Influence of cerebrospinal fluid on power absorption during transcranial magnetic resonance-guided focused ultrasound treatment

Abstract

Background:

Ultrasound beam aberration correction is vital when focusing ultrasound through the skull bone in transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) applications. Current methods make transducer element phase adjustments to compensate for the variation in skull properties (shape, thickness, and acoustic properties), but do not account for variations in the internal brain anatomy.

Purpose:

Our objective is to investigate the effect of cerebrospinal fluid (CSF) and brain anatomy on beam focusing in tcMRgFUS treatments.

Methods:

Simulations were conducted with imaging data from 20 patients previously treated with focused ultrasound for disabling tremor. The Hybrid Angular Spectrum (HAS) method was used to test the effect of including cerebral spinal fluid (CSF) and brain anatomy in determining the element phases used for aberration correction and beam focusing. Computer tomography (CT) and magnetic resonance imaging (MRI) images from patient treatments were used to construct a segmented model of each patient’s head. The segmented model for treatment simulation consisted of water, skin, fat, brain, CSF, diploë, and cortical bone. Transducer element phases used for treatment simulation were determined using time reversal from the desired focus, generating a set of phases assuming homogeneous brain in the intracranial volume, and a second set of phases assigning CSF acoustic properties to regions of CSF. In addition, for three patients, the relative effect of separately including CSF speed of sound values compared to CSF attenuation values was found.

Results:

We found that including CSF acoustic properties (speed of sound and attenuation) during phase planning compared to phase correction without considering CSF increased the absorbed ultrasound power density ratios at the focus over a range of 1.06 to 1.29 (mean of 17% ± 6%) for 20 patients. Separately considering the CSF speed of sound and CSF attenuation showed that the increase was due almost entirely to including CSF speed of sound; considering only the CSF attenuation had a negligible effect.

Conclusions:

Based on HAS simulations, treatment planning phase determination using morphologically realistic CSF and brain anatomy yielded an increase of up to 29% in the ultrasound focal absorbed power density. Future work will be required to validate the CSF simulations.

Introduction

Transcranial magnetic resonance-guided focused ultrasound (tcMRgFUS) is a noninvasive method with regulatory approval in the United States for the treatment of both essential tremor and Parkinson’s disease (1, 2). In tcMRgFUS, acoustic energy is transmitted through the intact scalp and skull to thermally ablate tissue within the brain at the beam’s focus. To reduce heating at the skull/tissue interface, tcMRgFUS uses as many as 1024 piezoelectric elements arranged over a large, 30-cm diameter, hemispherical transducer array to spread the acoustic energy over a large skull area (1, 3, 4). Due to the size of the transducer and the high variability in thickness and structure of the skull bone, phase aberrations are much more prominent using this system than systems with smaller diameter (higher f-number) transducers (5–7). The large difference in speed of sound between bone and surrounding soft tissue results in substantial phase variation upon passage through different regions of the skull, leading to beam distortion and defocusing. To improve focusing, accurate phase aberration correction must be used to compensate for the effects of the skull (8). The treatment itself is guided, monitored and evaluated by magnetic resonance imaging (MRI) and MR thermal imaging (MRTI) (9).

Focusing to the desired point is accomplished by individually adjusting the phases of each element of the phased-array transducer. These phases are currently obtained based on the patient’s pre-treatment CT images. To the extent that tissue acoustic and thermal properties are known, treatments can be modeled with the use of acoustic and thermal treatment simulations (6, 10). These simulations can then be used to screen patients for treatment eligibility and to estimate the efficiency of phase aberration correction before the clinical treatment. With accurate acoustic and thermal properties, simulations can potentially predict the potential for success of a treatment before it is performed.

Various acoustic simulation methods have been used for procedure planning and modeling. In addition to ray-tracing methods based on local skull orientation and thickness that are currently used clinically for phase aberration correction in the Exablate Neuro transcranial system (Insightec, Tirat Carmel, Israel), acoustic modeling has been performed using finite difference methods (11), the open-source k-Wave (12) or Hybrid Angular Spectrum (HAS) (3, 13) software packages. k-Wave has been used to create tcMRgFUS simulations in segmented models with water, bone, brain, and extracranial soft tissues, with bone acoustic properties assigned based on the patient pre-treatment CT images (10). In one study using HAS, the bone acoustic properties as a function of CT Hounsfield units (HU) were adjusted to best match the simulation-predicted heating to that obtained by MRTI during the treatment (6). After determining the acoustic intensity, a finite-difference time-domain implementation of the Pennes bioheat equation was used to simulate heating in the brain.

