Bioelectromagnetics 35:145^159 (2014)
Simulation Study of Delivery of Subnanosecond Pulses to Biological Tissues With an Impulse Radiating Antenna Fei Guo,1 ChenguoYao,1 Chandra Bajracharya,2 Swetha Polisetty,2 Karl H. Schoenbach,2 and Shu Xiao2* 1
Chongqing University, Chongqing, China Frank Reidy Research Center for Bioelectrics, Old Dominion University, Norfolk,Virginia
2
We have numerically studied the delivery of subnanosecond pulsed radiation to biological tissues for bioelectric applications. The antenna fed by 200 ps pulses uses an elliptical reflector in conjunction with a dielectric lens. Two numerical targets were studied: one was a hemispherical tissue with a resistivity of 0.3–1 S/m and a relative permittivity of 9–70 and the other was a realistic human head model (HUGO). The electromagnetic simulation shows that despite tissue heterogeneity of the human head, the electric field converges to a spot 8 cm in depth and the spot volume is approximately 1 cm 2 cm 1 cm in both cases when using only the reflector and a lens as an addition. Rather than increasing as it approaches the converging point, the electric field decreases strongly with distance from the skin to the converging point due to tissue resistive loss. The electric field distribution, however, can be reversed by making the dielectric lens lossy with the two innermost layers being partially resistive. The lossy lens causes an attenuation of the electric field near the axis, but the electric field generated by the waves which pass the lens at a wider angles compensate for this loss. A local maximum electric field in a deeper region of the tissue may form with the lossy lens. The study shows that it is possible to generate the desired electric field distribution in the complex biological target by modifying the dielectric properties of the lens used in conjunction with the reflector antenna. Bioelectromagnetics 35:145–159, 2014. © 2013 Wiley Periodicals, Inc. Key words: impulse radiating antenna; subnanosecond pulses; deep focus; dielectric lens; biological tissue
INTRODUCTION Since the 1960s, intense electromagnetic (EM) fields have been considered to be of therapeutic value. Biological studies have not only focused mostly on thermal effects such as raising tissue temperature for the purpose of hyperthermia but also as a tool to cauterize unwanted tissue. The application of EM radiation in the radio frequency and microwave range into tissues with an antenna or an applicator was studied extensively, with deep target access as the primary goal. Modeling and simulation were used to study the wave propagation in multiple tissue layers. The tissues studied were mainly fat and muscle. The skin was deliberately neglected due to the fact that its thickness is small compared to the wavelength, and the resistive loss is negligible. Such simple two-layer models (fat and muscle) provided important information on how the specific absorption rate (SAR) is distributed among the layers. Several points are reiterated here [Lin and Bernardi, 2007; SanchezHernandez, 2009]: (a) high SAR is found at the 2013 Wiley Periodicals, Inc.
interfaces between fat and muscle, which is primarily due to the abrupt change of dielectric permittivity at this interface and the requirement of continuity of the electric displacement vector; (b) standing waves can form in the tissue at certain frequencies and tissue thicknesses; (c) an incident electric field polarized in the tissue plane penetrates more easily; (d) a plane wave approximation cannot be used to predict the Grant sponsor: The Office of Research, Old Dominion University and Air Force Office of Scientific Research (AFOSR, USA). *Correspondence to: Shu Xiao, Department of Electrical and Computer Engineering, Frank Reidy Research Center for Bioelectrics, Old Dominion University, Norfolk, VA 23508. E-mail: [email protected] Received for review 24 December 2012; Accepted 18 September 2013 DOI: 10.1002/bem.21825 Published online 6 November 2013 in Wiley Online Library (wileyonlinelibrary.com).
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spatial distribution of the field intensity, which differs for different frequencies (3D models show that the spatial distribution of the field intensity is determined by interference pattern); and finally, (e) the permittivity seems to be more important than the conductivity in determining the field magnitude in the tissue. Focusing of EM radiation has been studied by means of narrowband antenna arrays. A limiting factor in all the approaches of using high frequency EM waves as diagnostic or therapy is the high attenuation of soft tissues. It requires the careful selection of a frequency that allows the balancing of the desired spatial resolution with the required penetration depth [Lin, 1985]. In a brain hyperthermia study, an array of four dipole antennas spaced 2.0 cm apart was capable of heating a volume of 5.9 cm 2.8 cm 2.8 cm [Ryan et al., 1994]. A careful selection of the source electric field distribution around the entire surface of the head can generate a well-defined focal volume [Dunn et al., 1996]. Time reversal with a large number of antennas was demonstrated as a method to confine the radiation spatially [Trefna et al., 2010]. A beam forming approach, with the intent of demonstrating treatment of brain cancer, allowed focusing of 1 GHz microwave radiation through constructive interference in the brain [Burfeindt et al., 2011]. In a deep brain monitoring system, the electric fields at 1.1 GHz that are radiated from one ellipsoidal reflector fed by a discone antenna can be focused into the center of the head [Gouzouasis et al., 2010; Karathanasis et al., 2010]. Left-handed meta-material was used as matching layers on the surface of the human head model to improve the sensitivity of the system [Giamalaki and Karanasiou, 2011]. Recently, wideband electric pulses in the ns or subnanosecond range were shown to induce various nonthermal effects, opening a new realm of bioelectrics [Schoenbach et al., 2004, 2008; Joshi and Schoenbach, 2010; Mitsutake et al., 2012]. While ns pulses are delivered with electrodes [Silve et al., 2012], delivering ultrashort electrical pulses with antennas to biological targets becomes attractive in reaching deep targets. One such antenna is an impulse radiating antenna that relies on a prolate spheroidal reflector [Baum, 2007; Altunc et al., 2008; Kumar et al., 2011]. At the first focus of this reflector, a transverse electromagnetic (TEM) wave launcher projects the EM waves to the reflector; from there they are redirected into the second focus. At the first focal point, the antenna’s wave launcher can be operated in a highly pressurized environment, with the possibility of launching wideband pulses with voltage amplitudes up to a few hundred kV or even 1 MV [Baum et al., 2004; Kumar et al., 2011]. Bioelectromagnetics
The electric field intensity required for inducing biological effects depends on the end-goal applications. The critical electric field for stimulation with subnanosecond pulses (e.g., 200 ps) can be extrapolated as 1 MV/m [Rogers et al., 2004] and may be decreased by a factor of 20–50 kV/m if the pusles are applied at high repetition rate, suggested by Jiang and Cooper [2011]. For cell killing, the electric field intensity in general is higher than the conditions for stimulation. For example, electric pulses of 800 and 200 ps have been studied in vitro on melanoma and hepatoma cells [Schoenbach et al., 2008; Xiao et al., 2011; Camp et al., 2012]. The magnitude of the electric field needs to be approximately 2 MV/m or higher in order to increase cell membrane permeability [Xiao et al., 2011]. The temperature increase due to high repetition rate (10 kHz) and prolonged exposure (up to 10 min) can no longer be ignored. In this paper, we report the feasibility of delivering electrical pulses in the subnanosecond range, by means of a simulation, through one antenna into soft tissue. The aim is to explore the conditions that allow us to focus the wideband radiation in brain tissue. Applications of a method, such as inducing cell death in brain tumors or neurostimulation, require the exploration of the necessary field intensity, pulse duration, and pulse number. We included a hemispherically shaped tissue as the target in the antenna configuration. We varied the electrical properties (permittivity and conductivity) of the tissue and studied the spatial distribution of the electric field intensity in the target, particularly in the deep region, which is defined as 6–8 cm below the surface. We further studied the temporal development and the spatial distribution of the electric field intensity in a human brain, with the aim of determining the electric pulse parameters required for deep brain stimulation [Vitek et al., 2011]. In particular, we aim to answer the following questions: How deep can the subnanosecond pulses penetrate and still achieve a reasonable confinement of the electric field distribution? Can we use one antenna to focus pulsed radiation into tissue? What spatial resolution can such antenna provide? Configuration of the Simulation To answer these questions, we have used a 3D EM simulation software, Computer Simulation Technology (CST) Microwave Studio (Framingham, MA). The transient solver based on finite integration technique was used for the time domain simulation. The human head model (HUGO) has a resolution of 1 mm 1 mm 1 mm. The basic configuration, reflector antenna and target, used in this modeling study are
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shown schematically in Figure 1a. The antenna has a prolate spheroidal reflector fed by a transverse electromagnetic (TEM) conical transmission line starting from the first focus as a wave launcher (Fig. 1a). The reflector is one-half of a prolate spheroid with the minor axis on the aperture plane. The geometry of the antenna was taken from an existing antenna [Xiao et al., 2010], constructed by Farr Research (Albuquerque, NM). The features of the antenna include: linearly polarized radiation, broadband radiation, and high power capability. The radiation at the second focus is vertically polarized, which is the mirror image of the electric field at the starting point of the transmission line fed by a differential input. A lens is used in conjunction with the impulse radiating antenna, aiming to improve the coupling of the EM energy to tissue (Fig. 1b). The lens is made of multiple layers with dielectric permittivity varying according to an exponential profile in order to allow for a maximum transmission [Altunc et al., 2009]. The innermost layer has the same dielectric constant as the targeted tissue. The electric pulses fed to the antenna have a Gaussian waveform with the pulse width 200 ps. In the CST transient solver, the frequency range was set to 0– 5 GHz. In the simulation, we used a tissue target which has a hemispherical shape (Fig. 1b). Such shape was chosen because the spherically incoming waves from the reflector antenna have the same phase along the circumference of the tissue, which results in a maximum field at the second focus for the same optical
