Ultrasonic Focusing and Steering Through Skull: Towards Brain Imaging

me time reversal process is applied to focus pulsed ultrasonic waves through the human skull bone. The aim is here whether to treat brain tumors, which are difficult to reach with classical surgery means, or to achieve ultrasonic imaging of the brain. Such medical applications require precise control of the size and location of the ultrasonic focal beam. But, the severe ultrasonic attenuation in the skull reduces the efficiency of the time reversal process. Nevertheless, an improvement of the time reversal process in absorbing media has been investigated and applied to the focusing through the skull (1). An extension of this technique is developed in order to focus on a set of points surrounding an initial artificial source implanted in the tissue volume to treat. Such technique could become completely non invasive and hence, be used in medical imaging if the initial source is locatcd on the other side of the skull, Most ultrasonic therapeutic or imaging systems don’t take into account the inhomogeneities of human tissues: The acoustic velocity is assumed to be constant, while steering and focusing the acoustic energy. In fact, the spatial variations of the speed of sound (from approximately 1440 m.s”] in fat to 1580 m.s-l in muscle) induce a phase and amplitude distortion of the wavefront propagating in the medium. These aberrations degrade the spatial resolution, which can reduce the therapeutic performance or mask important diagnostic information. This problem was first discovered by White et al (2) during investigation into brain imaging. Indeed, in the particular case of the skull, a large discrepancy in acoustic velocities between brain tissue and skull tissue (about 1500 m.s-l versus 3000 m.s-l respectively) and a severe attenuation of ultrasound in the skull bone magnify the degradation of the beam shape. Time reversal represents an original way to compensate for distortion due to various inhomogeneous media. Time reversal mirrors (TRM) take advantage of the invariance of the wave equation in a Iossless medium under a time reversal operation. This means that if focusing through any inhomogeneous medium is the objective, the distorted wavefield coming from a source (active or passive) located at the desired focal point should be recorded and then transmitted in time reversed form, The time reversed wavefield back propagates through the inhomogeneities and optimally focuses on (he source. Such an adaptive system is locked on the point-like reflector position or on the brightest point of an extended target, In most of practical situation, such an acoustic source is not available in the region of interest. Besides, the time reversal focusing is related to the invariance of the wave equation under the change of t to -t. This property implies that time appears in second order derivative only. However, this property becomes obsolete in an absorbing medium, like bone: Acoustic losses are taken into account in the wave equation by a first derivative in time and are not time reversal invariant. To solve these problems, another procedure has been developpcd. In the first step of a therapeutic procedure, a small artificial acoustic source is implanted inside the tumors during the biopsy. For medical imaging, the piezo-electric transducers are very small and omnidirectional and this source could be located on the other side of the skull. Then time reversal is combined with an amplitude compensation procedure which takes into account the absorption. In a second step, from the knowledge of the Green’s function matched to this initial source location we deduce the new Green’s function matched to various points of interest in order to treat or image the whole volume. In the case of absorbing heterogeneous media, time-reversal is no longer the optimal solution to focus on a source implanted in the medium. A transducer element that received a weak signal is located in front of a strongly absorbing area of the skull. After the time reversal operation, this weak signal backpropagates through the same area of the skull and hence, the amplitude modulation of the wavefront is increased by a power of two. However, in a particular case, when the aberrating and absorbing medium can be modeled as a thin layer placed at some distance from the transducers array, it is possible to take into account the amplitude modulation originating from acoustic losses and so, to improve the quality of TRM focusing. Thus, if this thin layer is located close to the array its effects can bc modeled by a time shift and an amplitude factor on each transducer. The time delay correction is automatically accomplished by the time reversal process and we can take into account the amplitude aberration due to attenuation by inverting the amplitude modulation of the wavefield received on the array of transducers. The amplitude modulation is estimated by comparison with a reference waveform obtained in the same condition in homogeneous and lossless medium. These estimates are then employed to invert the amplitude modulation. Nevertheless, this amplitude compensation is quite efficient only when the absorbing medium is a layer located close [o the array. Otherwise, additional amplitude and shape distortions may develop as the wavefront propagates in the