Pressure-volume Plane Research Articles

Energetics Equivalent of the Cardiac Force-Length End-Systolic Zone: Implications for Contractility and Economy of Contraction.

We have recently demonstrated the existence of a region on the cardiac mechanics stress-length plane, which we have designated “The cardiac end-systolic zone.” The zone is defined as the area on the pressure-volume (or stress-length) plane within which all stress-length contraction profiles reach their end-systolic points. It is enclosed by three boundaries: the isometric end-systolic relation, the work-loop (shortening) end-systolic relation, and the zero-active stress isotonic end-systolic relation. The existence of this zone reflects the contraction-mode dependence of the cardiac end-systolic force-length relations, and has been confirmed in a range of cardiac preparations at the whole-heart, tissue and myocyte levels. This finding has led us to speculate that a comparable zone prevails for cardiac metabolism. Specifically, we hypothesize the existence of an equivalent zone on the energetics plane (heat vs. stress), and that it can be attributed to the recently-revealed heat of shortening in cardiac muscle. To test these hypotheses, we subjected trabeculae to both isometric contractions and work-loop contractions over wide ranges of preloads and afterloads. We found that the heat-stress relations for work-loop contractions were distinct from those of isometric contractions, mirroring the contraction mode-dependence of the stress-length relation. The zone bounded by these contraction-mode dependent heat-stress relations reflects the heat of shortening. Isoproterenol-induced enhancement of contractility led to proportional increases in the zones on both the mechanics and energetics planes, thereby supporting our hypothesis.

Extended Phase Space in the Framework of Holography**Supported by Iranian National Science Foundation (INSF)

We consider a holographic extended phase space in the presence of Reissner-Nordstrom-Anti-de Sitter (RN-AdS) and Born-Infeld-Anti-de Sitter (BI-AdS) black holes in the bulk. In this extended phase space the cosmological constant is investigated as pressure and volume is defined as the codimension one-time slice in the bulk geometry enclosed by the minimal area appearing in the computation of the holographic entanglement entropy. These thermodynamics quantities can serve as probes of the underlying phase transition dictated by black hole thermodynamics, but do not describe different structures. We find that the isocharges on the pressure-volume plane exhibit a Van der Waals-like structure, for RN-AdS black holes in the background. For BI-AdS black holes, we observe the analogy with a Van der Waals liquid-gas system for βQ > 1/2 and Reentrant phase transition for βQ < 1/2 in the holographic extended phase space. The same holographic thermodynamic behavior is observed when we use the fidelity susceptibility as the volume and the cosmological constant as the pressure for RN-AdS black hole in the background.

Effect of acoustic impedance matching on kinetics of titanium phase transformation

The phase transition experiments under ramp wave compression of titanium have been done by using a magnetic diven device CQ-4, and the influence of the acoustic impedance of the back surface of titanium on the phase transition has been studied. The experimental results show that when the acoustic impedance of the window is low, free surface or LiF, the particle velocity corresponding to the beginning of phase transition is about 408.9 m/s, while at the high impedance sapphire window, is about 373.9 m/s. The pressures corresponding to the characteristic velocities are not the phase change onset pressures. A simulation was done to well describe this complicated dynamic response including physical models of multi-phase equation of state based on Helmholtz free energy, strength model, and non-equilibrium dynamic equation of phase transition. The calculated results are in excellent agreement with the experimental data, and they exhibit the dynamic physical characteristics of Tin involving the elastoplastic transition and evolution of mass fraction of different phase. The results show that the velocity wave forms of the samples near the loading surface are the same, but the amplitude of the wave forms varies greatly due to the impedance matching of Tin and windows in the vicinity of Tin’s rear surface. The phase transition pressure of Ti is about 10.5 GPa, which is a rate dependent non-equilibrium dynamic process. In the pressure-volume thermodynamic plane, the calculated isentrope coincides with Hugoniot before phase transition, but is below the Hugoniot after phase change. The obvious decrease in sound velocity after phase transition is due to the discontinuity of the specific volume due to phase transition.

