Anderson Joseph C, Babb Albert L, Hlastala Michael P
Department of Chemical Engineering, University of Washington, Seattle, WA 98195, USA.
J Appl Physiol (1985). 2005 Mar;98(3):850-5. doi: 10.1152/japplphysiol.00801.2004. Epub 2004 Nov 12.
We analyzed published measurements of the bronchial circulation and airway wall (Anderson JC, Bernard SL, Luchtel DL, Babb AL, and Hlastala MP. Respir Physiol Neurobiol 132: 329-339, 2002) and determined that the radial distribution of bronchial capillary cross-sectional area was fractal. We limited our analysis to bronchial capillaries, diameter < or =10 mum, that resided between the epithelial basement membrane and adventitia-alveolar boundary, the airway wall tissue. Thirteen different radial distributions of capillary-to-tissue area were constructed simply by changing the number of annuli (i.e., the annular size) used to form each distribution. For the 13 distributions created, these annuli ranged in size from to of the size of the airway wall area. Radial distributions were excluded from the fractal analysis if the sectioning procedure resulted in an annulus with a radial thickness less than the diameter of a capillary. To determine the fractal dimension for a given airway, the coefficient of variation (CV) for each distribution was calculated, and ln(CV) was plotted against the logarithm of the relative piece area. For airways with diameter >2.4 mm, this relationship was linear, which indicated the radial distribution of bronchial capillary cross-sectional area was fractal with an average fractal dimension of 1.27. The radial distribution of bronchial capillary cross-sectional area was not fractal around airways with diameter <1.5 mm. We speculated on how the fractal nature of this circulation impacts the distribution of bronchial blood flow and the efficiency of mass transport during health and disease. A fractal analysis can be used as a tool to quantify and summarize investigations of the bronchial circulation.
我们分析了已发表的支气管循环和气道壁的测量数据（安德森·J·C、伯纳德·S·L、卢赫特尔·D·L、巴布·A·L和赫拉斯拉拉·M·P。《呼吸生理学与神经生物学》132: 329 - 339，2002年），并确定支气管毛细血管横截面积的径向分布是分形的。我们将分析局限于直径≤10μm的支气管毛细血管，这些毛细血管位于上皮基底膜和外膜 - 肺泡边界之间，即气道壁组织内。通过简单改变用于形成每种分布的环带数量（即环形大小），构建了13种不同的毛细血管与组织面积的径向分布。对于所创建的13种分布，这些环带的大小范围为气道壁面积大小的[具体范围未给出]。如果切片过程导致一个环带的径向厚度小于毛细血管直径，则将该径向分布排除在分形分析之外。为了确定给定气道的分形维数，计算每种分布的变异系数（CV），并将ln(CV)与相对片段面积的对数作图。对于直径>2.4mm的气道，这种关系是线性的，这表明支气管毛细血管横截面积的径向分布是分形的，平均分形维数为1.27。直径<1.5mm的气道周围支气管毛细血管横截面积的径向分布不是分形的。我们推测了这种循环的分形性质如何影响健康和疾病状态下支气管血流的分布以及物质运输效率。分形分析可作为一种工具，用于量化和总结对支气管循环的研究。
