Modeling left ventricular diastolic dysfunction: classification and key indicators

Background

Mathematical modeling can be employed to overcome the practical difficulty of isolating the mechanisms responsible for clinical heart failure in the setting of normal left ventricular ejection fraction (HFNEF). In a human cardiovascular respiratory system (H-CRS) model we introduce three cases of left ventricular diastolic dysfunction (LVDD): (1) impaired left ventricular active relaxation (IR-type); (2) increased passive stiffness (restrictive or R-type); and (3) the combination of both (pseudo-normal or PN-type), to produce HFNEF. The effects of increasing systolic contractility are also considered. Model results showing ensuing heart failure and mechanisms involved are reported.

Methods

We employ our previously described H-CRS model with modified pulmonary compliances to better mimic normal pulmonary blood distribution. IR-type is modeled by changing the activation function of the left ventricle (LV), and R-type by increasing diastolic stiffness of the LV wall and septum. A 5^th-order Cash-Karp Runge-Kutta numerical integration method solves the model differential equations.

Results

IR-type and R-type decrease LV stroke volume, cardiac output, ejection fraction (EF), and mean systemic arterial pressure. Heart rate, pulmonary pressures, pulmonary volumes, and pulmonary and systemic arterial-venous O₂ and CO₂ differences increase. IR-type decreases, but R-type increases the mitral E/A ratio. PN-type produces the well-described, pseudo-normal mitral inflow pattern. All three types of LVDD reduce right ventricular (RV) and LV EF, but the latter remains normal or near normal. Simulations show reduced EF is partly restored by an accompanying increase in systolic stiffness, a compensatory mechanism that may lead clinicians to miss the presence of HF if they only consider LVEF and other indices of LV function. Simulations using the H-CRS model indicate that changes in RV function might well be diagnostic. This study also highlights the importance of septal mechanics in LVDD.

Conclusion

The model demonstrates that abnormal LV diastolic performance alone can result in decreased LV and RV systolic performance, not previously appreciated, and contribute to the clinical syndrome of HF. Furthermore, alterations of RV diastolic performance are present and may be a hallmark of LV diastolic parameter changes that can be used for better clinical recognition of LV diastolic heart disease.     

Left ventricular chamber stiffness at rest as a determinant of exercise capacity in heart failure subjects with decreased ejection fraction.

Impaired exercise tolerance, determined by peak oxygen consumption (VO2 peak), is predictive of mortality and the necessity for cardiac transplantation in patients with chronic heart failure (HF). However, the role of left ventricular (LV) diastolic function at rest, reflected by chamber stiffness assessed echocardiographically, as a determinant of exercise tolerance is unknown. Increased LV chamber stiffness and limitation of VO2 peak are known correlates of HF. Yet, the relationship between chamber stiffness and VO2 peak in subjects with HF has not been fully determined. Forty-one patients with HF New York Heart Association [(NYHA) class 2.4 +/- 0.8, mean +/- SD] had echocardiographic studies and VO2 peak measurements. Transmitral Doppler E waves were analyzed using a previously validated method to determine k, the LV chamber stiffness parameter. Multiple linear regression analysis of VO(2 peak) variance indicated that LV chamber stiffness k (r2 = 0.55) and NYHA classification (r2 = 0.43) were its best independent predictors and when taken together account for 59% of the variability in VO2 peak. We conclude that diastolic function at rest, as manifested by chamber stiffness, is a major determinant of maximal exercise capacity in HF.     

Left ventricular diastolic function in diabetics

Left ventricular diastolic function was studied in 29 young diabetic patients (aged from 14 to 44 years) without any clinical sign of heart disease. The metabolic state, the presence and the degree of microvascular and neuropathic complications have been established. Age and sex matched 32 healthy subjects served as controls. The parameters of left ventricular diastolic function were determined by means of phonomechanocardiography. By this method in diabetic patients impaired diastolic function of the left ventricle was found. This alteration could be best characterized by the values of normalized relaxation index referring to the isovolumetric relaxation of the left ventricle. A close correlation was found between the microvascular and neuropathic complications and the left ventricular diastolic dysfunction, while no correlation could be demonstrated between the metabolic state and the diastolic cardiac disorder.     

