Noninvasive estimation of transmitral pressure drop across the normal mitral valve in humans: importance of convective and inertial forces during left ventricular filling

Assessing cardiac mechanics through left ventricular haemodynamic forces

Haemodynamic forces (HDFs), which represent the forces exchanged between blood and surrounding tissues, are critical in regulating the structure and function of the left ventricle (LV). These forces can be assessed on cardiac magnetic resonance or transthoracic echocardiography exams using specialized software, offering a non-invasive alternative for measuring intraventricular pressure gradients. The analysis of HDFs can be a valuable tool in improving our understanding of cardiovascular disease and providing insights beyond traditional diagnostic and therapeutic approaches. For instance, HDF analysis has the potential to identify early signs of adverse remodelling and cardiac dysfunction, which may not be detected by standard imaging methods such as bidimensional or speckle-tracking echocardiography. This review aims to summarize the principles of HDF analysis and to reappraise its possible applications to cardiac disorders.

Turbulent blood dynamics in the left heart in the presence of mitral regurgitation: a computational study based on multi-series cine-MRI

In this work, we performed a computational image-based study of blood dynamics in the whole left heart, both in a healthy subject and in a patient with mitral valve regurgitation. We elaborated multi-series cine-MRI with the aim of reconstructing the geometry and the corresponding motion of left ventricle, left atrium, mitral and aortic valves, and aortic root of the subjects. This allowed us to prescribe such motion to computational blood dynamics simulations where, for the first time, the whole left heart motion of the subject is considered, allowing us to obtain reliable subject-specific information. The final aim is to investigate and compare between the subjects the occurrence of turbulence and the risk of hemolysis and of thrombi formation. In particular, we modeled blood with the Navier-Stokes equations in the arbitrary Lagrangian-Eulerian framework, with a large eddy simulation model to describe the transition to turbulence and a resistive method to manage the valve dynamics, and we used a finite element discretization implemented in an in-house code for the numerical solution.

CMR-derived left ventricular intraventricular pressure gradients identify different patterns associated with prognosis in dilated cardiomyopathy

AIMS

Left ventricular (LV) blood flow is determined by intraventricular pressure gradients (IVPG). Changes in blood flow initiate remodelling and precede functional decline. Novel cardiac magnetic resonance (CMR) post-processing LV-IVPG analysis might provide a sensitive marker of LV function in dilated cardiomyopathy (DCM). Therefore, the aim of our study was to evaluate LV-IVPG patterns and their prognostic value in DCM.

METHODS AND RESULTS

LV-IVPGs between apex and base were measured on standard CMR cine images in DCM patients (n = 447) from the Maastricht Cardiomyopathy registry. Major adverse cardiovascular events, including heart failure hospitalisations, life-threatening arrhythmias, and sudden/cardiac death, occurred in 66 DCM patients (15%). A temporary LV-IVPG reversal during systolic-diastolic transition, leading to a prolonged transition period or slower filling, was present in 168 patients (38%). In 14%, this led to a reversal of blood flow, which predicted outcome corrected for univariable predictors [hazard ratio (HR) = 2.57, 95% confidence interval (1.01-6.51), P = 0.047]. In patients without pressure reversal (n = 279), impaired overall LV-IVPG [HR = 0.91 (0.83-0.99), P = 0.033], systolic ejection force [HR = 0.91 (0.86-0.96), P < 0.001], and E-wave decelerative force [HR = 0.83 (0.73-0.94), P = 0.003] predicted outcome, independent of known predictors (age, sex, New York Heart Association class ≥ 3, LV ejection fraction, late gadolinium enhancement, LV-longitudinal strain, left atrium (LA) volume-index, and LA-conduit strain).

CONCLUSION

Pressure reversal during systolic-diastolic transition was observed in one-third of DCM patients, and reversal of blood flow direction predicted worse outcome. In the absence of pressure reversal, lower systolic ejection force, E-wave decelerative force (end of passive LV filling), and overall LV-IVPG are powerful predictors of outcome, independent of clinical and imaging parameters.

Precise Estimation of Intravascular Pressure Gradients

This study presents a method for noninvasive pressure gradient estimation, which allows the detection of small pressure differences with higher precision compared to invasive catheters. It combines a new method for estimating the temporal acceleration of the flowing blood with the Navier-Stokes equation. The acceleration estimation is based on a double cross-correlation approach, which is hypothesized to minimize the influence of noise. Data are acquired using a 256-element, 6.5-MHz GE L3-12-D linear array transducer connected to a Verasonics research scanner. A synthetic aperture (SA) interleaved sequence with 2 ×12 virtual sources evenly distributed over the aperture and permuted in emission order is used in combination with recursive imaging. This enables a temporal resolution between correlation frames equal to the pulse repetition time at a frame rate of half the pulse repetition frequency. The accuracy of the method is evaluated against a computational fluid dynamic simulation. Here, the estimated total pressure difference complies with the CFD reference pressure difference, which yields an R -square of 0.985 and an RMSE of 3.03 Pa. The precision of the method is tested on experimental data, measured on a carotid phantom of the common carotid artery. The volume profile used during measurement was set to mimic flow in the carotid artery with a peak flow rate of 12.9 mL/s. The experimental setup showed that the measured pressure difference changes from -59.4 to 31 Pa throughout a single pulse cycle. This was estimated with a precision of 5.44% (3.22 Pa) across ten pulse cycles. The method was also compared to invasive catheter measurements in a phantom with a 60% cross-sectional area reduction. The ultrasound method detected a maximum pressure difference of 72.3 Pa with a precision of 3.3% (2.22 Pa). The catheters measured a maximum pressure difference of 105 Pa with a precision of 11.2% (11.4 Pa). This was measured over the same constriction and with a peak flow rate of 12.9 mL/s. The double cross-correlation approach revealed no improvement compared to a normal differential operator. The method's strength, thus, lies primarily in the ultrasound sequence, which allows precise and accurate velocity estimations, at which acceleration and pressure differences can be acquired.

Relative pressure estimation from 4D flow MRI using generalized Bernoulli equation in a phantom model of arterial stenosis

OBJECTIVE

Arterial stenosis is a significant cardiovascular disease requiring accurate estimation of the pressure gradients for determining hemodynamic significance. In this paper, we propose Generalized Bernoulli Equation (GBE) utilizing interpolated-based method to estimate relative pressures using streamlines and pathlines from 4D Flow MRI.

METHODS

4D Flow MRI data in a stenotic phantom model and computational fluid dynamics simulated velocities generated under identical flow conditions were processed by Generalized Bernoulli Equation (GBE), Reduced Bernoulli Equations (RBE), as well as the Simple Bernoulli Equation (SBE) which is clinically prevalent. Pressures derived from 4D flow MRI and noise corrupted CFD velocities were compared with pressures generated directly with CFD as well as pressures obtained using Millar catheters under identical flow conditions.

