Theoretical model of ventricular interdependence: pericardial effects

Review of zero-D and 1-D models of blood flow in the cardiovascular system

Background

Zero-dimensional (lumped parameter) and one dimensional models, based on simplified representations of the components of the cardiovascular system, can contribute strongly to our understanding of circulatory physiology. Zero-D models provide a concise way to evaluate the haemodynamic interactions among the cardiovascular organs, whilst one-D (distributed parameter) models add the facility to represent efficiently the effects of pulse wave transmission in the arterial network at greatly reduced computational expense compared to higher dimensional computational fluid dynamics studies. There is extensive literature on both types of models.

Method and Results

The purpose of this review article is to summarise published 0D and 1D models of the cardiovascular system, to explore their limitations and range of application, and to provide an indication of the physiological phenomena that can be included in these representations. The review on 0D models collects together in one place a description of the range of models that have been used to describe the various characteristics of cardiovascular response, together with the factors that influence it. Such models generally feature the major components of the system, such as the heart, the heart valves and the vasculature. The models are categorised in terms of the features of the system that they are able to represent, their complexity and range of application: representations of effects including pressure-dependent vessel properties, interaction between the heart chambers, neuro-regulation and auto-regulation are explored. The examination on 1D models covers various methods for the assembly, discretisation and solution of the governing equations, in conjunction with a report of the definition and treatment of boundary conditions. Increasingly, 0D and 1D models are used in multi-scale models, in which their primary role is to provide boundary conditions for sophisticate, and often patient-specific, 2D and 3D models, and this application is also addressed. As an example of 0D cardiovascular modelling, a small selection of simple models have been represented in the CellML mark-up language and uploaded to the CellML model repository http://models.cellml.org/. They are freely available to the research and education communities.

Conclusion

Each published cardiovascular model has merit for particular applications. This review categorises 0D and 1D models, highlights their advantages and disadvantages, and thus provides guidance on the selection of models to assist various cardiovascular modelling studies. It also identifies directions for further development, as well as current challenges in the wider use of these models including service to represent boundary conditions for local 3D models and translation to clinical application.

Using a human cardiovascular-respiratory model to characterize cardiac tamponade and pulsus paradoxus

BACKGROUND

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.

METHODS

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.

RESULTS

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.

CONCLUSION

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.

Interventricular coupling coefficients in a thick shell model of passive cardiac chamber deformation

Mechanical interplay between the adjacent ventricles is one of the principal modulators of physiopathological heart function, and the underlying mechanisms of interaction are only partially understood, hence hampering clinically useful interpretation of imaging data. In order to characterize the influence of chamber geometry on ventricular coupling, the ventricles and septum are modeled as portions of ellipsoidal shells, and configuration is derived as a function of pressure gradients by combining shell element equilibrium equations through static boundary conditions applied at the sulcus. Diastolic volume (v) surfaces are calculated as a function of pressure (p), contralateral pressure (clp) and intrathoracic pressure (p ( t )) and match literature data where available. Ventricular interaction is characterized in terms of partial derivatives in v-p-clp-p ( t ) space both under physiological and altered (selectively stiffened walls) conditions. The model allows prediction of diastolic ventricular v-p-clp-p ( t ) interplay in a variety of physiopathological circumstances.

Sensitivity and specificity of echocardiographic evidence of tamponade: implications for ventricular interdependence and pulsus paradoxus

The reported sensitivity of the echocardiographic finding of right atrial collapse for the diagnosis of tamponade ranges from 50% to100%; specificities have ranged from 33% to 100%. Its sensitivity in identifying right ventricular collapse ranges from 48% to 100% whereas the specificity ranges from 72% to 100%. Collapse of either the right atrium or right ventricle is not reliable except in cases where the risk of tamponade is high, consistent with Bayes' theorem. If the patient has hypotension, tachycardia, dyspnea, increased venous pressure, and a pericardial effusion, the diagnosis of tamponade will likely be sustained. To explain pulsus paradoxus, most echocardiographic reports have invoked Dornhorst's theory that inspiratory filling of the right ventricle actively collapses the left ventricle by successfully competing for a fixed total pericardial space ("ventricular interdependence"). However, the pericardial space is not fixed in tamponade but increases with inspiration, and the right heart is much more likely to collapse than the left, given their relative thickness. Pulsus paradoxus depends on the inspiratory surge to the right heart, exaggerated by the small stroke volume of both ventricles induced by tamponade, and vascular coupling between the pulmonary and systemic beds, with a transit time of one to two heart beats.

