A Multi-Phasic, Continuum Damage Mechanics Model of Mechanically Induced Increased Permeability in Tissues
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A Multi-Phasic, Continuum Damage Mechanics Model of Mechanically Induced Increased Permeability in Tissues* Brian E. O'Neill1, Timothy P. Quinn1, Victor Frenkel2 and King C. P. Li2 1 Materials Reliability Div., National Institute of Standards and Technology, Boulder CO 80305 2 Diagnostic Radiology Dept., Clinical Center, National Institutes of Health, Bethesda MD 20892 ABSTRACT Recently, we have reported enhanced permeability of tissues due to in vivo treatment with pulsed high intensity focused ultrasound (pHIFU). This new therapy has shown promise as a way of increasing the penetration of large drug molecules, both out of the vasculature and through the tissue. To date, no clear physical model of tissue exists that can account for these effects. A new model is proposed that clearly establishes the link between tissue structure and fluid flow properties on one hand, and the history of applied mechanical forces on the other. The model draws inspiration from two different theoretical fields of materials science, multi-phase theory and continuum damage mechanics. The theory differs from the traditional bi-phasic solidfluid model of tissues in that the fluid part here is broken into trapped (moving with the solid) and free (moving through the solid) parts. A damage-like variable links the effective elasticity of the tissue to the ratio of the trapped to free fluids. As the damage increases, the tissue becomes, in effect, less stiff and more permeable. Release of elastic energy drives the process. A distribution of energy barriers opposes the process and governs how the fluid is released as damage increases. INTRODUCTION Most current therapeutic applications of high intensity focused ultrasound (HIFU) involve continuous application, which promotes temperature elevations sufficient to cause tissue ablation in the focal zone [1]. Recently, more attention has been paid to pulsed mode high intensity focused ultrasound (pHIFU), which can introduce significant mechanical stresses without significant thermal elevation. Although instantaneous energy deposition remains high during each pulse, the time-average energy deposition is much lower. This means that the short timescale visco-elastic processes become more important than the long timescale thermal processes. Whereas very high intensity pulses (>4000 W/cm2) are known to cause cavitation and subsequent pulverization and erosion of tissue [2], lower intensities (
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