Acoustic Attenuation: Multifrequency Measurement and Relationship To CT and MR Imaging

Abstract

Transcranial magnetic resonance guided focused ultrasound (tcMRgFUS) is gaining significant acceptance as a non-invasive treatment for motion disorders and shows promise for novel applications such as blood brain barrier opening for tumor treatment. A typical procedure relies on CT derived acoustic property maps to simulate the transfer of ultrasound through the skull. Accurate estimates of the acoustic attenuation in the skull are essential to accurate simulations, but there is no consensus about how attenuation should be estimated from CT images and there is interest in exploring MR as a predictor of attenuation in the skull. In this study we measure the acoustic attenuation at 0.5, 1, and 2.25 MHz in 89 samples taken from two ex-vivo human skulls. CT scans acquired with a variety of x-ray energies, reconstruction kernels, and reconstruction algorithms and MR images acquired with ultra short and zero echo time sequences are used to estimate the average Hounsfield unit value, MR magnitude, and T2* value in each sample. The measurements are used to develop a model of attenuation as a function of frequency and each individual imaging parameter.

I. Introduction

Applications of transcranial focused ultrasound (FUS) include the treatment of neurological disorders such as Parkinsonian tremor [1, 2], essential tremor [3], neuropathic pain [4], and obsessive-compulsive disorder [5]. Drug delivery through blood brain barrier opening, using a combination of systemically injected microbubbles and FUS is being investigated with initial studies recently performed in humans [6–9], and US mediated neural modulation is also being researched [10–16].

Transfer of ultrasound to the brain is complicated by a large variation in the shape, thickness, and composition of skulls across patients. These variations, which can result in blurring and translation of the focal spot, are partially accounted for using phase corrections that rely on CT based estimates of acoustic velocity [17–20]. While these corrections improve acoustic focusing, Vyas et al. [21] showed that a fourfold variation in the energy required to obtain ablative temperatures in the brain persists even after these corrections are applied. This remaining variation across patients is probably due to reflection at the skull interface and attenuation of the ultrasound by absorption and incoherent scattering. Treatment planning would be greatly improved by the ability to predict the energy transmission in a specific patient before a treatment in order to adjust transducer parameters to maximize treatment safety and efficacy. This type of prediction can be achieved by simulation if the acoustic attenuation of the skull is known.

Early measurements of the attenuation in skull bone showed that attenuation is a strong function of both frequency and bone type [22, 23]. This dependency on bone composition implies that the attenuation will vary substantially across an individual skull and simulations relying on a single value of attenuation in bone are unlikely to produce accurate results. Thus, several investigators have proposed using CT images to estimate the attenuation in a specific patient, providing attenuation estimates with a spatial resolution equal to that of the CT image. However, despite substantial literature on the topic, there is no consensus about the proper transformation between Hounsfield units (HU) and attenuation [18, 19, 21, 24–27]. A direct measurement of attenuation as a function of HU and frequency would illuminate the proper relationship between HU and attenuation, lending clarity about how to best simulate treatments and predict the efficiency of transcranial ultrasound transmission in specific patients.

A further improvement would be the capacity to predict attenuation using MR imaging. Because tcMRgFUS treatments are done under MR guidance, current clinical practice requires the registration of the CT dataset to an MR dataset of the patient. Eliminating this step would streamline treatments and remove a source of error. Several recent studies have shown a strong correlation between HU and magnitude images generated with ultrashort (UTE) or zero echo time (ZTE) MR [28–31], suggesting that MR should be able to predict attenuation with an accuracy similar to CT. However, the relationship between MR-derived imaging parameters and attenuation has not been studied.

In this work we report measurements of acoustic attenuation at frequencies ranging from 0.35 to 3 MHz in 89 skull bone fragments from two ex-vivo human skulls. Each fragment is imaged using CT and MR. CT images are acquired on two systems with a variety of x-ray energies and reconstruction techniques. Magnitude MR images are acquired using UTE and ZTE and a T2* reconstruction is obtained using a UTE sequence. An estimate of the function relating attenuation to CT/MR-derived imaging parameters and frequencies is then determined using a simultaneous fit of the measured attenuation to frequency and each imaging parameter.

II. Methods

The relationship between four imaging parameters (HU, magnitude measured with UTE and ZTE, and T2*) and acoustic attenuation was measured directly in 89 fragments from two ex-vivo human skulls. The sample preparation and CT imaging methods were described previously in [17] and are briefly reviewed here.

A. Sample Preparation

Bone cores with a diameter of 13 mm were removed from two (62 year old male and 60 year old female) ex-vivo dried human skulls [Skulls Unlimited, Oklahoma City, OK]. The inner and outer table were separated from the diploë and the samples were then sanded to provide flat and parallel interfaces. 89 fragments were generated with 41 from the outer table, 38 from the diploë, and 9 from the inner table. All fragments were degassed in water in a vacuum chamber before any experiments were performed. The vacuum pressure was approximately 25 in/Hg and fragments were degassed for a minumum of 12 hours before experiments began.

B. CT Imaging

The average HU in each fragment was determined by computing the mean in a region of interest generated with an automatic segmentation algorithm. The algorithm combines thresholding [32] and hole filling [33] to generate the region of interest. A more complete explanation of the algorithm can be found in [17].

CT images were acquired on two scanners with a variety of x-ray energies and reconstruction algorithms. On a Discovery CT750 [GE, Waukesha, WI] images were acquired using both a soft tissue and bone reconstruction kernel at 80, 100, 120, and 140 kVp. Dual energy images were also acquired and effective monoenergetic reconstructions were obtained at 60, 80, 100, 120, and 140 keV. The 60 and 140 keV reconstructions were used to generate bone mineral density (BMD) estimates [34]. Images were also acquired using the system’s iterative reconstruction algorithm (commercially know as Veo) at 80, 120, and 140 kVp.

Images from a Somatom Force [Siemens, Erlangen, Germany] were acquired at 70, 80, 90, 100, 110, 120, 130, 140, and 150 kVp using both a soft tissue and bone reconstruction kernel. At 120 and 140 kVp, a series of images reconstructed with kernels ranging from broad to narrow were acquired and, at 150 kVP, some images were acquired using an x-ray tin filter.