Ventricular-Arterial Coupling in Chronic Heart Failure.

Measures of interaction between the left ventricle (LV) and arterial system (ventricular-arterial coupling) are important but under-recognised cardiovascular phenotypes in heart failure. Ventriculo-arterial coupling is commonly assessed in the pressure-volume plane, using the ratio of effective arterial elastance (EA) to LV end-systolic elastance (EES) to provide information on ventricular-arterial system mechanical efficiency and performance when LV ejection fraction is abnormal. These analyses have significant limitations, such as neglecting systolic loading sequence, and are less informative in heart failure with preserved ejection fraction (HFpEF). EA is almost entirely dependent on vascular resistance and heart rate. Assessment of pulsatile arterial haemodynamics and time-resolved myocardial wall stress provide critical incremental physiological information and should be more widely utilised. Pulsatile arterial load represents a promising therapeutic target in HFpEF. Here, we review various approaches to assess ventricular-arterial interactions, and their pathophysiological and clinical implications in heart failure.

Solid-liquid critical behavior of a cylindrically confined Lennard-Jones fluid.

Extensive molecular dynamics simulations have been performed to study the phase behavior of Lennard-Jones particles confined in a quasi-one-dimensional hydrophobic nanopore. We provide unambiguous evidence for a solid-liquid critical point by investigating (i) isotherms in the pressure-volume plane, (ii) the spontaneous solid-liquid phase separation below a certain temperature, (iii) diverging heat capacity and isothermal compressibility as a certain point is approached, (iv) continuous change of dynamical and structural properties above the point, (v) the finite-size scaling analysis of the density distribution below and above the point. The result combined with earlier studies of confined water suggests that the solid-liquid critical point is not uncommon in quasi-one- and quasi-two-dimensional fluids.

Maxwell’s Equal Area Law and the Hawking-Page Phase Transition

We study the phases of a Schwarzschild black hole in the Anti-deSitter background geometry. Exploiting fluid/gravity duality, we construct the Maxwell equal area isotherm in the temperature-entropy plane, in order to eliminate negative heat capacity BHs. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates unphysical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable BHs are formed at the temperature , while pure radiation persists for . turns out to be below the standard Hawking-Page temperature and there are no unstable BHs as in the usual scenario. Also, we show that, in order to reproduce the correct BH entropy , one has to write a black hole equation of state, that is, , in terms of the geometrical volume .

Ventricular–arterial coupling: Invasive and non-invasive assessment

Interactions between the left ventricle (LV) and the arterial system, (ventricular–arterial coupling) are key determinants of cardiovascular function. Ventricular–arterial coupling is most frequently assessed in the pressure–volume plane using the ratio of effective arterial elastance (EA) to LV end-systolic elastance (EES). EA (usually interpreted as a lumped index of arterial load) can be computed as end-systolic pressure/stroke volume, whereas EES (a load-independent measure of LV chamber systolic stiffness and contractility) is ideally assessed invasively using data from a family of pressure–volume loops obtained during an acute preload alteration. Single-beat methods have also been proposed, allowing for non-invasive estimations of EES using simple echocardiographic measurements. The EA/EES ratio is useful because it provides information regarding the operating mechanical efficiency and performance of the ventricular–arterial system. However, it should be recognized that analyses in the pressure–volume plane have several limitations and that “ventricular–arterial coupling” encompasses multiple physiologic aspects, many of which are not captured in the pressure–volume plane. Therefore, additional assessments provide important incremental physiologic information about the cardiovascular system and should be more widely used. In particular, it should be recognized that: (1) comprehensive analyses of arterial load are important because EA poorly characterizes pulsatile LV load and does not depend exclusively on arterial properties; (2) The systolic loading sequence, an important aspect of ventricular–arterial coupling, is neglected by pressure–volume analyses, and can profoundly impact LV function, remodeling and progression to heart failure. This brief review summarizes methods for the assessment of ventricular–arterial interactions, as discussed at the Artery 12 meeting (October 2012).

