Microwave beamforming for non-invasive patient-specific hyperthermia treatment of pediatric
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PHYSICS IN MEDICINE AND BIOLOGY
Phys. Med. Biol. 56 (2011) 2743–2754
Microwave beamforming for non-invasive
patient-specific hyperthermia treatment of
pediatric brain cancer
Matthew J Burfeindt1, Earl Zastrow1, Susan C Hagness1,
Barry D Van Veen1and Joshua E Medow2,3
1Department of Electrical and Computer Engineering, University of Wisconsin—Madison, WI,
2Department of Neurological Surgery, University of Wisconsin—Madison, WI, USA
3Department of Biomedical Engineering, University of Wisconsin—Madison, WI, USA
E-mail: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org,
email@example.com and firstname.lastname@example.org
Received 8 January 2011, in final form 6 March 2011
Published 5 April 2011
Online at stacks.iop.org/PMB/56/2743
We present a numerical study of an array-based microwave beamforming
approach for non-invasive hyperthermia treatment of pediatric brain tumors.
The transmit beamformer is designed to achieve localized heating—that is,
to achieve constructive interference and selective absorption of the transmitted
destructive interference elsewhere. The design process takes into account
patient-specific and target-specific propagation characteristics at 1 GHz. We
evaluate the effectiveness of the beamforming approach using finite-difference
time-domain simulations of two MRI-derived child head models from
the Virtual Family (IT’IS Foundation). Microwave power deposition and the
resulting steady-state thermal distribution are calculated for each of several
randomly chosen focus locations. We also explore the robustness of the design
Lastly, we demonstrate the ability of the beamformer to suppress hot spots
caused by pockets of cerebrospinal fluid (CSF) in the brain. Our results show
in the head models for focus locations that are not surrounded by large amounts
of CSF. These promising results suggest that the technique warrants further
investigation and development.
(Some figures in this article are in colour only in the electronic version)
0031-9155/11/092743+12$33.00 © 2011 Institute of Physics and Engineering in MedicinePrinted in the UK2743
2744 M J Burfeindt et al
The goal of hyperthermia treatment is to elevate the temperature of a tumor above a certain
threshold (commonly 42◦C) for an extended period of time, thereby weakening or destroying
the cancer cells, while maintaining safe temperatures in healthy tissues.
treatment has been shown to be an effective adjuvant to other treatment modalities for a
variety of cancers (e.g., Overgaard et al 1995, Kapp 1996, Van der Zee et al 2000, Harima
et al 2001, Sneed et al 2004). For brain tumors, favorable outcomes have been achieved after
interstitial hyperthermia treatment (e.g., Winter et al 1985, Tanaka et al 1987, Sneed et al
Inducing localized hyperthermia in the pediatric brain via a microwave transmit
beamforming is a non-invasive process and thus may allow the treatment of brain tumors that
cannot be treated safely by surgical excision. Microwave radiation is also non-ionizing, unlike
tumors in children carries risk, as it is linked with developmental disorders (Pollack 1999,
Duffner 2004). In a study by Packer et al (1989), children who received cranial radiation
treatment and were 7 years of age or younger at diagnosis experienced a mean decline of
25 points in full-scale IQ 2 years after treatment. Duffner et al (1985) found that 86% of
children who received cranial radiation treatment experienced growth hormone deficiencies in
the year following treatment.
numerical simulations. Dunn et al (1996) investigated the use of a spherical array of sources
to focus electromagnetic energy in a numerical human head phantom. Gouzouasis et al (2007)
conducted simulations of an ellipsoidal reflecting cavity for focusing energy into a numerical
human head phantom. The lattergroupalsodeveloped aprototype ofthiscavity andhas tested
it on a physical phantom (Karanasiou et al 2008). To the best of our knowledge, neither of
these techniques incorporates patient-specific propagation data into their design.
