Reconstruction of Electrical Impedance Tomography Using Fish School Search, Non-Blind Search, and Genetic Algorithm

Reconstruction of Electrical Impedance Tomography Using Fish School Search, Non- Blind Search and Genetic Algorithm Valter A. F. Barbosa a,* , Reiga R. Ribeiro a , Allan R. S. Feitosa a , Victor L. B. A. Silva b , Arthur D. D. Rocha b , Rafaela C. Freitas b , Ricardo E. Souza a , Wellington P. Santos a,b a Departamento de Engenharia Biomédica, Unive rsidade Federal de Pernambuco, Cidade Universitária, Recife, PE, 50670-901, Brazil b Escola Politécnica da Universidade de Pernambuco, POLI-UPE, Madalena, Recife, PE, 50720-001, Brazil A BSTR ACT Electrical I mpedance Tomography (EIT) is a no ninvasive imaging t echnique that does not use ionizing radiation, with application both in environmental sciences and in health. Image reconstruction is p erformed b y solving an inve rse p roblem and ill-posed. Evolutionary Computation and Swarm I ntelligence have become a source of methods for solving invers e problems. Fish School Search (FSS) is a promising searc h and optimization method, based on the dynamics of schools of fish. In th is article we pres ent a method for reconstr uction of EIT images based on FSS and Non-Blind Search (NBS). The method was evaluated using numerical ph antoms consisting of e lectrical conductivity images with subjects in the center, between the center and the edge and on the edge of a circular section, with meshes of 415 finite eleme nts. We performed 20 simulations for each configuration. Results showed that both FSS and FSS -NBS were able to converge faster than genetic algorithms. Keywords: Elect rical To mography Impedance, image reconstruction, reconstruction algorithm, fish school search, non-blind search, genetic algorithm INTRODUCTION Ionizing radiation is commonly us ed in medic al im age machines, as m ammography, positron emission tomography or x -rays. Besides the benefits that using those electromagnetic waves ma y provide, there are many associated risks to whom operates those machines or is submitted to these kind of exams. Also, the prolonged exposition to ionizing radiation may cause many diseases, such as ca ncer (Rolnik & S eleghim Jr, 2006). Possibly , this issue is one of the most debated subjects in Public He alth all over the world, strengthening the search for imaging technolo gies that a re: efficient, low-cost, simple and safe to those that uses them. A promising im aging te chnique, that does not use ioniz ing radiation, is Electric I mpedance Tomography (E IT) (Be ra & Nagaraju, 2014; Rolnik & Sele ghim J r, 2006). E IT is about a non - invasive technique that builds images of an interior body (or an y object), using electrical properties, measured over the surface of interest. Those measure ments are acquired from electrodes’ disposition around the transversa l section of interest, and the application of a low amplitude and hig h frequency current through the m cre ates an ele ctric potential, known as ”border potential”. This low -voltage signal is measured and, in a computer, the y are used in a reconstruction al gorithm that rebuilds the image of the bod y’s inside regio n of interest (Rasteiro, Silva, Garcia, & F aia, 2011; Tehrani, Jin, McEw an, & van Scha ik, 2010; Brown, Barber, & Seagar, 1985). In medical sciences, EIT can be applied in several situations, such as: breast cancer (Cherepenin et al., 2001) , pulmonary ve ntilation monitoring (Alves, Amato, Terra,Vargas, & Caruso, 2014) , in the detection of pulmonary embolism or blood clots in the lungs (Chene y, Isaacson, & Newell, 1999). Likewise, it can be applied in fields as Botanics, generating ima ges of the trees’ trunks’ insides, allowing the knowledge of its biolo gical conditions without damaging it (Filipowicz & Rymarczyk, 2012 ); in monitoring multiphasic outflow in pipes (Rolnik & Seleghim J r, 2006); in Geophysics, E IT is largel y used to find underground storage of mi neral and different geological formations (Cheney et al., 1999). When compared with techniques, like Magnetic Resonance Tomograph y, or X-Ra y Tomography, EIT has a relatively low cost, since, in sim ple manners, it needs an equipment able to generate and measur e current and electric pote ntial, and a computer, able to rebuild the image (Tehrani et al., 2010) . Also, since it uses only the electrical properti es (conductivity and permittivity) of the bod y, there are no associated risk to its use, unlike acquisition methods that uses ionizing radiation. However, Electric Impedance Tomograph y ima ges