Because of the substantial effect of the skull on the ultrasound beam, treatment simulations have paid little attention to the 3D distribution of brain tissue and CSF within the skull. One study performed a numerical simulation in two dimensions, including effects of variations in skull geometry and of multiple tissues including scalp, skull, CSF, and gray/white matter. It concluded that transcranial wave propagation is strongly influenced by the cranium but largely insensitive to small changes in material properties. It further found that CSF in sulci at the cortical surface can have a small impact on wave propagation (14). The study modeled a 30-mm diameter transducer with 30-mm focal length and did not evaluate the full three-dimensional anatomy of the skull, brain tissue, and CSF. Of the studies that are referenced above that performed 3D simulations to improve ultrasound beam focusing in tcMRgFUS, none included the relative distributions of brain tissue and CSF.

The purpose of this study was to investigate the effect that the 3D distribution of soft tissues and CSF has on phase aberration and acoustic fields in the head during tcMRgFUS treatments with a clinically used system. Simulation studies were performed with two types of segmented models of the intracranial tissues: 1) the entire intracranial space considered to be homogeneous brain tissue, and 2) the intracranial tissues segmented into CSF and brain tissue. Using the CT scans of 20 essential tremor patients, the rapid HAS method simulated and compared the power density deposition Q patterns for the two assumed models. In three subjects, the relative effect of separately including CSF speed of sound values compared to CSF attenuation values was investigated. In one subject, the Pennes bioheat equation was applied to compare temperature maps.

Methods

Hybrid Angular Spectrum (HAS)

The HAS method was used for all acoustic simulations in this work (13). HAS was developed to simulate ultrasound propagation through inhomogeneous media based on a segmented tissue model and has been employed in models similar to the ones in this study (6, 13, 15, 16). The 3D model assigns individual values for attenuation α (Np/MHz·cm), absorption μ (Np/MHz·cm), speed of sound c (m/s), and density ρ (kg/m³) to each voxel and calculates the steady-state acoustic pressure distribution (Pa) and corresponding absorbed acoustic power density Q (W/m³).

HAS first uses the Rayleigh-Sommerfeld integral to calculate the individual pressure patterns from each transducer element as propagated through water to an intermediate plane in front of the tissue model. From that plane, HAS approximates transmission through the inhomogeneous tissue in incremental steps from plane-to-plane, alternating between a space-domain step that accounts for locally varying attenuation and speed of sound values within each plane, and a spatial-frequency-domain step that accounts for propagation to the next plane using an angular spectrum transfer function based upon the average speed of sound for that plane.

The space-domain step through each plane employs a transfer function t_n(x, y) that includes local attenuation and speed of sound differences from the average speed of sound, as described in (11):

$$p_n^{\prime }\left(x,y\right)=p_{n-1}\left(x,y\right)\cdot t_n\left(x,y\right),$$ (1a)

where $p_n^{\prime }\left(x,y\right)$ describes the pressure pattern in the n^th plane before propagation to the next plane. Then a fast Fourier transform (FFT) of this pattern finds the corresponding pressure pattern in the spatial-frequency domain $A_n^{\prime }\left(f_x,f_y\right)$, where the propagating pressure wave is decomposed into a set of tilted plane waves (the angular spectrum). Propagation through plane n is calculated in the spatial-frequency domain by a transfer function ${\tau }_n\left(f_x,f_y\right)$ that depends on spatial frequency using the planar average speed of sound:

$$A_n\left(f_x,f_y\right)=A_n^{\prime }\left(f_x,f_y\right)\cdot {\tau }_n\left(f_x,f_y\right),$$ (1b)

where A_n(f_x, f_y) is the angular spectrum of the wave at the entrance to the next plane. An inverse FFT transforms the pattern back to the space domain for transfer through that next plane. This proceeds through the entire tissue volume. Possible reflections at each planar interface are included by propagating them in the reverse direction. The Q pattern for the volume is then obtained as:

$$Q={\left|p\right|}^2*\mu /\left(\rho *c\right),$$ (2)

where the values are specific to each voxel.

In this study, the tcMRgFUS simulations were performed using a transducer model corresponding to the Insightec 650-kHz Exablate Neuro clinical system, which consists of a 30-cm diameter hemispherical large-aperture transducer with 1024 total piezoelectric elements placed around the hemisphere. At the start of the treatment for each patient, the geometric focus of the transducer was placed at the ventral intermediate (VIM) nucleus on the side of the thalamus to be treated. For each patient simulated, the actual number of elements employed was less than 1024 because some elements were inoperative or turned off due to oblique incidence or passage through air-filled sinuses or intracranial calcifications. Because of approximations made by the angular spectrum approach, HAS is limited to model only transducers with relatively high f-numbers (long focal length compared to diameter) with beams falling within a moderate cone of angles aligned with the original cartesian z-axis. Thus, to simulate a hemispherical transducer that surrounds the skull with an f-number as low as 0.5, it is necessary to divide the transducer into segments. For this work, the hemispherical transducer is split into seven segments as shown in Figure 1. For the six transducer segments on the periphery whose individual axes of propagation fall outside the angular acceptance limits of the skull model, each transducer segment and the entire skull model are temporarily rotated such that the segment’s nominal axis of propagation is along the z-axis used by HAS. After the beam from each segment is propagated through the corresponding rotated model, the complex pressure pattern is rotated back to the original orientation of the segment. Then, assuming linearity in pressure response, the individual pressure patterns are combined to obtain the predicted pressure pattern for the entire transducer. The absorbed acoustic power density pattern Q (W/m³) is generated from the total complex pressure distribution according to