The widespread availability of MRI-derived, anatomically realistic human phantoms and
the relative ease with which they are constructed and used in full-wave electromagnetic
simulations make it possible to design microwave beamformers based on patient-specific and
focus-location-specific propagation data. Numerical studies of beamforming for focusing
in the breast have recently been conducted (Zastrow et al 2010). Using such an approach
for the brain presents different challenges, as most matter in the brain is lossy high-water-
content tissue. In contrast, one of the major constituents of the breast is lower-loss adipose
tissue. The existence of cerebrospinal fluid (CSF) in the brain further complicates selective
microwave heating. CSF is highly conductive in comparison to other brain tissue and is also
not cooled by the blood supply. Therefore, it is prone to heat accumulation under microwave
illumination, resulting in unsafe temperatures. Because of the challenges imposed by high-
water-content tissue and CSF, the demonstrated feasibility of microwave beamforming for
breast hyperthermia does not guarantee feasibility for brain hyperthermia.
invasively inducing localized hyperthermia in the pediatric brain. Adult brains tend to have a
higher volume of CSF than pediatric brains and thus represent a more challenging treatment
scenario. Given this challenge and the risks of radiation therapy in children, this feasibility
study is directed to treatment of pediatric brain cancer. The beamformer is designed to focus
microwave energy at a specific location within the brains of two numerical MRI-derived
child head phantoms. We evaluate the beamformer’s performance using electromagnetic and
thermal simulations of the phantoms. Selective heating performance at 1 GHz is evaluated for
Microwave beamforming for hyperthermia treatment of pediatric brain cancer2745
a set of randomly chosen focus locations in the brain. In addition, we explore the robustness
of beamforming to modest mismatch between the actual and assumed dielectric properties of
the patient. The ability of the beamforming approach to suppress unwanted hot spots due to
CSF in the brain is also demonstrated.
The remainder of the paper is organized as follows. Section 2 describes the transmit
beamforming strategy as well as the numerical models we use in the study. The results of the
study are presented and discussed in section 3. Concluding statements are made in section 4.
2. Models and methods
2.1. Transmit beamforming
Our transmit beamforming goal is to achieve selective absorption of microwave energy at
a desired location in the brain. The beamformer is designed so that narrowband signals
transmitted from the antennas in the array achieve constructive interference and increased
energy deposition at the desired focus location. We may also suppress energy deposition at
other locations in the brain by designing the beamformer to achieve destructive interference
at those locations.
The beamformer comprises one complex channel weight for each antenna. Each channel
weight determines the magnitude and phase of the input signal to the corresponding antenna.
The channel weight for the ith channel is denoted by wi. Define the vector w as
w = [w1w2...wN]H,
where the superscript H denotes conjugate transpose.
For a given location in the head r, each antenna has a complex transfer function that
relates the signal fed to the antenna to the electric field phasor seen at r. Denote the channel
transfer function for the ith channel and location r by hi(r). Define the vector h(r) as
h(r) = [h1(r)h2(r)...hN(r)]T.
For this study, we use the copolarized component of the electric field to determine h(r).
In a clinical setting, h(r) is not known exactly for all r of interest, so a patient-specific
approximation of h(r) is needed. This approximation may be obtained by acquiring an MRI
of the patient’s head, assigning dielectric properties to each tissue type in the MRI, and
conducting electromagnetic simulations of the MRI-derived head model. The latter step in
this clinical treatment planning protocol is identical to that used to obtain h(r) in this study
involving virtual patients.
Suppose that the desired focus is located at rf. Also suppose that there are M locations
(rs1,rs2,...,rsM) where we wish to suppress energy deposition.
beamformer design goal by choosing w to solve the following optimization problem:
We accomplish our
w = argmax
The scalars (α1,α2,...,αM) determine the relative importance of suppressing energy
deposition at locations (rs1,rs2,...,rsM). We define S(rf) to be an N×N diagonal matrix,
where Sii(rf) = |hi(rf)|. Defining S(rf) in this way penalizes solutions where the magnitudes
of the widiffer much from each other. For example, it is straightforward to show that when
αi= 0, i = 1,2,...,M, this choice results in |wi| = 1. Keeping the output power across the
array relatively constant prevents a concentration of heating at any point on the head surface.
