Finite Element Method based Modeling of a Sensory ...

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ScienceDirect Procedia Technology 10 (2013) 262 – 270

International Conference on Computational Intelligence: Modeling Techniques and Applications (CIMTA) 2013

Finite Element Method Based Modeling of a Sensory System for Detection of Atherosclerosis in Human using Electrical Impedance Tomography Deborshi Chakrabortya*, Madhurima Chattopadhyayb* a Department of Instrumentation Science, Jadavpur University, Kolkata: 700 032, West Bengal , India Department of Applied Electronics and Instrumentation Engineering, Heritage Institute of Technology, Kolkata: 700 107, West Bengal, India

b

Abstract This paper presents a simulation based study on identification of atherosclerosis in human blood vessels through Electrical Impedance Tomography (EIT) technique. Atherosclerosis is a vital coronary disease in which plaque (a solid substance made of fat, cholesterol, calcium and other substances found in blood) builds up inside the arteries and can lead to serious problems, including heart attack, stroke, or even death. In this work, a non-invasive imaging technique based on the variation of electrical conductivity (and/or relative permittivity) values of the body tissues have been proposed for detection of atherosclerosis. Here, we have modeled the 2D structure of vessels within a closed specified environment. The 2D model is then transformed to 3D platform for analysis. The clots inside the blood vessels have varying electrical conductivities (and/or relative permittivity’s) in comparison to that for the blood vessels. Thus, by maintaining a potential difference on the electrodes, which are placed on the body surface, the variation of potential field are obtained along a 2D plane by utilizing the forward solver problem of Electrical Impedance Tomography (EIT). The simulation model and their respective studies are performed in Finite Element Method based Multiphysics Software platform. © 2013 2013 The © The Authors. Authors.Published Publishedby byElsevier ElsevierLtd. Ltd. Selection and peer-review under responsibility of the University of Kalyani, Department of Computer Science & Engineering. Selection and peer-review under responsibility of the University of Kalyani, Department of Computer Science & Engineering Keywords : Finite Element Method (FEM); atherosclerosis;Electrical Impedance Tomography (EIT) ;Potential distribution; blood vessels

1. Introduction * Corresponding author. Tel.: ,+91-9674789961, +91-9433041667;

E-mail address:madhurima02gmail.com, [email protected]

2212-0173 © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the University of Kalyani, Department of Computer Science & Engineering doi:10.1016/j.protcy.2013.12.360

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The main cause of unstable angina, acute myocardial infarction, and sudden cardiac death is the rupture of high-risk vulnerable plaques. Therefore, techniques capable of detecting vulnerable plaques play an important role in evaluating the coronary arteries. By taking advantage of the significantly low electrical conductivity of plaques, an impedance-based tomography approach is proposed in this study for detecting stenotic plaques. Image reconstructions, carried out with the differential imaging method, yield fairly good cross-sectional images of the modelled conductivity changes induced by atheroma, and demonstrate the feasibility of the proposed approach for plaque detection [1, 2]. In relation to this context, atherosclerosis is a vital coronary disease in which plaque (plak) develops inside the arteries. Arteries are blood vessels that carry oxygen-rich blood to our heart and other parts of our body. Plaque is made up of fat, cholesterol, calcium, and other substances found in the blood. Over time plaque hardens and narrows our arteries. This limits the flow of oxygen-rich blood to our organs and other parts of our body. Serious problems including heart attack, stroke, or even death can be caused by atherosclerosis.

Fig. 1. Picture explaining the principle of atherosclerosis [3]

Researchers and scientists all round the world are finding viable techniques for the detection of atherosclerosis. Detection of Coronary Atherosclerosis by Multi–detector Row CT Coronary Angiography was proposed by Vogl, Thomas J. et al.[1], Ruehm, Stefan G., et al. suggested rapid magnetic resonance angiography for detection of atherosclerosis [2] etc. In this paper, relatively new approach is made to detect arthrosclerosis utilising the principle of Electrical Impedance Tomography (EIT). EIT is based on the principle of image reconstruction technique in ( LV UHFRQVWUXFWHG IURP WKH ERXQGDU\ which the electrical conductivity or resistivity of a conducting domainŸ  potentials developed by a constant current or voltage signal injected at the domain boundary (˜Ÿ DVVKRZQLQ)LJ 2(a) [4,5] and this can be applied for the detection of the arthrosclerosis in humans. (a)

(b)

Fig. 2. (a) Explanation of EIT Principle, (b) A medical EIT schematic: Electrode array attached to the patient’s body

