However, more effort is still needed to bring the technology to a fully mature readiness level. In this paper, recent research and applications in structural health monitoring of composite aircraft structures using FOS have been critically reviewed, considering both the multi-point and distributed sensing techniques.In-service structural health monitoring of composite aircraft structures plays a key role in the assessment of their performance and integrity. In recent years, Fibre Optic Sensors (FOS) have proved to be a potentially excellent technique for real-time  Today, high percentages of advanced composite materials are integrated into the primary flight structures of aircraft. For example, over 50% of the structural components of the Boeing 787 and Airbus 350 XWB are made of composite materials rather than conventional aluminium alloys. Military airplanes such as the U.S. F-22, F-35 and F-117A fighters also make extensive use of composite materials. The increased use of fibre-reinforced materials is due to their light weight and superior strength properties with respect to conventional metallic materials, which make their deployment fundamental for the reduction of weight and hence the operational costs of aircraft 82] it waDue to their small size and flexibility, optical fibres can be embedded in composite structures during the manufacturing process. The advantages are the enhanced protection of the fragile fibre sensor and the possibility of strain monitoring and damage detection in different locations inside the material. However, sensor integration in composites presents a number of issues and shortcomings that need to be addressed properly. Some of the most relevant among them will be discussed briefly in the following sections.Despite being very small, a standard telecom fibre has a size (125 µm) which is much larger than commonly used composite fibres . As a result, resin rich regions are created around the fibre, especially in the woven fabric. Ingress and egress points of the fibre in the material are critical locations due to the sharp pressure gradient and therefore the severe bending experienced by the fibre. The concentrated stress acting during some of the manufacturing processes, such as the vacuum bag technique, and later under operating conditions, cause severe optical loss , and mayPartially embedded  or embedded connectors offer another possible solution. In the first case, the connector can be positioned on one of the surfaces of the composite structure . A miniaMost of the mentioned problems can be avoided by using the so-called free-space coupling , which eFinally, during composite part manufacturing it is important to protect the outer section of the fibre from excess resin that may escape from the layers pile.The spectral sensitivity of an embedded fibre optic sensor can deviate from that of the non-embedded sensor for a number of reasons. During the heating phase of the manufacturing process, the fibre is subjected to the stress created at the boundary between the coating and the composite ply; however, during the cooling phase, this stress is only partially released. This results in residual strains acting inside the material and on the fibre. Consequently, the sensor spectral response is affected by the existence of transverse, and often non-uniform, strain fields.In the literature, various works have addressed this issue. In  it was oWhen it comes to damage detection rather than simple strain monitoring, the information given by the distorted spectrum of bare embedded FBG can be quite useful ,104. By Deformation shape prediction plays an important role in structural health monitoring and control of aerospace structures. Estimation of the deflection shape of a wing during flight enables in-flight monitoring of various lightweight aeroelastic systems, such as flexible flying wings or unmanned air vehicles (UAV), and commercial aircrafts. Fiber Bragg gratings can be applied beneficially to these structures instead of electrical strain gauges in order to obtain strain measurements useful for shape-detection algorithms.et al. [et al. [et al. [et al. investigated shape reconstruction for rotating structures [Various studies have been reported in the literature regarding the estimation of displacement starting from strain measurement. One possible approach consists in the use of an inverse finite element method that relies on a least squares variational principle to predict the deformation shape of 3D plate and shell elements from strain measurements . The appet al.  and Rapp [et al.  used mea [et al.  estimateructures .Following the in-flight break-up of NASA’s Helios wing in 2003 see  and the et al. analyzed the method, compared it to the modal-based approach and applied it to a cantilever swept wing-like plate, which is shown in In  DerkevorThe rectangular plate was mounted at a 45 degrees angle from the test plate and subjected to different loading conditions in order to simulate a wing representing a variety aerospace structures. In particular, three loading cases were considered by applying point loads: (1) only at the trailing edge; (2) uniformly see b and (3)A finite element (FE) model was created to represent the plate and the different loading conditions. In order to estimate the deflection shape, the FOSS (fiber optic strain sensor) algorithm was developed so as to use the strain data measured directly by FBG sensors. The algorithm relies on the classical beam theory to derive the displacement transfer functions in segments of the structure surface; details can be found in ,114,115.The estimated error was calculated by comparing this set of data with the displacements from the FE model. In the FOSS algorithm, the deflection shape was compared instead with the results from photogrammetry. The rms error value between the FOSS estimate and photogrammetry results was below 2%, while the average normalized error with the FE analysis displacements was between 2 and 3.7%. This difference can probably be attributed to modeling errors, which can be more serious in the case of complicated structures such as a real composite wing. The error can also be reduced by increasing the number of modes, but this would require a greater computational effort. Furthermore, the advantage related to the need for a few sensor locations to obtain the displacement information over a large area has become less important following the advent of optical strain sensors, which can be used in large numbers on lightweight structures. This opportunity also decreases the possible adverse effect of a damaged or inaccurate sensor.Overall, an algorithm based on a large number of measured strain information obtained from FBG sensors has the advantage of being relatively independent from modeling errors and requires less computational effort in the case of real-time monitoring of high-aspect-ratio aircraft wings, to which the classical one-dimensional beam theory applies.Currently composites are used mainly for load-bearing primary structures such as the wing box, which is a structural component with “skins” comprising the top and bottom, and the front and back formed by I-beams (“spars”), interior stiffeners (“ribs”), and in-out stiffeners (“stringers”) see a.et al. [i.e., where the strain change was most pronounced. The instrumented wing box was then subjected to an up-bending test in order to simulate the lift-induced bending of a wing during flight. When buckling actually started in the front spar and afterwards, during the test, in the top skin near the clamped edge of the wing box, the corresponding FBG sensors were able to detect it in real-time in good agreement with the electrical strain gauges used as reference at the same locations.Recently structural health monitoring systems based on fibre optical sensors have been developed to monitor dynamic strains in a wing spar under wind tunnel conditions  or in thet al.  