RESULTS

It was found that SBE and RBE methods underestimated the relative pressure for lower flow rates while overestimating the relative pressure at higher flow rates. Specifically, compared to the reference pressure, SBE underestimated the maximum relative pressure by 22[Formula: see text] for a pulsatile flow data with peak flow rate [Formula: see text] and overestimated by around 40[Formula: see text] when [Formula: see text]. In contrast, for GBE method the relative pressure values were overestimated by 15[Formula: see text] with [Formula: see text]and around 10[Formula: see text] with [Formula: see text].

CONCLUSION

GBE methods showed robust performance to additive image noise compared to other methods. Our findings indicate that GBE pressure estimation over pathlines attains the highest level of accuracy compared to GBE over streamlines, and the SBE and RBE methods.

Introduction to Hemodynamic Forces Analysis: Moving Into the New Frontier of Cardiac Deformation Analysis

The potential relevance of blood flow for describing cardiac function has been known for the past 2 decades, but the association of clinical parameters with the complexity of fluid motion is still not well understood. Hemodynamic force (HDF) analysis represents a promising approach for the study of blood flow within the ventricular chambers through the exploration of intraventricular pressure gradients. Previous experimental studies reported the significance of invasively measured cardiac pressure gradients in patients with heart failure. Subsequently, advances in cardiovascular imaging allowed noninvasive assessment of pressure gradients during progression and resolution of ventricular dysfunction and in the setting of resynchronization therapy. The HDF analysis can amplify mechanical abnormalities, detect them earlier compared with conventional ejection fraction and strain analysis, and possibly predict the development of cardiac remodeling. Alterations in HDFs provide the earliest signs of impaired cardiac physiology and can therefore transform the existing paradigm of cardiac function analysis once implemented in routine clinical care. Until recently, the HDF investigation was possible only with contrast‐enhanced echocardiography and magnetic resonance imaging, precluding its widespread clinical use. A mathematical model, based on the first principle of fluid dynamics and validated using 4‐dimensional‐flow‐magnetic resonance imaging, has allowed HDF analysis through routine transthoracic echocardiography, making it more readily accessible for routine clinical use. This article describes the concept of HDF analysis and reviews the existing evidence supporting its application in several clinical settings. Future studies should address the prognostic importance of HDF assessment in asymptomatic patients and its incorporation into clinical decision pathways.

Reference Ranges of Left Ventricular Hemodynamic Forces in Healthy Adults: A Speckle-Tracking Echocardiographic Study

BACKGROUND

The normal limits of left ventricular (LV) hemodynamic forces (HDFs) are not exactly known. The aim of this study was to explore the full spectrum of HDF parameters in healthy subjects and determine their physiologic correlates.

METHODS

269 healthy subjects were enrolled (mean age: 43 ± 14 years; 123 (45.7%) men). All participants underwent an echo-Doppler examination. Tri-plane tissue tracking from apical views was used to measure 2D global endocardial longitudinal strain (GLS), circumferential strain (GCS), and LV HDFs. HDFs were normalized with LV volume and divided by specific weight.

RESULTS

LV systolic longitudinal HDFs (%) were higher in men (20.8 ± 6.5 vs. 18.9 ± 5.6, p = 0.009; 22.0 ± 6.7 vs. 19.8 ± 5.6, p = 0.004, respectively). There was a significant correlation between GCS (increased) (r = -0.240, p < 0.001) and LV longitudinal HDFs (reduced) (r = -0.155, p = 0.01) with age. In a multivariable analysis age, BSA, pulse pressure, heart rate and GCS were the only independent variables associated with LV HDFs (β coefficient = -0.232, p < 0.001; 0.149, p = 0.003; 0.186, p < 0.001; 0.396, p < 0.001; -0.328, p < 0.001; respectively).

CONCLUSION

We report on the physiologic range of LV HDFs. Knowledge of reference values of HDFs may prompt their implementation into clinical routine and allow a more comprehensive assessment of the LV function.

Noninvasive quantification of cerebrovascular pressure changes using 4D Flow MRI

PURPOSE

Hemodynamic alterations are indicative of cerebrovascular disease. However, the narrow and tortuous cerebrovasculature complicates image-based assessment, especially when quantifying relative pressure. Here, we present a systematic evaluation of image-based cerebrovascular relative pressure mapping, investigating the accuracy of the routinely used reduced Bernoulli (RB), the extended unsteady Bernoulli (UB), and the full-field virtual work-energy relative pressure ( ν WERP) method.

METHODS

Patient-specific in silico models were used to generate synthetic cerebrovascular 4D Flow MRI, with RB, UB, and ν WERP performance quantified as a function of spatiotemporal sampling and image noise. Cerebrovascular relative pressures were also derived in 4D Flow MRI from healthy volunteers ( n = 8 ), acquired at two spatial resolutions (dx = 1.1 and 0.8 mm).

RESULTS

The in silico analysis indicate that accurate relative pressure estimations are inherently coupled to spatial sampling: at dx = 1.0 mm high errors are reported for all methods; at dx = 0.5 mm ν WERP recovers relative pressures at a mean error of 0.02 ± 0.25 mm Hg, while errors remain higher for RB and UB (mean error of -2.18 ± 1.91 and -2.18 ± 1.87 mm Hg, respectively). The dependence on spatial sampling is also indicated in vivo, albeit with higher correlative dependence between resolutions using ν WERP (k = 0.64, R2 = 0.81 for dx = 1.1 vs. 0.8 mm) than with RB or UB (k = 0.04, R2 = 0.03, and k = 0.07, R2 = 0.07, respectively).

CONCLUSION

Image-based full-field methods such as ν WERP enable cerebrovascular relative pressure mapping; however, accuracy is directly dependent on utilized spatial resolution.

Ultrasonic biomechanics method for vortex and wall motion of left ventricle: a phantom and in vivo study

Background

The non-invasive quantitative evaluation of left ventricle (LV) function plays a critical role in clinical cardiology. This study proposes a novel ultrasonic biomechanics method by integrating both LV vortex and wall motion to fully assess and understand the LV structure and function. The purpose of this study was to validate the ultrasonic biomechanics method as a quantifiable approach to evaluate LV function.

Methods

Firstly, B-mode ultrasound images were acquired and processed, which were utilized to implement parameters for quantifying the LV vortex and wall motion respectively. Next, the parameters were compared in polyvinyl alcohol cryogen (PVA) phantoms with different degree of stiffness corresponding to different freezing and thawing cycles in vitro. Finally, the parameters were computed in vivo during one cardiac cycle to assess the LV function in normal and abnormal subjects in vivo.

Results

In vitro study, the velocity field of PVA phantom differed with stiffness (varied elasticity modulus). The peak of strain for wall motion decreases with the increase of elasticity modulus, and periodically changed values. Statistical analysis for parameters of vortex dynamics (energy dissipation index, DI; kinetic energy fluctuations, KEF; relative strength, RS; and vorticity, W) based on different elasticity (E) of phantom depicted the good viability of this algorithm. In vivo study, the results confirmed that subjects with LV dysfunction had lower vorticity and strain (S) compared to the normal group.

Conclusion

Ultrasonic biomechanics method can obtain the vortex and wall motion of left ventricle. The method may have potential clinical value in evaluation of LV dysfunction.