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In this paper, model of blood vessels with and without colts are designed in 2D plane. These 2D structures are then transformed to 3D platform. A rectangular block is considered within which the vessel is placed. This block is assumed to be a slice of human body having relative permittivity similar to that of the body fluid. The clots within the blood vessels have different relative permittivities in comparison to that of the vessel and also the medium enclosing it. Thus, by EIT principle the variation of the potential field is obtained along the x-y plane. From which the presence or absence of any clots or atherosclerosis within the vessel can be determined. Nomenclature conducting domain domain boundary electrical conductivity spatial potential outward normal vector to the electrode surface transformation matrix relating Ɏ to ı

Ÿ ˜Ÿ ı ĭ Ș K

2. Mathematical Model )RU D NQRZQ FRQGXFWLYLW\ D UHODWLRQVKLS FDQ EH HVWDEOLVKHG EHWZHHQ WKH HOHFWULFDO FRQGXFWLYLW\ ı  DQG Vpatial SRWHQWLDOĭ ZKLFKIXUWKHUEHXVHG for calculating the nodal potentials [6, 7]. Electro-dynamics of EIT is governed by a nonlinear partial differential equation, called the Governing Equation [6,7] of EIT, is given by, ’ x ı ’ĭ

0

(1)

The potential field inside of the conductor must satisfy Eq. (1) as it does not carry any internal electrical sources or sinks. To solve this equation, the following boundary conditions are to be known. 2.1. Dirichlet Boundary Condition:

)

)i

(2)

where, i =1…N, are the measured potentials on the electrodes. 2.2. Neumann Boundary Condition:

³

w) V wK

w:

­ I ° ® I °0 ¯

     

Here, +I is represents the source electrode, and -I is for sink electrode and 0 for other boundary values. ˜ɎLV WKH ERXQGDU\DQGȘLVWKHRXWZDUGQRUPDOYHFWRUWRWKHHOHFWURGHVXUIDFH 2.3. Forward Problem A relation can be obtained between the voltage measurements made on the boundary ˜Ÿ  DQG ( WKH GRPDLQ

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Deborshi Chakraborty and Madhurima Chattopadhyay / Procedia Technology 10 (2013) 262 – 270

conductivity can be found [6, 7] as, )



KV

:KHUHıLV D YHFWRU RI FRQGXFWLYLW\ YDOXHV Ɏ LV WKH YHFWRU RI YROWDJH PHDVXUHPHQWV DQG . LVWKH WUDQVIRUPDWLRQ matrix relating Ɏ to ı.

ı ’ x V’)

ĭ 0

.

Fig. 3. Block diagram representation of the Forward Problem in Electrical Impedance Tomography

In order to calculate the nodal potentials of the domain, Eq. 1 can be solved numerically using FEM if .DQGıare known. It is known as the “forward problem”. Thus, for a known value of a constant current, the nodal potentials within the phantom area are computed using the forward solver problem of EIT [8, 9]. The value of the conductivity and permittivity of the blood, body fluids etc. of the designed FEM model are obtained from Luepschen et al. [10], T. Sun et al.[11] and D. Ferrario et al.[12]. 2.4. Inverse Problem Using Eq. 4, we have

V

1

K )

(5)

That means if transformation matrix K DQGWKHVXUIDFHSRWHQWLDOVɎDUHNQRZQWKHQWKHFRQGXFWLYLW\ ıFDQEH mapped. This is known as the “inverse problem” [13]. 2.5. Forward Problem computation in Electrical Impedance Tomography Forward Problem (FP) is the basis of EIT and it is essentially to be solved to calculate the boundary potentials for obtaining the update value of the conductivity for all the iteration in inverse problem (IP). A FEM based EIT forward solver on FEM Multiphysics software platform is used to solve the boundary potentials of the phantom under consideration. Due to its ability to model arbitrary geometries and various boundary conditions the FEM is the most currently method used for obtaining the numerical solutions for EIT problems [14, 15]. The finite element method reduces continuum problem of infinite dimension to discrete problem of finite dimension in which the nodal values of the field variables and the interpolating functions completely defines the behaviour of the field within the elements and thus the individual elements collectively define the behaviour of the field over the entire medium [16]. Most of EIT systems work with the linear shape functions in which all the nodes lies on the element boundaries where the adjacent elements are connected [16].

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2.6. Steps computed during the simulation x

Step1. Geometrical modeling of the sensor Includes: 1. Selection of Spa p ce dimension 2. Ad 2. Add d Ph Phys ysiics ics Mod Modul dule le (AC AC/D /DC /D C, C, Elec El ectr tros osta tati tics ics etc.)) 3. Sellectiion off stud d y typ ype (S ( tationary, i y, Transient etc.))

x

Includes: 1. Selection of units (m/cm (m/ /cm et etc. tc.)) 2. Angu Angullar lar un uniit it ( eg (d grees,, radi dians))

Step 2. Initialization of electrical parameters and the boundary conditions Includes: 1. Setting g the conductivity y, relative p rmit pe itiivit itiies vallues off th the obj bjects t und un der co der cons nsid ider id erat ati tion ion (B (Bas ased d on AC//DC AC /DC, ellectro t sttati tics sttuddy). )

Relati Rela tive ve Permittivity value of body fluid = 98.56 56 and d Conduc d tiivity i = 1.5500 0000 00(S (S//m)) [10 10]]

Includes: 1. Setting g the values of the ap ppl p ied p tenti po tiall and d init itiiali lizing i g the cond ndit dit itiion ion off insullat ati tion ion on the he sid si ides des off the he co cons nsid ider id ered d phant hantom om.

