Dosimetric and thermal properties of a newly developed thermobrachytherapy seedwith ferromagnetic core for treatment of solid tumorsBhoj Gautam, E. Ishmael Parsai, Diana Shvydka, John Feldmeier, and Manny Subramanian

Citation: Medical Physics 39, 1980 (2012); doi: 10.1118/1.3693048 View online: http://dx.doi.org/10.1118/1.3693048 View Table of Contents: http://scitation.aip.org/content/aapm/journal/medphys/39/4?ver=pdfcov Published by the American Association of Physicists in Medicine Articles you may be interested in Practical considerations for maximizing heat production in a novel thermobrachytherapy seed prototype Med. Phys. 41, 023301 (2014); 10.1118/1.4860661 TUDBRB05: ThreeDimentional Dosimetric and Thermal Properties of a Newly Developed Ferromagnetic CoreThermobrachytherapy Seed for Treatment of Solid Tumors Med. Phys. 37, 3391 (2010); 10.1118/1.3469254 Dosimetric characteristics of the Leipzig surface applicators used in the high dose rate brachy radiotherapy Med. Phys. 31, 3372 (2004); 10.1118/1.1812609 Dosimetric characteristics of a linear array of or -emitting seeds in intravascular irradiation: Monte Carlo studiesfor the AAPM TG-43/60 formalism Med. Phys. 30, 403 (2003); 10.1118/1.1538229 Dosimetric characteristics of the Pharma Seed™ model BT-125-I source Med. Phys. 27, 2174 (2000); 10.1118/1.1289897

Dosimetric and thermal properties of a newly developedthermobrachytherapy seed with ferromagnetic corefor treatment of solid tumors

Bhoj Gautam, E. Ishmael Parsai,a) Diana Shvydka, and John FeldmeierUniversity of Toledo Medical Center, Toledo, Ohio 43614

Manny SubramanianBest Medical International, Inc., Springfield, Virginia 22153

(Received 18 July 2011; revised 14 February 2012; accepted for publication 16 February 2012;

published 20 March 2012)

Purpose: Studies of the curative effects of hyperthermia and radiation therapy on treatment of can-

cer show a strong evidence of a synergistic enhancement when both radiation and hyperthermia

modalities are applied simultaneously. Varieties of tissue heating approaches developed up to date

still fail to overcome such essential limitations as an inadequate temperature control, temperature

nonuniformity, and prolonged time delay between hyperthermia and radiation treatments. The

authors propose a new self-regulating thermobrachytherapy seed, which serves as a source of both

radiation and heat for concurrent administration of brachytherapy and hyperthermia.

Methods: The proposed seed is based on the BEST Medical, Inc., Seed Model 2301-I125, where

tungsten marker core and the air gap are replaced with a ferromagnetic material. The ferromagnetic

core produces heat when subjected to alternating electromagnetic (EM) field and effectively shuts

off after reaching the Curie temperature (TC) of the ferromagnetic material thus realizing the tem-

perature self-regulation. The authors present a Monte Carlo study of the dose rate constant and

other TG-43 factors for the proposed seed. For the thermal characteristics, the authors studied a

model consisting of 16 seeds placed in the central region of a cylindrical water phantom using a

finite-element partial differential equation solver package “COMSOL Multiphysics.”

Results: The modification of the internal structure of the seed slightly changes dose rate and other

TG-43 factors characterizing radiation distribution. The thermal modeling results show that the

temperature of the thermoseed surface rises rapidly and stays constant around TC of the ferromag-

netic material. The amount of heat produced by the ferromagnetic core is sufficient to raise the tem-

perature of the surrounding phantom to the therapeutic range. The phantom volume reaching the

therapeutic temperature range increases with increase in frequency or magnetic field strength.

Conclusions: An isothermal distribution matching with the radiation isodose distribution can be

achieved within a target volume by tuning frequency and intensity of the alternating magnetic

field. The proposed combination seed model has a potential for implementation of con-

current brachytherapy and hyperthermia. VC 2012 American Association of Physicists in Medicine.

[http://dx.doi.org/10.1118/1.3693048]

Key words: hyperthermia, brachytherapy, thermobrachytherapy, ferromagnetic induction heating,

self-regulating implants

I. INTRODUCTION

Cancer treatment through hyperthermia is achieved when the

temperature of tumor tissue is raised to 42–45 �C. In an ideal

hyperthermia, all cancerous tissue should reach a temperature

in the interval of 42–45 �C while the surrounding normal

tissue should remain at normal temperature.1 The biologic

mechanism of cell killing by heat is fairly complex, involving

denaturation of proteins, damage to cell membranes, nuclei,

and other cytoplasm organelles. A variety of methods have

been developed to induce temperature rises either locally in

selected regions of specific organs or over the whole body.2–6

The currently available modalities of hyperthermia are often

limited by deficiencies in tumor targeting ability and the

resultant inadequate tissue temperature distribution for deep

seated tissues.7–9 One of the common methods for heating

small tissue volumes was suggested first by Burton et al. in

1971 using self-regulating implants.10 The implant consists of

ferromagnetic material whose Curie temperature is slightly

above the therapeutic temperature range and produce heat via

inductive heating process if an appropriate alternating mag-

netic field (having a high field strength and frequency) is

employed.11–14 This type of implant offers relative ease of the

heat delivery and adjustment in the thermal dose distribution,

in particular, if heat self-regulation is employed via use of

the materials with a proper Curie temperature.15 Inductively

heated, thermally regulating ferromagnetic implants have

certain conceptual advantages. No leads need be attached to

the thermal sources in contrast to other interstitial techniques;

