Sexuality is one of the most important aspects of human life that relates to sex, one's identification, sexual role, sexual preferences, eroticism, pleasure and intimacy. It fulfils such functions as procreative, hedonistic and relationship-building as well as constitutes an integral part of human's personality. The sexuality of people with intellectual disability is a special case - both from medical, pedagogical, psychological and ethical point of view. Little available research shows that it may become a significant factor that modifies their psychological and sexual functioning. The basic poll involved altogether 133 people with mild intellectual disability. The work was carried out in 11 schools and special institutions of three provinces in Poland: kujawsko - pomorskie, wielkopolskie and dolnośląskie  The respondents qualified to take part in the poll constituted a very uniform group - homogenous as regards their age of 18-25 as well as IQ level that was average for the people with higher degree of intellectual disability (HDID). Their age was of importance as in that life period one can observe the formation of first partner relationships with the clear aim of establishing a family. It is accompanied by a quick development of sexual desire and taking up various forms of sexual activity. People with intellectual disability don't form a homogenous group as regards their psychological and sexual development. In this group, one can observe both different forms of clinical mental handicap which definitely affects the whole process of sexual development. The sexual development is delayed by an average period of 3 years. The people with intellectual disability take up mostly autoerotic behaviour whereas partner relationships wthin that group are more seldom. The phenomenon of sexuality of people with higher degree of intellectual disability is an issue that needs further constant analysis. The research has also made it possible to detect what kind of sexual behaviour people with intellectual disability undertake and the value of sexuality for such people. The article deals also with some important dilemmas connected with sexual education and what factors trigger off incorrect sexual reaction including their lack in the above mentioned group. The sexuality of people with intellectual disability has recently become the topic of professional discussion and public debate. The normalization rule introduced into society made it necessary to understand and accept an intellectually disabled person as a sexual person. Unfortunately there is still a lack of knowledge on people with higher degree of intellectual disability.The presented studies are related to three areas: the sexual development of HDID people, knowledge of HDID people on selected aspects of sexual life and selected forms of sexual activities of HDID people. The studies presented in this article have been co-financed by the Polish Ministry of Science and Higher Education under Grant No. N N106 149434.The studies have been preceded by pilot studiesThe present work concentrates on presenting the knowledge of the people questioned on private body parts, fertilization, pregnancy, childbirth and contraception. Various forms of sexual behavior practiced by people with HDID have also been described as well as the evaluation of the sexual development of the group in question.What is the level of sexual development of the tested people with a higher degree of intellectual disability?private parts of their bodies?insemination?giving birth?pregnancy?contraception?What is the level of knowledge of the tested people with a higher degree of intellectual disability on the following subjects:Whether and with what frequency are masturbation activities taken up?Whether and with what frequency are petting activities conducted?Whether and at what age does their sexual life start?What forms of sexual activities are taken up by people with a higher degree of intellectual disability?The work formulates three basic research problems:In the applied research project, the presented material was based on genuine source input—real comments, but described not as individual examples but as a more or less typical common sexual experiences of a group of people with HDID. The input material for such a definition of the issue was provided by the research work with 133 people with a higher degree of ID.The first method used was an interview with a nurse and a doctor in order to estimate sexual development of participants according to J. M. Tanner’s scale. The next method used was an interview questionnaire .The research work made use, primarily of the technique of a standard interview in the form of a guided conversation with people with HDID. It was prepared according to a precise described sample that comprised a set of questions, their correct sequence as well as the manner of asking them. It was also exceptionally important to provide similar interview circumstances for all the people interviewed. These circumstances were very important for the material collected to be compared and then generalized. As the character of the conducted research was connected with exceptionally sensitive and personal areas, which are usually hidden and not easily shared, it was necessary to put the prepared interview questionnaire and poll to a wide range of consultations. The interview questionnaire was first discussed by psychologists and psychotherapists as well as a psychiatric doctor. Their remarks concerned mainly the applied inventory of notions and consequently their suggestions were contained in the interview questionnaire and elaborated on in such a way as to ensure that they met the criteria of correctness as regards questions asked and applied terminology.It should be emphasized that the results achieved during the research work with youths with a higher degree of ID were later discussed with their teachers in charge and teachers who had direct contact with them. All suggestions and remarks by these teachers were noted and then taken into account while elaborating the results.The interview comprised of three stages. Stage 1 was to establish good contact with the person being interviewed. The questions concerned their general physical and mental state (mood) as well as their interests. The aim of that stage was to create an atmosphere of safety and trust. The next stage, called the main one, consisted of conducting the interview according to previously prepared questions. Stage 3—was the stage of ending, summarizing the interview results, explicating potential misunderstandings and a small talk to finish the whole procedure. Each interview was conducted directly with the person with a higher degree of ID and lasted for about 3 or 4 h with breaks.An interview questionnaire from a school nurse destined to evaluate sexual development, an interview questionnaire to evaluate the sexual experiences of the youths with HDID (DSMN). There were two versions of the questionnaire, one for men and one for women.The research work made use of the following testing tools:The part concerning knowledge was categorized into 3-scale answers, giving an opportunity to describe the level as low, medium or high. This part dealt with the problems of human sex identification, the physiology of the genitalia of one’s own body and that of the opposite sex, the physiology of fertilization and pregnancy, contraception, sexually transmitted diseases (STD), HIV/AIDS, changes within the body occurring during the adolescent period, body hygiene in that period, the feeling of shame as well as sexual activity in public and private places. In this manuscript there was presented only the level of knowledge on private body parts, fertilization, pregnancy, child delivery and contarception.The interview questionnaire consists of 3 parts, each of them testing different aspects such as knowledge, behavior and emotions connected with one’s own sexual life. The present work presents only the results obtained from parts I and II of the interview questionnaire i.e. the ones concerning knowledge and behavior. The interview questionnaire had two versions, a version for men and for women and was supplemented by charts that contained notions connected with human sexuality.The tested people achieved high scores when they were able to correctly name external attributes of their own and opposite sex (women/men—each 3 attributes). The study subjects were tasked to indicate, in the picture of a man, testicles, penis and pubic hair and in the picture of a woman—breasts, vagina and pubic hair. The score was referred to as a middle when the study subjects named 2 attributes, and too low—when they were unable to indicate any or just one.It was found that the tested group could achieve high level of knowledge on physiology of insemination if they could respond to 3 asked questions  as well as to explain correctly how the process of insemination takes place. Average results were scored when they could do the same with 1–2 such problems and the tested people had difficulties in explaining the idea of insemination, whereas low score was ascribed when none of the above problems was correctly answered and no explanation of insemination given.As regards physiology of pregnancy, high score was reserved for the tested people who could determine the time necessary for a full development of an inseminated egg into a human being. Average results were scored by those who, in spite of not giving correct response, were aware that the development of an inseminated egg is a long-lasting process. Low score reflecting very little knowledge on physiology of pregnancy was obtained when the tested people had no idea of pregnancy and could not respond whether it takes long or short time for an inseminated egg to develop into a human being.In the questions concerning physiology of giving birth, the tested people could score high if they could explain that a woman gives birth to a child through her procreative tracts; average score when they had difficulties in precise explanation of the phenomenon of birth and low score when no explanation was given at all.In the part dealing with undertaking sexual activity, the people interviewed were asked to answer “yes–no” questions, with the possibility to express their opinion in detail. Many of those under study have openly discussed sexual experience. The presented study results are illustrated with several selected sentences in their original wording, expressed by the people under study. The atmosphere of these conversations is difficult to precisely depict, e.g. the voice, the look of eyes, reflection, unsure look, laugh or emotion, the nervous movement of hands, clapping of hands or whispers. A lot of non-verbal information often accompanied words. The expressions have been selected in such a way as to present, as wide as possible, the different opinions of the people under study on the described issue.As regards knowledge on contraception, the tested group could score high when named 3 contraceptions methods, average with two and low when no contraception methods were named.The tools were of an auxiliary nature and merely supplemented the conducted studies. The people tested took part in a doctor’s or nurse’s interview that contained questions about the age and time when first menstruation among women and first wet dreams among men appeared. According to these factors, the sexual ages of the people concerned were determined. Every respondent had his/her pubescent stage evaluated applying a simplified J. M. Tanner’s scale.Pre-pubescent period, ,Early pubescent period, ,Middle pubescent period, ,Late pubescent period, ,The level of sexual development and all specific data connected with the somatic aspect of sexual maturity were diagnosed by a school nurse according to the patient’s medical record or by consulting the doctor in charge in the case of incomplete records. The level of development of secondary sexual attributes (features appearing during each stage of adolescence differentiating an adult from a child) such as different sexual tracts and copulative organs, puberty hair (P), hair in the armpit (A), development of genitals (X), breast increase (Y), facial hair were also settled. The test made use of a simplified model of describing sexual development among the tested group and was applied taking account of possibly the most precise and complete interview with a doctor or a nurse. As a result of the above, their sexual development was described according to a modified J. M. Tanner’s scale that finally took the following shape:Bioethical Committee—independent organization giving opinion and supervising clinical trials, established to provide proper protection of human dignity during the studies. The Bioethical Committee controls, among others: the legitimacy, feasiblity and clinical study scheme, anticipated benefit and risks analysis, clinical study protocol correctness. A clinical study cannot start without the consent of a bioethical committee.The people to be examined were selected according to formal certificatesThe respondents qualified to take part in the research constituted a uniform group—homogenous as regards their age of 18–25 as well as an IQ level that was average for the people with a higher degree of ID. Their age was of importance, as in that life period one can observe the creation of first partner relationships with the aim of