Obstructive lung diseases in the lower airways are a leading health concern worldwide. To improve our understanding of the pathophysiology of lower airways, we studied airflow characteristics in the lung between the 8th and the 14th generations using a three-dimensional computational fluid dynamics model, where we compared normal and obstructed airways for a range of breathing conditions. We employed a novel technique based on computing the Pearson?s correlation coefficient to quantitatively characterize the differences in airflow patterns between the normal and obstructed airways. We found that the airflow patterns demonstrated clear differences between normal and diseased conditions for high expiratory flow rates (>2300ml/s), but not for inspiratory flow rates. Moreover, airflow patterns subjected to filtering demonstrated higher sensitivity than airway resistance for differentiating normal and diseased conditions. Further, we showed that wall shear stresses were not only dependent on breathing rates, but also on the distribution of the obstructed sites in the lung: for the same degree of obstruction and breathing rate, we observed as much as two-fold differences in shear stresses. In contrast to previous studies that suggest increased wall shear stress due to obstructions as a possible damage mechanism for small airways, our model demonstrated that for flow rates corresponding to heavy activities, the wall shear stress in both normal and obstructed airways was <0.3Pa, which is within the physiological limit needed to promote respiratory defense mechanisms. In summary, our model enables the study of airflow characteristics that may be impractical to assess experimentally.
Although gating of mechanoelectrical transducer (MET) channels has been successfully described by assuming that one channel is associated with a tip link in the hair bundle, recent reports indicate that a single tip link is associated with more than one channel. To address the consistency of the model with the observations, gating of MET channels is described here by assuming that each tip link is associated with two identical MET channels, which are connected either in series or in parallel. We found that series connection does not lead to a single minimum of stiffness with respect to hair bundle displacement unless the minimum is above a certain positive value. Thus, negative stiffness must appear in pairs in the displacement axis. In contrast, parallel connection of the two channels predicts gating compliance similar to that predicted by the one-channel-per-tip-link model of channel gating, within the physiological range of parameters. Parallel connection of MET channels is, therefore, a reasonable assumption to explain most experimental observations. However, the compatibility with series connection cannot be ruled out for experimental data on turtle hair cells.
A "release" mechanism, which has been experimentally observed as the fast component in the hair bundles response to mechanical stimulation, appears similar to common mechanical relaxation with a damping effect. This observation is puzzling because such a response is expected to have an amplifying role in the mechanoelectrical transduction process in hair cells. Here it is shown that a release mechanism can indeed have a role in amplification, if it is associated with negative stiffness due to the gating of the mechonoelectric transducer channel.
The effectiveness of hair bundle motility in mammalian and avian ears is studied by examining energy balance for a small sinusoidal displacement of the hair bundle. The condition that the energy generated by a hair bundle must be greater than energy loss due to the shear in the subtectorial gap per hair bundle leads to a limiting frequency that can be supported by hair-bundle motility. Limiting frequencies are obtained for two motile mechanisms for fast adaptation, the channel re-closure model and a model that assumes that fast adaptation is an interplay between gating of the channel and the myosin motor. The limiting frequency obtained for each of these models is an increasing function of a factor that is determined by the morphology of hair bundles and the cochlea. Primarily due to the higher density of hair cells in the avian inner ear, this factor is approximately 10-fold greater for the avian ear than the mammalian ear, which has much higher auditory frequency limit. This result is consistent with a much greater significance of hair bundle motility in the avian ear than that in the mammalian ear.
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