the only exception is electrical implants heated with a

1980 Med. Phys. 39 (4), April 2012 0094-2405/2012/39(4)/1980/11/$30.00 VC 2012 Am. Assoc. Phys. Med. 1980

radiofrequency electric field, but these implants are not ther-

mally regulating.16

Studies have shown that the hyperthermia alone is most

likely useful for palliative treatments in situations of local

recurrence after irradiation and it does not result in signi-

ficant therapeutic outcome on the human cancer

treatment.17–19 However, it has been demonstrated to be one

of the most effective radiation sensitizers.19,20 It can be uti-

lized as an adjunctive therapy with various established can-

cer treatments such as radiotherapy and chemotherapy. It

offers significant improvement in both tumor control and

survival rate if administered after radiation therapy without

considerable increase in side effects.19,21–26 For the radiation

sensitization to be successful, the time interval between the

administrations of both the modalities has to be rather short,

preferably, within an hour.21–23,27

One of the most commonly utilized treatments for early

stage prostate cancer is interstitial implant radiation therapy

(brachytherapy), alone, or in combination with other modal-

ities including hormonal therapy and/or initial external beam

radiation therapy. Although a highly effective modality,

brachytherapy alone is not sufficient for all patients needing

radiation therapy for their cancer treatment. Extensive pre-

clinical data demonstrate that adjuvant administration of

hyperthermia offers one of the most efficient enhancements

of local and regional cancer control, acting both as a radia-

tion sensitizer and a complimentary treatment.22,28–30 The

efficacy of the radiation therapy combined with interstitial

hyperthermia guided us to design a source capable of both

radiation and heat delivery for treatment of solid tumors

including prostate cancer.31,32 This combination of a mag-

netic field and a specifically engineered alloy seed will pre-

clude the need for invasive thermometry. We propose the

development and clinical implementation of a new Thermo-

brachytherapy seed that combines a sealed radioactive

source with a ferromagnetic core serving as a source for self-

regulating hyperthermia when placed in an alternating elec-

tromagnetic field. This seed has the potential to address

some of the shortcomings of other hyperthermia methods,

such as, achieving better temperature uniformity through a

more appropriate placement of the seeds, avoiding complex

invasive thermometry, and feedback loops.9 On the other

hand, with recent advancements in image guided rectal ultra-

sound prostate seed implantation, achieving optimal seed

placement for radiation delivery has become a routine. In

our experience, the postimplant dosimetry using CT images

shows very good agreement with the preimplant treatment

plan objectives. In current study, we present both the dosi-

metric and thermal characterization of the proposed seed via

Monte Carlo simulations and finite-element modeling with

COMSOL Multiphysics partial differential equation solver.

II. MATERIALS AND METHODS

II.A. Seed design

The proposed thermobrachytherapy seed is based on one

of the standard iodine seed implants, BEST seed model 2301125I, where solid core marker made of tungsten is replaced

with self-regulating ferromagnetic alloy material. Figure 1

shows schematics of both the current seed and that of the

BEST seed Model 2301. The proposed combination seed

retains the outer titanium capsule (and its dimension; i.e.,

physical length¼ 5 mm, outer diameter¼ 0.8 mm, and the

thickness¼ 0.08 mm) unchanged, allowing relative ease of

the prototype implementation from the manufacturing stand-

point. The cylindrical ferromagnetic core has diameter of

0.44 mm with the physical length of 4.64 mm. The ferromag-

netic core is coated with a 0.08 mm thick layer of an organic

carbon layer impregnated with 125I similar to the standard

seed design. We have eliminated the air gap (see Fig. 1)

between the titanium shell and the radioactive source. The

volume of the ferromagnetic material in the current seed is

greater than the volume of the tungsten marker in the BEST

seed 2301. Such modification in the internal structure is nec-

essary to accommodate proper heat conduction and maximize

the heating power of the seed. In this study, the ends of the

ferromagnetic core marker are considered to be rounded.

