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A Theragnostic HIFU Transducer and System for Inherently Registered Imaging and Therapy
A Theragnostic HIFU Transducer and System for Inherently Registered Imaging and Therapy
A Theragnostic HIFU Transducer and System for Inherently Registered Imaging and Therapy
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II. METHODS AND MATERIALS. A. Theory of VA Imaging and Acoustic Radiation Force. To better understand the proposed method in this study, it is worth having an in-depth revisit of theVAimaging in theory. The VA imaging requires precise vibrations within a small targeted volume so that acoustic emission signals could be produced and detected for high resolution imaging. Acoustic radiation force(ARF) is normally applied to induce the vibrations. The ARF is a time-averaged force exerted by the acoustic field, which is fundamentally generated by transferring the propagating wave energy into the tissue in the form of momentum. This transformation can only happen when there are attenuations in the medium, such as acoustic scattering and absorption. If a plane wave propagation is assumed, the radiation force F can be expressed as, where E is the time-averaged energy density of the incident wave at the targeted volume within the object tissue; S is the projected area of the object, and dr is the vector drag coefficient representing the scattering and absorbing properties of the tissue. For a particular acoustic stimulation device or system, the parameters E and S can be approximately considered to be stable factors and well controlled. It is the dr, which is closely related to the tissue's acoustic properties, that could be manifested by the resulting acoustic radiation force F. Noted that the E has to be dynamic to generate the time-varying force for tissue vibration. To relate (1) with typical parameters such as acoustic pressure in the acoustic field, it requires solutions to the basic nonlinear equations of fluid dynamics. Simplified deviations based on a plane wave propagation can be achieved by series expansion of the pressure p, density q and velocity u: The first-order terms p1 and q1 for pressure and density respectively in (2) are assumed to be much smaller than the corresponding terms p0 and q0 that are the values in the equilibrium; the second-order terms p2 and q2 are also much smaller than the first-order terms. The particle velocity u0 in the equilibrium is zero. When only the particle motion in the wave propagating direction(z component) is considered, we have. Let the first-order terms represent the linear planewave acoustic field. Based on the equation of momentum conservation, also called the motion equation, the radiation force applied on a unit volume is related to the mean change of its momentum. As the radiation force is related to time-averaged effect, after inserting (2) into (4) and doing the time-averaging calculations, we can get. Where the angle brackets b represent time averaging. If we expand the right side of the equation and only keep the terms no smaller than the second order, (5) becomes. It should be noted that the time-averaged first terms q1 and uz1 are zero because they are harmonic time-vibrating variables as shown in (3).
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1 II. 2 METHODS AND MATERIALS. 3 A. Theory of VA Imaging and Acoustic Radiation Force. 4 To better understand the proposed method in this study, it is worth having an in-depth revisit of theVAimaging in theory. 5 The VA imaging requires precise vibrations within a small targeted volume so that acoustic emission signals could be produced and detected for high resolution imaging. 6 Acoustic radiation force(ARF) is normally applied to induce the vibrations. 7 The ARF is a time-averaged force exerted by the acoustic field, which is fundamentally generated by transferring the propagating wave energy into the tissue in the form of momentum. 8 This transformation can only happen when there are attenuations in the medium, such as acoustic scattering and absorption. 9 If a plane wave propagation is assumed, the radiation force F can be expressed as, where E is the time-averaged energy density of the incident wave at the targeted volume within the object tissue; S is the projected area of the object, and dr is the vector drag coefficient representing the scattering and absorbing properties of the tissue. 10 For a particular acoustic stimulation device or system, the parameters E and S can be approximately considered to be stable factors and well controlled. 11 It is the dr, which is closely related to the tissue's acoustic properties, that could be manifested by the resulting acoustic radiation force F. Noted that the E has to be dynamic to generate the time-varying force for tissue vibration. 12 To relate (1) with typical parameters such as acoustic pressure in the acoustic field, it requires solutions to the basic nonlinear equations of fluid dynamics. 13 Simplified deviations based on a plane wave propagation can be achieved by series expansion of the pressure p, density q and velocity u: The first-order terms p1 and q1 for pressure and density respectively in (2) are assumed to be much smaller than the corresponding terms p0 and q0 that are the values in the equilibrium; the second-order terms p2 and q2 are also much smaller than the first-order terms. 14 The particle velocity u0 in the equilibrium is zero. 15 When only the particle motion in the wave propagating direction(z component) is considered, we have. 16 Let the first-order terms represent the linear planewave acoustic field. 17 Based on the equation of momentum conservation, also called the motion equation, the radiation force applied on a unit volume is related to the mean change of its momentum. 18 As the radiation force is related to time-averaged effect, after inserting (2) into (4) and doing the time-averaging calculations, we can get. 19 Where the angle brackets b represent time averaging. 20 If we expand the right side of the equation and only keep the terms no smaller than the second order, (5) becomes. 21 It should be noted that the time-averaged first terms q1 and uz1 are zero because they are harmonic time-vibrating variables as shown in (3).