R. C. Schroter

FLOW PATTERNS IN MODELS OF THE HUMAN BRONCHIAL AIRWAYS

Abstract Flow profiles were studied in two successive generations of large scale symmetrical models of typical junctions of the human bronchial tree (steady flows, Re = 100 to 1500). Inspiratory and expiratory flows were investigated with either flat or parabolic profiles entering the first branch. Downstream, profiles were obtained in the plane of the bifurcation and normal to it. Flow patterns were visualised for the range Re = 50 to 4500. Secondary motions were observed at all flow rates, their form depending upon direction of flow. Depending upon the curvature of the junction, flow separation with sluggish reversed flow could be observed in daughter tubes during inspiration. Inspiratory flow velocity profiles are highly asymmetric. In the plane of the junction, peak velocities swing to the inner walls. During expiration velocity profiles normal to the junction plane become flat while profiles in the plane develop an axial peak. The results suggest that flow patterns are complex and parabolic flow cannot be assumed.

The prediction of pressure drop and variation of resistance within the human bronchial airways.

Abstract Pressure drop and distribution of resistance within the lower airways on inspiration are predicted, from the theory developed earlier, for a wide range of flow rates using a symmetrical rigid model of the anatomy of the bronchial tree based upon data from lungs fixed at 75 % TLC. The resistance depends upon flow rate, the major part being in the trachea and larger bronchi. Airways beyond generation 10 (diameter approximately 0.5 mm) contribute less than 10% to lower AWR. The overall pressure drops obtained are in close agreement with experimental observations.The relationship between pressure and flow is given by ΔP = K (ρμ) 1 2 V V 3 2 where K is a constant depending only on lung anatomy. This relationship is non-linear and concave to the pressure axis. The non-linearity may not be apparent at flow rates below 2 L/sec.Theequation allows prediction of the effect of gas mixtures on airway resistance, where results again agree with most experimental values available, and overcomes the difficulties associated with theuse of Rohrers equation. The relation between AWR and lung volume is examined. Assuming the airways are all equally compliant thin-walled elastic tubes, the expected hyperbolic relation between lung volume and AWR is obtained. This agrees closely with recent measurements of lower airway resistance in atropinised subjects.

Mechanics of airflow in the human nasal airways

The mechanics of airflow in the human nasal airways is reviewed, drawing on the findings of experimental and computational model studies. Modelling inevitably requires simplifications and assumptions, particularly given the complexity of the nasal airways. The processes entailed in modelling the nasal airways (from defining the model, to its production and, finally, validating the results) is critically examined, both for physical models and for computational simulations. Uncertainty still surrounds the appropriateness of the various assumptions made in modelling, particularly with regard to the nature of flow. New results are presented in which high-speed particle image velocimetry (PIV) and direct numerical simulation are applied to investigate the development of flow instability in the nasal cavity. These illustrate some of the improved capabilities afforded by technological developments for future model studies. The need for further improvements in characterising airway geometry and flow together with promising new methods are briefly discussed.

Is airway closure caused by a liquid film instability

A physical model for small airway closure is developed, based on the assumption that closure occurs as a result of a surface tension-induced instability of the thin liquid film lining the airways. To distinguish this mechanism from others involving airway compliance, experiments were performed in rigid tubes, 1 mm in diameter, with length-to-diameter ratios between one and ten. Oil was added to the film in small increments and photographed at each stage. For total liquid volumes (V) less than some critical value (Vc) surface tension draws the oil into an axi-symmetric film on the tube walls leaving the lumen relatively unobstructed. When V exceeds Vc, the film becomes unstable and collapses, bridging the lumen and causing obstruction. The ratio of Vc to the tube diameter cubed was found to be approximately 0.7 for the entire range of tube lengths studied. These experimental findings were then used to predict airway closure in a morphometric model of the bronchial tree. Assuming that the liquid film at TLC is 10 microns and that the volume of each airway varies in direct proportion to lung volume, the model predicts that airway closure will first occur in the terminal bronchioles at a lung volume of 23% TLC, in approximate agreement with observed values of residual volume.

Energy losses and pressure drop in models of human airways

Abstract The work done by the pressure drop in forcing fluid through a system of tubes is balanced by changes in kinetic energy and by viscous energy dissipation. From measured inspiratory flow profiles in symmetrical models of typical junctions of the human bronchial tree, the viscous energy dissipation downstream of a junction is computed, and is always greater than in Poiseuille flow. It varies with distance downstream and with Reynolds number (Re). We formulate a theory of the factors governing dissipation which agrees with the experimental results. The ratio of actual energy dissipation to Poiseuille dissipation (Z) is given by Δ P=K (ρμ) 1 2 V 3 2 (d = tube diameter, L = length) where C is a constant, =1.85 for the branching angle and area ratios of our model. This can be used to predict the overall pressure drop in a branched system provided that kinetic energy changes are included.