Shock behaviour of a phenolic resin

Phenolic resins are used in many aspects of everyday life, e.g. as the matrix material for carbon fibre laminates used in the aerospace industry. Consequently, detailed knowledge of this material, especially while under shock loading, is extremely useful for the design of components that could be subjected to impact during their lifespan. The shock Hugoniot equations of state for phenolic resin (Durite SC-1008), with initial density of 1.18 g cm−3 have been determined using the plate-impact technique with in situ manganin stress gauges. The Hugoniot equation in the shock velocity–particle velocity plane was found to be non-linear in nature with the following equation: US = 2.14 + 3.79up − 1.68u 2p . Further, the Hugoniot in the pressure–volume plane was observed to largely follow the hydrostatic curve. Lateral gauge measurements were also obtained. An ANSYS AutodynTM 2D model was used to investigate the lateral stress behaviour of the SC-1008. A comparison of the Hugoniot elastic limit calculated from the shear strength and measured sound speeds gave reasonable agreement with a value of 0.66 ± 0.35 GPa obtained.

Containing Hypertrophy With a PICOT Fence

See related article, pages 307–314 Cardiac hypertrophy is the common myocardial response to chronic hemodynamic overload. It currently affects nearly 5 million Americans and is responsible for &50 000 deaths annually. From the perspective of cardiac mechanics, it seems surprising that cardiac hypertrophy is a killer. The physics of reactive hypertrophy date to the 19th century1 and predict that hypertrophy will compensate for increased hemodynamic loading through normalization of ventricular wall stress, the phylogenetically conserved set point for cardiac load.2 The Laplace relationship (stress=½ pr/h), describes wall stress increasing in direct proportion with intraluminal pressure (p) and chamber radius (r), but decreasing as wall thickness (h) grows. Accordingly, whether the ventricle dilates or is subjected to increased pressure, hypertrophic thickening of its walls should compensate.3 And it does. However, long-term functional compensation relies on the quality of hypertrophied myocardium being invariant as quantity increases, which is not the case. Multiple studies have defined molecular, cellular, and functional characteristics of reactive hypertrophy that differentiate it from normal myocardium and from cardiac enlargement caused by physiological conditioning.4–6 Such findings gave rise to the notions of pathological and physiological hypertrophies7 and provide a mechanistic framework for why reactive hypertrophy ultimately fails,8 whereas physiological conditioning of the heart does not. Cardiac hypertrophy also has effects unrelated to contractility and ventricular ejection performance. To quote Joseph Stalin out of context, “Quantity has a quality all its own”, meaning that a steady quantitative change can create a sudden qualitative shift. The heart aptly demonstrates this principle because reactive hypertrophy and wall thickening increase ventricular stiffness, which leads to diastolic dysfunction and heart failure with preserved ejection fraction.9 Moreover, a number of studies have suggested that cardiac hypertrophy is not essential to …

The Riemann Problem for the Euler Equations with Nonconvex and Nonsmooth Equation of State: Construction of Wave Curves

The Riemann problem is considered for the investigation of nonclassical wave phenomena in Bethe--Zel'dovich--Thompson (BZT)-fluids and fluids which undergo a phase transition, i.e., the isentropes suffer kinks at the saturation boundaries. These fluids are modeled by a general equation of state that also takes into account regions of negative nonlinearity where the isentropes are nonconvex in the pressure-volume plane. Here the physical model is based on thermodynamical equilibrium. Both nonsmoothness as well as nonconvexity significantly influence the composition of the wave curves which are crucial for determining the solution for the Riemann problem for the Euler equations. This work gives explicit criteria for the composition of these wave curves by elementary wave types such as shocks, simple waves, and composite waves. Numerous examples for different wave curve compositions are presented.

Right ventricular pacing lead location for optimal left ventricular function during biventricular pacing varies in patients without resynchronization therapy indication: A pressure volume plane analysis

Right ventricular pacing lead location for optimal left ventricular function during biventricular pacing varies in patients without resynchronization therapy indication: A pressure volume plane analysis

A hybrid mock circulatory system: testing a prototype under physiologic and pathological conditions.

