Using a human cardiovascular-respiratory model to characterize cardiac tamponade and pulsus paradoxus
© Ramachandran et al; licensee BioMed Central Ltd. 2009
Received: 12 February 2009
Accepted: 6 August 2009
Published: 6 August 2009
Cardiac tamponade is a condition whereby fluid accumulation in the pericardial sac surrounding the heart causes elevation and equilibration of pericardial and cardiac chamber pressures, reduced cardiac output, changes in hemodynamics, partial chamber collapse, pulsus paradoxus, and arterio-venous acid-base disparity. Our large-scale model of the human cardiovascular-respiratory system (H-CRS) is employed to study mechanisms underlying cardiac tamponade and pulsus paradoxus. The model integrates hemodynamics, whole-body gas exchange, and autonomic nervous system control to simulate pressure, volume, and blood flow.
We integrate a new pericardial model into our previously developed H-CRS model based on a fit to patient pressure data. Virtual experiments are designed to simulate pericardial effusion and study mechanisms of pulsus paradoxus, focusing particularly on the role of the interventricular septum. Model differential equations programmed in C are solved using a 5th-order Runge-Kutta numerical integration scheme. MATLAB is employed for waveform analysis.
The H-CRS model simulates hemodynamic and respiratory changes associated with tamponade clinically. Our model predicts effects of effusion-generated pericardial constraint on chamber and septal mechanics, such as altered right atrial filling, delayed leftward septal motion, and prolonged left ventricular pre-ejection period, causing atrioventricular interaction and ventricular desynchronization. We demonstrate pericardial constraint to markedly accentuate normal ventricular interactions associated with respiratory effort, which we show to be the distinct mechanisms of pulsus paradoxus, namely, series and parallel ventricular interaction. Series ventricular interaction represents respiratory variation in right ventricular stroke volume carried over to the left ventricle via the pulmonary vasculature, whereas parallel interaction (via the septum and pericardium) is a result of competition for fixed filling space. We find that simulating active septal contraction is important in modeling ventricular interaction. The model predicts increased arterio-venous CO2 due to hypoperfusion, and we explore implications of respiratory pattern in tamponade.
Our modeling study of cardiac tamponade dissects the roles played by septal motion, atrioventricular and right-left ventricular interactions, pulmonary blood pooling, and the depth of respiration. The study fully describes the physiological basis of pulsus paradoxus. Our detailed analysis provides biophysically-based insights helpful for future experimental and clinical study of cardiac tamponade and related pericardial diseases.
Cardiac tamponade is a condition whereby the accumulation of fluid in the pericardial sac causes a hemodynamically significant in the intra-pericardial pressure (PPERI) which is conventionally defined as a liquid pressure. In a healthy subject, PPERI is approximately equal to the pleural pressure (PPL). PPERI rises with increasing effusion and may equalize to diastolic right atrial (RA) and right ventricular (RV) pressures, and at higher levels of effusion to diastolic left atrial (LA) and left ventricular (LV) pressures. Heightened pericardial pressure may lead to partial chamber collapse for a portion of the cardiac cycle [1, 2] wherein PPERI exceeds chamber pressure. Clinical cardiac tamponade occurs when there is significant component of decreased cardiac output, stroke volume, systemic blood pressure, attendant tachycardia, and manifestation of pulsus paradoxus (an exaggerated respiratory fluctuation of systolic pressure by a greater amount than 10 mmHg or 10% ).
Cardiac tamponade may present as an acute clinical emergency or in a less emergent fashion that requires timely intervention . Low-pressure tamponade has also been described . Here we demonstrate a case of virtual subacute tamponade, modeled on the hemodynamic data reported by Reddy et al.  concerning a case of tamponade requiring pericardiocentesis.
Pericardial effusion leads to increased chamber interaction. A parallel interaction occurs whereby expansion of the RV during inspiration compresses the LV; likewise, a smaller RV volume during expiration allows more blood to be drawn into the LV [6–10]. The septum and pericardium are involved in this interaction. The septum is driven directionally by the prevailing pressure gradient across it, but is not a passive interventricular partition; it acts as a contractile pump in its own right [11–14]. Localized chamber pressure changes are transferred throughout the heart via the surrounding effusion-filled pericardium [7, 15] aiding chamber interaction. An exaggerated series form of ventricular interaction occurs in tamponade when an augmented right heart volume upon inspiration travels to the left heart within two to three beats, contributing to an increase in LV stroke volume (LVSV) at the expiratory phase of respiration [16, 17]. Parallel and series ventricular interaction have been hypothesized to be the important mechanisms involved in the generation of pulsus paradoxus [3, 9, 16–18] but their individual contributions have not been quantified. Additionally, atrioventricular (AV) interaction  causes systole-dominant atrial filling in the setting of elevated pericardial constraint and may change the filling patterns of all four chambers. We show that in severe tamponade this mechanism can lead to lowered filling volumes that changes septal motion and affects ventricular ejection times. AV interaction thus plays an important role in the generation of pulsus paradoxus.