have, sti ll, low resolution and undefined borders, which harms its popularity and diffusion among the imaging field. This motivates researchers of E IT to see k new methods of image reconstruction that are also able to o vercome these techniques disabilities, creating ima ges with good resolution and low computational cost, making of it a reliable and easy tool on disease s’ diagnostics. Mathematically, EIT reconstruction problem is known as ill -posed and il l-conditioned, meanin g that there are not onl y one solution (image) for a given potential bo rder distribution. Many algorithms are applied in order to solve E I T problem, and, however, the i mage generated is not totally reliable or well defined (Rolnik & Seleghim Jr, 2006). Thus, an alternative w ay used in the attempt of solving the EIT problem is managing it as an optimization problem, which the objective is minimize the relative error between the measured border pot ential of an object and the calculated border potential of the solution candidate ( Feitosa, Ribeiro, Barbosa, de Souza, & dos Sa ntos, 2014; Ribeiro, Fe itosa, de Souza, & dos Santos, 2014a, 2014b, 2014c). A heuristic that ma y be used in order to solve th is as an optimization proble m is the F ish S chool Search (FSS) (Bastos-Filho, de Lima Neto, Lins, Nascimento, & Lima, 2008; Bastos-Filho & Guimarães, 2015) . This technique is inspired in fish schools’ behavior on f ood search. The search process on FSS is made by a population which its individuals (the fishes) has a limited memor y. Each school r epresents a possible solution for the s ystem. The fishes inter act amon g e ach other and with the environment that surrounds them, an d, by influence of the col lective and individual movement’s opera tor and food operator, the sch ool incre ases the possi bility of c onvergence to the food surroundin gs, which means the best positi on a nd solution to that problem (Lins, Bastos-Filho, Nascimento, Junior, & de L ima-Neto, 2012). In this work, a re latively simple approach to image reconstruction problem of EI T is proposed, using Fish School S earch (FSS). However, it was modified, pr esenting two wa ys of solut ion candidates (fish) initialization: one completely random and other, amon g the random candidates, one solution derived from the Gauss-Newton reconstruction method. Taking into account Saha and Bandyopadhyay (2008) this initialization method was called Non-Blind Search. This work is organized a s following. In section Materials and Methods we present a brief on the theoretical foundations of Electrical Impedance Tomograph y and inverse problems, F ish School Search, Non- Blind Search, the experimental infrastru cture, and our proposal. In se ction Results and Discussion we present e xperimental result s and detailed discussi on. Finall y , in section Conclusion we present conclusions and some highlights of future developments. MATERIALS AND METHODS Electrical Impedan ce Tomography : Mathematical Formulation And Reconstruction Problems In EIT the estimate of the electrical conductivity distribution, inside a heterogeneous body or object, is made b y the resolution of a partial differential equation named Poisson’s Equation (Borcea, 2002; Cheney et al., 1999). The process to obtain the P oisson’s Equation is originated from the Maxwell’s Equations, it is starting from the Gauss’s law in point form (Tombe, 2012):     D (1) Where   is the divergent operator,  is the free electric ch arge in the int erest region, and D is the electric elasticit y given b y the multiplication of the electrical conductive distributi on ) ( u  in the point ) , , ( = z y x u and the Electrical field E , as a follow: E u D ) ( =  (2) Knowing that the electri cal field E is determined by the negative gradient (denoted b y the nabla symbol -  ) of the electrical potentials ( ) ( u  ), we have that: ) ( = u E   (3) In the reconstruction problem of E IT imag es we consider that there is no free electric charge in the interest region (i.e. 0 =  ). Taking that into account and replacing the Equati ons (2) and (3) in (1) we get the Poisson’s Equation (Borcea, 2002; Cheney et al., 1999) as given below: 0 = )] ( ) ( [ u u       (4) Besides, we also need to consider the following boundary conditions (Borcea, 2002):     u u u ext ), ( = ) (   (5)        u u n u u u I ), ( ˆ ) ( ) ( = ) (   (6) Where ) , , ( = z y x u is the position of a given object, ) ( u  is the potentials’ global dist ribution, ) ( u ext  is the electric potentials distribution on the surface electrodes, ) ( u I is the electric current