Frequency-based analysis of diastolic function: detrimental phase-shift of the pressure-flow relation characterizes the 'delayed relaxation'; transmitral flow pattern

Cardiologists assess the filling (diastolic) function (DF) of the heart by visually determining whether Doppler echocardiographic transmitral E-waves appear to have "normal", "delayed-relaxation" or "constrictive restrictive" patterns. To achieve a causal method of quantitative DF assessment we present a frequency-based approach. In analogy to impedance of electrical circuits, we characterize DF by analysis of the left ventricular (LV) diastolic pressure (P) to transmitral flow (Q) relation during the Doppler E-wave in the frequency domain in terms of Z(omega) = P(omega) / Q(omega), characteristic and input impedance. This allows DF to be expressed in terms of a complex reflection coefficient R* =/R*/e(iphi). Twenty subjects had simultaneous pressure-flow data recorded during catheterization, were dichotomized according to deceleration time (DT) and had E-waves subjected to model-based image processing (MBIP) to determine model parameter c, related to E-wave deceleration. Results show that phase angle phi is linearly related to c ; that both phi and c were significantly different (p < 0.05) between the short (n=12) and long (n=8) DT group. We conclude that the 'delayed relaxation'; pattern is associated with deviation of the phase angle phi from its optimal (pi) value that minimizes reflection and maximizes filling, resulting in modification of the optimal pressure - flow relation in early diastole.

Echocardiographic characterization of fundamental mechanisms of abnormal diastolic filling in diabetic rats with a parameterized diastolic filling formalism

Abnormalities of diastolic function (DF) precede systolic dysfunction in diabetic cardiomyopathy. Transmitral Doppler flow analysis is the primary method for noninvasively assessing DF. We used model-based Doppler E-wave analysis to evaluate diastolic function differences between normal and diabetic rat hearts. Control rats and those with diabetes underwent echocardiography with analysis by traditional Doppler indexes and by the parameterized diastolic filling (PDF) formalism, generating 3 parameters, x0, c, and k, that uniquely characterize each E-wave. Significant intergroup differences in the E/A ratios (P <.01), isovolumic relaxation times (P <.01), and the modeling parameter c (P <.05) were found. There were no significant differences in shortening fraction, deceleration time, myocardial collagen content, or the parameters x0 and k between diabetic and control rats. These results indicate that differences in diastolic function may be noninvasively quantified and that diabetic hearts may exhibit defects in uncoupling of the contractile apparatus without concomitant increases in chamber stiffness.

Chamber properties from transmitral flow: prediction of average and passive left ventricular diastolic stiffness

A chamber stiffness (K(LV))-transmitral flow (E-wave) deceleration time relation has been invasively validated in dogs with the use of average stiffness [(DeltaP/DeltaV)(avg)]. K(LV) is equivalent to k(E), the (E-wave) stiffness of the parameterized diastolic filling model. Prediction and validation of 1) (DeltaP/DeltaV)(avg) in terms of k(E), 2) early rapid-filling stiffness [(DeltaP/DeltaV)(E)] in terms of k(E), and 3) passive (postdiastasis) chamber stiffness [(DeltaP/DeltaV)(PD)] from A waves in terms of the stiffness parameter for the Doppler A wave (k(A)) have not been achieved. Simultaneous micromanometric left ventricular (LV) pressure (LVP) and transmitral flow from 131 subjects were analyzed. (DeltaP)(avg) and (DeltaV)(avg) utilized the minimum LVP-LV end-diastolic pressure interval. (DeltaP/DeltaV)(E) utilized DeltaP and DeltaV from minimum LVP to E-wave termination. (DeltaP/DeltaV)(PD) utilized atrial systolic DeltaP and DeltaV. E- and A-wave analysis generated k(E) and k(A). For all subjects, noninvasive-invasive relations yielded the following equations: k(E) = 1,401. (DeltaP/DeltaV)(avg) + 59.2 (r = 0.84) and k(E) = 229.0. (DeltaP/DeltaV)(E) + 112 (r = 0.80). For subjects with diastasis (n = 113), k(A) = 1,640. (DeltaP/DeltaV)(PD) - 8.40 (r = 0.89). As predicted, k(A) showed excellent correlation with (DeltaP/DeltaV)(PD); k(E) correlated highly with (DeltaP/DeltaV)(avg). In vivo validation of average, early, and passive chamber stiffness facilitates quantitative, noninvasive diastolic function assessment from transmitral flow.

