Article

Simplified Bernoulli's method significantly underestimates pulmonary transvalvular pressure drop: General vs. Simplified Bernoulli Equation

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Abstract

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 4 V 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 . 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.

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Medical imaging techniques, such as MRI and CT scanning, are valuable tools for getting a lot of information non-invasively and it is useful for reconstructing the geometry of complex objects about the patients. Medical-GiD is a medical image platform that incorporates a module to read directly the blood velocity profile from the MR scan, in particular for deformable registration of 4D MRI images, Electrocardiography (ECG)-synchronized and respiration controlled 3D magnetic resonance (MR) velocity mapping (flow-sensitive 4D MRI), 3D morphologic and three-directional blood flow data. Furthermore, Medical-GiD is focus in the medical image processing in the biomechanical research field to generating meshes from the medical images, to apply in Computational Fluid Dynamics (CFD) or structural mechanics (stress analysis). To date, these techniques have largely been applied to compute meshes for numerical simulations, but with Medical-GiD, we will have the integration between the real data and numerical simulations. KeywordsComputational Fluid Dynamics-Mesh generation-Blood flow-Aorta-Magnetic resonance
Book
Linear Mixed-Effects * Theory and Computational Methods for LME Models * Structure of Grouped Data * Fitting LME Models * Extending the Basic LME Model * Nonlinear Mixed-Effects * Theory and Computational Methods for NLME Models * Fitting NLME Models
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Despite inherent discrepancies between Doppler and catheter gradients in aortic stenosis, the simplified Bernoulli equation is still the accepted noninvasive technique to quantitate severity. The Reynolds number is a dimensionless parameter that characterizes the nature of flow as being viscous, turbulent, or transitional. Recently, in vivo and animal studies have successfully used a Reynolds number-based approach to reconcile Doppler-estimated and catheter-measured discrepancies. At the midrange of Reynolds number, pressure recovery effects are most evident, resulting in "overestimation" of catheter gradients by Doppler. At the lower range of the Reynolds number viscous effects are important, whereas at a higher range, turbulent factors are dominant; both result in a tendency toward agreement. We recorded 18 peak instantaneous gradients from dual left ventricular catheters (15 to 95 mm Hg), while simultaneously recording Doppler velocities before and after intervention in 11 pediatric patients (ages 0.5 to 16 years, mean 4.5). Doppler correlated but overestimated catheter-measured peak instantaneous gradients (y = 0.84x + 18.4, r = 0.8, SEE +/- 15.2 mm Hg, mean percent difference 29.9 +/- 36) over the range of catheter gradients measured. Accounting for the Reynolds number successfully collapsed data onto a single curve. Our study confirms in a clinical setting the importance of applying fluid dynamic principles such as the Reynolds number to explain apparent discrepancies between catheter and Doppler gradients. These principles provide a foundation for developing clinically appropriate correction factors.
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We hypothesized that color M-mode (CMM) images could be used to solve the Euler equation, yielding regional pressure gradients along the scanline, which could then be integrated to yield the unsteady Bernoulli equation and estimate noninvasively both the convective and inertial components of the transmitral pressure difference. Pulsed and continuous wave Doppler velocity measurements are routinely used clinically to assess severity of stenotic and regurgitant valves. However, only the convective component of the pressure gradient is measured, thereby neglecting the contribution of inertial forces, which may be significant, particularly for nonstenotic valves. Color M-mode provides a spatiotemporal representation of flow across the mitral valve. In eight patients undergoing coronary artery bypass grafting, high-fidelity left atrial and ventricular pressure measurements were obtained synchronously with transmitral CMM digital recordings. The instantaneous diastolic transmitral pressure difference was computed from the M-mode spatiotemporal velocity distribution using the unsteady flow form of the Bernoulli equation and was compared to the catheter measurements. From 56 beats in 16 hemodynamic stages, inclusion of the inertial term ([deltapI]max = 1.78+/-1.30 mm Hg) in the noninvasive pressure difference calculation significantly increased the temporal correlation with catheter-based measurement (r = 0.35+/-0.24 vs. 0.81+/-0.15, p< 0.0001). It also allowed an accurate approximation of the peak pressure difference ([deltapc+I]max = 0.95 [delta(p)cathh]max + 0.24, r = 0.96, p<0.001, error = 0.08+/-0.54 mm Hg). Inertial forces are significant components of the maximal pressure drop across the normal mitral valve. These can be accurately estimated noninvasively using CMM recordings of transmitral flow, which should improve the understanding of diastolic filling and function of the heart.