applied on the interest region’s surface, ) ( u  is the electric conductivity distribution (i.e., the goal image),  is the interest volume,   is the volume border and ) ( ˆ u n is the border’s normal vector on    u position. Finding the electric potential of the surface electrodes ) ( u ext  , given the e lectric currents ) ( u I and the conductivit y distribut ion ) ( u  is named EIT’s Direct Problem, and modeled b y the following relation:        u u u u I f u ext ) ) , ( ), ( ( = ) (   (7) In Di rect Problem’s sit uation, the surface electric potentials estimative, when the internal conductivity distribution is already known, is calculated using the Poisson’s equation, shown in (4). Considering the contour condition, given by the following equation: J n = ˆ     (8) Where n ˆ is the surface’s normal vector and J corresponds to the electric current densit y (Baker, 1989) . It is important to e mphasize that there are no analytical solutions to (4) and (8), for an arbitrary given domain  . Nevertheless, an approximate solut ion to the border’s potentials ma y be obtained b y the Finite Elements Method (FEM), which converts the nonli near s ystem in (4) and (8) in the following linear equation’s system (Bathe, 2006; Castro Martins, Camargo, Lima, Amato, & Tsuzuki, 2012): 0 = ) ( C K     (9) Where ) (  K is a conductivity-dependent (  ) coefficients matrix and C is a constant’s values vector. In this w ay, it is possi ble to obtain an approxim ated value for the border potentials  , known as conductivity distribution  . While the conductivity distribution determination problem ) ( u  (tomographic image), given ) ( u I and ) ( u ext  is known as EIT Inverse Problem, modeled as follows:         u u u u I f u ext )), ( ), ( ( = ) ( 1   (10) In this situation it is possible to o btain the conductivity distribution ) ( u  by Poisson’ s equation solution (4), considering the contour conditions, mentioned in Equations (5) a nd (6). The Objective Function On EIT’s Reconstruction Images To consider the EIT’s image recon struction as an opti mization problem, the relative squared error was considered as the objective function (fitness function) b etween the object’s border measured electric potentials and the calculated ones, orig inated by the g enerated images, given by the candidate search algorithm (Feitosa et al., 2014; Ribeiro et al., 2014a, 2014b, 2014c) . In Equation (11), the fitness function ( ) ( x f o ) is given by:     2 1 1 2 1 2 ) ( = ) (                  e e n i i n i i i o V V x U x f (11) T n e V V V V ) , .. . , , ( = 2 1 (12) T n x U x U x U x U e )) ( ... , ), ( ), ( ( = ) ( 2 1 (13) Wh ere x represents a solution candidate on the search algorithm, V and ) ( x U the e lectrical conductivity distribution, measured and calculated on the border, and, e n the border’s electrodes number. Fish School Search Fish School Search (FSS) al gorithm is a meta -heuristic based on fish behavior for food se arch, developed b y Bastos Filho e Lima Neto, in 2007 (Bastos-Filho et al., 2 008; Bastos- Filho & Guimarães, 2015). The s earch pro cess on FSS is made by a population which its individuals (the fishes) have limi ted memory. Also, each fish in the school represents a p oint on fitness function domain. The FSS algorithm has four operators that can be classified in two classes: food and swimming. Food Operator Aiming to find more food, the fish on the school may move. Therefore, accordingly to its positions, each fish can be heavier or lighter (increase or de crease its wei ght), depending on how close th e y are from food (Lins et al., 2012 ). The food operator, then, quantifies how successful a fish is, due its fitness function variation. The fish weight is g iven by Equation 14, below: |} )] ( [ 1 )] ( [ {| m ax )] ( [ 1 )] ( [ ) ( = 1) ( t x f t x f t x f t x f t W t W i i i i i i       (14) Where ) ( t W i , )] ( [ t x f i represents the fish ’ i ’ weight and it s fitness function value at ) ( t x i , respectively. According t o Bastos-Filho et al (2008) the concept of food is related to the fitness function, i.e., in a mi nimization problem the amo unt of food in a regi on is inversel y proportional to the function evaluation in this region. Thus, in this case, the fish weight is given by the following expression: |} 1 )] ( [ )] ( [ {| m ax 1 )] ( [ )] ( [ ) ( = 1) (       t x f t x f t x f t x f t W t W i i i i i i . Swimming Operators The swimming op erators are responsible for the fish movements when the y are in th e food search, and are named as: individual movement operator, collective-inst inctive