Phase plane analysis of left ventricular hemodynamics

We sought to extract additional physiological information from the time-dependent left ventricular (LV) pressure contour and thereby gain new insights into ventricular function. We used phase plane analysis to characterize high-fidelity pressure data in selected subjects undergoing elective cardiac catheterization. The standard hemodynamic indexes of LV systolic and diastolic function derived from the time-dependent LV pressure contour could be easily obtained using the phase plane method. Additional novel attributes of the phase plane pressure loop, such as phase plane pressure loop area, graphical representation of the isovolumic relaxation time constant, and quantitative measures of beat-to-beat systolic-diastolic coupling were characterized. The asymmetry between the pressures at which maximum isovolumic pressure rise and pressure fall occur, as well as their load dependence, were also easily quantitated. These results indicate that the phase plane method provides a novel window for physiological discovery and has theoretical and applied advantages in quantitative ventricular function characterization.

The relation of the peak Doppler E-wave to peak mitral annulus velocity ratio to diastolic function

Previous observations (Garcia et al. 1998; Sohn et al. 1997; Nagueh et al. 1997) indicate that mitral annulus velocity may be viewed as a "load-independent" index of filling and that wedge pressure is linearly related to the transmitral flow velocity (V(E)) to mitral annulus velocity (V(MA)) ratio (V(E)/V(MA)) measured at maximum velocity. In healthy subjects, the mean value observed for [V(E)](max)/[V(MA)](max) was 1:0.23 approximately 4. No prior physiologic or physical explanation for the basis of, or for the magnitude of, the ratio has been proposed. We propose a physiologic, model-based, quantitative explanation for these observations and test our simplified model's prediction in an invasive (n = 30) and noninvasive (n = 34) test groups of subjects. The simplified geometric model is based on the known constant volume (within a few percentage points) attribute of the four-chambered heart. Accordingly, left-atrial and left-ventricular volumes reciprocate so that their sum is constant throughout the cardiac cycle. The model predicts that: 1. the ratio (V(E)/V(MA)) is a constant approximately 3 in healthy hearts; and 2. V(E)/V(MA) should be linearly proportional to left ventricular end-diastolic pressure (LVEDP). Model prediction was tested using V(E) and V(MA) echocardiographic data from 34 subjects (noninvasive group), and simultaneous echocardiographic and high-fidelity hemodynamic (LVEDP) data in 30 subjects (invasive group). Excellent agreement was observed between model prediction and observed data. For the noninvasive (healthy) group, [V(E)](max)/[V(MA)](max) = 4.20 +/- 1.11. For the invasive group, [V(E)](max)/[V(MA)](max) was observed to be linearly related to LVEDP, [V(E)](max)/[V(MA)](max) = 0.19 (LVEDP) + 1.54, r = 0.92. Hence, [V(E)](max)/[V(MA)](max) is a legitimate flow-derived index of diastolic function because it is a derivable consequence of the heart's constant-volume pump attribute.

Modeling of diastole

Modeling methods have been employed to further characterize the physical and physiologic processes of filling and diastolic function. They have led to more detailed understanding of the effect of alteration of physiologic parameters on the Doppler E-wave contour as well as pulmonary vein flow. Depending on the modeling approach, different aspects of the filling process have been considered from AV gradient and net compliance to atrial appendage function to the mechanical suction pump attribute of the heart. The models have been applied for further characterization of diastolic function and elucidation of novel basic physiologic relations. We trust that readers recognize that this article could not serve as a comprehensive and global review of the state-of-the-art in physiologic modeling, but rather as a selective overview, with emphasis on the main modeling principles and options currently in use. Modeling of systems physiology, especially as it relates to the function of the four-chamber heart, remains a fertile area of investigation. Future progress is likely to have profound influence on (noninvasive) diagnosis and quantitation of the effect of therapy and lead to continued discovery of "new" (macroscopic, cellular, and molecular biologic) physiology.

