Novel Applicators for Local Microwave Hyperthermia Based on Zeroth-Order Mode Resonator Metamaterial

It is demonstrated that a theory of zero-order mode resonator (ZOR) metamaterial (MTM) structure can be used for the development of a novel class of applicators for microwave thermotherapy, for example, for hyperthermia in cancer treatment or for physiotherapy. The main idea of creating such an applicator is to generate and radiate a plane electromagnetic (EM) wave into the treated biological tissue, at least in a certain extent. The main aim of this paper is to investigate whether an EM wave generated by ZOR MTM structure and emitted into the biological tissue can produce a homogeneous SAR distribution in the planes parallel to the applicator aperture and achieve a penetration depth approaching the theoretical limit represented by SAR distribution and penetration depth of an ideal EM plane wave. EM field distribution inside a virtual phantom of the treated region generated by the applicator that is based on the proposed ZOR MTM principle is investigated using a well-proven full-wave commercial simulation tool. The proposed applicator type shows both a low unwanted leaked electromagnetic field and a fairly homogeneous electric field in its aperture as well as in the virtual phantom of the treated region.


Introduction
e main aim of this paper is to verify whether it is feasible to apply principles of ZOR MTM radiating structures in the design of e cient applicators for radiofrequency (RF)/ microwave (MW) thermotherapy, especially for hyperthermia cancer treatment and for physiotherapy. For this aim, MTM antennas inspired by those described in [ , ]willbe investigated and adapted with respect to requirements of e ective hyperthermia treatment (i.e., we will study the homogeneity of SAR distribution in the treated region). In order to achieveanoptimalwaveformshapeoftheradiatedEMwave, applicatorshavetobedesignedinacertainway. ebestpossibleresultscanbeobtainedbycomparingvariousshapesof waveforms of EM waves (e.g., plane wave, cylindrical wave, and spherical wave) for local and deep local treatment waveform of plane wave. is can ensure (i) the best possible value of the e ective treatment depth; (ii) the best possible homogeneity of SAR D distribution (i.e., its distribution on the surface and in the whole volumeoftheareatobetreated).
SAR distribution inside the virtual phantom of the treated region, created using the proposed applicator, and the re ection coe cient of the proposed applicator are investigated using the well-proven full-wave commercial simulation tool COMSOL Multiphysics. Based on our previous experience [ -], an excellent agreement between simulation and measurement results can be expected. at is why the conclusions made in this paper are based on the results of numerical simulations only.

MTM Zeroth-Order Mode Resonator
e concept of MTM phenomenon was rst comprehensively introduced by Veselago in [ ]. In the aforementioned publication, he speculated on the existence of materials whose permittivity ( ) and permeability ( ) were simultaneously negative. He named these materials le -handed (LH), as the E, H,a n dk v e c t o r so ft h es t u d i e dE Mw a v ef o r m e dal ehanded triad if the wave propagated through such environment. e rst experimental veri cation of MTM phenomena was performed by a research group at the University of California, San Diego (UCSD), in [ ].
International Journal of Antennas and Propagation (a) : (a) In nitesimal element of MTM (b) and its equivalent circuit consisting of inherent series inductor , shunt capacitor , arti cially inserted series capacitor , and shunt inductor .
An in nitesimally short lossless transmission line (TL) section can be described by a simple equivalent circuit consisting of a series inductor and a shunt capacitor [ ]. e lossless MTM cell implemented in planar technology consists of a TL section with arti cially inserted series capacitors and shunt inductors (with subscript denoting its le -handed properties). e equivalent circuit of t h eM T Mc e l lc a nbet h e nr e p r e s e n t e db yf o u r -l u m pe de l ements (as shown in Figure )[ ].
Several di erent EM radiating structures based on the MTM principle were introduced in the past [ -]. Since the very beginning of the development, however, real implementation possibilities of such antennas, for example, in communication technology, have been very limited because of their poor radiation e ciency. MTM antennas with very good radiation e ciency were rst presented in [ , ].

