The kinematic filling efficiency index of the left ventricle: contrasting normal vs. diabetic physiology

The size of myocardial infarction and peri-infarction edema are not major determinants of diastolic impairment after acute myocardial infarction

To study the relationship between myocardial infarction size (IS), myocardial edema, and diastolic dysfunction after acute myocardial infarction (MI) both in the acute phase, and in the development of diastolic dysfunction in the follow-up setting. A further purpose is to study diastolic function using a mechanistic model as well as conventional parameters. Patients underwent cardiovascular magnetic resonance (CMR) imaging and echocardiography including mechanistic analysis using the parameterized diastolic filling method within 4-7 days (acute) and 6 months after a first acute anterior MI (n = 74). Linear regression modeling of echocardiographic diastolic parameters using CMR IS with and without inclusion of the myocardium at risk (MAR) and model comparisons with likelihood ratio tests were performed. Diastolic parameters at 6 months follow-up were modelled using final IS. For most parameters there was no association with acute IS, except for deceleration time (R2 = 0.24, p < 0.001), left atrial volume index (R2 = 0.13, p = 0.01) and the mechanistic stiffness parameter (R2 = 0.21, p < 0.001). Adding MAR improved only the e' model (adjusted R2 increase: 0.08, p = 0.02). At 6 months follow-up, final IS was only associated with viscoelastic energy loss (R2 = 0.22, p = 0.001). In acute MI, both IS and MAR are related to diastolic function but only to a limited extent. At 6 months after infarction, increasing IS is related to less viscoelastic energy loss, albeit also to a limited extent. The relationship between IS and diastolic dysfunction seems to be mediated by mechanisms beyond simply the spatial extent of ischemia or infarction.

Diastolic function: modeling left ventricular untwisting as a damped harmonic oscillator

Objective.We developed a method using cardiovascular magnetic resonance imaging to model the untwisting of the left ventricle (LV) as a damped torsional harmonic oscillator to estimate shear modulus (intrinsic myocardial stiffness) and frictional damping, then applied this method to evaluate the torsional stiffness of patients with resistant hypertension (RHTN) compared to a control group.Approach.The angular displacement of the LV during diastole was measured. Myocardial shear modulus and damping constant were determined by solving a system of equations modeling the diastolic untwisting as a damped, unforced harmonic oscillator, in 100 subjects with RHTN and 36 control subjects.Main Results.Though overall torsional stiffness was increased in RHTN (41.7 (27.1-60.7) versus 29.6 (17.3-35.7) kdyn*cm;p = 0.001), myocardial shear modulus was not different between RHTN and control subjects (0.34 (0.23-0.50) versus 0.33 (0.22-0.46) kPa;p= 0.758). RHTN demonstrated an increase in overall diastolic frictional damping (6.13 ± 3.77 versus 3.35 ± 1.70 kdyn*cm*s;p< 0.001), but no difference in damping when corrected for the overlap factor (74.3 ± 25.9 versus 68.0 ± 24.0 dyn*s/cm3;p = 0.201). There was an increase in the polar moment (geometric component of stiffness; 11.47 ± 6.95 versus 7.58 ± 3.28 cm4;p<0.001).Significance.We have developed a phenomenological method, estimating the intrinsic stiffness and relaxation properties of the LV based on restorative diastolic untwisting. This model finds increased overall stiffness in RHTN and points to hypertrophy, rather than tissue- level changes, as the major factor leading to increased stiffness.

Normal Reference Values for Assessing Diastolic Function Using the Parameterized Diastolic Filling Formalism Method in Patients with Normal Results of Rest and Stress Echocardiography

The parameterized diastolic filling (PDF) method can be used to study the mechanics of early diastolic left ventricular (LV) filling. However, there are no publications describing the reference ranges of the PDF parameters. This study retrospectively recruited patients with normal results on rest and stress echocardiography and no diabetes or hypertension (n=138, 45% female). DICOM images of the resting E-wave from transmitral pulsed wave Doppler flow velocities were analyzed using freely available software. Viscoelastic energy loss (c) and stiffness (k) were higher in males compared to females (p≤0.001 for both). There were no correlations between any of the PDF parameters and age (p>0.05 for all). In males, stiffness was correlated with systolic blood pressure (r=0.24, p=0.04), and load and filling energy were correlated with diastolic blood pressure (r=-0.27, p=0.02, and r=-0.29, p=0.01, respectively). Sex-specific normal 95% reference limits for PDF analysis of early LV filling are presented for clinical use.