The solution to (1) is w =?S(rf) +?M
2746 M J Burfeindt et al
Figure 1. Numerical models of (a) the 6 year old patient and (b) the 11 year old patient (Virtual
Family, IT’IS Foundation). The cross-sections show the interior effective conductivity in S m−1.
The locations of the sources are signified by the black dots on the rings encircling the phantoms.
2.2. Numerical models for beamformer design and performance evaluation
Numerical phantoms of a 6 year old male and an 11 year old female are used as virtual patients
(Zurich, Switzerland)4. The anatomically realistic 3D phantoms are derived from MRI scans
of human subjects. The phantoms are segmented into a number of tissue types (up to 84 in the
The phantoms used here have a 1 mm resolution. Treatment planning for the virtual patients is
performed by determining h(r) using finite-difference time-domain (FDTD) simulations (see
Taflove and Hagness 2005) of the human head models and designing the beamformer weights
according to (1). Note that this approach is an ideal approximation to the clinical scenario
evaluatethebeamformer’sperformance. Inaclinicalsetting, therewillbedifferencesbetween
the MRI-derived propagation model and the actual propagation environment of the patient’s
head. These differences arise from mismatch between the assumed and actual dielectric
properties of the tissues in the patient’s head.
simulations in this study are conducted using SEMCAD X version 14 from Schmid and
Partner Engineering AG (SPEAG). The head phantoms and the surrounding antenna array are
illustrated in figure 1. The virtual patients are oriented upright in the positive z-direction.
The array elements in the simulations are 1 mm long, z-directed voltage sources with internal
resistance 50 ?. These sources are distributed on elliptical rings encircling the phantoms. The
plane of each ring is parallel to the xy-plane. Five rings of antennas are separated by a vertical
spacing of 2 cm, with the bottom ring 2 cm above eye level. The in-plane spacing between
sources on each ring is 2 cm. The major and minor axes of each ring are chosen so that the
minimum in-plane distance from any source to the skin surface is 2 cm. A total of 147 sources
are used for the 6 year old patient, while 152 sources are used for the 11 year old patient. The
slight increase in the number of sources between phantoms is due to the slightly larger extent
of the 11 year old patient’s head in some planes. A de-ionized (DI) water half-space extends
Electromagnetic model for beamformer design.
Electromagnetic (EM) FDTD
Microwave beamforming for hyperthermia treatment of pediatric brain cancer2747
upward from a plane located 7 mm below the bottom ring of sources. The DI water provides
effective coupling of microwave power into the head interior. Below the DI water half-space,
the surrounding medium is air.
The frequency of operation for the EM simulations is 1 GHz. This frequency is chosen to
balance the need for high spatial resolution with the need for an adequate penetration depth.
The relative permittivity, ?r, and effective conductivity, σeff, at 1 GHz were taken from the
report by Gabriel (1996)5. Brain structures for which dielectric data were not reported by
Gabriel (1996), such as the medulla oblongata, pons, and midbrain, were assumed to have
dielectric properties averaged between gray matter and white matter.
The propagation vector h(r) for any r of interest is found via FDTD simulation using
reciprocity. A source is placed at r and the simulation is run until the sinusoidal steady state
is reached. The resulting phasors recorded across the beamforming array are then used as an
approximation to h(r).
state heating potential, Q(r), inside the head is computed and saved for use in the thermal
FDTD simulation. The thermal simulation is also conducted using SEMCAD X. The thermal
model solves the well-known Pennes bioheat equation, given by
where Cpis the specific heat, ρ is the mass density, K is the thermal conductivity, A0is the
metabolic heat production, Q is the electromagnetic heating potential calculated from the EM
FDTD simulation, B is a constant representing heat exchange due to capillary blood perfusion,
and TBis the blood temperature (set to 37◦C). Thermal properties for each tissue type were
taken from Duck (1990) and Bernardi et al (2003). Due to the dearth of data regarding
metabolic heat generation in the literature, A0is assumed to be proportional to the blood
perfusion. This follows the convention used by Gordon et al (1976) and Bernardi et al (2003).
