Asymptotic solutions of the Helmholtz equation: generalised Friedlander-Keller ray expansions of fractional order

Applications of a WKBJ-type `ray ansatz' to obtain asymptotic solutions of the Helmholtz equation in the high{frequency limit are now standard, and underpin the construction of `geometrical optics' ray diagrams in many electromagnetic, acoustic and elastic reflection, transmission and other scattering problems. These applications were subsequently extended by Keller to include other types of rays - called `diffracted' rays - to provide an accessible and impressively accurate theory which is relevant in wide-ranging sets of circumstances. Friedlander and Keller then introduced a modified ray ansatz to extend yet further the scope of ray theory and its applicability to certain other classes of diffraction problems (tangential ray incidence upon an obstructing boundary, for instance), and did so by the inclusion of an extra term proportional to a power of the wavenumber within the exponent of the initial ansatz. Our purpose here is to generalise this further still by the inclusion of several such terms, ordered in a natural sequence in terms of strategically-chosen fractional powers of the large wavenumber, and to derive a systematic sequence of boundary value problems for the coefficient phase functions that arise within this generalised exponent, as well as one for the leading-order amplitude occurring as a pre-exponential factor. One particular choice of fractional power is considered in detail, and waves with specified radially-symmetric or planar wavefronts are then analysed, along with a boundary value problem typifying two-dimensional radiation whereby arbitrary phase and amplitude variations are specified on a prescribed boundary curve. This theory is then applied to the scattering of plane and cylindrical waves at curved boundaries with small-scale perturbations to their underlying profile

Do changes in pulmonary capillary wedge pressure adequately reflect myocardial ischemia during anesthesia? a correlative preoperative hemodynamic, electrocardiographic, and transesophageal echocardiographic study

Pulmonary capillary wedge pressure (PCWP) is monitored during anesthesia in an attempt to detect changes in myocardial function in patients at risk of preoperative cardiac complications. Because the sensitivity with which preoperative PCWP monitoring indicates myocardial ischemia is uncertain, we monitored PCWP, 12-lead electrocardiogram, and left ventricular wall motion abnormalities as defined by transesophageal echocardiography (TEE) in 98 anesthetized patients before coronary artery bypass grafting. Measurements were made five times in each patient, before and after induction of anesthesia. Myocardial ischemia was identified by TEE in 14 patients; in 10 of these, it was associated with concomitant ST segment depression of at least 1 mm. The onset of ischemia, as defined by TEE, was accompanied by a mean increase in PCWP of 3.5 +/- 4.8 mm Hg, as compared with a mean change of 0 +/- 2.2 mm Hg between observations not associated with the onset of ischemia (p less than 0.01). An increase in PCWP of at least 3 mm Hg, tested as an indicator of ischemia, had a sensitivity of 25% and a positive predictive value of 15%; after correction for background changes associated with anesthetic induction, the sensitivity of this indicator was 33%, and its positive predictive value was 16%. These figures were not improved by selecting cutoff points higher or lower than 3 mm Hg. In this study, the onset of myocardial ischemia was associated with a small yet significant increase in mean PCWP at group level

Do changes in pulmonary capillary wedge pressure adequately reflect myocardial ischemia during anesthesia? A correlative preoperative hemodynamic, electrocardiographic, and transesophageal echocardiographic study.

Pulmonary capillary wedge pressure (PCWP) is monitored during anesthesia in an attempt to detect changes in myocardial function in patients at risk of preoperative cardiac complications. Because the sensitivity with which preoperative PCWP monitoring indicates myocardial ischemia is uncertain, we monitored PCWP, 12-lead electrocardiogram, and left ventricular wall motion abnormalities as defined by transesophageal echocardiography (TEE) in 98 anesthetized patients before coronary artery bypass grafting. Measurements were made five times in each patient, before and after induction of anesthesia. Myocardial ischemia was identified by TEE in 14 patients; in 10 of these, it was associated with concomitant ST segment depression of at least 1 mm. The onset of ischemia, as defined by TEE, was accompanied by a mean increase in PCWP of 3.5 +/- 4.8 mm Hg, as compared with a mean change of 0 +/- 2.2 mm Hg between observations not associated with the onset of ischemia (p less than 0.01). An increase in PCWP of at least 3 mm Hg, tested as an indicator of ischemia, had a sensitivity of 25% and a positive predictive value of 15%; after correction for background changes associated with anesthetic induction, the sensitivity of this indicator was 33%, and its positive predictive value was 16%. These figures were not improved by selecting cutoff points higher or lower than 3 mm Hg. In this study, the onset of myocardial ischemia was associated with a small yet significant increase in mean PCWP at group level

The Assessment of 24-Hr Physical Behavior in Children and Adolescents via Wearables: A Systematic Review of Laboratory Validation Studies

Purpose: To raise attention to the quality of published validation protocols while comparing (in)consistencies and providing an overview on wearables, and whether they show promise or not. Methods: Searches from five electronic databases were included concerning the following eligibility criteria: (a) laboratory conditions with humans (<18 years), (b) device outcome must belong to one dimension of the 24-hr physical behavior construct (i.e., intensity, posture/activity type outcomes, biological state), (c) must include a criterion measure, and (d) published in a peer-reviewed English language journal between 1980 and 2021. Results: Out of 13,285 unique search results, 123 articles were included. In 86 studies, children <13 years were recruited, whereas in 26 studies adolescents (13–18 years) were recruited. Most studies (73.2%) validated an intensity outcome such as energy expenditure; only 20.3% and 13.8% of studies validated biological state or posture/activity type outcomes, respectively. We identified 14 wearables that had been used to validate outcomes from two or three different dimensions. Most (n = 72) of the identified 88 wearables were only validated once. Risk of bias assessment resulted in 7.3% of studies being classified as “low risk,” 28.5% as “some concerns,” and 71.5% as “high risk.” Conclusion: Overall, laboratory validation studies of wearables are characterized by low methodological quality, large variability in design, and a focus on intensity. No identified wearable provides valid results across all three dimensions of the 24-hr physical behavior construct. Future research should more strongly aim at biological state and posture/activity type outcomes, and strive for standardized protocols embedded in a validation framework