Hydraulic models of circulation are used to test mechanical heart assist devices and for research and training purposes. However, when compared with numerical models, they are rather expensive and often not sufficiently flexible or accurate. Flexibility and accuracy can be improved by merging numerical models with physical models, thus obtaining a hybrid model where numerical and physical sections are connected by an electrohydraulic interface. This concept is applied here to represent left ventricular function. The resulting hybrid model is inserted into the existing closed loop model of circulation. The hybrid model reproduces ventricular function by a variable elastance numerical model. Its interaction with the hydraulic sections is governed by measuring left atrial and systemic arterial pressures and computing the left ventricular output flow by the resolution of the corresponding equations. This signal is used to control a flow generator reproduced by a gear pump driven by a DC motor. Results obtained under different circulatory conditions demonstrate the behavior of the ventricular model on the pressure-volume plane and report the trend of the main hemodynamic variables.

Experimental configuration for isentropic compression of solids using pulsed magnetic loading

A capability to produce quasi-isentropic compression of solids using pulsed magnetic loading on the Z accelerator has recently been developed and demonstrated [C. A. Hall, Phys. Plasmas 7, 2069 (2000)]. This technique allows planar, continuous compression of materials to stresses approaching 1.5 Mbar. In initial stages of development, the experimental configuration used a magnetically loaded material cup or disk as the sample of interest pressed into a conductor. This installation caused distortions that limited the ability to attach interferometer windows or other materials to the rear of the sample. In addition, magnetic pressure was not completely uniform over sample dimensions of interest. A new modular configuration is described that improves the uniformity of loading over the sample surface, allows materials to be easily attached to the magnetically loaded sample, and improves the quality of data obtained. Electromagnetic simulations of the magnetic field uniformity for this new configuration will also be presented. Comparisons between data on copper to ∼300 kbar using the old and new experimental configurations will also be made. Results indicate that to within experimental error, the configurations produce similar results in the pressure-volume plane.

Nonideal Plasma Thermodynamics: Separate Account of Short- and Long-Range Interaction

The method is developed to calculate the thermodynamic functions of strongly non-ideal plasma by separate treating of short- and long-range interaction contributions, the border of the separation depending on the charge number density as ∼n1/3. The result for one-component plasma (OCP) reproduce the Monte Carlo results in the overall interval of non-ideality parameter values. The method is generalized to treat two-component plasma (TCP) in the most essential range of non-ideality parameter. The existence of a double-phase domain in the pressure-volume plane is discussed.

A Hybrid (Numerical-physical) Model of the Left Ventricle

Hydraulic models of the circulation are used to test mechanical devices and for training and research purposes; when compared to numerical models, however, they are not flexible enough and rather expensive. The solution proposed here is to merge the characteristics and the flexibility of numerical models with the functions of physical models. The result is a hybrid model with numerical and physical sections connected by an electro-hydraulic interface - which is to some extent the main problem since the numerical model can be easily changed or modified. The concept of hybrid model is applied to the representation of ventricular function by a variable elastance numerical model. This prototype is an open loop circuit and the physical section is built out of a reservoir (atrium) and a modified windkessel (arterial tree). The corresponding equations are solved numerically using the variables (atrial and arterial pressures) coming from the physical circuit. Ventricular output flow is the computed variable and is sent to a servo amplifier connected to a DC motor-gear pump system. The gear pump, behaving roughly as a flow source, is the interface to the physical circuit. Results obtained under different hemodynamic conditions demonstrate the behaviour of the ventricular model on the pressure-volume plane and the time course of output flow and arterial pressure.