The air and DI water surrounding the head are assumed to be at 15◦C. The DI water
therefore acts as a superficial cooling medium. A convective boundary condition is applied
at the skin–water interface with a convective coefficient of 200 W (m2K)−1. This value is
more conservative than the value of 300 W (m2K)−1used by Converse et al (2006), which
was found by extrapolating the experimental results for a cooling system used in ultrasound
vasectomy. The convective coefficient for the air–skin interface is set to 10 W (m2K)−1.
All body tissue temperatures are initialized to 37◦C. A preliminary cooling period of
100 s is simulated. The heating potential Q(r) is then applied until steady state is reached.
= ∇ · (K(r)∇T(r)) + A0(r) + Q(r) − B(r)(T(r) − TB),
3. Simulation results and discussion
3.1. 6 year old patient, ideal beamformer with no suppression points
First we consider beamforming performance for eight randomly chosen focus locations in
the numerical models of the 6 year old patient. The focus locations were constrained to be
separated by at least 2 cm and to be at least 1 cm deep in the brain. The focus locations were
also constrained to have at most 0.1 mL of CSF within a 1.5 cm radius. The CSF volume
constraint was included to avoid focusing directly onto a large CSF pocket. Focusing near
a large CSF pocket causes the heating zone to move from the desired focus location to the
5A compilation can be found at http://www.fcc.gov/oet/rfsafety/dielectric.html.
2748 M J Burfeindt et al
Table 1. Coordinates of the focus locations in the model of the 6 year old patient.
location of the pocket. No suppression points were used, resulting in an equal transmit power
distribution across the array.
We define the following nomenclature to describe the simulation results.
rfi: the ith focus location,
rpi: the location of peak temperature obtained when focusing at rfi,
P: the total output power of the array,
T(r): the steady-state temperature distribution.
The coordinates for the focus locations are given in table 1. We refer to the tissue within
surrounding rpiwhere T(r) > 41◦C are termed hot spots. We scaled P to maximize T(rfi)
such that the hottest point exterior to the 41◦C contour had a temperature T(r) = 40.95 ±
0.15◦C. The extents of the heating zone in the x-, y-, and z-directions are referred to as Lx,
Ly, and Lz, respectively.
Figure 2 shows three orthogonal cross-sectional views of the thermal distributions for
two representative focus locations, rf1and rf2. The focus location rf1is in the front left
of the brain, while rf2is in the central left. The orthogonal cuts pass through rp1and rp2,
respectively. The focus locations are projected onto each cross-sectional plane and are marked
with a white cross-hair. The heating zone is shown by the solid lines, while the dashed lines
correspond to the 41◦C contour. For rf1, T(rf1) = 44.0◦C, Lz= 28, Lx= 15, and Ly= 15
mm. For rf2, T(rf2) = 42.2◦C, Lz= 14, Lx= 10, and Ly= 9 mm.
Figure 3 relates T(rfi) and T(rpi) to Lzfor all eight focus locations. We chose to plot
4 to 28 mm, with larger Lztending to coincide with higher temperatures. The range of T(rfi)
was 41.8–44.8◦C. The range of T(rpi) was 42.3–44.8◦C. Six of the eight focus locations had
T(rfi) ? 42.0◦C.
In general, raising the focus temperature results in a larger heating zone. For the case
of rf1, if we re-scale P so that T(rf1) = 42.5◦C, then the new heating zone extents are
Lz= 13, Lx= 8, and Ly= 7 mm. In a clinical setting, re-scaling P in this way may be useful
in balancing the benefits of a high focus-location temperature with the benefits of a desired
heating zone size.
