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. Author manuscript; available in PMC: 2009 Feb 8.

Published in final edited form as: Ultrasound Med Biol. 2007 May 3;33(7):1140–1148. doi: 10.1016/j.ultrasmedbio.2006.12.009

The bubble natural frequency as a function of the vessel inner radius for bubbles lying in the center of rigid vessels with L = 500μm: (a) dimensional natural frequency; (b) dimensionless natural frequency, which is the normalized natural frequency of a bubble in the corresponding unbounded field predicted by the Rayleigh-Plesset equation $f_{0} = \frac{1}{2 π} \sqrt{\frac{3 κ (p_{0} + 2 σ / a_{0})}{ρ a_{0}^{2}} - \frac{2 σ}{ρ a_{0}^{3}}}$ .

The bubble natural frequency as a function of the vessel inner radius for bubbles lying in the center of rigid vessels with L = 500μm: (a) dimensional natural frequency; (b) dimensionless natural frequency, which is the normalized natural frequency of a bubble in the corresponding unbounded field predicted by the Rayleigh-Plesset equation $f_{0} = \frac{1}{2 π} \sqrt{\frac{3 κ (p_{0} + 2 σ / a_{0})}{ρ a_{0}^{2}} - \frac{2 σ}{ρ a_{0}^{3}}}$ .