The Natural Frequency of Nonlinear Oscillation of Ultrasound Contrast Agents in Microvessels

Abstract

Ultrasound Contrast Agent (UCAs) are under intensive investigation for their applications in physiological and molecular imaging and drug delivery. Prediction of the natural frequency of the oscillation of UCAs in microvessels has drawn increasing attention. To our knowledge, the existing models to predict the natural frequency of oscillation of UCAs in microvessels all apply the linear approximation and treat the blood vessel wall as a rigid boundary. In the potential applications of ultrasound imaging drug and gene delivery, the compliance of small vessels may play an important role in the bubble's oscillation. The goal of this work is to provide a lumped-parameter model to study the natural frequency of nonlinear oscillation of UCAs in microvessels. Three types of the blood vessel conditions have been considered. i.e. rigid vessels, normal compliable vessels and vessels with increasing stiffness that could correspond to tumor vasculature. The corresponding bubble oscillation frequencies in the vessels with radius less than 100 μm are examined in detail. When a bubble with a radius of 4 μm is confined in a compliable vessel (inner radius 5 μm and length 100μm), the natural frequency of bubble oscillation increases by a factor of 1.7 as compared with a bubble in an unbounded field. The natural frequency of oscillation of a bubble in a compliable vessel increases with decreasing vessel size while decreasing with increasing values of vessel rigidity. This model suggests that contrast agent size, blood vessel size distribution and the type of vasculature should be comprehensively considered for choosing the transmitted frequency in ultrasound contrast imaging and drug delivery.

The mechanism of interaction between focused ultrasound and microbubbles in blood-brain barrier opening in mice

“…The highest percentage of mice with dark neurons is in the case of 4-5 lm bubbles. As the resonance frequency of 4-5 lm bubbles embedded in a compliant vessel is close to 1.5 MHz, 26 i.e., the FUS frequency used in this study, the inertial cavitation at this bubble size may induce more damage.…”

“…For a bubble constrained in a vessel, regardless of the shell property, the resonance frequency increases when the bubble size decreases. 25,26 For example, when the bubble is confined in a compliant, 10-lm-diameter vessel, its resonance frequency at a diameter of 2, 4, 6, and 8 lm is 3.92, 1.93, 1.41, and 1.26 MHz, respectively. 26 Therefore, the FUS frequency used in this study (1.5 MHz) is close to the resonance frequency of 4-5 lm bubbles.…”

“…25,26 For example, when the bubble is confined in a compliant, 10-lm-diameter vessel, its resonance frequency at a diameter of 2, 4, 6, and 8 lm is 3.92, 1.93, 1.41, and 1.26 MHz, respectively. 26 Therefore, the FUS frequency used in this study (1.5 MHz) is close to the resonance frequency of 4-5 lm bubbles. High-speed camera findings have also indicated that the pressure threshold of bubble fragmentation increases with bubble size.…”

Mechanisms of microbubble–vessel interactions and induced stresses: A numerical study

“…A number of confined bubble models have been developed over the years. [19][20][21] However, these models either neglected shell effects, assumed a spherical bubble, or they lacked the usage of appropriate vessel properties. While these models are suitable for low acoustic pressures and bubble spherical oscillations, at relatively high acoustic pressures ($1 MPa) the bubble in a small blood vessel deviates from its spherical shape and forms an ellipsoid.…”

Air entrapment and drop formation in piezo inkjet printing

“…However, many important cases of bubble dynamics occur under constraint conditions, in finite volumes of liquid, rather than infinite volumes, such as in confined spaces and near a wall [23][24][25][26]. Examples include the behavior of gas bubbles in blood vessels, aiming at improving ultrasound diagnostics and treatment [27], or thermal inkjet printing and other microfluidic …”