II.B. Monte Carlo simulation method

Monte Carlo simulations were performed using version 5

of the Monte Carlo N-Particle code (MCNP5) in Windows

based personal computer. For the photon, the MCNP5 code

accounts for incoherent and coherent scattering, the possibil-

ity of fluorescent emission after photoelectric absorption,

absorption in pair production with local emission of annihi-

lation radiation and bremsstrahlung. All simulations were

operated in the photon and electron transport mode _Mode:

p,e in the MCNP5 code so that both primary photons and

resulting secondary electrons were properly transported. The

energy cut off was set to be 5 keV for both photons and elec-

trons. The photon interaction cross-section data used in this

study were the P04 library distributed by the Radiation

Shielding Information Computing Center.33

The energy spectrum for the 125I source was taken from the

AAPM TG-43U report.34 For MCNP simulations, a seed was

FIG. 1. Sketch of BEST 125I, Model 2301 brachytherapy seed (left); the proposed thermobrachytherapy seed (right).

1981 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1981

Medical Physics, Vol. 39, No. 4, April 2012

positioned at the center of a 30 cm diameter spherical water

phantom. The long axis of the source has been chosen as the

z-axis in Cartesian coordinates (which coincides with the polar

axis in polar coordinates) and the y-axis along the transverse

bisector. At low photon energies, absorbed dose to water can

be approximated by collision kerma.35 For the determination

of dosimetric parameters, absorbed dose to water was scored

using an MCNP F6:p tally feature at radii ranging from 0.3 to

10.0 cm along the transverse axis and at angles ranging from

0� to 180� in 5� bins. The MCNP5 F6 tally calculates the energy

absorbed per gram of material comprising each tally volume.

The number of photon histories was about 1� 106 to

1� 1010. The dose calculation formalism proposed by AAPM

Task Group 43 has been followed to calculate the radiation

characteristics air kerma strength, dose rate constant, geome-

try function, radial dose function, and anisotropy function.34

II.C. Air kerma strength (Sk)

The air kerma strength (Sk) was estimated from air kerma

rate at distance “d” [ _KdðdÞ] along the transverse axis and

correcting for the inverse square of the distance to obtain the

value at 1 cm. The scoring region at 5 cm distance in a

sphere of 5 m diameter filled with air was chosen to closely

simulate the setup used to obtain NIST measured value.36,37

For the simulations in air, the titanium characteristic x-ray

production was suppressed within the code using the energy

cut off at 5 keV.35 The air kerma rate was calculated using

the following relation38

_Kdðd; hÞ ¼ 2:134� 103 � Ic � KMC � c Gy

mCi :h; (1)

where KMC is the output from the MCNP5 and Ic is the average

number of photons per disintegration associated with the

source radioactivity. The air kerma strength is then calcu-

lated using the formula

Sk ¼ _KdðdÞ � d2: (2)

II.D. Dose rate constant (K)

Dose rate constant is the ratio of a dose rate at a reference

point [D�ðr ¼ 1 cm; h ¼ 90oÞ] and air kerma strength Sk

K ¼ D:ðr0; h0Þ

Sk

: (3)

II.E. Geometrical factor G(r, h)

The geometrical factor for the current seed model was

calculated using TG-43 formalism for source length L¼ 0.5

cm. In the line source approximation, the geometrical factor

of infiltrated source, GL (r, h) is evaluated as

GL ¼Db

L r sinhif h 6¼ 0�

GL ¼�

r2 � L2

4

�if h ¼ 0�;

(4)

where, Db is the angle (in radian) subtended by the active

length, L, with respect to the dose calculation point P (r, h)

II.F. Radial dose function g(r)

The radial dose functions were calculated using equation

gðrÞ ¼ D:ðr; 90�Þ Gð1cm; 90�Þ

D:ð1cm; 90�Þ Gðr; 90�Þ

; (5)

where D:ðr; 90

�Þ is the dose rate at a distance of r cm and at

an angle of 90�. The dose rate is obtained from the Monte

Carlo output DKMCwater (collision kerma for water) using

Eq. (1). The DKMCwater value is calculated in a spherical water

phantom of 30 cm diameter and for 0.3< r< 10 cm. The

scoring regions for this calculation are spheres of radius

0.02 cm.

II.G. Anisotropy function F(r,h)

Two dimensional anisotropy function, F(r,h) is defined as

Fðr; hÞ ¼ D:ðr; hÞ GLðr; 90�Þ

D:ðr; 90�Þ GLðr; hÞ

: (6)

One dimensional anisotropy function uan(r) at a radial dis-

tance r is calculated as a ratio of solid angle weighted dose

rate, averaged over entire 4p steradian angle to the dose rate

at the same distance r on the transverse plane

Uan ¼Ð p

0D:ðr; hÞ sin ðhÞdh

2 D:ðr; hÞ

: (7)

The angular distribution of collision kerma in water, DKMCwater

(r, h) was calculated for 37 polar angles, h, at distances r¼ 0.5,

0.75, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, and 10.0 cm

from a source position at the center of a 30-cm diameter liquid

water sphere from 0 to 180� in the interval of 5�.

II.H. Seed thermal properties

From the physics perspective, the magnetically mediated

heat induction process can be divided in two parts: induction

of eddy and hysteretic currents in the ferromagnetic core

under alternating electromagnetic field and transfer of the

induced heat from the core to the surrounding medium.