Non-invasive estimation of relative pressure for intracardiac flows using virtual work-energy

Intracardiac blood flow is driven by differences in relative pressure, and assessing these is critical in understanding cardiac disease. Non-invasive image-based methods exist to assess relative pressure, however, the complex flow and dynamically moving fluid domain of the intracardiac space limits assessment. Recently, we proposed a method, νWERP, utilizing an auxiliary virtual field to probe relative pressure through complex, and previously inaccessible flow domains. Here we present an extension of νWERP for intracardiac flow assessments, solving the virtual field over sub-domains to effectively handle the dynamically shifting flow domain. The extended νWERP is validated in an in-silico benchmark problem, as well as in a patient-specific simulation model of the left heart, proving accurate over ranges of realistic image resolutions and noise levels, as well as superior to alternative approaches. Lastly, the extended νWERP is applied on clinically acquired 4D Flow MRI data, exhibiting realistic ventricular relative pressure patterns, as well as indicating signs of diastolic dysfunction in an exemplifying patient case. Summarized, the extended νWERP approach represents a directly applicable implementation for intracardiac flow assessments.

Cavitation phenomenon in mechanical prosthetic valves: Not only microbubbles

INTRODUCTION

Microbubbles (MBs) or cavitation is high-velocity, echo-bright findings present during the closing or opening of a mechanical valve (MVP). Cavitation bubble growth or gas emboli are less frequently described. We evaluated the hemodynamic parameters involved in the formation of gas emboli and the impact of gas emboli on requests for additional investigations.

METHODS AND RESULTS

Transthoracic echocardiographic studies (TTE) of 57 patients (31 males, mean age 46.8 ± 13.8 years) with gas emboli were evaluated after heart valve replacement surgery. The majority (72%, n = 42) had a mitral or combined mitral/aortic MVP, with 28% (n = 16) an aortic MVP. The last TTE with and without gas emboli were considered for the same patient and the no emboli group was the control group (42 patients). The patient's blood pressure (BP) and heart rate (HR) were available for each TTE. Comparing the two TTEs, the systolic and diastolic BP, transmitral and aortic gradients, and left ventricular ejection fraction were similar but the HR (80.9 ± 18.7 vs 72.5 ± 13.9 bpm, P = .02) was significantly higher in the group with gas emboli. A TEE was performed 52 times in 27 patients, due to gas emboli, with one case positive for thrombus/vegetation. For 19 patients, a brain CT was requested. In two patients, the indication for the brain CT was gas emboli but the result was negative.

CONCLUSION

Gas emboli are frequently present and associated to an increased HR. They can cause the misdiagnosis of endocarditis or thrombus formation with significant additional requests for diagnostic examinations.

Analysis of inter-system variability of systolic and diastolic intraventricular pressure gradients derived from color Doppler M-mode echocardiography

Assessment of intraventricular pressure gradients (IVPG) using color Doppler M-mode echocardiography has gained increasing interest in the evaluation of cardiac function. However, standardized analysis tools for IVPG quantification are missing. We aimed to evaluate the feasibility, the test-retest observer reproducibility, and the inter-system variability of a semi-automated IVPG quantification algorithm. The study included forty healthy volunteers (50% were men). All volunteers were examined using two ultrasound systems, the Philips Epiq 7 and the General Electric Vivid 6. Left ventricular diastolic (DIVPG) and systolic (SIVPG) intraventricular pressure gradients were measured from the spatiotemporal distribution of intraventricular propagation flow velocities using color Doppler M-mode in standard apical views. There was good feasibility for both systolic and diastolic IVPG measurements (82.5% and 85%, respectively). Intra and inter-observer test-retest variability measured with the intraclass correlation coefficient were 0.98 and 0.93 for DIVPG respectively, and 0.95 and 0.89 for SIVPG respectively. The inter-system concordance was weak to moderate with Lin’s concordance correlation coefficient of 0.59 for DIVPG and 0.25 for SIVPG. In conclusion, it is feasible and reproducible to assess systolic and diastolic IVPG using color Doppler M-mode in healthy volunteers. However, the inter-system variability in IVPG analysis needs to be taken into account, especially when using displayed data.

Echocardiographic evidence of left ventricular untwisting-filling interplay

Background

Left ventricular untwisting generates an early diastolic intraventricular pressure gradient (DIVPG) than can be quantified by echocardiography. We sought to confirm the quantitative relationship between peak untwisting rate and peak DIVPG in a large adult population.

Methods

From our echocardiographic database, we retrieved all the echocardiograms with a normal left ventricular ejection fraction, for whom color Doppler M-Mode interrogation of mitral inflow was available, and left ventricular untwisting rate was measurable using speckle tracking. Standard indices of left ventricular early diastolic function were assessed by Doppler (peaks E, e’ and Vp) and speckle tracking (peak strain rate Esr). Load dependency of DIVPG and untwisting rate was evaluated using a passive leg raising maneuver.

Results

We included 154 subjects, aged between 18 to 77 years old, 63% were male. Test-retest reliability for color Doppler-derived DIVPG measurements was good, the intraclass correlation coefficients were 0.97 [0.91–0.99] and 0.97 [0.67–0.99] for intra- and inter-observer reproducibility, respectively. Peak DIVPG was positively correlated with peak untwisting rate (r = 0.73, P <  0.001). On multivariate analysis, peak DIVPG was the only diastolic parameter that was independently associated with untwisting rate. Age and gender were the clinical predictive factors for peak untwisting rate, whereas only age was independently associated with peak DIVPG. Untwisting rate and DIVPG were both load-dependent, without affecting their relationship.

Conclusions

Color Doppler-derived peak DIVPG was quantitatively and independently associated with peak untwisting rate. It thus provides a reliable flow-based index of early left ventricular diastolic function.

Non-invasive intraventricular pressure differences estimated with cardiac MRI in subjects without heart failure and with heart failure with reduced and preserved ejection fraction

Objective

Non-invasive assessment of left ventricular (LV) diastolic and systolic function is important to better understand physiological abnormalities in heart failure (HF). The spatiotemporal pattern of LV blood flow velocities during systole and diastole can be used to estimate intraventricular pressure differences (IVPDs). We aimed to demonstrate the feasibility of an MRI-based method to calculate systolic and diastolic IVPDs in subjects without heart failure (No-HF), and with HF with reduced ejection fraction (HFrEF) and HF with preserved ejection fraction (HFpEF).

Methods

We studied 159 subjects without HF, 47 subjects with HFrEF and 32 subjects with HFpEF. Diastolic and systolic intraventricular flow was measured using two-dimensional in-plane phase-contrast MRI. The Euler equation was solved to compute IVPDs in diastole (mitral base to apex) and systole (apex to LV outflow tract).

Results

Subjects with HFpEF demonstrated a higher magnitude of the early diastolic reversal of IVPDs (−1.30 mm Hg) compared with the No-HF group (−0.78 mm Hg) and the HFrEF group (−0.75 mm Hg; analysis of variance p=0.01). These differences persisted after adjustment for clinical variables, Doppler-echocardiographic parameters of diastolic filling and measures of LV structure (No-HF=−0.72; HFrEF=−0.87; HFpEF=−1.52 mm Hg; p=0.006). No significant differences in systolic IVPDs were found in adjusted models. IVPD parameters demonstrated only weak correlations with standard Doppler-echocardiographic parameters.

