Energy-based adaptive focusing of waves: application to noninvasive aberration correction of ultrasonic wavefields

Abstract

An aberration correction method based on the maximization of the wave intensity at the focus of an emitting array is presented. The potential of this new adaptive focusing technique is investigated for ultrasonic focusing in biological tissues. The acoustic intensity is maximized noninvasively through direct measurement or indirect estimation of the beam energy at the focus for a series of spatially coded emissions. For ultrasonic waves, the acoustic energy at the desired focus can be indirectly estimated from the local displacements induced in tissues by the ultrasonic radiation force of the beam. Based on the measurement of these displacements, this method allows determination of the precise estimation of the phase and amplitude aberrations, and consequently the correction of aberrations along the beam travel path. The proof of concept is first performed experimentally using a large therapeutic array with strong electronic phase aberrations (up to 2pi). Displacements induced by the ultrasonic radiation force at the desired focus are indirectly estimated using the time shift of backscattered echoes recorded on the array. The phase estimation is deduced accurately using a direct inversion algorithm which reduces the standard deviation of the phase distribution from sigma = 1.89 radian before correction to sigma = 0.53 radian following correction. The corrected beam focusing quality is verified using a needle hydrophone. The peak intensity obtained through the aberrator is found to be -7.69 dB below the reference intensity obtained without any aberration. Using the phase correction, a sharp focus is restored through the aberrator with a relative peak intensity of -0.89 dB. The technique is tested experimentally using a linear transmit/receive array through a real aberrating layer. The array is used to automatically correct its beam quality, as it both generates the radiation force with coded excitations and indirectly estimates the acoustic intensity at the focus with speckle tracking. This technique could have important implications in the field of high-intensity focused ultrasound even in complex configurations such as transcranial, transcostal, or deep seated organs.

The information age in optics: Measuring the transmission matrix

“…It perfectly fits with the use of a phase-only SLM and it also maximizes the measured intensity and consequently improves the experimental signal to noise ratio (SNR) [21]. For all Hadamard basis vectors, the intensity is measured on the canonical basis of the pixels on the CCD camera and an observed transmission matrix K obs is acquired, which is related to the real one K by K obs ¼ K Â S ref , where S ref is a diagonal matrix representing the static reference.…”

Transcranial phase aberration correction using beam simulations and MR-ARFI

“…MR-ARFI based phase aberration correction techniques [3][4] consider the measured displacement phase as an estimate of the beam's intensity pattern. These techniques measure the change in displacement magnitude at the focus due to each element's phase and derive the optimum phase correction for all elements analytically [3][4][5] using transducer groupings derived from basis functions or iteratively [6]. Many displacementmeasurements per element are required to recover the focal intensity (4 x number of transducer elements [3], resulting in about 2000-4000 pretreatment ultrasound pulses for different transcranial MRgFUS systems).…”

Spatiotemporal control of light in turbid media

“…The intensity is then measured at the intended focal point. This can be done directly in measuring the pressure field with a hydrophone or, in the case of a soft elastic medium, in measuring the displacement induced at the focal point by the radiation force, which is proportional to the acoustic intensity [157]. Then the phase of the first transducer is cycled between 0 and 2π while the intensity is recorded.…”

“…Narrowband optimization by the Hadamard method. Instead of using such an optimization scheme element by element, we perform a basis transformation to construct virtual transmittersÊ j , defined as linear combinations of real ones, which greatly improves the sensitivity of the method and reduces the number or iterations [157]. The coefficients of the combination are taken as the columns H n (1 < n < N ) of an N by N Hadamard matrix H, with elements H jn {−1; 1}.…”

“…For instance the fluorescence from dye molecules allows to focus on objects hidden inside a complex medium [14]. The concept has been applied to other types of waves, such as surface waves [31] and ultrasonic waves in the single scattering regime for medical imaging [157] and MR-guided ultrasonic therapy [158].…”