C. MR Imaging

ZTE images were acquired on a 3 Tesla system [GE, Waukesha, WI] with the product sequence Silenz (TR=200 ms, TE=20 μs, averages=4, FOV=18 cm, slice thickness=0.5 mm, in plane resolution=0.70 mm, flip angle=5°). UTE images were acquired using a center out sequence (TE=32μs, TR=6 ms, FOV=18 cm, slice thickness=0.7 mm, inplane resolution=0.63 mm, flip angle=5°). In both the UTE and ZTE images coil shading was removed by normalizing the average magnitude in the fragment to the average magnitude in the same region of interest acquired in a 2% agar phantom. Phantom images were acquired immediately after imaging the bone fragments without changing any parameters. Similar normalization could be achieved in-vivo by normalizing to soft tissue values [30]. All images were acquired using a 6-channel GE Flex coil.

Regions of interest for each fragment were generated using a template matching technique. The algorithm generated a three dimensional cylinder matching the radius and height of the fragment and used cross correlation to determine the optimal location of the template. The final region of interest had a thickness that was smaller than the fragment thickness by two times the resolution in that dimension and a radius that was smaller by 3 mm. This helps to avoid partial voluming and any artifacts from the susceptibility difference between air, water, and the bone samples. To further limit partial voluming, fragments with a thickness less than two times the in-plane resolution were excluded.

T2* was estimated using the UTE sequence described above. This was done by fitting the average magnitude in the fragment, measured at 5 echo times, to a single decaying exponential. The 5 echo times were TE = 32, 200, 500, 700, and 900 μs and the repetition time was 10 ms. A constant noise term was subtracted before performing the fit. To find this term, a least squared optimization function minimized the difference between the measured data and the exponential fit across different possible noise terms.

D. Measuring Attenuation

Figure 1 shows a schematic of the setup used to measure the attenuation in each fragment. Measurements were done with a 2.5 mm aperture HNR 0500 hydrophone [Onda, Sunnyvale, CA] and three single element piston transducers [Olympus, Tokyo Japan] with center frequencies of 500 kHz (Model V301, 1” diameter), 1 MHz (Model V302 1” diameter), and 2.25 MHz (Model V306, 0.5” diameter). The distances between the transducer and the aluminum plate were 26, 61, and 45 mm and the distances between the aluminum and the hydrophone were 28, 59, and 42 mm for the 0.5, 1, and 2.25 MHz transducers respectively. These distances were selected to center the fragment between the transducer and hydrophone, with the hydrophone placed at the natural focus (last intensity maxima) of each transducer. The fragment is held on an aluminum plate with a 10 mm diameter opening, just smaller than the diameter of the fragments.

Fig. 1.

Diagram of experimental setup

An individual attenuation measurement was performed by emitting a short pulse from the transducer and measuring the resulting waveforms at the hydrophone with and without the bone fragment present. The transducer was excited by a single cycle at the center frequency which was generated by a function generator [Keysight, Santa Rosa CA, model 33220A] connected to an amplifier [AR Souderton, PA, model 150A100B]. Each waveform measured by the hydrophone was digitized by an oscilloscope.

A Fourier transform was then performed on each of the recorded pulses. At a given frequency, the pressure lost due to transmission through the fragment was estimated by dividing the relevant Fourier coefficient measured with the bone fragment present by the same coefficient measured without the fragment present,

$$L=\frac{P_{\text{b}}}{P_{\text{w}}}.$$ (1)

Here, L is the loss, P_b is the Fourier coefficient measured with the bone fragment present, and P_w is the Fourier coefficient measured in water alone. Loss measurements were only considered valid if the magnitude of the Fourier coefficient measured without the fragment present was within 10 dB of the peak magnitude and the Fourier coefficient measured with the bone present was within 50 dB of the peak magnitude (see Figure 2). These thresholds result in a frequency range of 0.35 to 0.7 MHz, 0.5 to 1.4 MHz, and 1.3 to 3 MHz for the 0.5, 1, and 2.25 MHz transducers respectively. The 10 dB threshold was selected to maximize SNR while achieving good overlap between the three transducers. The 50 dB threshold was applied because the spectra of the 0.5 and 1 MHz transducer become highly variable below that threshold.

Fig. 2. Sample Data.

Fourier transform and time domain traces of the raw signal for three different fragments. The signal measured with no fragment present is shown with a solid line and the signal measured with the fragment in the beam path is shown with a dotted line. The 0.5, 1, and 2.25 MHz data are shown in blue, red, and yellow respectively. Each transducer provides attenuation information across a spectrum of frequencies. In this study, a frequency is considered to be within the transducer’s spectrum if the magnitude of its corresponding free field Fourier coefficient is within 10 dB of the free field peak. Any frequencies for which the Fourier coefficient fell below this threshold were excluded. Frequencies for which the magnitude of the Fourier coefficient after transmission through the sample were more than 50 dB down from the free field peak were also excluded (this 50 dB threshold is the minimum value displayed in these plots).

The loss term defined by Equation (1) is the result of both attenuation and reflection and the loss due to reflection must be accounted for in order to obtain an accurate estimate of attenuation. Folds and Loggins [35] provide a method to predict the acoustic transmission through layered media given the density, acoustic velocity, thickness, and acoustic attenuation in each layer. If the density, velocity, and thickness, are known, attenuation can be estimated by finding the value that results in agreement between the measured loss and the loss predicted by the Folds’ and Loggins’ model. These three parameters were measured in each fragment according to the methods described below.

