Investigation of the correlation between diffuse infrared and ultrasound for transcranial ultrasound

Abstract

Over the past two decades the feasibility for using transcranial ultrasound as both a therapeutic and diagnostic tool has been established. Various aberration-correction techniques have been proposed to achieve transcranial focusing, including CT-derived model based corrections, ultrasound-derived model based corrections, magnetic resonance acoustic radiation force (MR-ARFI) techniques, and techniques involving the invasive introduction of an acoustic source or receiver into the brain. Here, we investigate the correlation between transcranial infrared light (IR) and transcranial ultrasound, where we examine whether IR could be an indicator of any of the key acoustic properties that affect transcranial transmission (signal attenuation, speed of sound, and bone density). Nine human skull samples were utilized in the study. The interior of each sample was illuminated over its inner surface using a diffuse light source. Light transmitted to the outer surface was detected by a 3-mm diameter 940-nm infrared sensor. Acoustic measurements were likewise obtained in a water tank using a 12.7-mm diameter 1-MHz source and a needle hydrophone receiver. Results reveal a positive correlation between the acoustic time-of-flight and optical intensity (the correlation coefficient is between 0.5 and 0.9). Subsequent investigation shows this correlation to hold independent of the presence or absence of dura mater on the samples. Poor correlation is observed between acoustic amplitude and optical intensity (the correlation coefficient is between 0.1 and 0.7).

1 INTRODUCTION

Although it has been reported that ultrasound can propagate through human skulls, including thicker parts of the bone [1, 2], coherent focusing generally requires some form of correction to offset wave distortion [3]. A variety of approaches for performing this offset have been proposed [4], including time reversal techniques [5], the introduction of a scattering source [6, 7, 8], or receiver [9] into the brain, computed tomography (CT)-based [10, 11] or MR-based [12] model correction, ultrasound based-correction [13], and MR-ARFI [14, 15]. In the first steps toward identifying a potentially simpler and more direct means for transcranial ultrasound windowing, we have conducted a study comparing acoustic transmission parameters to those of diffuse infrared transmitted through the skull. The study was originally inspired by the observation that skulls possess certain locations which are relatively transparent to ultrasound waves. This includes not only the temporal bone window [16], but also locations that can appear on the thicker frontal, occipital, and parietal bones. Unfortunately, the precise locations of such windows tend to vary greatly between different skulls [17]. Casual examination of ex vivo skull specimens, however, led us to hypothesize that transmitted light intensity at a given location correlates positively with ultrasound transmission [18], motivating us to explore trends between transmitted optical data and ultrasound data.

The study was performed using infrared light transmitted through ex vivo human skull specimens under the auspice that, should correlation be found between acoustic and optic data, it might motivate further work aimed at detecting similar correlations in a reflection mode and through the scalp. Ultrasound measurements were acquired along the surfaces of skull specimens situated between a transducer and a hydrophone, with the skull surfaces positioned normal to the transducer. Optical measurements were subsequently obtained in a dark room by transmitting infrared light through the skull sections using an infrared sensor to measure intensity variance on the skull surface.

As shown below, when acoustic amplitudes were compared to the optical intensity, a poor correlation was found. However, a good correlation was observed between the ultrasound time-of-flight and optical intensity. The procedure and results of this preliminary work are described below, along with discussion on plausible physical explanation of our findings, and the limitations of this transmission-based study.

2 Methodology

Ultrasound and infrared transmission measurements were performed on nine formalin-fixed skull samples representing two sagittally sectioned half skulls and seven calvaria, among which two calvaria had intact dura mater. Because the skull is a porous material, one concern was that presence of trapped gases within the ex vivo skull bone might affect both the ultrasound and infrared measurement. Therefore one skull specimen was examined before and after degassing. The skull was kept under vacuum for approximately 18 hours before repeating the infrared measurement. This skull was then immersed in degassed water and the whole system was degassed for another 20 minutes before repeating the ultrasound measurement. Excellent before- and after-degassing agreement was found at all measurement locations for both the acoustic and infrared data (The absolute value error for each point is less than 0.6%). So we assumed that only negligible amount of gas was trapped in our formalin-fixed skull specimens, and the degassing process is not essential.

