A new diversity index.

We introduce here a new index of diversity based on consideration of reasonable propositions that such an index should have in order to represent diversity. The behaviour of the index is compared with that of the Gini-Simpson diversity index, and is found to predict more realistic values of diversity for small communities, in particular when each species is equally represented and for small communities. The index correctly provides a measure of true diversity that is equal to the species richness across all values of species and organism numbers when all species are equally represented, as well as Hill's more stringent 'doubling' criterion when they are not. In addition, a new graphical interpretation is introduced that permits a straightforward visual comparison of pairs of indices across a wide range within a parameter space based on species and organism numbers.

Comment on 'Comparative analysis of the isovolume calibration method for non-invasive respiratory monitoring techniques based on area transduction versus circumference transduction using the connected cylinders model' (2011 Physiol. Meas. 32 1265-74).

An analysis introduced by the authors in 2011 examining the robustness of the isovolume method for the calibration of the respiratory inductive plethysmograph based on the connected cylinders particular model of Konno and Mead's generalized two-compartment model of respiration is extended. It is demonstrated that extending this to a more physically realistic geometrical model, termed the connected prismatic elliptical segments model, does not enhance the earlier analysis, and that the analysis can easily be proven to cover all area-based transduction sensors, irrespective of the actual geometry of the compartments.

Comparative analysis of the isovolume calibration method for non-invasive respiratory monitoring techniques based on area transduction versus circumference transduction using the connected cylinders model.

An analytical formalism developed previously to examine the robustness of the isovolume calibration technique for non-invasive respiratory monitoring devices based on measurements of torso circumference (e.g. fibre-optic respiratory plethysmography) is extended here to techniques based on area measurement (e.g. respiratory inductive plethysmography), and the results are compared. The earlier perturbation approach is adopted, and an exact method is also presented. It is demonstrated that the area-based techniques have less dependence on the cylindrical compartmental parameters of radius and height, and are independent of compartmental volume if height variations are negligible, in contrast to circumference-based techniques. It is also demonstrated that both the area- and the circumference-based techniques provide similar inferences of volume when calibrated using the isovolume method under reasonable assumptions for the dimensions of the compartments that constitute a model of the torso.

Evaluation of cardiac monitoring using fiber optic plethysmography.

A fiber optic plethysmograph (FOP) has been redesigned and used to monitor cardiac activity in real time during apnoea. The device was tested using four healthy subjects aged between 23 and 31, and it is concluded that the device performs reliably. Advanced algorithms have been developed and implemented to perform the cardiac signal extraction. A strong correlation is noted between the signals derived using the FOP and the respiratory inductive plethysmograph (RIP) when the latter has also been applied to monitor cardiac activity. The approach developed for interpreting thoracocardiograms (TCGs) and abdominocardiograms (ACGs) derived from the RIP is therefore directly applicable to the interpretation of the corresponding FOP signals. The prospect of using the FOP system for real-time gating in a magnetic resonance (MR) scanner environment is discussed.

Improved fibre optic respiratory monitoring using a figure-of-eight coil.

The macro-bending loss effect in optical fibres has been used to redevelop a sensor for the measurement of thoracic and abdominal circumferences in non-invasive respiratory monitoring. The new sensor uses a novel figure-of-eight loop configuration, which results in increased linearity of response, less mechanical resistance and hysteresis, as well as other benefits. The performance of the new sensor as applied to respiratory monitoring is examined, and indicates a higher resolution and sensitivity than the old. This enhanced performance enables measurement of respiratory and cardiac function using the same transducing fibre.

A theoretical study of the robustness of the isovolume calibration method for a two-compartment model of breathing, based on an analysis of the connected cylinders model.

The use of the isovolume manoeuvre method as a calibration technique for respiratory monitoring instrumentation that detects the movement of the ribcage and the abdominal wall is analysed based on a model of two connected cylinders whose radii and heights may vary, and evidence is presented which suggests that this calibration method is robust in most circumstances. Some possible functional forms relating the variations in cylinder radius and height are examined, and methods for obtaining calibration constants based on these functional forms, purely from measurements of variations in the cylinder radius, are presented.