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path. The relative permittivity of muscle and fat tissue is on the order of 45 (for muscle) and 5 (for fat). Their conductivity is in the range of 0.1–2 S/m. The values could vary for real tissues [Lazebnik et al., 2007]. The dielectric properties are dependent on the frequency, which can be described by the second order Debye model [Gabriel, 2007]. This type of model is not available in the software, so we did not include the effect of dispersion. In addition to the hemispherical target, we also used the CST HUGO model to determine the temporal and spatial distribution of the pulsed electric fields in a human brain (Fig. 1c). In the human head model used in this study, the dielectric constants and conductivities of the tissues considered in this study are: bone (er ¼ 11.78, s ¼ 0.28); gray matter (er ¼ 50, s ¼ 1.39); fat tissue (er ¼ 5.35, s ¼ 0.08); nervus opticus (er ¼ 30.87, s ¼ 0.84); white matter (er ¼ 37, s ¼ 0.91); and skeletal muscle (er ¼ 55.33, s ¼ 1.44). These tissue dielectric properties are the values chosen at 1.8 GHz. In the frequency range of 0.9–5 GHz, the tissue properties stay relatively flat as the bulk tissue dispersion is mainly dominated by the water contained in the tissue. For example, white mater has er ¼ 38.89 and s ¼ 0.59 at 0.9 GHz and er ¼ 33.44 and s ¼ 2.86 at 5 GHz. The dispersion of the dielectrics in general broadens the pulse waveforms and lowers the pulse intensity; the results of the simulation without dispersion loss therefore serves as the best scenario estimate of the pulse delivery in terms of pulse intensity and focal spot size. In this study, we have focused on the
Fig.1. a: The impulse antenna sends subnanosecond pulses to the hemispherical tissue. The minor axis of the reflector is located on the aperture of the antenna. b: A dielectric lens consisting of five layers was used in conjunction with the reflector antenna. The last layer of the lens is the biological tissue with radius of 6.0 cm. The dielectric constants of these five layers from the outermost to the innermost are 1.6, 2.4, 3.7, 5.8, and 9.0, respectively. The biological tissue (innermost layer) has the same dielectric constant as the 5th layer. c: The human head model used in this study. The grid size of the model is 1mm 1mm 1mm. The top of the head coincides with z-axis. In (b) and (c), the reflector antenna was used in the simulation but not shown. Bioelectromagnetics
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attenuation of the pulse in the brain, the size of the focal volume and the required input pulse parameters to create the electric fields that are at the level of inducing any biological effects. We note that the accuracy of the CST software is satisfactory. As reported previously by Kumar et al. [2011], using the same software to simulate the impulse radiating antenna gave results that are very close to the measurement results. We therefore assume that the simulation yield is sufficiently accurate in predicting the effect of wideband pulses on a human brain. RESULTS Hemispherical Tissue Directly Exposed to the Reflector Antenna The EM waves emitted from the elliptical reflector are spherical waves, converging at the second geometric focus of the reflector. The phases of the incoming spherical waves on the circumference of the target are identical. Because the electric fields of the converging spherical waves are parallel to the surface of the hemispherical tissue, the transmittance into the tissue is optimum [Lin and Bernardi, 2007]. In our simulation, we varied the relative permittivity of the tissue from a value of 9 to 70, and varied the conductivity from 0 to 1 S/m. The tissue conductivity near 0.5 S/m is close to that of breast tissue [Lazebnik et al., 2007]. An input Gaussian pulse was fed into the antenna (Fig. 2a). For a relative permittivity of er ¼ 9 and a conductivity of the target of s ¼ 0, the electric pulse at
the focal point (6 cm deep) is shown in Figure 2b. The pulse consists of a prepulse and an impulse. The prepulse reaches the second focal point at an approximate time, (t ¼ 27.16/30 þ 6 √9/30 ¼ 1.505 ns). The pulse reflected from the prolate-spheroidal reflector surface converges at the second focal point F2. This constitutes the impulse part of the wave at the focal point and occurs at approximately t ¼ 54/30 þ 6 √9/ 30 ¼ 2.4 ns. The shape of the impulse is close to the time derivative of the Gaussian wave form [Baum, 2007]. The electric field component that contributes mostly to the electric field at the focal point is the ycomponent. The amplitudes in the direction of x and z are negligible. The electric field intensities along the z-axis for er ¼ 9 and for various values of s are plotted in 1 cm steps from the surface to the target (Fig. 3a). It can clearly be seen that the field has its maximum at the second focus for s ¼ 0.3 S/m. However, this focusing effect diminishes as the conductivity increases from 0.3 to 0.5 S/m: the maximum field is located on the surface and it decreases monotonically on the z-axis. The decreasing trend of the z-axis electric field, however, is reversed when the tissue permittivity was changed from 9 to 70 (Fig. 3a). With the tissue dielectric permittivity of 70, the field is focused at the geometric focus even for a conductivity of 1 S/m. Clearly, the focusing effect is more pronounced in tissue with higher permittivity. The field distribution in the radial direction at different angles u is shown in Figure 3b. In this case, the tissue dielectric constant is 9 and the conductivity is 0.5 S/m. The electric field amplitudes on the z-axis
Fig. 2. a: Gaussian pulses of 200 ps were used as input pulses. b: The electric fields at the second focus with an input Gaussian pulse. The y-component is dominant among the electric fields in all directions. This result is for the hemispherical tissue that has a radius of 6 cm with e ¼ 9 and s ¼ 0. Bioelectromagnetics
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Fig. 3. a: The electric field distribution on the z-axis for different tissue conductivities (s). The tissue dielectric permittivity (e) was varied as 9, 40, and 70. The desired focus, also the geometric focus, is at z ¼ 6 cm. b: The electric field distribution in the radial direction at different azimuthal angles (u). The tissue has dielectric permittivity (e ¼ 9) and conductivity (s ¼ 0.5).
as well as those of the EM waves with a small azimuthal angle (608. We note that such distribution is for the tissue conductivity of 0.5 S/m, and for the tissue conductivity of 1 S/m, a similar field distribution was obtained. The field distribution can be schematically shown in Figure 5b. In the case of a non-lossy lens, the field distribution can be schematically depicted by the pie-shaped distribution in Figure 5a. A comparison of Figure 5a and b shows a localized focus may be formed in the deep region of the tissue. This change in distribution is made at the cost of the reduction of the absolute field intensity at the targeted region and two extra “hot spots” near the surface. Application of Subnanosecond Pulses to the Brain We have shown that it is possible to confine the electric field of subnanosecond pulses in a homogeneous, dielectric hemisphere. The attenuation loss of the target can be offset by using a partially lossy lens so that a deep-seated focal region can be created. While the targeted hemisphere is simple in structure, a real tissue contains multiple layers, making the formation of a focal spot more challenging. Three cases have been investigated: (1) the subnanosecond pulses are directed to the brain by the ellipsoidal reflector only; (2) a lens is placed on top of a human head; and (3) the lens is made partially lossy in order to attenuate the field along the axis. The lens, with the same structure as in Figure 1b, is used with the antenna and placed on top of the human head (Fig. 1c). The
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dielectric constant of each layer was the same as in Figure 1b. Because the head is not exactly round in shape, the top of the head coincides with the lens axis and the head appears to project into the lens structure. But at the lens-head interface, the priority is given to the head, which overrides the lens in any overlapped region. For the lossy lens, the innermost layer was assigned a conductivity of 5 S/m and the second-inner layer was assigned a conductivity of 4 S/m. The values of the conductivities were selected based on the consideration that the electric field on the axis increases as the wave penetrates deeper and nears the geometric focus. However, that does not mean that the electric fields in other radial paths of the penetration are lower than the fields near the geometric focus, as will be shown later. Human Head Exposure Directly to the Reflector Antenna We first examine the case where the pulse is directly delivered to the brain through the impulse radiating antenna without lens. Figure 6 shows the pulse waveform at the geometric focus in the brain (6 cm deep from the top of the skull). Again, the y-component dominates the overall field and the x and z components are negligible. Figure 7 shows the propagation of subnanosecond pulses in the head. The intensity of the electric fields is shown as the linear isoline in the clamped range 0.1–0.3 V/m, meaning any values that are greater than 0.3 are clamped to 0.3. At 1.8 ns, the prepulse already reaches the brain. In the meantime,
Fig.6. The pulse waveform at the 6 cm depth on the z-axis in the brain exposed to a reflector antenna. Bioelectromagnetics
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Fig. 7. The isoline plots of electric field distribution in the human brain exposed to a reflector antenna at various times with a clamp range of 0.1 to 0.3 V/m along X-axis (side view), Y-axis (back view), and Z-axis (top view).