instrumeet al. ,121, demDue to the capability of simultaneously gathering data from a high number of sensors through multiplexing technologies and fast processing techniques, in general a system of this type would be suitable for full-scale detection of relatively slow dynamic processes such as buckling induced by operating loads in large composite structures.Instead a previous study focused on the durability and damage tolerance of a composite wing structure . In partet al. [More recently, as already mentioned in the section on FBG interrogation systems, Costa et al.  reportedL-shaped parts used in complex aircraft composite structures as wing spars, for example, are a critical element due to spring-in distortion introduced during manufacturing and through-thickness tensile stress: Spring-in distortion is due to the anisotropic nature of laminated composites and can cause problems in assembly when the part is forced to achieve the desired geometry, resulting in the accumulation of stresses; in addition, the sharp curvature of L-shaped components causes through-thickness radial stress to build up under operating conditions.et al. developed a FBG-based life cycle monitoring system for L-shaped corner parts, embedding optical fibres in the corners of an L-shaped composite specimen in order to monitor the cross-sectional strain change during the whole structural lifecycle. Based on the berefringence effect of an embedded FBG sensor, it was possible to retrieve the cross-sectional strain history during cure, demolding and a four-point bend test which simulated operating conditions. The FBG sensors were able to capture internal deformation stresses during cure and demolding, offering an indirect measure of the corner angle and hence also a valuable tool for quality inspection of L-shaped composite parts. During the four-point bending test to simulate operation of the part, the embedded sensors could continuously monitor the non-axisymmetric strain change until failure due to crack propagation in the corner part. In this test, the through thickness tensile strain arising at the specimen sharp curvature was clearly predominant. When longitudinal stress is not negligible, the method should be improved either by adding another FBG sensitive only to strain in the longitudinal direction or by modifying the microstructure of the FBG embedded in the corner in order to detect transverse strain only [In ,126 Minaain only .i.e., the tapered edges of the patch undergoing the highest stress  F-111C aircraft , where aThis arrangement allows compensation of temperature fluctuations and minimisation of possible strain gradients due to bending. The relative wavelength shift causes a change in the output optical power, which is measured using a high-speed, lightweight photodiode. When the repair begins to disbond, the active grating expands due to thermal residual strain release and transmits light as a result of the mismatch with the unchanged reference FBG wavelength. During a fatigue test of specimen, FBGs survived 700.000 cycles at strains of up to 3150 µε while the electrical strain gauges used as a reference failed. Overall, the strain ratio technique proved to be robust, low-cost and suited to the miniaturisation of the opto-electronic components and to embedding of the sensors directly into the tapered region of the repair.et al. applied a recently developed dynamic full-spectrum FBG sensor interrogator [The maintenance and inspection of adhesively bonded composite lap joints are also challenging activities, since these joints cannot be disassembled like bolted metallic joints. In-flight or between-flight inspections monitoring of the joints could improve the description of their conditions and therefore enable the detection of premature failure. Direct measurements of the joint condition can be performed by embedding sensors into the adhesive layer, provided that these sensors do not affect the performance of the joint. Fiber Bragg gratings were applied for this purpose in ,131, wherrogator  to invesThe composite lap joint specimens were subjected initially to cyclic loading in order to induce fatigue damage and then excited using a multicomponent harmonic excitation frequency range representing that of a typical in-flight load spectrum. During the fatigue test, the dynamic response of the joint became nonlinear and then potentially chaotic, as the fatigue-induced damage progressed.In parallel, the FBG dynamic response changed accordingly to damage growth, as could be seen using thermal imaging and a finite element model of the joint. The detection and localization of impact is of the highest importance in composite aircraft structures monitoring. This is a major concern due to the mechanical strength of the composite outer skins which can sustain a large deformation without developing cracks, even though the internal sub-structure is damaged. As a consequence, in some cases this type of damage can be undetectable during visual inspections.The most likely causes of aircraft impact damage during operating conditions include bird strike, hail, blade-off and lightning. Due to the high relevance of this issue, much research work has focused on the detection of impact damage in composite structures using fibre optic sensors. Whilst the use of advanced processing techniques for networks of multiple FBG sensors will be treated in et al. [One possible technique to monitor the occurrence, energy and position of impact is based on the detection of shock waves with surface-mounted FBG sensors and high speed interrogation systems. L.K. Cheng et al.  were amoet al. used the same detection method and developed a system specifically for the SHM of composite primary aircraft structures, capable of interrogating simultaneously 32 FBGs (eight sensors per channel), each at the maximum sampling frequency of 19.3 kHz.In , KostersInitially a quasi-isotropic carbon fibre reinforced plastic (CFRP) plate was fabricated and equipped with surface-mounted FBG sensors close to the edges of the plate for an impact hammer test. The impact energy related to the impact event could be inferred from the sum of the weighted sensor output amplitudes. Instead the location of the impact location was estimated from the difference between the arrival times of the impact-induced shock waves at the different sensor locations. In this way, it proved possible to identify impact location with an accuracy of less than 10 cm. Then a second experiment was performed on a composite wing-control surface element, consisting of an upper and lower skin plate, four ribs, two spars and a folded plate normally used at the trailing edge. Four FBG sensors were positioned at the specimen edges and a metal object dropped from a defined height in order to hit the top plate; varying the weight and dropping height of the object made it possible to investigate different values of impact energy and velocity. In some cases, the accuracy of the impact location was larger than 10 cm due most probably to the anisotropy of the material.et al. [Since 1998 Tsutsui et al. ,137,138 et al.  a stiffeet al. [Recently, Vella et al.  used theet al.  based onThe maximum full-spectrum acquisition rate proved suitable to capture the data during low-velocity impact events and transient strain distributions due to openings in delamination phenomena. The significant increase in the reading rate was made possible by driving the tunable filter with a sinusoidal voltage, recording the power as a function time and post-processing the data to obtain a time-varying spectrum rather than processing it in real-time. Details of the system operation can be found in . The autThe results are shown in Nevertheless, it is necessary to bear in mind that the use of the Bragg spectrum, and the modifications to its shape occurring in case of damage, requires the optic fibre sensor to be in close proximity to the impact location. Therefore, to use