A system of two equations, the Ampere’s law for vector

potential ~A and the conduction heat equation, were the gov-

erning equations for the thermal distribution calculation. The

equations are expressed as

ixr� x2e� �

~Aþr� l�1r� ~A� �

¼~Je; (8)

qCP

@T

@t�r � krT ¼ Q T; ~A

� �: (9)

Here, time average of the inductive heating over one period

Q ¼ 1=2r ~E�� ��2, ~Je—external current density, x—frequency,

r—electric conductivity, e and l—electric permittivity and

magnetic permeability, respectively, q—density, T—temper-

ature, CP—specific heat capacity of the medium, and k—its

thermal conductivity. As the first approximation, we

1982 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1982

Medical Physics, Vol. 39, No. 4, April 2012

consider water rather than tissue as a medium and ignore the

blood flow contribution to the heat conduction Eq. (9).

In order to evaluate thermal distribution of the heat induced

in the ferromagnetic core of the proposed seed, we employed

a finite-element partial differential equation solver package

COMSOL Multiphysics (COMSOL Inc., Burlington, MA).

The model layout for the evaluation of thermal properties

and the temperature distribution is shown in Fig. 2, where 16

seeds in the form of a 4� 4 array were located in the central

region of a cylindrically shaped water phantom (diameter 12

cm) surrounded by air. Relatively small model size resulted in

rapid simulation times thus allowing calculations for a set of

different parameter combinations to be conducted. The model

still captures the essential trends and heat patterns achievable

in a larger phantom with more seeds. We employed five

induction coils (cross sectional diameter 0.4 cm) wrapped

around the phantom as shown in Fig. 2. The seeds were placed

parallel to the magnetic field vector and were spaced (distance

between two adjacent seeds) at 1 cm. Temperature dependent

magnetic permeability for ferromagnetic Ni (70.4%)—Cu

(29.6%) alloy was used and the system was solved for the fre-

quency of 75, 100, 125, and 150 kHz and magnetic field at the

middle of the phantom (H0) of 16, 22, 27, and 33 kA/m. The

following boundary conditions were set to solve the model

problem. Initial reference temperature of the water phantom

was set to the normal body tissue temperature 37 �C and the

temperature of the surrounding air was set to be 22 �C. All the

boundaries of the air medium outside the phantom were set to

be at thermal insulation and the water air interface was set to

flow heat continuously. The thermal insulation in the real

patient treatment can be achieved using the thermal insulating

blankets wrapped around the patient during the hyperthermia

treatments.

III. RESULTS AND DISCUSSION

III.A. Monte Carlo calculation

In all simulations, the center of the seed was placed in the

middle of a 30 cm diameter water phantom. The simulation

results were converted to dose rates. The dose rate at a point

P(r, h) at the radial distance r, and the polar angle h, from a

cylindrically symmetric line source centered at the origin of

the water phantom, was used to calculate the dose rate con-

stant, the radial dose function, and the anisotropy function.

For verification of our MC model, we calculated dosimet-

ric properties of both standard 2301 seed model and our new

thermobrachytherapy seed. The direct comparison with data

previously published on the standard BEST 2301 (Ref. 36) is

made for every calculated TG-43 parameter.

III.B. Air kerma strength (Sk) and dose rate constant (K)

The Monte Carlo output for the air kerma rate was cal-

culated to be KMC(d, 90�)¼ 9.438� 10�6 MeVg�1 photon�1

or, converted to conventional units, KMC(d, 90�)¼ 2.973

� 10�2 cGy mCi�1 h�1. This resulted in the value of the air

kerma strength Sk¼ 0.742 U mCi�1.

The relative error associated with the output of Monte

Carlo simulation for the air kerma strength (rrelair kerma) is

equal to 0.013. The absolute uncertainty associated with the

air kerma strength is estimated using rabsSK¼rrel

air kerma. Sk, and

is equal to 0.009 U mCi�1. Hence, the calculated air kerma

strength is written as Sk¼ 0.742 6 0.009 U mCi�1.

The Monte Carlo output for the dose rate at 1 cm along the

transverse direction is computed as 2.192� 10�4 MeV/g. This

gives the dose rate constant value K¼ 0.930 cGy h�1 U�1.

The relative uncertainty associated with the dose rate con-

stant is given by

rrelK ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðrrel

MCðr0; h0ÞÞ2 þ ðrrelair kermaÞ

2q

;

where rrelMCðr0; h0Þ is the relative error from the Monte Carlo

simulation at the position r¼ 1 cm and h¼ 90� and it is equal

to 0.015 and rrelair kerma¼ 0.013. Then, rrel

K ¼ 0.020, and the

absolute uncertainty which is given by rabsK ¼K rrel

K , has a

value of rabsK ¼ 0.018. The dose rate constant for the current

seed model can be written as K¼ 0.930 6 0.018 cGy h�1 U�1.