Design of the Applicator Based on ZOR MTM Structure
In this section, we will study the possibility of creating MTM based applicators for local microwave hyperthermia cancer treatment at a frequency of MHz. e basic part of the proposed applicator will consist of the ZOR. ew o r k i n gi d e ao fZ O Ri sb a s e do nas p e c i a lc a s eo f resonance that can occur when the TL meets the conditions of the MTM phenomenon. e phase constant =0 is at working frequency in this case, which implies in nite guided wavelength = 2 /| | along the MTM structure as well as zero phase shi ( =− =0 )[ ]. It is very important to note that this phenomenon enables creation of a very special kind of resonator whose physical length is completely independent of the classical resonance condition (i.e., required to be a natural number multiple of the half working wavelength in case of either open-circuited or short-circuited TL) [ ].
e typical voltage wave distribution along the resonant length for the negative ( < 0) and zero ( = 0) resonances is shown in Figure . In the case of zeroth-order mode resonance ( = 0), the value of the voltage along the e zeroth-order resonant frequency of the proposed ZOR MTM applicator is equal to the working frequency of apa rti cul a rR F / M Wh y pe rth e rm i as y s t e m .P l ea sen o t eth a t the ideas and principles of MTM applicator design described here are expected to be valid at any usual working frequency of RF/MW hyperthermia systems. e initial idea of the mechanical and EM arrangements of the ZOR MTM applicator proposed here is displayed in Figure . In order to obtain high radiation e ciency and thus the best possible transfer of EM energy to the treated area, we can use the main ideas, experiences, contributions, and conclusions described in [ -]. at means to combine the ZOR MTM structure with relatively long inductive elements along which electric current with equal phase will ow. ese currents will then excite an EM wave propagating into the area to be treated. Optimal choice of positions of these inductive elements then enables us to approximate the preferred waveform (we want to excite International Journal of Antennas and Propagation y x z F : Example of the ZOR MTM applicator consisting of a fourunit cell. thewa veformofaplanewa ve,butthewa veformofeithera cylindrical or a spherical wave can be obtained as well). is will enable us to approximate the possible shape as well as the dimensions of the treated area. For the above mentioned main aim, some results and experiences obtained by applicators described in [ -]canbeused. e design rules of this structure are the same as in [ ]. anks to the excitation of zeroth-order mode vectors of surface current density in all vertical parts of the antenna (including feeding), all these surface currents are in phase; that is, the radiated contributions from all individual vertical parts are in a very good superposition in the applicator aperture (i.e., the Huygens principle phenomenon can be applied todescribetheresultingEM elddistributionintheareato be treated). For the design of the ZOR MTM applicators, the following dimensions of antenna elements were chosen. In this special discussed case, the length of the vertical part of the antenna is equal to 0 /10. e longitudinal dimension of the unit cell can vary (or be adjusted) in a relatively large range [ ]. Depending on the selected size of this dimension, it is necessary to adjust the dimensions of interdigital capacitors. For the presented applicator, the overall length of one unit cell is =70mm, the length of gures of the interdigital capacitor equals capacitor =68mm,andthewidthandthegapofthe interdigital capacitor are = =1mm;pleasenotethatthe same notation has been used as in [ ]. e overall physical dimensions of the applicator prototype are × × mm which represents relative dimensions (with respect t ow a v e l e n g t ho fp l a n eE Mw a v ei nv a c u u m 0 at working frequency) as follows: the relative width of the aperture is equal to 0 /3, the relative height of the aperture is 0 /10, and the relative depth of the applicator is 0 /10. ic kn es s, relative permittivity, and equivalent conductivity of the considered substrate are . mm, . , and . S/m, respectively. Alternatively, the ZOR MTM radiating structure can be inserted into the rectangular waveguide section to ensure that the whole radiated power would be perfectly directed to thebiologicaltissueintheareatobetreated.Anotherpossible and interesting use for real clinical therapy is the case where the ZOR MTM radiating structure would be surrounded by metal plates from the top and the back sides and the lateral sides would be made of a dielectric substrate material to : Top view of the applicator, water bolus, and the tissue to be treated. SAR distribution in the area to be treated is also displayed here. y x z F : SAR distribution calculated on the surface of the area to be treated. e color bar here is the same as in Figure . ensure that we would not excite the dominant rectangular waveguide mode 10 . One of the basic features of the ZOR MTM radiating structure, observed during our investigations, is that it resonates at almost the same frequency irrespective of whether the structure is surrounded by metal from thebackandlateralsides.Onlyifweplacedthemetalplane closer to the top of ZOR, the capacity of interdigital capacitors would change and thus the resonant frequency could be shi ed from the working frequency. is phenomenon can be used for frequency adjusting or impedance matching of this applicator if necessary.