Unsolved problems in diastole

It is now recognized that a sizable portion of patients who exhibit symptoms of congestive heart failure have relatively well-preserved systolic function, but have significantly elevated LV filling pressures. This syndrome, termed "diastolic heart failure," is associated with various conditions such as aging, anatomic abnormalities, hypertension, ischemic disease, tachycardia, and atrial fibrillation. Advances in the proper medical and surgical management of these patients will depend on the continued delineation of the basic physiologic mechanisms that account for normal and pathologic cardiac diastolic function. This goal can only be achieved by the integration of information acquired from basic science investigations conducted in vitro and in vivo, mathematic modeling simulation studies, and prospective, community-based investigations that characterize the incidence, prevalence, and natural history of the disease. In addition, randomized clinical trials will be needed to determine the optimal treatment strategies for this group of patients--strategy choices undoubtably complicated by a disease whose treatment is influenced to a large extent by its origin. The future therapies evaluated in these randomized clinical trials will most likely range from medical therapies that target either the heart directly or the peripheral vascular system, to surgical interventions such as direct myocardial revascularization, to gene therapy. Finally, it is worth mentioning one more unresolved issue that is of general practical concern not only to the physiologist studying diastolic function, but also to the clinician: whether or not it is even feasible to develop a single, sensitive, specific, clinically relevant index of diastolic function that is free from the contaminating influences of rate, contractility, and load. As observed by Glantz 20 years ago, developing indexes with the hope that one might fully delineate the left ventricle's diastolic properties, rather than concentrating on discovering the physiologic significance of such indexes, is probably counterproductive. More recently, in a related article, Slinker implied that an operational definition of any aspect of cardiac function must allow for the measurement of that function over an adequate range of essential variables. Therefore, as previously mentioned, the physiologist studying cardiac function has the daunting task of trying to understand, in a precise way, how the processes and mechanisms of the various phases of the cardiac cycle couple together to produce either a normal or abnormal functioning heart. It seems clear that because of the complex weave of factors that control overall cardiac diastolic function, the derivation of any single index that adequately describes LV diastolic function in vivo may not be possible.

Prognostic value of diastolic filling parameters derived using a novel image processing technique in patients > or = 70 years of age with congestive heart failure

Conventional echocardiographic characterization of diastolic function requires manual analysis of Doppler E-and A-wave amplitudes, deceleration times, isovolumic relaxation times, and pulmonary venous flow patterns. Mathematic modeling of the suction pump activity of the heart permits characterization of diastolic function through model-based image processing, which relies solely on transmitral Doppler images. This automated method uniquely specifies the entire E-wave contour using 3 parameters (x(o), k, and c) that determine E-wave amplitude, width, and rate of decay. Moreover, the index beta = c2 - 4k, reflecting the balance between chamber viscosity and stiffness/recoil, represents a novel parameter for characterizing diastolic function. We analyzed Doppler E waves from 39 patients (mean age 79 years, 61% women, mean ejection fraction 47%) using the model-based image processing technique. A value of beta <-900 was selected as indicative of severe diastolic dysfunction. Of 17 subjects with beta <-900, 8 (47%) were no longer alive at 1 year. Of 22 subjects with beta >-900, all were alive (p = 0.001). The index beta, dichotomized at <-900, had a predictive accuracy of 0.769 (30 of 39), a negative predictive value of 1.0 (22 of 22 alive), and a positive predictive value of 0.471 (8 of 17 deceased) for 1-year vital status. Of 14 subjects with deceleration time < or =160 ms, 5 (36%) were deceased at 1 year, whereas for deceleration time >160 ms, 22 of 25 patients were alive (p = NS). Of 16 subjects with ejection fraction <45%, 6 (38%) were deceased at 1 year. Of 23 subjects with ejection fraction >45%, 21 were alive at 1 year (p = 0.074). On multivariate analysis, beta dichotomized at -900 was the strongest independent predictor of 1-year mortality. We conclude that evaluation of diastolic function using model-based image processing provides valuable prognostic information in elderly patients with heart failure.

Blood pool agent strongly improves 3D magnetic resonance coronary angiography using an inversion pre-pulse

The ability of a blood pool contrast agent to enhance MR coronary angiography was defined. The proximal coronary vessels of pigs were imaged before and after administration of Gd-DTPA bound covalently to bovine serum albumin (0.2 mmol/ kg). The contrast agent resulted in a reduction of the blood T1 value to 33+/-5 msec, as determined in vivo with a Look-Locker technique. Both 2D and 3D imaging techniques were performed. An inversion pulse suppressed the signal of nonblood tissue postcontrast. After contrast agent administration, in the 3D data set the signal-to-noise ratio (SNR) of blood and contrast-to-noise ratio (CNR) of blood to myocardium were improved by factors of 2.0+/-0.2 and 15+/-8, respectively (P < 0.05). Postcontrast, the 3D acquisition was superior to the 2D technique in terms of spatial resolution, SNR of blood, and CNR of blood to myocardium. The high contrast of the 3D data set allowed for direct and rapid display of coronary arteries using a "closest vessel projection."

Beat averaging alternatives for transmitral Doppler flow velocity images

To characterize diastolic function from transmitral Doppler data, the image's maximum velocity envelope (MVE) is fit by a model for flow velocity. To reduce the physiologic beat-to-beat variability of best-fit determined model parameters, averaging of multiple cardiac cycles is indicated. To assess variability mathematically, we modeled physiologic noise as a random (normally-distributed) process and evaluated three methods of averaging (1, averaging model parameters from single images; 2, averaging images; and 3, averaging MVEs) using clinical datasets (50 continuous beats from 5 subjects). Method 2 generates a positive bias because low-velocity beats will not contribute to the composite MVE. The difference between Methods 3 and 1 is less than 2.0 E-5 (m/s)2 for uncorrelated model parameters. Input having 10% beat-to-beat variation yields a bias of <4% for model parameter mean. Hence, Method 1 was, in general, more robust than Method 3.