The dose rate constant for the new seed is about 8% less

than the dose rate constant of the BestVR

Model 2301 125I seed,

(1.01 cGy h�1 U�1), Monte Carlo computations calculated by

Sowards et al.36 The difference of the dose rate constant for

the new seed from that of the BestVR

Model 2301 125I seed is

most likely due to the removal of the air gap and redistribution

of the I-125 source inside the seed. Even though the thickness

of the source is kept the same as in the BestVR

Model 2301 125I,

the removal of the air gap and redistribution of the I-125

source and change in the effective length of the source results

in different air kerma strength and the dose distribution around

the seed.

III.C. Radial dose function g(r)

The radial dose functions, g(r), derived from Monte Carlo

simulations are presented in the Fig. 3. Figure 3 also shows

the comparison of the radial dose functions of current seed

and the BestVR

Model 2301 125I seed. The data indicate a

good agreement (within 1% difference) between the two val-

ues for most of the radial distances. Our calculated radialFIG. 2. A model layout for the thermal properties and temperature distribu-

tion evaluation with 16 seeds in the water phantom.

1983 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1983

Medical Physics, Vol. 39, No. 4, April 2012

dose data for the new source matches favorably with pub-

lished g(r) data for BestVR

Model 2301 125I seed except for

the small radial distance (r< 1cm). One can see (see inset of

Fig. 3) the deviation of g(r) values for the new seed from

that of the BestVR

Model 2301 125I. In the new seed, the radial

function increases with increase of the radial distance up to

0.75 cm. It has a highest value at the distance of 0.75 cm and

then, it starts decreasing. On the other hand, the radial dose

function for BestVR

Model 2301 125I seed stays more or less

constant for the radial distance up to 0.75 cm and then

decreases.

The relative uncertainty associated with the radial dose

function is estimated by

rrelg ðrÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðrrel

MCðr; h0ÞÞ2þðrrel

MCðr0; h0ÞÞ2q

:

The relative uncertainty rrelg ðrÞ is found to be less than 1%

for r � 5.5 cm and less than 1.7% for r¼ 5.5–10 cm. The

absolute uncertainty associated with the radial dose function

is then projected as rabsg ðrÞ¼rrel

g ðrÞ�gðrÞ.The calculated radial dose function is fitted to a fifth order

polynomial function as follows:

gðrÞ ¼ a0þa1rþ a2r2þa3r3þa4r4þa5r5; (10)

where, a0¼ 0.9584, a1¼ 0.1635, a2¼�0.1555, a3¼ 0.0319,

a4¼�0.0028, and a5¼�9.231� 10�5, respectively.

III.D. Anisotropy functions F(r, h)

2D anisotropy functions F(r, h) for the new seed model

are given in a tabular form in Table I as functions of radius r

and polar angle h. From the calculated dose distributions

around the seed in water, 1D anisotropy functions, UanðrÞ,and anisotropy constant, �Uan, were also determined. The

F(r, h) value decreases with increase of the angle (h) and

reaches at the minimum value around at an angle in between

10� and 15� and again starts increasing to become unity at

the transverse direction (h¼ 90�). The minimum value of

F(r, h) increases with increase of radial distance. The Monte

Carlo calculated anisotropy function F(r, h) for the new seed

is also compared with the corresponding published values

for BestVR

Model 2301 125I seed. Figures 4(a) and 4(b) show

the comparisons of the F(r, h) values for the current seed

with that of BestVR

Model 2301 125I seed. Anisotropy func-

tion for the new seed slightly deviates from anisotropy func-

tions of BestVR

Model 2301 125I seed.

For the small radial distances (small r values), the large

deviation was observed for the intermediate angles (20 � h� 75). For the large radial distances, the deviation persists

for almost all angles but the relative deviation decreases as

compared to the corresponding values for small radial dis-

tances. The variation between anisotropy functions of cur-

rent seed and BestVR

Model 2301 125I seed at different radii

was within 610%. The relative uncertainty associated

with the anisotropy function F(r, h) is estimated by

rrelF ðrÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðrrel

MCðr; hÞÞ2þðrrel

MCðr; h0ÞÞ2

qand the average rela-

tive uncertainty was estimated to be less than 2% for all of

the calculated radial distances and angles.

The absolute uncertainty associated with the anisotropy

function F(r, h) is then projected as rabsF ðrÞ¼rrel

F ðrÞ�Fðr; hÞ.Table I also contains the UanðrÞ values for the radial dis-

tance 1–8 cm. The maximum value (0.940) of UanðrÞ was

estimated for radial distance of 2 cm and the minimum value

(0.845) was estimated for distance 8 cm. The anisotropy con-

stant, �Uan, for the current seed model is estimated to be

0.903. The �Uan value for the current seed is about 8% less

than that of BestVR

Model 2301 125I seed (0.98).36

FIG. 3. Radial dose function g(r) for the BEST 125I, Model 2301 (our calcu-

lation and the published data) and the ferromagnetic core seed [inset shows

the deviation of the g(r) values from the published data].