Cardiac Amyloidosis Shows Decreased Diastolic Function as Assessed by Echocardiographic Parameterized Diastolic Filling

Cardiac amyloidosis is a rare but serious condition with poor survival. One of the early findings by echocardiography is impaired diastolic function, even before the development of cardiac symptoms. Early diagnosis is important, permitting initiation of treatment aimed at improving survival. The parameterized diastolic filling (PDF) formalism entails describing the left ventricular filling pattern during early diastole using the mathematical equation for the motion of a damped harmonic oscillator. We hypothesized that echocardiographic PDF analysis could detect differences in diastolic function between patients with amyloidosis and controls. Pulsed-wave Doppler echocardiography of transmitral flow was measured in 13 patients with amyloid heart disease and 13 age- and gender matched controls. E- waves (2 to 3 per subject) were analyzed using in-house developed software. Nine PDF-derived parameters were obtained in addition to conventional echocardiographic parameters of diastolic function. Compared to controls, cardiac amyloidosis patients had a larger left atrial area (23.7 ± 7.5 cm² vs. 18.5 ± 4.8 cm², p = 0.04), greater interventricular septum wall thickness (14.4 ± 2.6 mm vs. 9.3 ± 1.3 mm, p < 0.001), lower e' (0.06 ± 0.02 m/s vs. 0.09 ± 0.02 m/s, p < 0.001) and higher E/e' (18.0 ± 12.9 vs. 7.7 ± 1.3, p = 0.001). The PDF parameter peak resistive force was greater in cardiac amyloidosis patients compared to controls (17.9 ± 5.7 mN vs. 13.1 ± 3.1 mN, p = 0.03), and other PDF parameters did not differ. PDF analysis revealed that patients with cardiac amyloidosis had a greater peak resistive force compared to controls, consistent with a greater degree of diastolic dysfunction. PDF analysis may be useful in characterizing diastolic function in amyloid heart disease.

Kinematic analysis of diastolic function using the freely available software Echo E-waves - feasibility and reproducibility

BACKGROUND

Early diastolic left ventricular (LV) filling can be accurately described using the same methods used in classical mechanics to describe the motion of a loaded spring as it recoils, a validated method also referred to as the Parameterized Diastolic Filling (PDF) formalism. With this method, each E-wave recorded by pulsed wave (PW) Doppler can be mathematically described in terms of three constants: LV stiffness (k), viscoelasticity (c), and load (x ₀). Also, additional parameters of physiological and diagnostic interest can be derived. An efficient software application for PDF analysis has not been available. We aim to describe the structure, feasibility, time efficiency and intra-and interobserver variability for use of such a solution, implemented in Echo E-waves, a freely available software application ( www.echoewaves.org ).

RESULTS

An application was developed, with the ability to open DICOM files from different vendors, as well as rapid semi-automatic analysis and export of results. E-waves from 20 patients were analyzed by two investigators. Analysis time for a median of 34 (interquartile range (IQR) 29-42) E-waves per patient (representing 63 %, IQR 56-79 % of the recorded E-waves per patient) was 4.3 min (IQR 4.0-4.6 min). Intra-and intraobserver variability was good or excellent for 12 out of 14 parameters (coefficient of variation 2.5-18.7 %, intraclass correlation coefficient 0.80-0.99).

CONCLUSION

Kinematic analysis of diastolic function using the PDF method for Doppler echocardiography implemented in freely available semiautomatic software is highly feasible, time efficient, and has good to excellent intra-and interobserver variability.