Human Cardiovascular Respiratory System (H-CRS) Model
Large-scale integrated cardiovascular-respiratory closed-loop models provide informative analysis of normal and diseased human physiology [11, 12, 20–27], since they can capture the global aspects of cardiovascular-respiratory interactions. Our group has developed a model of the human cardiovascular respiratory system (H-CRS) that integrates hemodynamics, whole-body and cerebral gas exchange, and baro- and chemoreceptor reflexes. This model accurately simulates the complex ventricular and cardio-respiratory interactions that occur during the Valsalva maneuver , apnea , left ventricular diastolic dysfunction , and interventricular septal motion . Here, we update our composite model of the human subject with an appropriate pericardial pressure-volume characteristic to better simulate chronic cardiac tamponade.
Sun et al.  have modeled tamponade in a closed-loop, baroreflex-controlled, circulatory model by incorporating right-left heart interaction via a septal elastic compartment. Their septum is limited to a passive coupling of the ventricles via the ventricular pressure gradient. With a completely passive septum, septal motion could not oppose the established trans-septal pressure gradient. Our H-CRS model contains a septal subsystem model that is both active and passive in that it acts as a contractile pump that assists left chamber ejection and the RV in filling. We hold this to be a key distinction, in that biphasic septal motion has been demonstrated experimentally in normal hearts [13, 14] and our simulations show that in tamponade it can be an important contributing factor to systolic operation. Additionally, their pulmonary component does not model pulmonary mechanics or pulmonary circulatory changes as a function of breathing movements, but is limited to a specification of pleural pressure drive. These circulatory changes mediated by respiration are important in tamponade and especially in the production of pulsus paradoxus, as will be shown. Finally, our model demonstrates important physiological alterations of gas exchange in the setting of cardiac tamponade.
In this work, we first examine the model-generated predictions of cardiovascular pressures, volumes, and flows in tamponade, with particular focus on the role of an active septum. We then analyze the contributory role of breathing pattern, and by introducing artificial isolation of the right and left hearts, dissect the separate contributions of serial and parallel ventricular interactions. Lastly, we analyze the important role of the septum as an active, tertiary pump assisting both systolic ejection and diastolic filling, and demonstrate the relevance of this previously neglected component in the physiology of cardiac tamponade.
Our H-CRS model [11, 12, 24–26] has three major parts: models of the cardiovascular, respiratory, and neural control systems. The cardiovascular component includes a lumped pump-type model of the heart chambers, lumped models of the inlet and outlet valves, as well as the systemic and pulmonary circulations considered as pump loads. Specifically, the walls of the heart chambers and septum are described in terms of time-varying elastance functions. The pericardium enveloping the heart is modeled as a passive nonlinear elastic membrane enclosing the pericardial fluid volume. Distributed models of the systemic, pulmonary, and cerebral circulations are included as previously described  and nonlinear pressure-volume (P-V) relationships are used to describe the peripheral venous system. The respiratory element in the H-CRS model includes lumped models of lung mechanics and gas transport, which are coupled with the pulmonary circulation model. Specifically, the nonlinear resistive-compliant properties of the airways are described as well as the nonlinear P-V relationship of the lungs. In the pulmonary circulation model, pulmonary capillary transmural pressure (hence volume) is dependent on alveolar pressure, whereas pulmonary arterial and venous transmural pressures are dependent on pleural pressure . Whole-body gas transport is included in the respiratory element with gas exchange equations given for each gaseous species (O2, CO2, and N2) at the lung and in major tissues of the body at the capillary level (i.e., skeletal muscle and brain). The neural control system model includes baroreceptor control of heart rate, contractility, and vasomotor tone, and chemoreceptor control of heart rate and vasomotor tone . Parameters associated with the systemic and pulmonary circulations have been adjusted to fit typical input impedance data (systemic and pulmonary) from normal human patients .
Differential equations for the H-CRS model were programmed in C and solved numerically using a 5th-order Cash-Karp Runge-Kutta method . Typically, a 50-second simulation required a run time of five minutes on an AMD Turion 1.6-GHz platform (Dell Inspiron 1501). Specific modifications made to the H-CRS model for this study of tamponade and pulsus paradoxus are described in the subsections below.
The new and old transmural pressure-volume characteristics of the pericardial space differ in that their slopes in the normal range of volumes are approximately the same, however at high volumes, the new characteristic develops significantly greater pressures.
Apart from gas exchange modeled in the lung and airways , time-varying pleural pressure due to breathing is also simulated in the respiratory section of the model. In order to better characterize the cardio-respiratory interactions in tamponade, we employed a spontaneous tidal breathing waveform digitized from a canine study of tamponade  and scaled it to human proportions of mean PPL -3.0 mmHg. This pseudo-human respiratory waveform has PPL range estimated from  and .
Three septal models were compared: two passive septa, whose P-V relationship was fixed at either end-systolic or end-diastolic behavior throughout the cardiac cycle, and an active septum for which the P-V relationship is modulated by a time-dependent activation function in synchrony with free wall contraction, thereby undergoing biphasic operation. The passive septum models are used only for this comparison study – all simulations of control and tamponade employ the active septum model detailed previously [11, 12].