Density was measured in the wet bone state using Archimedes’ principle. Fragments were first degassed over night and weighed in water. After being weighed in water, the fragments were removed from water and allowed to dry for three minutes before being weighed in air. This process allows the surface water to evaporate while maintaining the pore water [36]. According to Archimedes’ principle, the difference between these two measurements is the mass of the water displaced by the fragment. Therefore, the volume of the fragment can be determined by

$$v=\frac{\left(m_{\text{m}}-m_{\text{w}}\right)}{{\rho }_{\text{w}}},$$ (2)

where ρ_w is the density of water, m_m is the mass of the moist fragment measured in air, and m_w is the mass of the fragment measured in water. The density, ρ, of each fragment is then given by

$$\rho =\frac{m_{\text{m}}{\rho }_{\text{w}}}{\left(m_{\text{m}}-m_{\text{w}}\right)}.$$ (3)

The velocity was estimated using measurements of the arrival time of a signal with and without the fragment present. These measurements were reported previously and can be found in Webb et al. [17]. The thickness of each fragment was measured using a digital caliper.

A limitation in measuring the attenuation coefficient arises from the spatial length of the pulse relative to the thickness of the bone fragments. Attempts to limit each fragment to a single bone type result in fragments with thicknesses ranging from about 1 to 8 mm. If the thickness of a fragment is less than ½ of the spatial pulse length, then reflections of the pulse will interfere with the initial pulse, resulting in errors. While the model developed by Folds et al. accounts for this, in the presence of these resonances small errors in the measurement of thickness and velocity can introduce large errors in the measurement of attenuation. As a result, only fragments with a thickness of at least 1 wavelength were included in the results. The wavelength for each measurement was determined assuming an acoustic velocity of 2200 m/s and using the center frequency of each transducer. This results in a minimum thicknesses of 4.4, 2.2, and 1 mm for the 0.5, 1, and 2.25 MHz transducers, respectively. Table I provides the number of fragments that meet this requirement for each transducer.

TABLE I.

Summary of the number and type of fragments thick enough to be measured at each frequency.

Frequency (MHz)	Layer	Fragments
0.5	Inner table	0
	Outer table	1
	Diploë	4
1	Inner table	3
	Outer table	21
	Diploë	28
2.25	Inner table	11
	Outer table	41
	Diploë	37

E. Data Fitting

Attenuation is a function of frequency and bone composition. The imaging parameters (HU value, UTE and ZTE magnitude, or T2* value) can be thought of as measures of bone composition and we used a non-linear, least squares approach to estimate the attenuation, α, as a function of frequency, f, and imaging parameter, p. The fit assumed a relationship of the form

$$\alpha ={\alpha }_0{f}^{\beta }{e}^{cp}.$$ (4)

Here, α₀, β, and c are coefficients assigned by the algorithm. This equation assumes the traditional power law relationship between frequency and attenuation [37, 38] and that the imaging parameter, p, provides a rough estimate of the pore structure in each sample. For example, the HU value has been shown to have significant correlation (R-squared > 0.5) with bone fraction and trabecular spacing [39, 40]. Of necessity, each imaging parameter represents only a rough approximation of pore structure. CT HU, MR magnitude, and T2* value are all complex functions of the material properties of bone and bone marrow as well as the shape, size, and distribution of the pores. However, because of the large difference between the material properties of bone and marrow, the value of each imaging parameter is dominated by the overall fraction of bone and marrow. Thus, each can be reasonably thought of as monotonically related to this fraction. Following prior studies that found an exponential relationship between pore volume and attenuation [41, 42]we therefore assumed an exponential relationship between p and α.

The fit was performed for all possible imaging parameters, including the HU value measured using all of the energies and reconstruction algorithms outlined in [17], the UTE and ZTE magnitude, and the T2* values. The primary figure of merit for each fit is the standard error of the regression (also known as the root mean square error) defined as

$$s=\sqrt{\frac{{\sum }_{n=1}^N{(\widehat{\alpha }-\alpha )}^2}{N-M}},$$ (5)

where N is the number of attenuation measurements (1,710) and M is the number of degrees of freedom (3). The standard error is also computed at specific frequencies (0.65, 1, and 2.25 MHz). For this computation the definition is the same but N changes to reflect the number of measurements available at that particular frequency (57, 52, and 89 respectively).

III. Results

This section details the attenuation measurements and their relationship to frequency and CT/MR-derived imaging parameters. Each analysis excludes the data from one fragment from the diploë which had exceptionally large pores. More information on this fragment can be found in Section IV-A.

Figure 2 shows examples of the raw and Fourier transformed signal for three different fragments (a 2.2 mm cortical fragment and 1.5 mm and 5.3 mm trabecular fragments). Traces are shown with and without the fragment present. The presence of the fragment attenuates the spectrum with more attenuation at higher frequencies. Attenuation measurements are acquired at all frequencies that meet the inclusion criteria. A histogram of the measured thickness in each fragment is shown in Figure 3.

Fig. 3.

Histogram of fragment thickness separated by bone type.

Figure 4 shows sample CT images of five fragments selected from across the HU range and imaged at four different energies using the BONEPLUS kernel on the GE system. The energies are shown above each column. Next to the CT are MR images of the same fragments. The first two fragments are from the diploë and the last three fragments are from the inner or outer tables.

Fig. 4. Sample Images.

CT and MR images of 5 fragments selected from across the HU spectrum. CT images are acquired using the BONEPLUS kernel on the GE system. The first two fragments are medullary fragments from the diploë and the last three are cortical fragments from the inner or outer table. Each fragment shows only the ROI used to compute the average imaging value. MR fragments had a smaller ROI to limit partial voluming effects due to the larger voxel size.

A. Attenuation Measurements

Table II summarizes the attenuation measured at the center frequency of each transducer in each bone type. The attenuation was measured three times for each sample, fully removing and replacing the sample each time. An estimate of the variability of the measurement can be obtained using the standard deviation across these three measurements. At 500 kHz the average standard deviation, measured across each fragment, was 4.1%. At 1 and 2.25 MHz it was 11%. No significant difference between the attenuation in the fragments from the two different skulls was measured.

TABLE II.

Average attenuation (mean ± standard deviation) measured at each frequency in each bone layer. All values are in np/cm.

