Giovanni Caruso

A critical analysis of electric shunt circuits employed in piezoelectric passive vibration damping

Vibration damping of an elastic structure can be obtained by bonding a piezoelectric actuator onto the vibrating structure, and by shunting the actuator to a suitable electric resonant circuit, tuned to the structural eigenmode to be damped. The achievable damping depends on the particular electric circuit used. In this paper three different electric shunt circuits are analyzed and their performances are compared. In particular, the optimal values of the electric components belonging to each shunt circuit and the corresponding exponential time decay rates of the free vibrations relevant to the controlled structural eigenmode are explicitly determined, also taking into account the inherent structural damping. Finally, some experimental results are reported, obtained by using two of the shunt circuits analyzed, which are in good agreement with the theoretical predictions.

Active vibration control of an elastic plate using multiple piezoelectric sensors and actuators

Abstract This paper is addressed to the vibration control of an elastic plate, clamped along one side and excited by an impulsive transversal force acting in correspondence of a free corner. The plate is equipped with three couples of piezoelectric patches, used as sensors and actuators. A modal model of the coupled electromechanical structure, obtained by employing a suitable finite-element formulation together with a modal reduction, is used in the controller design. Different H2 control laws have been designed and compared by simulation, in order to evaluate the performance obtained using different combinations of sensors and actuators together with models taking into account an increasing number of structural eigenmodes.

Diffusion of the Second Messengers in the Cytoplasm Acts as a Variability Suppressor of the Single Photon Response in Vertebrate Phototransduction

The single photon response in vertebrate phototransduction is highly reproducible despite a number of random components of the activation cascade, including the random activation site, the random walk of an activated receptor, and its quenching in a random number of steps. Here we use a previously generated and tested spatiotemporal mathematical and computational model to identify possible mechanisms of variability reduction. The model permits one to separate the process into modules, and to analyze their impact separately. We show that the activation cascade is responsible for generation of variability, whereas diffusion of the second messengers is responsible for its suppression. Randomness of the activation site contributes at early times to the coefficient of variation of the photoresponse, whereas the Brownian path of a photoisomerized rhodopsin (Rh*) has a negligible effect. The major driver of variability is the turnoff mechanism of Rh*, which occurs essentially within the first 2-4 phosphorylated states of Rh*. Theoretically increasing the number of steps to quenching does not significantly decrease the corresponding coefficient of variation of the effector, in agreement with the biochemical limitations on the phosphorylated states of the receptor. Diffusion of the second messengers in the cytosol acts as a suppressor of the variability generated by the activation cascade. Calcium feedback has a negligible regulatory effect on the photocurrent variability. A comparative variability analysis has been conducted for the phototransduction in mouse and salamander, including a study of the effects of their anatomical differences such as incisures and photoreceptors geometry on variability generation and suppression.

Evaluation of higher-order theories of piezoelectric plates in bending and in stretching

Many models for the flexural and membranal behaviour of piezoelectric plates are available in the literature. They are based on different assumptions concerning the strain, stress, electric and electric-displacement fields inside the plate. A critical comparison among such models is presented here in a completely analytic way, in order to assess the accuracy of the results they provide and determine their range of applicability. The comparison is made by using a class of case-study problems, whose analytical solutions in the framework of the linear theory of piezoelectricity are available, as benchmarks for the solutions supplied by the plate models. The evaluated models are also here rationally derived from the three-dimensional theory of piezoelectricity, and a consistent treatment of the stress and electric-displacement relaxation conditions is proposed.

Rhodopsin Expression Level Affects Rod Outer Segment Morphology and Photoresponse Kinetics

Background The retinal rod outer segment is a sensory cilium that is specialized for the conversion of light into an electrical signal. Within the cilium, up to several thousand membranous disks contain as many as a billion copies of rhodopsin for efficient photon capture. Disks are continually turned over, requiring the daily synthesis of a prodigious amount of rhodopsin. To promote axial diffusion in the aqueous cytoplasm, the disks have one or more incisures. Across vertebrates, the range of disk diameters spans an order of magnitude, and the number and length of the incisures vary considerably, but the mechanisms controlling disk architecture are not well understood. The finding that transgenic mice overexpressing rhodopsin have enlarged disks lacking an incisure prompted us to test whether lowered rhodopsin levels constrain disk assembly. Methodology/Principal Findings The structure and function of rods from hemizygous rhodopsin knockout (R+/−) mice with decreased rhodopsin expression were analyzed by transmission electron microscopy and single cell recording. R+/− rods were structurally altered in three ways: disk shape changed from circular to elliptical, disk surface area decreased, and the single incisure lengthened to divide the disk into two sections. Photocurrent responses to flashes recovered more rapidly than normal. A spatially resolved model of phototransduction indicated that changes in the packing densities of rhodopsin and other transduction proteins were responsible. The decrease in aqueous outer segment volume and the lengthened incisure had only minor effects on photon response amplitude and kinetics. Conclusions/Significance Rhodopsin availability limits disk assembly and outer segment girth in normal rods. The incisure may buffer the supply of structural proteins needed to form larger disks. Decreased rhodopsin level accelerated photoresponse kinetics by increasing the rates of molecular collisions on the membrane. Faster responses, together with fewer rhodopsins, combine to lower overall sensitivity of R+/− rods to light.