Evaluation of model-based processing algorithms for averaged transmitral spectral Doppler images

In an effort to characterize more fully diastolic function using Doppler echocardiography, we have previously developed an automated method of model-based image processing for spectral Doppler images of transmitral blood flow. In this method, maximum velocity envelopes (MVEs) extracted from individual Doppler images are aligned and averaged over several cardiac cycles. The averaged waveform is fit by the solution of a kinematic model of diastolic filling. The results are estimates of the model parameters. As expected, the mean and standard deviation of the model parameter estimates depend on many factors such as noise, the number of cardiac cycles averaged, beat-to-beat variation, waveform shape, observation time and the processing methods used, among others. A comprehensive evaluation of these effects has not been performed to date. A simulation was developed to evaluate the performance of three automated processing methods and to measure the influence of noise, beat-to-beat variation and observation time on the model parameter estimates. The simulation's design and a description and analysis of the three automated processing methods are presented. Of the three methods evaluated, using the inflection point in the acceleration portion of the velocity contour as the first data point to be fit was found to be the most robust method for processing averaged E-wave MVE waveforms. Using this method under nominal conditions, the average bias was measured to be < 3% for each of the model parameters. As expected, the biases and standard deviations of the estimates increased as a result of increased noise levels, increased beat-to-beat variation and decreased observation time. Another important finding was that the effects of noise, beat-to-beat variation and waveform observation time on the parameter estimates are dependent on the location in model parameter space.

Can trasmitral Doppler E-waves differentiate hypertensive hearts from normal?

Physiological models of transmitral flow predict E-wave contour alteration in response to variation of model parameters (stiffness, relaxation, mass) reflecting the physiology of hypertension. Accordingly, analysis of only the E-wave (rather than the E-to-A ratio) should be able to differentiate between hypertensive subjects and control subjects. Conventional versus model-based image processing methods have never been compared in their ability to differentiate E-waves of hypertensive subjects with respect to age-matched control subjects. Digitally acquired transmitral Doppler flow images were analyzed by an automated model-based image processing method. Model-derived indexes were compared with conventional E-wave indexes in 22 subjects: 11 with hypertension and echocardiographically verified ventricular hypertrophy and 11 age-matched nonhypertensive control subjects. Conventional E-wave indexes included peak E, E, and acceleration and deceleration times. Model-based image processing-derived indexes included acceleration and deceleration times, potential energy index, and damping and kinematic constants. Intergroup comparison yielded lower probability values for model-based compared with conventional indexes. In the subjects studied, Doppler E-wave images analyzed by this automated method (which eliminates the need for hand-digitizing contours or the manual placement of cursors) demonstrate diastolic function alteration secondary to hypertension made discernible by model-based indexes. The method uses the entire E-wave contour, quantitatively differentiates between hypertensive subjects and control subjects, and has potential for automated noninvasive diastolic function evaluation in large patient populations, such as hypertension and other transmitral flow velocity-altering pathophysiological states.

Relationship of the fourth heart sound to atrial systolic transmitral flow deceleration

The fourth heart sound (S4) is thought to be due to cardiohemic vibrations, powered by deceleration of transmitral blood flow, that occur when atrial systole leads to a disproportionately high rise in ventricular end-diastolic pressure (relative to diastasis), associated with an enhanced atrial systolic blood filling volume or a stiff ventricular wall. To characterize S4 production, we modeled the cardiohemic system as a forced, damped nonlinear harmonic oscillator. The forcing term used a closed-form expression for the Doppler A-wave contour. We simultaneously recorded transthoracic phonocardiograms and Doppler A waves in subjects with and without audible S4 and compared model predictions for S4 amplitude, frequency, and power spectrum with those of the recorded S4. Excellent agreement was observed between the model-predicted amplitude, duration, timing, and power spectrum and those of the phonocardiographic S4. We conclude that, with a normal mitral valve, there should always be an oscillation of the cardiohemic system during A-wave deceleration. However, oscillations may not have high enough amplitude, frequency, or coupling to the chest wall to be clinically audible as an S4.