Conclusions

Our findings suggest distinct patterns of systolic and diastolic IVPDs in HFpEF and HFrEF, implying differences in the nature of diastolic dysfunction between the HF subtypes.

Estimation of Cardiovascular Relative Pressure Using Virtual Work-Energy

Many cardiovascular diseases lead to local increases in relative pressure, reflecting the higher costs of driving blood flow. The utility of this biomarker for stratifying the severity of disease has thus driven the development of methods to measure these relative pressures. While intravascular catheterisation remains the most direct measure, its invasiveness limits clinical application in many instances. Non-invasive Doppler ultrasound estimates have partially addressed this gap; however only provide relative pressure estimates for a range of constricted cardiovascular conditions. Here we introduce a non-invasive method that enables arbitrary interrogation of relative pressures throughout an imaged vascular structure, leveraging modern phase contrast magnetic resonance imaging, the virtual work-energy equations, and a virtual field to provide robust and accurate estimates. The versatility and accuracy of the method is verified in a set of complex patient-specific cardiovascular models, where relative pressures into previously inaccessible flow regions are assessed. The method is further validated within a cohort of congenital heart disease patients, providing a novel tool for probing relative pressures in-vivo.

Cardiac fluid dynamics meets deformation imaging

Cardiac function is about creating and sustaining blood in motion. This is achieved through a proper sequence of myocardial deformation whose final goal is that of creating flow. Deformation imaging provided valuable contributions to understanding cardiac mechanics; more recently, several studies evidenced the existence of an intimate relationship between cardiac function and intra-ventricular fluid dynamics. This paper summarizes the recent advances in cardiac flow evaluations, highlighting its relationship with heart wall mechanics assessed through the newest techniques of deformation imaging and finally providing an opinion of the most promising clinical perspectives of this emerging field. It will be shown how fluid dynamics can integrate volumetric and deformation assessments to provide a further level of knowledge of cardiac mechanics.

Assessment of methodologies to calculate intraventricular pressure differences in computational models and patients

Intraventricular pressure differences (IVPDs) govern left ventricular (LV) efficient filling and are a significant determinant of LV diastolic function. Our primary aim is to assess the performance of available methods (color M-mode (CMM) and 1D/2D MRI-based methods) to determine IVPDs from intracardiac flow measurements. Performance of three methods to calculate IVPDs was first investigated via an LV computational fluid dynamics (CFD) model. CFD velocity data were derived along a modifiable scan line, mimicking ultrasound/MRI acquisition of 1D (IVPD_CMM/IVPD_{1D MRI}) and 2D (IVPD_{2D MRI}) velocity-based IVPD information. CFD pressure data (IVPD_CFD) was used as a ground truth. Methods were also compared in a small cohort (n = 13) of patients with heart failure with preserved ejection fraction (HFpEF). In silico data showed a better performance of the IVPD_{2D MRI} approach: RMSE values for a well-aligned scan line were 0.2550 mmHg (IVPD_{1D MRI}), 0.0798 mmHg (IVPD_{2D MRI}), and 0.2633 mmHg (IVPD_CMM). In vivo data exhibited moderate correlation between techniques. Considerable differences found may be attributable to different timing of measurements and/or integration path. CFD modeling demonstrated an advantage using 2D velocity information to compute IVPDs, and therefore, a 2D MRI-based method should be favored. However, further studies are needed to support the clinical significance of MRI-based computation of IVPDs over CMM.

On estimating intraventricular hemodynamic forces from endocardial dynamics: A comparative study with 4D flow MRI

Intraventricular pressure gradients or hemodynamic forces, which are their global measure integrated over the left ventricular volume, have a fundamental importance in ventricular function. They may help revealing a sub-optimal cardiac function that is not evident in terms of tissue motion, which is naturally heterogeneous and variable, and can influence cardiac adaptation. However, hemodynamic forces are not utilized in clinical cardiology due to the unavailability of simple non-invasive measurement tools. Hemodynamic forces depend on the intraventricular flow; nevertheless, most of them are imputable to the dynamics of the endocardial flow boundary and to the exchange of momentum across the mitral and aortic orifices. In this study, we introduce a simplified model based on first principles of fluid dynamics that allows estimating hemodynamic forces without knowing the velocity field inside the LV. The model is validated with 3D phase-contrast MRI (known as 4D flow MRI) in 15 subjects, (5 healthy and 10 patients) using the endocardial surface reconstructed from the three standard long-axis projections. Results demonstrate that the model provides consistent estimates for the base-apex component (mean correlation coefficient r=0.77 for instantaneous values and r=0.88 for root mean square) and good estimates of the inferolateral-anteroseptal component (r=0.50 and 0.84, respectively). The present method represents a potential integration to the existing ones quantifying endocardial deformation in MRI and echocardiography to add a physics-based estimation of the corresponding hemodynamic forces. These could help the clinician to early detect sub-clinical diseases and differentiate between different cardiac dysfunctional states.

Beyond Bernoulli: Improving the Accuracy and Precision of Noninvasive Estimation of Peak Pressure Drops

BACKGROUND

Transvalvular peak pressure drops are routinely assessed noninvasively by echocardiography using the Bernoulli principle. However, the Bernoulli principle relies on several approximations that may not be appropriate, including that the majority of the pressure drop is because of the spatial acceleration of the blood flow, and the ejection jet is a single streamline (single peak velocity value).

METHODS AND RESULTS

We assessed the accuracy of the Bernoulli principle to estimate the peak pressure drop at the aortic valve using 3-dimensional cardiovascular magnetic resonance flow data in 32 subjects. Reference pressure drops were computed from the flow field, accounting for the principles of physics (ie, the Navier-Stokes equations). Analysis of the pressure components confirmed that the spatial acceleration of the blood jet through the valve is most significant (accounting for 99% of the total drop in stenotic subjects). However, the Bernoulli formulation demonstrated a consistent overestimation of the transvalvular pressure (average of 54%, range 5%-136%) resulting from the use of a single peak velocity value, which neglects the velocity distribution across the aortic valve plane. This assumption was a source of uncontrolled variability.

CONCLUSIONS

The application of the Bernoulli formulation results in a clinically significant overestimation of peak pressure drops because of approximation of blood flow as a single streamline. A corrected formulation that accounts for the cross-sectional profile of the blood flow is proposed and adapted to both cardiovascular magnetic resonance and echocardiographic data.

