Electrical Impedance Tomography - Thorax

Rafael Filipe Lopes Goncalvesrafael.goncalves@ist.utl.pt

Instituto Superior Tecnico, Lisboa, Portugal

October 2014

Abstract

In this paper a linear reconstruction software is proposed to reconstruct a human thorax. Thissoftware is intended to simulate an existing tomographic imaging technology, the Electrical ImpedanceTomography (EIT), that consists in the reconstruction of body interior distribution maps of thepassive electromagnetic properties. To accomplish this goal a numerical forward method, basedon the Finite Integration Technique, was first developed to modulate the interaction between theelectromagnetic radiation and the body, producing the required data to be subsequently used in theimage reconstruction process. This method was designed to be fully automatic, requiring minimal inputfrom the user. For the image reconstruction, the Back-Projection and the Filtered Back-Projectionmethods were implemented, along isopotencial lines calculated through the M”obius transformation.Still regarding the EIT image reconstruction, the applicability of the developed inverse problem wasfirst tested in a set of two dimensional phantoms, and later applied to a thorax obtained throughimage segmentation of a CT-scan. The results were satisfying in the sense that they demonstrate theapplicability of these technologies to the clinical environment.Keywords: Electrical Impedance Tomography, Thorax, Finite Integration Technique, 3D Reconstruc-tion

1. Introduction

Medical imaging, as a scientific investigation fieldthat constitutes a discipline in biomedical engineer-ing, refers to a large set of noninvasive technologiesused to “view” the human body in order to studyor treat medical conditions. In this bounded defini-tion, medical imaging can be seen as the solution ofmathematical inverse problems were properties ofliving tissues are inferred from the observed signal.

Since each of the existing medical tomographictechnologies, providing different information in a2D cross-section view of the body being imaged,consist in a way to measure the interaction of dif-ferent radiation types with the body under analysisone must first comprehend the underlying physi-cal phenomenon to understand and correctly inter-pret the obtained measurements. So, a model thatmimics these interactions must be formulated andextensively studied for a better insight of all phe-nomenons between the source and the sensing sys-tem.

Current tomographic techniques, like CT, mag-netic resonance imaging (MRI) and positron emis-sion tomography (PET), consists in a very expen-sive, huge and bulky system at the hospital. Forthese reasons a safe, low-cost, portable, and easy touse bedside system is needed for versatile clinical

diagnosis. Since Electrical Impedance Tomographyas the capability to fulfill all these specifications,but is still in the early stage of development andwith a lot of studies to be made regarding its effi-ciency and effectiveness, the author was allured totake part in this investigation effort.

Electrical Impedance Tomography (denoted byEIT) can be seen as an application of theBioimpedance method, that as been for the pastdecades studied and applied to a wide range of de-vices, in the biomedical field. EIT is an non-invasiveimaging technique that involves the formation of 2Dimages or 3D volumes from a map of the internaladmittivity distribution obtained from voltage mea-surements made at the boundary (δΩ) of the body(Ω) under analysis.

In the above stated the conditions, EIT may beregarded as the inverse problem to determine theadmittivity inside Ω. Besides ill-posed, because thesystem is under-determined due to the higher num-ber of variables that must be estimated when com-pared the independent data points in the EIT ac-quisition protocol, the problem of determining theimpedance inside the body is also non-linear.

To perform an EIT a four-electrode method is im-plemented to placed the electrodes in the δΩ bound-ary with respect to the Ω region under investigation.

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Figure 1: Domain and boundary regions for theEIT problem. Current injection and voltage sens-ing sites are also depicted. Electrodes marked asred circles.

A small amplitude current (1-10mA that flows in-side Ω) with a fixed frequency is applied in a set ofelectrodes, henceforth known as drive pair, and theelectrical potential at the other electrodes positionis recorded in a differential way between two otherelectrodes, known as receiver pairs [1]. This processis repeated for different drive and receiver pairs tocomplete a frame acquisition. For a high indepen-dent number of measurements at the disposal of thereconstruction there must be a high number of thisdrive and receiver pairs in each frame.

