chest. The model shows that a decrease in ITP is associated with an initial decrease in aortic pressure and flow and an increase in left ventricular end-diastolic and end-systolic volumes. A transient decrease in left ventricular volume which was suggested to occur by a few studies cannot be predicted based on this model. Such a decrease in left ventricular volume can be only predicted when a pericardial constraint is included, as done in the second model. Positive pressure interventions are associated with decreased heart volumes and cardiac output which is primarily a "preload" effect. In general the model reasonably predicts the hemodynamics as a function of the ITP changes and may be used as a tool to investigate the response of the cardiovascular system to various ITP interventions.