	0.5 MHz	1 MHz	2.25 MHz
Inner Table	NA	2.9±0.48	6.5±3
Medullary Table	1.2±0.13	2.6±1.1	9.2±3.8
Outer Table	0.7± NA	2.3±0.9	4.4±1.7

B. Attenuation as a Function of Frequency and Imaging Parameter

Figures 5(a)–5(d) show the sample space used to fit attenuation to frequency and each imaging parameter. Attenuation measurements acquired by the 0.5, 1, and 2.25 MHz transducers are shown in blue, red, and yellow respectively. Figures 5(e)–5(h) show the estimate of attenuation for each imaging parameter. The estimate is the result of fitting the attenuation measurements to a model of the form given in Equation (4). The HU values shown in these figures reflect those measured using GE’s BONEPLUS kernel with an energy of 120 kVp, matching the CT parameters used at Stanford to acquire patient CT scans for ablative thalamotomy procedures [43]. As measured by the standard error of each regression, HU provide the best prediction of attenuation with a minimum standard error of 1.7 Np/cm (1.8 Np/cm for the data displayed in Figure 5(e)). The ZTE, UTE, and T2* values had standard errors of 2.0, 2.0, and 2.1 respectively.

Fig. 5. Attenuation as a Function of Frequency and CT or MR Derived Imaging Parameters.

a-d) Sampling Density: Values of frequency and imaging parameter (HU, ZTE, UTE, and T2*) at which estimates of attenuation were obtained. The x-axis shows the average imaging parameter measured in each available sample and the y-axis shows the frequencies at which each sample was thick enough to provide an attenuation measurement. Attenuation measurements acquired by the 0.5, 1, and 2.25 MHz transducers are shown in blue, red, and yellow respectively.

e-h) Attenuation: Estimates of attenuation as a function of frequency and HU, ZTE, UTE, or T2* value. The value of the function along the white dotted lines is shown in Figure 6

To give a better sense of the variation in attenuation as a function of frequency and imaging parameter, Figure 6 shows the predicted attenuation at three different frequencies and three different values of HU and ZTE. The plots also provide the measured attenuation (asterisks) and the standard regression of the error measured at each individual value of frequency/imaging parameter. The predicted attenuation for some individual samples (shown in Figures 6(b) and 6(d)) deviates from the measured value but the average fit across all samples (visible in Figures 6(a) and 6(c)) shows good agreement.

Fig. 6. Variation in Attenuation with Frequency and HU or ZTE Value.

a-b) Attenuation and HU: Variation in attenuation as a function of HU value (a) and frequency (b). Standard error of the regression when considering each curve individually is given in the legend (number of samples used to compute standard error is 57, 52, and 89 for the 0.5, 1, and 2.25 MHz data respectively).

c-d) Attenuation and ZTE: Variation in attenuation as a function of ZTE magnitude (c) and frequency (d). Standard error of the regression when considering each curve individually is given in the legend (number of samples used to compute standard error is 13, 23, and 23 for the blue, red, and yellow curves respectively).

A summary of these results can be found in Tables IV through VI which give the coefficients, α₀, β, and c (see Equation (4)) for each measurement of HU (varying by CT energy, reconstruction kernel, and vendor) and for the ZTE, UTE, and T2* measurements. As in [17], Tables IV and V show that CT parameters have a large impact on the estimated transformation between HU value and acoustic attenuation.

TABLE IV.

Coefficients found when using HU measured on GE scanner and fitting the attenuation data to Equation (4) Legend: BW: beam wobble, Veo: model based iterative reconstruction, DE: dual energy, BMD: bone mineral density reconstruction

Energy (kVp)	Kernel	Other Identifier	Resolution in mm (axial, slice)	α 0	β	c	s	s @ 0.65 MHz	s @ 1 MHz	s @ 2.25 MHz
60	ST	DE	0.49, 0.63	20	1.2	−0.0015	2.1	0.6	1.1	2.6
60	B	DE	0.49, 0.63	22	1.2	−0.0016	2.0	0.6	1.1	2.5
80	ST		0.49, 0.63	21	1.2	−0.0012	2.0	0.6	1.1	2.5
80	ST	Veo	0.24, 0.63	29	1.2	−0.0014	1.8	0.7	1.1	2.2
80	ST	BW	0.49, 0.63	25	1.2	−0.0014	1.9	0.6	1.1	2.3
80	ST	DE	0.49, 0.63	21	1.2	−0.0022	2.0	0.6	1.1	2.5
80	B		0.49, 0.63	26	1.3	−0.0012	1.8	0.7	1.2	2.0
80	B	BW	0.49, 0.63	27	1.3	−0.0012	1.7	0.7	1.2	1.9
80	B	DE	0.49, 0.63	21	1.2	−0.0022	2.0	0.6	1.1	2.5
100	ST		0.49, 0.63	22	1.2	−0.0015	2.0	0.6	1.1	2.5
100	ST	BW	0.49, 0.63	25	1.2	−0.0016	1.9	0.6	1.1	2.3
100	ST	DE	0.49, 0.63	21	1.2	−0.0028	2.0	0.6	1.1	2.5
100	B		0.49, 0.63	26	1.3	−0.0014	1.8	0.7	1.2	2.0
100	B	BW	0.49, 0.63	28	1.2	−0.0014	1.8	0.7	1.2	2.0
100	B	DE	0.49, 0.63	22	1.2	−0.0028	2.0	0.6	1.1	2.4
120	ST		0.49, 0.63	24	1.2	−0.0018	1.9	0.6	1.1	2.4
120	ST	Veo	0.24, 0.63	30	1.2	−0.0019	1.8	0.7	1.1	2.1
120	ST	BW	0.49, 0.63	25	1.2	−0.0018	1.8	0.6	1.1	2.3
120	ST	DE	0.49, 0.63	21	1.2	−0.0032	2.0	0.6	1.1	2.5
120	B		0.49, 0.63	26	1.3	−0.0016	1.8	0.7	1.2	1.9
120	B	BW	0.49, 0.63	27	1.2	−0.0016	1.8	0.7	1.2	2.0
120	B	DE	0.49, 0.63	21	1.2	−0.0032	2.0	0.6	1.1	2.4
140	ST		0.49, 0.63	22	1.2	−0.0019	2.0	0.6	1.1	2.5
140	ST	Veo	0.24, 0.63	30	1.2	−0.0021	1.8	0.7	1.2	2.1
140	ST	BW	0.49, 0.63	26	1.2	−0.0021	1.8	0.6	1.1	2.2
140	ST	DE	0.49, 0.63	21	1.2	−0.0034	2.0	0.6	1.2	2.4
140	B		0.49, 0.63	26	1.3	−0.0017	1.8	0.7	1.2	2.0
140	B	BW	0.49, 0.63	26	1.3	−0.0017	1.7	0.7	1.2	1.9
140	B	DE	0.49, 0.63	21	1.2	−0.0034	2.0	0.6	1.2	2.4
	B	BMD	0.49, 0.63	7.1e+02	1.2	−0.0035	2.0	0.6	1.2	2.4
	ST	BMD	0.49, 0.63	4.4e+02	1.2	−0.0032	2.1	0.6	1.1	2.7