EIT systems can be seen in application through-out hospital departments like Cardiology, Gastroen-terology, and Tumor diseases due to the differencein admittivity recorded between tissues. Most EITsystems developed so far apply a small alternatingcurrent at a single frequency, however, there can befound some EIT devices that apply several frequen-cies to better differentiate tissues within the sameorgan.

The first images that appear to be made usingBioimpedance information are attributed to [2]. Animpedance camera, using a rectangular array of 100electrodes, was built to generate impedance maps ofthe thorax at rates up to 32 frames per second.

Even though [3] proposed a system for brainimpedance tomography made of a set of 128 elec-trodes, surrounded by an electrode guarding tomade the electric field uniform and to enable a fo-cused measure of the impedance by each electrode,the first system commercially available for clini-cal practice was the Sheffield Mark 1 - Mk1 - by[4]. In the Mk1 system 16 electrodes are placed,equidistantly, in the δΩ boundary. A 50KHz cur-rent is ejected between adjacent electrodes, in whatis known as the Sheffield Protocol, and then the po-

tential difference is measured in all the other re-maining adjacent electrodes. The reconstruction ofthe 2D image from the data obtained was conductedalong the equipotencial lines according the simplelinear backprojection algorithm.

It was after the Mk1 launch that EIT received anincreased attention within the scientific community,leading to a wide range of applications, that evenincluded neonatal brain imaging proposed by [5] forthe study of cerebral haemodynamic. In fact, andaccording to [1], in the mid to late 1980’s abouta dozen groups have developed their own systemand reconstruction software and by the mid 1990’sa study by [6] concluded that more than 30 re-search groups were actively engaged in EIT relatedresearch with main objectives areas like imaging oflung ventilation, cardiac function, gastric empty-ing, brain function and pathology, and screeningfor breast cancer.

The acquisition of anatomical and functional in-formation within the chest is very important for theproper treatment of cardiac, circulatory and venti-latory disorders. Given the variation of electricalimpedance within the thorax (strongly related tocardiac and ventilatory events) the EIT takes natu-ral place in the hospital environment for these tho-rax data acquisition. In the case of the lungs, tissueimpedance varies with the air content. Thus ven-tilation and changes of end-expiratory lung volumeresults in changes of the voltages measured by elec-trodes at the body surface.

Til this day, there were several research papersthat prove the benefits of EIT with animal mod-els. For example, in [7], EIT is compared withX-ray Computed Tomography (CT) to detect re-gional changes in lung volume in healthy lung an-imal models, a good correlation between the twomethods was demonstrated . Later, in [8] animalswere used to validate EIT for measuring regionalventilation distribution by comparing it with sin-gle photon emission CT (SPECT) scanning. Morerecently, in [9], EIT and PET were compared in or-der to quantify the changes in regional ventilation,obtaining in both models an excellent correlation.

In human testing it has been proven the possi-bility to perform cardiosynchronous averaging andproduce dynamic impedance images describing dif-ferent times in the cardiac cycle [10]. Later, sourcesof a cardiac-related electrical impedance waveformwere reconstructed using data from thoracic surfacemeasurements, which corresponded well with MRImeasurements of surface area changes of the tho-racic organs during the cardiac cycle [11]. More re-cently the influence of heart motion on EIT-basedstroke volume estimation was studied having ob-tained an EIT-based total ventricular volume es-timation error of −10.1 ± 15.7 ml and considered

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sufficiently low to be clinically useful in normal sub-jects [12].

All these studies showed that, despite EIT signalsbeing affected by myocardial motion, the results ob-tained are not compromised and so may be usefuland used in clinical environment.

