In the context of decompression sickness, this paper presents analytical formulae and explanations for growth of a gas bubble in blood and other tissues in an unsteady diffusion field with a source or a sink. The formulae are valid for variable (through decompression) and constant (concerning diving stops/at sea level) ambient pressure. Under a linear decompression regime for ambient pressure, the gas bubble growth is proportional to ascent rate, tissue diffusivity and initial tissue tension and inversely proportional to surface tension, initial ambient pressure and the strength of the source/sink parameter [Formula: see text] which gives the conditions for bubble growth. We find that the growth process is noticeably affected by changing k-values within a specified range, with no significant effect on the value of the bubble radius when k is outside this range. We discuss the effect of the presence of multiple bubbles, and of repetitive diving. Of the three available models for bubble growth, the predicted time to completion is longest in the model by Srinivasan et al. (J Appl Physiol 86:732-741, 1999), where the bubble grows in a steady diffusion field, but shortest in the model we describe for k-values closest to the boundaries of the interval [Formula: see text]. This is because our model considers the effect of the presence of a source, increasing the bubble growth rate and not taken into account in our previous (2010) model predicting an intermediate timeframe for bubble growth. We believe our new model provides a more accurate and widely applicable description of bubble growth in decompression sickness than previous versions.

中文翻译：

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在源或汇不稳定的压力场中，灌注组织中气泡的生长。

在减压病的背景下，本文提供了在具有源或汇的不稳定扩散场中血液和其他组织中气泡生长的分析公式和解释。该公式对于可变（通过减压）和恒定（关于潜水站/在海平面）环境压力有效。在环境压力的线性减压条件下，气泡的生长与上升速率，组织扩散度和初始组织张力成正比，与表面张力，初始环境压力和源/汇参数的强度成反比[公式：请参见文本]这为泡沫增长提供了条件。我们发现，在指定范围内更改k值会明显影响生长过程，当k超出此范围时，对气泡半径的值没有明显影响。我们讨论了多个气泡的存在以及重复潜水的影响。在三个可用的气泡增长模型中，Srinivasan等人的模型中，预计完成时间最长。（J Appl Physiol 86：732-741，1999），其中气泡在稳定的扩散场中生长，但是在我们描述的模型中，最短的是k值最接近区间的边界[公式：请参见文本]。这是因为我们的模型考虑了源的影响，增加了气泡的增长率，而在我们之前（2010年）的模型中没有考虑到气泡增长的中间时间，因此没有考虑到这一点。