the prepulse in the face and back side of the head travels faster than the prepulse in the brain. At 3.1 ns, the impulse appears in the brain along the axis of the antenna. It gradually reduces its size and at 3.7 ns, seems at its smallest size. As the wave penetrates deeper, the intensity decreases. The isoline plot clearly indicates that there is no resonance in the brain except the impulse. In the side view of the wave propagation (Fig. 7), at 3.1 ns, one can see that the impulse actually consists of two parts indicated by two bright spots. In the time domain, the corresponding impulse waveform is bipolar (Fig. 6). At 3.7 ns, the wave converges, which is consistent with the side view. A top view of the wave propagation is also shown in Figure 7. The view is taken at a depth of 8 cm from the top of the head. Because the wave intensity is shown as a clamped isoline, we placed a number of probes in the brain to measure the actual peak amplitudes as the pulse passes. The probes were placed in 1 cm steps along the radius centered at the second geometric focal point, which is 6 cm deep from the top of the skin fat (Fig. 1c). Figure 8a shows the field distribution along various radii from the skin. The largest field is on the 08 axis and the fields on the two sides seem symmetriBioelectromagnetics
cal about the axis. They all decrease due to the strong absorption in the brain. Despite the fact that the field decreases as the penetration depth increases, the field values converge at 7–8 cm, slightly deeper than the geometric focus (6 cm in depth). This is consistent with the results shown in Figure 7. The inhomogeneity of the brain does not seem to create any difference in the arrival time of the spherical waves along different radii, but the strong attenuation of brain tissue prevents the wave from reaching the highest amplitude near the focal point. To evaluate the focal spot size at 3.7 ns, we examine the sliced views by shifting the cutting plane from the antenna symmetry plane. In Figure 9, when the human head is viewed from x ¼ 2 to 2 cm, the focal spot in the brain is seen confined from 0 to 1 cm (side view). In the back view from y ¼ 2 to 2 cm, it becomes harder to tell where exactly the focal spot size is. But if we compare the region which contains electric field value of 0.3 V/m (maximum clamped value, red), the focal spot in this dimension can be approximately estimated as y ¼ 1 to 1 cm. In the top view (along z-direction), the focal spot size is seen from 1 cm (from 7 to 8 cm). In general, we can
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Fig. 8. a: The electric field distribution in the brain exposed to the reflector antenna without the dielectric lens. b: The electric field distribution when the antenna was shifted from the y-direction by 1cm while the human head remained at the same location.
estimate the focal volume is approximately 1 cm 2 cm 1 cm. The volume is narrow in both the x- and z-directions, but wider in the y-direction. When delivering the subnanosecond pulses to the deep targets, the relative position of the human head to the antenna could affect the location of the focal spot. Figure 8b shows the electric field distribution (on the z-axis, side view) at three different positions of the
human head when the z axis of the human head was at y ¼ 0, and 1 cm with respect to the antenna shifting in the y direction. For y ¼ 1 cm, the field distributions almost overlap that for y ¼ 0 cm. This observation can be understood as that the focal spot tends to spread mostly in the y-direction, so the focal spot location is not sensitive to the human head position when displacing 1 cm in the y-direction. However, we
Fig. 9. The isoline plots of electric field distribution with a clamp range of 0.1 to 0.3 V/m in the human brain without dielectric lens at 3.7 ns along X-axis (side view, top), Y-axis (back view, middle), and Z-axis (top view, bottom). The sliced views were taken from x ¼ 2 to 2 cm, y ¼ 2 to 2 cm, and z ¼ 6 to 9 cm in a step of 1cm. Bioelectromagnetics
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anticipate the focal spot location is more sensitive to the displacement in both the x- and z-directions, as the focal spot tends to be narrower than in the y-direction. Human Head Exposure to the Reflector Antenna Through a Lens When we placed a non-lossy lens on top of the head, the field distribution in isoline plot is shown in Figure 10. In this case, the isoline was clamped between 0.1 and 0.5 V/m due to the increased coupling of EM waves to the tissues by the lens. At 3.7 ns, the impulse becomes constricted in size and it reaches 8 cm deep at 3.9 ns. After that, the impulse decreases in intensity and becomes almost invisible in the clamped range. The addition of the lens creates a delay compared with the case without a lens. The amplitudes of the field are shown in Figure 11a. The field distribution is similar to the case where there is no lens added, except the amplitude at the skin is slightly higher due to the higher transmission of the lens. The field values converge to 0.5 V/m at the depth of 8 cm, also higher than the case without lens. Still, the highest field is on the axis and the fields on both sides are lower. The overall trend is decreasing as the impulse penetrates. One question arising is whether the introduction of the lens affects the focal spot size. We again examine the sliced views in the x-, y-, and z-directions. Figure 10 shows that the region contains the maximum
clamped value (0.5 V/m) is approximately 0–1 cm in the x-direction, 1 to 1 cm in the y-direction and 1 cm in the z-direction. The volume of the region is close to the case where only the reflector antenna was used. The addition of the lens increases the coupling of the EM radiations to the tissue, but does not change the focal spot size. The spatial sensitivity of the human head to the lens and antenna was investigated by shifting the lens and antenna in the y-direction. The lens layers overlapped with the human head were automatically changed into human head with no space created in between. In reality, it is not possible as the lens has a fixed structure and to do so different lenses have to be used. Still, we could numerically assess how sensitive the location of the focal spot is to the position of the human head. Figure 11b again shows that no significant change in electric field distribution when the human head is displaced by y ¼ 1 cm with respect to the lens and antenna as compared to y ¼ 0 cm. This observation is again due to the fact that the field spread mostly in the y-direction. A small dislocation in z- and x-axis could result in a more sensitive change in the focal spot location. Human Head Exposure to the Reflector Antenna in Conjunction With a Lossy Lens In the third case, we used the reflector antenna and the lens but we attenuated the field on the axis by
Fig. 10. The isoline plots of electric field distribution with a clamp range of 0.1 to 0.5 V/m in the human brain with the reflector antenna and dielectric lens at 3.7 ns along X-axis (side view), Y-axis (back view) and at 3.9 ns along Z-axis (top view). The sliced views were taken from x ¼ 2 to 2 cm, y ¼ 2 to 2 cm, and z ¼ 6 to 9 cm in a step of 1cm. Bioelectromagnetics
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Fig.11. a: The electric field distribution in the brain with the reflector antenna and non-lossy lens. b: The electric field distribution when the antenna and the lens were shifted in y-direction by 1cm from the original position while the human head remained at the same location. We note that the z-axis of human head overlapped the z-axis of antenna (and lens) before the shift, but became off axis after the antenna and lens were shifted in y.
assigning conductivities to the 4th and 5th layer of the lens. This idea originated from the study of a lossy lens coupling to the hemispherical tissue (Fig. 5b). In the side view of the wave propagation (Fig. 12), the impulse field, shows a “wishbone-like” distribution (at 3.7 ns). This is obviously different than the non-lossy
lens case as the fields in the z-axis is largely damped and the off-axis fields become higher. At 3.9 ns, the impulse is confined at 8 cm from the top of the skull. In Figure 13a, the field distribution is shown. On the axis (R vs. 08), the field becomes the lowest among all the radial directions and is slightly increased at 8 cm,
Fig. 12. The isoline plots of electric field distribution with a clamp range of 0.1 to 0.2 V/m in the human brain with the reflector antenna and lossy dielectric lens at 3.7 ns along X-axis (side view), Y-axis (back view), and at 3.9 ns along Z-axis (top view). The sliced views were taken from x ¼ 2 to 2 cm, y ¼ 2 to 2 cm, and z ¼ 6 to 9 cm in a step of 1cm. Bioelectromagnetics
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Fig. 13. a: The electric field distribution in the brain with the reflector antenna and lossy lens. b: The electric field distribution when the antenna and the lossy lens were shifted in y-direction by 1cm from the original position while the human head remained at the same location.