3.2. 6 year old patient, mismatched beamformer with no suppression points
Next we consider the performance of the beamformer when there is a mismatch between the
assumed and actual dielectric properties of the patient. For the same eight focus locations, we
Microwave beamforming for hyperthermia treatment of pediatric brain cancer2749
Figure 2. Steady-state temperature distributions through the maximum temperature location in
the 6 year old patient for (top) rf1(−2.2, −4.0, 5.5) cm and (bottom) rf2(−2.2, 1.8, 7.9) cm. The
white cross-hairs mark the projection of the focus onto each orthogonal cross-section. The solid
line depicts the heating zone (T > 42◦C), while the dashed line is a 41◦C contour. T(rf1) =
44.0◦C, while T(rf2) = 42.2◦C.
3579 11 13 15 17 19 21 23 25 27 29
Figure 3. Peak and focus-location temperatures (T(rp) and T(rf), respectively) as a function of
the vertical extent of the heating zone for the eight focus locations in the 6 year old patient.
obtained h(rfi) from a treatment planning simulation wherein ?rand σefffor each tissue type
were increased by 10% relative to the actual properties of the virtual patient. We chose 10%
as a representative level of uncertainty based on 1 GHz data for gray matter (Gabriel 1996),
the single largest constituent tissue in the region surrounded by the array. We applied an equal
2750 M J Burfeindt et al
Figure 4. Steady-state temperature distributions for rf2(−2.2, 1.8, 7.9) cm for the 6 year old
patient. For the top row, the assumed dielectric properties of the patient were 10% higher than
the properties used for performance evaluation. T(rf2) = 42.1◦C (top row). For the bottom
row, the assumed dielectric properties of the patient were 10% lower than the properties used for
performance evaluation. T(rf2) = 41.6◦C (bottom row). The cross-hairs, the solid line, and the
dashed line have the same connotation as in figure 2.
mismatch to all voxels in order to obtain relatively severe propagation model error for a given
level of mismatch.
The weights w were then chosen according to (1). To test the effectiveness of this
phantom (with the unaltered dielectric properties). The steady-state thermal distribution for
rf2is given in figure 4 (top row). The distribution is very similar to the distribution obtained
from the matched case that is shown in figure 2 (bottom row).
and evaluated its performance. The thermal distribution for rf2is shown in figure 4 (bottom
row). The heating zone for rf2is considerably smaller. The use of underestimated dielectric
properties in the treatment planning simulation has degraded the focus and exacerbated a
potential hot spot near the target, requiring P to be scaled down so that the hot spot falls in the
temperature range 40.95 ± 0.15◦C.
The effect of a dielectric properties’ mismatch on the size of the heating zone is shown in
figure 5 for all eight points. Overestimating the dielectric properties in the treatment planning
we observed a significantly larger Lz. Conversely, underestimating the dielectric properties in
the treatment planning simulation resulted in Lz= 0 for two cases (rf4, rf7). This signifies
that no heating zone (T > 42◦C) could be created without also creating hot spots. These
Microwave beamforming for hyperthermia treatment of pediatric brain cancer2751
Figure 5. The vertical extent of the heating zone in the model of the 6 year old patient when the
dielectric properties assumed in the beamformer design are equal to 10% over and 10% under the
actual properties. Underestimation of dielectric properties results in Lz= 0 mm (no heating zone)
for rf4and rf7.
properties and inconsistent for modest underestimation of dielectric properties. This finding
is consistent with Zastrow et al (2010).
3.3. 11 year old patient, matched beamformer with suppression
Lastly, we consider the suppression of hot spots using an iterative design procedure. We chose
to use the numerical model of the 11 year old patient for this study, as the model’s higher CSF
levels potentially lead to more hot spots. The 11 year old patient has 177 mL of CSF in the
brain. The 6 year old patient has similar head dimensions as the 11 year old patient, but only
151 mL of CSF in the brain.
One focus location was chosen at random using the same CSF and depth constraints as
were used for the previous eight focus locations in the 6 year old’s head. This focus location,
denoted as rf, has coordinates (2.1, −2.0, 3.9) cm. The propagation function h(rf) was
obtained using the exact dielectric properties. The weights w were designed according to (1)
assuming no suppression points. Steady-state temperature slices through rp(the location of
peak temperature) are shown in figure 6 (top row). Note that P has again been scaled so that
the maximum T(rf) is achieved (in this case, 41.2◦C) without creating hot spots.