Identification of key factors that reduce the variability of the single photon response

Rod photoreceptors mediate vision in dim light. Their biological function is to discriminate between distinct, very low levels of illumination, i.e., they serve as reliable photon counters. This role requires high reproducibility of the response to a particular number of photons. Indeed, single photon responses demonstrate unexpected low variability, despite the stochastic nature of the individual steps in the transduction cascade. We analyzed individual system mechanisms to identify their contribution to variability suppression. These include: (i) cooperativity of the regulation of the second messengers; (ii) diffusion of cGMP and Ca2+ in the cytoplasm; and (iii) the effect of highly localized cGMP hydrolysis by activated phosphodiesterase resulting in local saturation. We find that (i) the nonlinear relationships between second messengers and current at the plasma membrane, and the cGMP hydrolysis saturation effects, play a major role in stabilizing the system; (ii) the presence of a physical space where the second messengers move by Brownian motion contributes to stabilization of the photoresponse; and (iii) keeping Ca2+ at its dark level has only a minor effect on the variability of the system. The effects of diffusion, nonlinearity, and saturation synergize in reducing variability, supporting the notion that the observed high fidelity of the photoresponse is the result of global system function of phototransduction.

Mindlin-Type Finite Elements for Piezoelectric Sandwich Plates

New finite-element formulations are developed for the analysis of a plate having thin piezoelectric actuators bonded on its upper and/or lower surfaces. The proposed finite elements are two-dimensional, quadrangular, four-node, Mindlin-type, locking-free, and have five degrees of freedom per node. These are the deflection of the middle plane of the plate, the rotations of the fibers normal to the middle plane and the actuation electric potentials of the piezoelectric actuators. The effectiveness of the proposed finite-element formulations is shown by studying some case problems, whose analytical solutions are available.

Dynamics of mouse rod phototransduction and its sensitivity to variation of key parameters

The deep understanding of the biochemical and biophysical basis of visual transduction, makes it ideal for systems-level analysis. A sensitivity analysis is presented for a self-consistent set of parameters involved in mouse phototransduction. The organising framework is a spatio-temporal mathematical model, which includes the geometry of the rod outer segment (ROS), the layered array of the discs, the incisures, the biochemistry of the activation/deactivation cascade and the biophysics of the diffusion of the second messengers in the cytoplasm and the closing of the cyclic guanosine monophosphate (cGMP) gated cationic channels. These modules include essentially all the relevant geometrical, biochemical and biophysical parameters. The parameters are selected from within experimental ranges, to obey basic first principles such as conservation of mass and energy fluxes. By means of the model they are compared to a large set of experimental data, providing a strikingly close match. Following isomerisation of a single rhodopsin R * (single photon response), the sensitivity analysis was carried out on the photo-response, measured both in terms of number of effector molecules produced, and photocurrent suppression, at peak time and the activation and recovery phases of the cascade. The current suppression is found to be very sensitive to variations of the catalytic activities, Hills coefficients and hydrolysis rates and the geometry of the ROS, including size and shape of the incisures. The activated effector phosphodiesterase (PDE *) is very sensitive to variations of catalytic activity of G-protein activation and the average lifetimes of activated rhodopsin R * and PDE *; however, they are insensitive to geometry and variations of the transduction parameters. Thus the system is separated into two functional modules, activation/deactivation and transduction, each confined in different geometrical domains, communicating through the hydrolysis of cGMP by PDE *, and each sensitive to variations of parameters only in its own module.

A layer-wise Reissner–Mindlin-type model for the vibration analysis and suppression of piezoactuated plates

A layer-wise model of three-layer piezoelectric sandwich plates is presented. Each layer is modeled according to a first-order shear deformation theory. Both a variational formulation and a locking-free finite-element formulation of the sandwich-plate problem are developed. The latter is based on a new bilinear quadrangular four-node finite element with 13 degrees of freedom per node and is validated by comparing the numerical and the analytical solution of a special problem. The proposed model is applied to the analysis of the vibration suppression problem of a thick cantilever steel plate equipped with a piezoelectric actuator, and turns out to be especially useful when a thick piezoelectric actuator is used.

Kinetics of rhodopsin deactivation and its role in regulating recovery and reproducibility of rod photoresponse

The single photon response (SPR) in vertebrate phototransduction is regulated by the dynamics of R* during its lifetime, including the random number of phosphorylations, the catalytic activity and the random sojourn time at each phosphorylation level. Because of this randomness the electrical responses are expected to be inherently variable. However the SPR is highly reproducible. The mechanisms that confer to the SPR such a low variability are not completely understood. The kinetics of rhodopsin deactivation is investigated by a Continuous Time Markov Chain (CTMC) based on the biochemistry of rhodopsin activation and deactivation, interfaced with a spatio-temporal model of phototransduction. The model parameters are extracted from the photoresponse data of both wild type and mutant mice, having variable numbers of phosphorylation sites and, with the same set of parameters, the model reproduces both WT and mutant responses. The sources of variability are dissected into its components, by asking whether a random number of turnoff steps, a random sojourn time between steps, or both, give rise to the known variability. The model shows that only the randomness of the sojourn times in each of the phosphorylated states contributes to the Coefficient of Variation (CV) of the response, whereas the randomness of the number of R* turnoff steps has a negligible effect. These results counter the view that the larger the number of decay steps of R*, the more stable the photoresponse is. Our results indicate that R* shutoff is responsible for the variability of the photoresponse, while the diffusion of the second messengers acts as a variability suppressor.