Table VI.

Coefficients found when using MR-derived imaging parameters and fitting the attenuation data to Equation (4)

Parameter	α 0	β	c	s	s @ 0.65 MHz	s @ 1 MHz	s @ 2.25 MHz
ZTE	0.62	1.3	3.5	2.0	0.7	1.3	2.3
UTE	0.77	1.3	2.5	2.0	0.7	1.3	2.4
T2*	1.2	1.3	0.7	2.1	0.8	1.2	2.5

TABLE V.

Coefficients found when using HU measured on a Siemens scanner and fitting the attenuation data to Equation (4) Legend: Ub: Soft Tissue Stepped, Ur: Bone Stepped, Tin: using a tin filter, LR: low resolution (1 mm slices)

Energy (kVp)	Kernel	Other Identifier	Resolution in mm (axial, slice)	α 0	β	c	s	s @ 0.65 MHz	s @ 1 MHz	s @ 2.25 MHz
70	ST		0.39, 0.5	26	1.2	−0.0017	1.7	0.7	1.2	1.9
70	B		0.39, 0.5	26	1.2	−0.0017	1.7	0.7	1.2	1.9
70	B	LR	0.39, 1	25	1.2	−0.0017	1.7	0.7	1.2	1.9
80	ST		0.39, 0.5	24	1.2	−0.0017	1.7	0.7	1.2	1.9
80	B		0.39, 0.5	26	1.3	−0.0017	1.8	0.7	1.2	2.0
90	ST		0.39, 0.5	28	1.3	−0.0018	1.8	0.7	1.2	2.0
90	B		0.39, 0.5	25	1.3	−0.0017	1.8	0.7	1.2	2.0
90	B	LR	0.39, 1	11	1.1	−0.0013	2.4	0.6	0.9	3.2
100	ST		0.39, 0.5	10	1.1	−0.00079	2.4	0.6	0.9	3.2
100	B		0.39, 0.5	30	1.3	−0.0012	1.8	0.7	1.2	2.0
100	B	LR	0.39, 1	28	1.3	−0.0012	1.8	0.7	1.2	2.0
110	ST		0.39, 0.5	10	1.1	−0.00088	2.4	0.6	1.0	3.3
110	B		0.39, 0.5	30	1.3	−0.0014	1.8	0.7	1.2	2.0
110	B	LR	0.39, 1	10	1.1	−0.00099	2.4	0.6	1.0	3.2
120	ST		0.39, 0.5	28	1.3	−0.0014	1.8	0.7	1.2	2.0
120	ST	Ub36	0.53, 0.4	17	1.1	−0.0017	2.3	0.6	1.0	3.0
120	ST	Ub44	0.53, 0.4	25	1.2	−0.0019	1.9	0.7	1.1	2.2
120	ST	Ub49	0.53, 0.4	26	1.2	−0.0018	1.9	0.7	1.2	2.1
120	ST	Ub59	0.53, 0.4	20	1.3	−0.0015	1.9	0.7	1.2	2.1
120	B		0.39, 0.5	26	1.3	−0.0014	1.8	0.7	1.2	2.0
120	B	Ur77	0.53, 0.4	28	1.3	−0.0019	1.8	0.7	1.2	2.0
120	B	Ur81	0.53, 0.4	26	1.2	−0.0019	1.7	0.7	1.2	1.9
120	B	Ur85	0.53, 0.4	26	1.2	−0.0019	1.7	0.7	1.2	1.9
120	B	Ur89	0.53, 0.4	25	1.2	−0.0019	1.7	0.7	1.2	1.9
120	B	LR	0.39, 1	11	1.1	−0.0011	2.4	0.6	0.9	3.2
130	B		0.39, 0.5	28	1.3	−0.0015	1.8	0.7	1.2	2.0
130	B	LR	0.39, 1	25	1.3	−0.0015	1.8	0.7	1.2	2.0
140	ST		0.39, 0.5	11	1.1	−0.0012	2.4	0.6	0.9	3.2
140	ST	Ub36	0.53, 0.4	24	1.2	−0.0019	1.7	0.7	1.2	1.9
140	ST	Ub44	0.53, 0.4	25	1.3	−0.0018	1.8	0.7	1.2	2.0
140	ST	Ub49	0.53, 0.4	11	1.1	−0.0014	2.4	0.6	1.0	3.2
140	ST	Ub59	0.53, 0.4	11	1.1	−0.0017	2.4	0.6	1.0	3.2
140	B		0.39, 0.5	29	1.3	−0.0017	1.8	0.7	1.2	2.0
140	B	Ur77	0.53, 0.4	27	1.3	−0.0019	1.8	0.7	1.2	2.0
140	B	Ur81	0.53, 0.4	23	1.3	−0.0022	1.8	0.7	1.2	2.0
140	B	Ur85	0.53, 0.4	21	1.3	−0.0021	1.8	0.7	1.2	2.0
140	B	Ur89	0.53, 0.4	24	1.3	−0.0018	1.8	0.7	1.2	2.0
140	B	LR	0.39, 1	27	1.3	−0.0016	1.8	0.7	1.2	2.0
150	ST		0.39, 0.5	10	1.1	−0.0012	2.4	0.6	1.0	3.2
150	ST	Tin	0.39, 0.5	27	1.2	−0.0017	1.9	0.7	1.2	2.0
150	B		0.39, 0.5	17	1.1	−0.0016	2.3	0.6	1.0	2.9
150	B	Tin	0.39, 0.5	20	1.3	−0.0014	1.9	0.7	1.2	2.1
150	B	Tin,LR	0.39, 1	28	1.3	−0.0017	1.8	0.7	1.2	2.0
150	B	LR	0.39, 1	25	1.2	−0.0017	1.9	0.7	1.1	2.2