$$Q={\left|{\sum }_{j=1}^7{p}_j\right|}^2*\mu /\left(\rho *c\right),$$ (3)

where the sum is over the seven segments and the parameters are specific to each voxel of the model as defined earlier.

Figure 1:

Schematic diagram of seven-segment hemispherical transcranial MRgFUS transducer. a) A 3D perspective view where the element position is enhanced by the changing color. b) A flattened view showing the elements grouped into seven segments. The central segment has 256 elements; each of the outer six segments has 128. Elements that are not functional are not shown.

Model segmentation

The models used in this simulation study were based on 20 essential tremor patients treated at the University of Utah. All studies were performed with IRB approval and signed informed consent. The segmented model of each patient was created using CT and MR images acquired before, during or after the treatment.

In the first segmentation step, the CT scan that was used clinically in the pretreatment planning was segmented into cortical bone, diploë (cancellous bone), fat, skin and brain tissue based upon Hounsfield Unit (HU) thresholds and locations relative to the skull (Table I). The skull cortical bone was defined as all voxels with HU > 1000. Diploë (cancellous bone) was defined as all voxels between the inner and outer cortical tables of the skull with values in the range 300 to 1000 HU. Any voxels between the tables with values −1000 to 300 HU were defined as marrow (fat). Within the cranium (between the brain and the skull inner table), voxels adjacent to cortical voxels (internal cortical table) with values in the range between 650 HU (midpoint threshold between 300 and 1000) to 1000 HU were defined as partial volume cortical voxels that were mostly cortical and therefore considered as cortical. All other voxels within the cranium were defined as generic brain tissue. External to the skull, tissues were defined as skin or fat depending on HU values (Table I). All voxels external to the skin and fat were defined as water comprising the ultrasound coupling region.

Table I.

Threshold values from CT images (in Hounsfield units, HU) and MRI used for segmentation and acoustic properties used for simulations. All values from IT’IS database (14).

	Segmentation Ranges	Absorption (Np/cm·MHz)	Attenuation (Np/cm·MHz)	Density (kg/m3)	Speed of Sound (m/s)
1. Water	CT: −1000<HU<0*	0	0	1000	1500
2a. Fat	CT: −200<HU<0	0.044	0.044	911	1440
2b. Marrow+	CT: −200<HU<300	0.044	0.044	911	1440
3. Skin	CT: 0<HU<300	0.21	0.21	1109	1624
4. Brainx	CT: −100<HU<300	0.068	0.068	1046	1546
5. Cerebral Spinal Fluid	Threshold midway between CSF and brain in T2w MRI images	0.001	0.001	1007	1505
6. Cortical Bone	CT: HU > 1000	0.47	0.47	1908	2814
7. Diploë	CT: 300<HU<1000	0.545	0.545	1178	2118

^*In the water coupling region,

⁺In diploë region (between inner and outer skull tables)

^xInternal to cranium

In the second step, using T2-weighted (T2w) MR images, the brain tissue was further segmented into brain and CSF using a threshold in the T2w image midway between CSF and brain. Generally, in these T2w images CSF is much brighter than brain tissue and therefore is easily segmented. Although the boundaries of large CSF-filled structures such as the ventricles are relatively independent of the selected threshold, the image voxels at the convoluted cortical surface may only partially contain CSF, and therefore a low threshold may segment voxels that are less than 50% CSF but are still brighter than the surrounding brain. To minimize these partial volume effects, care was taken to select the threshold. Two observers (DLP and JM) carefully reviewed the CSF segmentation for each patient and adjusted the threshold to match the segmented CSF to the visual thickness of the CSF in the T2w MR images. Then the affine transformations that registered the skull in the pre-treatment CT scans to the skull in the selected MRI scans were used to register the model with the patient’s MR images.

The acoustic values used for each segmented tissue type were obtained from the Information Technologies in Society (IT’IS) Foundation database (14), as shown in Table I.

Acoustic Simulations

This study was designed to test the effects of including CSF in determining the planned tcMRgFUS treatment phases when the model to be simulated contains both CSF and brain tissue. As such, two models were created for each of the 20 patients using relevant sections of the segmentation methods described above:

Model I - Each patient’s clinical CT scan was used to segment the anatomy into skin, fat, cortical bone, diploë and brain, with the entire cranium filled with generic brain tissue.

