Ultrasound beam steering of oxygen nanobubbles for enhanced bladder cancer therapy

New intravesical treatment approaches for bladder cancer are needed as currently approved treatments show several side effects and high tumor recurrence rate. Our study used MB49 murine urothelial carcinoma model to evaluate oxygen encapsulated cellulosic nanobubbles as a novel agent for imaging and ultrasound guided drug delivery. In this study, we show that oxygen nanobubbles (ONB) can be propelled (up to 40 mm/s) and precisely guided in vivo to the tumor by an ultrasound beam. Nanobubble velocity can be controlled by altering the power of the ultrasound Doppler beam, while nanobubble direction can be adjusted to different desired angles by altering the angle of the beam. Precise ultrasound beam steering of oxygen nanobubbles was shown to enhance the efficacy of mitomycin-C, resulting in significantly lower tumor progression rates while using a 50% lower concentration of chemotherapeutic drug. Further, dark field imaging was utilized to visualize and quantify the ONB ex vivo. ONBs were found to localize up to 500 µm inside the tumor using beam steering. These results demonstrate the potential of an oxygen nanobubble drug encapsulated system to become a promising strategy for targeted drug delivery because of its multimodal (imaging and oxygen delivery) and multifunctional (targeting and hypoxia programming) properties.


Fig. S1: Contour plot for cell viability (%) w/o beam steering (top and bottom respectively).
Ultrasound Doppler beam significantly reduced cell viability when ONB-MMC were both at medium concentrations.    Method S1. Theoretical model to predict the behavior of nanobubbles and fundamental mechanisms governing beam steering.
A theoretical model to predict the velocity ONBs was developed, taking into account the nature of the media (urine inside the bladder), comprehensively approximating the pressure profile inside the bladder and, finally, incorporating the significant forces acting on the bubble. The forces considered in this model are Bjerkens force, buoyance force, drag force and gravitational force. The primary Bjerkens is responsible for the translational motion of the bubble and results from out of phase bubble oscillations and ultrasound wave oscillations. Buoyancy force, known as the force exerted by the fluid on an object immersed in it, equals the weight of the liquid displaced by the bubble. Drag force is acting opposite to the direction of the bubble movement in the fluid. Gravitational force acting on the nanobubble is neglected due to the infinitesimal mass of the bubble.

Bjerkens Force.
The frequency of the wave, the base pressure (amplitude) corresponding to the transducer used are known and are constant. The distance between the transducer and the bubble can be easily approximated. An accepted standard in the field of acoustics is an assumption that the pressure wave is made of small amplitude oscillations and is written as following: By inspecting equation (1), relative magnitudes of the terms wt and kz were estimated. Since k = , where c is the speed of light in urine (for reference, the speed of sound in water is 1484 m/s). z, which represents the distance along the bladder, has a magnitude of 10 −3 m. It becomes clear that the magnitude of wt is significantly larger than that of kz; thus, kz can be omitted from the equation to simplify initial modeling.
The wave equation thus becomes the following: Since the volume of the bubble was assumed to be constant (oscillations are negligible, bubble mean radius is a considerably smaller than the wavenumber), mean Bjerkens force is as follows: Since the volume of the bubble is assumed to be constant, the average Bjerkens force acting on the bubble can be written as: The buoyancy force is constant, and can be expressed as follows:

Drag Force.
Average velocity of the bubble was used to calculate Reynold number to characterize the type of flow. The average velocity was found to be 6.6 mm/s at 40% power and 22 mm/s at 100 % power. Thus, the Reynolds number was computed as follows: Where 'ρ' is density of urine, 'v' is velocity of the nanobubble, 'D' is nanobubble diameter, and µ is the dynamic viscosity of urine. This calculation yielded a Reynolds number of 3.75×10 -3 .
Since laminar flow exists when Re < 0.1, the drag force can be estimated as follows: where, 6 bR   'η' is the urine viscosity and 'R' is radius of nanobubble.
The resulting net force can thus be expressed as following: Since the objective of the model is to describe the velocity profile of the bubble, the defining differential equation of Newton's law was used and the net force acting on the bubble was plugged into the equation.