Luis Augusto Motta Mello

Three-Dimensional Electrical Impedance Tomography: A Topology Optimization Approach

Electrical impedance tomography is a technique to estimate the impedance distribution within a domain, based on measurements on its boundary. In other words, given the mathematical model of the domain, its geometry and boundary conditions, a nonlinear inverse problem of estimating the electric impedance distribution can be solved. Several impedance estimation algorithms have been proposed to solve this problem. In this paper, we present a three-dimensional algorithm, based on the topology optimization method, as an alternative. A sequence of linear programming problems, allowing for constraints, is solved utilizing this method. In each iteration, the finite element method provides the electric potential field within the model of the domain. An electrode model is also proposed (thus, increasing the accuracy of the finite element results). The algorithm is tested using numerically simulated data and also experimental data, and absolute resistivity values are obtained. These results, corresponding to phantoms with two different conductive materials, exhibit relatively well-defined boundaries between them, and show that this is a practical and potentially useful technique to be applied to monitor lung aeration, including the possibility of imaging a pneumothorax.

Electrical impedance tomography through constrained sequential linear programming: a topology optimization approach

Electrical impedance tomography (EIT) is an imaging method that estimates conductivity distribution inside a body. In EIT, images are obtained by applying a sequence of low intensity electrical currents through electrodes attached to the body. Although in EIT there are serious difficulties to obtain a high-quality conductivity image, for medical applications this technology is safer and cheaper than other tomography techniques. The EIT deals with an inverse problem in which given the measured voltages on electrodes and a finite element (FE) model, it estimates the conductivity distribution, which are parameters of the FE model. In this work, the topology optimization method is applied as a reconstruction algorithm to obtain absolute images in EIT. It is an optimization method that has been applied successfully to structural mechanical applications and consists of systematically finding a conductivity distribution (or material distribution) in the domain that minimizes the difference between measured voltages and voltages calculated by using a computational model. This algorithm combines the finite element method and sequential linear programming (SLP) to solve the inverse problem of EIT. The SLP allows us to easily apply some regularization schemes based on included constraints in the topology optimization problem. Constraints based on image tuning control and weighted distance interpolation (WDI) are proposed, while a material model is applied to ensure the relaxation of the optimization problem. A new formulation to analytically perform the sensitivity analysis is proposed, using Maxwells reciprocity theorem. To illustrate, the implemented algorithm is applied to obtain conductivity image distributions of some 2D examples using numerical and experimental data.

Design of quasi-static piezoelectric plate based transducers by using topology optimization

Sensors and actuators based on piezoelectric plates have shown relevance in the field of smart structures. Recently, modern design techniques such as the topology optimization method have been applied to design laminated piezoelectric transducers, and design requirements such as maximizing static displacements (actuator design) and output voltages (sensor design) have been employed. However, it may be desirable to keep the transducer working range before its first resonance frequency. In this case, the (displacement or voltage) amplitude is expected to be constant with excitation frequency, which may not be the case when only static design requirements are employed. Thus, considering sensor design, if the amplitude is constant, an undetected change in the excitation frequency would cause a small measurement error. Regarding actuators, on the other hand, if the first resonance frequency is small, oscillations in the response to a step excitation (which is usually applied in quasi-static applications, i.e. applications in which the transducer operates under the first resonance frequency) could be high, ultimately causing overshoot, for instance. Thus, in this work, the topology optimization method has been applied to design piezoelectric transducers considering quasi-static operation, by distributing piezoelectric material over a metallic plate and by selecting the material polarization sign, in order to fulfil quasi-static design requirements. This is achieved by maximizing an objective function that depends on both displacements (for actuators) or output voltages (for sensors), and first resonance frequencies. The applied methodology, which encompasses the optimization problem formulation and numerical implementation, is presented. The achieved computational results, corresponding to the design of different types of transducers, clearly show the potential of the proposed methodology to increase the quasi-static working frequency range.

Foil Strain Gauges Using Piezoresistive Carbon Nanotube Yarn: Fabrication and Calibration

Carbon nanotube yarns are micron-scale fibers comprised by tens of thousands of carbon nanotubes in their cross section and exhibiting piezoresistive characteristics that can be tapped to sense strain. This paper presents the details of novel foil strain gauge sensor configurations comprising carbon nanotube yarn as the piezoresistive sensing element. The foil strain gauge sensors are designed using the results of parametric studies that maximize the sensitivity of the sensors to mechanical loading. The fabrication details of the strain gauge sensors that exhibit the highest sensitivity, based on the modeling results, are described including the materials and procedures used in the first prototypes. Details of the calibration of the foil strain gauge sensors are also provided and discussed in the context of their electromechanical characterization when bonded to metallic specimens. This characterization included studying their response under monotonic and cyclic mechanical loading. It was shown that these foil strain gauge sensors comprising carbon nanotube yarn are sensitive enough to capture strain and can replicate the loading and unloading cycles. It was also observed that the loading rate affects their piezoresistive response and that the gauge factors were all above one order of magnitude higher than those of typical metallic foil strain gauges. Based on these calibration results on the initial sensor configurations, new foil strain gauge configurations will be designed and fabricated, to increase the strain gauge factors even more.