m ovement operator and collective-volitive movement operator, explained in details as below. The first swimming operator is the individual movement executed at the beginning of each algorithm’s iteration, wh ere each fish is displaced to a random position of its surroundings. An important characteristic of this movement is that the fish onl y executes th e individual movement if the new position, randoml y deter mined, is bett er than the previous one, meaning that it onl y occurs if the new position provides a better fitness function value. Otherwise, the fish will not execute the movement. The individual movement of each fish is given in Equation (15), 1 , 1 ] [  ran d is a vector composed by several numbers randomly generated with values between 1 , 1] [  , and ind st ep is a parameter that represents the fish ability o f exploration on the individual movement. After the individual mo vement’s calculus, the fish position is updated by Equation (16). 1 , 1 ] [ = 1) (     r an d st ep t x ind ind i (15) 1) ( ) ( = 1) (     t x t x t x i i i ind ind ind (16) This movement can be u nderstood as a disturbance in the fish position, to guarantee a wider way to explore the search space. There fore, to assure convergence at the end of the algorithm’s operation, the value o f ind st ep linearly decays, accordingly to Equation (17), where init i n d step and end i n d step are the initi al and final values of ind st ep , and, i t er a tio ns is the maximum iterations possible value of the algorithm. i t erati o n s st ep step t st ep t st ep end init i n d in d i n d i n d     1) ( = 1) ( (17) The second swimming operator of the FSS is the collective -instinctive movement. Is the one where the most well succ eeded fishe s on their individual m ovements attr acts to themselves other fishes. To execute thi s movement, it is considered the resultant direction vector, ) ( t I , given b y the weighted average of all individual movements of each fish, having as weight , its fitness value variation, given in Equation (18), where N is the total of fishes in the school. In the same wa y of the feeding operator, in minim ization problems the fitness variation in Equation (18) must be inverted. After the direction vector calculation, the fish position is updated, as shown in Equation (19).          N i i i N i i i in d t x f t x f t x f t x f x t I i 1 1 )] ( [ 1 )] ( [ )] ( [ 1 )] ( [ = ) ( (18) ) ( ) ( = 1) ( t I t x t x i i   (19) The colle ctive-volitive movement (the third and the last swimmin g ope rator) is based on the school’s global perf ormance (Lins et al., 2012). The collective-volitive movement is the tool that provides to the algorithm the ability to adjust the searc h space radius. Therefore, if the fish global weight incr eases, the search is characterized as well-succeeded and the fish radius search must diminish; otherwise, the same given search radius must increase, in order to enlarge the fish exploration, aiming to find better reg ions. In this movement, the fish’s position is updated in relation to the school’s mass center, as sho wed in (20).     N i i N i i i t W t W t x t Bary 1 1 ) ( ) ( ) ( = ) ( (20) Still, each fish’s moveme nt is made by (21), if the school’s weight is increasing, or b y Equ ation (21), if the school’s weight is decreasing. Also, in the same equations, mentioned above, [0 , 1 ] ran d is a v ector which values are randoml y generated between [0 , 1] , and vo l st ep is the parameter that represents the intensity of the fish searc h adjust intensity. )) ( ) ( [0 , 1 ]( ) ( = 1) ( t B ary t x rand st ep t x t x vol     (21) )) ( ) ( [0 , 1 ]( ) ( = 1) ( t B ary t x rand st ep t x t x vol     (22) Fish S chool Search algorithm’s pseudocode is given in Algorithm 1. Algorithm 1: Fish School Search 1. Initialize all the fish in random positions 2. Repeat the following (a) to (f) until some stopping criterion is met a) For each fish do: i) Execute the individual movement ii) Evaluate the fitness function iii) Execute the feeding operator b) Calculate the resulting direction vector - I(t). c) For each fish do: i) Execute the collective-instinctive movement d) Calculate the barycenter. e) For each fish do: i) Execute the collective-volitive movement f) Update the values of individual and collective- volitive step 3. Select the fish in the final school that has better fitness. Genetic Algorithm Genetic Al gorithm (GA) consists in a heuristic iterative process applied in search and optimization problems constituted by metaphors inspired b y the Evolutions Theories and Genetic p rinciples (Eberhart & Shi, 2011). The GA pseudocode is given in Algorithm 2. Algorithm 2: Genetic Algorithm 1. Initialize a random initial population 2. Repeat the following (a) to (e) until the stopping criterion is met a) Evaluate the fitness function to each individual b) Parent selection: Using Roulette Wheel individuals are selected to be rec ombined c) Recombination: New individuals are generated through 2-points crossover d) Mutation: gene of descendants is randomly selected and modified. e) Survivor selection: individuals of the next generation are selected using elitism and roulette whee l. 3. Select the individual's final population that has better fitness Non-Blind Search According to Saha and Bandyopadhyay (2008) i n order to avoid a totally random search and accelerate the optimization algorithm convergence, we need define the ini tial population of candidate solutions using s olutions obtained by imprecise, simple and direct methods (Saha & Bandyopadhyay, 2008). Our hypothesis is that the using of th e FSS to solve the ill-posed problem of EIT c an get reasonable solutions using a small number of iterations, when the initial population has one candidate solution constructed using noisy versions of the solution obtained by the Gauss- Newton method. Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software Electrical Impedance Tomography and Dif fuse Optical Tomography Reconstruction Software (EIDORS) is an open so urce so ftware developed for MAT LAB/Octave th at has as goal to solve the direct and inverse p roblems of the electrical impeda nce tom ography and diffu se optical tomography (Adler & L ionheart, 2006; Vauhkonen, L ionheart, Heikkinen, Va uhkonen, & Kaipio, 2001). This software allows its free modification , thus, we can easily ad apt it to the problem of this work. With EIDORS it is possi ble simulate different kinds o f meshes of finite elements that represents computationall y one cross-s ection of an object as well as its internal conductivity distribution in the form of colors. Proposed Method And Experiments Using E IDORS, three ground-truth images were created with mesh of 41 5 finite elements. The goal was detectin g irregular objects isolated in three positions: in the center, between the center and the edge and on the edge of the circular domain. The E IDORS parameters to create thes e images were: 16 electrodes, two- dimensional mesh (2D) with elements density ’b’ and electrode refinement level ’2’. The Figure 1 shows the three ground -truth images considered in this work. Twenty (20) simulations for each ground -truth image using Fish School Search without and with Non-Blind S earch and Genetic Algorithm were performed. The relative squared error w as used between the distribution of electrical potentials measured and calculated at the edge as fitness function for the heuristics considered in thi s work. Solution candidates (fish to FSS and individuals to GA) are real-valued vectors utilized as theoretical abstractions for possible dist ributions conductivity, where each dimension of the vector corresponds to a particul ar finite el ement on the mesh. For the simulations using Fish School Search, 100 fishes (solution candidates) were set as the school’s population, and the following parameters were de fined: 1 0 0 = 0 W , 0 . 0 1  init i n d st ep , 0 .0 0 0 1 = end ind st ep and i n d vol st ep st ep 2 = . Where as for the gene tic algorithm we used a population with 100 individuals, selec tion for the 10 best evaluated individuals, proba bility of r ecombination and mutation in 100 % and elitism of 10 individuals. The stop criterion for all methods was the number of iterations in 500 iterations. Figure 1. Ground-truth images with 415 elements for the object placed in (a) the c enter, (b) between the center and the edge and (c) on the edge of the circular domain. RESULTS AND DISCUSSION In this section, the obtained results, generated b y FSS with and without non-blind search will be compared with the previous results, obtained by the E IT research group of UFPE, using genetic algorithm. The main reason of this choice is ba sed on the fact that genetic algorithm produces ver y good and reliable results, making o f it a comparison para m eter for the new algorithms, used in this work. The Table 1 gives the fitness values of the best and the worst solutions obtained in twent y simulations for each ground-truth im age and each method. It is also given the mean and the standard deviation of the results obtained. As a m inimization problem, it is worth noting that the best solutions