which is the opposite of that in Figures 8a and 11a, where the largest field is on the axis. Instead, the fields at 458 become the largest. The strong attenuation in the lossy lens allows us to modify the field distribution in the brain. Despite the strong attenuation, the field intensity near the focal point (8 cm in depth) is 0.2 V/ m, reduced by a factor of three from that in the nonlossy lens case (Fig. 11a). The focal spot volume in this case can be again estimated from different sliced views. If we examine the region having the maximum clamped range (0.2 V/m), Figure 12 shows the focal spot size becomes smaller. The side view indicates the focal dimension is less than 1 cm in x- and z-direction. The y-direction focal dimension is not as obvious as in the other two directions, but can still be seen becoming smaller. Such reduction in the focal spot size suggests that its location is more sensitive to the relative position between the antenna and the human head, which can be verified by the results obtained when the lens and antenna was shifted in y-direction to 1 cm (again, the human head remained at y ¼ 0). Apparently, the electric field distributions as a result of these shifts are modified (Fig. 13b). The field in y-direction becomes sensitive to the position of the human head with respect to the antenna and lens. This is rather different than the other two cases (no lens and nonlossy lens). On one hand, the lossy lens allows us to shrink the spot size, but on the other hand, the focal spot location becomes sensitive to the relative position of the antenna to human head. Meanwhile, the overall field intensity is decreased due to the extra attenuation introduced in the lens. Bioelectromagnetics
DISCUSSIONS The transmission of subnanosecond pulses to a homogeneous tissue was studied using an impulse antenna. A spherical wave with a propagation vector perpendicular to a spherical target converges on the geometric center of the spherical wave. This offers a rather simple prediction of the field distribution in the target. The conductivity of the tissue, however, changes the geometric-optics picture. It creates a decreasing electric field with increasing penetration distance. For the generation of large field intensities in the shallow region of the tissue, a single antenna is sufficient. As the antenna radiation is an inhomogeneous spherical wave, the highest field is along the axis, which means the highest field distribution in the target also coincides with the axis. For deeper focusing, the loss due to the conductivity of the dielectric can be alleviated by applying this method to tissue with high dielectric constants, such as muscle tissue. In a target which contains composite tissues, such as the brain, the multiple layers in the propagation path (skin and skull) do not pose a significant change to the waveforms of the converging waves, since, in Figure 6, both prepulse and impulse can be clearly identified for the case when a reflector antenna was used. In addition, the converging point in the brain can be clearly identified to be 8 cm deep from the top of the human head, which is 2 cm deeper than the geometric focus of the reflector antenna. The volume is 1 cm 2 cm 1 cm in the xyz-directions and is situated in the white-matter region. As white matter has a dielectric constant of 37, the spatial width
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of such pulse is 1 cm, which is consistent with the simulation result for an input pulse of 200 ps (Fig. 9). It is therefore reasonable to predict the focal spot size simply by estimating the pulse spatial width in the dielectric where the focal point is to be created. On the other hand, the amplitude of the electric field decreases from the human head surface to the converging point along the radial paths of small azimuthal angles with the field on the z-axis being the strongest among all the radial paths. Adding a dielectric lens in addition to the reflector antenna does not change the converging point and still allows the radiation to converge at 8 cm in depth. It increases the coupling of radiation to the tissue and the electric field intensity at the converging point. Similar to the case without the lens, the electric field also decreases along the paths of small azimuthal angles and it is still the strongest on the z-axis. Using a dielectric lens with two innermost layers being partially lossy does not change the location of the converging point and still allows the radiation to converge at 8 cm in depth. The field on the z-axis in this case, however, becomes the lowest because of the attenuation in the lens, leaving the fields higher along other radial paths with wider angles. The electric field distributions obtained in a hemispherical tissue (Fig. 5a and b) and a brain model (Figs. 11a and 13a) show two extreme cases of electric field distribution. One has the highest field on the z-axis while the fields on the side are smaller. The other case is that high fields penetrate from the two sides about the z-axis, while leaving the axial field small, but in the deep region, a local maximum can be formed. The first case can be used for delivering subnanosecond pulses to the shallow regions along the axis and the second case can be used for delivering subnanosecond pulses to the shallow region on the sides. The targeted region can be selected by placing lossy materials in the corresponding incident angles of the lens, which offers one way of varying the focal zone by utilizing different lenses. On the other hand, the two entirely opposite cases suggest that it may be possible to find a specific lens case where the pulse amplitude in deep region has a local maxima and the fields on the sides are higher, but the side regions may be controlled to be as shallow as skin or bone area and they are not physiologically as sensitive as brain tissue. The lens design need be optimized and could consist of a number of lossy elements in the same layer of the lens with each layer having different values of conductivities. A typical multi-variable optimization method, such as a generic algorithm [Pham and Karaboga, 2000], can be used to find the
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optimum values of the lens segments. This aim will be our next-step study. We noticed that in Figures 9, 10, and 12, the electric field scattering on the head surface remains large. To reduce the impact of such scattering to the clinical environment, the reflector can be increased in the reflection area and extended to an elliptical cavity with the opening aperture at the patient’s neck. Microwave absorbers can be placed in the cavity to absorb the scattering. In addition, the face of the patient can be protected by wearing a resistive mask to damp the surface waves. In terms of the choice of delivery, the reflector antenna has the ability of steering the converging point just by shifting the antenna position. Adding a dielectric lens can improve the coupling of the radiation (for non-lossy lens) or modify the electric field distribution in the tissue (for lossy lens), but is only useful for a fixed converging point. Furthermore, the lens design and construction is patient-specific and cannot be used for other patients. What implication does this study suggest? As shown in Figure 11a, for a voltage of 1 V fed to the antenna, an electric field is in the range of 1.5 V/m at a depth of 2 cm, which is the motor cortex region in the brain. This means an input voltage of 33.3 kV may be sufficient for an effective stimulation to meet the stimulation threshold of 50 kV/m as mentioned in the Introduction Section. For deep stimulation, Figures 8a, 11a, and 13a indicate there is a locally confined region at a depth of 8 cm. For a 1V pulse input, the field intensity was found to be 0.2–0.5 V/m for the three cases, which suggests that pulses of 250 kV–2.5 MV need to be fed into the antenna in order to meet the estimated stimulation threshold of 50 kV/m. Such a high-amplitude pulse generator becomes technically challenging (if not impossible) even though a 1-MV pulse generator has been built [Baum et al., 2004]. CONCLUSIONS Delivery of subnanosecond pulses to tissues has been studied using a single impulse radiating antenna. The electric field distribution shows a steadily decreasing trend and is primarily caused by the tissue conductivity. But increasing the tissue dielectric constant, meaning applying the method to a different tissue, can reverse the trend and allows for a deep focusing (e.g., 6 cm in depth). A second approach that could possibly create deep focusing is to use a dielectric lens in conjunction with the antenna. The lens can modify the electric field distribution in the tissue. In one case, the lens is loss-free and the electric fields along the axis are the highest. In the other case, Bioelectromagnetics
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the lens is assigned with lossy material to attenuate the axial incident electric fields, but allowing the incident fields from the sides to pass. This case results in the opposite distribution as the first case: the largest fields on the side, and the small fields along the axis. A local maximum near the geometric focus exists in this case. When the target is replaced by a human brain, the field along the axis is still strongest if the human head is directly exposed to the antenna. Despite a slight asymmetry of the human head, the spherical wave still converges near the geometric focus. However, the overall intensity decreases from the surface as the wave penetrates, due to a strong resistive loss of the tissue. Adding a dielectric lens allows one to increase the field intensity near the geometric focus, but the strongest intensity is still found along the axis and decreases as the wave penetrates deeper. When the lens is made lossy, the field on the axis can be made lower in the brain, while maintaining a higher field distribution near the 458. This study suggests the possibility of designing a dielectric lens with heterogeneous distribution of lossy material to create a desirable electric field distribution in the brain. ACKNOWLEDGMENT We thank the China Scholarship Council (CSC) for providing the visiting graduate research assistantship. REFERENCES Altunc S, Baum CE, Christodoulou CG, Schamiloglu E, Buchenauer CJ. 2008. Focal waveforms for various source waveforms driving a prolate-spheroidal impulse radiating antenna (IRA). Radio Sci 43:RS4S13. Altunc S, Baum CE, Christodoulou CG, Schamiloglu E, Buchenauer CJ. 2009. Design of a special dielectric lens for concentrating a subnanosecond EM pulse on a biological target. IEEE Trans Dielectr Electr Insul 16:1364–1375. Bajracharya C, Xiao S, Baum CE, Schoenbach KH. 2011. Target detection with impulse radiating antenna. IEEE Antennas Wireless Propagat Lett 10:496–499. Baum CE. 2007. Focal waveform of a prolate-spheroidal impulseradiating antenna (IRA). Radio Sci 42:RS6S27. Baum CE, Baker WL, Prather WD, Lehr JM, O’Loughlin JP, Giri DV, Smith ID, Altes R, Fockler J, McLemore D, Abdalla MD, Skipper MC. 2004. JOLT: A highly directive, very intensive, impulse-like radiator. Proc IEEE 92:1096–1109. Burfeindt MJ, Zastrow E, Hagness SC, Van Veen BD, Medow JE. 2011. Microwave beamforming for non-invasive patientspecific hyperthermia treatment of pediatric brain cancer. Phys Med Biol 56:2743. Camp JT, Jing Y, Zhuang J, Kolb JF, Beebe SJ, Song J, Joshi RP, Xiao S, Schoenbach KH. 2012. Cell death induced by subnanosecond pulsed electric fields at elevated temperatures. IEEE Trans Plasma Sci 40:2234–2347. Bioelectromagnetics
Dunn D, Rappaport CM, Terzuoli AJ Jr. 1996. FDTD verification of deep-set brain tumor hyperthermia using a spherical microwave source distribution. IEEE Trans MTT 44:1769– 1777. Gabriel C. 2007. Dielectric properties of biological material. In: Barnes FS, Greenebaum B, editors. Handbook of biological effects of electromagnetic fields, 3rd edition. New York, NY: CRC Press. Giamalaki MI, Karanasiou IS. 2011. Enhancement of a microwave radiometry imaging system’s performance using left handed materials. Prog Electromagn Res 117:253–265. Giri DV. 2004. High-power electromagnetic radiators: Nonlethal weapons and other applications. Cambridge, MA: Harvard University Press. Gouzouasis IA, Karathanasis KT, Karanasiou IS, Uzunoglu NK. 2010. Contactless passive diagnosis for brain intracranial applications: A study using dielectric matching materials. Bioelectromagnetics 31:335–349. Jiang N, Cooper BY. 2011. Frequency-dependent interaction of ultrashort E-fields with nociceptor membranes and proteins. Bioelectromagnetics 32:148–163. Joshi RP, Schoenbach KH. 2010. Bioelectric effects of intense ultrashort pulses. Crit Rev Biomed Eng 38:255–304. Karathanasis KT, Gouzouasis IA, Karanasiou IS, Giamalaki MI, Stratakos G, Uzunoglu NK. 2010. Noninvasive focused monitoring and irradiation of head tissue phantoms at microwave frequencies. IEEE Trans Inf Technol BioMed 14:657–663. Kumar P, Baum CE, Altunc S, Buchenauer J, Xiao S, Christodoulou CG, Schamiloglu E, Schoenbach KH. 2011. A hyperband antenna to launch and focus fast high-voltage pulses onto biological targets. IEEE Trans Microw Theory Tech 59:1090–1101. Lazebnik M, Popovic D, McCartney L, Watkins CB, Lindstrom MJ, Harter J, Sewall S, Ogilvie T, Magliocco A, Breslin ATM, Temple W, Mew D, Booske JH, Okoniewski M, Hagness SC. 2007. A large-scale study of ultrawideband microwave dielectric properties of normal, benign and malignant breast tissues obtained from cancer surgeries. Phys Med Biol 52:6093–6115. Lin JC. 1985. Frequency optimization for microwave imaging of biological tissues. Proc IEEE 73:374–375. Lin JC, Bernardi P. 2007. Computational methods for predicting field intensity and temperature change. Barnes FS, Greenebaum B, editors. Handbook of biological effects of electromagnetic fields, 3rd edition. New York, NY: CRC Press. Mitsutake K, Satoh A, Mine S, Abe K, Katsuki S, Akiyama H. 2012. Effect of pulsing sequence of nanosecond pulsed electric fields on viability of HeLa S3 cells. IEEE Trans Plasma Sci 19:337–342. Pham DT, Karaboga D. 2000. Intelligent optimisation techniques. London: Springer. Rogers WR, Merritt JH, Comeaux JA Jr, Kuhnel CT, Moreland DF, Teltschik DG, Lucas JH, Murphy MR. 2004. Strengthduration curve for an electrically excitable tissue extended down to near 1 nanosecond. IEEE Trans Plasma Sci 32: 1587–1599. Ryan TP, Trembly BS, Roberts DW, Strohbehn JW, Coughlin CT, Hoopes PJ. 1994. Brain hyperthermia: I. Interstitial microwave antenna array techniques—The Dartmouth experience. Int J Radiat Oncol Biol Phys 29:1065. Sanchez-Hernandez DA. 2009. High frequency electromagnetic dosimetry. Norwood, MA: Artech House.