TABLE I. 2D anisotropy function [F(r, h)] and 1D anisotropy function

[UanðrÞ] values for the ferromagnetic core seed at different angle and radial

distance.

Radial distance “r” (cm)

Angle (h) 1 2 3 4 5 6 7 8

0 0.841 0.923 0.935 0.923 0.905 0.876 0.867 0.840

5 0.671 0.658 0.675 0.680 0.692 0.701 0.709 0.716

10 0.626 0.648 0.672 0.688 0.697 0.707 0.710 0.711

15 0.680 0.695 0.723 0.733 0.740 0.740 0.742 0.752

20 0.738 0.751 0.765 0.770 0.788 0.778 0.780 0.780

25 0.789 0.787 0.795 0.803 0.813 0.805 0.817 0.807

30 0.818 0.838 0.833 0.843 0.848 0.848 0.848 0.847

35 0.856 0.863 0.864 0.866 0.867 0.865 0.873 0.873

40 0.891 0.886 0.891 0.885 0.897 0.891 0.895 0.898

45 0.914 0.903 0.913 0.921 0.914 0.909 0.915 0.906

50 0.933 0.926 0.933 0.934 0.928 0.923 0.932 0.929

55 0.949 0.949 0.948 0.953 0.948 0.935 0.949 0.942

60 0.965 0.963 0.962 0.972 0.951 0.953 0.956 0.958

65 0.975 0.971 0.977 0.980 0.967 0.964 0.974 0.969

70 0.984 0.978 0.983 0.986 0.969 0.975 0.987 0.970

75 0.993 0.986 0.991 0.991 0.983 0.984 0.992 0.988

80 0.998 0.992 0.996 0.995 0.989 0.993 1.00 0.986

85 0.999 0.995 0.997 0.997 0.994 0.999 0.999 0.992

UanðrÞ 0.922 0.940 0.939 0.921 0.902 0.881 0.872 0.845

1984 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1984

Medical Physics, Vol. 39, No. 4, April 2012

III.E. Thermal properties and temperature distribution

COMSOL Multiphysics package (heat transfer model on theAC/DC module) was used to model result of the thermalproperties and the 3D temperature distribution produced by aset of 16 seeds with ferromagnetic core. We employed thetransient analysis type for heat transfer and time harmonicanalysis for the induction current in time dependent segre-gated solver. The simulations are performed for up to time

30 min with the relative tolerance of 0.01 and absolute toler-

ance of 0.001. The constants employed in the modeling are

presented in Table II along with the references from which

the values are taken from.

A cross sectional view of the temperature distribution along

the seed bisector plane for magnetic field H0¼ 22 kA/m and

frequency 100 kHz is shown in Fig. 5. The data show that

the highest temperature is observed near the seed surface,

FIG. 4 (a) Anisotropy function F (h, r) for the BEST 125I, Model 2301 (our calculation and the published data) and the ferromagnetic core seed at a radial

distance 1–4 cm. (b) Anisotropy function F (h, r) for the BEST 125I, Model 2301 (our calculation and the published data) and the ferromagnetic core seed at a

radial distance 5–8 cm.

1985 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1985

Medical Physics, Vol. 39, No. 4, April 2012

decreasing as we move away from the seed. Furthermore,

higher temperature region is located around the middle seed

as compared to the region around the peripheral seeds. Space

around the corner seed has the lowest temperature coverage.

To alter the temperature distribution within the targeted

volume and attain a better coverage we can change variables

such as intensity (H0) and the frequency (f) of magnetic field.

Figure 6 shows the comparison of temperature distribution

for fixed magnetic field of 22 kA/m and varying frequency.

Figure 6(a) shows the cross sectional isothermal surfaces for

the frequency of 75 kHz. Clearly, only a very small fraction

of the volume between the seeds heats above the therapeutic

temperature range (T�42 �C). For this set of variables, most

of the volume is under heated, exhibiting islands of “cold”

spots. The data for magnetic field H0¼ 22 kA/m and fre-

quency 100 [Fig. 6(b)] show most of the volume around the

seed distribution heated up to the therapeutic temperature

range (T> 42). From Fig. 6(b), one can also see that only

the 40 �C isothermal surfaces cover the entire seed configu-

ration where as the 42 �C isothermal surface missed some

volume around the corner seed. For the frequency of

125 kHz [see Fig. 6(c)], the larger volume is covered by the

therapeutic temperature range: the 42 �C isothermal surface

covers the whole seeds volume around. The better tempera-

ture coverage over larger volume was obtained for this con-

dition but there are some hot spots in areas near the seed

surfaces. For the frequency of 150 kHz [see Fig. 6(d)], even

a higher temperature coverage over larger volume is

achieved but there is a large fraction of the volume near seed

surfaces being overheated. As in the case of the treatment

planning for radiation dose distribution, achieving the best

isothermal distribution requires optimization of placement of

the seeds, adjustment of intensity (H0), and the frequency (f)

of the magnetic field.

