**Ultrasound Axicon: Systematic Approach to Optimize Focusing Resolution through Human Skull Bone**

**Fabián Acquaticci 1,2,\*, Sergio E. Lew <sup>1</sup> and Sergio N. Gwirc 3,\***


Received: 16 August 2019; Accepted: 17 October 2019; Published: 20 October 2019

**Abstract:** The use of axicon lenses is useful in many high-resolution-focused ultrasound applications, such as mapping, detection, and have recently been extended to ultrasonic brain therapies. However, in order to achieve high spatial resolution with an axicon lens, it is necessary to adjust the separation, called stand-off (δ), between a conventional transducer and the lens attached to it. Comprehensive ultrasound simulations, using the open-source k-Wave toolbox, were performed for an axicon lens attached to a piezo-disc type transducer with a radius of 14 mm, and a frequency of about 0.5 MHz, that is within the range of optimal frequencies for transcranial transmission. The materials properties were measured, and the lens geometry was modelled. Hydrophone measurements were performed through a human skull phantom. We obtained an initial easygoing design model for the lens angle and optimal stand-off using relatively simple formulas. The skull is not an obstacle for focusing of ultrasound with optimized axicon lenses that achieve an identical resolution to spherical transducers, but with the advantage that the focusing distance is shortened. An adequate stand-off improves the lateral resolution of the acoustic beam by approximately 50%. The approach proposed provides an effective way of designing polydimethylsiloxane (PDMS)-based axicon lenses equipped transducers.

**Keywords:** ultrasonic lens; axicon lens; focused ultrasound; transcranial ultrasound