Tamponade was simulated by graded increases in pericardial volume. Following each step-increase, the model was brought to steady-state and data was analyzed using MATLAB . Effusion levels from 15 ml to 1100 ml were used. We consider effusion of 15 ml as control case, 900 ml as moderate tamponade, and 1000 ml as severe tamponade.
Pulsus Paradoxus: Ventricular Interaction Studies
To analyze ventricular interaction, we tracked a fixed volume of blood as it was transported from the right atrium to left ventricle. In Experiment 1 (see Results section), we simulated an inspiratory increase in venous return to the right heart by delivering a triangular pulse volume to the vena cava within a period of two seconds at fixed PPL.
In Experiment 2, to dissect the relative importance of each type of ventricular interaction, the model was modified to eliminate one type of interaction at a time (see Experiment 2 in Results section). To study series interaction, parallel interactions via the septum and pericardium were respectively eliminated by increasing the septal stiffness parameter λ by 100× from 0.05 to 5.0, and holding PPERI constant. To study parallel interaction, the pulmonary venous volume was held constant thus creating an independent left heart venous return, thereby eliminating series interaction. Parallel and series ventricular interactions were analyzed and compared based on a triangular pulse of venous return to the right atrium such as in Experiment 1, and PPL was held constant.
Effects of Pericardial Effusion
Equilibration of Diastolic Pressures and Chamber Collapse
Right Heart Relationships in Tamponade
To examine the right heart hemodynamics in tamponade without overlying respiratory variations, PPL is set to the mean, thus simulating breath-holding. The atrium may be envisioned as a contractile storage chamber with an inflow from the vena cava compartment and an outflow through the tricuspid valve to the RV chamber. Diastole is defined as the interval between tricuspid valve opening and closure .
Model-Generated Common Clinical Indices
1000 (severe tamponade)
Left Heart Relationships in Tamponade
The pre-ejection period for the LV (LPEP) is normally slightly longer than that for the RV (RPEP) as noted in  (compare Figure 4E and Figure 5E). This asynchrony in ventricular ejection times becomes much more pronounced in tamponade (discussed later) and plays a role in modifying the shape of the x-descent feature of the PRA waveform. The x-descent waveform is shaped by PPERI which has two components, the first corresponding to RV ejection and the second LV ejection. Figure 4F and Figure 5F indicate that the ventricles each eject 52 ml, however the end-diastolic filling volumes are quite different (68 ml VRV and 80 ml VLV) indicating that the RV is compressed to a much higher degree than the LV.
Diastolic and Systolic Venous Return Volumes with Pericardial Effusion
D/S Vol. Ratio
D/S Vol. Ratio
Chamber Pressure-Volume Relationships
Atrial P-V loops show general movement upward and to the left, toward higher atrial pressures and lower minimum volumes (Figure 6A and 6B). This is especially true for the RA, where with progression of tamponade there is a steady decline in the minimum volume point on the loop. The maximum RA volume point also declines slightly with higher level of tamponade (compare maximum volume in Figure 4C and 4D). The flattened appearance of the RA loops of Figure 6A with minimum chamber volume reaching very low levels convey a powerful image of the constrictive effect of pericardial effusion on thin-walled heart chambers. The slope of the y-descent declines in the RA P-V domain (Figure 6A) with increasing tamponade, and the y-descent is followed by a slowly increasing pressure for the remainder of the RV diastolic interval (upper portion of the loop). A slow v-wave follows a delayed and reduced x-descent feature in the systolic portion of the RA P-V loop. PRA remains relatively constant over the latter portion of the RV systolic interval. VRA excursion is increased in tamponade relative to control. Progressive pericardial constraint is associated with elevation of PLA and flattening of atrial P-V loops (Figure 6B). With increasing effusion (Figure 6C and Figure 6D), the ventricles exhibit a rise in diastolic pressure and a reduction in volume and pressure excursion. In tamponade and during the ventricular filling phase, the complex changes in the PPERI waveform sculpt the diastolic P-V relationship including the notching effect observed in Figure 6C.
Graded increases in pericardial volume simulate tamponade hemodynamic changes both at the right and left heart. The right heart hemodynamic changes can be summarized as follows: 1) the pericardial pressure tracks the chamber pressures and not the pleural pressure; 2) RA filling is delayed and diminished such that the x-descent occurs after the onset of RV ejection, rather than at the onset of RV isovolumic contraction; 3) the early diastolic filling (E-wave) is diminished and the late filling (A-wave) assumes greater proportion, due to a markedly decreased vena cava D-component; 4) atrial filling is restricted significantly to ventricular systole, in contrast to the normal filling during both ventricular systole and diastole, leading to a diminished or absent y-descent. The left heart hymodynamics are altered in parallel. Informative findings of these changes in tamponade are well visualized with atrial and ventricular P-V loops. There is evidence >11% pulsus paradoxus and atrial collapse (34% RA, 20% LA). The CO and MAP are compromised and there is demonstration of baroreflex activation and tachycardia.