Distribution of SAR Created by ZOR MTM in the Treated Area
To study and verify how these ZOR MTM structures would radiate into the biological tissue in the area to be treated, several numerical simulations of the discussed case were performed. SAR distribution inside a virtual phantom of the treated region generated by the proposed applicator was investigated using COMSOL Multiphysics [ ]. Muscle tissue dielectric parameters were considered as follows: the real part of the complex permittivity is equal to =5 7 and the equivalent electric conductivity is equal to = 0.81 S/m[ ]. In the studied model displayed in Figure , : Top view of the applicator with symmetrical feeding, water bolus, and the tissue. SAR distribution in the area to be treated is also displayed here.
It can be observed that when the EM power penetrates the biological tissue, it has very good SAR homogeneity and that the penetration depth is approaching the theoretical limit [ ].
Figure displays SAR distribution in the plane parallel to the applicator aperture. Homogeneous absorption of EM at the surface of the area to be treated can be observed. Similar distribution of SAR will be observed in all planes parallel to theapplicatoraperture,butthelevelofSARwilldecreasewith increasing depth.

Improvement of SAR Homogeneity by AidofSymmetricFeedingofZORMTM
e ZOR MTM applicator discussed in this paper and the distribution of SAR achieved by the use thereof (displayed in Figures and ) can be considered very suitable for practical treatment of cancer patients. As already mentioned in this paper, it approaches the homogeneity level and the e ective treatment depth of the plane wave. However, a certain level of asymmetry of SAR distribution is evident in Figures and .
is e ect can be explained by asymmetrical feeding of the ZOR MTM applicator displayed in Figures and and also by thefactthatthesurfacecurrentdensityonthefeedingvertical parthasthesamephaseasthesurfacecurrentdensityonthe other vertical parts. e contribution to radiation is not as it could be if the feeding part would be in the same line as the others. In this part, a modi ed mechanical and EM arrangement of the ZOR MTM is proposed, which would help us improve the homogeneity of SAR distribution in the treated area. As can be seen in Figure ,am o d i e dZ O RM T Ma p p l i c a t o rw i t h symmetric feeding is proposed. Furthermore, another vertical radiating part connected to the feeding point via an interdigital capacitor and a section of microstrip TL that was added to ensure the same phase shi as that of the other vertical parts. e working principle of this ZOR MTM structure is the same as in the previous case. anks to the excitation of the zeroth-order mode, the vectors of surface current density on y x z F : SAR distribution in the plane parallel to the symmetrical fed applicator aperture. e color bar here is the same as in Figure . all vertical parts of the antenna including the feeding are in phase. Again, we can say that the phenomenon of the Huygens principle can be applied to describe the resulting EM eld distribution in the area to be treated. erefore, the radiated contributions from all vertical parts constructively interfere in the applicator aperture. e dimensions of the vertical parts of the antenna were chosen to be /10 again. e longitudinal dimension of the unit cell can be varied (be adjusted) in a relatively large range [ ].Basedonthechoice of this dimension, it is necessary to adjust the dimensions of interdigital capacitors.
In Figures and ,itisevidentthatthehomogeneityof SARinfrontof vesymmetricallyfedradiatingpartsismuch better than the one described in the previous case (chapters and ). Figure displays SAR distribution in the plane perpendicular to the applicator aperture, illustrating how deep EM energy penetrates the area to be treated. It can be observed that when the EM wave penetrates the biological tissue, it has very homogeneous SAR distribution and that both the SAR distribution and the depth of penetration of the treated area approach the theoretical limit of a plane EM wave.
Figure displays SAR distribution in the plane parallel to the applicator aperture, illustrating the homogeneity of EM energy absorption at the surface of the area to be treated. Similar distribution of SAR will be observed in all planes parallel to the applicator aperture, but the level of SAR will decrease with increasing depth.