The Importance Of Large Artery Pressure-Volume Curve Changes In Hypertension Studied With A Closed-Loop Circulatory Model

A closed-loop model of the cardiovascular system was used to study the effect of the pressure-volume (P-V) curve of the large arteries on systemic blood pressure. Three types of P-V alterations were considered: constant compliance with altered unstressed volume, compliance change, and nonlinear P-V with altered unstressed volume. It was hypothesized that the P-V relation of large arteries can alter blood pressure equally as well as the pressure-flow relation of the small resistance vessels. Results showed that a compliance change or P-V curve shift were equally capable of affecting average blood pressure, with the compliance, in addition, able to affect pulse pressure. The nonlinear P-V relationship with P-V shift most resembled hypertension and was highly effective in achieving elevated pressures and pulse pressure. The authors found that changes in peripheral resistance were not necessary to alter blood pressure. If resistance was allowed to vary such that cardiac output is held constant, that is, whole body autaregulation, the effects of large artery P-V alterations were augmented. Hence, peripheral resistance was only required to change when cardiac output was restored to pre-altered pressure levels. The authors conclude that a change in the pressure-volume curve of large arteries is a necessary condition of chronic elevation in blood pressure and is observable from the systemic arterial pressure-volume plane. Detailed knowledge of the P-V curve permits identification of the possible sources of hypertension relative to the large arteries.

Left ventricular dysfunction after open repair of simple congenital heart defects in infants and children: Quantitation with the use of a conductance catheter immediately after bypass

Objective: Quantification of myocardial injury after the simplest pediatric operations by load-independent indices of left ventricular function, using conductance and Mikro-Tip pressure catheters (Millar Instruments, Inc., Houston, Tex.) inserted through the left ventricular apex. Methods: Sixteen infants and children with intact ventricular septum undergoing cardiac operations had left ventricular function measured, immediately before and after bypass. Real-time pressure-volume loops were generated by conductance and Mikro-Tip pressure catheters placed in the long-axis via the left ventricular apex, and preload was varied by transient snaring of the inferior vena cava. Results: Good quality pressure-volume loops were generated in 13 patients (atrial septal defects, n = 11; double-chambered right ventricle, n = 1; supravalvular aortic stenosis, n = 1; age 0.25 to 14.4 years, weight 3.1 to 46.4 kg). Their mean bypass time was 41 ± 14 minutes and mean aortic crossclamp time 27 ± 11 minutes. End-systolic elastance decreased by 40.7% from 0.34 ± 0.17 to 0.21 ± 0.15 mm Hg -1·ml -1·kg -1 ( p < 0.001). There were no significant changes in the slope of the stroke work–end-diastolic volume relationship, end-diastolic elastance, time constant of isovolumic relaxation, and normalized values of the maxima and minima of the first derivative of developed left ventricular pressure. Conclusion: Load-independent indices of left ventricular function can be derived from left ventricular pressure-volume loops generated by conductance and Mikro-Tip pressure catheters during the perioperative period in infants and children undergoing cardiac operations. Incomplete myocardial protection was demonstrated by a deterioration in systolic function after even short bypass and crossclamp times. Ignorance of the cause of postoperative myocardial dysfunction in the immature heart is compounded by the incomplete myocardial protection afforded by current cardioplegic strategies. 1,5 Investigations of the mechanisms and treatment of postoperative ventricular dysfunction are hampered by use of nonspecific clinical end points as indirect estimates of ventricular function, for example, requirement for inotropic agents, duration of ventilation, intensive care unit stay, and mortality. These clinical indices are relatively insensitive to changes in ventricular function and necessitate large cohorts of patients to detect even major differences in outcome from differing myocardial protective strategies. To measure left ventricular function optimally during the perioperative period, with its dramatic changes in loading conditions, necessitates the use of load-independent indices of systolic and diastolic function. In infants and children with an intact ventricular septum undergoing cardiac operations (mainly atrial septal defect closure), we report the changes in left ventricular function assessed from the pressure-volume plane with the use of a conductance catheter and Mikro-Tip pressure catheter (Millar Instruments, Inc., Houston, Tex). In animal and human studies the conductance catheter is placed in the long axis of the left ventricle, most commonly through the aortic valve, with the use of retrograde arterial cannulation or aortotomy. 6-11 This is clearly impractical in children undergoing bypass procedures, and in this study we report the first clinical use of custom-built miniature catheters placed in the same long axis, but via the left ventricular apex.