Importantly, the pericardial pressure waveform in tamponade reflects local volumetric changes in the heart chambers, in particular the diastolic and systolic dips in pressure, which in turn influence the filling capability of the chambers. As a result of this pericardial constraint, venous return to the atria is progressively higher in systole rather than in diastole, as the ventricles are contracted and the heart occupies less volume, producing atrioventricular interaction that largely determines the heart's filling volume.
Effects of Respiration
During inspiration, there is an increase in venous return to the right atrium. Lowered intrathoracic pressure on inspiration lowers pressure in intrathoracic systemic veins, pericardium, and cardiac chambers. Consequently, flow from extrathoracic systemic veins is increased and more blood flows to the right heart. This augmented blood flow appears in the left heart two to three beats later (during expiration for a person at rest), i.e., the "transit time" for blood to travel through the pulmonary vasculature [16, 17]. In severe tamponade, the high PPERI due to effusion creates a competition for filling space, which increases interaction between the ventricles. During the inspiratory increase in systemic venous return, filling of the left heart is compromised, lowering LVSV and aortic pressure [3, 6, 17, 33]. Alternately, during expiration, left heart filling is favored over the right heart. The resulting variation in LVSV can cause more than a 10% variation in arterial pressure with inspiration, or pulsus paradoxus . In our model, the critical pericardial effusion volume for production of pulsus paradoxus at normal breathing levels is 950 ml.
Septal motion in tamponade has been studied in an effort to suggest mechanisms underlying abnormal hemodynamics and respiratory variation . We first present the septal model followed by our model results with regard to septal contribution in tamponade.
The septal model we have employed encompasses septal motion for the complete cardiac cycle, mimicking biphasic motion as noted by others [13, 14]. As detailed in our own studies [12, 35], a storage compartment of volume VSPT is defined as the volume bound by the current septal position and its unstressed position (Figure 1A), where positive and negative VSPT indicate rightward and leftward septal curvature, respectively. LV volume is therefore defined as the volume bound by the LV free wall and the unstressed septum plus VSPT, and RV volume is defined as the volume bound by the RV free wall and the unstressed septum minus VSPT. The transmural pressure PSPT is defined as the difference between PLV and PRV. There is a systolic and diastolic phase in the pressure-volume (P-V) relationship for the septal compliant compartment, linear in systole, nonlinear in diastole. Secondly, the septum undergoes active contraction synchronized with RV and LV free wall contraction in systole, behaving as a third pump. Septal activation and the trans-septal pressure gradient both shape septal motion.
Septal Motion in Tamponade
Model-Generated Ejection Time and Volume Indices During Various Phases of the Respiratory Cycle
(Cardiac Period = 0.96 sec)
1000 ml Effusion
(Cardiac Period = 0.84 sec)
With pericardial effusion, the combined effect of prolonged PEP and increase in heart rate shortens the LV ejection time (LVET) as noted in . LVET is greatest in expiration and lowest in inspiration as evident in Figure 11, with a respiratory variation of 3% in control and 28% in severe tamponade (Table 3). Prior to ejection, LV filling volume varies as shown by respiratory variation in LVEDV of 6% in control and 19% in tamponade. As a result of both of these effects, LV stroke volume (LVSV) on inspiration is reduced by 5% in control and 26% in tamponade compared to expiration.
Respiratory variation occurs in RV ejection time (RVET) as well, but with an increase in RVET of 3% for control and 13% for tamponade on inspiration compared to expiration. RV end-diastolic volume (RVEDV) varies by 26% for control and 49% for tamponade. RV stroke volume (RVSV) also varies by 39% for control and 59% for tamponade with maximum RVSV at inspiration. As can be noted to occur with tamponade, ejection time is more varied in the LV than the RV , but end-diastolic volume varies more in the right. The combined effect of both gives a variation in stroke volume that is greater in the right. Results are tabulated in Table 3.
With tamponade, septal motion reflects abnormal hemodynamics associated with the pericardial constraint, i.e., the asynchrony and shortening of RV and LV ejection times which is exacerbated with inspiration. It should be noted that the use of term asynchrony to describe different ejection intervals should not be confused with asynchrony of electrical conduction through ventricles, as ventricular activation functions in the model are synchronized in time.
Model Parameters of Gas Exchange Function
Gas Exchange Parameter
15 ml effusion
1000 ml effusion
PO 2 (mmHg)
PCO 2 (mmHg)
SO 2 (%)
A-V O 2 concentration difference (%)
A-V CO 2 concentration difference (%)
PO 2 (mmHg)
PCO 2 (mmHg)
SO 2 (%)
A-V O 2 concentration difference (%)
A-V CO 2 concentration difference (%)
PO 2 (mmHg)
PCO 2 (mmHg)
SO 2 (%)
A-V O 2 concentration difference (%)
A-V CO 2 concentration difference (%)
Respiration produces variation in cardiac pressures and flows. While in the control case respiration predominantly affects the right heart, with pericardial effusion, left heart respiratory variation becomes more significant and comparable to right heart respiratory variation. Pulsus paradoxus is present with 1000 ml effusion, with systolic blood pressure variation increasing further with deeper inspiration.