is given b y the lower values. Ana lyzing this table , we can notice that the perf orm of the three methods are similar. Actually, neither method outperformed the other s. One can say that in some case one method gave the best solution, for example, in the case where the object is between the center and the edge FSS+NBS gave the best solution, but the best solution for object in the edge was obtained by GA. In the same wa y, betwe en the worst solutions found by the methods, FSS gave the best and obtained the smaller standard deviation for object in the center. Table 1. The best and worst solutions, the mean and standard de viation for 20 simulations for FSS, FSS+NBS and GA. The results in C, CE and E are for the object in center, between the center and the edge and on the edge of the circular domain, respectively. Best Worst Mean Stnd. deviation FSS C 0.0198 0.0242 0.0219 0.0012 CE 0.0245 0.0306 0.0265 0.0013 E 0.0242 0.0600 0.0351 0.0089 FSS+ NBS C 0.0148 0.0308 0.0186 0.0038 CE 0.0174 0.0286 0.0229 0.0032 E 0.0376 0.0590 0.0446 0.0054 GA C 0.0182 0.0279 0.0220 0.0027 CE 0.0176 0.0276 0.0223 0.0029 E 0.0208 0.0467 0.0338 0.0069 The reconstruction algorithm’s behavior can be investi gated through results’ visual anal y sis , obtained from the reconstruction images’, generated by th e algorithms discussed in this article. Figures 2, 3 and 4 show the reconstruction results acquired from the Fish School Search algorithms without (FSS) and with (FSS-NBS) non-blind se arch, and Genetic Al gorithm, respectively, for objects placed in the center (a1, a2 and a3), between the center and the edge (b1, b2 and b3) and on the edge (c1, c2 and c3); in the circular domain for 50, 300 and 500 ite rations. Observing the ima ges mentioned above, it is possible to note that, with 50 it erations, the FSS+NBS algorithm, besides its low resolution, is capable of identif ying the objects on the circular domain, unlike the other methods (having, however, an exception for the result of pure FSS, with the object placed on the edg e of the interest’s region). I n 300 iterations, all methods are able to get images anatomicall y correct, c onsidering the low resolution of EIT’s images, being important to note that FSS and FSS+NBS showed better results than GA for this number of iterations. The algorithms’ final results (in 500 iterations) are of anatomically consistent and conclusive images, presenting little noise and good resolution. These results allow to conclude that the final obtained images of the three methods are similar in a qualitative analysis. Be ing so, the non-blind search application to FSS alg orithm made little difference on the anatomical quality of the image, instead happened in previous works made by o ur research group, where the non -blind search algorithm, applied to Genetic Algorithm (Ribeiro et al., 2014c) and Particle Swarm Optimiz ation (Feitosa et al., 2014) on the EIT problem, gave better results. Figure 2. Results using F SS for an object placed i n the center (a1, a2 and a3), be tween the center and the edge (b1, b2 and b3) and on the edg e (c1, c2 and c3 ) of the circular domain for 50, 300 and 500 iterations. Figure 3. Results using fish school search with non-blind search for an obj ect place d in the center (a1, a2 and a3 ), between the center and the edge (b1, b2 and b3) and on th e edge (c1, c2 and c3 ) of the circular domain for 50, 300 and 500 iterations. Figure 4. Results using genetic algorithm for an object placed in the center (a1, a2 and a3), between the center and the edge (b1, b2 and b3) and on the edge (c1, c2 and c3) of the circular domain for 50, 300 and 500 iterations. Quantitatively, the algorithm ’s performance can b e evaluated throu gh the me dium relative error (i.e., the fitness function) versus the it erations number graphic. The Fi gures 5, 6 and 7 show th e 20 simulations average error deca y versus the iterations number for the three reconstructio n image’s methods, in th e situations where the object is plac ed at the center, between the c enter and the edge, and on the edge, respectively. Through these graphics, it is possible to observe that the behavior of these algorithms convergence is similar to an ex ponential decay, and, in the qualitative analysis, the mentioned d ecay of the objective fun ction for FSS and FSS+NBS is quite similar to GA algorithm, having as an exception the f act tha t in the first iterations, th is fall for the formers algorithms is more a ccentuated than the latter on e. These quantitative results corroborate what was first noticed for the