Modeling subharmonic response from contrast microbubbles as a function of ambient static pressure.

Variation of subharmonic response from contrast microbubbles with ambient pressure is numerically investigated for non-invasive monitoring of organ-level blood pressure. Previously, several contrast microbubbles both in vitro and in vivo registered approximately linear (5-15 dB) subharmonic response reduction with 188 mm Hg change in ambient pressure. In contrast, simulated subharmonic response from a single microbubble is seen here to either increase or decrease with ambient pressure. This is shown using the code BUBBLESIM for encapsulated microbubbles, and then the underlying dynamics is investigated using a free bubble model. The ratio of the excitation frequency to the natural frequency of the bubble is the determining parameter--increasing ambient pressure increases natural frequency thereby changing this ratio. For frequency ratio below a lower critical value, increasing ambient pressure monotonically decreases subharmonic response. Above an upper critical value of the same ratio, increasing ambient pressure increases subharmonic response; in between, the subharmonic variation is non-monotonic. The precise values of frequency ratio for these three different trends depend on bubble radius and excitation amplitude. The modeled increase or decrease of subharmonic with ambient pressure, when one happens, is approximately linear only for certain range of excitation levels. Possible reasons for discrepancies between model and previous experiments are discussed.