Delivery of Subnanosecond Pulses toTissues Schoenbach KH, Joshi RP, Kolb JF, Chen N, Stacey M, Blackmore PF, Buescher ES, Beebe SJ. 2004. Ultrashort electrical pulses open a new gateway into biological cells. Proc IEEE 92:1122–1137. Schoenbach KH, Xiao S, Joshi RP, Camp JT, Heeren T, Kolb JF, Beebe SJ. 2008. The effect of intense subnanosecond electrical pulses on biological cells. IEEE Trans Plasma Sci 36:414–422. Silve A, Vezinet R, Mir LM. 2012. Nanosecond-duration electric pulse delivery in vitro and in vivo: Experimental considerations. IEEE Trans Instrum Meas 61:1945– 1954.
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Trefna HD, Vrba J, Persson M. 2010. Time-reversal focusing in microwave hyperthermia for deep-seated tumors. Phys Med Biol 55:2167–2185. Vitek JL, DeLong MR, Starr PA, Hariz MI, Metman LV. 2011. Intraoperative neurophysiology in DBS for dystonia. Mov Disord 26:31–36. Xiao S, Altunc S, Kumar P, Baum CE, Schoenbach KH. 2010. A reflector antenna for focusing in the near field. IEEE Antennas Wireless Propagat Lett 9:12–15. Xiao S, Guo S, Nesin V, Heller R, Schoenbach KH. 2011. Subnanosecond electric pulses cause membrane permeabilization and cell death. IEEE Trans Bio-Med Eng 58:1239–1245.
Bioelectromagnetics
Simulation Study of Delivery of Subnanosecond Pulses to Biological Tissues With an Impulse Radiating Antenna Fei Guo,1 ChenguoYao,1 Chandra Bajracharya,2 Swetha Polisetty,2 Karl H. Schoenbach,2 and Shu Xiao2* 1
Chongqing University, Chongqing, China Frank Reidy Research Center for Bioelectrics, Old Dominion University, Norfolk,Virginia
2
We have numerically studied the delivery of subnanosecond pulsed radiation to biological tissues for bioelectric applications. The antenna fed by 200 ps pulses uses an elliptical reflector in conjunction with a dielectric lens. Two numerical targets were studied: one was a hemispherical tissue with a resistivity of 0.3–1 S/m and a relative permittivity of 9–70 and the other was a realistic human head model (HUGO). The electromagnetic simulation shows that despite tissue heterogeneity of the human head, the electric field converges to a spot 8 cm in depth and the spot volume is approximately 1 cm 2 cm 1 cm in both cases when using only the reflector and a lens as an addition. Rather than increasing as it approaches the converging point, the electric field decreases strongly with distance from the skin to the converging point due to tissue resistive loss. The electric field distribution, however, can be reversed by making the dielectric lens lossy with the two innermost layers being partially resistive. The lossy lens causes an attenuation of the electric field near the axis, but the electric field generated by the waves which pass the lens at a wider angles compensate for this loss. A local maximum electric field in a deeper region of the tissue may form with the lossy lens. The study shows that it is possible to generate the desired electric field distribution in the complex biological target by modifying the dielectric properties of the lens used in conjunction with the reflector antenna. Bioelectromagnetics 35:145–159, 2014. © 2013 Wiley Periodicals, Inc. Key words: impulse radiating antenna; subnanosecond pulses; deep focus; dielectric lens; biological tissue
INTRODUCTION Since the 1960s, intense electromagnetic (EM) fields have been considered to be of therapeutic value. Biological studies have not only focused mostly on thermal effects such as raising tissue temperature for the purpose of hyperthermia but also as a tool to cauterize unwanted tissue. The application of EM radiation in the radio frequency and microwave range into tissues with an antenna or an applicator was studied extensively, with deep target access as the primary goal. Modeling and simulation were used to study the wave propagation in multiple tissue layers. The tissues studied were mainly fat and muscle. The skin was deliberately neglected due to the fact that its thickness is small compared to the wavelength, and the resistive loss is negligible. Such simple two-layer models (fat and muscle) provided important information on how the specific absorption rate (SAR) is distributed among the layers. Several points are reiterated here [Lin and Bernardi, 2007; SanchezHernandez, 2009]: (a) high SAR is found at the 2013 Wiley Periodicals, Inc.
interfaces between fat and muscle, which is primarily due to the abrupt change of dielectric permittivity at this interface and the requirement of continuity of the electric displacement vector; (b) standing waves can form in the tissue at certain frequencies and tissue thicknesses; (c) an incident electric field polarized in the tissue plane penetrates more easily; (d) a plane wave approximation cannot be used to predict the Grant sponsor: The Office of Research, Old Dominion University and Air Force Office of Scientific Research (AFOSR, USA). *Correspondence to: Shu Xiao, Department of Electrical and Computer Engineering, Frank Reidy Research Center for Bioelectrics, Old Dominion University, Norfolk, VA 23508. E-mail: [email protected] Received for review 24 December 2012; Accepted 18 September 2013 DOI: 10.1002/bem.21825 Published online 6 November 2013 in Wiley Online Library (wileyonlinelibrary.com).
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spatial distribution of the field intensity, which differs for different frequencies (3D models show that the spatial distribution of the field intensity is determined by interference pattern); and finally, (e) the permittivity seems to be more important than the conductivity in determining the field magnitude in the tissue. Focusing of EM radiation has been studied by means of narrowband antenna arrays. A limiting factor in all the approaches of using high frequency EM waves as diagnostic or therapy is the high attenuation of soft tissues. It requires the careful selection of a frequency that allows the balancing of the desired spatial resolution with the required penetration depth [Lin, 1985]. In a brain hyperthermia study, an array of four dipole antennas spaced 2.0 cm apart was capable of heating a volume of 5.9 cm 2.8 cm 2.8 cm [Ryan et al., 1994]. A careful selection of the source electric field distribution around the entire surface of the head can generate a well-defined focal volume [Dunn et al., 1996]. Time reversal with a large number of antennas was demonstrated as a method to confine the radiation spatially [Trefna et al., 2010]. A beam forming approach, with the intent of demonstrating treatment of brain cancer, allowed focusing of 1 GHz microwave radiation through constructive interference in the brain [Burfeindt et al., 2011]. In a deep brain monitoring system, the electric fields at 1.1 GHz that are radiated from one ellipsoidal reflector fed by a discone antenna can be focused into the center of the head [Gouzouasis et al., 2010; Karathanasis et al., 2010]. Left-handed meta-material was used as matching layers on the surface of the human head model to improve the sensitivity of the system [Giamalaki and Karanasiou, 2011]. Recently, wideband electric pulses in the ns or subnanosecond range were shown to induce various nonthermal effects, opening a new realm of bioelectrics [Schoenbach et al., 2004, 2008; Joshi and Schoenbach, 2010; Mitsutake et al., 2012]. While ns pulses are delivered with electrodes [Silve et al., 2012], delivering ultrashort electrical pulses with antennas to biological targets becomes attractive in reaching deep targets. One such antenna is an impulse radiating antenna that relies on a prolate spheroidal reflector [Baum, 2007; Altunc et al., 2008; Kumar et al., 2011]. At the first focus of this reflector, a transverse electromagnetic (TEM) wave launcher projects the EM waves to the reflector; from there they are redirected into the second focus. At the first focal point, the antenna’s wave launcher can be operated in a highly pressurized environment, with the possibility of launching wideband pulses with voltage amplitudes up to a few hundred kV or even 1 MV [Baum et al., 2004; Kumar et al., 2011]. Bioelectromagnetics