Article
Congenital aortic valve stenosis is a common problem in pediatric cardiology. The catheter peak to peak systolic gradient is the accepted standard used for prognosis and intervention, but noninvasive correlation in pediatric patients is frequently associated with underestimation or overestimation of this gradient. The purpose of this study was to compare different noninvasive measurements with simultaneous catheter gradients to identify which best predicts the catheter peak to peak gradient. Twenty-five simultaneous Doppler and catheter measurements of aortic stenosis gradient were performed in 14 children (all 14 before valvuloplasty and 11 after valvuloplasty). Noninvasive estimates of pressure gradient were compared with catheter measurements with linear regression and Bland-Altman analysis. The Doppler peak instantaneous pressure gradient overestimated the catheter peak to peak gradient but correlated well with the catheter peak instantaneous gradient. The Doppler mean systolic gradient correlated well with the catheter peak to peak gradient at low gradients and underestimated higher catheter gradients but agreed well at all levels with the catheter mean gradient. The modification of a catheter-derived correlation equation produced good correlation with the catheter peak to peak gradient (slope, 1.14; intercept, -1.8; R, 0.92), as did the use of estimated pressure recovery (slope, 1.04; intercept, 5.0; R, 0.94), calculated from a defined fluid mechanic equation. The catheter peak to peak gradient can be accurately estimated noninvasively using estimated pressure recovery or correlation equations incorporating Doppler measurements.
Article
Prior validation studies have established that simultaneously measured catheter (cath) and Doppler mean pressure gradients (MPG) correlate closely in evaluation of aortic stenosis (AS). In clinical practice, however, cath and Doppler are rarely performed simultaneously; which may lead to discrepant results. Accordingly, our aim was to ascertain agreement between these methods and investigate factors associated with discrepant results. We reviewed findings in 100 consecutive evaluations for AS performed in 97 patients (mean age 72 +/- 10 yr) in which cath and Doppler were performed within 6 weeks. We recorded MPG, aortic valve area (AVA), cardiac output, and ejection fraction (EF) by both methods. Aortic root diameter, left ventricular end-diastolic dimension (LVIDd) and posterior wall thickness (PWT) were measured by echocardiography and gender, heart rate, and heart rhythm were also recorded. An MPG discrepancy was defined as an intrapatient difference > 10 mmHg. Mean pressure gradients by cath and Doppler were 36 +/- 22 mmHg and 37 +/- 20 mmHg, respectively (P = 0.73). Linear regression showed good correlation (r = 0.82) between the techniques. An MPG discrepancy was found in 36 (36%) of 100 evaluations; in 19 (53%) of 36 evaluations MPG by Doppler was higher than cath, and in 17 (47%) of 36, it was lower. In 33 evaluations, EF differed by >10% between techniques. Linear regression analyses revealed that EF difference between studies was a significant predictor of MPG discrepancy (P = 0.004). Women had significantly higher MPG than men by both cath and Doppler (43 +/- 25 mmHg versus 29 +/- 15 mmHg [P = 0.001]; 42 +/- 23 mmHg versus 32 +/- 15 mmHg [P = 0.014], respectively). Women exhibited discrepant results in 23 (47%) of 49 evaluations versus 13 (25%) of 51 evaluations in men (P = 0.037). After adjustment for women's higher MPG, there was no statistically significant difference in MPG discrepancy between genders (P = 0.22). No significant interactions between MPG and aortic root diameter, relative wall thickness (RWT), heart rate, heart rhythm, cardiac output, and time interval between studies were found. In clinical practice, significant discrepancies in MPG were common when cath and Doppler are performed nonsimultaneously. No systematic bias was observed and Doppler results were as likely yield lower as higher MPGs than cath. EF difference was a significant predictor of discrepant MPG. Aortic root diameter, relative wall thickness, heart rate, heart rhythm, cardiac output, presence or severity of coronary artery disease, and time interval between studies were not predictors of discrepant results.