Model II - For the same 20 subjects, the patient’s T2w MR image was used to further segment the brain tissue into brain and CSF (see Figure 2 for transverse examples, and Supplement Figure 1 for coronal and sagittal examples).

Figure 2:

Example of four axial slices from the first three patient models showing segmentation into the tissue types listed. All patient models were segmented from pre- and post-treatment CT and MR images. The last slice on the right shows the plane at the transducer geometric focus and the point (red asterisk) where the simulated focus for time reversal is placed. See Supplement Figure 1 for orthogonal views.

All acoustic simulations were performed with the HAS method to take advantage of its computational speed. The simulation flow diagram consisted of two main steps, as illustrated in Figure 3:

1. The time-reversal method (17) was used to first back-propagate the acoustic field from the intended focus to each element of the transducer array. For this study, the intended focus was chosen as the geometric focus of the ultrasound transducer, which was placed at the target used for clinical essential tremor treatment. HAS enables time-reversal phase correction by simulating excitation of a single point at the intended focus and back-propagating the pressure wave from that point to the center of each transducer element to determine the phase of the received wave. This time-reversal step was performed once using Model I (which doesn’t include CSF, we label this as Plan:noCSF) and a second time using Model II (which includes CSF, labeled as Plan:CSF).

2. These two sets of phases were then inverted and used by HAS to forward propagate the acoustic field from the transducer elements into the same Model II (including CSF) to the intended focus to simulate the intracranial acoustic power deposition pattern Q for each of the two phase-determining conditions found in the first step. The same incident acoustic power was used in all simulations and was normalized to 1-Watt total power.

Figure 3:

Modeling flow diagram. Two models of each patient are created based on the individual’s MR and CT images: Model I assumes all tissue inside the cranium is uniform brain; Model II segments the region into brain and CSF. Employing a time reversal technique, transducer element phases are obtained for the patient using each of the two models. Then a forward beam simulation calculates a resulting Q pattern in Model II for the two cases, allowing comparison of the effect of including CSF in the phase planning. For both planning methods, the aberration corrected phases for Patient 1 are shown on the seven segments of the ultrasound transducer.

A convergence test was performed to establish the voxel spacing needed in HAS to adequately represent the pressure and power profiles at the focus. To accomplish this, the numerical models for each patient were created with 0.25 mm, 0.5 mm, and 1.0 mm isotropic voxel spacing. The 0.25-mm model consisted of an array of 901 × 901 × 1200 voxels, with the center of the transducer bowl (geometric focus) at the point (451,451,600). The 0.5-mm models were obtained by retaining the geometric focus point and every other alternating point of the 0.25-mm models. The 1.0-mm models were obtained in the same manner from the 0.5-mm model. During the course of these experiments, we found that one effect of using the phases obtained from planning with brain only and then forward simulating with CSF and brain was a shift in the position of the focus. If this shift is less than a full voxel spacing, the peak pressure value will also be reduced by the voxel sensitivity function (18). To reduce this effect the complex pressure fields were zero-filled-interpolated to a finer spacing, down to 0.25 mm and 0.125 mm.

As a sub-study to ascertain whether the CSF speed of sound or attenuation had the largest effect on the observed difference in Q, the simulations were repeated using the 0.5-mm models of three patients with all CSF acoustic properties in Model II of each patient set to brain values except for the speed of sound. The experiment was repeated with the CSF acoustic properties set to brain values except for the attenuation.

To observe the effects of the CSF segmentation threshold on the improvement in Q for seven of the 20 patients (chosen to represent the distribution of improvement), the CSF segmentation threshold for the 0.5-mm model was adjusted over a range of equally spaced values determined from a histogram of the intensity of all intracranial voxels in the T2w MR images. Adjusting the segmentation threshold resulted in a variation in the number of voxels defined as CSF or brain. For each threshold value, the fraction of CSF voxels relative to the brain voxels was determined (defined as CSF fraction) and the corresponding Q value was found.

A potential flaw in this study is due to the fact that the same acoustic values for CSF and brain tissue were used both in the planning to determine the element phases and in the forward simulation to determine the Q-value distributions (the so-called “inverse crime”). In real-life clinical situations, the actual acoustic properties will not be known exactly for the planning/phase determination process. To address this, the element phases obtained by planning with the table values were applied in forward simulation to the situations where the actual acoustic speed of sound values were changed by c_CSF = c_CSF-table (1+δ_c) and c_brain = c_brain-table (1-δ_c) for δ_c values of 0.000, 0.002, 0.004, and 0.006, corresponding to a percent change of 0.0, 0.2, 0.4, and 0.6%, respectively. For a 0.6% change, the values become: c_CSF = 1514 m/s and c_brain = 1537 m/s, with a separation of 23 m/s.