establishing a family.In the tested group, most people are placed in the middle (40 %) or late (49 %) stage of pubescence with only 10 % at an early pubescent stage, whereas with one person a pre-pubescent period was diagnosed. A breakdown of the factor within that group is presented in the Table The tests tried to determine the age when the first wet dreams and menstruation took place. The presented data revealed that people with a higher degree of ID are not a homogenous group and the occurrence of the first menstruation and wet dreams may take place even 3 years later than among fit people.On the basis of the research, one may conclude that the first wet dreams among men with a higher degree of ID took place at the age of 14.5, whereas in the case of women—first menstruation at 13.4 years of age. There are different opinions as to the age when fully fit women and men start to sexually mature. It can be stated that although the process is individually differentiated, generally women tend to sexually mature faster than men. On average, women start to mature sexually at the age of 10.6–13 years whereas men—12.6–15 years  as women (48 %). As a result of the analysis, one can state that autoerotism is the most frequent form of their sexual behavior. The analysis of masturbation frequency showed that such an activity was carried out mostly a few times a week (41 %); whereas as many as 18 % of the tested youths masturbated a few times a month, 28 % once a day and 14 % a few times a day.Masturbation can be stated to be a normal sexual practice when it is undertaken at the age excluding partner relations. The masturbation acceptance is of a conditional nature, depending on age, duration and circumstances of the person masturbating. Based on the studies conducted it can be stated that for the majority of the study subjects masturbation has a developmental nature and constitutes an integral and natural phase of sexual development. However the interpretation of the study results requires reference to certain theoretical positions which, among others, perceive masturbation as the only form of sexual activity accessible for the disabled. It is difficult to explicitly agree with this thesis. As a result of studies, it has been discovered that the majority of the studied intellectually disabled teenagers, who masturbated, have not excluded taking up sexual activity with a partner Table .Table 5FLooking further into masturbation, we can go through the places where the intellectually disabled teenagers studied, masturbated. 100 % of the teenagers studied, masturbated at home on their own. The exact analysis of empirical material allowed drawing extra conclusions. It has been determined that the studied intellectually disabled teenagers masturbated in other places as well, outside home. These places included schools, parks, squares, public toilets, shops, trams, buses, and forests as well as healthcare facilities Table .Table 6MDuring the studies it has also been determined that 7 % of the studied teenagers stimulate themselves in an untypical manner. The teenagers studied admitted to masturbating with tools, certain objects or to masturbating in a way other than a natural one. The study subjects masturbate using grease, food, furniture and even vacuum cleaners. Such masturbation can be determined as dangerous, mainly due to the fact that it fixes a certain, repeatable chain of strange rituals, often impossible to use in a partner relationship, and may result in a pleasure decrease.People with HDID do take up sexual activities and, similarly to the group of those intellectually fit, one can observe differences as regards this aspect. The evaluation of sexual behavior showed that 13 % of people with a higher degree of ID had already started some kind of sexual activity, and the average age of doing this does not differ from that of intellectually fit people and amounts to 18 years of age. The age of first sexual intercourse among men averaged 17.5 years of age, whereas for women, 19 years of age.Although women and men with HDID have their first sexual intercourse later than intellectually fit young people (the difference amounts to 3 years) it is not justifiable, however, to say this is based only on the collected results that we deal with here with regards to the retardation and acceleration of that activity in both groups respectively. On the other hand, such interpretation cannot be completely excluded. All discussions concerning the topic of the optimal time of first sexual intercourse within the group of people with HDID reveal ambiguous opinions, mainly because taking up sexual activities within that group is an exceptionally rare phenomenon. The main stimuli of taking such decision are: curiosity (39 %), need to prove one’s adulthood (33 %), emotional relation with one’s partner (22 %) as well as encouragement from others 17 %) ,I have already had sex. The girl lived in my district. She doesn’t study here anymore as she has already completed school. She left school last year. Now she spends time at home. I did it out of curiosity to find out how what it is like; one has to do it eventually. The girl cried afterwards and she said that it hurt her or something like that. It didn’t hurt me. It was not bad but now it has got better. Some of my friends have already had sex. I also wanted to do it. Now, I have a different girlfriend. I have also had sex with her a few times. I am a little worried about getting her pregnant so I don’t do it very often. .To illustrate the presented analysis one may quote a few chosen comments from the tested participants:The conducted empirical analysis shows that 15 people took up sexual activity after the first sexual encounter, which accounted for 11 % of the total participants. 10 people continued having sex with the same partner and 8 had more than one sexual partner (in most cases the number varied from one to three). In one case, a person had homosexual relations with a partner whom he/she considered his/her friend. These people studied in the same school and lived in a dormitory. They had sexual contact mostly at weekends when they were alone in the dormitory.It was found that only 39 % of the tested people used any contraceptives. The rest did not use any form of protection against pregnancy or sexually transmitted diseases. The main reasons for not doing so, were a lack of knowledge and a feeling of ‘discomfort ‘or a feeling of disgust as well as difficulty in applying the contraception Table .Table 12The conducted research allows me to claim that as many as 90 % of the youths examined with a higher degree of ID can differentiate physiological attribute peculiar to their own sex. This skill as regards the opposite sex was displayed by 10 % fewer respondents. 7 % of the youths tested had difficulty in telling apart one’s own private body parts, with 16 % in the case of the opposite sex. Only 4 % could not identify correctly one’s own private body parts and 7 % could not do it with the opposite sex Table .Table 13Following the analysis, it was found that 52 % of the people tested with a higher degree of ID could correctly describe the idea of fertilization. They knew how a child is conceived. They gave incorrect answers when asked if a woman could become pregnant through kissing a man, hugging or touching through clothing. An average level of knowledge was scored by 11 % but as many as 37 % achieved a low score. The youths lacking knowledge on fertilization believed that a man does not take part in the process of fertilization. It was believed that a man’s responsibility consisted of supporting a family by taking up work Table .Table 14The conducted research revealed a severe lack of knowledge on pregnancy. The sample group could not explain the idea of pregnancy. Almost 65 % did not know how long it takes for a fertilized egg to develop into an independent human being and they could not describe if the time was long or short. Their answers concerning that topic were simplified and often not correct. 14 % of the youths with a higher degree of ID showed average (medium level) knowledge on the physiology of pregnancy. They knew that a child is conceived within a female’s body, develops there and after achieving final form is delivered. In spite of giving imprecise and often wrong answers, they were aware that the development of a fertilized egg into a human being is a long process but only 21 % of them could precisely describe the time necessary for it Table .Table 15As many as 81 % of the youths with a higher degree of ID knew very little about childbirth. When asked, they gave made up answers on the topic. The most frequent answer concerned women staying in hospital. Very few of them made use of proper terminology such as ‘giving birth’ to a child. Most respondents associated childbirth with something difficult and painful. They believed that a woman gives birth to a child on a table in hospital in the presence of a doctor but at this point their knowledge ended.The woman gets pregnant and feeds her baby with her breast. To have a baby, a woman must have sex with a man. Then, the woman and man have an orgasm and the man gets her pregnant. The man has sperm and it gets into the womb so a fetus is created. A child is in the stomach and when it grows, the woman will have a baby. When the woman’s stomach is growing, she goes to a doctor. She should buy a pregnancy test; she may feel sick. The doctor touches her stomach and the fetus can be seen on a computer screen. I have seen it on TV on a program. Men can’t be pregnant and give birth to a child. The woman gives birth by pushing to get the child out. When she can’t do it, they cut her stomach and get the child out .To illustrate the above, one may quote a few chosen comments made by the sample group of people with HDID.Another comment proves that the youth in question had some knowledge on fertilization, pregnancy and childbirth but even then, it is incomplete and not precise enough. The people questioned knew very little about childbirth. Very often, one can find in their opinions such expressions as ‘a child is born through a womb, navel or breast in hospital.’It was determined that only 10 % of the tested youths understood the notion of contraception. These people were able to name at least three methods of contraception; condoms and contraceptive pills were mentioned most often.The obtained results show that adults with a higher degree of ID have certain sexual experience but not enough knowledge on human sexual life. According to the conducted research, it was found that the group in question mostly identify with their own sex and can differentiate their gender from the opposite one. In most cases, the youths surveyed could match the external attributes to the proper sex and they seem to accept the physical aspect of their gender.Masturbation and petting were found to be the most frequent ways of expressing one’s sexual needs, with masturbation playing the major role, whereas touching and sexual intercourse proved less popular. The masturbation activities were found to occur in various circumstances, most frequently in intimate situations. A deficiency of information on how to deal properly with this form of sexual expression results in the fact that people with HDID often make use of pathological forms of masturbation jeopardizing their health and even life. It has also been found that the youths surveyed prefer autoerotic to socially-oriented sexual activities  Socially-oriented sexual activities such as kissing, petting and sexual intercourse were found to be rather rare. As many as 24 % had petting experiences, while only 14 % started having sexual intercourse. Men, more often than women, were involved in socially-oriented sexual activities.The phenomenon of the sexuality of people with a higher degree of ID is an issue that still needs constant analysis. It is mainly connected with the change of attitude towards perceiving and understanding disability. One may claim that we are undergoing a process of shifting from taking a strictly biological perspective towards sexual rehabilitation. Among other factors, the time of making that shift is connected with granting certain rights and sexual freedom to those people. However, there is a lot of evidence to suggest that we still deal with the problem by infantilizing people with HDID.People with HDID masturbate in various circumstances; in most cases, however, it takes place at home. The higher the degree of ID, the more often it happens that masturbation may take place in the presence of family members, during school classes or somewhere in the street. It should be mentioned that among these people, masturbation appears not only as a response to lowered intellectual abilities but more often is a result of improper socialization and a lack of school education. It may also be a form of satisfying one’s emotional hunger, especially, in the case of people who experience some rejection, lack of acceptance, love and caressing or live in loneliness and isolation and are not able to verbalize their emotional state of mind. According to the research work conducted in the 1970′s, c. by Edmonson and Wish (, p. 11–1The research results by Goldstein  conducteThere is a constant need for studies in this field. The presented results are not extensive and constitute merely an invitation to discuss the sexuality of HDID people.