Regarding thorax imaging and pathology diagno-sis, recent breakthroughs in the detection of pneu-mothorax (due to the presence of low-conductingair) and heamothorax (due to the presence of high-conducting liquids) were made using a system of16 electrodes with a 50 KHz and 5mApp injectioncurrent placed around the thorax[13]. At the sametime, a portable bio-impedance system was devel-oped for monitoring pulmonary edema [14]. Thesystem comprises an eight-electrode belt adjustableto different thorax sizes and injects currents with 3mA of amplitude and frequency of 20 kHz sequen-tially to the body in an opposite configuration whilevoltages are recorded by the tetrapolar method tobe used in a Newton-Raphson algorithm for imagereconstruction.

2. Forward ProblemResorting to the Finite Integration Technique forsimulation of the discrete space, and adopting theharmonic regime for temporal schemes, Maxwell’sequations and its physical entities are discretizedalong with the respective electromagnetic proper-ties of the materials matrices. In the end, and inorder to reduce computational complexity, an algo-rithm for local grid refining is applied and the cor-rect adjustments to the electromagnetic operatorsmade accordingly.

Finite integration technique (henceforth FIT) isa spacial discretization scheme for numerical imple-mentation of Maxwell’s Equations in both time andfrequency domain that preserves basic topologicalproperties of continuous equations such as conser-vation of charge and energy. This technique wasfirst introduced in 1977[15] and since then has beenenhanced and applied to solve electromagnetic fieldproblems over the years. This method stands outbecause of its flexibility in geometrical modeling ofthe domain of simulation with a limited number ofregular-shaped cells that can handle curved bound-aries and complex shapes[16][17].

With proven numerical efficiency and solidity[18],FIT generates exact algebraic analogues toMaxwell’s equations, which guarantee that physicalproperties of fields are maintained in the discretespace, and lead to a unique solution[19].

According to [18], a set of steps are defined forthe correct discretization of the problem:

1. Restriction of the electromagnetic problem,that usually represents an open boundaryproblem, to a simply connected and bounded

space domain of the region of interest.

2. Decomposition of the computational domaininto a finite number of disjoint cells, i.e. the in-tersection of two different cells is either emptyor it must be a two-dimensional polygon, aone-dimensional edge shared by both cells ora point.

This decomposition defines the main grid G, anda dual-grid G (see Figure 2(a)) is also defined un-der the premise that barycenters of cubes in grid Gform vertices of cubes in grid G according to Fig-ure 2(a). This brick-shaped decomposition is givenby a tensor product grid, in the cartesian space, de-fined by Equation 1 where the nodes (xi, yj , zk) areenumerated with the coordinates i, j and k alongthe x−,y− and z−axis, and the allocation of po-tencials, voltages and fluxes are on cell barycenters,edges and surfaces according to Figure 2(b).

G := Vi,j,k ∈ R3|Vi,j,k:= [xi, xi+1]× [yi, yi+1]× [zi, zi+1]

(1)

(a) Representation of a cell and dual cell.

(b) Electromagnetic quantities allocation.

Figure 2: FIT grid doublet - G; G

As stated before, local mesh refinement arise fromtime and computational impossibilities of solvinglarge problems with a single resolution mesh. Thisrefinement, consisting in the division of regular el-ements into sub-elements, is therefore a mandatoryrequirement to solve 3D problems once it enablesthe allocation of higher resolution elements wherethey are required (to better approximate to curvi-linear geometries or to accommodate a large varia-tion on the electromagnetic material properties like

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air-skin transition) and the allocation of lower reso-lution elements where the solution is of less interest.This prolongation and restriction in the mesh gridmay be responsible for some numerical instabilitiesdue to some level of geometry mismatch in the tran-sitions zones.

There is an extensive bibliography for local meshrefinement applied to electromagnetism problems.The first record dates back to 1962[20] in order tosolve elliptic partial differential equations, but itwas after the work of [21] that a consistent sub-gridding scheme was developed for FIT applica-tion. Since then several authors presented a va-riety of algorithms which led to an overall increaseof the flexibility of G,G while preserving the al-gebraic properties of the Maxwell-Grid-Equations[22, 23, 24, 25].

