An experimental investigation to model wheezing in lungs.

A quarter of the world's population experience wheezing. These sounds have been used for diagnosis since the time of the Ebers Papyrus (ca 1500 BC). We know that wheezing is a result of the oscillations of the airways that make up the lung. However, the physical mechanisms for the onset of wheezing remain poorly understood, and we do not have a quantitative model to predict when wheezing occurs. We address these issues in this paper. We model the airways of the lungs by a modified Starling resistor in which airflow is driven through thin, stretched elastic tubes. By completing systematic experiments, we find a generalized 'tube law' that describes how the cross-sectional area of the tubes change in response to the transmural pressure difference across them. We find the necessary conditions for the onset of oscillations that represent wheezing and propose a flutter-like instability model for it about a heavily deformed state of the tube. Our findings allow for a predictive tool for wheezing in lungs, which could lead to better diagnosis and treatment of lung diseases.

The elastic theory of shells using geometric algebra.

We present a novel derivation of the elastic theory of shells. We use the language of geometric algebra, which allows us to express the fundamental laws in component-free form, thus aiding physical interpretation. It also provides the tools to express equations in an arbitrary coordinate system, which enhances their usefulness. The role of moments and angular velocity, and the apparent use by previous authors of an unphysical angular velocity, has been clarified through the use of a bivector representation. In the linearized theory, clarification of previous coordinate conventions which have been the cause of confusion is provided, and the introduction of prior strain into the linearized theory of shells is made possible.

Using geometric algebra to represent curvature in shell theory with applications to Starling resistors.

We present a novel application of rotors in geometric algebra to represent the change of curvature tensor that is used in shell theory as part of the constitutive law. We introduce a new decomposition of the change of curvature tensor, which has explicit terms for changes of curvature due to initial curvature combined with strain, and changes in rotation over the surface. We use this decomposition to perform a scaling analysis of the relative importance of bending and stretching in flexible tubes undergoing self-excited oscillations. These oscillations have relevance to the lung, in which it is believed that they are responsible for wheezing. The new analysis is necessitated by the fact that the working fluid is air, compared to water in most previous work. We use stereographic imaging to empirically measure the relative importance of bending and stretching energy in observed self-excited oscillations. This enables us to validate our scaling analysis. We show that bending energy is dominated by stretching energy, and the scaling analysis makes clear that this will remain true for tubes in the airways of the lung.

Estimating missing marker positions using low dimensional Kalman smoothing.

Motion capture is frequently used for studies in biomechanics, and has proved particularly useful in understanding human motion. Unfortunately, motion capture approaches often fail when markers are occluded or missing and a mechanism by which the position of missing markers can be estimated is highly desirable. Of particular interest is the problem of estimating missing marker positions when no prior knowledge of marker placement is known. Existing approaches to marker completion in this scenario can be broadly divided into tracking approaches using dynamical modelling, and low rank matrix completion. This paper shows that these approaches can be combined to provide a marker completion algorithm that not only outperforms its respective components, but also solves the problem of incremental position error typically associated with tracking approaches.

Influence of pulmonary factors on pulse oximeter saturation in preterm infants.

AIM: To describe how the stability of oxygen saturation measured by pulse oximetry (SpO2%) varies within and between infants with bronchopulmonary dysplasia (BPD). METHODS: Clinically stable infants with BPD had SpO2 measured at different inspired oxygen concentrations (FIO2 expressed as %). A computer model of gas exchange, that is, ventilation/perfusion ratio (VA/Q) and shunt, plotted the curve of SpO2 versus FIO2 best fitting these data. The slope of this curve is the change in SpO2 per % change in FIO2, hence SpO2 stability, calculated at each SpO2 from 85% to 95%. RESULTS: Data from 16 infants with BPD previously described were analysed. The dominant gas exchange impairment was low VA/Q (median 0.35, IQR, 0.16-0.4, normal 0.86). Median shunt was 1% (IQR, 0-10.5; normal <2%). Slope varied markedly between infants, but above 95% SpO2 was always <1.5. In infants with least severe BPD (VA/Q ≈0.4, shunt ≤2%) median slope at 85% SpO2 was 5.1 (IQR, 3.7-5.5). With more severe BPD (VA/Q ≤0.3) slope was flatter throughout the SpO2 range. The highest FIO2 for 90% SpO2 was in infants with the lowest VA/Q values. CONCLUSIONS: In infants with BPD, there was large variation in the slope of the curve relating SpO2% to inspired oxygen fraction in the SpO2 range 85%-95%. Slopes were considerably steeper at lower than higher SpO2, especially in infants with least severe BPD, meaning that higher SpO2 target values are intrinsically much more stable. Steep slopes below 90% SpO2 may explain why some infants appear dependent on remarkably low oxygen flows.

Restoration of images from the scanning-tunneling microscope.

During the acquisition of an image from any probe microscope instrument, various noise sources cause distortion in the observed image. It is often the case that impulsive disturbances cause bright groups of pixels to replace the actual image data in these locations. Furthermore, the images from a probe microscope show some amount of blurring caused both by the instrument function and the material properties. In almost all image-processing applications it is important to remove any impulsive distortion that may be present before deblurring can be attempted. We give a technique for detecting these impulses and reconstructing the image. This technique is superior to the standard global application of median filters for the case considered. The reconstruction is limited only to the affected regions and therefore results in a much sharper and more meaningful image. With the assumption of Gaussian blur it is then possible to propose several different deblurring methodologies. We present a novel Wiener-filter deblurring implementation and compare it to both maximum-entropy and Richardson-Lucy deblurring.