Microwave imaging techniques are prone to signal corruption from unwanted multipath signals. Near-field systems are especially vulnerable because signals can scatter and reflect from structural objects within or on the boundary of the imaging zone. These issues are further exacerbated when surface waves are generated with the potential of propagating along the transmitting and receiving antenna feed lines and other low-loss paths. In this paper, we analyze the contributions of multi-path signals arising from surface wave effects. Specifically, experiments were conducted with a near-field microwave imaging array positioned at variable heights from the floor of a coupling fluid tank. Antenna arrays with different feed line lengths in the fluid were also evaluated. The results show that surface waves corrupt the received signals over the longest transmission distances across the measurement array. However, the surface wave effects can be eliminated provided the feed line lengths are sufficiently long independently of the distance of the transmitting/receiving antenna tips from the imaging tank floor. Theoretical predictions confirm the experimental observations. Multipath signals occur in numerous microwave and RF applications when an unwanted portion of the original transmission propagates along any alternate path and ultimately couples to the receiver distorting the amplitude and phase of the desired signal –4. If thThe potential for interference from multipath signals increases substantially in near-field applications , especiaEqually important in near-field imaging is the multiple paths a signal can take within the imaging zone. Figures With respect to reflections off the bottom surface, the base of the tank was at least 1.8 wavelengths (at the lowest frequency) below the active sections of the antennas in our initial clinical installation when the array was located at its lowest position during an exam. Since minimal multipath signals resulted from reflections off the top liquid surface, symmetry would suggest that the same should be true for the base of the tank . HoweverIt should be noted that these investigations have stemmed partially from our efforts to perform microwave tomographic images on patients in an actual MR scanner for the purpose of exploiting the refined spatial resolution of the MR along with the more specific nature of the tissue dielectric properties. The MR bore is quite small and places a significant constraint of space for the microwave system. Initial attempts included shortening the antenna feed lines associated with the shorter illumination tank. This was where we first encountered multipath signal corruption which subsequently led to this study.In the following sections, we discuss the theoretical underpinnings of these modes for the geometries present in our system. We demonstrate cases from our current imaging system, where the measurements indicate corruption of the desired signals from multipath signals associated with the base of the tank. We then show experiments that allow us to partially isolate the effects to surface waves propagating along other pathways. We realize that there are a number of propagation modes around the antennas, their feedlines and the tank surfaces, of which the surface waves are only one possible contributor, but understanding these contributions is important. We present an initial strategy for minimizing the effects of these signals which may be instructive for designing other near-field imaging systems, including simulations confirming the earlier theoretical discussion and validating our feedline design strategy.A challenging situation occurs when a portion of the transmitted signal propagates along an unwanted path and recombines with the original signal at the receiver. Because both occur at the same frequency, filtering is generally ineffective. Time-gating strategies can sometimes be effective when the nature of the multipath signal is well understood , 2. AtteAde, Amp, ϕde, and ϕmp are the desired and multipath signal amplitudes and phases, respectively, ω is the operating frequency, and t is time. For example, if the magnitude of the multipath signal is 25 dB below that of the desired signal, the maximum possible amplitude and phase errors in the resultant signal would be 0.48 dB and 3.22°, respectively. For a −15 dB multipath signal, these values increase to 1.42 dB and 10.24°. Clearly, the resultant phase and amplitude errors can become very significant for multipath signals that are on the same order of magnitude as the desired signals. It should be noted that there can be many multipath contributions with a range of amplitude and phase contributions. This single contributor analysis serves to give a flavor that the unwanted effects can be significant and is generalizable to multiple sources.x = 0) with Region 2. In this case, the magnetic field (Hy) is only oriented in the y-direction (out of the page). The complex relative dielectric properties in the two regions are ε1 = ε1′ − jε1′′ and ε2 = ε2′ − jε2′′, respectively. The classic surface wave solution occurs when the reflection coefficient is zero (at the Brewster angle), which is complex-valued in this instance. If A is the amplitude of the incident plane wave, then the magnetic component of the incident and transmitted waves can be represented asThe first surface mode to be considered involves propagation along the interface between the tank base and coupling liquid. Following the analysis by Stratton , Figure h12 + β2 = k12 and h22 + β2 = k22 are needed to satisfy the wave equation, k1 and k2 are the wave numbers for the two regions, and β is the propagation constant. The wave impedances for the two regions are given bypedances , 22. ThiIn this situation, we are primarily interested in surface waves propagating along the outside of a coaxial cable, and their associated attenuation as a function of distance after the mode has been sufficiently established. For this analysis, we will consider the case of a coaxial line which is abruptly terminated by an open end .εc and ε1 are the complex-valued permittivity of the coaxial cable insulator and the surrounding dielectric materials, respectively, a and b are inner and outer coaxial radii, respectively, ω is the operating frequency in radians, and k is the wavenumber in the coupling liquid, where μ0 is the free space magnetic permeability. ρ′ and ρ are the radial cylindrical coordinates within and outside of the coaxial cable, respectively, ϕ′ is the angular coordinate within the coaxial cable, and r is defined as Kc is represented asA coaxial cable supports a TEM-mode electromagnetic field which is incident on the cable opening. Part of the signal is partially reflected into the cable, while a second portion is transmitted as a surface wave propagating along the outside of the surrounding cable. The fields transmitted into the surrounding space can be determined from the distribution at the coaxial opening which can be found by solving the integral equation for the radial component of the electric field over the opening:γn are solutions of the characteristic equation:Jn and Yn are Bessel functions of the first and second kind of order n, respectively, and kc is the wavenumber inside the coaxial line. Once Eρ is determined, then electric and magnetic fields can be found at any point  in the surrounding medium fromejkR′−.Figures εr = 2.7 that was effectively lossless in this frequency range [In these experiments, we used Plexiglas for the tank materials with a dielectric constant of cy range . The dieUtilizing the clinical system described in In this set of experiments, we utilized the illumination tanks and antennas described in More likely, the multipath signals in Along with the analytical discussion in Sections The results for the serpentine feedlines are consistent with previous results in that the field strength in the Plexiglas is lower than that for the short, straight line case. The potentially debilitating effects of unwanted multipath signals is a critical consideration in translating near-field microwave imaging approaches into clinical and commercial systems. For our noncontacting antenna approach, surface waves  appear to cause the biggest effects as they propagate along the outside of the transmitting coaxial line across the illumination tank floor and back up the coaxial feed lines of the receivers. When the imaging tank is deep and the transmitting/receiving antenna tips are sufficiently far above the tank base, the surface wave signals are adequately suppressed relative to the transmissions through tissue. The results presented here indicate that 9-10 cm of distance along the feed line is adequate. However, reducing the tank depth is of interest for practical reasons and is essential in some settings and appears possible because reflections from the floor of the tank are still too small to degrade the measured signals propagating through tissue. Indeed, we found that antenna tip distances as little as 5 cm from the tank floor maintain receiver signal fidelity across the array provided the surface wave contributions are attenuated through an equivalent feedline length approaching 10 cm. These findings are significant because they indicate that the antenna array and imaging tank geometry can be altered substantially by manipulating the shape of the antenna feed line, which can be exploited to ensure sufficient surface wave attenuation. There are certainly other mechanisms for multipath propagation including coupling of fields from the feedlines directly to portions of the breast tissue outside the immediate plane of propagation and are certainly good topics for further investigation.