Despite several types of refinement found in liter-ature, in this paper the OcTree type mesh[26] wasconsidered because it enables high resolution cellsover the desired tissues but not in the space be-tween them. The OcTree is generated in a top-down approach by recursively subdividing each cellinto eight octants. Although this method effectiveapproach to subgridding problems, it lacks in effi-ciency due to its recursive nature, and so insteadof a tree like structure to allocate the grid cells amulti-linked list from coarser to finer resolution ele-ments was implemented (allowing a faster and morenatural navigation protocol within the grid).

Figure 3: Grid refinement structure. a) OcTree top-down approach. b) Multi-linked List

Because FIT requires an exact knowledge of eachcell position and its neighbors on every direction,in each subgriding step the neighbors are updatedand is established a connection between parent andchild as presented in Figure 3b). In regular grid thisneighbor attribution does not present great chal-lenge because in each direction the neighbors sharefour vertices, but for irregular grids the same is notverified.

3. Inverse Problem - ResultsThis Section will present the results for a linearmethod - Backprojection Algorithm - in image re-construction. Before this method application to the

3D image of a thorax from a set of CT images,the backprojection algorithm is studied in 2D forvariable phantom geometries, sizes and positions toaccess the model behavior and predict possible ar-tifacts present in the 3D EIT.

3.1. 2D Phantoms

The first result, in Figure 4, consists in one pro-jection of simple voltage difference. This poor out-come is due to the fact that the admittivity insidethe phantom besides being a function of the scalarelectric potential at the boarder is also dependenton the area between the isopotentials. For thisreason the backprojection data must be normal-ized using the potential between electrodes whenthe phantom has constant admittivity, also knownas reference data. This method, named differen-tial imaging, can only be applied if both data andreference data are acquired with the same injec-tion current.

(a) Isopotentials for sim-ple voltage difference be-tween electrodes. Color-bar in V

(b) Isopotentials in dif-ferential imaging. Color-bar in V/V

Figure 4: Backprojection isopotentials with adja-cent electrodes protocol for phantom with an in-creased conductivity sphere with 0.04cm radius atthe center of the mesh.

A more subtle argument implied that imagesshould be reconstructed with the log conductivityratio rather than the conductivity[27]. The resultsobtained for both cases, shown in Figure 5, are clearon the benefits of the log conductivity reconstruc-tion.

Artifacts, like the ones presented in the previ-ous figure, are commonly encountered in most clin-ical imaging systems, and may obscure or simulatepathologies. The artifacts that streaks the recon-structed images here presented, and in a similar wayas it is verified in CT, arise from the limited numberof projections used in the numerical reconstructionformula of the backprojection algorithm.

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(a) Ratio between dataand reference data.Colorbar in V/V

(b) log of the ratiobetween data andreference data. Color-bar in V/V

Figure 5: Backprojection reconstruction of thesame phantom presented in Figure 4 for a systemof 16 electrodes with adjacent electrode protocol.

If the number of electrodes increases, the influ-ence of these streaks in the image decreases as ex-hibit in Figure 6.

(a) 16 electrodes. Color-bar in V/V

(b) 32 electrodes. Color-bar in V/V

(c) 64 electrodes. Color-bar in V/V

(d) 128 electrodes. Col-orbar in V/V

Figure 6: Backprojection reconstruction with in-creasing number of electrodes.

In all Figures that follows a set of 64 electrodeswere chosen as a god compromise between imagesartifacts and computational burden.

