Growth of a gas bubble in a perfused tissue in an unsteady pressure field with source or sink.

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.

The concentration distribution around a growing gas bubble in a bio tissue under the effect of suction process.

The concentration distribution around a growing nitrogen gas bubble in the blood and other bio tissues of divers who ascend to surface too quickly is obtained by Mohammadein and Mohamed model (2010) for variant and constant ambient pressure through the decompression process. In this paper, the growing of gas bubbles and concentration distribution under the effect of suction process are studied as a modification of Mohammadein and Mohamed model (zero suction). The growth of gas bubble is affected by ascent rate, tissue diffusivity, initial concentration difference, surface tension and void fraction. Mohammadein and Mohamed model (2010) is obtained as a special case from the present model. Results showed that, the suction process activates the systemic blood circulation and delay the growth of gas bubbles in the bio tissues to avoid the incidence of decompression sickness (DCS).

Concentration distribution around a growing gas bubble in tissue.

This paper presents the concentration distribution around a growing nitrogen gas bubble in the blood and other tissues of divers who surface too quickly, when the ambient pressure through the decompression process is variable and constant. This effort is a modification of Sirinivasan et al. model (1999) [9]. The mathematical model is solved analytically to find the growth rate of a gas bubble in a tissue after decompression in the ambient pressure. Moreover, the concentration distribution around the growing bubble is introduced. The growth process is affected by ascent rate alpha (t), tissue diffusivity D(T), initial concentration difference DeltaC(0), surface tension sigma and void fraction varphi(0).