In this study, the efficiency of surgical manipulation with and without CGC for controlling a pair of bimanual surgical robots is evaluated by analysing the level of coordination of two independent operators. Fitts’ law is used to compare the quality of movement with or without CGC. A total of 40 subjects have been recruited for this study and the results show that the proposed CGC framework exhibits significant improvement (p < 0.05) on all the motion indices used for quality assessment. This study demonstrates that visual guidance is an implicit yet effective way of communication during collaborative tasks for robotic surgery. Detailed experimental validation results demonstrate the potential clinical value of the proposed CGC framework.The use of multiple robots for performing complex tasks is becoming a common practice for many robot applications. When different operators are involved, effective cooperation with anticipated manoeuvres is important for seamless, synergistic control of all the end-effectors. In this paper, the concept of Collaborative Gaze Channelling (CGC) is presented for improved control of surgical robots for a shared task. Through eye tracking, the fixations of each operator are monitored and presented in a shared surgical workspace. CGC permits remote or physically separated collaborators to share their intention by visualising the eye gaze of their counterparts, and thus recovers, to a certain extent, the information of mutual intent that we rely upon in a  Remote collaboration through a common robotic platform has been the main motivation of many early attempts of tele-operation  has become a matured surgical discipline that reduces scarring, blood loss, and patient recovery time. The introduction of surgical robots has further enhanced manual dexterity, precision, and ergonomic control of MIS. Master–slave systems such as the da VinciCollaborative surgery has several advantages compared to the conventional master–slave approach since it allows several expert surgeons with complementing skills to perform a surgical procedure simultaneously. It permits the sharing of expertise and knowledge whilst enabling each surgeon to manage or lead different parts of the procedure. This brings the current robotic surgery closer to the traditional workflow and is particularly useful for complex tissue manipulation tasks that are beyond the capability of bimanual control of a single surgeon. The platform also permits remote mentoring or assistance, with which the remote expert surgeon can take over a part of the procedure when it is deemed to be too difficult to the local surgeon or trainee.Although collaborative robotic surgery represents an attractive approach, it suffers from a number of difficulties mainly due to the physical divide of the operators, since this removes many of the perceptual cues we rely upon for gauging the anticipated actions of their collaborators. For the current systems, although verbal exchange is always maintained, shared control of the surgical instruments over the same surgical scene still leads to confusion and hinders efficient and safe interaction between the collaborating surgeons. These can lead to instrument collision and inadvertent tissue damage, raising significant patient safety concerns. During a complex collaborative surgical procedure, it is necessary that collaborators can share their intention without explicit verbal exchange of words. It is because verbal guidance can be cumbersome and misleading when manipulating along complex anatomical pathways. During verbal interaction, clear understanding of the meaning of certain words and phrases may also require contextual information and often involves gestures or other communication media. During interaction between surgeons, linguistic disambiguation is often performed with simple referencing gestures. Pointing is a simple and direct way of referencing. For example, Clarkperceptual docking for robotic control, with which eye-tracking has been used as one of the key perceptual cues for robotic control.et al.,et al.,Most recently published work uses eye gaze as a means of more effective human–machine interaction and for facilitating hand-eye coordination.In order to facilitate or enhance collaboration in a shared multi-robot surgical environment, it would be desirable to reveal the visual attention of the collaborating counterparts. The study presented here aims at demonstrating how the concept of Collaborative Gaze Channelling (CGC) can achieve this goal. In this paper, the efficiency of surgical manipulation with and without CGC for controlling a pair of bimanual surgical robots is evaluated by analysing the level of coordination of two independent operators. Fitts’ law is used to compare the quality of instrument movement with or without CGC in a study group of 40 subjects. The results show that CGC can enhance cooperation amongst surgeons on a master/assistant paradigm by improving speed, accuracy, and reliability during a collaborative task.For studying the role of eye-gaze and the effectiveness of CGC, a remote collaborative surgical environment has been developed. This involves the use of two mirrored remote visualisation and control stations. The two stations Fig.  are sepa3 (W × H × D).For capturing visual attention, each of the two surgical consoles is equipped with a video-oculography eye tracker. Due to the geometry of the eye, the corneal reflection vector can be uniquely assigned to a gaze direction. After a brief calibration routine, such reflection vectors can be mapped into unique fixation points onto the stimulus screen in use. Figure For collaboration within the shared surgical scene, both surgical stations provide visualisation on 17-inch LCD monitors at a resolution of 1024 × 768 pixel. It is worth noting that the resolution of the eye tracker is determined by the visual angle. The current screen resolution used already exceeds the achievable per-pixel accuracy of the eye tracker. For the experimental setting used for this study, approximately ten effective pixels are covered by a visual angle of 0.5°, which is the average accuracy of the Tobii eye tracker used. Control of the two laparoscopic instruments, which are linked with two virtual robotic arms, is achieved using two PHANToM Omni haptic devices from SensAble Technologies (MA). Figure For the simulated surgical task for nodule extraction, a total of seven nodules are located on a 3D tissue surface rendered with realistic prostate tissue texture Fig. . To simpleft/right upper corner or centre, or further left/right/up/down, express instantaneous indication of the direction respect to the left/right instrument tip. Confirmations such as yes or no somehow are required. For the fair evaluation, the communication is only in one way from the master to the assistant. Verbal dialogue for disambiguation is allowed when necessary and the master can also repeat the instructions. Guidance in the CGC case is implied by the position of the master’s fixation point as this is relayed and visualised on the assistant’s screen. Similarly, in parallel, the master is able to see the assistant’s fixation point on their monitor. The typical sequence of events for both the vocal and CGC guidance tasks is outlined in Table Verbal guidance is used for the control experiment. Having standardised the set, the master is only allowed to describe the nodule locations using a limited set of instructions. These instructions referring to the location of the target nodule, such as The above procedure is also illustrated in Fig. For analysing eye tracking data, time integral of gaze displacement is defined, where gaze displacement represents the spatial offset between the master’s and assistant’s fixations at the moment when the master requests removal of a specific nodule. Perfect gaze convergence between the master and the assistant occur when both fixation points are collocated at the point where the master was intending to attract the assistant’s attention.Gaze Latency is defined as the amount of time between a nodule removal request and the eventual gaze convergence. In determining gaze latency, two conditions should be satisfied when the respective regions-of-interest (ROIs) are fixated upon: (1) The convergence tolerance should be within the average size of the nodule on the display (13 mm in this study); (2) The assistant’s gaze should dwell for more than 300 ms within the convergence tolerance. This is the time from the beginning of two gazes’ convergence until reaching the dwell time threshold.The Gaze Convergence is an integral of the gaze displacement between the master and the assistant over the time it takes for the two to merge within the defined convergence tolerance. It represents the actual visual search that took place. In addition to gaze convergence, the correlation R-value needs to be examined between the master and the assistant fixations. For this, scatter plots of the assistant’s vs. the master’s fixation coordinates need to be generated and the correlation to be calculated through linear regression. These three parameters are essential performance indices for revealing the assistant’s performance and understanding of the task.The eye tracker operates and measures gaze positions at a sampling rate of 50 Hz. Although inadvertent or involuntary gazes do happen occasionally (e.g. due to distraction), the gaze is only used to convey the attention cues of the collaborating surgeon. It is therefore important to show this information as is to the collaborating partner. Only basic filtering (median) is performed to reduce noise due to the eye tracking