Thermal Simulations

For Patient 3, whose treatment included ten sequential sonications, the temperature effect due to heating using the two respective Q patterns (planned with and without considering CSF) was evaluated. Each simulated Q pattern, now scaled by the actual acoustic power values used during each sonication, was input to a finite-difference time-domain implementation of the Pennes bioheat equation to create maps of temperature T (19):

$$\rho c_t\frac{\partial T}{\partial t}=k{\nabla }^{2}T-w{c}_b\left(T-T_a\right)+Q,$$ (4)

where thermal conductivity k = 0.55 × 10⁻³ W/mm/ °C, tissue density ρ = 1.045 × 10⁻⁶ kg/mm³, and tissue heat capacity c_t = 3400 J/kg/°C. For simplicity, perfusion was neglected, w = 0. In these simulations, the initial temperature was zero throughout the volume (we measured temperature change only) and it was assumed that the volume around the calculation volume was a large thermal reservoir that held the outer boundary at a constant temperature. We believe this was justified because the heating pulse was localized (< 5 mm) and of short duration (<30 s), the calculation space was large (> 150 mm in all directions), such that heat from the heating pulse did not diffuse to the boundary during the heating. To test this, these simulations for Patient 3 were repeated with an explicit adiabatic boundary condition (Neumann: ∂T/∂x = 0) and the results were identical to those shown in Figure 9.

Figure 9:

a) Simulated Q (top) and heating (bottom) patterns observed for the second sonication of Patient 3. The left column shows the peak Q distribution and maximum temperature rise obtained when planning uses all-brain (Plan:noCSF). The right column shows the peak Q distribution and maximum temperature rise obtained by planning using CSF and brain (Plan:CSF). b) Percent temperature increase when including CSF (Q Plan:CSF) in planning over not including CSF (Q Plan:noCSF) in planning. The percent improvement is plotted for all 10 sonications. c) Fractional increase in the peak temperature between using Q Plan:noCSF and Q Plan:CSF as a function of time during and after the sonication.

Analysis

The volumetric Q patterns simulated for each of the 20 subjects were used in a comparison of the two treatment planning assumptions based on the peak Q value obtained at the focus. In addition, the total power being deposited for each subject was calculated by integrating the Q patterns over the large intracranial tissue volume included in the simulation to determine whether any reduction in the peak Q value was due to a less focused beam (less efficient aberration correction) or to an overall decrease in total power. Also, for Patient 3, as mentioned above, the simulated peak temperatures were compared.

Results

The ratio of power deposition, Qratio, with and without inclusion of CSF was calculated from the models at 1.0 mm, 0.5 mm and 0.25 isotropic spacing for all 20 subjects. For all 20 subjects, the average Qratio was 1.37 (±0.20) at 1-mm isotropic compared to 1.30 (±0.10) at 0.5-mm isotropic spacing and reduced to 1.17 (± 0.06) at 0.25-mm isotropic spacing. Because of this reduction at the finer spacing, the primary experiments were all repeated at all three spacings using the two phase-determining methods for each subject. In Figure 4a, the images of the Q patterns (at the plane of the peak Q near the focus) obtained using the phases obtained using the two planning methods (Plan:CSF and Plan:noCSF) are shown for three subjects at 0.25-mm, 0.5-mm and 1.0-mm voxel spacing. The 0.25-mm images show a more accurate representation of the Q at the focus, especially for the Plan:noCSF images. Figure 4b gives the comparison Q patterns at 0.25-mm resolution for all 20 subjects. These images show a consistent increase in power deposited at the plane of peak Q relative to when CSF in the model is not included in the planning (Plan:noCSF). This increase is more clearly seen in Figure 5, comparing the Q values from Figure 4b plotted along three orthogonal lines through the peak value for each planning method. The last plot in each group of three is along the transducer axis and thus slightly wider than the two lines orthogonal to the axis. There was also a small average shift (< 0.5 mm) in the focal spot position between the two phase-determining methods.

Figure 4:

a) Comparison of peak Q patterns at the plane of focus at 1.0 mm, 0.5 mm and 0.25 mm isotropic voxel spacing for 3 patient simulations. In each pair, the left image shows the result when the planning phases were obtained assuming homogeneous brain tissue within the cranium (Plan:noCSF); the right image shows the result when planning included CSF and brain (Plan:CSF). The maximum value of the colorbar (units are W/dm³) varies between patients but is the same for both planning scenarios. b) Comparison of peak Q patterns at the plane of focus for all 20 patient simulations using 0.25 mm voxel spacing. The leftmost image shows the result when the planning phases were obtained assuming homogeneous brain tissue within the cranium (Plan:noCSF); the rightmost image show the result when planning included CSF and brain (Plan:CSF). The maximum value of the colorbar (units are W/dm³) varies between patients but is the same for both planning scenarios.