reconstructed images, in the qualitative analysis: FSS and FSS+NBS w ere able to generate consistent im ages with 300 iterations, although images obtained after 500 iterations were very similar for the three methods. During the experiments’ execution, it was noticed a very high dependence of the Fish School Search algorithm relied on individual movement. I n fact, this movement affects the fish weight update, the collective-i nstinctive and collective -volitive movements. Thus, the more well- succeeded fishes are those ones that presents bigger v ariation values of the fitness function (considering a minimization problem). This also explains the fact that the insertion of a fish on the first population, generated b y another method as Non -Blind Search did not significantly enh ance the algorithm’s performance. Figure 5. Average error of 20 simul ations in function of the number of iterations for the object in the center of the domain using Fish School Search without (FSS) and with Non -Blind Search (FSS+NBS) and Genetic Algorithm (AG). Figure 6. Average error of 20 simulations in function of the number of ite rations for the object between the center and t he edge of the domain using Fish School Search without (FSS) and wit h Non-Blind Search (FSS+NBS) and Genetic Algorithm (AG). Figure 7. Average error of 20 simulations in function of the number of iterations for the object on the edge of the domain using Fish School Search without (FSS) and with Non-Blind Search (FSS+NBS) and Genetic Algorithm (AG). CONCLUSION Electric impedance tomog raphy is a promising imaging technique, tha t has applications on engineering, s ciences and medical sciences field s. No wadays, the technique still presents low resolution image s, which explains the researchers’ efforts in this area. Thi s work proposed and investigated the F ish School Searc h algorithm with and without Non- Blind Search on EI T images’ reconstruction. In a general persp ective, w e can conclude that the use o f fish school search with solution candidates obta ined by usin g non -blind search bas ed on Saha and Bandyopadhyay’s Criterion (Saha & Bandy opadh yay , 2008) presented low contribution to the quantitative and qua litative FSS algorithm’s performance, fact th at can be explained by th e algorithm’s b ehavior, that fa vors the solution candidates considering its fitness variation during t he itera tive process and not the fitness value itself. The obtained re sults for the here propos ed methods for EIT problem’s solution we re compared to Genetic Algorithm, where the quantitative and qualitative results confirmed that Fish School Search is capable of generating results as good as the ones given by Genetic Algorithm. For future works, looking forward to solve pro blems related to software, we propose the investigation of FSS’ algorithm’s h ybridization with other methods, in order to improve E IT’s image reconstruction, a nd to compare it with other methods in the a ctual Evolutionary Computing state of Art, including t he h ybridization with NBS. This r esearch group will also focus on the migration of EIDORS from Matlab/Octave to a compiled or, at least, precompiled language, that supports experiments with parallel techniques and architecture, investigating software infrastructure and programming language s to achieve this goal. From the hardware point of vie w, parallel arc hitectures will be investigated, suc h as GPUs and clusters as and par allelism techniques, all of them to reduce the execution ti me of those al gorithms. Evolutionary algorithms tend to load in its definitions a hig h parallelism level, and, with FSS, this situation is not different, explaining why it is important to invest in researches on the fi elds mentioned above. AC KNOWLEDGMENTS The authors are grateful t o the Brazilian scientific agencies C APES and FACEPE, for the partial financial support of this work. REFERENCES Adler, A., & Lionheart, W. R. (2006). Uses and abuses of E IDORS: An extensible software base for EIT. Physiological Measure ment, 27(5), S25. Alves, S. H., Amato, M. B., Terra, R. M., Vargas, F . S., & Caruso, P. (2014). Lung re aeration and reventilation after aspiration of pleural effusions. a stud y using electrical impedance tomograph y. Annals of the American Thoracic Society, 11(2), 186 – 191. Baker, L. E. (1989). Prin ciples of the impedance technique. IEEE Engineering in Medicine and Biology Magazine: The Quarterly Magazine of t he En gineering in Medicine & Biology Soci ety, 8(1), 11. Bastos-Filho, C. J ., de Lima Neto, F. B., Lins, A. J ., Nascimento, A. I., & Lima, M. P. (2008). A novel search algorithm based on fish school behavior. In Systems, Man and Cybernetics, 2008. SMC 2008. IEEE International Conference on (pp. 2646 – 2651). Bastos-Filho, C. J. A., & Guimarães, A. C. S. (2015). Multi-objective fish school search. International Journal of Swarm Intelligence Research (I J SIR), IGI Global, 23 – 40. Bathe, K.