For a hyperthermia treatment to be practical, the initial

temperature rise after the EM field is turned on has to be

reasonably short. Figure 7 shows time dependent tempera-

ture variation for the seed surface and the middle point

of the phantom with time. The thermoseed surface tempera-

ture rises rapidly and stays constant around the Curie tem-

perature (TC) of the ferromagnetic material used. The

temperature control mechanism at the temperature around

the TC of the ferromagnetic core is explained as follows. As

soon as the magnetic field is turned on, eddy current is pro-

duced on the surface of the ferromagnetic core due to the

electromagnetic induction. The resistive heating of the

induced current produces heat rapidly. This causes the rapid

rise on the temperature of the ferromagnetic core. As the

temperature of the core rises gradually and reaches to the TC

TABLE II. List of the constants used for the modeling for the thermal distribution.

S.N. Symbol Value/unit Name of the parameter References

1 Cp1 4.178 [J/(g K)] Heat capacity of water 38

2 k1 0.599 [W/(m K)] Thermal conductivity of water a

3 q2 8954 [kg/m3] Density of copper a

4 Cp2 381 [J/(kg K)] Heat capacity of copper a

5 k2 386 [W/(m K)] Thermal conductivity of copper a

6 Cp3 1.01� 103 [J/(kg K)] Heat capacity of air a

7 q3 1.205 [kg/m3] Density of air a

8 k3 0.0259 [W/(m K)] Thermal conductivity of air a

9 k_shell 15.12 [W/(m K)] Th. conductivity of Ti a

10 rho_shell 4540 [kg/m3] Density of Ti shell a

11 Cp_shell 531 [J/(kg K)] Sp. heat capacity of Ti a

12 k_source 140 [W/(m K)] Th. conductivity of C 38

13 rho_source 2667 [kg/m3] Density of carbon and I-125 b

14 Cp_source 709 [J/(kg K)] Sp. heat C and I-125 b

15 k_core 26.0 [W/(m K)] Th. conductivity of Ni-Cu b

16 rho_core 8900 [kg/m3] Density of Ni-Cu b

17 Cp_core 440 [J/(kg K)] Specific heat of Ni-Cu b

18 r 2.57� 106 X�1 m�1 Electric conductivity of Ni-Cu 38

19 l Plot Magnetic permeability of Ni-Cu 12

aC. P. Kothandaraman and S. Subramanyan, Heat and mass transfer data book, 3rd ed. (John Wiley and Sons, New York), ISBN 0-470-99078-3.b

COMSOL Multiphysics coefficient library.

FIG. 5. Cross sectional temperature distribution profiles (in degree Celsius)

of the seed bisector cross-sectional plane for magnetic field intensity (H0)

22 kA/m and frequency (f) 100 kHz.

1986 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1986

Medical Physics, Vol. 39, No. 4, April 2012

of the Ni-Cu alloy the relative magnetic permeability

decreases gradually and reaches unity. The decrease of the

relative permeability decreases the production of the thermal

power in the ferromagnetic core. As a result, the temperature

starts decreasing and the magnetic permeability starts

increasing. This starts increasing the thermal power produc-

tion in the ferromagnetic core.39 The temperature of the

middle of the phantom rises slower and reaches the therapeu-

tic range within a few minutes. The thermoseed acts as self-

controlled heat source for the surrounding volume helping to

exclude the invasive thermometry and simplifies the treat-

ment procedure. The TC of the alloy can be altered by chang-

ing the composition of the constituent elements of the alloy.

This property allows one to set the TC according to desired

level to get the more uniform temperature distribution

throughout the volume of interest.

To study the fraction of the volume covered by certain

isothermal surface, we defined a physical quantity called

cumulative temperature–volume histogram (CTVH). An

ideal volume of interest called target is also defined as the

region which encloses the seed configuration under study.

The rectangular target has the volume (VT) of 7.2 cm3. The

CTVHs data (normalized with target volume) are presented

in Fig. 8 for fixed frequency with variable magnetic field

[Fig. 8(a)] and fixed magnetic field with variable frequency

[Fig. 8(b)]. The data show that the volume of the therapeutic

temperature range increases with increase of frequency (f) or

intensity of the magnetic field (H0).

The temperature coverage over the target volume can be

optimized by changing the variables H0 and f of the mag-

netic field. Once the target volume is defined and the pre-

scribed radiation dose is planned using the treatment

planning system for the radiation, the temperature dose also

can be prescribed over the target volume and planned using

FIG. 6. Cross sectional (seed bisector) isothermal profiles (in degree Celsius) for magnetic field strength of 22 kA/m and frequency: (a) 75 kHz, (b) 100 kHz,

(c) 125 kHz, and (d) 150 kHz.

FIG. 7. Variation of temperature at the seed surface and middle point of the

phantom with time (H0¼ 22 kA/m and f¼ 125 kHz).