Relative Permittivity y value of blo lood od = 519 197 7.70 70 and an d Co Cond nduc ucti tivi vity ty = 0.70 7008 080( 0(S/ S/m)) [10 10]]

Deborshi Chakraborty and Madhurima Chattopadhyay / Procedia Technology 10 (2013) 262 – 270

x

Step 3. FEM based discretization of the geometry under consideration (Meshing)

Includes: 1. Selection of mesh ty ype p ( riangu (t i g lar,, tetrah t hed dral, l, bi biqu q ad, d, pollygo po l ygon n et etc tc.)), mes esh h si size ize (i.ee. no. off eleme lement ntss, seq eque uenc ncee ty type pe (us user er controlled).

x

Step 4.Computation of study and analysis of results

Incl In clud cl udes ud es:: es 1. Co 1. Comp mput mp utat ut atiio at ion off Stud ion udy dy Includes: 1. An 1. Anal alys al ysis ys is of th thee re resu sult su lt wit ith h 2 dime di mens me nsio ns iona io nall an na and/ d/or d/ or 3 dim imen ensi en sion si onal on al g ou gr oupp pl p ot ots. s. 3. Simulation Model

Fig. 4. Images of the constructed models (a) blood vessels without blood clots (2-D and 3-D view) and (b) blood vessels with clots at two different positions (2-D and 3-D view).

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(b)

(a)

Fig. 5. Images of the constructed models with meshing (Maximum element size: 0.044 cm, Minimum element size: 4.4e-4 m, Maximum element growth rate: 1.3, Resolution of the curvature: 0.2, Resolution of the narrow region: 1)

Two simulation models are considered which are shaped like human blood vessels, shown in Fig. 4, in which Fig. 4(a) represents a vessel without any clots and Fig. 4(b) represents vessels with blood clots at two different positions. The two models are first considered in two dimensional (2-D) plane and then transfer to three dimensional o (3-D) simulation platform. The relative permittivity and conductivity values of the blood vessels and body fluids designed in the simulation model are a noted from Luepschen et al. [10]. A potential of 10V p-p (4mA, 1 kHz) is applied at the top face and reverse side is kept grounded. All the other sides of the considered block (within which the blood vessel is placed) are insulated. To compute the FEM based study of the models meshing were performed. The details of the meshing are provided in Fig. 5. 4. Results and Discussions

Position along x axis Fig. 6. Variation of potential distribution (microvolt) on x-y plane for the vessel without clots

It is observed from the Fig. 6 that when there are no clots within the vessel, the change of the potential distribution on the x-y plane is not sharp. But, presence of clots shows a sharp change of the potential distribution along their respective positions as can be distinctly visualised from Fig. 7.

Deborshi Chakraborty and Madhurima Chattopadhyay / Procedia Technology 10 (2013) 262 – 270

Position along x axis Fig. 7. Variation of the potential distribution (microvolt) on x-y plane for the vessel with clots

5. Conclusions In this simulation based study the atherosclerosis in human is determined by Electrical Impedance Tomography. Thus, the variation of the potential distribution in the results reveals the presence or absence of colts within the blood vessels. A study and detection of atherosclerosis is required since it leads to coronary thrombosis of a coronary artery, causing myocardial infarction (a heart attack). The same process in an artery to the brain is commonly called stroke. Another common scenario in very advanced disease is claudication from insufficient blood supply to the legs, typically caused by a combination of both stenosis and aneurysmal segments narrowed with clots. EIT is a non radiating, safe, portable and affordable medical imaging technique [19]. A real time analysis to detect atherosclerosis in the human thorax is carried with 16 Ag-AgCl electrode arrays and is demonstrated in Fig. 8(a). A sinusoidal potential of 8 volt with frequency 100 KHz is injected across a pair of the electrodes and the potentials from the other electrode pairs are measured using the neighbouring protocol of EIT [17]. The data are stored and reconstructed in FEM Multiphysics software platform using forward solver to obtain the voltage density plot (shown if Fig. 8(b)). Fig. 8(b) shows the variation of the potential within the thorax due to the variation of the conductivity of the tissues [18].

