Does diaphragmatic breathing technique really improve its range of motion? An objective assessment

Purpose - To verify the results of a diaphragmatic breathing technique (DBT) on diaphragmatic range of motion in healthy subjects. Methods - A total of 51 healthy subjects (10 male; 41 female), mean age 20 years old and a body mass index (BMI) ranging from 15.6 to 34.9 kg/m2, were enrolled in this study. Diaphragmatic range of motion was assessed by M-mode ultrasound imaging. Measurements were made before and after the DBT implementation in a standard protocol, based on 3 seconds of inspiration starting from a maximum expiration. Differences between assessments were analyzed by descriptive statistics and t-test (p < 0.05). Results - Mean value range of motion before DBT was 55.3 ± 13.4 mm and after DBT was 63.8 ± 13.2 mm showing a significant improvement of 8.5 ± 14.7 mm (p < 0.001). A strong correlation between the slope and the range of motion was found (r = 0.71, p < 0.001). Conclusions - Based on ultrasound measurements, it has been proved that DBT really contributes to a higher diaphragmatic range of motion. Future studies are needed in order to understand the influence of protocol parameters (e.g. inspiration time). Clinical implications - In the contest of evidence-based practice in physiotherapy, it has been showed by objective measurements that DBT improves the diaphragm range of motion, translating into a more efficient ventilatory function and thus can be used in clinical setting. To our knowledge this is the first study to assess the effects of DBT on range of motion of diaphragm muscle with ultrasound imaging.

On the requirements of interpolating polynomials for path motion constraints

In the framework of multibody dynamics, the path motion constraint enforces that a body follows a predefined curve being its rotations with respect to the curve moving frame also prescribed. The kinematic constraint formulation requires the evaluation of the fourth derivative of the curve with respect to its arc length. Regardless of the fact that higher order polynomials lead to unwanted curve oscillations, at least a fifth order polynomials is required to formulate this constraint. From the point of view of geometric control lower order polynomials are preferred. This work shows that for multibody dynamic formulations with dependent coordinates the use of cubic polynomials is possible, being the dynamic response similar to that obtained with higher order polynomials. The stabilization of the equations of motion, always required to control the constraint violations during long analysis periods due to the inherent numerical errors of the integration process, is enough to correct the error introduced by using a lower order polynomial interpolation and thus forfeiting the analytical requirement for higher order polynomials.

Simple thermodynamics of jet engines

We use the first and second laws of thermodynamics to analyze the behavior of an ideal jet engine. Simple analytical expressions for the thermal efficiency, the overall efficiency, and the reduced thrust are derived. We show that the thermal efficiency depends only on the compression ratio r and on the velocity of the aircraft. The other two performance measures depend also on the ratio of the temperature at the turbine to the inlet temperature in the engine, T-3/T-i. An analysis of these expressions shows that it is not possible to choose an optimal set of values of r and T-3/T-i that maximize both the overall efficiency and thrust. We study how irreversibilities in the compressor and the turbine decrease the overall efficiency of jet engines and show that this effect is more pronounced for smaller T-3/T-i.