such a method, the deployment of a large number of FBG sensors over the area to be monitored is necessary.etc. using dynamic strain measurements obtained with a network of FBG sensors, research has focused on the use of advanced pattern recognition techniques, based on independent component analysis (ICA) or principal component analysis (PCA) and specific indices.In order to estimate more precisely the location of possible defects such as impact damage, delamination i.e., 1 kHz, was sufficient to capture the specimen dynamics using FBG sensors.In ,141 the Furthermore the optimal locations for the sensors were evaluated so as to be able to measure the highest strain values for the greatest number of mode shapes. Based on these results, three sensors were surface mounted on the frame and one on the skin. An excitation force generated using a frequency sweep in the 0–500 Hz range was then applied to the specimen by using an electromechanical shaker. Different damage scenarios were simulated by attaching six lumped masses in six different areas of the test structure; the number and weight of the masses were changed to represent different damage cases. The results obtained from the four FBG sensors in terms of strain time signals up to 500 Hz were used for modal identification. The frequency spectrum was calculated, and the modal parameters extracted, and were found to be in close agreement with those estimated using the FE model and measured by a reference accelerometer. However, no significant difference between the various damage scenarios was exhibited. Indeed, the variation of the modal parameters such as the modal frequency or amplitude was too limited to detect small defects, making this approach rather useless in many practical situations. To overcome this limitation, the authors developed a method based on advanced pattern recognition techniques. Firstly, a series of parameters was extracted from the time signals in the time, frequency and combined time-frequency domains, using discrete wavelet transforms. Then, feature reduction was performed using the independent component analysis (ICA) technique to generate a new set of parameters, statistically independent from the original ones. Finally the resulting set of features was processed using a support vector machines (SVM) method to make a classification of the data and distinguish between the different damage states. However, for the validation of the method, only one added mass was considered in each damage scenario. In this case, the results were highly encouraging, demonstrating that, after training, the system was able to recognize with high reliability the presence of the single damage and its position on the structure.et al. [In 2013 Sierra et al.  used a set al.  more comet al. [One specific, typical aircraft structure, to which FBG sensors may be successfully applied for damage detection, is the advanced grid structure (AGS) made of carbon fibre reinforced plastic (CFRP). AGS see  is oftenet al.  developePreliminary low-energy impact tests were conducted to analyse statistically the failure modes in the grid structure, the results demonstrating that damage phenomena affect only the ribs and not their intersections, and that the primary failure mechanism, in the case of low-energy impact, consists in the micro buckling of carbon fibres. An improved finite element model was also developed in order to determine the best indicator for the presence of damage in the ribs. It was found that the change in static strain at the rib level in the carbon fibre direction is the most sensitive signal to rib cracking. Therefore, a significant and detectable difference between the strains in damaged and undamaged grid structure, Δε, is able to provide precious information regarding the health status of the ribs. In order to determine whether or not these differences are actually significant with respect to the normal expected values, the authors applied a statistical method based on a discordancy test. The SHM system was verified on an advanced structural grid with a network of embedded FBG sensors, as shown in The first verification test consisted in the application of a three-point bending loading at a velocity of 1 mm/s. Data from the FBG sensors was gathered using an optical spectrum analyser with 10 pm wavelength resolution. Results from the optical and electrical strain gauges agreed reasonably well, demonstrating the reliability of the embedded FBG sensors in measuring the correct strain values in the ribs.The second verification test was conducted after two of the ribs were notched, approximately at the midpoint between the FBG and the nearest intersection. This time the load was applied in one point of the composite grid and the difference between strains in the damaged and undamaged case, after load application, was used according to the discrepancy test. The strain difference measured by the FBG sensors proved clearly the existence of damage in the notched ribs, even if it was only possible to provide approximate information concerning the damage location.Since their discovery by Lamb in 1917  and theiIn recent years, FBG sensors have been applied with success as receivers of Lamb waves instead of piezoelectric probes ,149. In In order to monitor Lamb waves, the grating length of the FBG sensor should not exceed the wavelength of the propagating wave which would in fact cause non-uniform strains and therefore broadening of the spectrum width; beyond requiring difficult interrogation, the distortion of the spectrum would give ambiguous information . Differeet al. used and hybrid system with lead zirconate titanate (PZT) actuators and FBG sensors and develop a high-speed interrogation system using an arrayed waveguide grating (AWG) filter to detect disbonds in CFRP box structures. They embedded small-diameter FBG sensors in the bonding areas of the CFRP structure to monitor them during fatigue testing. Disbonds were detected by conventional ultrasonic inspection and from changes in the transmitted Lamb waves. Time signals measured with the AWG-based interrogation system showed that before the occurrence of debonding, two modes could be clearly seen in the plots and that another mode appeared between the first two while the disbond length increased. A wavelet transform algorithm was applied to better highlight the change in the waveforms due to the presence of disbonds [Various works have investigated the use of such hybrid systems for structural health monitoring purposes. In  Ogisu etdisbonds . Two pardisbonds ,154.et al. [a secondary FBG filter cascaded with the FBG sensor. This architecture used a broadband source (BBS) with two FBG sensors. The first FBG caused a phase shift in the reflected spectrum that intersected with the spectrum of the second FBG sensor. However, this architecture required the center wavelength of the two FBGs to be within close range for successful operation. Using the cascaded FBG interrogation architecture, Tsuda [et al. [Tsuda  and, latet al.  proposede, Tsuda  was able [et al.  reportedet al. [In 2013, Tan et al.  investiget al. [S0 with a group velocity of 400 m/s) which was not significantly affected by interference with the slower fundamental antisymmetric mode . Based on the estimated dispersion behavior, the selected frequency range for the S0 mode was between 50 and 400 kHz. The FBG sensors and piezoceramic disc actuator used in the study were surface mounted on the plate.More recently, in 2014, Barazanchy et al.  developeet al.  allowed et al.  gave theS0 waves at a frequency of 325 kHz, which corresponded to a velocity of 4800 m/s and a wavelength of approximately 15 mm. The length of the FBG sensors was selected based on the previously mentioned work by Takeda et al. [oS wave velocity at 325 kHz, the distance travelled by the actuated propagating wave being the sum of the distance from the actuator to the damage and that between