Fig. 8.(a) 16 Ag-AgCl micro electrode array attached to the human thorax for detection of atherosclerosis, (b) voltage density plot of the arrangement shown in (a).

However, the spatial resolution of EIT system is poor. In real time analysis, the performance of EIT system can be

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improved by using more number of electrodes and increasing frequency of the current source. The colour of FEM graph indicates the presence, the type and the location of the clots within the specified area of interest. Acknowledgements Authors like to acknowledge Heritage Institute of Technology for providing financial assistantship to carry out this research work. References 1. Vogl, Thomas J., et al. "Techniques for the Detection of Coronary Atherosclerosis: Multi–detector Row CT Coronary Angiography1." Radiology 223.1 (2002):212-220. 2. Ruehm, Stefan G., et al. "Rapid magnetic resonance angiography for detection of atherosclerosis." The Lancet 357.9262 (2001):1086-1091. 3. http://cardiologydoc.wordpress.com/2012/02/14/optimal-medical-therapy. 4. Denyer; C.W.L., “Electronics for Real-Time and Three-Dimensional Electrical Impedance Tomographs”, PhD Thesis, Oxford Brookes University, January 1996. 5. Metherall; Peter, “Three Dimensional Electrical Impedance Tomography of the Human Thorax”, PhD Thesis, University of Sheffield. 1998. 6. Alistair Boyle, Andy Adler, and William R. B. Lionheart; “Shape Deformation in Two-Dimensional Electrical Impedance Tomography”; IEEE Transactions on Medical Imaging, Vol. 31, No. 12, December 2012. 7. Tushar kanti Bera, J.Nagaraju; “A FEM-Based Forward Solver for Studying the Forward Problem of Electrical Impedance Tomography (EIT) with A Practical Biological Phantom”; Proceeding of 2009 IEEE International Advance Computing Conference (IACC 2009),6-7 March, 2009, Patiala, India. 8. Bushberg; J. T., Seibert; J. A., Leidholdt Jr.; E. M., Boone; John M., “The Essential Physics of Medical Imaging”, 2nd Edition, Lippincott Williams & Wilkins, ISBN-10: 0683301187. Bryan R. Loyola, Valeria La Saponara, Kenneth J. Loh, Timothy M. Briggs,Gregory O’Bryan, and Jack L. Skinner; “Spatial Sensing Using Electrical Impedance Tomography”, IEEE Sensors Journal, Vol. 13, No. 6, June 2013. 9. Yorkey; T. J. “Comparing reconstruction methods for electrical impedance tomography” PhD thesis, University of. Wisconsin at Madison, Madison, WI 53706, 1986. 10. Henning Luepschen et al., “Modeling of Fluid Shifts in Human Thorax for Electrical Impedance Tomography”, IEEE Transactions On Magnetics, Vol. 44. No. 6. June 2008. 11. Tao Sun, Soichiro Tsuda, Klaus-Peter Zauner, Hywel Morgan, “On-chip electrical impedance tomography for imaging biological cells”, Biosensors and Bioelectronics 25 (2010) 1109–1115. 'DPLHQ)HUUDULR%DUWáRPLHM*U\FKWRO$QG\$GOHU-RVHS6ROD6WHSKDQ+%RKPDQG0DUF%RGHQVWHLQ³7RZDUG0RUSKRORJLFDO Thoracic EIT: Major Signal Sources Correspond to Respective Organ Locations in CT”; IEEE Transactions on Biomedical Engineering, Vol. 59, No. 11, November 2012. 13. Li; Ying et al., “A Novel Combination Method of Electrical Impedance Tomography Inverse Problem for Brain Imaging”, IEEE Transactions on Magnetics, Vol. 41, No. 5, May 2005 14. Murai T, Kagawa Y, “Electrical impedance computed tomography based on finite element model”, IEEE Transactions on Biomedical Engineering, 1985, 32, 177-184. 15. Pilkington TC, et al., “A comparison of finite element and integral equation formulations for the calculation of electrocardiographic Potentials”, IEEE Trans Biomed Eng, 1985, 32, 166-173. 16. Bradley Michael Graham, “Enhancements in Electrical Impedance Tomography (EIT) Image Reconstruction for 3D Lung Imaging”, PhD thesis, University of Ottawa, April 2007. 17. Brown BH, Segar AD: “The Sheffield data collection system”, Clin.Phys. Physiol. Measurement 8 (Suppl. A): 91-7, 1987. 18. Ma Y. et al., “Tomography as a measurement method for density and velocity distributions”, Western Dredging Association Twenty-third technical conference & Thirty-fifth Texas A&M Dredging Seminar, Chicago, Illinois, June, 2003, 25-36. 19. Brown; B. H., "Medical impedance tomography and process impedance tomography: a brief review," Measurement Science & Technology, vol. 12, pp. 991-996, Aug 2001.