Flow and pressure drop in systems of repeatedly branching tubes

The airways of the lung form a rapidly diverging system of branched tubes, and any discussion of their mechanics requires an understanding of the effects of the bifurcations on the flow downstream of them. Experiments have been carried out in models containing up to two generations of symmetrical junctions with fixed branching angle and diameter ratio, typical of the human lung. Flow visualization studies and velocity measurements in the daughter tubes of the first junction verified that secondary motions are set up, with peak axial velocities just outside the boundary layer on the inner wall of the junction, and that they decay slowly downstream. Axial velocity profiles were measured downstream of all junctions at a range of Reynolds numbers for which the flow was laminar. In each case these velocity profiles were used to estimate the viscous dissipation in the daughter tubes, so that the mean pressure drop associated with each junction and its daughter tubes could be inferred. The dependence of the dissipation on the dimensional variables is expected to be the same as in the early part of a simple entrance region, because most of the dissipation will occur in the boundary layers. This is supported by the experimental results, and the ratio Z of the dissipation in a tube downstream of a bifurcation to the dissipation which would exist in the same tube if Poiseuille flow were present is given by \[ Z = (C/4\surd{2})(Re\,d/L)^{\frac{1}{2}}, \] where L and d are the length and diameter of the tube, Re is the Reynolds number in it, and the constant C (equal to one for simple entry flow) is equal to 1·85 (the average value from our experiments). In general, C is expected to depend on the branching angles and diameter ratios of the junctions used. No experiments were performed in which the flow was turbulent, but it is argued that turbulence will not greatly affect the above results at Reynolds numbers less than and of the order of 10000. Many more experiments are required to consolidate this approach, but predictions based upon it agree well with the limited number of physiological experiments available.

Nasal architecture: form and flow

Current approaches to model nasal airflow are reviewed in this study, and new findings presented. These new results make use of improvements to computational and experimental techniques and resources, which now allow key dynamical features to be investigated, and offer rational procedures to relate variations in anatomical form. Specifically, both replica and simplified airways of a single subject were investigated and compared with the replica airways of two other individuals with overtly differing geometries. Procedures to characterize and compare complex nasal airway geometry are first outlined. It is then shown that coupled computational and experimental studies, capable of obtaining highly resolved data, reveal internal flow structures in both intrinsically steady and unsteady situations. The results presented demonstrate that the intimate relation between nasal form and flow can be explored in greater detail than hitherto possible. By outlining means to compare complex airway geometries and demonstrating the effects of rational geometric simplification on the flow structure, this work offers a fresh approach to studies of how natural conduits guide and control flow. The concepts and tools address issues that are thus generic to flow studies in other physiological systems.

Transport Phenomena in the Human Nasal Cavity: A Computational Model

AbstractNasal inspiration is important for maintaining the internal milieu of the lung, since ambient air is conditioned to nearly alveolar conditions (body temperature and fully saturated with water vapor) on reaching the nasopharynx. We conducted a two-dimensional computational study of transport phenomena in model transverse cross sections of the nasal cavity of normal and diseased human noses for inspiration under various ambient conditions. The results suggest that during breathing via the normal human nose there is ample time for heat and water exchange to enable equilibration to near intraalveolar conditions. A normal nose can maintain this equilibrium under extreme environments (e.g., hot/humid, cold/dry, cold/humid). The turbinates increase the rate of local heat and moisture transport by narrowing the passageways for air and by induction of laminar swirls downstream of the turbinate wall. However, abnormal blood supply or mucous generation may reduce the rate of heat or moisture flux into the inspired air, and thereby affect the efficacy of the process.

Inflow boundary profile prescription for numerical simulation of nasal airflow

Knowledge of how air flows through the nasal passages relies heavily on model studies, as the complexity and relative inaccessibility of the anatomy prevents detailed in vivo measurement. Almost all models to date fail to incorporate the geometry of the external nose, instead employing a truncated inflow. Typically, flow is specified to enter the model domain either directly at the nares (nostrils), or via an artificial pipe inflow tract attached to the nares. This study investigates the effect of the inflow geometry on flow predictions during steady nasal inspiration. Models that fully replicate the internal and external nasal airways of two anatomically distinct subjects are used as a reference to compare the effects of common inflow treatments on physiologically relevant quantities including regional wall shear stress and particle residence time distributions. Inflow geometry truncation is found to affect flow predictions significantly, though slightly less so for the subject displaying more pronounced passage area contraction up to the internal nasal valve. For both subject geometries, a tapered pipe inflow provides a better approximation to the natural inflow than a blunt velocity profile applied to the nares. Computational modelling issues are also briefly outlined, by comparing quantities predicted using different surface tessellations, and by evaluation of domain-splitting techniques.

Frequency domain analysis of heart rate variability in horses at rest and during exercise

The pattern of variation in heart rate on a beat-to-beat basis contains information concerning sympathetic (SNS) and parasympathetic (PNS) contributions to autonomic nervous system (ANS) modulation of heart rate (HR). In the present study, heart period (RR interval) time series data were collected at rest and during 3 different treadmill exercise protocols from 6 Thoroughbred horses. Frequency and spectral power were determined in 3 frequency bands: very low (VLF) 0-< or = 0.01, low (LO) >0.01-< or = 0.07 and high (HI) >0.07-< or = 0.5 cycles/beat. Indicators of sympathetic (SNSI = LO/HI) and parasympathetic (PNSI = HI/TOTAL) activity were calculated. Power in all bands fell progressively with increasing exercise intensity from rest to trot. At the gallop VLF and LO power continued to fall but HI power rose. SNSI rose from rest to walk, then fell with increasing effort and was lowest at the gallop. PNSI fell from rest to walk, then rose and was highest at the gallop. Normalised HI power exceeded combined VLF and LO power at all gaits, with the ratio HI to LO power being lowest at the walk and highest at the gallop. ANS indicators showed considerable inter-horse variation, and varied less consistently than raw power with increasing physical effort. In the horses studied, the relationship between power and HR changed at exercise intensities associated with heart rates above approximately 120-130 beats/min. At this level, humoral and other non-neural mechanisms may become more important than autonomic modulation in influencing heart rate and heart rate variability (HRV). HRV at intense effort may be influenced by respiratory-gait entrainment, energetics of locomotion and work of breathing. HRV analysis in the frequency domain would appear to be of potential value as a noninvasive means of assessing autonomic modulation of heart rate at low exercise intensities, only. The technique may be a sensitive method for assessing exercise response to experimental manipulations and disease states.