the damage and the detecting FBG sensor. This means that all possible damage positions lay on ellipses with focal points at the actuator and sensor locations [Considering the selected frequency range and the actuator diameter (6.35 mm), it was decided to generate a et al.  demonstrocations . A “ringIn this operation, the only unknown variable was the length of the minor axis of the ellipse. By repeating this process for all the actuator-sensor pairs, the probable damage location on the plate could be associated with the area where most of the rings intersected see a.The algorithm was applied to the detection of the mentioned defects for verification, and the results for the case of the through thickness hole of 2 mm are shown in In recent years, the use of shape memory alloy (SMA) wires integrated into composite structures to create “smart composites” has attracted much research work owing to their capability of providing control on the shape and mechanical properties of composite structures . SMAs arThe operational effectiveness of SMA actuators in a smart composite is dependent on the interfacial bonding between the embedded SMA wires and the surrounding matrix. Although wire twisting and surface heat treatment methods can be used to enhance the bonding quality of SMA wires, poor bonding performance affects strain transfer and increases the possibility of debonding. Therefore, an effective sensor technology for monitoring the correct operation of SMA actuators in smart composites is highly desirable. In this respect, embedded FBG sensors have been shown to be a promising option, as they are able to provide static and dynamic strain information on the SMA actuators operation .FBG sensors can also be employed beneficially when alternative concepts for morphing composite structures using SMAs are considered, without the actual embedding of the actuators in the material. In this case, e.g., a wing only partially made of composite, FBG sensors allows monitoring of the composite element subjected to shape change.The application of SMAs to aircraft structures  includeset al. investigated a morphing wing with variable camber using FBG sensors. The wing consisted of two graphite/epoxy composite skins and a steel supporting frame. The SMA wire actuators were attached to the bottom skin, and the FBG sensors were surface-mounted close to the wing root  technique. More recently, Guemes et al. [The detection of debonding in structural elements, such as stiffeners for example, is another potentially attractive field of application for distributed sensing systems: Indeed, areas between bonded elements can be instrumented with optical fibres over their whole length. In  Minakuchs et al.  conducteet al. reported a series of experiments on CFRP panels to detect delamination caused by impact. In this case, the advantage offered by distributed sensors is the possibility of creating a very high-density sensor network with a single optical fibre. By deploying the optical fibre over the entire structure, and taking care to avoid sharp curvatures which may cause significant losses of light, a sensing grid can be created to monitor a wide structural area with spatial resolution down to a few millimetres. Even without a-priori knowledge of the damage location, the chances of detecting it are increased substantially with respect to the use of quasi-distributed techniques which also require more complicated schemes of detection based on multiplexing techniques. Strain measurements obtained from a full area can then be used to create a map of strain distribution. Each time a damage causes a change in the strain field, it is possible to visualise it through images representing the strain level over the structure and its local gradients. In [In ,174 Guemet al. applied a Pre-pump pulse Brillouin Optical Time-Domain Analysis (PPP-BOTDA) system to the investigation of impact damage on composite sandwich structures, exploiting the enlargement of the Brillouin gain spectrum (BGS) due to non-uniform strain along the fibre. In general, the central frequency of a measured Brillouin gain spectrum (BGS) is related to the average value of axial strain over the sensing system spatial resolution. Thus, the strain variation in a damaged area smaller than the spatial resolution hardly changes the BGS peak frequency. However, the BGS shape contains information regarding the strain distribution within the spatial resolution [In  Minakuchsolution  thus makA grid of optical fibres was embedded in the adhesive layer between the composite facesheet and the lightweight core in order to measure strain variation at the interface between the two materials. Indentation of the panel surface induces non-uniform tensile and compressive strain in the optical fibre, hence resulting in a variation in the BGS profile: Results are shown in In order to be fully mature for the structural health monitoring of aerospace structures, critical issues such as robustness and maintainability need to be addressed in particular as regards the systems based on fibre optic sensors described so far in this paper. For example, replacing a damaged fibre is relatively complicated, especially if embedded. In order to overcome these problems and to increase the spatial resolution, in  the authIn this paper, recent advances and applications of FBG sensors, Brillouin and Rayleigh distributed sensors to the structural health monitoring of composite aircraft structures have been reviewed. The performance characteristics and intrinsic limitations of currently available fibre optic sensors and systems have been discussed with reference to the basic principles and the specific technologies of sensors and their sensor deployment in composite structures and possible application cases.A number of systems that have been proposed to date have been demonstrated to be already technologically mature for application in real situations, such as strain-based shape and operational load monitoring, included in smart composites , or the detection of disbonds or damage in composite repair patches, lap joints, bonded or joining elements. In these cases, distributed sensing may already offer several advantages over quasi-distributed sensorsin situations in which large rather than local areas are to be monitored, with high spatial resolution at relatively low frequency. In other cases, particularly the detection and evaluation of damage caused by impact, the location of which is difficult to determine in advance, there is much promising ongoing research focusing on the joint use of dynamic strains measured with FBG sensors and advanced pattern recognition algorithms, such as those based on principal component analysis (PCA) or independent component analysis (ICA) techniques, or piezoelectric sensors to generate Lamb waves. These SHM systems offer the possibility of monitoring the presence, size and progression of small impact damage (currently in the order of millimetres) in real time, in flight, and also on demand in the case of piezoelectric actuators. In this respect, distributed sensing systems are currently limited by the relatively low acquisition frequency allowed by the technology; their use for impact damage detection would need to be based on a different strategy, such as the deployment of a network of optical fibres which would enable the measurement of static strain changes with high spatial resolution, thus increasing the chances of detection in close proximity to the damage area.To achieve the ultimate goal of establishing a standardisation framework for sensor quality, application and integration in the aircraft environment, as envisaged by Airbus in the forthcoming years, some additional research and development are required to ensure highly reliable detection capability, robustness in order to avoid signal loss in the case of fibre breakage, and maintainability to permit the replacement of damaged fibre sensors.