Modeling the biphasic motion of the septum, in which the septum actively recoils rightward and thrusts leftward during systole, is possible only with an active septal model, as demonstrated by comparison to two passive septum models. Motion of the active septum demonstrates the mechanisms for prolonged LPEP, shortened ejection times, and right-left asynchrony of filling and ejection periods.
The pulmonary vasculature demonstrates blood volume congestion in tamponade, in association with the elevated chamber pressures, and decreased equilibrium cardiac output.
Demonstration of gas exchange variation with pericardial effusion yields observations consistent with literature on cardiac failure revealing the state of hypoperfusion in tamponade.
Mechanism of Pulsus Paradoxus
Shabetai, et al. [6, 17] concluded that the mechanistic explanation for the inspiratory LV stroke volume (LVSV) drop in pulsus paradoxus is the increase in right heart venous return. We conducted two virtual experiments using the H-CRS model to examine this hypothesis, namely that right heart venous return is the primary cause for a change in LVSV. Two possible types of right-left interaction (parallel and series ventricular interaction) are demonstrated and their relative contributions to pulsus paradoxus are assessed.
Experiment 1: Effect of Increased Right Heart Venous Return
A virtual experiment based on the canine study of Shabetai et al.  was performed to observe the effect of increased right heart venous return on the hemodynamics of the left heart independent of respiration. Specifically, at a constant PPL of -3 mmHg, a triangular volume pulse of venous return to the right atrium mimicking a single inspiratory increase in venous return was introduced in the model and tracked over several heart cycles. In the control case, the volume pulse caused a 4-mmHg increase in pulmonary arterial pressure followed three beats later by a 10-mmHg increase in aortic pressure. However, under conditions of severe tamponade, the same volume pulse caused a 5-mmHg increase in pulmonary arterial pressure and a simultaneous 5-mmHg drop in aortic pressure, followed by a 9-mmHg increase from baseline in aortic pressure three beats later. The stroke volume variation demonstrated takes place over a period of roughly 7 seconds, or the duration of a single breathing cycle, and the arterial pressure excursion matches that seen in a single breath. This experiment demonstrates two effects of increased venous return that are exaggerated in tamponade: the immediate drop in LVSV as well as an increase in LVSV occurring three beats later.
Experiment 2: Isolated Series and Parallel Ventricular Interactions
Percent Changes in Stroke Volume in Isolated Ventricular Interactions
Series Ventricular Interaction
Parallel Ventricular Interaction
% Change in RVSV
% Change in LVSV
% Change in RVSV
% Change in LVSV
1000 (severe tamponade)
To isolate parallel ventricular interaction, control and severe tamponade simulations were run under conditions of constant pulmonary venous pressure with an independent constant pressure pump placed at the input to the LA. This virtual setup eliminates right heart serial influence on the left heart (i.e., venous filling conditions for the LV are constant). The triangular venous return pulse technique described earlier in Experiment 1 was again employed under conditions of normal septal stiffness and breath-holding at mean PPL. In order for a fair comparison of the LVSV percent variation in both isolated ventricular interaction setups, the chamber volumes in this experiment were scaled down to match the steady-state control stroke volume with that of the isolated series interaction control case. The percent change from steady-state in RVSV and LVSV was calculated for both the control and severe tamponade cases. With the perturbational venous volume increase under normal effusion level, RVSV increased by 41.1% and LVSV simultaneously decreased by 2.6%. With 1000 ml effusion, RVSV increased by 40.0% while LVSV decreased by 28.9% (see Table 5). The percent change in LVSV is greatly increased with tamponade. Comparing the isolated series interaction experiment with that of the isolated parallel interaction experiment, the percent variation caused by parallel interaction in severe tamponade is roughly the same as that for series interaction.
In severe tamponade, ventricular end-diastolic volumes tend to be 180° out of phase over the respiratory cycle . Such a phasic relationship occurs as the result of parallel ventricular interaction and is due to the strong competition for filling space in tamponade. A sinusoidal breathing pattern was introduced for a clear calculation of the phasic relationship between ventricular end-diastolic volumes. The control case showed a phase difference between peak RVEDV and peak LVEDV of 138°. With heightened parallel interaction in severe tamponade, this phase difference increased to 167°. In a virtual experiment where PLA was controlled by a constant pressure source, thus eliminating the series effect, the phase difference increased further to 178°.
The involvement of ventricular interaction in pulsus paradoxus is examined by way of tracking the effect on both ventricles of a vena caval volume pulse equivalent to a single inspiratory venous return increase. Parallel and series type ventricular interactions are isolated to compare the contributions of each to respiratory variation in LVSV. Model results reveal equally significant contributions to variation in LVSV.