A novel methodology for personalized simulations of ventricular hemodynamics from noninvasive imaging data

Current state-of-the-art imaging techniques can provide quantitative information to characterize ventricular function within the limits of the spatiotemporal resolution achievable in a realistic acquisition time. These imaging data can be used to personalize computer models, which in turn can help treatment planning by quantifying biomarkers that cannot be directly imaged, such as flow energy, shear stress and pressure gradients. To date, computer models have typically relied on invasive pressure measurements to be made patient-specific. When these data are not available, the scope and validity of the models are limited. To address this problem, we propose a new methodology for modeling patient-specific hemodynamics based exclusively on noninvasive velocity and anatomical data from 3D+t echocardiography or Magnetic Resonance Imaging (MRI). Numerical simulations of the cardiac cycle are driven by the image-derived velocities prescribed at the model boundaries using a penalty method that recovers a physical solution by minimizing the energy imparted to the system. This numerical approach circumvents the mathematical challenges due to the poor conditioning that arises from the imposition of boundary conditions on velocity only. We demonstrate that through this technique we are able to reconstruct given flow fields using Dirichlet only conditions. We also perform a sensitivity analysis to investigate the accuracy of this approach for different images with varying spatiotemporal resolution. Finally, we examine the influence of noise on the computed result, showing robustness to unbiased noise with an average error in the simulated velocity approximately 7% for a typical voxel size of 2mm(3) and temporal resolution of 30ms. The methodology is eventually applied to a patient case to highlight the potential for a direct clinical translation.

Non-invasive pressure difference estimation from PC-MRI using the work-energy equation

Pressure difference is an accepted clinical biomarker for cardiovascular disease conditions such as aortic coarctation. Currently, measurements of pressure differences in the clinic rely on invasive techniques (catheterization), prompting development of non-invasive estimates based on blood flow. In this work, we propose a non-invasive estimation procedure deriving pressure difference from the work-energy equation for a Newtonian fluid. Spatial and temporal convergence is demonstrated on in silico Phase Contrast Magnetic Resonance Image (PC-MRI) phantoms with steady and transient flow fields. The method is also tested on an image dataset generated in silico from a 3D patient-specific Computational Fluid Dynamics (CFD) simulation and finally evaluated on a cohort of 9 subjects. The performance is compared to existing approaches based on steady and unsteady Bernoulli formulations as well as the pressure Poisson equation. The new technique shows good accuracy, robustness to noise, and robustness to the image segmentation process, illustrating the potential of this approach for non-invasive pressure difference estimation.

Simplified Bernoulli's method significantly underestimates pulmonary transvalvular pressure drop

PURPOSE

To determine whether neglecting the flow unsteadiness in simplified Bernoulli's equation significantly affects the pulmonary transvalvular pressure drop estimation.

MATERIALS AND METHODS

3.0T magnetic resonance imaging (MRI) 4D velocity mapping was performed on four healthy volunteers, seven patients with repaired tetralogy of Fallot, and thirteen patients with transposition of the great arteries repaired by arterial switch. Pulmonary transvalvular pressure drop was estimated based on two methods: General Bernoulli's Equation (GBE), ie, the most complete form; and Simplified Bernoulli's Equation (SBE), known as 4V(2) . More than 2300 individual pressure drop measurements were used to compare the simplified and the general Bernoulli's methods. A linear mixed-effects model was employed for statistical analyses, fully accounting for clustering of observations among the methods and systolic phases.

RESULTS

The simplified Bernoulli's method systematically underestimated the pressure drop compared to general Bernoulli's method during the entire systolic phase (P < 0.05), including the peak systole, where on average ΔpSBE/ΔpGBE=78%.

CONCLUSION

The simplified Bernoulli method underestimated the pressure drop during all systolic phases in all the studied subjects. Therefore, it is necessary to take into account the flow unsteadiness for more accurate estimation of the pressure drop. J. Magn. Reson. Imaging 2016;43:1313-1319.

Clinical Diagnostic Biomarkers from the Personalization of Computational Models of Cardiac Physiology

Computational modelling of the heart is rapidly advancing to the point of clinical utility. However, the difficulty of parameterizing and validating models from clinical data indicates that the routine application of truly predictive models remains a significant challenge. We argue there is significant value in an intermediate step towards prediction. This step is the use of biophysically based models to extract clinically useful information from existing patient data. Specifically in this paper we review methodologies for applying modelling frameworks for this goal in the areas of quantifying cardiac anatomy, estimating myocardial stiffness and optimizing measurements of coronary perfusion. Using these indicative examples of the general overarching approach, we finally discuss the value, ongoing challenges and future potential for applying biophysically based modelling in the clinical context.

Estimation of maximum intraventricular pressure: a three-dimensional fluid-structure interaction model

Background

The aim of this study was to propose a method to estimate the maximum pressure in the left ventricle (MPLV) for a healthy subject, based on cardiac outputs measured by echo-Doppler (non-invasive) and catheterization (invasive) techniques at rest and during exercise.

Methods

Blood flow through aortic valve was measured by Doppler flow echocardiography. Aortic valve geometry was calculated by echocardiographic imaging. A Fluid–structure Interaction (FSI) simulation was performed, using an Arbitrary Lagrangian–Eulerian (ALE) mesh. Boundary conditions were defined as pressure loads on ventricular and aortic sides during ejection phase. The FSI simulation was used to determine a numerical relationship between the cardiac output to aortic diastolic and left ventricular pressures. This relationship enabled the prediction of pressure loads from cardiac outputs measured by invasive and non-invasive clinical methods.

Results

Ventricular systolic pressure peak was calculated from cardiac output of Doppler, Fick oximetric and Thermodilution methods leading to a 22%, 18% and 24% increment throughout exercise, respectively. The mean gradients obtained from curves of ventricular systolic pressure based on Doppler, Fick oximetric and Thermodilution methods were 0.48, 0.41 and 0.56 mmHg/heart rate, respectively. Predicted Fick-MPLV differed by 4.7%, Thermodilution-MPLV by 30% and Doppler-MPLV by 12%, when compared to clinical reports.

Conclusions

Preliminary results from one subject show results that are in the range of literature values. The method needs to be validated by further testing, including independent measurements of intraventricular pressure. Since flow depends on the pressure loads, measuring more accurate intraventricular pressures helps to understand the cardiac flow dynamics for better clinical diagnosis. Furthermore, the method is non-invasive, safe, cheap and more practical. As clinical Fick-measured values have been known to be more accurate, our Fick-based prediction could be the most applicable.

Aortic relative pressure components derived from four-dimensional flow cardiovascular magnetic resonance

Purpose

To describe the assessment of the spatiotemporal distribution of relative aortic pressure quantifying the magnitude of its three major components.

Methods

Nine healthy volunteers and three patients with aortic disease (bicuspid aortic valve, dissection, and Marfan syndrome) underwent 4D-flow CMR. Spatiotemporal pressure maps were computed from the CMR flow fields solving the pressure Poisson equation. The individual components of pressure were separated into time-varying inertial (“transient”), spatially varying inertial (“convective”), and viscous components.

Results

Relative aortic pressure is primarily caused by transient effects followed by the convective and small viscous contributions (64.5, 13.6, and 0.3 mmHg/m, respectively, in healthy subjects), although regional analysis revealed prevalent convective effects in specific contexts, e.g., Sinus of Valsalva and aortic arch at instants of peak velocity. Patients showed differences in peak transient values and duration, and localized abrupt convective changes explained by abnormalities in aortic geometry, including the presence of an aneurysm, a pseudo-coarctation, the inlet of a dissection, or by complex flow patterns.

