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The computational detection of pulmonary lobes from CT images is a challenging segmentation problem with important respiratory health care applications, including surgical planning and regional image analysis. Several authors have proposed automated algorithms and we present a methodological review. These algorithms share a number of common stages and we consider each stage in turn, comparing the methods applied by each author and discussing their relative strengths. No standard method has yet emerged and none of the published methods have been demonstrated across a full range of clinical pathologies and imaging protocols. We discuss how improved methods could be developed by combining different approaches, and we use this to propose a workflow for the development of new algorithms., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

The Grodins model of respiratory control (Grodins et al., 1967) describes cardio-respiratory control for a lung with homogeneous gas concentrations. In this study we modify the Grodins model to take account of the inhomogeneities in gas concentration within the lung that are seen in many subjects with respiratory illnesses. This modification has the effect of lowering arterial oxygen partial pressure significantly. We investigate the effect on cardio-respiratory control of this low arterial oxygen signal and find that the governing equations may be reduced to a single delay-differential equation. This reduced model is found to be a good approximation to the full model and gives predictions that are similar to reported clinical data.

We investigate the effects on arterial P(CO(2)) and on arterial-end tidal P(CO(2)) difference of six different ventilation patterns of equal tidal volume, and also of various combinations of tidal volume and respiratory rate that maintain a constant alveolar ventilation. We use predictions from three different mathematical models. Models 1 (distributed) and 2 (compartmental) include combined convection and diffusion effects. Model 3 incorporates a single well-mixed alveolar compartment and an anatomical dead-space in which plug flow occurs. We found that: (i) breathing patterns with longer inspiratory times yield lower arterial P(CO(2)); (ii) varying tidal volume and respiratory rate so that alveolar ventilation is kept constant may change both PA(CO(2)) and the PA(CO(2))-PET(CO(2)) difference; (iii) the distributed model predicts higher end-tidal and arterial P(CO(2)) than the compartmental models under similar conditions; and (iv) P(CO(2)) capnograms predicted by the distributed model exhibit longer phase I and steeper phase II than other models.

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error., (Copyright 2001 Academic Press.)

The tidal breathing model conservation of mass equations for the sinewave technique have been described for a homogeneous alveolar compartment by Gavaghan and Hahn, 1996 [Gavaghan, D.J., Hahn, C.E.W., 1996. A tidal breathing model of the forced inspired gas sinewave technique. Respir. Physiol. 106, 209-221]. We develop these equations first to a multi-discrete alveolar compartment lung model and then to a lung model with a continuous distribution of volume, ventilation and perfusion. The effect on the output parameters of a multi-compartment model is discussed, and the results are compared to those derived from the conventional continuous-ventilation model. Using the barely soluble gas argon as the tracer gas, an empirical index of alveolar inhomogeneity is presented which uses the end-expired and mixed-expired partial pressures on each breath. This index distinguishes between a narrow unimodal distribution of ventilation-volume, a wide unimodal distribution of ventilation-volume and a bimodal distribution of ventilation-volume. By using Monte Carlo simulations, this index is shown to be stable to experimental error of realistic magnitude.

The coupled conservation of mass equations for oxygen, carbon dioxide and nitrogen are written down for a lung model consisting of two homogeneous alveolar compartments (with different ventilation-perfusion ratios) and a shunt compartment. As inspired oxygen concentration and oxygen consumption are varied, the flux of oxygen, carbon dioxide and nitrogen across the alveolar membrane in each compartment varies. The result of this is that the expired ventilation-perfusion ratio for each compartment becomes a function of inspired oxygen concentration and oxygen consumption as well as parameters such as inspired ventilation and alveolar perfusion. Another result is that the "inspired ventilation-perfusion ratio and the "expired ventilation-perfusion ratio differ significantly, under some conditions, for poorly ventilated lung compartments. As a consequence, we need to distinguish between the "inspired ventilation-perfusion distribution, which is independent of inspired oxygen concentration and oxygen consumption, and the "expired ventilation-perfusion distribution, which we now show to be strongly dependent on inspired oxygen concentration and less dependent oxygen consumption. Since the multiple inert gas elimination technique (MIGET) estimates the "expired ventilation-perfusion distribution, it follows that the distribution recovered by MIGET may be strongly dependent on inspired oxygen concentration., (Copyright 2000 Academic Press.)

We consider two and 50 compartment lung models for use with two techniques used to investigate the efficiency of the lungs: the Multiple Breath Nitrogen Washout (MBNW) technique used for investigating the ventilation-volume distribution; and the Multiple Inert Gas Elimination Technique (MIGET) used for investigating the ventilation-perfusion distribution. In each of these techniques pulmonary respiratory gas exchange is described by conservation of mass equations which may be written in identical form, and in each the underlying distributions of ventilation to volume and ventilation to perfusion are assumed to be continuous functions (usually assumed to be a linear sum of log-normal distributions). The mathematical models used to describe the lung have predominantly used a collection of discrete compartments to approximate these continuous distributions. The most commonly used models have used one, two or 50 compartments. In this paper, we begin by showing that in the limit as the width of the peaks of the distribution tend to zero, the continuous distributions may be replaced by a single discrete compartment placed at each peak of the distribution. We investigate the various methods used previously for parameter recovery, and show that one commonly used method for the MBNW is not suitable and suggest a modification to this recovery technique. Using simulated error-free data, we show that both the two compartment model and the 50 compartment model contain information about the ventilation-volume (or ventilation-perfusion) distribution, and investigate the extent to which this information can be used to recover the parameters which define these distributions. We go on to use Monte-Carlo methods to investigate the stability of the recovery process., (Copyright 1998 Academic Press)

In a model lung, airways dead-space can be accurately measured using a forced inspired oscillating argon signal, which varies sinusoidally about a mean concentration of 6% v/v with an amplitude of +/- 4% v/v. With sinusoid forcing periods longer than 120 seconds, and at a breathing rate of 13.4 breaths minute-1, the mean airways dead-space can be measured with a standard error of less than 5%. Sinusoid forcing periods shorter than 120 s provided inaccurate estimates of dead-space and so should not be used with this technique.