Figure 5:

Plots of Q in three orthogonal directions through the maximum Q point for both planning methods for all 20 patient simulations using 0.25 mm voxel spacing. The blue line is obtained when both planning and simulation use the actual brain and CSF anatomy (Plan:CSF). The red line is obtained when planning is done using homogeneous brain only (Plan:noCSF); the forward simulation uses the actual CSF-brain anatomy. (Vertical axis in W/dm³ and horizontal axis in mm)

Figure 6 gives a quantitative measure of the ratio of the peak Q values for the two planning methods (defined as Qratio) for the three assumed voxel spacings. For Figure 6, the Qratio values for the 3 resolutions were reported. The relatively large Qratio values seen in the measurements using the 0.5-mm spacing (1.30 ± 0.10 with a spread from 1.15 to 1.50) are reduced in general for the measurements at 0.25-mm spacing (1.17 ± 0.06 with a spread from 1.06 to 1.29). We also investigated whether interpolation to 0.25 mm spacing could reduce the sensitivity to the effect of the focus shifted to an intermediate spot. Supplementary Figure 2 shows the effect of interpolating the 0.5 mm spacing HAS predictions to 0.25 and to 0.125 mm spacing. The Qratios at 0.25 and 0.125 mm spacings are similar in value and in general indicate lower Qratios compared to the 0.5 mm original measurements. Supplementary Figure 3 shows the Qratios obtained using 0.25 mm spacing, and those obtained using zero-filled interpolation from 1.0 and 0.5 mm to 0.25 mm spacing during the simulations. Although not identical, the results do indicate the stability of the measurements at 0.25 mm spacing.

Figure 6:

Qratio: Ratio of peak Q obtained when CSF was used in the planning (Plan:CSF) to that obtained using homogeneous brain in the planning (Plan:noCSF). The forward simulation was performed using the model containing both CSF and brain (Model II). Results are plotted for models with 0.25 mm, 0.5 mm, and 1.0 mm isotropic spacing.

Although not shown, we also found the total power deposited in a 2-cm³ volume centered around the focus for both planning methods. For 1.0-W nominal input power, the average over all 20 patients of the total power deposited in that volume for each of the two methods was 5.4 mW. The difference in the total power deposited in this volume between the two methods, averaged over all 20 patients, was 1.1 ± 106 μW.

Table II gives the results of the sub-study that tested whether the improvement in Q was mostly due to using the correct CSF speed of sound or the correct CSF attenuation, which show that CSF speed of sound is the predominant factor in determining the improvement in deposited power density. For the effects of speed of sound vs. attenuation and the effect of the amount of CSF segmented, the 0.5-mm model was used. These results were so definitive, they were not repeated at smaller voxel spacings.

Table II.

Results of sub-study of the relative effect of speed of sound versus attenuation on the improvement in Qratio.

Simulation Condition	Patient #	Qratio
All CSF values set to brain except speed of sound	13	1.20
	14	1.33
	15	1.41
All CSF values set to brain except attenuation	13	1.01
	14	1.01
	15	1.02

Figure 7 shows the value of Qratio as a function of the fraction of modeled voxels that are segmented as CSF compared to brain. This CSF fraction varies with the threshold value used in segmenting CSF in the brain. The red solid squares indicate the Qratio value at the threshold that gave the least visual partial volume error in the CSF segmentation.

Figure 7:

Qratio (as defined in Figure 6) as a function of the CSF fraction (the ratio of the number of CSF voxels to brain voxels within the model) for seven of the 20 subjects. The CSF fraction is varied by adjusting the segmentation threshold. The filled square shows the point for each patient giving the least CSF partial volume error.

Figure 8 illustrates the change in Qratio improvement that might occur when the acoustic properties used in the forward simulation, specifically speed of sound, do not match those used in the planning. In this paper, we planned using table values for the speed of sound of brain (1546 m/s) and CSF (1505 m/s), which differ by 41 m/s. For Figure 8, the difference in these values was decreased by 15%, 29% and 44%, down to a difference of 23 m/s. The Qratio improvement decreases, as would be expected.

Figure 8:

Box and whisker plot of the Qratio over all 20 subjects when the speed of sound values differed from those used in planning. For the % deviation values shown the speed of sound values (m/s) were: CSF:Brain - 1505:1546 (0.0), 1508:1543 (0.2), 1511:1540 (0.4) and 1514:1537 (0.6).

Finally, Figure 9a shows a comparison of simulated Q patterns and maximum temperature distributions for the second sonication for Patient 3 using the Q patterns obtained with the 0.25-mm spacing models as inputs to the Pennes bioheat equation. In Figure 9b the percent increase in the temperature obtained from the difference between the temperature profiles normalized to the peak temperature of the Plan:noCSF phases is plotted for all 10 sonications. These results show that a Q improvement of 16% results in a temperature increase of up to 15% over the heated region at the end of the sonication pulse. The power applied for each of the ten sonications for this patient is plotted in Figure 9d.