Conclusion

The evaluation of the three components of relative pressure enables the quantification of mechanistic information for understanding and stratifying aortic disease, with potential future implications for guiding therapy. Magn Reson Med 72:1162–1169, 2014. © 2013 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Sensitivity analysis of left ventricle with dilated cardiomyopathy in fluid structure simulation

Dilated cardiomyopathy (DCM) is the most common myocardial disease. It not only leads to systolic dysfunction but also diastolic deficiency. We sought to investigate the effect of idiopathic and ischemic DCM on the intraventricular fluid dynamics and myocardial wall mechanics using a 2D axisymmetrical fluid structure interaction model. In addition, we also studied the individual effect of parameters related to DCM, i.e. peak E-wave velocity, end systolic volume, wall compliance and sphericity index on several important fluid dynamics and myocardial wall mechanics variables during ventricular filling. Intraventricular fluid dynamics and myocardial wall deformation are significantly impaired under DCM conditions, being demonstrated by low vortex intensity, low flow propagation velocity, low intraventricular pressure difference (IVPD) and strain rates, and high-end diastolic pressure and wall stress. Our sensitivity analysis results showed that flow propagation velocity substantially decreases with an increase in wall stiffness, and is relatively independent of preload at low-peak E-wave velocity. Early IVPD is mainly affected by the rate of change of the early filling velocity and end systolic volume which changes the ventriculo:annular ratio. Regional strain rate, on the other hand, is significantly correlated with regional stiffness, and therefore forms a useful indicator for myocardial regional ischemia. The sensitivity analysis results enhance our understanding of the mechanisms leading to clinically observable changes in patients with DCM.

Kinematic modeling-based left ventricular diastatic (passive) chamber stiffness determination with in-vivo validation

The slope of the diastatic pressure-volume relationship (D-PVR) defines passive left ventricular (LV) stiffness κ. Although κ is a relative measure, cardiac catheterization, which is an absolute measurement method, is used to obtain the former. Echocardiography, including transmitral flow velocity (Doppler E-wave) analysis, is the preferred quantitative diastolic function (DF) assessment method. However, E-wave analysis can provide only relative, rather than absolute pressure information. We hypothesized that physiologic mechanism-based modeling of E-waves allows derivation of the D-PVR(E-wave) whose slope, κ(E-wave), provides E-wave-derived diastatic, passive chamber stiffness. Our kinematic model of filling and Bernoulli's equation were used to derive expressions for diastatic pressure and volume on a beat-by-beat basis, thereby generating D-PVR(E-wave), and κ(E-wave). For validation, simultaneous (conductance catheter) P-V and echocardiographic E-wave data from 30 subjects (444 total cardiac cycles) having normal LV ejection fraction (LVEF) were analyzed. For each subject (15 beats average) model-predicted κ(E-wave) was compared to experimentally measured κ(CATH) via linear regression yielding as follows: κ(E-wave) = ακ(CATH) + b (R(2) = 0.92), where, α = 0.995 and b = 0.02. We conclude that echocardiographically determined diastatic passive chamber stiffness, κ(E-wave), provides an excellent estimate of simultaneous, gold standard (P-V)-defined diastatic stiffness, κ(CATH). Hence, in chambers at diastasis, passive LV stiffness can be accurately determined by means of suitable analysis of Doppler E-waves (transmitral flow).

Nonconvective forces: a critical and often ignored component in the echocardiographic assessment of transvalvular pressure gradients

Echocardiography is routinely used to assess ventricular and valvular function, particularly in patients with known or suspected cardiac disease and who have evidence of hemodynamic compromise. A cornerstone to the use of echocardiographic imaging is not only the qualitative assessment, but also the quantitative Doppler-derived velocity characteristics of intracardiac blood flow. While simplified equations, such as the modified Bernoulli equation, are used to estimate intracardiac pressure gradients based upon Doppler velocity data, these modified equations are based upon assumptions of the varying contributions of the different forces that contribute to blood flow. Unfortunately, the assumptions can result in significant miscalculations in determining a gradient if not completely understood or they are misapplied. We briefly summarize the principles of fluid dynamics that are used clinically with some of the inherent limitations of routine broad application of the simplified Bernoulli equation.

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 E-wave delayed relaxation pattern to LV pressure contour relation: model-based prediction with in vivo validation

The transmitral Doppler E-wave "delayed relaxation" (DR) pattern is an established sign of diastolic dysfunction (DD). Furthermore, chambers exhibiting a DR filling pattern are also expected to have a prolonged time-constant of isovolumic relaxation (tau). The simultaneous observation of a DR pattern and normal tau in the same heart is not uncommon, however. The simultaneous hemodynamic equivalent of the DR pattern has not been proposed. To determine the feature of the left ventricular (LV) pressure contour during the E-wave that is causally related to its DR pattern we applied kinematic and fluid mechanics based arguments to derive the pressure recovery ratio (PRR). The PRR is dimensionless and is defined by the left ventricular pressure difference between diastasis and minimum pressure, normalized to the pressure difference between a fiducial diastolic filling pressure and minimum pressure [PRR=(P(Diastasis)-P(Min))/(P(Fiducial)-P(Min))]. We analyzed 354 cardiac cycles from 40 normal sinus rhythm (NSR) subjects and 113 beats from nine atrial fibrillation (AF) subjects from our database of simultaneous transmitral flow-micromanometric LV pressure recordings. The fiducial pressure is defined by the end diastolic pressure in NSR and by the pressure at dP/dt(MIN) in the setting of AF. Consistent with derivation, PRR was linearly related to a DR pattern related, model-based relaxation parameter (R(2) = 0.77, 0.83 in NSR and AF, respectively). Furthermore, the PRR successfully differentiated subjects with a DR pattern from subjects with partial DR or normal E-wave pattern (p < 0.05). We conclude that the PRR may differentiate between subjects having a DR pattern and subjects with normal E-waves, even when tau cannot.

Impact of image spatial, temporal, and velocity resolutions on cardiovascular indices derived from color-Doppler echocardiography

Quantitative processing of color-Doppler echocardiographic images has substantially improved noninvasive assessment of cardiac physiology. Many indices are computed from the velocity fields derived either from color-Doppler tissue imaging (DTI), such as acceleration, strain and strain-rate, or from blood-flow color-Doppler, such as intracardiac pressure gradients (ICPG). All of these indices are dependent on the finite resolution of the ultrasound scanner. Therefore, we developed an image-dependent method for assessing the influence of temporal, spatial, and velocity resolutions, on cardiovascular parameters derived from velocity images. In order to focus our study on the spatial, temporal, and velocity resolutions of the digital image, we did not consider the effect of other sources of noise such as the interaction between ultrasound and tissue. A simple first-order Taylor's expansion was used to establish the functional relationship between the acquired image velocity and the calculated cardiac index. Resolutions were studied on: (a) myocardial acceleration, strain, and strain-rate from DTI, and (b) ICPG from blood-flow color-Doppler. The performance of Taylor's-based error bounds (TBEB) was demonstrated on simulated models and illustrated on clinical images. Velocity and temporal resolution were highly relevant for the accuracy of DTI-derived parameters and ICPGs. TBEB allow to assess the effects of ideal digital image resolution on quantitative cardiovascular indices derived from velocity measurements obtained by cardiac imaging techniques.