2.1 Ultrasound measurement

Acoustic signals were transmitted in a water tank between a transducer (Olympus NDT, V303-SU, 1MHz, 12.7-mm OD, Waltham, MA) and a hydrophone (Onda, HNC-1000, 1-mm diameter active area, Sunnyvale, CA) with and without a skull placed in front of the source transducer. Measurement positions on each skull were physically marked with circles corresponding to the approximate transducer diameter shown in Fig. 1. For the seven skulls void of dura mater, calipers were used to determine the skull thickness. Four positions in each circle were measured, one at center and three adjacent randomly picked. The ultrasound setup illustrated in Fig. 2 shows the relative transducer and hydrophone alignment with a separation of approximately 13 cm.

Fig. 1.

Marked sagittally sectioned half skull. Each marked circle position was numbered as 1,2,3,...

Fig. 2.

Schematic for ultrasound measurement.

For each measurement location, skulls were placed against the transducer and positioned so that the transducer was centered about a reference circle and angled approximately parallel to the transducer face. An impulsive voltage was supplied to the transducer (Panametrics 500PR, Waltham, MA), and the resulting hydrophone response was read by an oscilloscope (Tektronix, DPO3034, Beaverton, OR) triggered from the voltage source. The measurement procedure was repeated three times for each position and each time the skull sample was repositioned. No significant changes were found between the three measurement. Four sample waveforms are shown in Fig. 3: one is water-only measurement, one from the temporal bone window, one from parietal bone and one from frontal bone.

Fig. 3.

Waveforms from hydrophone with and without skull subject:Black is water-only measurement, blue is the measurement for the temporal window, green is for the parietal bone area and red is for the frontal bone area.

2.2 IR measurement

The optical measurement setup is shown in Fig. 4. All measurements were performed in a dark room. A heat lamp (Sylvania, 100 W) was used as a light source and a light shaping diffuser membrane was inserted to obtain uniformly diffused light upon the inner skull surface. Under this configuration it was assumed that the distribution of infrared intensity over skull location was even. A skull was situated above the membrane. One infrared sensor (TSAL4400-3 mm, 940nm), shown in the inset, was embedded in a cylindrical aluminum tube to take infrared measurement. On the sensor surface, a flexible padding shown as a yellow circle was used for better matching the irregular curved skull surface.

Fig. 4.

Schematic for IR measurement. The details of IR sensor was shown in the inset

3 Results

The number of measurement positions attainable by both the ultrasound and optic setups varied, depending on skull size and shape, ranging from 36 to 66 positions (mean = 46) over the 9 skulls examined and totaling 417 over all skulls. Data were analyzed to compare relative transmitted optic intensity, skull thickness (L_s), transmitted peak acoustic pressure amplitude (P_max) and time-of-flight (TOF), defined here as the first detectable time point from the ultrasound signal. Results from one skull sample are shown in Fig. 5. Both the correlation coefficient and p-value for the data, calculated in Matlab (Mathworks, R2011a, Natick, MA) using the command corrcoef, are listed in the inset of each figure.

Fig. 5.

The experimental results for the half-sliced skull subject: the comparison between IR intensity, thickness, peak pressure P_max and time-of-flight TOF.

The correlation coefficients for all skull measurements are shown in Fig. 6 and the “*” markers on each bar denote the significance of correlation measured by their p-values. Among the nine samples, all p-values between thickness and infrared intensity are below 0.01 which indicates that they correlate. In Fig. 6(b), it can be seen that skull 7 and skull 8 have poor correlations between peak relative pressure P_max (taken directly from the hydrophone voltage) and infrared intensity as the p-value is higher than 0.01. A better and more uniform correlation was found between the time-of-flight and infrared intensity with all p-values less than 0.0001. Figure 7 illustrates TOF and IR intensity as a function of position along one skull surface. It can be seen that the two groups of data correlate well across the entire skull.