Discussion

For the Insightec transcranial focused ultrasound system, the phases of the 1024 elements can be adjusted to maximize the absorbed power density at the desired focus relative to the power density absorbed in the skull and normal brain tissues. Currently, this phase adjustment is made based on the 3D morphology of the cortical bone and diploë of the skull, while the effect of intracranial anatomy (brain and CSF) is not considered. This simulation study tested the improvement in deposited power density that can be obtained by including both CSF and brain tissue properties during procedure planning over planning based on the assumption of homogeneous brain tissue. The increase in peak acoustic power density, Q, of between 6% to 29%, is consistent with the increase observed when using “echo-focusing”, which takes into account brain and CSF anatomy as well as variations in skull (20). As shown in Figure 9, the improvement in temperature profile depends on the improvement in Q but not on the actual power applied.

The Qratio determined after zero-filled interpolation of the pressure waveforms demonstrated that a major source of the apparent Qratio increase was due to positioning of the focused spot relative to the sample grid. Because of the Fourier implementation of the angular spectrum, the position of the grid can be shifted by applying a linear phase shift in the desired direction. Zero-filled interpolation creates intermediate grid points without reducing the dimensions of the Fourier kernel, thus reducing the spatial dependence of the shifted ultrasound focus.

While the peak values of Q increase between 6% to 29% when CSF and its acoustic properties are included in the time-reversal phase determination, the integration of Q over a 2-cm³ simulated volume centered on the focal spot is approximately the same (within < 2%) for both planning scenarios (Plan:CSF and Plan:noCSF). This indicates that the total power deposited is essentially the same for both planning methods. However, more power is deposited at the focus when using the correct CSF acoustic properties in planning the element phases.

The increased power at the focus could allow a reduction in applied power to achieve the same effect. Because all patients experience some discomfort due to heating around the skull, a reduction in power could make the treatment experience more tolerable. Further, it could enable treatment of subjects whose skulls make them borderline treatable currently, due to low SDR.

The CSF and brain acoustic properties specified in the simulation study of the 20 subjects were speed of sound, attenuation, and density. Using models of three subjects, simulations were performed to determine which parameter was the major contributor to improvement. Since density variation is small and only affects the minor reflections at CSF/brain interfaces, the effect of density was not evaluated. The results in Table II demonstrate that improvements observed were almost entirely due to the speed of sound.

The dependence of the improvement in Qratio on the fraction of CSF in the brain was tested using the 0.5-mm models for seven subjects as shown in Figure 7.

As described above, the CSF volume was determined in the segmentation step using a threshold value midway between bright-appearing CSF and less-bright brain in the T2w MR images. As the segmentation threshold increases, the CSF fraction decreases, and the fractional improvement also decreases. For very high threshold values, the CSF fraction approaches zero and Qratio essentially reduces to 1.0, or 0% improvement. Similarly, as the threshold is reduced, the CSF fraction increases. The red squares show the CSF fractions that were independently selected to minimize the partial volume error in the segmentation. In four of the subjects studied in Figure 7, the CSF fraction selected was at or near the peak Qratio value. In three subjects, the selected threshold resulted in lower CSF fractions and reduced the Qratio. For all subjects, the threshold was selected from visual inspection to reduce the partial volume bias in segmenting tissues as CSF or brain such that the binary brain/CSF images best matched the apparent brain/CSF distribution in the T2w images. For low threshold values, brain tissue will be segmented as CSF.

As Figure 9c shows, the 16% increase in peak Q observed for Patient 3 results in a 14% to 15% increase in peak temperature at the end of the ultrasound pulse. This percent increase in temperature is only slightly smaller than the percent increase in Q and is due in part to the fact that the temperature distribution is simulated at the end of the heating pulse. This time allows thermal conduction to spread some of the heat away from the focal spot, so the increased temperature is observed over an area of several voxels and is larger than the Q pattern. This small reduction with time in the ultrasound pulse is demonstrated in Figure 9c, where the initial improvement in temperature is about 15% and decreases to about 14% at the end of the 10-s ultrasound duration. Even though the increase in temperature obtained by including CSF is lower than the increased Qratio, the increased temperature is potentially very important clinically. The increased temperature at the focus will allow reduced heating at the skull and scalp, and therefore less pain and a more comfortable experience for the patient. This could even allow treatment of patients with lower skull density ratios with the same applied power.