Linagliptin prevents left ventricular stiffening by reducing titin cleavage and hypophosphorylation

The metabolic syndrome (MetS) is an escalating problem worldwide, causing left ventricular stiffening, an early characteristic of diastolic dysfunction for which no treatment exists. As diastolic dysfunction and stiffening in MetS patients are associated with increased circulating dipeptidyl peptidase-4 (DPP-4) levels, we investigated whether the clinically approved DPP-4 inhibitor linagliptin reduces left ventricular stiffness in MetS-induced cardiac disease. Sixteen-week-old obese ZSF1 rats, displaying the MetS and left ventricular stiffness, received linagliptin-supplemented or placebo diet for four weeks. Linagliptin significantly reduced obesity, hyperlipidaemia, and hyperglycaemia and improved left ventricular relaxation. This improved relaxation was related to decreased cardiac fibrosis and cardiomyocyte passive stiffness (F_passive). The reduced F_passive was the result of titin isoform switching from the stiff N2B to the more flexible N2BA and increased phosphorylation of total titin and specifically its N2Bus region (S4080 and S3391). Importantly, DPP-4 directly cleaved titin in vitro, resulting in an increased F_passive, which was prevented by simultaneous administration of linagliptin. In conclusion, linagliptin improves left ventricular stiffness in obese ZSF1 rats by preventing direct DPP4-mediated titin cleavage, as well as by modulating both titin isoform levels and phosphorylation. Reducing left ventricular stiffness by administering linagliptin might prevent MetS-induced early diastolic dysfunction in human.     

Patient-specific modeling of dyssynchronous heart failure: A case study

The development and clinical use of patient-specific models of the heart is now a feasible goal. Models have the potential to aid in diagnosis and support decision-making in clinical cardiology. Several groups are now working on developing multi-scale models of the heart for understanding therapeutic mechanisms and better predicting clinical outcomes of interventions such as cardiac resynchronization therapy. Here we describe the methodology for generating a patient-specific model of the failing heart with a myocardial infarct and left ventricular bundle branch block. We discuss some of the remaining challenges in developing reliable patient-specific models of cardiac electromechanical activity, and identify some of the main areas for focusing future research efforts. Key challenges include: efficiently generating accurate patient-specific geometric meshes and mapping regional myofiber architecture to them; modeling electrical activation patterns based on cellular alterations in human heart failure, and estimating regional tissue conductivities based on clinically available electrocardiographic recordings; estimating unloaded ventricular reference geometry and material properties for biomechanical simulations; and parameterizing systemic models of circulatory dynamics from available hemodynamic measurements.     

Computational modeling of left heart diastolic function: examination of ventricular dysfunction

A computational model that accounts for blood-tissue interaction under physiological flow conditions was developed and applied to a thin-walled model of the left heart. This model consisted of the left ventricle, left atrium, and pulmonary vein flow. The input functions for the model included the pulmonary vein driving pressure and time-dependent relationship for changes in chamber tissue properties during the simulation. The Immersed Boundary Method was used for the interaction of the tissue and blood in response to fluid forces and changes in tissue pathophysiology, and the fluid mass and momentum conservation equations were solved using Patankar's Semi-Implicit Method for Pressure Linked Equations (SIMPLE). This model was used to examine the flow fields in the left heart under abnormal diastolic conditions of delayed ventricular relaxation, delayed ventricular relaxation with increased ventricular stiffness, and delayed ventricular relaxation with an increased atrial contraction. The results obtained from the left heart model were compared to clinically observed diastolic flow conditions, and to the results from simulations of normal diastolic function in this model [1]. Cases involving impairment of diastolic function were modeled with changes to the input functions for fiber relaxation/contraction of the chambers. The three cases of diastolic dysfunction investigated agreed with the changes in diastolic flow fields seen clinically. The effect of delayed relaxation was to decrease the early filling magnitude, and this decrease was larger when the stiffness of the ventricle was increased. Also, increasing the contraction of the atrium during atrial systole resulted in a higher late filling velocity and atrial pressure. The results show that dysfunction can be modeled by changing the relationships for fiber resting-length and/or stiffness. This provides confidence in future modeling of disease, especially changes to chamber properties to examine the effect of local dysfunction on global flow fields.     

Myocardial diastolic elasticity in chronic adriamycin lesion

Isolated hearts of the majority of rats receiving 20 mg/kg adriamycin for 10 weeks exhibited normal pump function. Left ventricular diastolic stiffness of these hearts was approximately 1.5 times higher, as compared to control hearts, with the filling pressure in the range of 5 to 20 cm H2O and diastolic pause 23% longer due to bradycardia. Pacing-induced increase in the heart rate up to the control level resulted in further increase in left ventricular diastolic stiffness due to the rise in myocardial stiffness, associated with a fall in cardiac output by 36%. The heart and right atrial compliance determined in separate experiments did not differ significantly from the control. The results suggest that increased left ventricular diastolic stiffness of adriamycin-treated rats seems to be rather due to energy-dependent disturbance in myofibril relaxation than to usually arising myocardial fibrosis.     

