The Herschel-Quincke tube with modulated branches.

The Herschel-Quincke (HQ) tube concept for transmission loss in pipe systems is expanded to include cases of branches with modulated properties. Modulated waveguides, featuring corrugations in their geometry or speed of sound, are known to produce significant reflection even without the parallel branch of the HQ tube. The HQ tube, in its classical form, produces narrow banded transmission loss at frequencies related to the length, wavenumber and cross-section area of the parallel branch. The modulated Herschel-Quincke (MHQ) tube combines these attributes to produce enhanced transmission loss characteristics in terms of both width and number of transmission loss bands. Several modulated profiles for the speed of sound in different branches of the tube are considered and analytical expressions for the transmission loss and resonant conditions are derived. Detailed analysis of periodically stratified branch profiles demonstrates the effectiveness of the MHQ tube for fluid-borne noise attenuation in pipe systems. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'.

Respiratory muscles performance is related to oxygen kinetics during maximal exercise and early recovery in patients with congestive heart failure.

BACKGROUND: Dyspnea and fatigue are the main causes of exercise limitation in chronic heart failure (CHF) patients, whose peak inspiratory (Pi(max)) and expiratory pressures (Pe(max)) are often reduced. The aim of this study was to examine the relationship between respiratory muscle performance and oxygen kinetics. METHODS AND RESULTS: A total of 55 patients (NYHA class I to III) and 11 healthy subjects underwent cardiopulmonary exercise tests (CPET) on a treadmill. In 45 of the 55 patients (group I) and in healthy subjects (group II), pulmonary function tests, Pi(max), and Pe(max) were measured before and 10 minutes after exercise, and oxygen kinetics were monitored throughout and during early recovery from CPET. The first degree slope of oxygen consumption (VO(2)) decline during early recovery (VO(2)/t-slope) and VO(2) half-time (T(1/2)) were calculated. In 10 of the 55 CHF patients (group III), the measurements of Pi(max) were repeated 2, 5, and 10 minutes after CPET. A >10% reduction in Pi(max) after CPET (subgroup IA) was measured in 11 of 45 patients. In contrast, 34 of 45 CHF patients (subgroup IB) and all control subjects (group II) had Pi(max)>90% of baseline value after CPET. Subgroup IA patients had significantly lower peak VO(2) (13.5+/-2.1 versus 17.8+/-5.6 mL. kg(-1). min(-1); P<0.001), lower anaerobic thresholds (10.1+/-2.4 versus 13.6+/-4.6 mL. kg(-1). min(-1); P=0.003) and lower VO(2)/t-slopes (0.365+/-0.126 versus 0.519+/-0.227 L. min(-1). min(-1); P=0.008) than subgroup IB patients. CONCLUSIONS: The reduction of Pi(max) after exercise is associated with prolonged early recovery of oxygen kinetics, which may explain, in part, the role played by respiratory muscles in exercise intolerance in CHF patients.