Fig. 6.

The experimental results for 9 skulls: the correlation between IR intensity, thickness (the two skulls with dura mater were left blank), peak pressure P_max and first arrival time-of-flight TOF; The “*” markers listed above the blue bars denote p-values: “*” is for p < 0.01, “**” for p < 0.001, “***” for p < 0.0001 and no “*” markers while p ≥ 0.01.

Fig. 7.

Comparison between time-of-flight and IR measurement on one skull subject.

Finally, linear regression analysis was performed to study the correlation between infrared intensity and skull thickness, peak acoustic amplitude and time-of-flight for all the nine skulls’ experimental data. Both the linear fit and prediction intervals are calculated and shown in Fig. 8. The fitted equation for IR and skull thickness L_s is:

$$L_s\{mm\}=-0.11\{mm/mV\}\ast IR\{mV\}+40.97\{mm\}\pm 3.5\{mm\}$$ (1)

with coefficient of determination R² = 0.53.

Fig. 8.

The experimental data for all the skulls. The coefficient of determination R² is: (a) 0.53, (b)0.24 and (c) 0.61. The interval is: (a) ± 3.5 mm, (b)± 0.034 and (c)± 0.98 μs

The average human skull thickness is approximately 6.85 mm. An interval of ± 3.5 mm would introduce more than 50% error which implies that infrared intensity is probably not a good indicator for the thickness estimation.

The fitted equation for IR and peak acoustic pressure P_max is:

$$P_{\mathit{max}}\{au\}=0.0006\{au/mV\}\ast IR\{mV\}-0.15\{au\}\pm 0.034\{au\}$$ (2)

with coefficient of determination R² = 0.24.

A low R² value of 0.24 suggests a weak linear relationship between acoustic energy and optical energy. It is likely because the peak pressure is instantaneous while the infrared intensity measurement is spatially and temporally averaged. This result also explains why some skulls, e.g. skull 7 and skull 8 in Fig 6(b), have poor correlation due to different bone structure.

The fitted equation for IR and time-of-flight is:

$$\mathit{TOF}\{\mu s\}=0.035\{\mu s/mV\}\ast IR\{mV\}+72.23\{\mu s\}\pm 0.98\{\mu s\}$$ (3)

with coefficient of determination R² = 0.61.

For transcranial ultrasound at 500 kHz (which would be used in our transcranial imaging), an interval of ± 0.98 μs means the degree of error of TOF estimation based on infrared measurement will translate to ± 1/2 of a cycle, which is good enough to focus the beam with a phased array. However, for 1 MHZ and above, this interval translates to ± 1 or more cycles, which makes the estimation invalid for guiding the sound beam.

4 Conclusions and Discussion

A study with nine ex vivo human skulls was performed to examine the correlation between the optic intensity of diffuse infrared transmitted through the skull and ultrasound transmission. Based on the linear regression analysis of all the nine skull samples, we can conclude that the TOF estimation from the infrared measurement can be potentially used for our transcranial ultrasound focusing.

From Fig. 8, it can be seen that the thickness inversely correlates to the infrared intensity and the acoustic first arrival time-of-time positively correlates. Though the full nature of the optical scattering has yet to be fully investigated, a plausible explanation for correlation between light intensity and TOF entails the skull’s layered composition of relatively opaque (acoustically) trabecular bone sandwiched between layers of more transmissive cortical bone (Fig. 9). Moreover thicker bone tends to correspond to thicker trabecular layers, thus introducing a negative correlation between IR measurements and thickness as well as TOF vs thickness.

Fig. 9.

Skull bone: inner and outer layers are the cortical bone; in between is the trabecular bone.

While all the correlation study pertains to IR transmission mode, the relationship motivates further study as to whether a similar correlation can be found between backscattered IR and transmission ultrasound. If so, this could have direct application in transcranial ultrasound phase aberration correction [19] given that the light of wavelengths between 650 and 900 nm can penetrate skin and tissues by increasing the incident intensity of light [20].