Left ventricular chamber stiffness from model-based image processing of transmitral Doppler E-waves

BACKGROUND

Model-based image processing (MBIP) of Doppler E-waves eliminates the need for digitizing waveforms by hand or determining the contour 'by eye'. Little et al. (Circulation 1995, 92:1933-1939) used pressure-volume measurements for dogs to verify the physiologic-model-derived prediction that the left ventricular chamber stiffness, KLV1 can be determined from the deceleration time tdec, when that portion of the E-wave contour is fit by a cosine function. MBIP of clinical Doppler E-wave images to determine chamber stiffness KLV has not been performed.

OBJECTIVE

We sought to determine KLV by MBIP of clinical Doppler E-wave images and elucidate the physiologic meaning of the harmonic oscillator filling model's parameter k.

METHODS AND RESULTS

The unique mathematical relationship between the kinematic, harmonic oscillator model of filling and KLV predicts that the oscillator's spring constant k be linearly proportional to the chamber stiffness KLV. To verify this, digitally acquired, clinical Doppler transmitral flow velocity images from 21 subjects were analyzed. The parameter k and the stiffness KLV were computed independently for each subject and compared. In accordance with prediction, a linear relationship between k and the stiffness KLV, namely k = 1.16 [A/(rho L)]KLV+41, r = 0.96, was observed.

CONCLUSIONS

The oscillator parameter k is linearly proportional to the left ventricular chamber stiffness KLV. The MBIP approach allows automated computation of k and KLV, provides a robust, automated, observer independent method of Doppler transmitral flow velocity analysis, and eliminates the need for visual determination of the contour or measurement of its attributes by eye. It provides a stimulus for further validation of the relationships among K, KLV, and catheterization-based diastolic chamber properties in humans and their correlations with selected diastolic function-altering syndromes.

Echo machine-imposed limit on transmitral spectral Doppler velocity-profile analysis

We have previously developed a kinematic model of ventricular filling. Its application to in vivo transmitral Doppler velocity profiles provides a quantitative characterization of filling. However, the model parameters computed by solving the "inverse problem" may depend on ultrasound machine type and setting (e.g., gain, baseline filter, dynamic range). To determine machine-based effects on the computed model parameters, we performed a flow phantom study using Acuson and HP echocardiography machines at various settings. We compared maximum velocity envelopes (MVEs), as well as the model fit to these MVEs, for 3 simulated waveforms imaged by both machines. For all 3 waveforms, the machines generated comparable MVEs, fit by the model within a mean-square difference of 5E-5 (m/s)2. The associated variations in model parameters for the 3 waveforms were not uniform. Two waveforms showed slight variation between machines, with model parameters varying by less than 6%. The shortest duration waveform showed model parameter variations of 10-15%. Analysis of the parameter space for this waveform showed a constant mean-square error contour that was larger than that for the other two, causing similar small variations in measured MVEs to result in larger differences in the parameter estimates for this waveform. Because this method completely eliminates inter- and intraobserver variability, we conclude that, within the limits established, the slight contour variations due to machine type and setting should not affect this method's applicability in clinical Doppler-flow analysis.

Anatomically and physiologically based reference level for measurement of intracardiac pressures

BACKGROUND

Many reference levels have been proposed for the measurement of intracardiac pressures, but none have met with universal acceptance. In the first part of our study, we evaluated 10 cardiologists' understanding of how hydrostatic pressure influences intracardiac pressures as measured with fluid-filled catheters. In the second part, we proposed and validated a new zero level (H): the uppermost blood level in the left ventricular (LV) chamber relative to the anterior chest wall for a patient in the supine position. A comparison was made of LV minimum diastolic pressure measured by reference to H versus measurements made with the zero level at midchest.

METHODS AND RESULTS

Using two-dimensional echocardiography, we determined H in the LVs of seven normal patients (five male, two female; age, 49 +/- 9 years) undergoing routine cardiac catheterization. H was determined from a left parasternal short-axis view and calculated as the average distance between end diastole and end systole of the endocardium of the uppermost segment of the LV anterior wall below the fourth or fifth intercostal space of the left sternal border on the anterior surface of the chest wall, with the patient in the supine position. A micromanometer/fluid-filled lumen catheter was then positioned in the LV, and we compared the micromanometer LV minimum pressure (LVPmin) obtained when the reference fluid-filled transducer was aligned at midchest with the LVPmin obtained when the reference fluid-filled transducer was aligned at H. LVPmin referenced to a midchest fluid-filled external transducer was measured as 5.1 +/- 1.6 mm Hg (range, 2.4 to 7.2 mm Hg) versus -0.6 +/- 0.6 mm Hg (range, -1.6 to 0.4 mm Hg) when referenced to H (P < .001). A significant linear relation was found to exist between patient anterior-posterior chest diameter and the magnitude of hydrostatic pressure influences related to pressure referenced at midchest (r = .88; P < .01).