IV. Discussion

This study elucidates the relationship between both CT and MR images, frequency, and acoustic attenuation. This increased clarity will improve simulation accuracy, leading to better prediction of the acoustic intensity at the focal spot. Clinicians can leverage this accuracy to better predict the relationship between transducer power and temperature at the focal spot, resulting in safer treatments.

The measured attenuation presented in this study is within the range of attenuation measurements found by other authors. Direct comparisons are difficult as each study measures the attenuation at different frequencies and in bone fragments with different compositions. Bossy et al. [44] found attenuation values ranging from 0.6 to 5.2 Np/cm/MHz. Pinton et al [24] measured an attenuation of 2 ± 0.97 Np/cm at 1 MHz. Hüter [22] measured attenuation values on the order of 0.3–1 Np/cm, 0.9–1.3 Np/cm, and 4.4–5.4 Np/cm at 0.5, 1, and 2.25 MHz. These measurements from prior studies are comparable to the results of this study given in Table II.

A. Predicting Acoustic Attenuation with HU

Equation (4) is only one possible model of the relationship between HU and attenuation and other models may yield similar results. For example, fitting the data to a second order polynomial of the form

$$\alpha ={\alpha }_0{f}^{\beta }+x_0+x_{1}p+x_2{p}^2+cfp,$$ (6)

resulted in comparable prediction of attenuation as a function of HU and frequency. Equation (4) was selected because we do not expect the attenuation to be parabolic.

Figure 7 compares the result of this study to existing literature models. The comparison is done at 650 kHz because this is a common frequency for tcMRgFUS treatments [43]. The blue line shows the model presented in this work and the shaded region gives the 95% confidence interval. All models show relatively good agreement in the region near 1500 HU but as the HU value decreases several of the literature models diverge. A lack of fragments with HU values below 1000 makes it impossible to say for certain how the function should behave in this range but we can get some idea of its behavior by looking at the data from higher frequencies. At higher frequencies, the increase in the measured attenuation accelerates as the HU value decreases. We can expect similar behavior at 650 kHz but it appears that the rate of change remains low at HU values greater than 1000. Of the prior literature models, these data are most consistent with McDannold’s findings [27].

Fig. 7. Comparison of Prior Models to the Results of This Study.

The blue line shows the predicted attenuation using Equations (4) and the shaded region shows the 95% confidence interval. The source for each literature model is given in the legend. Models that were derived at a frequency other then 650 kHz were transformed according to α = α₀f^β using a β of 1.2.

The 2.25 MHz data does provide some insight into one possible reason that other models predict a decrease in attenuation with decreasing HU. The fragment that was excluded from linear fits because of its large pore size had an average HU of 829 and an attenuation of 5.7 Np/cm, a dramatic decrease in attenuation relative to other fragments in that HU range. This provides some evidence that if the pore size is large relative to a wavelength and the bone regions are small then the decrease in attenuation predicted by some literature models can occur. However, in the samples used in this experiment, the pore sizes were not large enough to observe this decrease in attenuation except in one fragment, suggesting that this is a condition unlikely to occur in tcMRgFUS treatments. Additional evidence of this is that, at frequencies more relevant to tcMRgFUS treatments, this drop in attenuation was not observed. The attenuation measured in this fragment at 500 kHz and 1 MHz was 2.2 and 3.9 Np/cm respectively which fits the overall trend measured at these frequencies.

B. Predicting Attenuation with MR

MR provides some inherent advantages as a pre-treatment imaging modality over CT. Using MR would remove the need to register the CT and MR datasets on the day of the treatment, eliminating an important source of error. MR images are often lower resolution than CT but some preliminary work [45] suggests that the accuracy of transcranial ultrasound simulations is not significantly affected until the voxel size exceeds 1.5mm. Using MR to both predict acoustic properties and provide real-time monitoring of the treatment creates the possibility of intra-operative updates to acoustic property maps. Pre-treatment MR would also remove the need for the ionizing radiation associated with CT. While the ionizing radiation of CT is not a barrier for most candidates of tcMRgFUS treatments, eliminating it would benefit pediatric applications and may enable the use of ultrasonic neuromodulation in healthy volunteers. The result that UTE and ZTE based MR methods estimate attenuation in skull bone with an accuracy comparable to that of CT suggests that MR does have the potential to replace pre-treatment CT in focused ultrasound procedures.

C. Frequency Dependence

The measured value of β shows excellent agreement with previous studies [38, 42, 46–48]. Fry and Barger use the relationship between frequency and insertion loss to evaluate the contributions of scattering and absorption to the overall attenuation. Their conclusions rely on analytical predictions of the relationship between scatterer size and frequency. In general, when a scatterer is small relative to a wavelength, the scattered pressure increases as the frequency to the fourth power [49]. Fry and Barger argue that, at lower frequencies, absorption must be the dominant mechanism since this kind of rapid increase with frequency is not observed. As the wavelength decreases, scattering plays a more prominent role and the attenuation begins to grow rapidly with frequency. Eventually, as the size of the wavelength becomes more comparable to the size of the scatterer, the rate of change reduces to the square of frequency [49]. Bossy et al. [44] similarly argue that absorption becomes more important as frequency decreases, resulting in poorer simulation results when using porosity to estimate attenuation. The data presented in this work agrees with these studies, showing the same general shape in the relationship between frequency and attenuation observed by both Fry and Barger [23] and Hüter [22].

