Dynamics and acoustics of a spherical bubble rising under gravity in an inviscid liquid.

The rising motion and the acoustic emission of a pulsating spherical gas/vapour bubble in an isochoric, inviscid liquid are investigated. The motion is driven by the uniform and constant force field due to the gravity. The liquid is assumed at rest at the initial time. Unlike previous work on this subject, the mass of the bubble is not neglected, so that the bubble motion is accurately simulated also in the presence of large volume variations. After developing the relationships between the bubble motion to the liquid flow, a system of two nonlinear ordinary differential equations (ODEs) for the radius and the position of the center of mass of the bubble is written. The near-field pressure disturbance produced in the liquid by the bubble motion is evaluated by means of elliptic integrals and an efficient approximation of it free from these special functions is also used. The numerical integration of the ODE system allows one to evaluate the acoustic signal. This is carried out with the above mentioned approximation, and several features of it are demonstrated through the study of a sample flow.

The 6-minute walking test and all-cause mortality in patients undergoing a post-cardiac surgery rehabilitation program.

BACKGROUND: The 6-minute walking test (6mWT) is used to prescribe physical activity in cardiac surgery patients. The clinical value of a pre-discharge 6mWT and its association with outcome is not well defined. DESIGN AND METHODS: We retrospectively analyzed data from 313 patients (age 66 ± 11 years, 23% females, left ventricular ejection fraction (LVEF) 52 ± 11%, Hb 10.5 ± 1.3 g/dl, serum albumin 3.9 ± 0.4 mg/dl) who were admitted to our rehabilitation institute following cardiac surgery. A 6mWT was performed at entry and at discharge and expressed as % of theoretical predicted values calculated on the basis of individual age, height, weight and sex. The endpoint was represented by all-cause mortality. The predictive value of 6mWT was tested in univariate and multivariate analysis. RESULTS: A pre-discharge 6mWT was completed by 284 out of 313 patients. Two patients died in hospital. During a median of 23 months, mortality was 9% (26/284) and 44% (12/27) (p < 0.0001) in patients who did or did not perform the pre-discharge 6mWT. The distance covered at the pre-discharge 6mWT as a continuous variable of % predicted values was a significant predictor of subsequent mortality (Hazard Ratio (HR) 0.97 (95% CI 0.96-0.99), p = 0.0019). After adjustment for all preselected covariates, the pre-discharge 6mWT (HR 0.97 (95% CI 0.95-0.99), p = 0.0038) and LVEF (HR 0.93 (95% CI 0.90-0.96), p < 0.0001) remained significantly associated with the outcome. CONCLUSIONS: In recent cardiac surgery patients, the pre-discharge 6mWT is not only a valid measurement of the impact of cardiac rehabilitation but also provides outcome information offering the possibility to identify patients who may need more intensive follow-up.

"Peak Summation" Left Ventricular Filling Pattern in Patients with Chronic Heart Failure: Frequency and Complementary Value of Pulmonary Venous Flow in Its Hemodynamic Interpretation.

In patients with chronic heart failure (CHF) and a "peak summation" left ventricular pattern, no hemodynamic and prognostic information can be drawn from Doppler examination of mitral flow. In 263 consecutive patients with CHF who were undergoing simultaneous right heart catheterization and echo-Doppler examination, we prospectively determined (1) the frequency of the peak summation left ventricular filling pattern and (2) the incremental information contributed by pulmonary venous flow velocity patterns in providing noninvasive hemodynamic profile estimation. Isovolumic relaxation time of mitral flow, peak systolic (X), diastolic forward (Y), reverse (Z) flow velocity, and systolic fraction (X/X + Y) of pulmonary venous flow were measured. Forty-six of 263 (17%) patients had a peak summation left ventricular filling pattern. This subgroup showed more clinical deterioration (New York Heart Association functional class III-IV, 57% vs 49%; P < 0.01) and left atrial dysfunction (left atrial ejection fraction, 31% vs 39%; P < 0.001). However, 40% of these patients had a pulmonary wedge pressure of <18 mmHg and a cardiac index of >2.2 L/min/m(2). The systolic fraction of peak velocities of pulmonary venous flow showed a good correlation with pulmonary wedge pressure (r = -0.70, P < 0.05). The correlation was stronger in patients without mitral regurgitation (r = -0.81, P < 0.05). A systolic fraction of <40% was accurate (sensitivity, 100%; specificity, 95%) in identifying patients with a pulmonary wedge pressure of >18 mmHg. In patients without mitral regurgitation, this variable was also correlated with cardiac index (r = -0.65, P < 0.05) and predicted a cardiac index of >2.2 L/min/m(2) (sensitivity, 91%; specificity, 71%). In conclusion, a peak summation left ventricular filling pattern is common in patients with CHF. Pulmonary venous flow provides useful information about the hemodynamic profile of these patients.