The next set of results aims to study the re-construction algorithm for different phantom sizesand positions within the mesh. From Figures 7(a)and 7(b), with decreasing phantom sizes, is possibleto view the effects of backprojection blurring in thereconstructed images. Despite a decreasing abso-lute value in each of the reconstruction, as expected,the size of the phantom becomes increasingly diffi-cult to retrieve as the phantom reduces size due tothe blur. Figures 7(c) and 7(d) portrait the recon-struction of the same phantom (with 0.04 m radius)as it approaches the border. Once again the streak

artifacts become increasingly more evident as thephantom becomes closer to the border because theisopotencial lines from each injection pattern tendto “close” through the electrodes near the phan-tom. This overlap causes an artificial increase ofadmittivity between the phantom and the borderelongating the reconstruction. Finally, Figures 7(e)and 7(f), intend to show the reconstruction result ofseveral geometries within the phantom. It is clearthe influence of the isopotentials arcs in the recon-structed images, with a tendency to reconstruct allobjects as circles or with round edges. This is mostevident in the quasi-symmetrical ellipse (results notshown) and in the square phantom reconstructions.

(a) Phantom with 0.1 mradius.

(b) Phantom with0.07 m radius.

(c) Phantom centered at(x, y) = (0.2, 0) m.

(d) Phantom centered at(x, y) = (0.8, 0) m.

(e) Phantom ellipse.Major and Minor axis of0.12 m and 0.02 m.

(f) Phantom square.Edge of 0.1 m.

Figure 7: Backprojection reconstruction with differ-ent phantom sizes, placement and geometries. Col-orbar in V/V

Some studies have shown the importance ofelectrode placement to increase the reconstructionaccuracy[28][29], and in 2004 a new set of elec-trodes placement was proposed to decrease the re-construction error[30]. In fact, the reconstructionof near boundary structures with greater anatomicand physiologic importance is increased if the elec-trodes in that boundary region are placed with

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higher density. This method is of most value in thecases that a low number of electrodes is imposedby a limited hardware capacity. Figure 8 depicts areconstruction of a circular phantom with regularlyspaced and methodically spaced electrodes.

(a) 64 regularly spacedelectrodes.

(b) 64 methodicallyspaced electrodes.

Figure 8: Backprojection reconstruction of circu-lar phantom with 0.03 m and centered at (x, y) =(−0.06, 0.06) m. Colorbar in V/V .

The following results correspond to image re-construction of several phantoms with two areaswith increased/decreased conductivity relative tothe body within the electrodes. In Figure 9(a) theoriginal image with two areas with equal conduc-tivity is portrait and in Figure 9(b) the respec-tive reconstruction result. In the central imagesthe same phantom is used but in this case the twoareas possesses different conductivities but higherthan the body (Figure 9(c) and 9(d)). Finally inFigure 9(e), one area has higher conductivity andthe other lower conductivity when compared withthe body within the electrodes.

This array of images show evidence of a limitationin the EIT imaging technique. Unlike other imagingmodalities, where each radiation beam is indepen-dent from its neighbors, the same is not verified inEIT. Meaning that when an area of increased con-ductivity is present within the body there is a ten-dency for the electric field lines to direct themselvesto that area, and by doing so decreasing the imagecontrast for the remaining phantom. This effect isvisible in Figure 10 where a CT projection (on theleft) is compared with an EIT projection (on theright) of the same phantom.

The last phantom presented here was built witha more complex conductivity distribution map tostudy thorax imaging with the backprojection al-gorithm. Several elliptical domains were used torepresent the lungs, heart and spinal column andthe admittivities assigned to them were intended tosimulate tissues within the body[31]. The originalconductivity map is presented in Figure 11(a) andthe reconstruction result in 11(b).

In the reconstruction is clear the presence of allfour structures with the correct conductivity rela-tion between them. However, and as it was visible

(a) (b)

(c) (d)

(e) (f)

Figure 9: Backprojection reconstruction of multipleconductivity phantoms. (a),(c) and (e) are conduc-tivity maps. (b),(d) and (f) are the reconstructionresults. Colorbar of Figures on the left in S/m andon the right in V/V .

(a) CT photodetectorsintensity

(b) EIT electrods inten-sity

Figure 10: Normalized plots for one projection of acircular phantom.

(a) Phantom conductiv-ity distribution.Colorbarin S/m.

(b) Phantom recon-struction.Colorbar inV/V .

Figure 11: Backprojection image reconstructionfrom a phantom of a thorax.