Noninvasive Assessment of the Right Ventricular Filling Pressure Gradient

Background— The physiological basis of right ventricular (RV) diastolic function remains incompletely studied in humans. The driving force responsible for RV filling, the pressure gradient along the RV inlet from the right atrium to the RV apex, has never been measured in the clinical setting.

Methods and Results— We validated a method for measuring the RV filling pressure difference (RVFPD) from color Doppler M-mode recordings in 12 pigs undergoing interventions on RV preload, afterload, and lusitropic states (error, −0.1±0.4 mm Hg compared with micromanometers; intraclass correlation coefficient, 0.88). Peak early RVFPD correlated directly with mean right atrial pressure and inversely with the time constant of RV relaxation. In 21 patients with dilated cardiomyopathy, the peak RVFPD was 1.0 mm Hg (95% CI, 0.8 to 1.2), significantly lower than in age-matched control subjects (1.4 mm Hg; 95% CI, 1.2 to 1.6). In another population of 19 young healthy volunteers, the peak RVFPD was 2.3 mm Hg (95% CI, 2.0 to 2.6), which was reduced by nitroglycerine and esmolol and was augmented by volume overload and atropine infusions. RVFPD was generated almost exclusively by inertial forces.

Conclusions— For the first time, the RV driving filling force can be accurately measured noninvasively in the clinical setting, and the method is sensitive to detect the effects of preload, chronotropic, and lusitropic states. In patients with dilated cardiomyopathy, the RV filling force is markedly reduced, indicating severely impaired RV relaxation. These findings suggest that this is a useful tool for improving the clinical assessment of RV diastolic function.

Assessment of left ventricular function by cardiac ultrasound

Our understanding of the physical underpinnings of the assessment of cardiac function is becoming increasingly sophisticated. Recent developments in cardiac ultrasound permit exploitation of many of these newer physical concepts with current echocardiographic machines. This review will first focus on the current approach to the assessment of cardiovascular hemodynamics by cardiac ultrasound. The next focus will be the assessment of global cardiac mechanics in systole and diastole. Finally, relationships between the cardiac structure and regional myocardial function, and the way regional function can be quantified by ultrasound, will be presented. This review also discusses the clinical impact of echocardiography and its future directions and developments.

Immediate impairment of left ventricular mechanical performance and force–frequency relation by rate-responsive dual-chamber, but not atrial pacing: Implications from intraventricular isovolumic relaxation flow

BACKGROUND

Despite the maintenance of atrioventricular (AV) synchrony, the detrimental effect of left ventricular asynchronization on mechanical performance and intraventricular flow by nonphysiologic right ventricular apical pacing in dual-chamber pacing, with and without rate adaptation, is not clear.

METHOD

Twenty-seven consecutive patients receiving permanent pacemakers for symptomatic bradyarrhythmias (18 with DDD and 9 with AAI mode pacemakers) were evaluated with standard and tissue Doppler echocardiography before and 24 h after pacemaker implantation. The rate-response effect of pacing was studied by programmed rate with increments of 20, from 60 to 100/min.

RESULTS

Color M-mode echocardiography demonstrated that much more DDD patients developed new biphasic intraventricular flow during isovolumic relaxation period than AAI patients (13/18 versus 0/9, P<0.001). In DDD patients, the ventricular relaxation represented by mitral annulus velocity in early diastole significantly attenuated (before vs. after DDDR, 8.5+/-2.8 vs. 5.2+/-1.2 cm/s, P<0.05), and also the mitral flow propagation velocity (33+/-11 vs. 25+/-5 cm/s, P<0.01). The myocardial performance index increased after DDD (0.70+/-0.15 vs. 0.79+/-0.24, P<0.05) but not after AAI (0.61+/-0.1 vs. 0.59+/-0.08, P=NS). For both pacing groups, the accelerated pacing rate prolonged the isovolumic relaxation time and shortened the diastole period (P<0.001). However, only DDD patients had a decreased mitral flow propagation velocity (P=0.026) and an attenuated force-frequency relation in programmed rate acceleration.

CONCLUSION

Despite the AV synchrony, right ventricular apical pacing immediately attenuates the left ventricular contraction and relaxation performance, which deteriorated further and suppressed the physiologically positive force-frequency relation after accelerated pacing rate.

Noninvasive assessment of ejection intraventricular pressure gradients

OBJECTIVES

The study was designed to validate in vivo a new method to measure ejection intraventricular pressure gradients (IVPGs) by processing color M-mode Doppler data and to assess the effects of inotropic interventions on IVPGs in the clinical setting.

BACKGROUND

In the absence of obstruction, ejection IVPGs cannot be estimated by Doppler using the simplified Bernoulli equation.

METHODS

High-fidelity micromanometers were placed in the left ventricle of eight minipigs, and synchronic Doppler images and pressure signals were obtained during different hemodynamic conditions. Twenty healthy volunteers and 20 dilated cardiomyopathy patients were studied at baseline and during esmolol, dobutamine, and atropine infusion (only dobutamine in patients).

RESULTS

Excellent agreement was observed between micromanometer and Doppler methods for measuring instantaneous pressure differences among the apex, the mid-cavity, and the outflow tract (R(intraclass) = 0.98, 0.81, 0.76, and 0.98 for the peak, time-to-peak, peak reverse, and time-to-peak reverse values, respectively; n = 810 beats). Error of the noninvasive method was -0.05 +/- 0.25 mm Hg for the peak pressure difference. Parametrical images demonstrated that IVPGs originate mainly in the mid-ventricle and then propagate to the outflow tract. Both the magnitude and the temporal course of IVPGs were different among volunteers and patients. Inotropic interventions induced significant changes in the apex-outflow tract pressure differences in both populations, whereas atropine had no effect on IVPGs.

CONCLUSIONS

For the first time, ejection IVPGs can be accurately visualized and measured by Doppler-echocardiography. Important aspects of the dynamic interaction among myocardial performance, load mechanics, and ejection dynamics can be assessed in the clinical setting using this method.

Improvement in diastolic intraventricular pressure gradients in patients with HOCM after ethanol septal reduction

We sought to validate measurement of intraventricular pressure gradients (IVPG) and analyze their change in patients with hypertrophic obstructive cardiomyopathy (HOCM) after ethanol septal reduction (ESR). Quantitative analysis of color M-mode Doppler (CMM) images may be used to estimate diastolic IVPG noninvasively. Noninvasive IVPG measurement was validated in 10 patients undergoing surgical myectomy. Echocardiograms were then analyzed in 19 patients at baseline and after ESR. Pulsed Doppler data through the mitral valve and pulmonary venous flow were obtained. CMM was used to obtain the flow propagation velocity (Vp) and to calculate IVPG off-line. Left atrial pressure was estimated with the use of previously validated Doppler equations. Data were compared before and after ESR. CMM-derived IVPG correlated well with invasive measurements obtained before and after surgical myectomy [r = 0.8, P < 0.01, Delta(CMM - invasive IVPG) = 0.09 +/- 0.45 mmHg]. ESR resulted in a decrease of resting LVOT systolic gradient from 62 +/- 10 to 29 +/- 5 mmHg (P < 0.001). There was a significant increase in the Vp and IVPG (from 48 +/- 5to 74 +/- 7 cm/s and from 1.5 +/- 0.2 to 2.6 +/- 0.3 mmHg, respectively, P < 0.001 for both). Estimated left atrial pressure decreased from 16.2 +/- 1.1 to 11.5 +/- 0.9 mmHg (P < 0.001). The increase in IVPG correlated with the reduction in the LVOT gradient (r = 0.6, P < 0.01). Reduction of LVOT obstruction after ESR is associated with an improvement in diastolic suction force. Noninvasive measurements of IVPG may be used as an indicator of diastolic function improvement in HOCM.