CONCLUSIONS

External fluid-filled transducers should be used with the goal of removing hydrostatic pressure and other influences so that the presence of subatmospheric pressure during diastole in any of the cardiac chambers is accurately measured. To achieve this goal, intracardiac pressure should be referenced to an external fluid-filled transducer aligned with the uppermost blood level in the chamber in which pressure is to be measured. The current practice of referencing the zero level of LV diastolic pressure to an external fluid-filled transducer positioned at the midchest level results in systematic overestimation due to hydrostatic effects and produces physiologically significant error in the measurement of diastolic intracardiac pressure.

Relationship of the third heart sound to transmitral flow velocity deceleration

BACKGROUND

The third heart sound (S3) occurs shortly after the early (E-wave) peak of the transmitral diastolic Doppler velocity profile (DVP). It is thought to be due to cardiohemic vibrations powered by rapid deceleration of transmitral blood flow. Although the presence, timing, and clinical correlates of the S3 have been extensively characterized, derivation and validation of a causal, mathematical relation between transmitral flow velocity and the S3 are lacking.

METHODS AND RESULTS

To characterize the kinematics and physiological mechanisms of S3 production, we modeled the cardiohemic system as a forced, damped, nonlinear harmonic oscillator. The forcing term used a closed-form mathematical expression for the deceleration portion of the DVP. We tested the hypothesis that our model's predictions for amplitude, timing, and frequency of S3 accurately predict the transthoracic phonocardiogram, using the simultaneously recorded transmitral Doppler E wave as input, in three subject groups: those with audible pathological S3, those with audible physiological S3, and those with inaudible S3.

CONCLUSIONS

We found excellent agreement between model prediction and the observed data for all three subject groups. We conclude that, in the presence of a normal mitral valve, the kinematics of filling requires that all hearts have oscillations of the cardiohemic system during E-wave deceleration. However, the oscillations may not have high enough amplitude or frequency to be heard as an S3 unless there is sufficiently rapid fluid deceleration (of the Doppler E-wave contour) with sufficient cardiohemic coupling.

Comparison of diastolic filling models and their fit to transmitral Doppler contours

Anatomic/physiologic and kinematic mathematical models of diastolic filling which employ (lumped) parameters of diastolic function have been used to predict or characterize transmitral flow. The ability to determine model parameters from clinical transmitral flow, the Doppler velocity profile (DVP), is equivalent to solving the "inverse problem" of diastole. Systematic model-to-model and model-to-data comparison has never been carried out, in part due to the requirement that DVPs be digitized by hand. We developed, tested and verified a computerized method of DVP acquisition and reproduction, and carried out numerical determination of model-to-model and model-to-data goodness-of-fit. The transmitral flow velocity of two anatomic/physiologic models and one kinematic model were compared. Each model's ability to fit computer-acquired and reproduced transmitral DVPs was assessed. Results indicate that transmitral flow velocities generated by the three models are 'graphically indistinguishable and are able to fit the E-wave of clinical DVPs with comparable mean-square errors. Nonunique invertibility of the anatomic/physiologic models was verified, i.e., multiple sets of model parameters could be found that fit a single DVP with comparable mean-square error. The kinematic formulation permitted automated, unique, model-parameter determination, solving the "inverse problem" for the Doppler E-wave. We conclude that automated, quantitative characterization of clinical Doppler E-wave contours using this method is feasible. The relation of kinematic parameters to physiologic variables is a subject of current investigation.

Automated method for characterization of diastolic transmitral Doppler velocity contours: early rapid filling

Doppler echocardiographic studies of transmitral flow have become a routine clinical tool for the assessment and characterization of ventricular diastolic (filling) function. We have previously derived a parametrized diastolic filling (PDF) formalism for the purpose of diastolic function assessment using Doppler echocardiography. The model accommodates the mechanical "suction" feature of early diastolic filling of the heart by using a simple harmonic oscillator (SHO) as a paradigm for the kinematics of filling. PDF model predictions of transmitral flow velocity have shown excellent agreement with human echocardiographic Doppler contours (temporal profiles) when a visual, transparency overlay method of model fit to clinical Doppler contour comparison was used. The determination of PDF model parameters from the clinical Doppler contour is equivalent to the solution of the "inverse problem" of diastole. Previously, this determination consisted of a manual, iterative method of graphical overlay, in which model predicted contours were visually compared with the echocardiography machine generated Doppler contour using transparencies. To automate the process of model parameter estimation (i.e., solution of the "inverse problem") for the early or "rapid filling" phase of diastole (known in cardiology as the E-wave of the clinical Doppler velocity profile [DVP]) we recorded the acoustic pulsed Doppler signal using the forward channel of a commercial echocardiography machine. The Doppler spectrogram for a particular E-wave was recreated using short-time Fourier transform processing. The maximum velocity envelope (MVE) was extracted from the spectrogram. The PDF model was fit to the E-wave MVE using a Levenberg-Marquardt (iterative) algorithm by the requirement that the mean-square error between the clinical data (MVE) and the model be minimized. Because the model is linear, all of the PDF parameters for the Doppler E-wave can be uniquely determined. We show that: (1) solution of the "inverse problem of diastole" is possible; (2) clinical Doppler E-wave contours can be accurately reproduced and quantified using the PDF formalism and its parameters; and (3) our proposed, automated method of PDF parameter determination for the E-wave is robust.