One potential weakness of the model proposed by Equation (4) is that the parameter β likely depends on the pore size and is thus itself a function of the imaging parameter, p. To test this we performed a fit in which β was assumed to have a linear relationship with p [41]

$$\alpha ={\alpha }_0{f}^{{\beta }_{1}p+{\beta }_0}{e}^{cp}.$$ (7)

The resulting function was very similar to the results presented in this paper with slightly increased standard errors, suggesting that β is well modeled as a constant over the samples tested in this work. The consistency across many studies with which β is measured to be slightly larger than one [38, 42, 46–48] provides further evidence of this.

D. Simulating Transcranial Ultrasound

To the extent that imaging resolution permits, simulation techniques that model heterogeneous velocity and density already account for acoustic scattering. Therefore, adding an additional attenuation term based on a simple transformation of imaging parameter to attenuation is likely to result in an overestimate of acoustic loss. Indeed, this may explain the discrepancy between the results of this study and the model proposed by McDannold et al [27]. In that study, rather than measure attenuation directly, the authors found the transformation between HU and attenuation that resulted in the best prediction of acoustic loss. Such an approach inherently accounts for any scattering that is already modeled by the simulation method, making it specific to that simulation technique and imaging resolution. Our model is more independent of simulation method and imaging resolution but application of the model is nontrivial since the investigator must take great care to avoid double counting losses due to scattering.

The imaging parameters used to acquire a patient image must also be accounted for in order to obtain accurate simulations. Webb et al. [17] noted that CT parameters have a strong impact on the measured transformation between HU and velocity and this study shows a similarly robust impact on estimates of attenuation. As in [17], x-ray energy is the most important factor but other parameters play a role as well. Tables IV and V provide individual fits for the same set of CT parameters that were presented in [17]. Investigators can find the set of parameters that best fits their setup in order to determine the appropriate transformation between HU and attenuation. MR parameters likely also alter the transformation between the MR image and the acoustic attenuation and future studies are needed to identify which parameters matter and how the relationship varies as those parameters change.

E. Limitations Of Measurements

Errors in the measurement of thickness, density, and velocity cause the predicted insertion loss to differ from the measured insertion loss, resulting in a corresponding error in the measured attenuation. This error oscillates with frequency because resonances in each individual fragment cause oscillations in the insertion loss as a function of frequency. An example of this is presented in Figure 8(a) which shows the measured attenuation in a 4.7 mm thick fragment with a density of 1783 kg/m³. This effect is removed when the attenuation can be averaged across multiple fragments (Figure 8(b)) and doesn’t, therefore, preclude fitting an equation to the data. It does, however, increase the standard error of the fit.

Fig. 8. Limitations.

Small errors in the measured thickness, velocity, or density can cause oscillations in the predicted attenuation as a function of frequency.

a) Measured attenuation as a function of frequency in an individual fragment (4.7 mm thick, 1783 kg/m³). The colors denote which transducer was used to acquire each measurement with blue representing the 0.5 MHz transducer, red representing the 1 MHz transducer, and yellow representing the 2.25 MHz transducer.

b) Average attenuation measured across all fragments as a function of frequency. Shaded error bars show the standard deviation of the measurement.

Imperfect emulation of in-vivo conditions introduces further limitations. Measurements were performed at room temperature and pores were filled with water rather than marrow. To enable the measurement of attenuation in individual bone types, each sample was divided into individual layers. In an in-vivo skull an acoustic beam will pass through all of these layers, resulting in additional reflection and refraction of the beam. Sanding of the surfaces of each fragment may also alter the behavior of the ultrasound since the creation of a flat interface may result in a stronger reflection at bone water interfaces and the cylindrical shape of each fragment may strengthen or create resonances that are less pronounced in the in-vivo condition. This sanding is necessary, however, because it enables a more reliable estimate of the thickness of each fragment. Some uncertainty remains (sanding of each fragment was done by hand) but the precision of thickness measurements is improved by this process of flattening each interface.

The accuracy of the attenuation measurements is impacted by the placement of the bone fragment in the beam path which alters the beam pattern. These alterations can include blurring of the natural focus and movement of the focus closer to the transducer, both of which are likely to lead to an overestimation of attenuation. These effects are somewhat mitigated by averaging three measurements of attenuation for each fragment. In between measurements, each fragment was completely removed and replaced into the setup, randomizing the position and, as a result, the beam shape artifacts. The standard deviation across these three measurements (as reported in Section III-A) was relatively small, suggesting that blurring and movement of the focal spot are not a dominant source of error. However, while the errors may not be large, they are always positive, resulting in an overestimation bias. While the experimental methods are designed to minimize this bias, there is no simple way to measure its magnitude or to remove it. Therefore, it is likely that the magnitude of the actual attenuation is slightly less than these measurements suggest.

The reliability of the result is impacted by the limited number of skulls used in the study and the way in which the skulls were prepared. Prior studies [21] have shown a large variation across the patient population in the total acoustic loss after transmission through the skull. While some of this variation is likely due to skull shape and thickness, further studies with a larger number of skull samples are required to measure patient to patient variation in the relationship between each imaging parameter and attenuation. The acoustic properties of the skull may also change after desiccation. For example, White et al. [50] has shown a small (2.3%) but significant variation in acoustic velocity between fresh and re-hydrated samples and it is possible that the attenuation will also be affected by this process. Because the skull samples were purchased in the desiccated state, the authors had no control over the desiccation process. Further studies are needed to measure the impact of desiccation on acoustic attenuation.

Due to these limitations it is important to understand this study as a demonstration of the overall shape of the relationship between frequency, CT/MR-derived imaging parameters, and attenuation. The detailed functions provided in the appendix provide some insight into the shape of this relationship but more data from more skulls are required to find optimal relationships. This is especially true at lower HU values where little data were available. A future study which examines attenuation in several skulls across the patient population would be of great benefit to the field.