Left ventricular pressure-volume relationship in a rat model of advanced aging-associated heart failure

Aging is associated with profound changes in the structure and function of the heart. A fundamental understanding of these processes, using relevant animal models, is required for effective prevention and treatment of cardiovascular disease in the elderly. Here, we studied cardiac performance in 4- to 5-mo-old (young) and 24- to 26-mo-old (old) Fischer 344 male rats using the Millar pressure-volume (P-V) conductance catheter system. We evaluated systolic and diastolic function in vivo at different preloads, including preload recruitable stroke work (PRSW), maximal slope of the systolic pressure increment (+dP/dt), and its relation to end-diastolic volume (+dP/dt-EDV) as well as the time constant of left ventricular pressure decay, as an index of relaxation. The slope of the end-diastolic P-V relation (EDPVR), an index of left ventricular stiffness, was also calculated. Aging was associated with decrease in left ventricular systolic pressure, +dP/dt, maximal slope of the diastolic pressure decrement, +dP/dt-EDV, PRSW, ejection fraction, stroke volume, cardiac and stroke work indexes, and efficiency. In contrast, total peripheral resistance, left ventricular end-diastolic volume, left ventricular end-diastolic pressure, and EDPVR were greater in aging than in young animals. Taken together, these data suggest that advanced aging is characterized by decreased systolic performance accompanied by delayed relaxation and increased diastolic stiffness of the heart in male Fischer 344 rats. P-V analysis is a sensitive method to determine cardiac function in rats.     

Parvalbumin Isoforms for Enhancing Cardiac Diastolic Function

Diastolic heart failure (DHF), characterized by depressed myocardial relaxation performance and poor ventricular filling, is a distinct form of heart failure accounting for nearly half of the heart failure patients with otherwise normal systolic performance. Defective intracellular calcium (Ca2+) cycling is an important mechanism underlying impaired relaxation in DHF. Recently, genetic manipulation of Ca2+ handling proteins in cardiac myocytes has been explored for its potential therapeutic application in DHF. Specifically, ectopic expression of the skeletal muscle Ca2+ binding protein parvalbumin (Parv) has been shown to accelerate myocardial relaxation in vitro and in vivo. Parv acts as a unique "delayed" Ca2+ buffer during diastole by promoting Ca2+ transient decay and sequestration and corrects diastolic dysfunction in an energy-independent manner. This brief review summarizes the rationale and development of Parv gene transfer approaches for DHF, and in particular, discusses the divergent effects of Parv isoforms on cardiac myocyte Ca2+ handling and contractile function with the long-range goal of alleviating diastolic dysfunction in DHF.     

Diastolic dysfunction and diastolic heart failure: diagnostic, prognostic and therapeutic aspects

Left ventricular (LV) diastolic dysfunction (DD) and diastolic heart failure (HF), that is symptomatic DD, are due to alterations of myocardial diastolic properties. These alterations involve relaxation and/or filling and/or distensibility. Arterial hypertension associated to LV concentric remodelling is the main determinant of DD but several other cardiac diseases, including myocardial ischemia, and extra-cardiac pathologies involving the heart are other possible causes. In the majority of the studies, isolated diastolic HF has been made equal to HF with preserved systolic function (= normal ejection fraction) but the true definition of this condition needs a quantitative estimation of LV diastolic properties. According to the position of the European Society of Cardiology and subsequent research refinements the use of Doppler echocardiography (transmitral inflow and pulmonary venous flow) and the new ultrasound tools has to be encouraged for diagnosis of DD. In relation to uncertain definitions, both prevalence and prognosis of diastolic heart failure are very variable. Despite an apparent lower death rate in comparison with LV systolic HF, long-term follow-up (more than 5 years) show similar mortality between the two kinds of HF. Recent studies performed by Doppler diastolic indexes have identified the prognostic power of both transmitral E/A ratio < 1 (pattern of abnormal relaxation) and > 1.5 (restrictive patterns). The therapy of LV DD and HF is not well established but ACE-inhibitors, angiotensin inhibitors, aldosterone antagonists and β-blockers show potential beneficial effect on diastolic properties. Several trials, completed or ongoing, have been planned to treat DD and diastolic HF.     