Automated method for characterization of diastolic transmitral Doppler velocity contours: late atrial filling

We develop an automated method of characterizing the late atrial filling phase of diastole by fitting a kinematic model for diastolic filling to the clinical Doppler A-wave contour. The result is a set of model parameters which completely characterizes the contour. We have previously derived a parameterized diastolic filling (PDF) model, which predicts the time-dependent transmitral blood flow velocity obtained by Doppler echocardiography. An automated method to determine the PDF model parameters for early rapid filling from the clinical Doppler E-wave has also been developed and validated. The method consists of digitizing the acoustic Doppler waveform, recreating the Doppler velocity profile, extracting the maximum velocity envelope, and fitting the PDF model for early filling to the envelope. In the current work, we apply the same general approach for PDF parameter determination for the late atrial filling phase of diastole. To assess the presence and significance of near-degeneracies in the model parameter set, numerical experiments (consisting of fitting the model to a model-generated contour to which Gaussian noise was added) were performed. These revealed a two-dimensional degeneracy in four-dimensional parameter space which could be removed by using two kinematic simplifications: critical damping and resonant forcing. We show that these degeneracy-eliminating approximations do not limit the ability of the model to predict clinical A-wave contours.

Physiological early diastolic intraventricular pressure gradient is lost during acute myocardial ischemia

A consistent pattern of intraventricular regional pressure gradients exists under physiological conditions during the rapid filling phase of diastole in the normal dog left ventricle. We hypothesized that this pressure gradient pattern is caused, in part, by early diastolic recoil of the left ventricular walls in conjunction with release of elastic potential energy stored during systole, generating suction and thus contributing to diastolic filling. If so, any condition that interferes with normal regional systolic function might be expected to modify the pattern of the normal early diastolic intraventricular pressure gradients. Accordingly, the present study was designed to determine whether acutely induced regional systolic left ventricular mechanical dysfunction is accompanied by changes in the pattern of the early diastolic intraventricular pressure gradients. Acute myocardial ischemia was induced by balloon occlusion of the left anterior descending coronary artery (LAD) in nine anesthetized closed-chest dogs. The maximum early diastolic intraventricular pressure gradient (MIVP) was measured between the mid-left ventricle and apex with a dual-sensor micromanometer (3-cm spacing between the sensors) before and 20 minutes after LAD occlusion. Ejection fraction (EF) and number of dyskinetic chords (DChords) were measured from left ventricular contrast ventriculograms. Twenty minutes after LAD occlusion, the nine dogs evidenced significant changes in EF (56 +/- 10% to 37 +/- 8%), DChords (0 +/- 0 to 17 +/- 16 chords), left ventricular minimum pressure (-1.7 +/- 0.5 to 0.0 +/- 1.5 mm Hg), left ventricular end-diastolic pressure (4.2 +/- 1.2 to 5.9 +/- 2.2 mm Hg), and heart rate (90 +/- 17 to 103 +/- 18 beats/min).(ABSTRACT TRUNCATED AT 250 WORDS)

Transmitral pressure-flow velocity relation. Importance of regional pressure gradients in the left ventricle during diastole