Article
To assess the accuracy of several noninvasive MRI-based estimators of pulmonary artery pressure by comparing them with invasive pressure measurement. We compared five MRI methods with invasive pressure measurement by catheterization, in one group of pulmonary hypertension (PH) patients. Doppler echocardiography was included as a reference method. Main inclusion criterion was a mean pulmonary artery pressure above 25 mmHg at catheterization. MRI velocity quantification was used to obtain pulmonary flow acceleration and ejection times, and pulse wave velocity. The ventricular mass index was also assessed on MRI. Two commercially available 1.5-T systems were used for this study. Data from 44 patients were analyzed. Correlation of acceleration time with mean pressure was: r = -0.21, P = 0.21, correlation of the acceleration/ejection time ratio with systolic pressure was: r = -0.26, P = 0.01. The ventricular mass index showed the best correlation with mean pressure, with r = 0.56, P < 0.001. Using the pulse wave velocity and the cross-sectional area of the pulmonary artery, the mean pressure could not be estimated accurately. Accurate estimation of pulmonary artery pressure in PH patients was not feasible by the MRI estimators studied. These noninvasive methods cannot replace right heart catheterization at this moment.
Article
Previous studies have suggested the feasibility of a non-invasive quantification of vascular trans-stenotic pressure gradients (DeltaP) by phase-contrast MR imaging (PC-MRI). Our purpose was to assess the value of MRI estimated pressure gradients as a screening tool for assessing hemodynamically significant (re-)coarctation of the aorta (CoA) in pediatric patients. Forty-three patients (median age (range), 16 (5-25) years) with CoA (38 postoperative and 5 native) and clinically suspected hemodynamically significant stenosis underwent quantitative and semi-quantitative PC-MRI blood flow measurements and 3D MR-angiography, Doppler ultrasound (US) and conventional catheter angiography (CCA, n=20). Estimated DeltaP for each modality was correlated with percent stenosis. The percent stenosis correlated only moderately with DeltaP(MRI) (r=0.55, p<0.001) and DeltaP(CCA) (r=0.48, p<0.001). Only moderate correlations were observed between DeltaP(MRI) vs. DeltaP(CCA) (r=0.54, p=0.02) and vs. DeltaP(US) (r=0.40, p=0.01). In contrast, semi-quantitative analysis of PC-MRI flow profiles predicted with good sensitivity (88%) and specificity (88%) who would be operated on. Thirteen patients met hemodynamic and percent stenosis criteria by CCA for surgical intervention. Measured pressure gradients using PC-MRI should be used cautiously when assessing patients for recoarctation of the aorta. The analysis of blood flow profiles by PC-MRI might be a promising alternative in assessing the hemodynamic significance of CoA.
Article
Goals of our study were to compare the pulmonary hemodynamics between healthy volunteers and patients with pulmonary arterial hypertension (PAH) and correlate MR flow measurements with echocardiography. Twenty-five patients with PAH and 25 volunteers were examined at 1.5 T. Phase-contrast flow measurements were performed in the ascending aorta and pulmonary trunk, resulting in the following parameters: peak velocity (cm/s), average blood flow (l/min), time to peak velocity (ms), velocity rise gradient and pulmonary distensibility (cm(2)). The bronchosystemic shunt was calculated. In PAH patients transthoracic echocardiography and right-heart catheterization (RHC) served as the gold standard. In comparison to volunteers, the PAH patients showed significantly reduced pulmonary velocities (P = 0.002), blood flow (P = 0.002) and pulmonary distensibility (P = 0.008). In patients, the time to peak velocity was shorter (P<0.001), and the velocity rise gradient was steeper (P = 0.002) than in volunteers. While in volunteers the peak velocity in the aorta was reached earlier, it was the reverse in patients. Patients showed a significant bronchosystemic shunt (P = 0.01). No meaningful correlation was found between MRI measurements and echocardiography or RHC. MRI is a feasible technique for the differentiation between PAH and volunteers. Further studies have to be conducted for the absolute calculation of pressure estimates.