Holograms to Focus Arbitrary Ultrasonic Fields through the Skull

We report three-dimensional (3D)-printed acoustic holographic lenses for the formation of ultrasonic fields of complex spatial distribution inside the skull. Using holographic lenses, we experimentally, numerically, and theoretically produce acoustic beams whose spatial distribution matches target structures of the central nervous system. In particular, we produce three types of targets of increasing complexity. First, a set of points are selected at the center of both right and left human hippocampi. Experiments using a skull phantom and 3D-printed acoustic holographic lenses show that the corresponding bifocal lens simultaneously focuses acoustic energy at the target foci, with good agreement between theory and simulations. Second, an arbitrary curve is set as the target inside the skull phantom. Using time-reversal methods, the holographic beam bends following the target path, in a similar way as self-bending beams do in free space. Finally, the right human hippocampus is selected as a target volume. The focus of the corresponding holographic lens overlaps with the target volume in excellent agreement between theory in free media, and experiments and simulations including the skull phantom. The precise control of focused ultrasound into the central nervous system is mainly limited due to the strong phase aberrations produced by refraction and attenuation of the skull. Using the present method, the ultrasonic beam can be focused not only at a single point but overlapping one or various target structures simultaneously using low-cost 3D-printed acoustic holographic lens. The results open alternative paths to spread incoming biomedical ultrasound applications, including blood-brain-barrier opening or neuromodulation.

Figure 1

(a) Scheme of the holographic lens focusing over a target CNS structure. (b) Focusing on a set of arbitrary points (bifocal holographic lens). (c) Focusing over an arbitrary line (self-bending holographic lens). (d) Focusing over an arbitrary volume (volumetric holographic lens).

Figure 2

Hologram generation process. (a) CT+MRI tomographic images. (b) Selected target (red volume) acting as a virtual acoustic source and holographic recording surface (blue area). (c) Lens design using the TR back-propagated field. (d) Forward propagation from the holographic lens (red area) to the target tissue (blue volume).

Figure 3

Geometry of the holographic lens. The lens, of aperture $2a$ is subdivided in pixels of height $h(x,y)$. The source is located at $z=0$, while the holographic plane is located at $z=d$.

Figure 4

Axial-field cross section obtained for the bifocal lens using simulations (a) and experiments (b). (c),(d) Corresponding transversal-pressure-field distributions. Color bar in units normalized to the peak pressure. (e),(f) Simulated and experimental normalized axial- and transversal-field cross sections, respectively.

Figure 5

Theoretical (a) axial- and (b) transverse-pressure-field distribution for the self-bending beam in water. Simulated (c) axial- and (d) transverse-pressure-field distribution for the self-bending beam in water. Corresponding experimental results are shown in the insets in (c) and (d). (e),(f) Simulated axial and transversal pressure field, including the skull phantom. Corresponding experimental results are shown in the insets in (e),(f).

Figure 6

Volumetric hologram results. (a)–(c) Theoretical, experimental, and simulated axial-pressure distribution in water. (d),(e) Transversal- and axial-field cross sections in water. (f)–(h) Simulated, experimental, and theoretical transversal-field distribution in water. (i),(j) Simulated and experimental axial-pressure distribution including the skull phantom. (k),(l) Corresponding transversal-pressure distribution and (m),(n) transversal and axial cross section, respectively.

Figure 7

Simulation results for the bifocal holographic lens designed for a realistic skull. (a) Axial cross section of the pressure distribution at $y=0\mathrm{mm}$. (b) Transversal cross section at $z=100\mathrm{mm}$. (c) Lateral cross section at $z=100\mathrm{mm}$ and $y=0\mathrm{mm}$. (d) Lateral cross section at $z=100\mathrm{mm}$ and $x=-26=0\mathrm{mm}$. (e) Axial cross section at $x=-26=0\mathrm{mm}$ and $y=0\mathrm{mm}$.

Figure 8

Simulation results for the self-bending holographic beam designed for a realistic skull. (a) Axial cross section of the pressure distribution at $y=0\mathrm{mm}$. (b) Transversal cross section at $z=35\mathrm{mm}$. (c) Lateral cross section at $z=35\mathrm{mm}$ and $y=0\mathrm{mm}$. (d) Lateral cross section at $z=35\mathrm{mm}$ and $x=2\mathrm{mm}$.

Figure 9

Simulation results for the volumetric hologram designed for a realistic skull. (a) Axial cross section of the pressure distribution at $y=0\mathrm{mm}$. (b) Transversal cross section at $z=95\mathrm{mm}$. (c) Lateral cross section at $z=95\mathrm{mm}$ and $y=0\mathrm{mm}$. (d) Lateral cross section at $z=95\mathrm{mm}$ and $x=-26=0\mathrm{mm}$. (e) Axial cross section at $x=-26=0\mathrm{mm}$ and $y=0\mathrm{mm}$.

Figure 10

Experimental setup showing the block diagram and skull phantom inside the water tank with the ultrasonic source and the acoustic hologram at the bottom.