What global diastolic function is, what it is not, and how to measure it

Despite Leonardo da Vinci's observation (circa 1511) that “the atria or filling chambers contract together while the pumping chambers or ventricles are relaxing and vice versa,” the dynamics of four-chamber heart function, and of diastolic function (DF) in particular, are not generally appreciated. We view DF from a global perspective, while characterizing it in terms of causality and clinical relevance. Our models derive from the insight that global DF is ultimately a result of forces generated by elastic recoil, modulated by cross-bridge relaxation, and load. The interaction between recoil and relaxation results in physical wall motion that generates pressure gradients that drive fluid flow, while epicardial wall motion is constrained by the pericardial sac. Traditional DF indexes (τ, E/E′, etc.) are not derived from causal mechanisms and are interpreted as approximating either stiffness or relaxation, but not both, thereby limiting the accuracy of DF quantification. Our derived kinematic models of isovolumic relaxation and suction-initiated filling are extensively validated, quantify the balance between stiffness and relaxation, and provide novel mechanistic physiological insight. For example, causality-based modeling provides load-independent indexes of DF and reveals that both stiffness and relaxation modify traditional DF indexes. The method has revealed that the in vivo left ventricular equilibrium volume occurs at diastasis, predicted novel relationships between filling and wall motion, and quantified causal relationships between ventricular and atrial function. In summary, by using governing physiological principles as a guide, we define what global DF is, what it is not, and how to measure it.

Diastolic function in heart failure

Heart failure has reached epidemic proportions, and diastolic heart failure or heart failure with preserved ejection fraction (HFpEF) constitutes about 50% of all heart failure admissions. Long-term prognosis of both reduced ejection fraction heart failure and HFpEF are similarly dismal. No pharmacologic agent has been developed that actually treats or repairs the physiologic deficit(s) responsible for HFpEF. Because the physiology of diastole is both subtle and counterintuitive, its role in heart failure has received insufficient attention. In this review, the focus is on the physiology of diastole in heart failure, the dominant physiologic laws that govern the process in all hearts, how all hearts work as a suction pump, and, therefore, the elucidation and characterization of what actually is meant by "diastolic function". The intent is for the reader to understand what diastolic function actually is, what it is not, and how to measure it. Proper measurement of diastolic function requires one to go beyond the usual E/A, E/E', etc. phenomenological metrics and employ more rigorous causality (mathematical modeling) based parameters of diastolic function. The method simultaneously provides new physiologic insight into the meaning of in vivo "equilibrium volume" of the left ventricle (LV), longitudinal versus transverse volume accommodation of the chamber, diastatic "ringing" of the mitral annulus, and the mechanism of L-wave generation, as well as availability of a load-independent index of diastolic function (LIIDF). One important consequence of understanding what diastolic function is, is the recognition that all that current therapies can do is basically alter the load, rather than actually "repair" the functional components (chamber stiffness, chamber relaxation). If beneficial (biological/structural/metabolic) remodeling due to therapy does manifest ultimately as improved diastolic function, it is due to resumption of normal physiology (as in alleviation of ischemia) or activation of compensatory pathways already devised by evolution. In summary, meaningful quantitative characterization of diastolic function in any clinical setting, including heart failure, requires metrics based on physiologic mechanisms that quantify the suction pump attribute of the heart. This requires advancing beyond phenomenological global indexes such as E/A, E/E', Vp, etc. and employing causality (mathematical modeling) based parameters of diastolic function easily obtained via the parametrized diastolic function (PDF) formalism.

Quantification of global diastolic function by kinematic modeling-based analysis of transmitral flow via the parametrized diastolic filling formalism

Quantitative cardiac function assessment remains a challenge for physiologists and clinicians. Although historically invasive methods have comprised the only means available, the development of noninvasive imaging modalities (echocardiography, MRI, CT) having high temporal and spatial resolution provide a new window for quantitative diastolic function assessment. Echocardiography is the agreed upon standard for diastolic function assessment, but indexes in current clinical use merely utilize selected features of chamber dimension (M-mode) or blood/tissue motion (Doppler) waveforms without incorporating the physiologic causal determinants of the motion itself. The recognition that all left ventricles (LV) initiate filling by serving as mechanical suction pumps allows global diastolic function to be assessed based on laws of motion that apply to all chambers. What differentiates one heart from another are the parameters of the equation of motion that governs filling. Accordingly, development of the Parametrized Diastolic Filling (PDF) formalism has shown that the entire range of clinically observed early transmitral flow (Doppler E-wave) patterns are extremely well fit by the laws of damped oscillatory motion. This permits analysis of individual E-waves in accordance with a causal mechanism (recoil-initiated suction) that yields three (numerically) unique lumped parameters whose physiologic analogues are chamber stiffness (k), viscoelasticity/relaxation (c), and load (xo). The recording of transmitral flow (Doppler E-waves) is standard practice in clinical cardiology and, therefore, the echocardiographic recording method is only briefly reviewed. Our focus is on determination of the PDF parameters from routinely recorded E-wave data. As the highlighted results indicate, once the PDF parameters have been obtained from a suitable number of load varying E-waves, the investigator is free to use the parameters or construct indexes from the parameters (such as stored energy 1/2kxo(2), maximum A-V pressure gradient kxo, load independent index of diastolic function, etc.) and select the aspect of physiology or pathophysiology to be quantified.