In this paper, a stiffness match method is proposed to reduce the vibration sensitivity of micromachined tuning fork gyroscopes. Taking advantage of the coordinate transformation method, a theoretical model is established to analyze the anti-phase vibration output caused by the stiffness mismatch due to the fabrication imperfections. The analytical solutions demonstrate that the stiffness mismatch is proportional to the output induced by the external linear vibration from the sense direction in the anti-phase mode frequency. In order to verify the proposed stiffness match method, a tuning fork gyroscope (TFG) with the stiffness match electrodes is designed and implemented using the micromachining technology and the experimental study is carried out. The experimental tests illustrate that the vibration output can be reduced by 73.8% through the stiffness match method than the structure without the stiffness match. Therefore, the proposed stiffness match method is experimentally validated to be applicable to vibration sensitivity reduction in the Micro-Electro-Mechanical-Systems (MEMS) tuning fork gyroscopes without sacrificing the scale factor. MEMS vibrational gyroscopes are a kind of inertial sensor for measuring angular rate or angle, based on an energy transfer of two vibrational modes with the Coriolis effects . MicromaA MEMS tuning fork gyroscope is a very common type to cancel the external linear vibration output using two identical masses that vibrate in anti-phase ,12,13,14This paper proposes a stiffness match method to reduce the vibration sensitivity using the stiffness match electrodes. A theoretical model of the stiffness match method is established and the vibration output of the non-ideal TFG is analyzed in The non-ideal TFG model with the match stiffness is shown in Left tine:Right tine:Subtracting Equation (2) from Equation (1):Adding Equations (1) and (2):To obtain the anti-phase vibration output, a coordinate transformation is used as follows:Substituting Equation (5) into Equations (3) and (4):Thus, Equation (6) can be written as a matrix representation:By using the characteristic equation, the natural frequency can be obtained:The modal superposition method is used to solve Equation (7), and the steady-state response is obtained:When Considering that Substituting Equation (11) into Equation (10):x axis) is The stiffness mismatch can be reduced using the stiffness match electrodes with the negative electrostatic spring effect . The stiThus, the electrostatic force in the left part of the left mass is:N denotes the total number of the stiffness match electrodes.Similarly, the electrostatic force in the right part of the left mass is:Therefore, the total electrostatic force is:The direction of the electrostatic force is opposite with the direction of the stiffness spring. According to Hooke’s law, the match stiffness Therefore, substituting Equation (17) into Equation (12), one obtains:From Equation (18), it is figured out that the anti-phase vibration output can be rejected by reducing the stiffness mismatch through the stiffness match method.In order to verify the stiffness match method we proposed, a dual-mass micromachined tuning fork gyroscope is designed and fabricated. The architecture in the sense axis direction  consists of two identical tines and a coupling spring, as shown in The fabrication is implemented using Silicon-on-Glass (SOG) technology. Finally, the fabricated MEMS tuning fork gyroscope is shown in In order to further analyze the anti-phase vibration output caused by the linear vibration due to the stiffness mismatch, the experimental study is carried out. The experimental setup is shown in First, the electrical frequency sweep is carried out using the control circuit. Specifically, the movable mass is imposed using a sinusoidal carrier signal of 5 V, and a dc bias voltage of 5 V and an ac voltage of 0.1 V with a frequency sweep range from 3000 to 4000 Hz is applied on the fixed electrodes. To change the degree of the stiffness match, the voltage of the stiffness match 2). The output voltage of the differential sense capacitance without the stiffness match is shown in Then, the mechanical frequency sweep is carried out using a vibration shaker. The printed circuit board is only powered by the DC power supply without the other electrical signals. The excitation acceleration signal with a frequency sweep range from 3000 to 4000 Hz is sinusoidal, and its amplitude is 1 g , the vibration output displacement difference can be expressed as:Finally, the theoretical output voltage of the differential sense capacitance in the anti-phase mode frequency is obtained under the different voltage Comparisons of the experimental and theoretical values are displayed in According to Equation (18), it is concluded that the anti-phase vibration output of the MEMS tuning fork gyroscope is proportional to the stiffness mismatch and inversely proportional to the coupling stiffness. Based on the theoretical analysis, it can be seen that there are two ways to effectively eliminate the anti-phase vibration output without sacrificing the scale factor. One way is to design a structure to increase the coupling stiffness by using the anchored coupling mechanism according to the previous study , which tHowever, the anti-phase vibration output is still not completely eliminated. The possible reasons are that there are also mismatch between the mass and damping of the left and right tines and the other possible causes such as the asymmetric electrostatic forces and the capacitance nonlinearity, which will induce the anti-phase vibration output. Because other complicated factors can affect the anti-phase vibration output, how to better reduce the anti-phase vibration output needs to be further studied in the future.This paper proposes a stiffness match method to reduce the vibration sensitivity of micromachined tuning fork gyroscopes. Making use of the coordinate transformation method, a theoretical model is set up to investigate the anti-phase vibration output caused by the stiffness mismatch due to the fabrication imperfections. The analytical results reveal that the stiffness mismatch is proportional to the output induced by the linear vibration from the sense direction in the anti-phase mode frequency. In order to verify the proposed stiffness match method, the TFG including the stiffness match electrodes are designed and implemented using micromachining technology and the experimental study is carried out. The experimental tests demonstrate that the linear vibration output can be reduced by 73.8% through the stiffness match method with stiffness match electrodes compared to the structure without the stiffness match. Therefore, the proposed stiffness match method is experimentally validated to be applicable to the vibration sensitivity reduction in the tuning fork gyroscopes without sacrificing the sensitivity.