We identified the hottest point exterior to the 41◦C contour surrounding rpias the first
suppression point, denoted as rs1. We obtained the propagation function, h(rs1), for this
suppression point. The weights w were re-designed according to (1) with α1= 200. After
using one suppression point, the maximum T(rf) such that no hot spots occurred decreased
We then repeated the design procedure described above four times. For each iteration, we
point rsnwas chosen to be the hottest point external to the 41◦C contour surrounding rpi
2752 M J Burfeindt et al
Figure 6. Steady-state temperature distributions for rf (2.1, −2.0, 3.9) cm in the 11 year old
patient. For the top row, no suppression points were used, and T(rf) = 41.2◦C. For the bottom
row, five suppression points were used, and T(rf) = 42.2◦C. The cross-hairs, the solid line, and
the dashed line have the same connotation as in figure 2.
Number of Suppression Points
T(rf ) ( oC)
Figure 7. Focus-location temperature as a function of the number of suppression points for rf
(2.1, −2.0, 3.9) cm in the 11 year old patient.
after n − 1 iterations. Each suppression point weight, αn, was chosen to be 200. The focus
temperature is plotted by iteration in figure 7. The maximum T(rf) such that no hot spots are
created reaches 42.2◦C after the last iteration, which is 1.0◦C higher than could be achieved
with no suppression points. Figure 6 (bottom row) shows steady-state thermal slices after the
last iteration. We see that decreasing energy deposition at the five suppression points came at
the expense of increasing the temperature at other locations in the brain.
Microwave beamforming for hyperthermia treatment of pediatric brain cancer2753
3.4. Practical issues
beamforming approach shows promise for non-invasive hyperthermia treatment of pediatric
brain cancer. Further work needs to be done in order to assess the feasibility of realizing
a practical system. Practical issues include designing compact, efficient antenna elements
and determining the optimal array configuration and coupling medium. Electrically small,
omnidirectional voltage sources are useful in evaluating the potential performance of
the proposed beamforming strategy. However, these sources would be too inefficient
for a clinical hyperthermia system. Techniques for shielding the patient’s eyes and
the environment outside the array from the microwave radiation will also need to be
The results of this study establish the feasibility of creating heating zones at desired focus
locations in the brain while maintaining temperatures below 41◦C elsewhere. Depending
on the focus location and the propagation environment for a particular patient, regions of
relatively high temperature (up to 41◦C) may still be created at locations in the brain where
such a temperature may be unsafe. The physician must weigh the benefits and risks of
treatment in considering whether microwave hyperthermia treatment is appropriate for each
patient. Our preliminary investigation suggests that beamforming may offer the flexibility in
treatment planning to accommodate input from the physician regarding regions to safeguard
This numerical study establishes the feasibility of an array-based microwave transmit-
beamforming approach for hyperthermia treatment of pediatric brain tumors.
beamforming approach is shown to be feasible despite the prevalence of lossy high-water-
content tissue and CSF in the brain. The beamformers are designed according to patient-
specific and focus-location-specific propagation data, and operate at 1 GHz in order to balance
resolutionwithpenetrationdepth. Beamformerperformanceisevaluated forasetofrandomly
chosen focus points in an MRI-derived human head model using electromagnetic FDTD
simulations to determine power deposition and thermal FDTD simulations to determine the
steady-state temperature distribution. The results show that localized heating zones can
be created in the child head model for focus locations that are not located near significant
amounts of CSF. We show that the beamforming approach is robust to modest overestimation
of dielectric properties in the propagation model. The beamforming approach is less robust
to modest underestimation of dielectric properties. The ability of the beamformer to suppress
unwanted hot spots in a human head model with higher levels of CSF is also demonstrated.
tumors non-invasively via focused microwave hyperthermia and that further investigation is
This work was supported by SEMCAD for Science, the Department of Defense
SMART Scholarship for Service Program, the National Science Foundation under grant
CMMI0625054, and the Philip D Reed chaired professorship.
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