Achieved Waveform and Comparison with Theoretical Limits
In this section, the achieved wave form in the biological tissue is compared to the theoretical limit represented by plane EM wave. SAR distribution in Figure shows very good homogeneity. In Figure , SAR distribution along three line segments (cut lines) which lie in the plane perpendicular to the water bolus/treated area interface is depicted. e plane cuts the inductive posts (vertical parts) in the middle. Cut lines , , and start at the interface, lead into the treated area, and are located between the rst and the second inductive posts, between the fourth and the h inductive posts, and in front of the third inductive post, respectively. SAR distribution is compared to that of plane EM wave propagating through the treated area considered here (muscle tissue). SAR values are given as percentages of the SAR value of the plane EM International Journal of Antennas and Propagation F : SAR distribution corresponding to plane EM wave propagating through the treated area considered here (muscle tissue). SAR distribution along three line segments (cut lines) which lie in the plane perpendicular to the water bolus/treated area interface. e plane cuts the inductive posts in the middle. Cut lines , , and start at the interface, lead into the treated area, and are located between the rst and the second inductive posts, between the fourth and the h inductive posts, and in front of the third inductive post, respectively. e SAR values are given as percentages of the SAR valueoftheplaneEMwaveatthedepthof cm.
wave at the depth of cm. Along all three cut lines, the SAR approximates very well the shape of the exponential form relatedtoplaneEMwave.InFigure , SAR distribution along three line segments (cut lines) which lie in the plane perpendiculartothewaterbolus/treatedareainterfaceisplotted. e plane cuts the inductive posts in the middle. e cut lines are parallel to the interface. Cut lines , , and are located at the interface, at a depth of , , and cm, respectively. SAR values a r egi v e na spe r c e n ta g e sa n da r er e l a t edt oth eh i gh e s tS A R value along cut line . At the depth of cm, SAR distribution is fairly homogeneous. e heat produced by the hotspots at the surface has to be removed using the water bolus, a common strategy used in RF/MW hyperthermia. Similarly, in Figure , SAR distribution along three line segments (cut lines) which lie in the plane perpendicular to the water bolus/ treated area interface is plotted. e plane is parallel and passes through the third inductive post. e cut lines are paralleltotheinterface.Cutlines , ,and arelocatedatthe interface, at a depth of , , and cm, respectively. SAR values are given in percent and are related to the highest SAR value along cut line .
In Figures and , contours of SAR values as percentages in two main planes are plotted, in the plane parallel to the surfaceofthetreatedbiologicaltissueinthedepthof cmin thetissueandintheplaneperpendiculartothisplane,cutting theinductivepostsinthemiddle. , ,and %SARlevels are plotted, related to the highest SAR value in the depth of cm in the tissue. Usually, the % SAR contour is considered  to bound the area where the treatment is e cient. From Figure , it follows that the surface area of a rectangular e ective treatment area (a rectangle inscribed in the % SAR contour) for the proposed applicator is about by cm 2 .

Ongoing Research of ZOR MTM Applicators
Our ongoing research of ZOR MTM applicators focuses on designing several practical clinical applicators and on preparing and performing basic experimental evaluations of these structures in order to verify the promising results presented here, obtained by numerical simulations only. We explore two basic structure types: (i) ZOR MTM structure inserted in the waveguide (thus gaining the advantages of waveguide applicators); (ii) ZOR MTM structure used as a at planar applicator.

Conclusions
In this paper, a novel principle for the design of applicators b a s e do nZ O RM T Ms t r u c t u r e sh a sb e e np r o p o s e d .I th a s been demonstrated here that when penetrating biological tissue EM waves generated by the proposed applicators generate very good SAR homogeneity and achieve penetration depth approaching, to a certain extent, the theoretical limit, that is, closetotha toftheEMplanewa ve. esurfaceofarectangular e ective treatment area (a rectangular inscribed into % SAR contour) is for the proposed applicator about × cm 2 .

Conflict of Interests
e authors declare that there is no con ict of interests regarding the publication of this paper.