We have used our large-scale model of the H-CRS to simulate the compressive effects of cardiac tamponade on atrial and ventricular hemodynamics under conditions of normal and elevated tidal breathing. At levels of breathing consistent with observed breathing waveforms in severe tamponade , our modeling correctly simulates a wide range of hemodynamic waveform changes including chamber pressure equalization, partial RA chamber collapse and AV interaction (Figure 4), abnormal septal motion, abnormal and highly varying flows (Figure 7), and pulsus paradoxus (Figure 8). The ability to characterize the hemodynamic waveforms in some detail greatly facilitates biophysical interpretation and yields insight into mechanisms underlying cardiac tamponade. This is particularly true of the subtle components of the right atrial and pericardial pressure waveforms that change dramatically in tamponade.
It should be noted that our composite model represents a patient whose heart has normal characteristics based on various data sources but is encased in an abnormal pericardium of the patient described by Reddy et al. . Therefore, qualitative and not quantitative correlation (i.e., Figure 3) is expected.
Our modeling study presents a unique view of tamponade ranging from the dynamics occurring in a single cardiac cycle and how they come to play over a cycle of respiration, including analysis of septal motion, valve flows, chamber volumes, and pressures. This is largely due to our characterization of the septum as a third contractile pump. This premise provides the platform for atrioventricular as well as right-left ventricular interactions. Our heart model thus yields accurate representations of ventricular pressures [11, 12, 37], including the specific septal contribution to RV systolic ejection, unlike the case when a passive septal model is used (see Figure 9). Moreover our work shows that with pericardial effusion, septal motion influences AV interaction, asynchrony of right and left heart ejection, and reduced ejection times, which are phenomena not demonstrated by the Sun et al. model . In addition, the respiratory section of the model is used to provide predictions of gas exchange with pericardial effusion, yielding additional insights consistent with clinical observations on hypoperfusion. The deeper respiratory pattern used in this study with asymmetric emphasis on expiration aids in the oxygenation of peripheral tissue, reducing the hypoxic and hypercapnic effects of severe tamponade. These elementary observations point out the need for in-depth observation of spontaneous breathing patterns in tamponade patients as well as laboratory experiments that examine ventilation patterns and effectiveness of gas transport in tamponade.
In the thin-walled right heart, clinically observed features such as an elevated PRA and lack of the y-descent feature  have been shown to be sensitive indicators of the effect of pericardial constraint and increased AV interaction . The display of model-generated hemodynamic variables shown in Figure 4 and Figure 5 allow us to interpret AV interaction and its enhancement by septal motion and the production of pulsus paradoxus at normal levels of breathing. With pericardial constraint, the pattern of atrial filling is largely dependent on ventricular size, and hence the septal position. Systolic ventricular emptying allows for maximum atrial filling. The systolic interval has two parts: PEP and ejection. In tamponade, LPEP increases due to reduced preload  whereas RPEP is relatively unaffected. Since the start of systole is the same for both ventricles, this produces a disparity in the start of ventricular ejection times, slowing aortic valve opening and delaying septal motion. This produces a largely labored systolic atrial filling, with maximum atrial volume when the septum is maximally leftward. Hence, the pericardial constraint that produces the lock-step atrial filling with the systolic dip of the PPERI waveform and ventricular filling with the diastolic dip is further impacted by septal motion. Elevated PPERI steers chamber pressures to undergo similar variations, particularly in the relatively more compliant right heart. In systole, the pericardial systolic dip draws PRV down as well, causing a premature pulmonic valve closure and early tricuspid flow. Normally, septal rightward motion upon deactivation administers a final aid to RV stroke output; however, due to the premature cessation of RV systole and commencement of tricuspid flow, this septal rightward thrust does no more than briefly interrupt RV filling. Therefore, pericardial constraint introduces asynchrony of outlet and AV valves, altering the nature and stroke volume impact of septal motion, respectively. Our simulation studies also show that pericardial constraint alone produces abnormality in septal mechanics regardless of the level of respiration (Figure 13), but to even greater degrees with deeper levels of breathing.
Changes in flow due to tamponade were demonstrated with the H-CRS model. Flow respiratory variation becomes equally significant in both sides of the heart (Figure 7). Venous flows exhibit lower D/S ratios with increased AV interaction. In transvalvular flows, there is a clinically observed reduction [1, 34] in the E-wave magnitude due to impaired filling in early diastole and there is a more dominant A-wave in late diastole. In severe tamponade (1000 ml), our simulations predict the existence of a split E-wave. We have explained the genesis of the early component of the split E wave in connection with Figure 11, implicating early relaxation of the RV pressure waveform and septal movement. The split E-wave occurs only in the tricuspid flow waveform, only at high levels of effusion (1000 ml and greater), and at low PPL. To our knowledge, the split E-wave phenomenon has not been documented in the clinical literature, and therefore it remains a model prediction that should be examined more closely in future studies.
