To the Editor:—
I read with considerable interest the article by Benavides et al. 1describing experiments of air bubble growth in water during exposure to 100% nitrous oxide, 100% xenon, or 50% xenon–50% oxygen. Although the experiments were nicely conducted, they explore a physics of gas flux in an unconstrained bubble permitted to grow spherically. Importantly, this geometry has limited biologic relevance for bubbles occluding vessels in the size range they have studied. The authors have referenced our previous work on xenon transport,2but they have mistakenly interpreted the findings presented therein to indicate the growth of bubbles as spheres. Rather, that study presents some simulations for bubbles that are initially spherical and just fill the vessel lumen. Such bubbles cannot grow radially because they are constrained by the vessel wall and therefore elongate during growth while maintaining a fixed curvature on the interface. This results in a much different force balance across the gas–liquid interface and, hence, a different pressure condition on the interior of the bubble from that which occurs in the case of a time-varying interfacial shape, which the authors have studied. We have described these differences in our previous theoretical and experimental studies of intravascular gas embolism.2–5
In addition, the initial internal gas content they have studied includes nitrogen, equilibrated with test solution A, but test solution B is nitrogen free. Hence, there are large gradients for nitrogen flux when the solutions are switched. We purposely avoided nitrogen as a component of either the bubble or perfusate in our predictions and considered only oxygen and xenon as the transportable species.2Whereas others have studied growth of similarly unconstrained air bubbles during cardiopulmonary bypass,6our work has not provided any data for direct comparisons such as the authors have made, based on the different gas constituents and the governing physics dictated by the shape constraint.
I find it fascinating, however, that they have couched their results in terms of bubble diameter growth. When transferred to the volume domain, one readily sees that the spherical bubbles exposed to 100% xenon or 100% nitrous oxide had grown to more than twice their initial volume in 25 min (figs. 2 and 3) and continued growing when the solutions were switched (downward arrow). The time required for this is surprisingly similar to the volume doubling times we reported for many of the cases we explored, despite the differences in our model and these experiments.
The curve fitting by a double exponential suggests that there will be continuous exponential growth of bubble diameter. So although the physics and gas transport are different from what we studied, the indication of the studies are the same.
University of Pennsylvania, Philadelphia, Pennsylvania. firstname.lastname@example.org