Left Atrial Structure and Function in Heart Failure with Preserved Ejection Fraction: A RELAX Substudy

Given the emerging recognition of left atrial structure and function as an important marker of disease in heart failure with preserved ejection fraction (HF-pEF), we investigated the association between left atrial volume and function with markers of disease severity and cardiac structure in HF-pEF. We studied 100 patients enrolled in the PhosphdiesteRasE-5 Inhibition to Improve CLinical Status and EXercise Capacity in Diastolic Heart Failure (RELAX) trial who underwent cardiac magnetic resonance (CMR), cardiopulmonary exercise testing, and blood collection before randomization. Maximal left atrial volume index (LAVi; N = 100), left atrial emptying fraction (LAEF; N = 99; including passive and active components (LAEF_P, LAEF_A; N = 80, 79, respectively) were quantified by CMR. After adjustment for multiple testing, maximal LAVi was only associated with age (ρ = 0.39), transmitral filling patterns (medial E/e’ ρ = 0.43), and N-terminal pro-BNP (NT-proBNP; ρ = 0.65; all p<0.05). Lower LAEF was associated with older age, higher transmitral E/A ratio and higher NT-proBNP. Peak VO₂ and V_E/VCO₂ slope were not associated with left atrial structure or function. After adjustment for age, sex, transmitral E/A ratio, CMR LV mass, LV ejection fraction, and creatinine clearance, NT-proBNP remained associated with maximal LAVi (β = 0.028, p = 0.0007) and total LAEF (β = -0.033, p = 0.001). Passive and active LAEF were most strongly associated with age and NT-proBNP, but not gas exchange or other markers of ventricular structure or filling properties. Left atrial volume and emptying function are associated most strongly with NT-proBNP and diastolic filling properties, but not significantly with gas exchange, in HFpEF. Further research to explore the relevance of left atrial structure and function in HF-pEF is warranted.     

Left atrial conduit volume is generated by deviation from the constant-volume state of the left heart: a combined MRI-echocardiographic study

Although modeling the four-chambered heart as a constant-volume pump successfully predicts causal physiological relationships between cardiac indexes previously deemed unrelated, the real four-chambered heart slightly deviates from the constant-volume state by ventricular end systole. This deviation has consequences that affect chamber function, specifically, left atrial (LA) function. LA attributes have been characterized as booster pump, reservoir, and conduit functions, yet characterization of their temporal occurrence or their causal relationship to global heart function has been lacking. We investigated LA function in the context of the constant-volume attribute of the left heart in 10 normal subjects using cardiac magnetic resonance imaging (MRI) and contemporaneous Doppler echocardiography synchronized via ECG. Left ventricular (LV) and LA volumes as a function of time were determined via MRI. Transmitral flow, pulmonary vein (PV) flow, and lateral mitral annular velocity were recorded via echocardiography. The relationship between the MRI-determined diastolic LA conduit-volume (LACV) filling rate and systolic LA filling rate correlate well with the relationship between the echocardiographically determined average flow rate during the early portion of the PV D wave and the average flow rate during the PV S wave (r = 0.76). We conclude that the end-systolic deviation from constant volume for the left heart requires the generation of the LACV during diastole. Because early rapid filling of the left ventricle is the driving force for LACV generation while the left atrium remains passive, it may be more appropriate to consider LACV to be a property of ventricular diastolic rather than atrial function.     

The complex dynamics of myocardial interstitial fibrosis in heart failure. Focus on collagen cross-linking

Myocardial interstitial fibrosis (MIF) is a common finding in heart failure (HF) patients, both with preserved and reduced ejection fraction, as well as in HF animal models. MIF is associated with impaired cardiac function and worse clinical outcome. The impact of MIF is influenced not only by the quantity but also by changes in the quality of collagen fibers and in the extracellular matrix components, such as a shift in collagen types proportion, increased fibronectin polymerization and increased degree of collagen cross-linking (CCL). In particular, CCL, a process that renders collagen fibers stiffer and more resistant to degradation, is increased both in patients and animal models of HF. Importantly, in HF patients increased cardiac CCL is directly associated with increased left ventricular stiffness and a higher risk of hospitalization for HF. The aim of this review is to address the complexity of MIF in HF, focusing on CCL.     