-J. (2006). Finite element procedures. Klaus-Jurgen Bathe. Bera, T. K., & N agaraju, J . (2014). Electrical impedance tomography (EIT): a harmless medical imaging modality. Res earch Developments in Computer Vision and I ma ge Processing: Methodologies and Applications, IGI Global, 235 – 273. Borcea, L. (2002). Electrical impedance tomography. I nverse prob lems, 18(6), R99. Brown, B., Barber, D., & Sea gar, A. (1985). A pplied potential tomograph y: possible clinical applications. Clinical Phy s ics and Ph y siological Measurement, 6(2), 109. Castro Martins, T. d., Camarg o, E. D. L. B . d., Lima, R. G., Amato, M. B. P., & Tsuzuki, M. d. S. G. (2012). I m age recon struction using interval simulated annealing in electrical im pedance tomography. IEEE Transactions on Biomedical Engineering, 59(7), 1861 – 1870. Cheney, M., Isaacson, D., & Newell, J. C. (1999). Electrical i mpedance tomograph y. S IAM review, 41(1), 85 – 101. Cherepenin, V., Karpov, A., Korjenevsky, A., Kornienko, V., Mazaletska ya, A., Mazourov, D., & Meister, D. (2001). A 3D electrical impedance tomogra phy (EIT) system for breast cancer detection. Physiological Measurement, 22(1), 9. Eberhart, R . C., & Shi, Y. (2011). Computational intelligence: concepts to implementations. Elsevier. Feitosa, A. R., Ribeiro, R . R., Barbosa, V. A., de Souza, R. E., & dos Santos, W . P. (2014). Reconstruction of electrical imped ance tomography ima ges usin g particle swarm optimization, genetic algorithms and non-blind search. I n 5 th ISSNI P- IEEE B iosignals and Biorobotics Conference (2014): Biosigna ls and Robotics for Better and Safer Living (BRC) (pp. 1 – 6). Filipowicz, S. F., & R ymarczy k, T. (2012). Me asurement methods and image reconstruction in electrical impedance tomography. Przegla˛d Elektrotechniczny , 88(6), 247 – 250. Lins, A., Bastos-Filho, C. J., Nascimento, D. N., Junior, M. A. O., & de Lima -Neto, F. B. (2012). Analysis of the performance of the fish school search algorithm running in graphic processing units. Theory and New Applications of Swarm Intelligence, 17 – 32. Rasteiro, M. G., Silva, R. C., Garc ia, F. A., & Fa ia, P. M. (2011). Elec trical tomog raphy: a review of configurations and applications to particulate processes. K ONA Powder and Particle Journal, 29(0), 67 – 80. Ribeiro, R. R ., Feitosa, A. R., de S ouza, R. E., & do s Santos, W. P. (2014a). A modified differential evolution algorithm for the reconstruction of electrical im pedance tomo graphy images. In 5 th ISSNIP-IEEE Biosignals and Biorobotics Conference (2014): Biosi gnals and Robotics for Better and Safer Living (BRC) (pp. 1 – 6). Ribeiro, R. R., Feitosa, A. R., de S ouza, R. E., & dos S antos, W. P . (20 14b). Reconstruction of electrical impedance tomography im ages using chaotic selfadaptive rin g-topology differentia l evolution and genetic algorithm s. In 2014 IEEE International Conf erence on S ystems, Man, and Cybernetics (SMC) (pp. 2605 – 2610). Ribeiro, R. R., Feitosa, A. R., de Souz a, R. E., & dos Santos, W. P. (2014c). Reconstruction of electrical impedance tomograph y ima ges using genetic algorithms and non-blind search. In 2014 IEEE 11 th International Sy m posium on Biomedica l Imaging (ISBI) (pp. 153 – 156). Rolnik, V. P., & Seleghim Jr, P. (2006). A s pecialized g enetic al gorithm for the e lectrical impedance tomography of two-phase flows. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 28(4), 378 – 389. Saha, S., & Band yopadhy a y, S. (2008). Application of a new s y mmetry- based cluster validit y index for satellite image segmentation. IEEE Geoscience and Remote Sens ing Letters, 5(2), 166 – 170. Tehrani, J. N., J in, C., McEwa n, A., & van Schaik, A. (2010 ). A comparison between compressed sensing a lgorithms in e lectrical impedance tomog raphy. In 2010 Annual I nt ernational Conference of the IEEE Engineering in Medicine and Biology (pp. 3109 – 3112). Tombe, F. D. (2012). Maxwell’s original equations. The General Science Journal. Vauhkonen, M., Lionheart, W. R ., Heikkinen, L. M., Vauhkonen, P. J., & Kaipio, J . P. (2001). A MATLAB package for the E IDORS project to reconstruct two-dimensional E IT images. Physiological Measurement, 22(1), 107.