Signs of Pulsus Paradoxus
With tamponade, respiratory-associated hemodynamic fluctuation is exaggerated in the left heart, and is increasingly out of phase with the right heart, signaling pulsus paradoxus. It has been noted that deep tidal levels of inspiration exaggerate pulsus paradoxus [8, 18, 31, 34, 46]. Elevated venous pressures in tamponade, combined with lowered pleural pressures during inspiration, causes a relatively larger atrioventricular pressure gradient in early diastole, and hence greater fluctuations in ventricular filling with respiration compared with control. Our simulations confirm this with exaggerated flow and pulse pressure variations.
Pulsus paradoxus is also a common occurrence in asthma patients, who tend to exhibit wide respiratory excursion and low pleural pressures on inspiration . Respiratory pattern changes are often associated with tamponade, i.e., dyspnea (shortness of breath) . Deeper spontaneous respiration has been observed in dog experiments with induced pericardial effusion [17, 34]. The influence of respiratory pattern on the level of pulsus paradoxus leads to possible future model investigation of the respiratory-related onset of pulsus paradoxus in cases such as asthma.
Mechanisms of Pulsus Paradoxus
Historically, pulsus paradoxus has been explained in several ways including: (a) diaphragmatic descent on inspiration causing an increase in pericardial pressure which impedes LV filling ; (b) failure to transmit pleural pressure changes to the left heart by a taut pericardium that results in lowered pulmonary venous return [46, 48, 49]; (c) increased ventricular interdependence due to competition for filling space which increases respiratory variation ; (d) increased trans-pericardial pressure on inspiration which lowers LV filling [17, 45]; and (e) inspiratory leftward septal bulge which decreases LV ejection .
It is generally agreed that in tamponade with a normal breathing pattern, inspiration produces an increase in right heart venous return and subsequently the left heart phenomenon of LVSV reduction [7, 10, 17]. This statement describes the phenomenon of pulsus paradoxus, but not the underlying mechanisms. Our modeling studies dig deeper to explore putative mechanisms and we propose that pulsus paradoxus in tamponade is the result of two types of exaggerated ventricular interaction (series and parallel), as well as AV interaction for each heart that changes the operating characteristics of the ventricles. In particular, series interaction plays a dominant role in producing pulsus paradoxus as the normal respiratory variation in filling volumes becomes significant with overall lowered stroke volume in tamponade. Parallel interaction is a result of space limitations imposed by pericardial constraint, increasing ventricular interaction both via the septum and via the pericardium. The manifestation of this dominant pericardial constraint as it affects chamber mechanics is AV interaction. Pericardial constraint increases AV interaction and results in lowered filling, decreasing LV preload and delaying leftward septal movement on systole; this shortens LVET and further reduces stroke volume, while the abnormal septal motion enhances AV interaction. RVET is also shortened with premature RV relaxation causing early pulmonic valve closure, and a reduction in RVSV. Thus, AV interaction in tamponade affects chamber mechanics during diastole directly, which carries through to affect ejection dynamics and the septal pathway by which the ventricles interact. The second aspect of parallel interaction is ventricular interaction via the pericardium. Localized, respiratory filling variation in one ventricle is transmitted to the pericardium as a pressure change, and hence transmitted to the other ventricle via the pericardium. Respiration-induced venous filling also has an important additional effect on septal position and consequently the swing of septal pumping. In tamponade, the leftward thrust during systole is delayed further on inspiration, bringing LVSV to a minimum, whereas RVSV is maximum at this point with greatest end-diastolic volume and RVET. The parallel ventricular interaction mechanism alone causes a near 180° phase difference between the RV and LV volumes in tamponade.
Experiment 2 (Results section) on Isolated Series and Parallel Ventricular Interactions shows that these two mechanisms for ventricular interaction cause a significant respiratory variation in LVSV with tamponade. By virtue of the matched stroke volumes in control cases for the isolated series and isolated parallel interaction experimental setups, the contribution of each mechanism to LVSV variation could be evaluated. This comparison shows that the contribution by the parallel mechanism (28.9% variation) is roughly the same as that of the series mechanism (25.3% variation) (Table 5).
Theories Regarding Other Mechanisms
Other mechanisms for production of pulsus paradoxus are quoted in various studies. Golinko, et al.  and Ruskin, et al.  support the theory that LV filling is impeded by a lowered and/or reversed pulmonary venous to LA pressure gradient on inspiration, which is accompanied by pulmonary blood pooling. Our simulations predict that pulmonary blood pooling is due to constriction of the cardiac chambers. As seen in Figure 5, our virtual experiments show that pulmonary venous reversal flow actually decreases with effusion. Furthermore, an experiment not detailed in this paper shows that the phasic relationship between RVEDV and LVEDV changes for various breathing frequencies indicating LV volume fluctuation is independent of pleural pressure, and dependent rather on RV volume fluctuation. Shabetai, et al.  demonstrates that LVSV decrease in pulsus paradoxus is a right-sided phenomenon that is manifested in the left heart. Our model results show right-sided contributions to the left heart respiratory variation via the pulmonary vascular pathway, via the pericardium, and via the septum. However, left heart AV interaction is also observed in our model, in which pericardial constraint independently alters LA and LV mechanics, thus contributing to the nature of the pericardial pressure waveform and hence septal movement.