hardware and ocular tremor. In order to visualise the recorded data intuitively, instead of plotting every discrete gaze position that makes the results unclear, fixation clustering was applied and presented as a hotspot map. Fixation clustering is achieved through convolution of the plotted fixations over the image space with a spectrum mask of adjustable diameter and weights. The convolution mask is formed by a Gaussian kernel with dimension 40 × 40 pixels out of the full screen resolution of 1024 × 768. It is set to be smaller than the size of a nodule in 2D and to be roughly equal to an area subtending an average fovea with 1° of visual angle. The standard deviation of the kernel is set to 6.5 and the maximum weight applied at the centre of the mask. When a fixation is plotted once at each sample time, the colour intensity at the centre of the mask will be increased by 1.8 units. If the fixation dwells at the same point for more than 2.83 s, a bright spot with maximum intensity of 255 will be observed. All these parameters introduced for the kernel are determined with the aim of having sharp and distinguishable fixation spots on the map. Hotspot maps, like the one shown in Figs. For analysing instrument motion, the total distance travelled by the instrument was measured. This is for evaluating performance efficiency during the task. In the context of this study, we use the accumulated distance travelled which is defined as the total distance travelled by the assistant’s instrument from the moment when the desired nodule was verbally or visually indicated by the master until it has been picked up from the tissue surface. The system recorded the accumulated distances travelled by both the left and right instruments held by the assistant. The time required to complete the task, the instrument tip distance travelled and the speed were also measured. Subject specific analysis was used to compare task performance between vocal and CGC guidance. The hypothesis to be evaluated is whether the application of CGC can enhance the cooperation in terms of speed, accuracy, and reliability.MT denotes the moving time required to hit the target. The ID is a logarithmic function of the spatial relative error varied by the parameters W and A, respectively, which are the width of the target nodule and the travelled distance of the tool tip when gripping the nodule. This distance is recorded from the point when the previous nodule is passed over to the master’s instrument to the other point when the target nodule is gripped. For this study, each task was repeated five times. In order to standardise the ID calculation, such recording is skipped for the first nodule gripping in each task. In Eq.  depends on its width W  and its distance A to the cursor (in this case the instrument tool tip). In order for the nodule to be picked up, the tool tip must fall within In the current study, Fitts’ law is applied to measure and compare the assistant’s response with and without CGC. This law was first developed by Fitts as an empirical model to analyse speed and accuracy trade-off of human muscle movement.ID of a target. In addition to the index of difficulty, Fitts also defined the Index of Performance (IP). The IP, is expressed in bits/time and can be used to characterise how quickly pointing can be done, independently of the involved target characteristics. Measuring the IP of different devices or systems allows their comparison with respect to their pointing capability. There are two different representations of IP in the literature. One of them is a is ignored and it is only valid under ideal circumstances such as no learning curve effect taking place, which is considered as a restriction of this representation. An alternative way of representing the IPIDaverage is the average of the index of difficulty for a target and MTaverage is the average of the moving time taken to hit this target. Although we endeavour to minimise the learning effect by using randomised control trials, both indices were calculated in order to present the performance with and without the consideration of the learning effect in this study.The logarithmic term is defined as the index of difficulty mentclass2pt{minimFor all 40 subjects studied, the following figures summarise the key findings. Figures In order to present these results quantitatively, Figs. p < 0.05 in between ). More specifically, the number of nodules extracted is increased by more than 40% with CGC, the task completion time is shortened by 33%, the total distances travelled by the active instrument is shorter by more than 40%. Table p-values (p < 0.05) obtained on the paired test  is too unexpected to follow the regression. Table IP1 and IP2 for all subjects. Higher values of IP1 = 2.6 and IP2 = 1.11 are shown for the CGC as compared to IP1 = 1.88 and IP2 = 0.51 for the control experiment. As the task does not require any specific surgical skill, there is no performance difference found between surgeons and the other 27 subjects.Figure In this study, we have presented a framework based on eye-tracking for improved collaborative manipulation of surgical robots. To minimise the distraction of motor memory for the surgical manipulation, as well as to intuitively describe the location of complex features in the surgical scene, eye gaze rather than explicit pointing and directing was used in this study to convey the attention cues of the surgeons. This is because during surgery the hands of the surgeons tend to be fully occupied with surgical instruments. This alleviates the need for the surgeon to leave control of the tools. It has been shown that eye gaze is more advantageous in terms of implicitly carrying information on the focus of the surgeon’s attention, compared to the use of other input modalities. Multiple performance indices were introduced to assess the performance of a surgical task. Fixation analysis reveals the subjects underlying visual attention and permits more detailed assessment of factors affecting surgical performance. The use of saccades would be interesting but it can be influenced many compounding factors, which are more difficult to decode. Other indices, such as blink rate, were not measured in this study, which can potentially be incorporated into the current framework as they have shown to be relevant to performance in general surgical procedures.Instrument motion analysis is excluded from the point that the nodule is being gripped by the assistant’s instrument. The reason for this exclusion is that the transfer movement is a well-identified task and does not require any further instruction or guidance. The transitions consist of very similar patterns of movement and behaviour with and without the use of CGC. It is also important to note that the same person (expert) acted as a master to assess the collaborative behaviour of all the 40 subjects studied. Although it may be argued that exhaustive pair-wise permutation would be useful to assess the performance of each subject when taking different roles and collaborating with different subjects, this would require 780 (=40 × 39/2) experiments, which is impractical in our laboratory settings. The advantage of having one experienced operator as the master ensures the consistency of the data and it better emulates the real-life situation in a collaborative surgical environment, as it typically involves at least one very experienced surgeon and another assistant or trainee. Further analysis of collaborative behaviour between experienced surgeons would be the next step of our study. Due to the nature of the designed task, it is unsurprising that with the same master, the instrument coordination, and trajectories are contrastingly different between subject pairs—highlighting the idiosyncrasy, as well as the importance of effective communication when performing collaborative tasks. Furthermore, in order to understand the brain behaviour during the collaboration task with or without CGC, functional Near Infrared Spectroscopy (fNIRS) is being used to assess the cortical activity patterns in our laboratory.®. We envisage that eye-tracking control incorporating CGC can be demonstrated by the use of da Vinci® Si HDIn this study, gaze convergence and latency have been considered as a key performance index of task quality. Both indices were significantly improved with the use of CGC. More specifically, gaze convergence has increased by 33% and gaze latency has decreased by almost 48%. These show that the subjects (assistants) tended to be more focused on the surgical target, rather than on the plan ahead. The indices of performance entclass1pt{minimamentclasspt{minimaIn conclusion, this study demonstrates the feasibility of CGC for robotic surgery. The framework was implemented for a multi-instrument manipulation environment, which is gaining significant interest in recent years with the increasing flexibility and miniaturisation of surgical robots and end-effectors. The results derived from this study suggest that CGC is an effective means of communication during surgery as it is natural and does not deviate attention during task performance. It has been shown to be beneficial for cooperative problem solving by preserving the relative gaze position of the operators and their gaze direction. In this paper, the task we used is simplified to allow a detailed assessment of different collaborative behaviour, it is anticipated that the current framework can be extended to complex surgical tasks that involve the navigation of tortuous anatomical pathways and require the use of multiple imaging, tissue manipulation, and focussed energy delivery.