V. Conclusion

The acoustic attenuation was measured in fragments from two ex vivo human skulls. The measurements were tested for correlation with CT HU, magnitude UTE and ZTE images, and T2* estimates. Attenuation was found to monotonically decrease with HU and monotonically increase with all three MR parameters. In every case the slope of the relationship was highly frequency dependent. CT predicted the attenuation best with MR achieving comparable, but slightly less accurate, predictions. Accurate prediction of the attenuation in the skull using CT and MR imaging will enable better simulation of tcMRgFUS treatments, leading to more efficient treatment planning and better prediction of the temperature at the focal spot.

VII. APPENDIX

Table III provides a summary of the fragments used to obtain measurements of attenuation, including raw values of density, thickness, and insertion loss. Tables IV and V summarize the results for the measured relationship between HU and attenuation.

TABLE III.

Properties of the fragments used to obtain imaging and attenuation measurements. Legend: IL: Insertion Loss, M: Medullary, IT: Inner Table, OT: Outer Table

Fragment	Density (kg/m3)	Thickness (mm)	Bone layer	IL @ 0.5 MHz	IL @ 1 MHz	IL @ 2.25 MHz	Fragment	Density (kg/m3)	Thickness (mm)	Bone layer	IL @ 0.5 MHz	IL @ 1 MHz	IL @ 2.25 MHz
1	1567	2.1	M	3.9	7.8	30	46	1774	2.3	OT	3.5	7.6	18
2	1708	1.4	IT	8	4.5	7.6	47	1694	2.4	M	6.2	8.4	22
3	1810	1.5	OT	9.7	4	9.7	48	1813	2.2	OT	4.6	6.2	9.2
4	1913	1.5	IT	8.2	6.9	9.8	49	1750	2.4	M	5.9	9.8	24
5	1545	2.6	M	4.3	8	40	50	1880	2.1	OT	4.6	7.8	15
6	1720	1.8	OT	7.3	4.8	16	51	1737	2.7	M	6.6	7.2	24
7	1842	1.6	M	6	4.4	9.8	52	1813	2.4	OT	4.1	5.9	14
8	1762	1.5	OT	8.4	4.9	7.4	53	1660	3.6	M	6.8	11	31
9	1658	6.1	M	8	12	52	54	1814	3.5	OT	5.6	9.6	17
10	1880	2.2	OT	6.1	7.5	9.6	55	1658	5.3	M	8.1	12	43
11	1698	4.1	M	9	10	40	56	1889	2.3	OT	4.1	11	12
12	1829	3.1	OT	4	5.8	14	57	1452	2.1	M	4.7	8.3	34
13	1814	3.4	M	6.2	9.6	29	58	1588	2.3	M	7	16	16
14	1909	1.6	OT	8.9	1.7	5.6	59	1560	1.7	M	6.9	5.4	8.8
15	1846	2.2	OT	6.8	9.8	11	60	1905	1.8	OT	7.5	5.6	7.5
16	1905	1.7	IT	6.6	5.6	8.4	61	1773	1.3	IT	7.7	1.9	4.8
17	1903	2.7	OT	3.6	9	17	62	1600	1.6	M	6	7.1	19
18	1658	2.8	M	5.6	8.9	30	63	1750	2.1	OT	4.4	7.4	16
19	1632	1.2	IT	7.7	3.9	10	64	1811	2.7	M	4.3	4.9	10
20	1789	1.2	IT	7.7	3.1	6.5	65	1947	1.5	OT	8.6	5.4	9.1
21	1800	2.2	IT	3.7	5.5	17	66	1818	3.4	M	6.2	8.5	19
22	1517	2	M	3.8	7.8	20	67	1875	1.8	OT	8.5	6.6	8.7
23	1857	2.6	OT	2.6	7.8	10	68	1783	4.7	M	7.7	11	33
24	1750	2.2	IT	3.9	6	20	69	1632	2.4	OT	4.8	10	10
25	1720	3.9	M	7	8.4	28	70	1857	2.3	M	3.6	9.6	14
26	1920	2.2	OT	6.5	6.2	11	71	1913	1.6	OT	8.6	7.9	7.4
27	1676	5.5	M	8	15	44	72	1750	3.1	M	5.2	5.4	13
28	1864	1.9	OT	8.2	8.5	8	73	1889	1.5	OT	8.7	3	7.2
29	1655	4.3	M	7.9	15	48	74	1600	1.5	M	6	6	23
30	1690	2.1	OT	4.8	8	9.8	75	1813	2.4	OT	3.7	7	13
31	1725	2.8	IT	8.2	9.9	29	76	1836	4.3	M	9.8	11	27
32	1900	2.4	OT	3.8	7.2	13	77	1778	2.7	M	4.8	9.7	20
33	1606	2.3	IT	4.1	6.8	20	78	1722	1.3	OT	7.3	3.8	6.2
34	1848	2.6	OT	3.9	7.1	13	79	1821	2.6	M	3.4	6.3	9.9
35	1775	2.8	M	6.6	8.1	20	80	2000	2.7	OT	3.4	8.6	7.1
36	1833	2.1	OT	4.2	6.8	12	81	1966	2.6	OT	3.7	9.9	13
37	1786	4.1	M	7	9.8	25	82	1943	3	OT	4.1	4.4	8.8
38	1625	2.2	M	3.5	6.7	21	83	1921	6.6	OT	7.3	10	17
39	1962	2.4	OT	4.8	7.9	14	84	1759	4	M	7.8	10	36
40	1833	2.9	IT	6.4	8.8	20	85	1865	2.6	OT	2.8	7.2	8.3
41	1778	2.1	OT	4.8	7.7	12	86	1829	2.6	M	3.6	7.7	12
42	1872	3	M	7.4	9.2	27	87	1800	2.8	OT	4.2	5.8	14
43	1833	2.4	OT	3.4	8.4	15	88	1794	2.6	OT	4.8	13	14
44	1814	3.4	M	6.9	8.9	29	89	1733	1.2	M	7.9	4.7	12
45	1900	3.1	OT	4.9	6.7	16