Modulation of the interstitial fluid pressure by high intensity focused ultrasound as a way to alter local fluid and solute movement: insights from a mathematical model.

High intensity focused ultrasound (HIFU) operated in thermal mode has been reported to reduce interstitial fluid pressure and improve the penetration of large macromolecules and nanoparticles in tumor and normal tissue. Little is understood about how the interstitial fluid pressure and velocity as well as the interstitial macromolecule transport are affected by HIFU exposure. A mathematical model is presented here which sheds light on the initial biophysical changes brought about HIFU. Our continuum model treats tissue as an effective poro-elastic material that reacts to elevated temperatures with a rapid drop in interstitial elastic modulus. Using parameters from the literature, the model is extrapolated to derive information on the effect in tumors, and to predict its impact on the convective and diffusive transport of macromolecular drugs. The model is first solved using an analytical approximation with step-wise changes at each boundary, and then solved numerically starting from a Gaussian beam approximation of the ultrasound treatment. Our results indicate that HIFU causes a rapid drop in interstitial fluid pressure that may be exploited to facilitate convection of macromolecules from vasculature to the exposed region. However, following a short recovery period in which the interstitial fluid pressure is normalized, transport returns to normal and the advantages disappear over time. The results indicate that this effect is strongest for the delivery of large molecules and nanoparticles that are in the circulation at the time of treatment. The model may be easily applied to more complex situations involving effects on vascular permeability and diffusion.

Modeling focused ultrasound exposure for the optimal control of thermal dose distribution.

Preclinical studies indicate that focused ultrasound at exposure conditions close to the threshold for thermal damage can increase drug delivery at the focal region. Although these results are promising, the optimal control of temperature still remains a challenge. To address this issue, computer-simulated ultrasound treatments have been performed. When the treatments are delivered without taking into account the cooling effect exerted by the blood flow, the resulting thermal dose is highly variable with regions of thermal damage, regions of underdosage close to the vessels, and areas in between these two extremes. When the power deposition is adjusted so that the peak thermal dose remains close to the threshold for thermal damage, the thermal dose is more uniformly distributed but under-dosage is still visible around the thermally significant vessels. The results of these simulations suggest that, for focused ultrasound, as for other delivery methods, the only way to control temperature is to adjust the average energy deposition to compensate for the presence of thermally significant vessels in the target area. By doing this, we have shown that it is possible to reduce the temperature heterogeneity observed in focused ultrasound thermal treatments.

An optimum method for pulsed high intensity focused ultrasound treatment of large volumes using the InSightec ExAblate® 2000 system.

Pulsed high intensity focused ultrasound (pHIFU) is a method for delivering ultrasound to tissue while avoiding high temperatures. The technique has been suggested for non-destructively enhancing local uptake of drugs. Side effects include thermal necrosis; therefore, real-time monitoring of tissue temperature is advantageous. This paper outlines a method for improving the treatment efficiency of pHIFU using the MR image-guided InSightec ExAblate® 2000 system, an ultrasound system integrated into a whole body human MRI scanner with the ability to measure temperature at the treatment location in near real time. Thermal measurements obtained during treatment of a tissue phantom were used to determine appropriate heating parameters, and compared to in vivo treatment of rabbit muscle. Optimization of the treatment procedure and ultrasound transducer steering patterns was then conducted with the goal of minimizing treatment time while avoiding overheating. The optimization was performed on the basis of approximate solutions to the standard bioheat equation. The commercial system software of the Exablate® system was modified to assist in this optimization. Depending on the size of the treatment volume, the presented results demonstrate that it is possible to use the technique described to cut treatment times significantly, up to one-third of that required by the current standard treatment cycle.

Linear behavior of a preformed microbubble containing light absorbing nanoparticles: insight from a mathematical model.

Microbubbles are used as ultrasonic contrast agents in medical imaging because of their highly efficient scattering properties. Gold nanoparticles absorb specific wavelengths of optical radiation very effectively with the subsequent generation of thermo-acoustic waves in the surrounding medium. A theoretical and numerical analysis of the possibility of inducing radial oscillations in a pre-existing spherical microbubble, through the laser excitation of gold nanoparticles contained within, is presented. A description of such a system can be obtained in terms of a confined two-phase model, with the nanoparticles suspended in a confined region of gas, surrounded by a liquid. The Rayleigh-Plesset equation is assumed to be valid at the boundary between the gas and the liquid. The confined two-phase model is solved in linear approximation. The system is diagonalized and the general solution is obtained. This solution is in the form of exponentially decaying oscillatory functions for the temperature and pressure inside the bubble, and radial oscillations of the bubble boundary. It was found that, for the right size of bubbles, the oscillatory behavior takes place in the low megahertz range, which is ideal for medical applications. This study suggests the possibility of new applications of microbubbles in photoacoustic imaging.

Numerical investigation of heating of a gold nanoparticle and the surrounding microenvironment by nanosecond laser pulses for nanomedicine applications.

We have modeled, by finite element analysis, the process of heating of a spherical gold nanoparticle by nanosecond laser pulses and of heat transfer between the particle and the surrounding medium, with no mass transfer. In our analysis, we have included thermal conductivity changes, vapor formation, and changes of the dielectric properties as a function of temperature. We have shown that such changes significantly affect the temperature reached by the particle and surrounding microenvironment and therefore the thermal and dielectric properties of the medium need to be known for a correct determination of the temperature elevation. We have shown that for sufficiently low intensity and long pulses, it is possible to establish a quasi-steady temperature profile in the medium with no vapor formation. As the intensity is increased, a phase-change with vapor formation takes place around the gold nanoparticle. As phase-transition starts, an additional increase in the intensity does not significantly increase the temperature of the gold nanoparticle and surrounding environment. The temperature starts to rise again above a given intensity threshold which is particle and environment dependent. The aim of this study is to provide useful insights for the development of molecular targeting of gold nanoparticles for applications such as remote drug release of therapeutics and photothermal cancer therapy.