The multiobjective design of digital filters using spiral optimization technique is considered in this paper. This new optimization tool is a metaheuristic technique inspired by the dynamics of spirals. It is characterized by its robustness, immunity to local optima trapping, relative fast convergence and ease of implementation. The objectives of filter design include matching some desired frequency response while having minimum linear phase; hence, reducing the time response. The results demonstrate that the proposed problem solving approach blended with the use of the spiral optimization technique produced filters which fulfill the desired characteristics and are of practical use. Digital filters exist in two types: Finite impulse response (FIR) and Infinite impulse response (IIR) or recursive. FIR filters suffer from the problem of high order (hence implementation and performance issues) if strict requirements are imposed at the design stage. Furthermore, IIR filters can have smaller group delay than its equivalent FIR filters Antoniou . The optDifferent techniques exist for the design of digital filters. Windowing method; in which the ideal impulse response is multiplied by a window function, is the most popular. There are various kinds of window functions , depending on the requirements on ripples in the passband and stopband, stopband attenuation and the transition width. These various windows limit the infinite length impulse response of ideal filter into a finite window to design an actual response. Furthermore, windowing methods do not allow sufficient control of the frequency response in the various frequency bands and other filter parameters such as transition width. The designer always has to compromise between the design specifications Antoniou .Due to the presence of the denominator of the transfer function, the stability condition of the filter should be taken into account in the optimal design Antoniou , resultiBecause of finite word length effects occurring in practical implementations of the designed filters, not only stability of the filter is of great importance but a stability margin is necessary as well. The poles of the transfer function should not lie too close to the unit circle. The sensitivity of pole locations to coefficient quantization increases with decreasing distance from the unit circle. Poles close to the unit circle may considerably enhance quantization noise and increase the maximum amplitude of small scale limit cycle. Consequently, it is desirable to have control over the maximum radius when designing IIR filters.Linear-phase filters are usually designed as non-recursive (FIR) filters which can have constant group delay over the entire base-band. However, when highly selective filters are required, a very high filter order is needed which makes these filters uneconomical or impractical. To eliminate this problem, attempts have been made to develop methods to design recursive (IIR) filters whose delay characteristics approximate a constant value in the passband. This includes IIR filter design approach that can satisfy both magnitude and phase characteristics simultaneously Inukai . The desUnder these circumstances, evolutionary and metaheuristic optimization methods find their place. These are referred to as global optimizers while the more familiar, traditional techniques such as conjugate gradient and the quasi-Newtonian methods are classified as local optimizers. The distinction between local and global search of optimization techniques is that the local techniques produce results that are highly dependent on the starting point or initial guess, while the global methods are totally independent of the initial conditions Recioui . Though Previously, global optimization techniques have been implemented in the design of digital filters. One such approach using neural networks has been described in  which are the magnitude response within small bandwidth including sharp frequency edges as well as an approximately constant group delay in this band are required too. Usually the best optimum value of all the objective functions of this filter design can be obtained for some values of design variables. A compromise or a trade-off between the objective functions must be made to achieve a satisfactory filter design.The considered recursive digital filter must satisfy three multi-objective functions. These functions are: 1) meet a specified or a desired magnitude response specification; 2) an approximately constant group delay; and 3) a minimum time response or settling time which involves a minimum phase or a group delay. The optimization approach considers the discrete-time transfer function which is formulated on the basis of some desired amplitude response and a stability margin parameter. A norm of the weighted error function is then minimized with respect to the transfer-function coefficients with a prescribed maximum pole radius referred to as stability margin. The stability margin parameter is varied to optimize the filter coefficients which minimizes mainly the magnitude response, satisfies the best approximately constant group delay and the lowest group delay that leads to minimum settling time or time delay of the system dynamic response.In the general case an IIR filter can be described by its discrete-time difference equationi and di are real coefficients a second order form transfer function can be obtained, having 2 M conjugate zeros and 2 N conjugate poles; called second order sections (SOS), as:Where x[n] and y[n] are discrete-time input and output signals. Equation  can be tii and bjj are real coefficients and H0 is a positive multiplier constant. The polar formulation is also useful and is written as:Where aaj, θaj and rbj,θbj are the radii and angles of the zeros and poles, respectively.Where rAs the poles are moved toward the origin (decreasing the pole radius), the system stability margin parameter increases and the system settling time decreases. This action, in fact, brings two required and important properties to the designed system. First, the system time or dynamic response is enhanced as settling time is decreased. Second, the system stability becomes more robust which is a very useful property, particularly in practical implementation. Indeed, the rounding or truncation of the filter coefficients may lead to an unstable implementation if the stability margin is too small. It is therefore desirable to approximate a given response by a transfer function with a prescribed maximum pole radius named stability margin as shown in Figure The amplitude and the phase responses of a recursive filter is given byWhere ω is the frequency and x is a column vector with 2 M + 2 N + 1 elements and depend on the used formulation, that is a Cartesian form asOr in polar form asWhereAndω) and the desired amplitude or magnitude response Μd(ω) as:The superscript T denotes the transpose operation. An approximation error can be formulated as the difference between the actual amplitude response M, the actual and the desired amplitude responses M and Md(ω) at frequencies: ω1, ω2, …, ωk, the column error vector is constructed as:By sampling the error function e = M − Md(ωi) and {ωi : i = 1, 2, ⋯ k} is a dense set of frequencies which are distributed over in the pass-band and stop-band of the filter. A weighting or penalty error is included to control portions of the actual filter response curve that are most important to the filter response. This involves modifying the error to the form:Where W(ω) is a weighting piece wise constant function over all frequency space, which is assigned a positive value greater than one or less than one to increase or decrease the magnitude approximation in a given band.Where A recursive filter can be designed by finding a point Md(ωi), can be performed by minimizing the error objective function in terms of Lp norm error which is formulated as:Such a point can be obtained when solving the optimization problem by minimizing the error function raj ≤  1 − δSubject to WhereAndμ(x) for increasing values of p.The p is a positive integer. The spiral technique is used to minimize The group delay is derived from the phase relation, as given in equation , and is φ is the phase response of the filter, and stated asWhere The group delay for a synthesized recursive filter is desired to be unchanged in the considered region on one hand. On the other hand, a minimum group delay is another required property needed in certain applications. In the present design, a constant group delay property is considered which is defined as:τc is constant, and ωp is the passband regions of the filter. In the present application τc is an unknown but can be considered as the mean value over the passband region, which can be determined as:Where Where The stability margin parameter is varied for discrete values, from which an optimal constant group delay is determined by minimizing the following objective error function:The multi-objective optimization problem is solved by discretizing the stability margin parameter, the magnitude optimization algorithm is used to generate the corresponding filter coefficients’, in which basis the group delay is synthesized where a feasible and optimal solution can be obtained by minimizing the objective function (19).The final multiobjective design is obtained by minimizing the sum combination of the errors in equations  and 19)19).Compared with traditional optimization techniques and other global optimizers, the spiral optimization method is easy to implement and very efficient in reaching optimum solutions. Spiral optimization method has been recently developed based on the analogy to spiral phenomena  and r is the convergence rate of distance between a point and the origin at each iteration k (0 < r < 1). The parameter r can be regarded as the “scaling” or radius of the logarithmic spiral curvature.Where x* as:The spiral model presented earlier has a center only at the origin. Hence, it should be extended to have center at an arbitrary point Preparation: select the number of search points m > 2, the parameters θ and r and the maximum number of iterations kmax.♦ Initialization: initialize randomly the points; xi(0) i = 1..m; in the feasible region and the center x* as the point with the least fitness value.♦ Updatingxi:♦ Updatingx*: Select x* as the point with the least fitness function in the updated set of points.♦ Check for termination criterion: If k = kmax then stop. Otherwise, start a new iteration.♦ Based on the previous formulation, the following optimization algorithm may be developed:i, j as:The extension of the two-dimensional optimization algorithm presented earlier is easy to do as one must understand how rotation in an n-dimensional space is done. Rotation in n-dimension is performed in the same way as the two-dimensional rotation taking two dimensions at a time. This is defined for dimensions Where the blank elements are zeros.Hence, there are Preparation: select the number of search points m > 2, the parameters θ and r and the maximum number of iterations kmax.♦ Initialization: initialize randomly the points; xi(0) i = 1..m; in the feasible region and the center x* as the point with the least fitness value.♦ Updatingxi:♦ Updating:x*: Select x* as the point with the least fitness function in the updated set of points.♦ Check for termination criterion: If k = kmax then stop. Otherwise, start a new iteration.♦ Hence the n-dimensional algorithm may be formulated similar to the two-dimensional algorithm as:The flowchart in Figure The digital filter to be optimized is to be used to eliminate harmonics and sub-harmonics in a power network with a fundamental frequency of 50 Hz. The filter is a bandpass type and is desired to satisfy the magnitude response to ideally pass only frequencies confined in the interval  while rejecting all other frequency content. The sampling frequency is taken to be 1800 Hz. The filter is of order 10 and is hence composed of 5 cascaded SOSs. At start up, the filter is optimized to match the magnitude response specifications only. Next, more constraints are added to the optimization process including minimum and linear phase and constant group delay to enhance the designed filter performance.The purpose of this part is to design a filter which only satisfies the magnitude response described earlier without considering any other performance criteria. The filter is designated single objective optimized filter (SOOF) hereafter. Figure However, the optimized filter is not of practical use as it suffers from drawbacks in the dynamic properties. First, as shown in Figure The inclusion of the constant and minimum group delay in the optimization task besides magnitude response criterion produced a filter which satisfies almost all requirements. The filter is thereafter called multiobjective optimized filter (MOOF). The magnitude response of the MOOF is shown in Figure However, the MOOF performs well in terms of the other criteria. In terms of phase response and group delay, Figures th optimized filter, the elliptic and Chebyshev type II filters.To validate the obtained results, the MOOF optimized filter is compared with the classical filter designs widely used in literature. The filters have the same order and should meet the same requirements described earlier. The filters considered are the least pThe classical filters have magnitude responses that meet well the requirements as compared to the MOOF. This can be explained by the fact that these filters are mainly designed to match a given magnitude response which can be considered to be similar to the SOOF optimized filter. However, according to Figures To better assess the performance of the filter (MOOF), two tests have been performed. In the first, a step sinusoidal signal of 50 Hz is input to the filter and Figure The application of the spiral optimization method to design a multiobjective digital filter has been considered in this paper. The objectives of the filter design were to match a desired magnitude response while having a minimum and linear phase. At start up, only magnitude response has been considered in the optimization task. The resulting filter was good in terms of this characteristic while it showed awful dynamic and phase performance. Next, the dynamic properties were included in the optimization algorithm to solve a multiobjective task. The spiral optimization method has succeeded in attaining the optimal design in terms of the previous requirements by achieving a compromise between them. The optimized filter has been tested and it showed good performance with required practical characteristics.