Another theory is that inspiration during tamponade creates an increased pressure afterload [8, 48, 50]. Simulations not included in this paper have examined the pressure difference between ventricular pressure and arterial pressure during systolic ejection, to look for an increase in this pressure difference ΔP as an indicator of increased afterload. Although an observable variation with respiration is seen in the left heart, with maximum ΔP at inspiration, the overall ΔP level is reduced when compared to the control case. The model predicts that this systolic effect of afterload is not increased with tamponade. Our studies show that in tamponade the fundamental mechanism in LVSV reduction is reduction in LV preload from pericardial constraint. It is further reduced by inspiration due to ventricular interaction, which in turn lowers LVSV. The underlying mechanism involved in systole is a variation of LPEP that is fundamentally attributed to AV interaction from pericardial constraint and modulated by respiration. One might observe this reduction in LVSV in inspiration and attribute it to an increased afterload presented to the ejecting ventricle. However, our simulations suggest that the mechanism for reduced stroke volume is the change in the operating characteristics of the septum and the influence that respiration has on those same mechanical characteristics. The septum after all is a vital part of the important parallel ventricular interaction pathway.
Large-scale integrated models of the human cardiovascular and respiratory systems can provide a means of analyzing complicated problems associated with critical care medicine. Cardiac tamponade with pulsus paradoxus is only one example. Our H-CRS model has allowed us to dissect the problem into two aspects: 1) pericardial constraint modifying ventricular and septal mechanics, hence, lowering stroke volume, and 2) ventricular interaction relating to how respiration varies RV and LV stroke volume.
Our model offers two explanations for lowered stroke volume seen in cardiac tamponade. They are independent effects of pericardial constraint, one occurring in diastole and the other occurring in systole. In diastole, pericardial constraint causes overall filling volume constraint, due to both ventricular constriction and AV interaction, which reduces the overall volume available from the atria. The reduction of filling volume contributes to a reduction in stroke volume. In systole, pericardial constraint causes reduced LV preload, resulting in abnormal septal movement in early systole and premature reduction in PRV. These effects prolong LPEP, reduce RV and LV ejection times, and thereby reduce stroke volume. Thus, with the aid of the model, we have been able to break down pericardial constraint into diastolic and systolic components. The diastolic effects are well known in literature, but our simulations suggest that the systolic effects come about because of AV interaction determining LV preload.
Respiratory variation in stroke volume manifests itself as pulsus paradoxus, and we have identified parallel and series ventricular interactions as mechanistic explanations. Specifically, parallel interaction occurs with respiratory fluctuation of right heart inflow because of filling volume constraint (imposed by the septum and pericardium) and abnormal septal movement. These are both a direct result of AV interaction stemming from pericardial constraint. Likewise, respiration controls septal movement, favoring one heart over the other in systolic ejection. Series interaction exists due to the nature of the series blood pathway, but the magnitude of filling volume variation is exaggerated in tamponade due to lower stroke volumes. The end result of these multifaceted parallel and series interactions is a 180° phasic relationship between the ventricular end diastolic volumes. Importantly, we show both these interactions have an equal and significant contribution to LVSV respiratory variation, and hence to pulsus paradoxus.
Our H-CRS model has the following impacts to the field of tamponade study:
(a) It fully describes the clinical hemodynamic spectrum of tamponade including right heart signs, pulsus paradoxus, transvalvular flow variation at the cardiac inlets and outlets, and cardiac output compromise;
(b) It introduces the concept that fluid pericardial pressure in tamponade directly modulates cardiac chamber dynamics in both diastole and systole;
(c) It quantitatively dissects the exaggerated right-left ventricular interaction, atrioventricular interaction, and the pleural (respiratory) pressure-mediated hemodynamic changes that is characteristic of pulsus paradoxus in tamponade;
(d) It introduces the concept that septal motion and septal characteristics directly affect ventricular interaction (i.e., septal motion is responsible for ventricular desynchronization in tamponade;
(e) It produces a full hemodynamic and respiratory analysis of tamponade which may serve as a roadmap for future study of pericardial diseases.
human cardiovascular-respiratory system
pulmonic (arterial) valve
pulmonic valve opening
pulmonic valve closure
aortic valve opening
aortic valve closure
mean arterial pressure
right ventricular pre-ejection period
left ventricular pre-ejection period
right ventricular stroke volume
left ventricular stroke volume
right ventricular ejection time
left ventricular ejection time
pericardial stiffness parameter
right atrial pressure
left atrial pressure
right ventricular pressure
left ventricular pressure
transmural pericardial pressure
pulmonary arterial pressure
pericardial pressure parameter
right atrial volume
left atrial volume
right ventricular volume
left ventricular volume
total heart volume
pericardial volume offset
vena cava flow
pulmonary venous flow
pulmonary arterial flow
O2 partial pressure
CO2 partial pressure
Percent O2 saturation
This work was supported by a training fellowship from the Keck Center for Interdisciplinary Bioscience Training of the Gulf Coast Consortia (NLM Grant No. 5T15LM07093).
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