Entropy and heat along reversible paths for fluids and magnets

An identity for the volume derivative of entropy along an arbitrary reversible path is derived and used to show that the heat to a fluid can attain both positive and negative values along certain negatively sloped paths in the pressure–volume plane. A temperature–entropy plot graphically illustrates this point. An analogous entropy identity for magnetic systems is derived and used together with a temperature–entropy plot to gain insights into paramagnetic behavior. In contrast with the ideal gas, a path for an ideal paramagnet can have both positive and negative heats only if it attains both positive and negative slopes in a magnetization vs magnetic field plot.

Alterations in myocardial free fatty acid clearance precede mechanical abnormalities in canine tachycardia-induced heart failure.

The purpose of this study was to evaluate whether abnormalities of free fatty acid metabolism are present before the onset of overt mechanical dysfunction in dogs with tachycardia-induced heart failure. We studied six dogs chronically instrumented to allow assessment of left ventricular function in the pressure-volume plane. Free fatty acid clearance was assessed according to the washout rate of a free fatty acid analog, iodophenylpentadecanoic acid ([123I]PPA or IPPA). IPPA clearance was measured within 1 hour of the hemodynamic assessment. The animals were studied under baseline conditions and 11.7 +/- 3.6 days after ventricular pacing at a rate of 240 beats/min. Hemodynamic studies after pacing showed a nonsignificant increase in left ventricular end-diastolic pressure (11.7 +/- 4.7 to 17.4 +/- 6.5 mm Hg) and a nonsignificant decrease in the maximum derivative of pressure with respect to time (1836 +/- 164 vs 1688 +/- 422 mm Hg/sec). There was also no change in the time constant of left ventricular relaxation, which was 34.8 +/- 7.67 msec before and 35.3 +/- 7.3 msec after pacing. However, a significant prolongation in the clearance half-time of [123I]PPA, from 86.1 +/- 23.9 to 146.5 +/- 22.6 minutes (p < 0.01) was found. Thus abnormal lipid clearance appears before the onset of significant mechanical dysfunction in tachycardia-induced heart failure. This suggests that abnormal substrate metabolism may play an important role in the pathogenesis of this condition.

Effect of exercise on left ventricular-arterial coupling assessed in the pressure-volume plane.

The left ventricle (LV) and arterial system are nearly optimally coupled to produce stroke work (SW) at rest. However, the effect of exercise on the coupling between the LV and arterial system has not been directly determined. We evaluated 11 dogs who were instrumented to determine LV volume from three diameters. The LV end-systolic pressure (Pes)-volume (Ves) relation was determined by transient caval occlusion at rest and while the animals ran at 5-7 mph on a treadmill. During exercise, the Pes-Ves relation was shifted toward the left and the slope [end-systolic elastance (Ees)] increased from 7.7 +/- 2.8 to 12.7 +/- 4.2 (SD) mmHg/ml (P < 0.05). The arterial end-systolic elastance (Ea), calculated as Pes divided by stroke volume, increased during exercise (8.8 +/- 3.0 to 10.9 +/- 4.7 mmHg/ml, P < 0.05). The ratio of Ees to Ea increased during exercise from 0.89 +/- 0.31 to 1.27 +/- 0.12 (P < 0.05). The portion of the pressure-volume area expressed as SW increased during exercise from 0.63 +/- 0.07 to 0.69 +/- 0.10 (P < 0.05). After adrenergic blockade, the Ees-to-Ea ratio was not significantly altered during exercise (0.90 +/- 0.24 vs. 0.83 +/- 0.15, P = NS). At rest and during exercise, both with intact reflexes and after beta-adrenergic blockade, the ratio of Ees to Ea remained within the range in which SW is > 95% of maximum. We conclude that during exercise, beta-adrenergic stimulation shifts the LV Pes-Ves relation to the left with an increased slope. This more than offsets the increase in Ea.(ABSTRACT TRUNCATED AT 250 WORDS)