On the determination of constitutive parametersin a hyperelastic model for a soft tissue

The aim of this paper is to study a model of hyperelastic materials and itsapplications into soft tissue mechanics. In particular, we first determine an unbounded domain of the constitutive parameters of the model making our smoothstrain energy function to be polyconvex and hence satisfying the Legendre–Hadamard condition. Thus, physically reasonable material behaviour are described by our model with these parameters and a plently of tissues can betreated. Furthermore, we localize bounded subsets of constitutive parameters in fixed physical and very general bounds and then introduce a family of descrete stress–strain curves. Whence, various classes of tissues are characterized. Ourgeneral approach is based on a detailed analytical study of the first Piola–Kirchhoff stress tensor through its dependence on the invariants and on the constitutive parameters. The uniqueness of parameters for one tissue is discussed by introducing the notion of manifold of constitutive parameters, whichis locally represented by possibly different physical quantities. The advantage of our study is that we show a possible way to improve of the usual approachesshown in the literature which are mainly based on the minimization of a costfunction as the difference between experimental and model results

Sensitivity-bandwidth limit in a multi-mode opto-electro-mechanical transducer

An opto--electro--mechanical system formed by a nanomembrane capacitively coupled to an LC resonator and to an optical interferometer has been recently employed for the high--sensitive optical readout of radio frequency (RF) signals [T. Bagci, \emph{et~al.}, Nature {\bf 507}, 81 (2013)]. Here we propose and experimentally demonstrate how the bandwidth of such kind of transducer can be increased by controlling the interference between two--electromechanical interaction pathways of a two--mode mechanical system. With a proof--of--principle device \new{operating at room temperature, we achieve a sensitivity of 300 nV/Hz^(1/2) over a bandwidth of 15 kHz in the presence of radiofrequency noise, and an optimal shot-noise limited sensitivity of 10 nV/Hz^(1/2) over a bandwidth of 5 kHz. We discuss strategies for improving the performance of the device, showing that, for the same given sensitivity, a mechanical multi--mode transducer can achieve a bandwidth} significantly larger than that of a single-mode one

Characterization of a defective PbWO4 crystal cut along the a-c crystallographic plane: structural assessment and a novel photoelastic stress analysis

Among scintillators, the PWO is one of the most widely used, for instance in CMS calorimeter at CERN and PANDA project. Crystallographic structure and chemical composition as well as residual stress condition, are indicators of homogeneity and good quality of the crystal. In this paper, structural characterization of a defective PbWO4 (PWO) crystal has been performed by X-ray Diffraction (XRD), Energy Dispersive Spectroscopy (EDS) and Photoelasticity in the unusual a-c crystallographic plane. XRD and EDS analysis have been used to investigate crystallographic orientation and chemical composition, while stress distribution, which indicates macroscopic inhomogeneities and defects, has been obtained by photoelastic approaches, in Conoscopic and Sphenoscopic configuration. Since the sample is cut along the a-c crystallographic plane, a new method is proposed for the interpretation of the fringe pattern. The structural analysis has detected odds from the nominal lattice dimension, which can be attributed to the strong presence of Pb and W. A strong inhomogeneity over the crystal sample has been revealed by the photoelastic inspection. The results give reliability to the proposed procedure which is exploitable in crystals with other structures.Comment: 18 pages, 10 figures, revised versio

Closed-Loop Control of Local Magnetic Actuation for Robotic Surgical Instruments

We propose local magnetic actuation (LMA) as an approach to robotic actuation for surgical instruments. An LMA actuation unit consists of a pair of diametrically magnetized single-dipole cylindrical magnets, working as magnetic gears across the abdominal wall. In this study, we developed a dynamic model for an LMA actuation unit by extending the theory proposed for coaxial magnetic gears. The dynamic model was used for closed-loop control, and two alternative strategies-using either the angular velocity at the motor or at the load as feedback parameter-were compared. The amount of mechanical power that can be transferred across the abdominal wall at different intermagnetic distances was also investigated. The proposed dynamic model presented a relative error below 7.5% in estimating the load torque from the system parameters. Both the strategies proposed for closed-loop control were effective in regulating the load speed with a relative error below 2% of the desired steady-state value. However, the load-side closed-loop control approach was more precise and allowed the system to transmit larger values of torque, showing, at the same time, less dependence from the angular velocity. In particular, an average value of 1.5 mN·m can be transferred at 7 cm, increasing up to 13.5 mN·m as the separation distance is reduced down to 2 cm. Given the constraints in diameter and volume for a surgical instrument, the proposed approach allows for transferring a larger amount of mechanical power than what would be possible to achieve by embedding commercial dc motors

Jacobian-Based Iterative Method for Magnetic Localization in Robotic Capsule Endoscopy

The purpose of this study is to validate a Jacobian-based iterative method for real-time localization of magnetically controlled endoscopic capsules. The proposed approach applies finite-element solutions to the magnetic field problem and least-squares interpolations to obtain closed-form and fast estimates of the magnetic field. By defining a closed-form expression for the Jacobian of the magnetic field relative to changes in the capsule pose, we are able to obtain an iterative localization at a faster computational time when compared with prior works, without suffering from the inaccuracies stemming from dipole assumptions. This new algorithm can be used in conjunction with an absolute localization technique that provides initialization values at a slower refresh rate. The proposed approach was assessed via simulation and experimental trials, adopting a wireless capsule equipped with a permanent magnet, six magnetic field sensors, and an inertial measurement unit. The overall refresh rate, including sensor data acquisition and wireless communication was 7 ms, thus enabling closed-loop control strategies for magnetic manipulation running faster than 100 Hz. The average localization error, expressed in cylindrical coordinates was below 7 mm in both the radial and axial components and 5° in the azimuthal component. The average error for the capsule orientation angles, obtained by fusing gyroscope and inclinometer measurements, was below 5°