Stochasticity ubiquitously inevitably appears at all levels from molecular traits to multicellular, morphological traits. Intrinsic stochasticity in biochemical reactions underlies the typical intercellular distributions of chemical concentrations, e.g., morphogen gradients, which can give rise to stochastic morphogenesis. While the universal statistics and mechanisms underlying the stochasticity at the biochemical level have been widely analyzed, those at the morphological level have not. Such morphological stochasticity is found in foral organ numbers. Although the floral organ number is a hallmark of floral species, it can distribute stochastically even within an individual plant. The probability distribution of the floral organ number within a population is usually asymmetric, i.e., it is more likely to increase rather than decrease from the modal value, or vice versa. We combined field observations, statistical analysis, and mathematical modeling to study the developmental basis of the variation in floral organ numbers among 50 species mainly from Ranunculaceae and several other families from core eudicots. We compared six hypothetical mechanisms and found that a modified error function reproduced much of the asymmetric variation found in eudicot floral organ numbers. The error function is derived from mathematical modeling of floral organ positioning, and its parameters represent measurable distances in the floral bud morphologies. The model predicts two developmental sources of the organ-number distributions: stochastic shifts in the expression boundaries of homeotic genes and a semi-concentric (whorled-type) organ arrangement. Other models species- or organ-specifically reproduced different types of distributions that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning. Biological systems ubiquitously and inevitably exhibit stochasticity in traits from the molecular level to the multicellular and morphological level. The stochasticity in the numbers of protein molecules within single cells has been extensively analyzed in species ranging from bacteria to mammals  widely reproduced the asymmetric variation found in nature. The error function is derived from mathematical modeling of the floral organ positioning, and its parameters represent measurable distances on the floral bud morphologies. Moreover, the model predicts several mechanisms for the observed distributions . The modified ERF model requires a semi-concentric organ arrangement  to give an asymmetric distribution, whereas it does not require such an arrangement to give a symmetric distribution. Other models, i.e., the Gaussian, the Poisson, and the log-normal distributions, reproduced different types of variations species- or organ-specifically that reflect different developmental processes. The organ-number variation could be an indicator of stochasticity in organ fate determination and organ positioning during floral development.n in each dataset is described at the top of each graph in Figures 4 and in column n in Table Populations of flowers were studied in natural and cultivated environments. The sampling of each floral population was limited both temporally 1–8 days) and spatially (diameter up to 100 m), because seasonal Weldon,  as well –8 days ahttp://www.r-project.org) with nlsLM function provided by the minpack.lm package  method, where the probability of each organ number was a single data point. Because the organ number in each population does not distribute to a very large number of states , which is represented by the parameter number of the model M denoting the number of the organ number with non-zero frequency  given byThe AIC can be used to autonomously select the best-fit statistical distribution, which gives the minimum value of the AIC. When the number of states M > k + 1 and converges to the AIC at the upper limit of M  and two discrete distributions (the Poisson and the modified ERF). We chose the four continuous models because the standard Gaussian distribution is the most basic distribution in statistics, the log-normal  and the scale θ (>0), and the gamma function Γ(k)  Figure . The meaThe probability density function of the beta distribution is given byX but also bimodal, depending on the two shape parameters α and β . By normalizing the factor maxc − minc, the probability density function of the modified beta distribution can be represented bywhere B is the beta function. The probability density function is not only skewed to either larger or smaller values of β Figure . BecauseX denotes the organ number and where c of candidate sites that usually grow one primordium but rarely have two primordia. When the probability of having two primordia is very low but not negligible , the organ number satisfies the condition for the Poisson distribution. Bachmann and Chambers . Also, the increase in perianth organ number accompanied by disruption of the perianth/stamen boundary was observed experimentally by silencing the homeotic gene APETALA3 paralog in Nigella damascena, Ranunculaceae . We defined the radial gap between two semi-whorls as ex + in, where the average position of expression boundary μr is located between the Mo-th and (Mo + 1)-th  primordia at distances ex and in, respectively. We used d as a scaling parameter . Thus, the probability of floral organ number X becomes In addition to the boundary variation, we assume that the organs take on the semi-whorled arrangement that is widely observed in the Ranunculaceae  integrates the probability that the expression boundary is located within the exterior whorl, resulting in a decrease in the organ number. The second line (X > Mo) integrates the probability that the expression boundary is within the interior whorl. The third line (X = Mo) integrates the probability that the expression boundary is located within the gap between the two whorls. Because we assumed semi-concentric arrangement, there are several situations that the ERF model is unlikely to account for. Many of the Oleaceae species, except for Jasminum , as in spiral phyllotaxis , we reconstructed the probability distributions for 49 species, which were sampled by either ourselves or other authors  of Eranthis pinnatifida  sepals and petals  of the Ranunculaceae data sets , in contrast to the morphogen gradients in Drosophila embryogenesis , the mode of the petal number is five, but the distribution has a second peak at 10  due to the change of fitting parameters for the beta distribution. We did not find any case that the best model changes depending on the initial conditions of the log-normal or the gamma distribution. A wide exploration of initial conditions could improve the selection of statistical models of organ-number variation.The parameters after the convergence of the non-linear least-square method generally depend on the initial set of fitting parameters. Although we set the initial conditions intuitively to avoid divergent parameter fitting, there might be other initial conditions resulting better parameter sets . The fitting parameters were occasionally sensitive to initial conditions for the log-normal, the gamma, and the beta distributions when The variation in the floral organ numbers of various eudicot species was fit to six statistical models. Statistical model selection revealed that the selection of the best model was reproducible for each species and organ. The modified ERF model, which we first proposed by assuming a semi-concentric arrangement of organ primordia following helical initiation and stochasticity in the concentric determination of organ fate during floral development, was widely selected for the perianth organs of eudicots, and even for the stamens and ray florets of some core eudicots. The standard Gaussian and log-normal distributions were selected, respectively, for the Oleaceae petals, which show the simultaneous initiation of the primordia, and the Papaveraceae ovules, which have a totally different developmental process compared with the perianth organs. We showed that the different distributions of morphological traits reflect different developmental processes. The modeling of developmental process of these organs and the statistical analyses of other species and organs will shed more light on the developmental and evolutionary sources of morphological variation.Conceived and designed the experiments: Miho S. Kitazawa, Koichi Fujimoto. Performed the data collection and the statistical analysis: Miho S. Kitazawa, Koichi Fujimoto. Analyzed the data: Miho S. Kitazawa, Koichi Fujimoto. Contributed materials/analysis tools: Miho S. Kitazawa, Koichi Fujimoto. Wrote the paper: Miho S. Kitazawa, Koichi Fujimoto.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