1987 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1987

Medical Physics, Vol. 39, No. 4, April 2012

the thermal dose planning system, or employing software

packages such as COMSOL to determine the best field parame-

ters to heat the seeds. Figure 9 presents the comparison of

the radiation isodose and the isothermal distributions

(f¼ 125 kHz and H0¼ 22 kA/m) for the 4� 4 square arrays

of seeds in a hypothetical target. The radiation dose is pre-

scribed as 160 cGy at the periphery of the target volume.

The isothermal distribution for magnetic field values f¼ 125

kHz and H0¼ 22 kA/m shows the similar coverage as the

radiation isodose distribution. One can also see that the

42 �C isothermal distribution almost perfectly overlaps with

the 100% radiation isodose distribution. This indicates that

one can easily get the desired isothermal distribution over

the certain target volume by changing the magnetic field var-

iables (frequency and the intensity) to match with the ideal

radiation dose distribution.

III.F. Possible treatment schedule

Even though the thermal enhancement ratio (TER) for the

combined continuous radiation and hyperthermia in humans

is not reported in literature, study shows40 that in C3H

mouse a significant cure rate for the combined hyperthermia

and low dose rate brachytherapy is achieved as compared to

hyperthermia and brachytherapy delivered independently.

Same study also shows that increasing the amount of

the radiation dose alone does not produce the same outcome

as the combined radiation and hyperthermia treatments.

Niedbala and associates in a 2006 publication demonstrated

that hyperthermia had significant sensitizing effects for both

low dose rate continuous radiation and pulsed dose rate radi-

ation.41 Obviously, the optimal combination of hyperthermia

and continuous radiation resulting from the nuclear decay of

I-125 or another isotope will need to be established by clini-

cal studies. We propose that patients treated with our custom

thermobrachytherapy seed receive one or two 30–60 min

hyperthermia treatments on a weekly basis for the first sev-

eral weeks after implantation of the seeds. This protocol is

selected in part as a reasonably convenient regimen for the

patients and provides heating soon after the implantation

while dose rate is at its highest. On the other hand providing

at least 72 h break between the consecutive hyperthermia

treatments will help avoiding development of thermal toler-

ance noted by some researchers.42,43 The TER resulting

from a few 30–60 min sessions of hyperthermia over months

of low dose rate irradiation is unknown. We can only offer a

very conservative estimate of TER based on the assumption

of clinically achievable TER¼ 2 for concurrent administra-

tion of heat and hyperthermia (TER values as high as 6.14

have been shown in some studies44), and comparison of the

half lives of the protein denaturation (6 h) and reoxigenation,

thought to be the main sensitization mechanism of heat20

(24 h) with the known half life of the Iodine-125 radioactive

isotope (59 days). For the case of 1 h long hyperthermia

once a week, we arrive at the value of TER¼ 2�(14/59)þ 1� (45/59)¼ 1.24, considering the protein denatu-

ration and the reoxigenation produce simply an additive sen-

sitization through a total of ten hyperthermia treatments.

For 20 of 1-h heat treatments delivered twice a week

TER¼ 1.47. While even 20% effect would warrant pursuing

this approach, this estimation is clearly not taking into

account the synergistic effect of the hyperthermia and radia-

tion (affecting cells under different pH environment, at the

different phases of the cell cycle), or any other factors, often

interrelated. Numerous studies demonstrated that the effect

is not achievable by a simple increase of the radiation dose,

especially in case of notoriously radiation-resistant tumors.

Experiments and clinical trials will need to be performed to

determine the TER for such treatment scenarios.

We would like to point out an additional benefit of the

proposed approach. The seeds are going to retain their ferro-

magnetic properties long after the activity of iodine become

negligible. Therefore, in case of the treatment failure, the

implanted seeds can be used for sensitization of a chemo-

therapy drug, typically used for treatment of recurrent

cancer.

IV. CONCLUSIONS

The proposed seed will require only small changes in the

internal structure of a standard commercial brachytherapy

seed model to gain thermal capability. The modification of

the internal structure of the seed slightly changes dose rate

FIG. 8. Normalized CTVHs: (a) for fixed magnetic field and varying fre-

quency and (b) fixed frequency and varying magnetic field.

FIG. 9. Comparison of cross sectional temperature distribution (f¼ 125 kHz

and H0¼ 22 kA/m) profiles and radiation dose distribution profiles.

1988 Gautam et al.: Thermal and radiation properties a new thermobrachytherapy seed 1988

Medical Physics, Vol. 39, No. 4, April 2012

and other TG-43 factors characterizing radiation distribution.

The dose rate constant for the new seed is about 8% less than

the dose rate constant of the BestVR

Model 2301 125I seed. The

modeling result of the thermal distribution shows that one can

obtain the isothermal distribution within the target volume to

match with the prescribed radiation isodose distribution for

the seed configuration by changing frequency and intensity of

the alternating applied magnetic field. The amount of heat

produced by the seeds for a typical distribution case com-

pared with radiation distribution indicated that sufficient heat

can be generated for achieving the therapeutic temperature

range if appropriate field parameters are used. The proposed

combination seed model has a potential for implementation

of concurrent brachytherapy and hyperthermia.

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