Determination of Cardiac Ejection Fraction by Electrical Impedance Tomography using a Hybrid Heuristic Approach, a Simulation Study

Abstract

Abstract. An important parameter to analyze the efficiency of the heart as a pump is Cardiac Ejection Fraction (EF), which is clinically highly correlated to the functional status of the heart. Diverse non invasive methods can be applied to measure EF, like Computer Tomography, Magnetic Resonance, Echocardiography, and others. Nevertheless, none of these techniques can be used to continuous monitoring of such parameter. On the other hand, electrical impedance tomography (EIT) may be applied to accomplish this goal. In addition, low cost and high portability are also EIT's features that justify the research for solutions involving such technique to monitor EF. EIT consists in reconstruct images of the conductivity distribution of the interior of a conductor domain by applying electric currents and measuring electrical potential on the boundary of the body. Mathematically, EIT can be classified as a non-linear inverse problem. This work proposes a method for the continuous estimation of cardiac ejection fraction, addressing it as an optimization problem. The models used in our approach assume that recent two-dimensional magnetic resonance images of the patient are available, and use them to reduce the search space. Another important feature is the parametrization of the geometry of internal inclusions inside the domain, which also reduces the cost of the method. This work proposes a Hybrid Iterated Local Search (ILS) heuristic for EIT inverse problem using Levenberg-Marquardt Method as local search. Experiments are performed on two-dimensional images with synthetically generated data for electric potentials. Two different protocols for current injection are tested in such experiments and preliminary results are presented.

Bioelectrical Impedance Methods for Noninvasive Health Monitoring: A Review

“…Electrical impedance tomography (EIT) [ 102 – 114 ], a computed tomographic image reconstruction technique, is a nonlinear inverse problem in which the electrical conductivity or resistivity of a conducting domain (Ω) is reconstructed from the surface potentials developed by a constant current signal injected ( Figure 13 ) at the domain boundary (∂Ω). A low frequency, constant amplitude sinusoidal current is injected to the boundary (∂Ω) of the object domain (Ω) to be imaged within a volume conductor surrounded by an array of surface electrodes and the boundary potentials are measured using an electronic instrumentation [ 115 – 123 ].…”

“…A basic EIT system contains three parts ( Figure 15 ): EIT instrumentation [ 115 – 123 ], a PC with reconstruction algorithm [ 124 – 133 ], and an array of EIT sensors or surface electrodes [ 57 , 102 , 106 , 110 , 186 ] attached to a practical phantom or a subject under test (SUT).…”

“…In EIT, an array of sensors or surface electrodes [ 57 , 102 , 106 , 110 , 186 ] is attached to the boundary of the DUT. A low frequency sinusoidal current of constant amplitude is generated by a constant current source and it is injected through the driving electrodes and the boundary potentials are measured on the sensing electrodes using a particular current injection and voltage measurement fashion called the current pattern [ 100 , 187 , 188 ].…”

“…The forward solver solves the characteristic equation or governing equation of EIT [ 102 – 110 , 189 – 194 ] and computes the boundary potentials called calculated boundary data ( V c ) for a known constant current simulation [ C ] in PC. The calculated potential data ( V c ) are then compared with the measured potential data ( V m ) in inverse solver (IS) and the conductivity distribution of DUT is reconstructed for which the difference between V m and V c (Δ V = V m − V c ) is minimized.…”

“…Therefore, the “EIT governing equation” could be obtained as the relationship between the elemental electrical conductivity ( σ e ) of the domain and their corresponding potential values (Φ) using the Maxwell's equations. EIT governing equation can be represented as a partial differential equitation [ 102 – 110 , 189 – 195 ] as shown in …”