A Ba2+-resistant, acid-sensitive K+ conductance in Na+-absorbing H441 human airway epithelial cells

By analysis of whole cell membrane currents in Na(+)-absorbing H441 human airway epithelial cells, we have identified a K(+) conductance (G(K)) resistant to Ba(2+) but sensitive to bupivacaine or extracellular acidification. In polarized H441 monolayers, we have demonstrated that bupivacaine, lidocaine, and quinidine inhibit basolateral membrane K(+) current (I(Bl)) whereas Ba(2+) has only a weak inhibitory effect. I(Bl) was also inhibited by basolateral acidification, and, although subsequent addition of bupivacaine caused a further fall in I(Bl), acidification had no effect after bupivacaine, demonstrating that cells grown under these conditions express at least two different bupivacaine-sensitive K(+) channels, only one of which is acid sensitive. Basolateral acidification also inhibited short-circuit current (I(SC)), and basolateral bupivacaine, lidocaine, quinidine, and Ba(2+) inhibited I(SC) at concentrations similar to those needed to inhibit I(Bl), suggesting that the K(+) channels underlying I(Bl) are part of the absorptive mechanism. Analyses using RT-PCR showed that mRNA encoding several two-pore domain K(+) (K2P) channels was detected in cells grown under standard conditions (TWIK-1, TREK-1, TASK-2, TWIK-2, KCNK-7, TASK-3, TREK-2, THIK-1, and TALK-2). We therefore suggest that K2P channels underlie G(K) in unstimulated cells and so maintain the driving force for Na(+) absorption. Since this ion transport process is vital to lung function, K2P channels thus play an important but previously undocumented role in pulmonary physiology.

Expression of intermediate-conductance, Ca2+-activated K+ channel (KCNN4) in H441 human distal airway epithelial cells

Electrophysiological studies of H441 human distal airway epithelial cells showed that thapsigargin caused a Ca(2+)-dependent increase in membrane conductance (G(Tot)) and hyperpolarization of membrane potential (V(m)). These effects reflected a rapid rise in cellular K(+) conductance (G(K)) and a slow fall in amiloride-sensitive Na(+) conductance (G(Na)). The increase in G(Tot) was antagonized by Ba(2+), a nonselective K(+) channel blocker, and abolished by clotrimazole, a KCNN4 inhibitor, but unaffected by other selective K(+) channel blockers. Moreover, 1-ethyl-2-benzimidazolinone (1-EBIO), which is known to activate KCNN4, increased G(K) with no effect on G(Na). RT-PCR-based analyses confirmed expression of mRNA encoding KCNN4 and suggested that two related K(+) channels (KCNN1 and KCNMA1) were absent. Subsequent studies showed that 1-EBIO stimulates Na(+) transport in polarized monolayers without affecting intracellular Ca(2+) concentration ([Ca(2+)](i)), suggesting that the activity of KCNN4 might influence the rate of Na(+) absorption by contributing to G(K). Transient expression of KCNN4 cloned from H441 cells conferred a Ca(2+)- and 1-EBIO-sensitive K(+) conductance on Chinese hamster ovary cells, but this channel was inactive when [Ca(2+)](i) was <0.2 microM. Subsequent studies of amiloride-treated H441 cells showed that clotrimazole had no effect on V(m) despite clear depolarizations in response to increased extracellular K(+) concentration ([K(+)](o)). These findings thus indicate that KCNN4 does not contribute to V(m) in unstimulated cells. The present data thus establish that H441 cells express KCNN4 and highlight the importance of G(K) to the control of Na(+) absorption, but, because KCNN4 is quiescent in resting cells, this channel cannot contribute to resting G(K) or influence basal Na(+) absorption.