Our observation that CSF and brain anatomy can have a moderately large effect for some patients has not been reported previously. The results are consistent with the experimentally observed 27% increase in efficiency reported with echo-focusing, which inherently takes the CSF into account, using the same transducer(20). Although there have been many studies to investigate the acoustic properties of skull morphology and its effect on beam focusing, the effect of brain and CSF anatomy has not been as thoroughly studied. This may be partly because the difference in acoustic properties between CSF and brain is relatively small compared to the very large difference between cortical and cancellous bone and between both bone types and soft tissues. We postulate that our observed effect of CSF and brain anatomy may be due to the relatively large path lengths involved within the brain. As an example, consider the case of a straight path length of 90 mm from the skull inner surface to the focus and assume that 30 mm of this is through CSF. The phase change along the path assuming it passes through all brain is 237.6 radians, while the phase change including the CSF is 239.6 radians, for a difference of 2.0 radians, which is enough to influence the amount and location of the wave interference pattern.

This study has several limitations. First, the simulations are performed using HAS, which uses approximations to obtain rapid computation times and therefore may not be as exact as other simulation methods. However, we believe the effect observed here primarily relates to simulations of ultrasound through soft tissues, where HAS has demonstrated reasonably good agreement with other methods (16). The rapid computational speed of the HAS method allowed time-efficient simulations of the several model configurations analyzed. Further, the resolution used in the simulation study was initially 0.5-mm isotropic. As shown in Figures 4 and 6, the improvement in Qratio observed decreased for the higher resolution (smaller voxel spacing), indicating that at least part of the improvement was due to partial volume effects and voxel positioning. The effect of voxel positioning was reduced by using band-limited interpolation to finer spacing, as shown in the supplementary figures. Bandlimited interpolation does not decrease the voxel sampling function size, but increases the likelihood that the center of the Q pattern is at the center of a voxel. For the effects of speed of sound vs. attenuation and the effect of the amount of CSF segmented, the 0.5-mm model was used. These results were so definitive, they were not repeated at smaller voxel spacings.

Second, this study is subject to the over-idealized results arising from the so-called “inverse crime,” where the inverse simulation (here, the time-reversal calculation using Model II for Plan:CSF) employs the same model and parameters as in the forward simulation (Model II). Thus, in actual clinical practice, the improvements noted here will likely be less. The acoustic properties used during planning will be estimates and may not match the specific values of the subject being treated. Therefore, the power deposition results of the actual treatment may not match those predicted. We found that the major contribution to the difference in the peak Q values for the two planning methods is due to the difference in speeds of sound between brain and CSF. Accordingly, if the speeds had a smaller difference, the simulated difference in peak Q values would be less. As an estimation of the magnitude of this effect, we considered the situation of planning using table values and then forward simulating using values closer together. These results, shown in Figure 8, indicate that reducing the difference between the speed of sound of brain and CSF will result in a corresponding decrease in the observed improvement. However, even decreasing the difference between the brain and CSF speed of sound by 44% only results in a 50% reduction in the Qratio improvement.

Third, there are several limitations inherent in HAS, itself. To the extent that the reverse and forward implementation of HAS are inverses of each other, the ultrasound should be optimally focused at the point specified. In nearly every subject in this study, that appeared to be the case, indicating this consistency.

In addition, the segmentation procedure required for aberration-correction calculations will not exactly replicate the actual subject anatomy, leading to a mismatch between predicted and clinical results. Further, since the inverse and forward simulations used the same HAS software simulation technique, any inaccuracies in that procedure may cancel in the round trip, leading to an overestimation of the improvement in the Q values. Finally, all focal points in this study were at the geometric focus. In actual patient treatments some steering occurs; however, it is unlikely that this would have any measurable changes to the results of this study.

Future work should be performed to validate these simulation observations. Future experiments could involve designing and creating physical models of the brain with CSF included to validate the CSF simulations. A comparison of how the simulated phases affect actual heating patterns in a physical model would clarify the importance of including the anatomy of the CSF in simulated time-reversal phase determination.

Conclusions

This simulation study has demonstrated that an increase in peak absorbed acoustic power density on the order of up to 29% (we observed between 6% and 29% in 20 patients) can be obtained by including the properties of CSF and brain in determining the phases for transcranial MRgFUS treatments. This improvement assumes that the geometry as well as the acoustic properties of the brain and CSF are known. To the extent that this increase can be realized, the improvement could result in an improvement in treatment efficiency for a large fraction of treated patients.

Supplementary Material

supp info

Supplement Figure 1: Central coronal and sagittal slices from the first three patient models showing segmentation into the tissue types listed.

Supplement Figure 2: Plot of Qratio for measurements obtained at 0.5 mm spacing, and for those pressures interpolated to 0.25 and 0.125 mm spacing.

Supplement Figure 3: Plot of Qratio for measurements obtained at 0.25 mm spacing and from 1.0 and 0.5 mm spacing interpolated to 0.25 mm spacing.

Data availability

Simulation data from this paper can be requested from the corresponding author.