Model and influence of mitral valve opening during the left ventricular filling

The flow inside a model left ventricle during filling (diastole) is simulated by the numerical solution of the equations of motion under the axisymmetric approximation. The left ventricle is taken with a truncated ellipsoid geometry, and a simple conceptual model is introduced to simulate the presence of the moving mitral valve. A relevant role during the left ventricle diastolic flow, as already discussed by other authors, is played by the travelling vortex wake that is formed from the transmitral jet during the early filling acceleration phase. The presence of a moving valve is found to produce a non-simultaneous spatial development of the entering bulk flow and a slightly more complex vortex wake structure; the results are discussed in comparison with fixed valve ones. They are analysed also in terms of M-mode representation suggesting a physical interpretation of the pattern detected in the clinical measurements that extends the one given previously on the basis of fixed valve models.

Impact of left ventricular function on the pulmonary vein Doppler spectrum: nonsimultaneous assessment with load-insensitive indices

Pulmonary vein Doppler spectrum is highly load-dependent and thus has been used to estimate left ventricular (LV) filling pressure. However, the impact of LV function on pulmonary vein Doppler spectrum remains obscure because only load-sensitive indices were studied previously. In the present study, measurements of the pulmonary vein Doppler spectrum were correlated with load-insensitive LV systolic (end-systolic elastance [Ees]) and diastolic (relaxation time constant [tau] and beta coefficient of the end-diastolic pressure volume relationship) function indices obtained from an invasive catheterization study nonsimultaneously. The peak velocity, velocity time integral, and duration of systolic forward spectrum were significantly correlated with Ees (r = 0.35, r = 0.36, and r = 0.41, respectively;P < 0.05). The pulmonary vein diastolic velocity time integral (PVDVTI) and duration of the diastolic forward spectrum were significantly correlated with Ees (r = 0.51 and r = 0.57, respectively;P < 0.01). PVDVTI was correlated with tau and the end-diastolic pressure-volume relationship (EDPVR) (r = 0.42 and r = 0.40 respectively,P < 0.05). On the other hand, the systolic fraction of the forward spectrum was significantly correlated with ejection fraction (for peak velocity,r = 0.63, P < 0.01; for velocity time integral,r = 0.37, P < 0.05) but not with Ees, and the diastolic fraction of the forward spectrum was significantly correlated with minimum pressure derivative over time (for peak velocity,r = 0.48, P < 0.05; for velocity time integral,r = 0.44, P < 0.05, respectively) but not with tau or EDPVR. In summary, the systolic and diastolic components of the pulmonary vein Doppler spectrum are affected variably by LV systolic and diastolic function, independent of the loading condition. The systolic and diastolic fraction of pulmonary vein Doppler spectrum appears to depend more on the loading condition than the LV systolic or diastolic function.

Evaluation of left ventricular diastolic function from spectral and color M-mode Doppler in genetically altered mice

Doppler indices of transmitral flow are commonly used to assess noninvasively left ventricular (LV) diastolic function in species larger than mice. The objective of our study was to characterize patterns of LV diastolic function in 2 genetically altered mouse models using Doppler- and color M-mode echocardiography. Phospholamban (PLB) reversibly inhibits the sarcoplasmic reticulum Ca(2+) ATPase (SERCA) and is a key regulator of myocardial relaxation. Twelve-week-old PLB knockout mice (PLB/KO) were examined in parallel with age-matched transgenic mice expressing a mutant form of PLB (PLB/N27A) that exhibited superinhibition of SERCA. Transmitral Doppler flow indexes, including isovolumic relaxation time, the ratio of peak early-to-late filling velocities, and deceleration time of peak early transmitral velocity indicate impaired diastolic filling in the PLB/N27A mutants, but improved LV diastolic function in the PLB/KO mice. In addition, a relatively load-independent parameter of LV relaxation measured by color M-mode Doppler, the propagation velocity of early flow into the LV cavity confirmed the observed differences. We conclude that transmitral filling patterns and color M-mode flow propagation velocity reflect changes in myocardial relaxation in mice with genetically altered levels of PLB and may be useful tools to characterize LV diastolic function in other mouse models of disease.

Tissue Doppler imaging for the assessment of left ventricular systolic and diastolic functions

Doppler tissue imaging is a technique that allows recording of the low Doppler shift frequencies of high energy generated by the ventricular walls motion that are purposely filtered out in standard Doppler blood flow studies. Doppler tissue imaging can be performed with the use of pulsed Doppler, color two-dimensional Doppler, and color M-mode Doppler. Pulsed Doppler tissue imaging offers a high temporal resolution and therefore can be appropriately used for analysis of temporal relation between myocardium systolic and diastolic velocity waves. Color two-dimensional Doppler provides a good spatial resolution that permits differentiation of the velocity profiles between subendocardial and subepicardial layers but is limited by its poor temporal resolution. M-mode color-coded tissue imaging is characterized by a high spatiotemporal resolution, but sampling is only performed on a single line. Both two-dimensional and M-mode color-coded tissue imaging require specific modification of the current ultrasound machines. The present article reviews how Doppler tissue imaging may contribute to the noninvasive assessment of systolic and diastolic myocardial functions.

Fluid dynamics of the left ventricular filling in dilated cardiomyopathy

Modifications in diastolic function occur in a broad range of cardiovascular diseases and there is an increasing evidence that abnormalities in left ventricular function may contribute significantly to the symptomatology. The flow inside the left ventricle during the diastole is here investigated by numerical solution of the Navier-Stokes equations under the axisymmetric assumption. The equation are written in a body-fitted, moving prolate spheroid, system of coordinates and solved using a fractional step method. The system is forced by a given volume time-law derived from clinical data, and varying the two-degrees-of-freedom ventricle geometry on the basis of a simple model. The solution under healthy conditions is analysed in terms of vorticity dynamics, showing that the flow field is characterised by the presence of a vortex wake; it is attached to the mitral valve during the accelerating phase of the E-wave, and it detaches and translate towards the ventricle apex afterwards. The flow evolution is discussed, results are also reported as an M-mode representation of colour-coded Doppler velocity maps. In the presence of ventricle dilatation the mitral jet extends farther inside the ventricle, propagation velocity decreases, and the fluid stagnates longer at the apex.