In ultrasound-guided High Intensity Focused Ultrasound (HIFU) therapy, the target tissue (such as a tumor) often moves and/or deforms in response to an external force. This problem creates difficulties in treating patients and can lead to the destruction of normal tissue. In order to solve this problem, we present a novel method to model and predict the movement and deformation of the target tissue during ultrasound-guided HIFU therapy.Our method computationally predicts the position of the target tissue under external force. This prediction allows appropriate adjustments in the focal region during the application of HIFU so that the treatment head is kept aligned with the diseased tissue through the course of therapy. To accomplish this goal, we utilize the cow tissue as the experimental target tissue to collect spatial sequences of ultrasound images using the HIFU equipment. A Geodesic Localized Chan-Vese (GLCV) model is developed to segment the target tissue images. A 3D target tissue model is built based on the segmented results. A versatile particle framework is constructed based on Smoothed Particle Hydrodynamics (SPH) to model the movement and deformation of the target tissue. Further, an iterative parameter estimation algorithm is utilized to determine the essential parameters of the versatile particle framework. Finally, the versatile particle framework with the determined parameters is used to estimate the movement and deformation of the target tissue.To validate our method, we compare the predicted contours with the ground truth contours. We found that the lowest, highest and average Dice Similarity Coefficient (DSC) values between predicted and ground truth contours were, respectively, 0.9615, 0.9770 and 0.9697.Our experimental result indicates that the proposed method can effectively predict the dynamic contours of the moving and deforming tissue during ultrasound-guided HIFU therapy. To experimentally validate our method, we applied it to the target tissue, which allowed us to both train our parameters and verify our experimental results based on both contour and DSC values.th frame, 18 HIFU ultrasound images of the selected cross section in every other 10 frames were used as the ground truth images, which were segmented manually by an experienced physician to obtain ground truth contours. We utilized 1st~9th ground truth contours as the training set, and the 10th~18th ground truth contours as the validation set. Using the versatile particle framework, we modeled the environment surrounding the target tissue. Starting from the 20th time steps, we output the calculation contours every other 10 time steps. We adopted the iterative parameter estimation algorithm in st~9th output contours within the deviation compared with that of the 1st~9th ground truth contours. In the experiment, the particle number of target tissue, fluids and rigid body were, respectively 4399, 3344 and 120. The acquired essential parameters of the versatile particle framework are shown in The ultrasound-guided HIFU equipment was used in our experiment to record time series of ultrasound images with mechanical movement and deformation. A single cross section of the target tissue was recorded while an external force was applied. Starting from the 20The ground truth contours (green) and predicted contour (red) are shown in Our method can predict the movement and deformation of the target tissue by analyzing the recorded images of dynamic changes in response to external forces. It provides the opportunity to adjust in a timely manner the focal region of ultrasound-guided HIFU equipment, allowing the HIFU treatment head to remain aligned with the tumorigenic tissue throughout the course of therapy. Compared with the Kalman filtering method , which at(x) cannot measure the grey level uniformity around each point perfectly. Second, the GLCV model inherits the drawback of the LCV model that the contour evolution process increases the amount of calculation. The average time for segmenting a HIFU ultrasound image is 15.1 seconds. However, segmentation by GLCV is still faster than manually segmenting the HIFU ultrasound images and some segmentation task can be accomplished in pre-computing process before prediction. Third, the performance of the proposed versatile particle framework depends on the number of particles. If the number is too large, the real-time capability of the model is affected. In our experiment, we achieved a frame rate of 11.5 frames/sec which is close to real-time computation. For more complex scenarios with a large number of particles, it could be a challenge to obtain real-time prediction results.However, there exist challenges and limitations. First, while the proposed GLCV method can accurately segment a single target tissue, it is still difficult to segment target tissue’s HIFU ultrasound images which are extremely non-homogeneous as the characteristic function Despite these limitations, this paper has proposed a new method to segment HIFU ultrasound images instead of manually segmenting and predicting the movement and deformation of target tissue during ultrasound-guided HIFU therapy to make adjustment to the HIFU treatment head, and the correctness of our method has been validated by the experimental results.in vivo is similar to the implementation process shown in in vivo, the motion of target tissue is more complex than that in our experiments. To implement our tissue motion prediction method in vivo, in our future work we will study more complex forms of external forces and accelerate the computation to enhance real-time performance with a high prediction accuracy.The implementation of our method We have presented a novel method to model and predict target tissue movement and deformation during ultrasound-guided HIFU therapy. We first proposed the GLCV model, which utilizes edge information and adopts a localized active contour model to segment HIFU images effectively. The segmentation results are then used to reconstruct a 3D model of the target tissue. To predict the movement and deformation that the target tissue undergoes when exposed to the external force, we propose a versatile particle framework to compute multiphase coupling among target tissue, rigid body and fluids. After estimating essential parameters of the versatile particle framework using the iterative parameter estimation algorithm, we utilize these parameters in the versatile particle framework to predict the movement and deformation of the target tissue. Our experimental results show that the lowest, highest and average DSC values of predicted contours and the ground truth contours are 0.9615, 0.9770 and 0.9697, respectively. Our experimental results also suggest that our method can predict the movement and deformation of target tissue effectively.


Ixodes ricinus ticks feeding on Apodemus flavicollis mice  sampled in Trentino . The tail of the distribution of the number of ticks per host was fitted by three theoretical distributions: Negative Binomial (NB), Poisson-LogNormal (PoiLN), and Power-Law (PL). The fit with theoretical distributions indicated that the tail of the tick infestation pattern on mice is better described by the PL distribution. Moreover, we found that the tail of the distribution significantly changes with seasonal variations in host abundance. In order to investigate the effect of different tails of tick distribution on the invasion of a non-systemically transmitted pathogen, we simulated the transmission of a TBE-like virus between susceptible and infective ticks using a stochastic model. Model simulations indicated different outcomes of disease spreading when considering different distribution laws of ticks among hosts. Specifically, we found that the epidemic threshold and the prevalence equilibria obtained in epidemiological simulations with PL distribution are a good approximation of those observed in simulations feed by the empirical distribution. Moreover, we also found that the epidemic threshold for disease invasion was lower when considering the seasonal variation of tick aggregation.The spread of tick-borne pathogens represents an important threat to human and animal health in many parts of Eurasia. Here, we analysed a 9-year time series of  Our work analyses a 9-year time series of tick co-feeding patterns on Yellow-necked mice. Our data shows a strong heterogeneity, where most mice are parasitised by a small number of ticks while few host a much larger number. We describe the number of ticks per host by the commonly used Negative Binomial model, by the Poisson-LogNormal model, and we propose the Power Law model as an alternative. In our data, the last model seems to better describe the strong heterogeneity. In order to understand the epidemiological consequences, we use a computational model to reproduce a peculiar way of transmission, observed in some cases in nature, where uninfected ticks acquire an infection by feeding on a host where infected ticks are present, without any remarkable epidemiological involvement of the host itself. In particular, we are interested in determining the conditions leading to pathogen spread. We observe that the effective