Adaptation to mechanical load determines shape and properties of heart and circulation: the CircAdapt model

With circulatory pathology, patient-specific simulation of hemodynamics is required to minimize invasiveness for diagnosis, treatment planning, and followup. We investigated the advantages of a smart combination of often already known hemodynamic principles. The CircAdapt model was designed to simulate beat-to-beat dynamics of the four-chamber heart with systemic and pulmonary circulation while incorporating a realistic relation between pressure-volume load and tissue mechanics and adaptation of tissues to mechanical load. Adaptation was modeled by rules, where a locally sensed signal results in a local action of the tissue. The applied rules were as follows: For blood vessel walls, 1) flow shear stress dilates the wall and 2) tensile stress thickens the wall; for myocardial tissue, 3) strain dilates the wall material, 4) larger maximum sarcomere length increases contractility, and 5) contractility increases wall mass. The circulation was composed of active and passive compliances and inertias. A realistic circulation developed by self-structuring through adaptation provided mean levels of systemic pressure and flow. Ability to simulate a wide variety of patient-specific circumstances was demonstrated by application of the same adaptation rules to the conditions of fetal circulation followed by a switch to the newborn circulation around birth. It was concluded that a few adaptation rules, directed to normalize mechanical load of the tissue, were sufficient to develop and maintain a realistic circulation automatically. Adaptation rules appear to be the key to reduce dramatically the number of input parameters for simulating circulation dynamics. The model may be used to simulate circulation pathology and to predict effects of treatment.

Cl- secretory effects of EBIO in the rabbit conjunctival epithelium

Experiments were conducted to determine whether the Cl- secretagogue, 1-ethyl-2-benzimidazolinone (EBIO), stimulates Cl- transport in the rabbit conjunctival epithelium. For this study, epithelia were isolated in an Ussing-type chamber under short-circuit conditions. The effects of EBIO on the short-circuit current (I(sc)) and transepithelial resistance (R(t)) were measured under physiological conditions, as well as in experiments with altered electrolyte concentrations. Addition of 0.5 mM EBIO to the apical bath stimulated the control I(sc) by 64% and reduced R(t) by 21% (P < 0.05; paired data). Under Cl(-)-free conditions, I(sc) stimulation using EBIO was markedly attenuated. In the presence of an apical-to-basolateral K+ gradient and permeabilization of the apical membrane, the majority of the I(sc) reflected the transcellular movement of K+ via basolateral K+ channels. Under these conditions, EBIO in combination with A23187 elicited nearly instantaneous 60-90% increases in I(sc) that were sensitive to the calmodulin antagonist calmidazolium and the K+ channel blocker tetraethyl ammonium. In the presence of an apical-to-basolateral Cl- gradient and nystatin permeabilization of the basolateral aspect, EBIO increased the Cl(-)-dependent I(sc), an effect prevented by the channel blocker glibenclamide (0.3 mM). The latter compound also was used to determine the proportion of EBIO-evoked unidirectional 36Cl- fluxes in the presence of the Cl- gradient that traversed the epithelium transcellularly. Overall, EBIO activated apical Cl- channels and basolateral K+ channels (presumably those that are Ca2+ dependent), thereby suggesting that this compound, or related derivatives, may be suitable as topical agents to stimulate fluid transport across the tissue in individuals with lacrimal gland deficiencies.

Hypoxia-induced inhibition of whole cell membrane currents and ion transport of A549 cells

In excitable cells, hypoxia inhibits K channels, causes membrane depolarization, and initiates complex adaptive mechanisms. It is unclear whether K channels of alveolar epithelial cells reveal a similar response to hypoxia. A549 cells were exposed to hypoxia during whole cell patch-clamp measurements. Hypoxia reversibly inhibited a voltage-dependent outward current, consistent with a K current, because tetraethylamonium (TEA; 10 mM) abolished this effect; however, iberiotoxin (0.1 microM) does not. In normoxia, TEA and iberiotoxin inhibited whole cell current (-35%), whereas the K-channel inhibitors glibenclamide (1 microM), barium (1 mM), chromanol B293 (10 microM), and 4-aminopyridine (1 mM) were ineffective. (86)Rb uptake was measured to see whether K-channel modulation also affected transport activity. TEA, iberiotoxin, and 4-h hypoxia (1.5% O(2)) inhibited total (86)Rb uptake by 40, 20, and 35%, respectively. Increased extracellular K also inhibited (86)Rb uptake in a dose-dependent way. The K-channel opener 1-ethyl-2-benzimidazolinone (1 mM) increased (86)Rb uptake by 120% in normoxic and hypoxic cells by activation of Na-K pumps (+60%) and Na-K-2Cl cotransport (+170%). However, hypoxic transport inhibition was also seen in the presence of 1-ethyl-2-benzimidazolinone, TEA, and iberiotoxin. These results indicate that hypoxia, membrane depolarization, and K-channel inhibition decrease whole cell membrane currents and transport activity. It appears, therefore, that a hypoxia-induced change in membrane conductance and membrane potential might be a link between hypoxia and alveolar ion transport inhibition.