Cardiac diastolic dysfunction in conscious dogs with heart failure induced by chronic coronary microembolization

Left ventricular (LV) diastolic dysfunction is a fundamental impairment in congestive heart failure (CHF). This study examined LV diastolic function in the canine model of CHF induced by chronic coronary embolization (CCE). Dogs were implanted with coronary catheters (both left anterior descending and circumflex arteries) for CCE and instrumented for measurement of LV pressure and dimension. Heart failure was elicited by daily intracoronary injections of microspheres (1.2 million, 90- to 120-microm diameter) for 24 +/- 4 days, resulting in significant depression of cardiac systolic function. After CCE, LV maximum negative change of pressure with time (dP/dt(min)) decreased by 25 +/- 2% (P < 0.05) and LV isovolumic relaxation constant and duration increased by 19 +/- 5% and 25 +/- 6%, respectively (both P < 0.05), indicating an impairment of LV active relaxation, which was cardiac preload independent. LV passive viscoelastic properties were evaluated from the LV end-diastolic pressure (EDP)-volume (EDV) relationship (EDP = be(alpha*EDV)) during brief inferior vena caval occlusion and acute volume loading, while the chamber stiffness coefficient (alpha) increased by 62 +/- 10% (P < 0.05) and the stiffness constant (k) increased by 66 +/- 13% after CCE. The regional myocardial diastolic stiffness in LV anterior and posterior walls was increased by 70 +/- 25% and 63 +/- 24% (both P < 0.05), respectively, after CCE, associated with marked fibrosis, increase in collagen I and III, and enhancement of plasminogen activator inhibitor-1 (PAI-1) protein expression. Thus along with depressed LV systolic function there is significant impairment of LV diastolic relaxation and increase in chamber stiffness, with development of myocardial fibrosis and activation of PAI-1, in the canine model of CHF induced by CCE.     

Reprint of “The complex dynamics of myocardial interstitial fibrosis in heart failure. Focus on collagen cross-linking”

Myocardial interstitial fibrosis (MIF) is a common finding in heart failure (HF) patients, both with preserved and reduced ejection fraction, as well as in HF animal models. MIF is associated with impaired cardiac function and worse clinical outcome. The impact of MIF is influenced not only by the quantity but also by changes in the quality of collagen fibers and in the extracellular matrix components, such as a shift in collagen types proportion, increased fibronectin polymerization and increased degree of collagen cross-linking (CCL). In particular, CCL, a process that renders collagen fibers stiffer and more resistant to degradation, is increased both in patients and animal models of HF. Importantly, in HF patients increased cardiac CCL is directly associated with increased left ventricular stiffness and a higher risk of hospitalization for HF. The aim of this review is to address the complexity of MIF in HF, focusing on CCL.     

The Nature of the Disorder of Function in Chronic Postinfarction Aneurysm of the Left Ventricle

Assessment of left ventricular function in five patients with chronic postinfarction left ventricular aneurysm was carried out at the time of left heart catheterization and compared with that in six normal subjects. One patient was investigated before and after surgical resection of the aneurysm. The presence of the aneurysm placed the left ventricle at a mechanical disadvantage in systole and increased the resistance to diastolic filling (impedance). This was true even in patients with normal cardiac indices who were not badly disabled. Resection of the aneurysm corrected both these abnormalities, and, as well, lowered the time-tension index at a time when calculated left ventricular work was much increased. These differences between normals and patients with aneurysms, and the changes occurring as a result of resection of an aneurysm, show that the presence of the aneurysm places the left ventricle at a mechanical disadvantage in systole as well as altering its diastolic filling characteristics.     

An integrated approach to patient-specific predictive modeling for single ventricle heart palliation

In patients with congenital heart disease and a single ventricle (SV), ventricular support of the circulation is inadequate, and staged palliative surgery (usually 3 stages) is needed for treatment. In the various palliative surgical stages individual differences in the circulation are important and patient-specific surgical planning is ideal. In this study, an integrated approach between clinicians and engineers has been developed, based on patient-specific multi-scale models, and is here applied to predict stage 2 surgical outcomes. This approach involves four distinct steps: (1) collection of pre-operative clinical data from a patient presenting for SV palliation, (2) construction of the pre-operative model, (3) creation of feasible virtual surgical options which couple a three-dimensional model of the surgical anatomy with a lumped parameter model (LPM) of the remainder of the circulation and (4) performance of post-operative simulations to aid clinical decision making. The pre-operative model is described, agreeing well with clinical flow tracings and mean pressures. Two surgical options (bi-directional Glenn and hemi-Fontan operations) are virtually performed and coupled to the pre-operative LPM, with the hemodynamics of both options reported. Results are validated against postoperative clinical data. Ultimately, this work represents the first patient-specific predictive modeling of stage 2 palliation using virtual surgery and closed-loop multi-scale modeling.     