Effects of regional diastolic pressure differences within the left ventricle on the measured transmitral pressure-flow relation were determined by simultaneous micromanometric left atrial (LAP) and left ventricular pressure (LVP) measurements, and Doppler echocardiograms in 11 anesthetized, closed-chest dogs. Intraventricular pressure recordings at sites that were 2, 4, and 6 cm from the apex were obtained. Profound differences between these sites were noted in the transmitral pressure relation during early (preatrial) diastolic filling. In measurements from apex to base, minimum LVP increased (1.6 +/- 0.7 to 3.1 +/- 0.8 mm Hg, mean +/- SD); the time interval between the first crossover of transmitral pressures and minimum LVP increased (31 +/- 3 to 50 +/- 17 msec); the slope of the rapid-filling LVP wave decreased (74 +/- 13 to 26 +/- 5 mm Hg/sec); the maximum forward (i.e., LAP greater than LVP) transmitral pressure gradient decreased (3.6 +/- 1.3 to 2.1 +/- 0.7 mm Hg); the time interval between the first and second points of transmitral pressure crossover increased (71 +/- 9 to 96 +/- 13 msec); and the area of reversed (i.e., LVP greater than LAP) gradient between the second and third points of transmitral pressure crossover decreased (101 +/- 41 to 40 +/- 33 mm Hg.msec). During atrial contraction, significant regional ventricular apex-to-base gradients were also noted. The slope of the LV A wave decreased (26 +/- 10 to 16 +/- 4 mm Hg/sec); LV end-diastolic pressure decreased (8.1 +/- 2.0 to 7.4 +/- 2.0 mm Hg), and the upstroke of the LV A wave near the base was recorded earlier than near the apex. All differences were significant at the 0.05 level. Simultaneous transmitral Doppler velocity profiles and transmitral pressures were measured at the 4-cm intraventricular site. The average interval between the first and second points of pressure crossover and between the onset of early rapid filling and maximum E-wave velocity were statistically similar (81 +/- 13 vs. 85 +/- 12 msec; NS); and the average area of the forward transmitral pressure gradient associated with acceleration of early flow was significantly greater than the area of reversed gradient associated with deceleration of early flow (133 +/- 36 vs. 80 +/- 46 msec.mm Hg; p less than 0.025).(ABSTRACT TRUNCATED AT 400 WORDS)

Evaluation of diastolic function with Doppler echocardiography: the PDF formalism

A new parametrized diastolic filling (PDF) formalism for evaluation of holodiastolic (left and right) ventricular function via Doppler echocardiography is presented. It is motivated by the empiric observation that during diastole the heart behaves as a suction pump whose dynamics, in certain respects, are those of a damped harmonic oscillator. An expression for elastic recoil (suction) initiated ventricular diastolic fluid inflow velocity v(t) is obtained by differentiation from the solution x(t) of the linear differential equation that describes the motion of a forced, damped harmonic oscillator. It is solved for "over-damped" motion, for zero initial velocity and initial displacement = xo cm. An explicit forcing term F(t) = Fosin(omega t) is included to account for late diastolic (atrial) filling. The quantitative parameters of the model include inertia (mass; m), viscosity (damping constant; c), source of stored energy for suction (spring constant; k), and its initial displacement xo, the amplitude and frequency of the (atrial) forcing term Fo, omega. The mathematical behavior of the solution v(t) and its dependence on the parameters xo, c, and k, which characterize the contour of the Doppler velocity profile (DVP), is discussed. When clinical examples of normal and abnormal transmitral DVPs are compared with v(t) calculated using the harmonic oscillator model, excellent agreement [DVP-v(t)]/v(t) approximately 0.05 is obtained throughout diastole. Thus the model allows accurate qualitative and quantitative characterization of global ventricular diastolic behavior by noninvasive means in a variety of normal and abnormal stiffness-compliance states. In addition, it may serve as a prototype for a class of mathematical models that can encompass the essential dynamic elements of ventricular diastolic function that couple to flow and further enhance the role of the heart as a suction pump.

The duration of the QT interval as a function of heart rate: a derivation based on physical principles and a comparison to measured values

Several quantitatively and qualitatively disparate formulas for the duration of electrical systole (the QT interval) as a function of the R-R interval are reviewed. These are compared by the use of dimensional analysis, which permits rectification of previously published algebraic and dimensional inconsistencies. With one exception, prior developments of formulas have been empiric in nature, with results therefore not based on or necessarily mathematically consistent with basic physical or biologic principles. In order to resolve ambiguity and determine which (if any) of the many proposed formulas is consistent with elementary principles, we began with physical principles as they relate to the results of experiments and derived a mathematical expression for the QT interval as a function of the R-R interval. By making use of equations for the conservation of energy for the heart as a pump and the first law of thermodynamics, a formula of the form QT alpha K'1 + K'2/R-R was derived. This derivation, stemming from first principles and founded on experimental data, does not quantitatively specify the additive (K'1) or multiplicative constant (K'2), but constrains the algebraic relationship of QT as a function of R-R. The formula is comprised of the sum of two terms, a HR (R-R) independent additive constant (K'1) and a term alpha (R-R)-1. The derivation resolves previous qualitative disparaties in proposed formulas and yields a finite limit for QT in the limit of large R-R intervals.(ABSTRACT TRUNCATED AT 250 WORDS)