The electric field intensity required for inducing biological effects depends on the end-goal applications. The critical electric field for stimulation with subnanosecond pulses (e.g., 200 ps) can be extrapolated as 1 MV/m [Rogers et al., 2004] and may be decreased by a factor of 20–50 kV/m if the pusles are applied at high repetition rate, suggested by Jiang and Cooper [2011]. For cell killing, the electric field intensity in general is higher than the conditions for stimulation. For example, electric pulses of 800 and 200 ps have been studied in vitro on melanoma and hepatoma cells [Schoenbach et al., 2008; Xiao et al., 2011; Camp et al., 2012]. The magnitude of the electric field needs to be approximately 2 MV/m or higher in order to increase cell membrane permeability [Xiao et al., 2011]. The temperature increase due to high repetition rate (10 kHz) and prolonged exposure (up to 10 min) can no longer be ignored. In this paper, we report the feasibility of delivering electrical pulses in the subnanosecond range, by means of a simulation, through one antenna into soft tissue. The aim is to explore the conditions that allow us to focus the wideband radiation in brain tissue. Applications of a method, such as inducing cell death in brain tumors or neurostimulation, require the exploration of the necessary field intensity, pulse duration, and pulse number. We included a hemispherically shaped tissue as the target in the antenna configuration. We varied the electrical properties (permittivity and conductivity) of the tissue and studied the spatial distribution of the electric field intensity in the target, particularly in the deep region, which is defined as 6–8 cm below the surface. We further studied the temporal development and the spatial distribution of the electric field intensity in a human brain, with the aim of determining the electric pulse parameters required for deep brain stimulation [Vitek et al., 2011]. In particular, we aim to answer the following questions: How deep can the subnanosecond pulses penetrate and still achieve a reasonable confinement of the electric field distribution? Can we use one antenna to focus pulsed radiation into tissue? What spatial resolution can such antenna provide? Configuration of the Simulation To answer these questions, we have used a 3D EM simulation software, Computer Simulation Technology (CST) Microwave Studio (Framingham, MA). The transient solver based on finite integration technique was used for the time domain simulation. The human head model (HUGO) has a resolution of 1 mm 1 mm 1 mm. The basic configuration, reflector antenna and target, used in this modeling study are
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shown schematically in Figure 1a. The antenna has a prolate spheroidal reflector fed by a transverse electromagnetic (TEM) conical transmission line starting from the first focus as a wave launcher (Fig. 1a). The reflector is one-half of a prolate spheroid with the minor axis on the aperture plane. The geometry of the antenna was taken from an existing antenna [Xiao et al., 2010], constructed by Farr Research (Albuquerque, NM). The features of the antenna include: linearly polarized radiation, broadband radiation, and high power capability. The radiation at the second focus is vertically polarized, which is the mirror image of the electric field at the starting point of the transmission line fed by a differential input. A lens is used in conjunction with the impulse radiating antenna, aiming to improve the coupling of the EM energy to tissue (Fig. 1b). The lens is made of multiple layers with dielectric permittivity varying according to an exponential profile in order to allow for a maximum transmission [Altunc et al., 2009]. The innermost layer has the same dielectric constant as the targeted tissue. The electric pulses fed to the antenna have a Gaussian waveform with the pulse width 200 ps. In the CST transient solver, the frequency range was set to 0– 5 GHz. In the simulation, we used a tissue target which has a hemispherical shape (Fig. 1b). Such shape was chosen because the spherically incoming waves from the reflector antenna have the same phase along the circumference of the tissue, which results in a maximum field at the second focus for the same optical
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path. The relative permittivity of muscle and fat tissue is on the order of 45 (for muscle) and 5 (for fat). Their conductivity is in the range of 0.1–2 S/m. The values could vary for real tissues [Lazebnik et al., 2007]. The dielectric properties are dependent on the frequency, which can be described by the second order Debye model [Gabriel, 2007]. This type of model is not available in the software, so we did not include the effect of dispersion. In addition to the hemispherical target, we also used the CST HUGO model to determine the temporal and spatial distribution of the pulsed electric fields in a human brain (Fig. 1c). In the human head model used in this study, the dielectric constants and conductivities of the tissues considered in this study are: bone (er ¼ 11.78, s ¼ 0.28); gray matter (er ¼ 50, s ¼ 1.39); fat tissue (er ¼ 5.35, s ¼ 0.08); nervus opticus (er ¼ 30.87, s ¼ 0.84); white matter (er ¼ 37, s ¼ 0.91); and skeletal muscle (er ¼ 55.33, s ¼ 1.44). These tissue dielectric properties are the values chosen at 1.8 GHz. In the frequency range of 0.9–5 GHz, the tissue properties stay relatively flat as the bulk tissue dispersion is mainly dominated by the water contained in the tissue. For example, white mater has er ¼ 38.89 and s ¼ 0.59 at 0.9 GHz and er ¼ 33.44 and s ¼ 2.86 at 5 GHz. The dispersion of the dielectrics in general broadens the pulse waveforms and lowers the pulse intensity; the results of the simulation without dispersion loss therefore serves as the best scenario estimate of the pulse delivery in terms of pulse intensity and focal spot size. In this study, we have focused on the
Fig.1. a: The impulse antenna sends subnanosecond pulses to the hemispherical tissue. The minor axis of the reflector is located on the aperture of the antenna. b: A dielectric lens consisting of five layers was used in conjunction with the reflector antenna. The last layer of the lens is the biological tissue with radius of 6.0 cm. The dielectric constants of these five layers from the outermost to the innermost are 1.6, 2.4, 3.7, 5.8, and 9.0, respectively. The biological tissue (innermost layer) has the same dielectric constant as the 5th layer. c: The human head model used in this study. The grid size of the model is 1mm 1mm 1mm. The top of the head coincides with z-axis. In (b) and (c), the reflector antenna was used in the simulation but not shown. Bioelectromagnetics
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attenuation of the pulse in the brain, the size of the focal volume and the required input pulse parameters to create the electric fields that are at the level of inducing any biological effects. We note that the accuracy of the CST software is satisfactory. As reported previously by Kumar et al. [2011], using the same software to simulate the impulse radiating antenna gave results that are very close to the measurement results. We therefore assume that the simulation yield is sufficiently accurate in predicting the effect of wideband pulses on a human brain. RESULTS Hemispherical Tissue Directly Exposed to the Reflector Antenna The EM waves emitted from the elliptical reflector are spherical waves, converging at the second geometric focus of the reflector. The phases of the incoming spherical waves on the circumference of the target are identical. Because the electric fields of the converging spherical waves are parallel to the surface of the hemispherical tissue, the transmittance into the tissue is optimum [Lin and Bernardi, 2007]. In our simulation, we varied the relative permittivity of the tissue from a value of 9 to 70, and varied the conductivity from 0 to 1 S/m. The tissue conductivity near 0.5 S/m is close to that of breast tissue [Lazebnik et al., 2007]. An input Gaussian pulse was fed into the antenna (Fig. 2a). For a relative permittivity of er ¼ 9 and a conductivity of the target of s ¼ 0, the electric pulse at
the focal point (6 cm deep) is shown in Figure 2b. The pulse consists of a prepulse and an impulse. The prepulse reaches the second focal point at an approximate time, (t ¼ 27.16/30 þ 6 √9/30 ¼ 1.505 ns). The pulse reflected from the prolate-spheroidal reflector surface converges at the second focal point F2. This constitutes the impulse part of the wave at the focal point and occurs at approximately t ¼ 54/30 þ 6 √9/ 30 ¼ 2.4 ns. The shape of the impulse is close to the time derivative of the Gaussian wave form [Baum, 2007]. The electric field component that contributes mostly to the electric field at the focal point is the ycomponent. The amplitudes in the direction of x and z are negligible. The electric field intensities along the z-axis for er ¼ 9 and for various values of s are plotted in 1 cm steps from the surface to the target (Fig. 3a). It can clearly be seen that the field has its maximum at the second focus for s ¼ 0.3 S/m. However, this focusing effect diminishes as the conductivity increases from 0.3 to 0.5 S/m: the maximum field is located on the surface and it decreases monotonically on the z-axis. The decreasing trend of the z-axis electric field, however, is reversed when the tissue permittivity was changed from 9 to 70 (Fig. 3a). With the tissue dielectric permittivity of 70, the field is focused at the geometric focus even for a conductivity of 1 S/m. Clearly, the focusing effect is more pronounced in tissue with higher permittivity. The field distribution in the radial direction at different angles u is shown in Figure 3b. In this case, the tissue dielectric constant is 9 and the conductivity is 0.5 S/m. The electric field amplitudes on the z-axis
Fig. 2. a: Gaussian pulses of 200 ps were used as input pulses. b: The electric fields at the second focus with an input Gaussian pulse. The y-component is dominant among the electric fields in all directions. This result is for the hemispherical tissue that has a radius of 6 cm with e ¼ 9 and s ¼ 0. Bioelectromagnetics
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Fig. 3. a: The electric field distribution on the z-axis for different tissue conductivities (s). The tissue dielectric permittivity (e) was varied as 9, 40, and 70. The desired focus, also the geometric focus, is at z ¼ 6 cm. b: The electric field distribution in the radial direction at different azimuthal angles (u). The tissue has dielectric permittivity (e ¼ 9) and conductivity (s ¼ 0.5).