Rigid reconstruction of the chest wall after sternal resection is needed for protection of the heart and to ensure effective breathing. A variety of surgical techniques are used to restore the integrity if the chest wall. For the last years the titanium implants “Ley™ prosthesis”, Geister®, Germany are widely used for such purpose.A partial resection of the sternum was performed on a 48 year old female patient with benign sternal tumor. The middle third of the sternum and the adjacent parts of left and right third ribs were resected. Reconstruction of the postoperative 7/6 cm. bone defect was achieved using titanium implant “Ley™ prosthesis”, Geister®, Germany. 5 years after surgery the patient complained of severe pain in the region of intervention. On the X-ray study were seen 4 fractures of the titanium implant and in 3 of the 4 surgical steel sutures. After a discussion with representatives of Geister® it was clear that this is the only case with fractured titanium “Ley™ prosthesis” implant of about 500 already implanted across Europe.Surgery was performed on 08.11.2012, and all titanium fragments were removed. The patient was discharged in good condition and without pain.Fracture of such implant is a unique precedent in thoracic surgery. We still do not have the results of X-ray scattering analysis and the conclusions of Geister®, Germany. As there is no reason to question the quality of the implant the most probable reason for the fracture seems to be metal fatigue as a result of the numerous respiratory movements.


Nonlinear microwave imaging heavily relies on an accurate numerical electromagneticmodel of the antenna system. The model is used to simulate scatteringdata that is compared to its measured counterpart in order to reconstruct the image. In this paper an antenna system immersed in water is used to image differentcanonical objects in order to investigate the implication of modeling errors on thefinal reconstruction using a time domain-based iterative inverse reconstruction algorithmand three-dimensional FDTD modeling. With the test objects immersedin a background of air and tap water, respectively, we have studied the impact ofantenna modeling errors, errors in the modeling of the background media, and madea comparison with a two-dimensional version of the algorithm. In conclusion evensmall modeling errors in the antennas can significantly alter the reconstructed image. Since the image reconstruction procedure is highly nonlinear general conclusions arevery difficult to make. In our case it means that with the antenna system immersedin water and using our present FDTD-based electromagnetic model the imagingresults are improved if refraining from modeling the water-wall-air interface andinstead just use a homogeneous background of water in the model. Microwave imaging has received significant attention in the research community during the last couple of decades as a modality that potentially could improve the diagnostics of, for example, breast cancer tumors. Recent progress in the field has been reviewed in  and 2]..2]. TodaWhen performing microwave tomography the aim is to quantitatively reconstruct the dielectric parameters in the region under test. This involves solving a computationally challenging nonlinear and ill-posed optimization problem. The image reconstruction algorithm utilizes measured data that are compared against a corresponding numerical simulation of the system, and the dielectric profile is iteratively updated based on the difference between the simulation and the measurement. Even though this comparison requires a realistic numerical model for the best accuracy, most of the published works have used 2D models together with a calibration procedure to enable the comparison with experimental data. Largely, this can be attributed to a significant increase in the computational load when moving from 2D to three-dimensional (3D) modeling. However the electromagnetic scattering and consequently the reconstruction problems are inherently a 3D problem. Furthermore it is usually not possible to create realistic antenna models in 2D, except for line source antennas. By using a 2D model to solve the inverse scattering problem inaccuracies will therefore inevitably be introduced in the reconstructed image. This problem has been identified by the research community, and, with the ever increasing computational resources available these days, the focus is now more and more turning to solving the full 3D problem. Recent works using 3D algorithm have been reported in –11.In this paper we show several examples where images have been reconstructed from scattering data in order to discuss and illustrate the need for accurate modeling of the antenna system and its geometry to enable robust image reconstruction. The aim is also to get an understanding of what accuracy we could realistically expect in the reconstruction and how it is affected by various modeling errors. Examples of targets placed in a surrounding of air are studied, and in an effort to approach more biologically relevant settings we have studied examples where the antenna system was entirely immersed in water. The examples studied in this paper are entirely based on experimental measurement data. Our reconstruction algorithm, described in , is baseThe paper is organized as follows. In An iterative electromagnetic time-domain inversion algorithm has been used and applied in estimating the dielectric parameters of different test objects. The foundation of the algorithm is an electromagnetic solver based on the FDTD method, , is usedF, defined asEmn is the calculated field from the computational model and Emnm(t) is the corresponding measured data when antenna number m has been used as transmitter and antenna n as receiver. M is the number of transmitters, N is the number of receivers, and T is the duration of the pulse. In a 2D TM-mode formulation only one spatial field component is used in =∫0In search for the minimum of the objective functional it is differentiated with respect to the dielectric components by a first order perturbation analysis. In this way the Fréchet derivatives with respect to the conductivity and the permittivity of the functional are used to define gradients, in every grid point, inside the region. The gradients are used with the conjugate-gradient method together with the successive parabolic interpolation line search to minimize the objective functional. The reconstruction procedure is then iterated with the objective functional as a measure to monitor the convergence and to determine when the reconstruction is completed. Usually the minimization procedure converges within 10–20 iterations.Ω impedance to model the feed at the transmitting, receiving, and inactive antennas, [In the 2D simulations it is not possible to construct a realistic antenna model, but the transmitter is only modeled with a hard point source, in which the field strength is prescribed at the source position. At the receiver locations the field values are sampled directly from the corresponding E-field component in the grid. By contrast, the 3D algorithm allows for realistic antenna models. We are using the thin-wire approximation to model the monopoles, , and thentennas, , 20. Furntennas, .Sscatm is the measured reflection and transmission coefficients of the test object, Srefm(f) is a reference measurement of an empty system, and Erefs(f) is a corresponding reference simulation. Finally Ecalm(f) is the calibrated data used for comparing the FDTD simulations in the reconstruction process. This calibration procedure has been applied to the measured data for both the 2D and the 3D imaging examples in this paper.As already mentioned the solution of the inverse problem heavily relies on the comparison between the measured and the simulated scattering data. To compensate for systematic modeling errors a calibration procedure of the measured data is used such thatz, above the ground plane. The gradients computed in the grid cell plane immediately above the ground plane were copied upwards to the height of the test object. This method needs a priori information about the height of the reconstructed target. Since the reconstruction problem is both nonlinear and ill-posed, the resulting image strongly depends on the adopted regularization technique, the initialization of the reconstruction, and also the spectral content of the pulse. Here we used the same techniques as described in [In our experimental prototype the antennas are positioned in a plane. The possibility to accurately reconstruct out-of-plane objects is thus very limited: to do so it would be necessary also to make additional measurements outside the antenna plane. To allow imaging with the 3D algorithm of a test object with finite height, we implemented a heuristic pseudo-3D technique that assumed constant properties of the test object as a function of height, ribed in  to overc2. To measure the multistatic matrix each antenna is operated as a transmitter as well as a receiver. The microwave measurements are made with network analyzer Agilent E8362 B PNA which is a two-port network analyzer. To fully control the experiment a 2:32 switch multiplexer module, Cytec CXM/128-S-W, is used to automatically connect and disconnect the different combinations of antenna pairs to the network analyzer. The measurement strategy is to measure the multistatic scattering matrix at a large number of frequencies and to use that data to generate a time-domain pulse via an inverse Fourier transformation. In the experimental system 20 monopole antennas, each of length 19.5 mm and diameter 0.8 mm, are arranged evenly distributed on a circle with radius 100 mm. The circle of antennas is centered on a square ground plane with side length 250 mm mounted at the bottom of a tank, made of 1 cm thick perspex sheets with inner measures 350 × 350 mmIn our previous publication, , a detaiΩ where r < Rrd,To enable a quantitative evaluation of the accuracy of the reconstructed images we have adopted the relative squared error of the image, and for the permittivity image it is defined in , and anaϵr = 2.7 and σ = 0.015 S/m at 2.3 GHz. It was shaped like a cylinder with diameter 56 mm and height 20 mm and was placed at 14 mm offset in the y direction from the center of the antenna array. It had constant properties along its height in the z direction, and thus it is only necessary to show a cross-sectional slice of the dielectric profile. The FDTD model data is summarized in Rrd = 90 mm centered in the antenna array was used as the reconstruction domain together with the pseudo-3D approach described earlier. To investigate the accuracy of the reconstructed image with respect to the modeling, different lengths of the monopoles were used in the numerical electromagnetic model. The length of the monopoles in the antenna system is 19.5 mm, but images were reconstructed modeling the length as 16, 18, 20, 22, and 24 mm, respectively. This resulted in a change in the computed resonance frequency and the associated signal strength. The reconstruction results together with an illustration of the original dielectric distribution are shown in ϵr = 2.1, 2.2, 2.4, 2.7, 3.0, respectively, for the various monopole lengths. The minimum value