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in all previous examples, the blurring effect makesit impossible to distinguish between structure bor-ders. To decrease this effect the filtered backpro-jection algorithm was studied.

The filtered backprojection algorithm consists inthe convolution, in time, of each one-dimensionalprojection with the 1/r blurring factor to removethe intensity of the backprojection image rolls. Thisis performed in the frequency space by multipli-cation of each projection Fast Fourier Transform(FFT) by a ramp filter that consists in the FFT ofthe 1/r blurring effect.

The filtered backprojection method, for instancein CT, works by assigning negative attenuationvalues to the radiation beams at transition placeswithin the phantom, reducing the 1/r blurring ef-fect induced in the backprojected image. How-ever, in the CT imaging technique the high numberof photodetectors allows some degree of projectiondata manipulation without compromising the endreconstruction. But in the EIT technique the lownumber of electrodes is directly proportional to thesignal resolution, which means that this manipu-lation may yield incorrect images reconstructions.This limitation is surpassed by a computational in-crease in the number of isopotencials. This waysome of the isopotencials may be assigned the nec-essary scalar potencial value to correct the overallblurring effect.

In the following set of Figures the results of mul-tiple filters in the filtered backprojection algorithmare presented.

(a) Ramlak filter. (b) Adapted blackman.

(c) Ramlak filter recon-struction.

(d) Adapted blackmanfilter reconstruction.

Figure 12: Filtered Backprojection reconstructionof phantom in Figure 11(a).

As expected and viewed in the spectral analy-sis of one EIT projection (Figure 13), the signal

is composed of small frequency components due tothe isopotentials geometry and the low number ofelectrodes. For this reason both standard Ramlak

(a) Full spectrum. (b) Close-up view.

Figure 13: Spectral analysis of one projection ofphantom in Figure 11(a).

and Blackman filters performed poorly in the recon-struction algorithm because of the low frequencycomponents attenuation when compared with thehigh frequency signal present in the data. With thisin mind an adaptation to the Blackman filter wasmade to reduce the high frequency signals influencein the reconstruction. This yielded a result whereall four thorax components are better distinguishedbetween them but with some level of geometry dis-tortion when compared with the original image.

3.2. 3D Thorax

In this section the computational mesh developedfor the simulation of the EIT forward problem wasbased on a CT scan of a male subject with 55 yearsold. Each CT slice was segmented, in a partition-ing process to divide each slice into a set of fivedifferent regions. This regions consisted in: Lung,Bone, Cardiac Muscle and Skeletal Muscle tissueand Blood. This segmentation was intended to sim-plify the CT scan into a more meaningful and easierto analyze model. The focus of the simulation is totest the backprojection algorithm in a 3D thoraxmodel. This mesh, subjected to refinements in theair to skin transition and in the heart region, pre-sented a total cell number Nc = 89370, a size of[x, y, z] = [0.40, 0.45, 0.15] meters centered at theorigin, a coarser element with edge Lc = 0.01 me-ters and the finer element with Lc = 0.005 meters.

The segmentation result from the CT-scan canbe seen in Figure 14.

The results of the backprojection algorithm in a3D thorax model were obtained in a similar wayas the one described previously. But unlike the2D case, in here a substantial approximation wasneeded to implement in order to accomplish the in-tended objective.

Because of the geometrical form of the isopoten-cial lines, 3D circumference arcs, it is not possible toplace the electrodes in the thorax (forming a sphere)

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(a) Posterior view.

(b) Lateral-Posterior view.

(c) Anterior view.

Figure 14: 3D Segmentation from CT-scan. Thoraxtransverse cut. Axis in meters

in a way that there are no possible escape paths be-tween the drive and receiver pair of electrodes. Forthis reason, the isopotencial line calculation wouldyield several pixels, increasing in number as theyapproximate the abdominal cavity and the cervicalregion, without any electrical scalar potential valueassigned from the distribution measured at the elec-trodes position. Because of this, a choice was madeto reconstruct the 3D thorax impedance model in asimilar way to the CT-scan were multiple 2D planesare reconstructed and later assembled in to the final3D model reconstruction.

