Local frequency dependence in transcranial ultrasound transmission

Abstract

The development of large-aperture multiple-source transducer arrays for ultrasound transmission through the human skull has demonstrated the possibility of controlled and substantial acoustic energy delivery into the brain parenchyma without the necessitation of a craniotomy. The individual control of acoustic parameters from each ultrasound source allows for the correction of distortions arising from transmission through the skull bone and also opens up the possibility for electronic steering of the acoustic focus within the brain. In addition, the capability to adjust the frequency of insonation at different locations on the skull can have an effect on ultrasound transmission. To determine the efficacy and applicability of a multiple-frequency approach with such a device, this study examined the frequency dependence of ultrasound transmission in the range of 0.6-1.4 MHz through a series of 17 points on four ex vivo human skulls. Effects beyond those that are characteristic of frequency-dependent attenuation were examined. Using broadband pulses, it was shown that the reflected spectra from the skull revealed information regarding ultrasound transmission at specific frequencies. A multiple-frequency insonation with optimized frequencies over the entirety of five skull specimens was found to yield on average a temporally brief 230% increase in the transmitted intensity with an 88% decrease in time-averaged intensity transmission within the focal volume. This finding demonstrates a potential applicability of a multiple-frequency approach in transcranial ultrasound transmission.

Figure 1

Transmission intensity coefficient (top) and the associated reflection intensity coefficient (bottom) for a 5-mm thick skull sample with parallel interfaces and a homogeneous mass density cross-section (ρ = 2450 kg/m³, c = 2650 m/s)

Figure 2

Thickness and mass density distribution for eight ex vivo human skulls over a total of 2484 points obtained from CT images. The mean measured mass density was 2132 kg/m³ with a standard deviation of 132 kg/m³ and the mean skull thickness was 6.1 mm with a standard deviation of 1.7 mm. Each bin in the upper histogram represents a span of 44.3 kg/m³ in density. Each bin in the lower histogram represents a span of 0.06 mm in thickness. [The bin sizes were chosen to correlate to a 10-kHz shift in the optimal frequency as measured from 1 MHz.]

Figure 3

Experimental setup

Figure 4

The superimposed rays on this CT image of an ex vivo human calvarium indicate the measurement points on each skull specimen as selected by rotation about the axis defined by the intersection of the anatomical midsagittal plane and the anatomical axial plane at the inferior extreme of the calvarium specimen.

Figure 5

A propagation model of ultrasound transmission through a 6.1-mm homogeneous layer (ρ = 2132 kg/m³, c = 2800 m/s) in water demonstrating correlation with the measured spectrum of transmission through an ex vivo calvarium

Figure 6

The calculated spectral dependence of ultrasound transmission on layer mass density and thickness. With increasing mass density and a constant thickness of 6.1 mm (left), a lowered optimal frequency was observed. With increasing layer thickness and a constant mass density of 2132 kg/m³ (right), a lowered optimal frequency was also observed.

Figure 7

Schematic of the acoustic pressure summations performed for the scenarios of a single-frequency insonation (left) and a multiple-frequency insonation (right). The plots show simulated frequency-dependent intensity transmission coefficients.

Figure 8

Time-dependent pressure-squared values at a single point in space calculated from the linear superposition of pressures from 500 sources of a single-frequency and the same from 500 sources of optimized frequencies. The time-averaged pressure-squared value for multiple-frequency superposition is 16% of that for the single-frequency case. This model was generated using calculated ultrasound transmission pressure-squared spectra. This calculation was performed for each of the 500 points on a skull specimen using the mass density and thickness distribution obtained from CT images. Five skulls were examined in this fashion.

Figure 9

Normalized pressure-squared reflection spectra for four of the seventeen applied ultrasound pulses superimposed on the transmission spectra for the same points on the skull specimens. Each transmission and reflection signal was normalized to its own peak value. The four examples demonstrate, in clockwise sequence from the upper-left, insonations with progressively weaker correlations between dips in reflection values and peaks in transmission values.

Figure 10

Percent change in power transmission when insonating at an optimized frequency as determined by observation of the reflected ultrasound spectrum. Four of the fifteen cases demonstrated a decrease in power transmission.