as well as those of the EM waves with a small azimuthal angle (608. We note that such distribution is for the tissue conductivity of 0.5 S/m, and for the tissue conductivity of 1 S/m, a similar field distribution was obtained. The field distribution can be schematically shown in Figure 5b. In the case of a non-lossy lens, the field distribution can be schematically depicted by the pie-shaped distribution in Figure 5a. A comparison of Figure 5a and b shows a localized focus may be formed in the deep region of the tissue. This change in distribution is made at the cost of the reduction of the absolute field intensity at the targeted region and two extra “hot spots” near the surface. Application of Subnanosecond Pulses to the Brain We have shown that it is possible to confine the electric field of subnanosecond pulses in a homogeneous, dielectric hemisphere. The attenuation loss of the target can be offset by using a partially lossy lens so that a deep-seated focal region can be created. While the targeted hemisphere is simple in structure, a real tissue contains multiple layers, making the formation of a focal spot more challenging. Three cases have been investigated: (1) the subnanosecond pulses are directed to the brain by the ellipsoidal reflector only; (2) a lens is placed on top of a human head; and (3) the lens is made partially lossy in order to attenuate the field along the axis. The lens, with the same structure as in Figure 1b, is used with the antenna and placed on top of the human head (Fig. 1c). The
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dielectric constant of each layer was the same as in Figure 1b. Because the head is not exactly round in shape, the top of the head coincides with the lens axis and the head appears to project into the lens structure. But at the lens-head interface, the priority is given to the head, which overrides the lens in any overlapped region. For the lossy lens, the innermost layer was assigned a conductivity of 5 S/m and the second-inner layer was assigned a conductivity of 4 S/m. The values of the conductivities were selected based on the consideration that the electric field on the axis increases as the wave penetrates deeper and nears the geometric focus. However, that does not mean that the electric fields in other radial paths of the penetration are lower than the fields near the geometric focus, as will be shown later. Human Head Exposure Directly to the Reflector Antenna We first examine the case where the pulse is directly delivered to the brain through the impulse radiating antenna without lens. Figure 6 shows the pulse waveform at the geometric focus in the brain (6 cm deep from the top of the skull). Again, the y-component dominates the overall field and the x and z components are negligible. Figure 7 shows the propagation of subnanosecond pulses in the head. The intensity of the electric fields is shown as the linear isoline in the clamped range 0.1–0.3 V/m, meaning any values that are greater than 0.3 are clamped to 0.3. At 1.8 ns, the prepulse already reaches the brain. In the meantime,
Fig.6. The pulse waveform at the 6 cm depth on the z-axis in the brain exposed to a reflector antenna. Bioelectromagnetics
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Fig. 7. The isoline plots of electric field distribution in the human brain exposed to a reflector antenna at various times with a clamp range of 0.1 to 0.3 V/m along X-axis (side view), Y-axis (back view), and Z-axis (top view).
the prepulse in the face and back side of the head travels faster than the prepulse in the brain. At 3.1 ns, the impulse appears in the brain along the axis of the antenna. It gradually reduces its size and at 3.7 ns, seems at its smallest size. As the wave penetrates deeper, the intensity decreases. The isoline plot clearly indicates that there is no resonance in the brain except the impulse. In the side view of the wave propagation (Fig. 7), at 3.1 ns, one can see that the impulse actually consists of two parts indicated by two bright spots. In the time domain, the corresponding impulse waveform is bipolar (Fig. 6). At 3.7 ns, the wave converges, which is consistent with the side view. A top view of the wave propagation is also shown in Figure 7. The view is taken at a depth of 8 cm from the top of the head. Because the wave intensity is shown as a clamped isoline, we placed a number of probes in the brain to measure the actual peak amplitudes as the pulse passes. The probes were placed in 1 cm steps along the radius centered at the second geometric focal point, which is 6 cm deep from the top of the skin fat (Fig. 1c). Figure 8a shows the field distribution along various radii from the skin. The largest field is on the 08 axis and the fields on the two sides seem symmetriBioelectromagnetics
cal about the axis. They all decrease due to the strong absorption in the brain. Despite the fact that the field decreases as the penetration depth increases, the field values converge at 7–8 cm, slightly deeper than the geometric focus (6 cm in depth). This is consistent with the results shown in Figure 7. The inhomogeneity of the brain does not seem to create any difference in the arrival time of the spherical waves along different radii, but the strong attenuation of brain tissue prevents the wave from reaching the highest amplitude near the focal point. To evaluate the focal spot size at 3.7 ns, we examine the sliced views by shifting the cutting plane from the antenna symmetry plane. In Figure 9, when the human head is viewed from x ¼ 2 to 2 cm, the focal spot in the brain is seen confined from 0 to 1 cm (side view). In the back view from y ¼ 2 to 2 cm, it becomes harder to tell where exactly the focal spot size is. But if we compare the region which contains electric field value of 0.3 V/m (maximum clamped value, red), the focal spot in this dimension can be approximately estimated as y ¼ 1 to 1 cm. In the top view (along z-direction), the focal spot size is seen from 1 cm (from 7 to 8 cm). In general, we can
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Fig. 8. a: The electric field distribution in the brain exposed to the reflector antenna without the dielectric lens. b: The electric field distribution when the antenna was shifted from the y-direction by 1cm while the human head remained at the same location.
estimate the focal volume is approximately 1 cm 2 cm 1 cm. The volume is narrow in both the x- and z-directions, but wider in the y-direction. When delivering the subnanosecond pulses to the deep targets, the relative position of the human head to the antenna could affect the location of the focal spot. Figure 8b shows the electric field distribution (on the z-axis, side view) at three different positions of the
human head when the z axis of the human head was at y ¼ 0, and 1 cm with respect to the antenna shifting in the y direction. For y ¼ 1 cm, the field distributions almost overlap that for y ¼ 0 cm. This observation can be understood as that the focal spot tends to spread mostly in the y-direction, so the focal spot location is not sensitive to the human head position when displacing 1 cm in the y-direction. However, we
Fig. 9. The isoline plots of electric field distribution with a clamp range of 0.1 to 0.3 V/m in the human brain without dielectric lens at 3.7 ns along X-axis (side view, top), Y-axis (back view, middle), and Z-axis (top view, bottom). The sliced views were taken from x ¼ 2 to 2 cm, y ¼ 2 to 2 cm, and z ¼ 6 to 9 cm in a step of 1cm. Bioelectromagnetics
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anticipate the focal spot location is more sensitive to the displacement in both the x- and z-directions, as the focal spot tends to be narrower than in the y-direction. Human Head Exposure to the Reflector Antenna Through a Lens When we placed a non-lossy lens on top of the head, the field distribution in isoline plot is shown in Figure 10. In this case, the isoline was clamped between 0.1 and 0.5 V/m due to the increased coupling of EM waves to the tissues by the lens. At 3.7 ns, the impulse becomes constricted in size and it reaches 8 cm deep at 3.9 ns. After that, the impulse decreases in intensity and becomes almost invisible in the clamped range. The addition of the lens creates a delay compared with the case without a lens. The amplitudes of the field are shown in Figure 11a. The field distribution is similar to the case where there is no lens added, except the amplitude at the skin is slightly higher due to the higher transmission of the lens. The field values converge to 0.5 V/m at the depth of 8 cm, also higher than the case without lens. Still, the highest field is on the axis and the fields on both sides are lower. The overall trend is decreasing as the impulse penetrates. One question arising is whether the introduction of the lens affects the focal spot size. We again examine the sliced views in the x-, y-, and z-directions. Figure 10 shows that the region contains the maximum
clamped value (0.5 V/m) is approximately 0–1 cm in the x-direction, 1 to 1 cm in the y-direction and 1 cm in the z-direction. The volume of the region is close to the case where only the reflector antenna was used. The addition of the lens increases the coupling of the EM radiations to the tissue, but does not change the focal spot size. The spatial sensitivity of the human head to the lens and antenna was investigated by shifting the lens and antenna in the y-direction. The lens layers overlapped with the human head were automatically changed into human head with no space created in between. In reality, it is not possible as the lens has a fixed structure and to do so different lenses have to be used. Still, we could numerically assess how sensitive the location of the focal spot is to the position of the human head. Figure 11b again shows that no significant change in electric field distribution when the human head is displaced by y ¼ 1 cm with respect to the lens and antenna as compared to y ¼ 0 cm. This observation is again due to the fact that the field spread mostly in the y-direction. A small dislocation in z- and x-axis could result in a more sensitive change in the focal spot location. Human Head Exposure to the Reflector Antenna in Conjunction With a Lossy Lens In the third case, we used the reflector antenna and the lens but we attenuated the field on the axis by
Fig. 10. The isoline plots of electric field distribution with a clamp range of 0.1 to 0.5 V/m in the human brain with the reflector antenna and dielectric lens at 3.7 ns along X-axis (side view), Y-axis (back view) and at 3.9 ns along Z-axis (top view). The sliced views were taken from x ¼ 2 to 2 cm, y ¼ 2 to 2 cm, and z ¼ 6 to 9 cm in a step of 1cm. Bioelectromagnetics
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Fig.11. a: The electric field distribution in the brain with the reflector antenna and non-lossy lens. b: The electric field distribution when the antenna and the lens were shifted in y-direction by 1cm from the original position while the human head remained at the same location. We note that the z-axis of human head overlapped the z-axis of antenna (and lens) before the shift, but became off axis after the antenna and lens were shifted in y.
assigning conductivities to the 4th and 5th layer of the lens. This idea originated from the study of a lossy lens coupling to the hemispherical tissue (Fig. 5b). In the side view of the wave propagation (Fig. 12), the impulse field, shows a “wishbone-like” distribution (at 3.7 ns). This is obviously different than the non-lossy
lens case as the fields in the z-axis is largely damped and the off-axis fields become higher. At 3.9 ns, the impulse is confined at 8 cm from the top of the skull. In Figure 13a, the field distribution is shown. On the axis (R vs. 08), the field becomes the lowest among all the radial directions and is slightly increased at 8 cm,
Fig. 12. The isoline plots of electric field distribution with a clamp range of 0.1 to 0.2 V/m in the human brain with the reflector antenna and lossy dielectric lens at 3.7 ns along X-axis (side view), Y-axis (back view), and at 3.9 ns along Z-axis (top view). The sliced views were taken from x ¼ 2 to 2 cm, y ¼ 2 to 2 cm, and z ¼ 6 to 9 cm in a step of 1cm. Bioelectromagnetics
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Fig. 13. a: The electric field distribution in the brain with the reflector antenna and lossy lens. b: The electric field distribution when the antenna and the lossy lens were shifted in y-direction by 1cm from the original position while the human head remained at the same location.
