Transcranial adaptive focusing of ultrasonic waves is a challenging problem in the field of medical ultrasound. The heterogeneities of biological tissues and skull bone in terms of speed of sound, density or ultrasonic absorption induce a distortion of the ultrasonic wavefield that can result in a partial destruction of the focusing pattern. In order to restore the focusing quality, adaptive focusing relies on the use of ultrasonic arrays to correct the distortions induced by the propagation medium. This correction is performed by estimating and applying different time shifts (or phase shifts for monochromatic waves) on each element of the array. In some situations, when the ultrasonic array relies both on transmit and receive channels, it may be possible to rely on the echoes of a bright reflector or a point like active source located inside the biological tissues. From the signals received on the array, the so called Green’s function, one has to time reverse the wavefield (or phase conjugate for monochromatic signals) to focus back on the initial position. For example, time reversal focusing or phase conjugation has encountered a significant success in the ultrasound community.
However, the direct measurement of the Green’s function between the target location and the ultrasonic array is not possible in the brain. For such configurations, we have recently introduced a novel method called energy-based adaptive focusing. The general principle, which can be applied to any kind of waves in physics, relies on the indirect estimation of the wave intensity at the target for different coded excitations in order to obtain the time shifts (or phase shifts) information correcting the aberrations. By transmitting Hadamard-coded signals with an array of transducers and estimating the beam intensity at the target, this approach was shown to achieve a direct and accurate phase aberration correction without any phase measurement. In medical ultrasound, this idea is particularly interesting because ultrasonic waves interact with biological tissues through physical effects linked to the wave intensity such as the acoustic radiation force or tissue heating due to the absorption of ultrasound. Thus, the quantitative measurement of tissue displacement or temperature elevation at the target can be used for the indirect estimation of the local beam intensity.
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