Mathematical modeling the neuroregulation of blood pressure using a cognitive top-down approach

Background:

The body′s physiological stability is maintained by the influence of the autonomic nervous system upon the dynamic interaction of multiple systems. These physiological systems, their nature and structure, and the factors which influence their function have been poorly defined. A greater understanding of such physiological systems leads to an understanding of the synchronised function of organs in each neural network i.e. there is a fundamental relationship involving sensory input and/or sense perception, neural function and neural networks, and cellular and molecular biology. Such an approach compares with the bottom-up systems biology approach in which there may be an almost infinite degree of biochemical complexity to be taken into account.

Aims:

The purpose of this article is to discuss a novel cognitive, top-down, mathematical model of the physiological systems, in particular its application to the neuroregulation of blood pressure.

Results:

This article highlights the influence of sensori-visual input upon the function of the autonomic nervous system and the coherent function of the various organ networks i.e. the relationship which exists between visual perception and pathology.

Conclusions:

The application of Grakov′s model may lead to a greater understanding of the fundamental role played by light e.g. regulating acidity, levels of Magnesium, activation of enzymes, and the various factors which contribute to the regulation of blood pressure. It indicates that the body′s regulation of blood pressure does not reside in any one neural or visceral component but instead is a measure of the brain′s best efforts to maintain its physiological stability.

The thermodynamics of diastole: kinematic modeling-based derivation of the P-V loop to transmitral flow energy relation with in vivo validation

Pressure-volume (P-V) loop-based analysis facilitates thermodynamic assessment of left ventricular function in terms of work and energy. Typically these quantities are calculated for a cardiac cycle using the entire P-V loop, although thermodynamic analysis may be applied to a selected phase of the cardiac cycle, specifically, diastole. Diastolic function is routinely quantified by analysis of transmitral Doppler E-wave contours. The first law of thermodynamics requires that energy (ε) computed from the Doppler E-wave (εE-wave) and the same portion of the P-V loop (εP-V E-wave) be equivalent. These energies have not been previously derived nor have their predicted equivalence been experimentally validated. To test the hypothesis that εP-V E-wave and εE-wave are equivalent, we used a validated kinematic model of filling to derive εE-wave in terms of chamber stiffness, relaxation/viscoelasticity, and load. For validation, simultaneous (conductance catheter) P-V and echocadiographic data from 12 subjects (205 total cardiac cycles) having a range of diastolic function were analyzed. For each E-wave, εE-wave was compared with εP-V E-wave calculated from simultaneous P-V data. Linear regression yielded the following: εP-V E-wave = αεE-wave + b ( R2 = 0.67), where α = 0.95 and b = 6 e−5. We conclude that E-wave-derived energy for suction-initiated early rapid filling εE-wave, quantitated via kinematic modeling, is equivalent to invasive P-V-defined filling energy. Hence, the thermodynamics of diastole via εE-wave generate a novel mechanism-based index of diastolic function suitable for in vivo phenotypic characterization.

The age dependence of left ventricular filling efficiency

Echocardiography has emerged as the preferred modality by which diastolic function (DF) is assessed for clinical or research purposes. Echocardiographic indexes and parameters of DF such as E/A, DT, E/E', etc., deteriorate with advancing age. Whether the efficiency of filling depends on age is unknown. To better characterize the filling process and DF in causal rather than correlative terms, we have previously modeled diastole kinematically. We introduced and validated a dimensionless measure of DF termed the kinematic filling efficiency index (KFEI). In the present study, we determined the effect of aging on DF in terms of KFEI in 72 control subjects without cardiovascular-related diseases or pathologies. We also evaluated the age dependence of other conventional parameters of DF. In concordance with other noninvasive DF measures known to decrease with age, KFEI decreases and correlates very strongly with age (R2=0.80). Multivariate analysis showed that age is the single most important contributor to KFEI (p=0.003). We conclude that KFEI provides novel insight into DF impairment mechanisms because of aging. These results support the clinical value of KFEI and advance our ability to characterize DF in mechanistic and quantitative terms based on the efficiency of filling.