which is the opposite of that in Figures 8a and 11a, where the largest field is on the axis. Instead, the fields at 458 become the largest. The strong attenuation in the lossy lens allows us to modify the field distribution in the brain. Despite the strong attenuation, the field intensity near the focal point (8 cm in depth) is 0.2 V/ m, reduced by a factor of three from that in the nonlossy lens case (Fig. 11a). The focal spot volume in this case can be again estimated from different sliced views. If we examine the region having the maximum clamped range (0.2 V/m), Figure 12 shows the focal spot size becomes smaller. The side view indicates the focal dimension is less than 1 cm in x- and z-direction. The y-direction focal dimension is not as obvious as in the other two directions, but can still be seen becoming smaller. Such reduction in the focal spot size suggests that its location is more sensitive to the relative position between the antenna and the human head, which can be verified by the results obtained when the lens and antenna was shifted in y-direction to 1 cm (again, the human head remained at y ¼ 0). Apparently, the electric field distributions as a result of these shifts are modified (Fig. 13b). The field in y-direction becomes sensitive to the position of the human head with respect to the antenna and lens. This is rather different than the other two cases (no lens and nonlossy lens). On one hand, the lossy lens allows us to shrink the spot size, but on the other hand, the focal spot location becomes sensitive to the relative position of the antenna to human head. Meanwhile, the overall field intensity is decreased due to the extra attenuation introduced in the lens. Bioelectromagnetics
DISCUSSIONS The transmission of subnanosecond pulses to a homogeneous tissue was studied using an impulse antenna. A spherical wave with a propagation vector perpendicular to a spherical target converges on the geometric center of the spherical wave. This offers a rather simple prediction of the field distribution in the target. The conductivity of the tissue, however, changes the geometric-optics picture. It creates a decreasing electric field with increasing penetration distance. For the generation of large field intensities in the shallow region of the tissue, a single antenna is sufficient. As the antenna radiation is an inhomogeneous spherical wave, the highest field is along the axis, which means the highest field distribution in the target also coincides with the axis. For deeper focusing, the loss due to the conductivity of the dielectric can be alleviated by applying this method to tissue with high dielectric constants, such as muscle tissue. In a target which contains composite tissues, such as the brain, the multiple layers in the propagation path (skin and skull) do not pose a significant change to the waveforms of the converging waves, since, in Figure 6, both prepulse and impulse can be clearly identified for the case when a reflector antenna was used. In addition, the converging point in the brain can be clearly identified to be 8 cm deep from the top of the human head, which is 2 cm deeper than the geometric focus of the reflector antenna. The volume is 1 cm 2 cm 1 cm in the xyz-directions and is situated in the white-matter region. As white matter has a dielectric constant of 37, the spatial width
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of such pulse is 1 cm, which is consistent with the simulation result for an input pulse of 200 ps (Fig. 9). It is therefore reasonable to predict the focal spot size simply by estimating the pulse spatial width in the dielectric where the focal point is to be created. On the other hand, the amplitude of the electric field decreases from the human head surface to the converging point along the radial paths of small azimuthal angles with the field on the z-axis being the strongest among all the radial paths. Adding a dielectric lens in addition to the reflector antenna does not change the converging point and still allows the radiation to converge at 8 cm in depth. It increases the coupling of radiation to the tissue and the electric field intensity at the converging point. Similar to the case without the lens, the electric field also decreases along the paths of small azimuthal angles and it is still the strongest on the z-axis. Using a dielectric lens with two innermost layers being partially lossy does not change the location of the converging point and still allows the radiation to converge at 8 cm in depth. The field on the z-axis in this case, however, becomes the lowest because of the attenuation in the lens, leaving the fields higher along other radial paths with wider angles. The electric field distributions obtained in a hemispherical tissue (Fig. 5a and b) and a brain model (Figs. 11a and 13a) show two extreme cases of electric field distribution. One has the highest field on the z-axis while the fields on the side are smaller. The other case is that high fields penetrate from the two sides about the z-axis, while leaving the axial field small, but in the deep region, a local maximum can be formed. The first case can be used for delivering subnanosecond pulses to the shallow regions along the axis and the second case can be used for delivering subnanosecond pulses to the shallow region on the sides. The targeted region can be selected by placing lossy materials in the corresponding incident angles of the lens, which offers one way of varying the focal zone by utilizing different lenses. On the other hand, the two entirely opposite cases suggest that it may be possible to find a specific lens case where the pulse amplitude in deep region has a local maxima and the fields on the sides are higher, but the side regions may be controlled to be as shallow as skin or bone area and they are not physiologically as sensitive as brain tissue. The lens design need be optimized and could consist of a number of lossy elements in the same layer of the lens with each layer having different values of conductivities. A typical multi-variable optimization method, such as a generic algorithm [Pham and Karaboga, 2000], can be used to find the
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optimum values of the lens segments. This aim will be our next-step study. We noticed that in Figures 9, 10, and 12, the electric field scattering on the head surface remains large. To reduce the impact of such scattering to the clinical environment, the reflector can be increased in the reflection area and extended to an elliptical cavity with the opening aperture at the patient’s neck. Microwave absorbers can be placed in the cavity to absorb the scattering. In addition, the face of the patient can be protected by wearing a resistive mask to damp the surface waves. In terms of the choice of delivery, the reflector antenna has the ability of steering the converging point just by shifting the antenna position. Adding a dielectric lens can improve the coupling of the radiation (for non-lossy lens) or modify the electric field distribution in the tissue (for lossy lens), but is only useful for a fixed converging point. Furthermore, the lens design and construction is patient-specific and cannot be used for other patients. What implication does this study suggest? As shown in Figure 11a, for a voltage of 1 V fed to the antenna, an electric field is in the range of 1.5 V/m at a depth of 2 cm, which is the motor cortex region in the brain. This means an input voltage of 33.3 kV may be sufficient for an effective stimulation to meet the stimulation threshold of 50 kV/m as mentioned in the Introduction Section. For deep stimulation, Figures 8a, 11a, and 13a indicate there is a locally confined region at a depth of 8 cm. For a 1V pulse input, the field intensity was found to be 0.2–0.5 V/m for the three cases, which suggests that pulses of 250 kV–2.5 MV need to be fed into the antenna in order to meet the estimated stimulation threshold of 50 kV/m. Such a high-amplitude pulse generator becomes technically challenging (if not impossible) even though a 1-MV pulse generator has been built [Baum et al., 2004]. CONCLUSIONS Delivery of subnanosecond pulses to tissues has been studied using a single impulse radiating antenna. The electric field distribution shows a steadily decreasing trend and is primarily caused by the tissue conductivity. But increasing the tissue dielectric constant, meaning applying the method to a different tissue, can reverse the trend and allows for a deep focusing (e.g., 6 cm in depth). A second approach that could possibly create deep focusing is to use a dielectric lens in conjunction with the antenna. The lens can modify the electric field distribution in the tissue. In one case, the lens is loss-free and the electric fields along the axis are the highest. In the other case, Bioelectromagnetics
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the lens is assigned with lossy material to attenuate the axial incident electric fields, but allowing the incident fields from the sides to pass. This case results in the opposite distribution as the first case: the largest fields on the side, and the small fields along the axis. A local maximum near the geometric focus exists in this case. When the target is replaced by a human brain, the field along the axis is still strongest if the human head is directly exposed to the antenna. Despite a slight asymmetry of the human head, the spherical wave still converges near the geometric focus. However, the overall intensity decreases from the surface as the wave penetrates, due to a strong resistive loss of the tissue. Adding a dielectric lens allows one to increase the field intensity near the geometric focus, but the strongest intensity is still found along the axis and decreases as the wave penetrates deeper. When the lens is made lossy, the field on the axis can be made lower in the brain, while maintaining a higher field distribution near the 458. This study suggests the possibility of designing a dielectric lens with heterogeneous distribution of lossy material to create a desirable electric field distribution in the brain. ACKNOWLEDGMENT We thank the China Scholarship Council (CSC) for providing the visiting graduate research assistantship. REFERENCES Altunc S, Baum CE, Christodoulou CG, Schamiloglu E, Buchenauer CJ. 2008. Focal waveforms for various source waveforms driving a prolate-spheroidal impulse radiating antenna (IRA). Radio Sci 43:RS4S13. Altunc S, Baum CE, Christodoulou CG, Schamiloglu E, Buchenauer CJ. 2009. Design of a special dielectric lens for concentrating a subnanosecond EM pulse on a biological target. IEEE Trans Dielectr Electr Insul 16:1364–1375. Bajracharya C, Xiao S, Baum CE, Schoenbach KH. 2011. Target detection with impulse radiating antenna. IEEE Antennas Wireless Propagat Lett 10:496–499. Baum CE. 2007. Focal waveform of a prolate-spheroidal impulseradiating antenna (IRA). Radio Sci 42:RS6S27. Baum CE, Baker WL, Prather WD, Lehr JM, O’Loughlin JP, Giri DV, Smith ID, Altes R, Fockler J, McLemore D, Abdalla MD, Skipper MC. 2004. JOLT: A highly directive, very intensive, impulse-like radiator. Proc IEEE 92:1096–1109. Burfeindt MJ, Zastrow E, Hagness SC, Van Veen BD, Medow JE. 2011. Microwave beamforming for non-invasive patientspecific hyperthermia treatment of pediatric brain cancer. Phys Med Biol 56:2743. Camp JT, Jing Y, Zhuang J, Kolb JF, Beebe SJ, Song J, Joshi RP, Xiao S, Schoenbach KH. 2012. Cell death induced by subnanosecond pulsed electric fields at elevated temperatures. IEEE Trans Plasma Sci 40:2234–2347. Bioelectromagnetics
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