is 12.5% smaller and the maximum value is 25% larger than what was obtained for the 20 mm monopole length. The recontructions of the conductivity are, however, not accurate, but it is clearly evident that the artifacts increase the more the monopole lengths deviate from the real value. The reason why the reconstruction is less accurate is that the difference in the imaginary part of the complex dielectric permittivity between the object and background is only a fraction in comparison with the difference in the real part. Reconstruction errors in the real part therefore overwhelm attempts to reconstruct the imaginary part, and consequently the accuracy is reduced. Compared to the original dielectric profile, however, the most accurate reconstruction of the permittivity is obtained for the 18 mm monopole. This reflects the deviaton of half a grid cell between the 20 mm antenna model and the precise length of the monopole with the real length being 19.5 mm. But also there is a tolerance in the cutting of the monopoles of about 0.5 mm. Numerical uncertainties in the FDTD solution and errors in the dielectric measurement of the sunflower oil are other reasons.With the purpose to study how the reconstructed image is affected by errors in the length of the monopole antenna model, we first studied a single dielectric target in an otherwise empty antenna array. The imaging situation was the same as in our previous publication, , that isIn ϵr = 77.5, σ = 0.05 S/m at 0.5 GHz. We also present a comparison between measured data and corresponding computed reflection and transmission coefficients. By replacing the air in the tank with water we further approach biologically relevant imaging scenarios. With the aim to study how modeling errors affect the reconstructed images we first studied how the forward modeling of the antenna system was affected by different antenna modeling errors.In this section we study the situation when the antenna array tank was filled with tap water, having dielectric properties The experimental situation was such that the tank was filled with ordinary tap water up to a level of 50 mm above the ground plane. In the FDTD model measured dielectric values of the water at 0.5 GHz were used as this was in the center of the frequency spectrum used for the imaging. In the FDTD modeling care was also taken to represent the physical reality as accurately as possible, and the corresponding settings are summarized in S21 for adjacent antennas has been plotted in Due to its simplicity, the hard source model is very appealing to use in FDTD simulations. However, it is not as accurate as the RVS when modeling the monopole feed. To quantify the errors associated with a hard source we investigate its applicability to model the monopole feed. In the first example, we replaced the RVS feed model with a hard source. In the second example, we used the hard source and completely removed the modeling of the rest of the monopole. The use of a hard source also implied that we could not use the transmitting antenna in the gradient computation as we do not calculate the reflection coefficient with the hard source model. Calculation of the reflection coefficient requires knowledge of the reflected wave, but since the E-field is directly set in the source cell, no update of the field will be made due to reflected waves. Instead we used only transmission data for the following reconstructions. As an illustration of the impact of the hard source on the simulated scattering data S11, and transmission, S21, coefficients have been plotted. For comparison the figures also contain the measured data and the data simulated with the full 3D FDTD model from S11 data show how the computed resonance frequency has increased about 0.5 GHz, and we can also see how the fast varying ripple due to the water-air interface reflections has vanished. Similar changes can also be seen in the S21 data.Solving the reconstruction problem is a computationally very demanding problem, and one strategy to reduce the simulation time is to reduce the size of the computational domain. Therefore we have investigated the need for modeling the exact volume of the water in the tank and instead modeled the water as a background directly terminated by CPML. The CPML is absorbing any outgoing wave and the result inside the computation domain is the same as if the simulation was made in an infinitely large space. In this FDTD simulation the entire computational grid was therefore assigned the properties of water, and as there were no need to model the water-air interface in the computational domain, the CPML could be moved closer to the antennas and thus the computational domain reduced. In We have also made a comparison with a 2D computational model. The reason is that the computation time is significantly reduced compared to the 3D case. Therefore a good understanding is desired of when the 2D approximation is applicable for imaging. In this section we show computed transmission data obtained with a 2D model, and also here two examples are considered. The first is the modeling of the volume of water in the tank as a 350 × 350 mm square in the 2D FDTD grid. In In the following section, we show the reconstructed images from experimental scattering data. Two different target models were used and reconstructed using the various antenna array models discussed above. The aim was to investigate the impact on the reconstruction caused by the different modeling introduced in Rrd = 80 mm. Two different targets were used in the reconstructions. The first was made of a mixture of deionized water and ethanol resulting in permittivity ϵr = 57 and conductivity σ = 0.11 S/m at the frequency 0.5 GHz. The mixture was filled up to height 50 mm in a thin-walled plastic cup with diameter 42 mm and immersed into the water for the measurement. The second target was a plastic rod with permittivity ϵr ≈ 2.5, conductivity σ ≈ 0 S/m, and diameter 15 mm.We have performed image reconstruction of targets immersed into ordinary tap water. In comparison to air a FDTD simulation of water is more time consuming due to the higher permittivity and the corresponding need for shorter time stepping in the FDTD algorithm. To save some computation time the reconstructions were therefore made using a multigrid technique where 10 iterations where performed on a (90 × 90 × 16) computational domain with grid size length 4 mm. The final reconstruction of the 10′th iteration was then taken as a starting point for 10 additional iterations on a (179 × 179 × 31) domain with grid size length 2 mm. The electromagnetic pulse had center frequency 0.5 GHz and FWHM bandwidth 0.5 GHz. The same pseudo-3D approach as previously described was used in a reconstruction domain of height 50 mm and radius Two different scenarios were reconstructed, the first with the center of the water/ethanol target positioned 39 mm from the center point of the antenna array. In δ = 0.42. In the conductivity we can perhaps see an indication of a target in the appropriate positions, but the image region is also cluttered with other artifacts, and comparison with the relative error is not meaningful. Furthermore the absolute values of the permittivity are not in total agreement with the original values, especially not for the small plastic target. With the same arguments as for the previous object in air where the conductivity also was badly reconstructed, it is not to expect anything else in this case. The difference between the background and the target made of water/ethanol mixture is about ℜ{Δϵr*} = 20 in the real part but for the imaginary part only ℑ{Δϵr*} = 2. For the plastic rod the difference is ℜ{Δϵr*} = 75 and ℑ{Δϵr*} = 2.The second scenario that was reconstructed included both targets, the water/ethanol mixture and the plastic target, and these results are shown in To assess the question of how the reconstructed image is affected by inaccuracies in the forward modeling we have taken the example with the two targets, the plastic rod, and the water/ethanol mixture and performed reconstructions with distorted electromagnetic models.δ = 0.54 and δ = 0.58, respectively. One can clearly see that, for the case where only the hard source was used to model the transmitter, the distortions of the reconstructed images are also the largest. This also corresponds to the case where the S-parameter data deviate the most from the measured data in Using the two altered antenna models with hard source feed new images of the original targets from Figures δ = 0.36 for the permittivity image, a decrease of about 14% compared to the reconstruction with the full 3D model in We have investigated the need of actually modeling the exact extent of the water volume in the tank. For this experiment we used the RVS feed thin-wire monopole model, and the algorithmic settings were otherwise identical to the previous examples but with the dielectric properties of water assigned to all the grid cells in the computational domain which was then terminated by seven layers of CPML. The reconstruction can be seen in For comparison we have also performed image reconstruction of the same targets using a 2D version of the algorithm. The first reconstruction made with the water tank modeled as a square of the single target as shown in Figures We have shown successful reconstruction of single and multiple targets immersed in water using a FDTD-based 3D reconstruction algorithm. By investigating various imaging scenarios we have also assessed the question of how the accuracy in the numerical forward model affects the reconstructed image. The results show that a realistic model of the antennas is necessary to achieve robust and reliable imaging. The same results also indicate that small modeling errors, such as in the length of the monopole, can have a clearly evident impact on the resulting image. For a simple antenna such as a monopole the modeling is very simple, and it is not difficult to produce a reasonably accurate numerical model using the thin-wire approximation and the RVS. However there is always an inherent limitation due to the finite grid size, and, when moving to more advanced antennas, such as patch antennas, modeling accuracy will become a more challenging task. Accurate antenna modeling requires a fine FDTD grid, but at the same time we must keep the grid as coarse as possible to lower the simulation time and memory requirement. Furthermore we have seen that when filling the tank containing the antenna system with normal tap water, the water-air interface causes significant reflections that are clearly identified in the scattering data. Despite this effect the accuracy of the reconstructed results is in fact improved when we instead use an open water model. This result shows that an apparent improvement in the antenna modeling and the corresponding computed scattering data is in fact not beneficial when it comes to imaging. One possible explanation could be that when comparing different models with similar modeling errors the nonlinearity of the reconstruction problem makes it impossible to predict the outcome. Instead the result will be strongly case dependent and to fully predict the result one would have to perform detailed studies of the particular imaging scenario.