Impact of pericardial restraint on right atrial mechanics during acute right ventricular pressure load

Optimization of right atrial (RA) mechanics is important for maintaining right ventricular (RV) filling and global cardiac output. However, the impact of pericardial restraint on RA function and the compensatory role of the right atrium to changes in RV afterload remain poorly characterized. In eight open-chest sheep, RA elastance (contractility) and chamber stiffness were measured (RA pressure-volume relations) at baseline and during partial pulmonary artery (PA) occlusion. Data were collected before and after pericardiotomy. With the pericardium intact and partial PA occlusion, RA elastance increased by 28% (P < 0.04), whereas RA stiffness tended to rise (P = 0.08). However, after pericardiotomy, there was a significant fall in both RA elastance (54%, P < 0.04) and stiffness (39%, P < 0.04), and subsequent PA occlusion failed to induce a change in elastance (P > 0.19) or stiffness (P > 0.84). After pericardiotomy, RA elastance and stiffness fell dramatically, and the compensatory response of the right atrium to elevated RV afterload was lost. The ability of the right atrium to respond to changes in RV hemodynamics is highly dependent on pericardial integrity.

Isolated systolic and diastolic ventricular interactions in pacing-induced dilated cardiomyopathy and effects of volume loading and pericardium

BACKGROUND

Interactions between the closely coupled right and left ventricles are known to play important roles as determinants of ventricular function, and the purpose of this study was to evaluate their effects in a model of heart failure.

METHODS AND RESULTS

A dilated cardiomyopathy resulting in congestive heart failure (CHF) was produced in pigs by rapid ventricular pacing at 230 beats per minute for 1 week. Blood was rapidly withdrawn from the left ventricular (LV) apex into a prosthetic ventricle, and the instantaneous effects on the right ventricle were studied during volume loading and before and after pericardiectomy. The systolic interaction gain between the right and left ventricles (Gs) was calculated as the ratio of changes in mean systolic pressure during isolated systolic LV unloading. Diastolic ventricular interaction gain (Gd) was calculated as the ratio of changes in mean diastolic pressures during LV unloading in the last 150 ms of diastole. With the pericardium closed, all interaction gains were significantly increased during volume loading from a right ventricular end-diastolic pressure of 3 to 9 mm Hg: Gs from 0.045 +/- 0.014 to 0.063 +/- 0.020 mm Hg/mm Hg (normal pigs) and from 0.077 +/- 0.040 to 0.103 +/- 0.019 (CHF pigs) and Gs from 0.196 +/- 0.116 to 0.493 +/- 0.117 mm Hg/mm Hg (normal pigs) and from 0.174 +/- 0.101 to 0.341 +/- 0.165 (CHF pigs). When the pericardium was opened, Gd was significantly reduced to 0.145 +/- 0.071 and 0.129 +/- 0.026 mm Hg/mm Hg (normal and CHF pigs, respectively), but Gs showed no significant change (0.067 +/- 0.027 and 0.109 +/- 0.012 mm Hg/mm Hg for normal and CHF pigs, respectively), and both were also significantly increased during volume loading. Gs was significantly greater in CHF versus normal pigs under all conditions, but there were no differences in Gd between CHF and normal pigs.

CONCLUSIONS

These results suggest that dilated cardiomyopathy increases systolic but not diastolic interactions, that the pericardium increases diastolic but not systolic ventricular interactions, and that volume loading with and without the pericardium opened increases both systolic and diastolic interactions.