The last approximation required for the 3D re-construction was due to the physical limitation ofthe electrode size and the current electronic de-vices capability to acquire, discretize and processthe electrical scalar potential obtained at each re-ceiver pair. And so, a set of twelve slices, each withsixty-four electrodes, were chosen to accommodatethe all the 768 electrodes. The slices in which theelectrodes were placed were chosen in order to ob-tain a better resolution in the central zone of themesh (where the heart is located) and decreasing inspace as one approximates the mesh Z- boundary.The remaining slices, where no electrodes are found,

were reconstructed via interpolation from the clos-est 2 pair of electrodes.

The results obtained with the backprojection al-gorithm for the 3D thorax reconstruction are pre-sented in Figures 15(a) and 15(b).

(a) Lateral-Posterior view. Colorbar in V/V .

(b) Superior view. Colorbar in V/V .

Figure 15: 3D Backprojection results for thoraximpedance imaging. Axis in meters

4. ConclusionsThroughout this article two problems were tack-led with computational electromagnetic models (theforward problem and the inverse problem) and eachof the bounded space was successfully discretizedto explore Electric Impedance Tomography imag-ing modality in 2D and 3D.

Based on the Finite Integration Technique, a soft-ware was designed to generate an octree type vari-able resolution mesh in a way that it allows a con-centration of increased resolution cells solely wherethey are needed (like the air-skin interface or theheart region) thus saving time to perform the dis-cretization of the domain and solve the forwardproblem. Given the mesh generation, as well as allother developed software, is automatic in the sensethat it only requires an input regarding the problemgeometry and its physical parameters (electrodesnumber and position, for instance) it is possible toperform quick changes in the computerized prob-lem to predict real prototypes behavior before theirdevelopment.

To measure the proximity of the FIT and gener-ated mesh behavior when compared with problemswith known results a set of tests were first imple-mented. Having established the correct modelingof the physics involved, a set of two dimensionalphantoms were proposed to access the reconstruc-tion method behavior, in particular the obtained ar-

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tifacts due to the phantom material properties (lo-cation, magnitude and geometry), number of elec-trodes and their distribution within the phantomborder. In the end, and as proposed in this the-sis, a software was developed to reconstruct thethorax internal electromagnetic properties from anCT-scan. In both inverse problems, solved usingthe Back-Projection and Filtered Back-Projectionlinear techniques, it was found that despite their se-rious limitations when more complex distributionswith multiple material properties are present theypreformed very well for objects with simple conduc-tivity distributions leading to the main conclusionthat Back-Projection EIT should only be used toapproximate tissue distribution within the thoraxor as an excellent first approximation to non-linearmethods.

Other important aspect that still needs develop-ment is the reproducibility of measurements notonly between patients but between measurementsin the same patient as well. This variability arisesbecause the calibration for every imaging recon-struction is made using a reference data set con-sisting in a measurement of a homogeneous field.But this, is not viable for in vivo reconstructions,and it may be that the mismatch between the mea-sured data and the predictions from the forwardmodel is dominated by the errors in electrode posi-tion, boundary shape and contact impedance ratherthan interior conductivity. And this difficulty leadsto problems in establishing a basal criteria or refer-ence value for particular measurement results. Thishappens because the scatter data results from prob-lems like electrode polarization, individual variabil-ity (the mesh used for each individual should bepersonalized for better results).

Although EIT presents some obstacles in the wayto became a common practice in clinical imaging,its capacity to perform real time monitoring in pa-tients or assist in medical guidance during smallarea surgeries (like the brain) allows an optimisticconclusion as far as the clinical perspective for EITin the near future.

Acknowledgements

The author would like to thank Professor Raul Mar-tins and Professor Isabel Rocha for the challeng-ing task proposed and for providing all the requiredconditions to carry out this project, and my fam-ily and friends, for giving me all the support andencouragement needed.

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