Dissociation between myocardial relaxation and diastolic stiffness in the stunned heart: its prevention by ischemic preconditioning

The effects of myocardial stunning and ischemic preconditioning on left-ventricular developed pressure and end-diastolic pressure (diastolic stiffness) as well as on coronary-perfusion pressure were examined in isolated isovolumic rabbit hearts. The isovolumic relaxation was evaluated, and the time constant of pressure decay during the isovolumic period was calculated. Our experimental protocol comprised: 1) myocardial stunning-global ischemia (15 min) followed by reperfusion (30 min); 2) myocardial stunning-global ischemia (20 min) followed by reperfusion (30 min); and 3) ischemic preconditioning — a single cycle of brief global ischemia and reperfusion (5 min each), before a second ischemic period, of 20-min duration. There was no effect upon systolic and diastolic parameters when 15 and 20 minutes of ischemia were evaluated. In both stunned groups the left ventricular developed pressure first recovered to near control values, but then stabilized at only 60% of the control values. Whereas the isovolumic relaxation time constant was increased after 5 min of reperfusion, and return to control values at late reperfusion, the end diastolic pressure remained elevated during the entire period. Values of dP/dV calculated at common pressure levels, were used as a second index of diastolic stiffness. They were increased after stunning, as also was the coronary perfusion pressure. When the heart was preconditioned with a single episode of ischemia, the systolic and diastolic alterations were completely abolished. We thus concluded that diastolic abnormalities incurred by myocardial stunning consist in both an increase in diastolic stiffness and an early impairment of isovolumic relaxation. The increase in stiffness cannot result from incomplete relaxation since these two parameters become temporally dissociated during the reperfusion period.     

Isovolumic pressure-to-early rapid filling decay rate relation: model-based derivation and validation via simultaneous catheterization echocardiography.

Transmitral Doppler echocardiography is the preferred method of noninvasive diastolic function assessment. Correlations between catheterization-based measures of isovolumic relaxation (IVR) and transmitral, early rapid filling (Doppler E-wave)-derived parameters have been observed, but no model-based, causal explanation has been offered. IVR has also been characterized in terms of its duration as IVR time (IVRT) and by tau, the time-constant of IVR, by approximating the terminal left ventricular IVR pressure contour as Pt= Pinfinity + P(o)e(-t/tau), where Pt is the continuity of pressure, Pinfinity and Po are constants, t is time, and tau is the time constant of IVR. To characterize the relation between IVR and early rapid filling more fully, simultaneous (micromanometric) left ventricular pressure and transmitral Doppler E-wave data from 25 subjects undergoing elective cardiac catheterization and having normal physiology were analyzed. The time constant tau was determined from the dP/dt vs. P (phase) plane and, simultaneous Doppler E-waves provided global indexes of chamber viscosity/relaxation (c), chamber stiffness (k), and load (xo). We hypothesize that temporal continuity of pressure decay at mitral valve opening and physiological constraints permit the algebraic derivation of linear relations relating 1/tau to both peak atrioventricular pressure gradient (kxo) and E-wave-derived viscosity/relaxation (c) but does not support a similar, causal (linear) relation between deceleration time and tau or IVRT. Both predicted linear relations were observed: kxo to 1/tau (r = 0.71) and viscosity/relaxation to 1/tau (r = 0.71). Similarly, as anticipated, only a weak linear correlation between deceleration time and IVRT or tau was observed (r = 0.41). The observed in vivo relationship provides insight into the isovolumic mechanism of relaxation and the changing-volume mechanism of early rapid filling via a link of the respective relaxation properties.     

Thermodynamic phase plane analysis of ventricular contraction and relaxation

Background  

Ventricular function has conventionally been characterized using indexes of systolic (contractile) or diastolic (relaxation/stiffness) function. Systolic indexes include maximum elastance or equivalently the end-systolic pressure volume relation and left ventricular ejection fraction. Diastolic indexes include the time constant of isovolumic relaxation - and the end-diastolic pressure-volume relation. Conceptualization of ventricular contraction/relaxation coupling presents a challenge when mechanical events of the cardiac cycle are depicted in conventional pressure, P, or volume, V, terms. Additional conceptual difficulty arises when ventricular/vascular coupling is considered using P, V variables.