transmission of this infection in nature is highly dependent on the capability of the implemented model to describe the tick burden. In addition, we also consider seasonal changes in tick aggregation on mice, showing its influence on the spread of the infection. Several ecological studies have shown that the distribution of ticks on their hosts is often highly aggregated, with a large number of hosts harbouring few parasites and a small number harbouring a large number of them . In addiRickettsia spp., the pathogen agents causing Rocky Mountain Spotted Fever, are maintained by systemic and trans-ovarial transmission in Dermacentor variabili and andersoniBorrelia Burgdoferi s.l. spirochaetes persist in nature by taking advantage of all three routes of transmission in I. ricinus, The transmission of tick-borne diseases is characterised by an intricate set of ecological and epidemiological relationships between pathogen, tick vector, vertebrate hosts and humans that largely determine their temporal and spatial dynamics Borrelia burgdorferi sensu lato and Anaplasma phagocytophilum, where other efficient routes of transmission have been observed.In the case of the tick-borne encephalitis virus (TBEv), which is an increasing public health concern in Europe Tick aggregation on hosts and correlation of tick stages facilitate co-feeding transmission and thus significantly increase the basic reproductive number, The degree of aggregation of ticks can be measured in a number of ways. Since the appearance of influential works by Randolph Ixodes ricinus ticks feeding on mice  to detect the best fit for the distribution of tick burden on mice by testing the performance of NB and PoiLN versus PL distribution, with particular interest in the shape of the distribution tail which is crucial to suitably describe the fraction of co-feeding ticks necessary for TBEv transmission. Then, we used a stochastic model to simulate the effect of fitting different tick distributions on the infection dynamics of a tick-borne pathogen. Specifically, we investigated the spread of a non-systemically transmitted pathogen (e.g. TBEv) by modelling the pathogen transmission between susceptible and infective ticks, considering only co-feeding transmission and distributing ticks on mice under the hypotheses of NB, PoiLN, and PL distributions. Finally, we investigated the seasonal variations in the pattern of tick burden distribution on mice and its implication on TBE-like infection dynamics.In the current study we used an extensive data set of All animal handling procedures and ethical issues were approved by the Provincial Wildlife Management Committee (renewed authorisation n. 595 issued on 04.05.2011)Rodent tick burden data was collected by trapping mice using capture-marking-recapture techniques during 2000–2008. The study area was a mixed broadleaf woodland Apodemus flavicollis captured with at least one tick attached. For each captured rodent the number and life stage of feeding ticks was carefully assessed and registered, without removal Apodemus flavicollis per trapping session is shown for the whole nine year period and for different grids (from A to I).In summary, the trapping effort consisted of p-value is defined as the relative number of times that the KS statistic of the fitted distributions on synthetic data exceeds that measured on real data. Therefore, the larger the p-value, the lower our confidence in rejecting the fit. We considered the conservative value Ticks patterns have usually been described as highly aggregated. Therefore, since the seminal works by Crofton p-value through KS statistics to indicate the goodness of the fit, as for the NB distribution As a first alternative to the NB distribution, we considered a power-law probability distribution (PL), in its discrete versionAnother aggregated distribution used for describe pattern of macroparasites Finally, we compared the PL hypothesis in fitting the tail of the real data distribution with the two alternatives NB and PoiLN by a log-likelihood ratio (LLR) test for different values of A. flavicollis abundance. To achieve this goal we smoothed the time series of captured mice with a quadratic polynomial curve. The parabola describing the mice abudance in a specific year and grid was normalised between 0 and 1 before isolating the time window where this normalised parabola was higher than a threshold value Beyond the estimate of the ticks-per-host distribution, we also investigated how the tick burden distributions vary over time and whether a significant difference was observed when different time periods were considered. In particular, we investigated the tick aggregation patterns during periods characterised by low and high A necessary condition for an effective non-systemic transmission of a pathogen is the coincidence of the larval and nymphal aggregation distributions on hosts To further evaluate the coincidence of tick stage distributions and the consequences on the non-systemic transmission of a pathogen, following Randolph et al. t+1). At each iteration t, with t being a discrete number between q. Then, on each mouse we said that of t among nymphs was t was parasitised by In order to explore the impact of different parasite aggregation distributions on the spread of a TBEv-like pathogen where the main transmission route is through co-feeding, we performed extensive numerical simulations informed by the data about tick aggregation on mice. In this setting, tick larvae were not infective  for each mouse qof the of the non-systemic transmission between infective nymphs and larvae on the same host occurs with probability (b) (c) if t will exit the infectious dynamics by moulting to the adult stage or dying.It is worth stressing that in the previous meta-code we did not consider ticks recovering from the infection, since we assumed that a feeding infective nymph at time t, we classified mice as observed during the mice peak activity  suggested that the optimum PL fit on the tail of the distribution should not be ruled out, and that the result holds for every PL fit with On the other hand, by fitting the tail of the distribution to a PL distribution, we found that the best fit was obtained for In The number of mice captured in different years and grids showed strong seasonal patterns as reported in t-test output: for t-statistic = p-value>0.1) and the LLR test indicated that the PL fitting outperforms the NB model  in the estimates both inside and outside the peak time window.On the data sets classified as inside (IN) and outside (OUT) the time window of mice abundance peak, we fitted for different time-window lengths . For synthetic distributions we considered the actual observed distribution below the estimated f) showed that Results, plotted in hold see . In addiiour see .qIN we considered a PL with exponent qOUT a PL distribution with exponent qIN and qOUT we further set Furthermore, we investigated the effect of differences in the distribution of the tick burden as a function of the abundance of mice on the spreading of a non-systemic infectious disease. To this end, we fixed fat tailed distributions other than the NB one can also adequately reproduce tick aggregation, as shown by Elston et al. Tick aggregation on hosts is the result of several complex interactions of biotic and abiotic factors, such as host exposure and susceptibility to ticks, ticks' phenology and host behaviour, environmental factors, availability of resources, and others Ixodes ricinus ticks on mice, we showed that a PL distribution is better able to describe the right tail of the tick distribution on hosts than a NB or a PoiLN distribution  infesting plaice (Pleuronectus platessa) decreases during summer months. They mainly ascribed the observed variation to significant differences in mean parasite burden among months. On the other hand, we did not find significant differences in tick burden inside and outside the window of high rodent abundance. Specifically, in the case of p>0.05). However, the second moment of the number of ticks per host drastically changed between high and low abundance periods, driving the difference in the aggregation distributions observed in the two time windows. Seasonal variations in resource availability and host abundance can have a significant effect on the space used by mice. Males and females tend to respond to these changes in different ways, since space use for females is driven largely by food availability, whereas the distribution of males is related primarily to mating opportunities. Yellow-necked mouse (A. flavicollis) females exhibited reduced spatial exclusivity and larger home ranges during lower food availability while males varied their spatial distribution accordingly by also expanding their home ranges Apodemus sylvaticus) In order to fully understand the different tick attachment behaviours on hosts, we identified different time windows related to rodent seasonal dynamics. Using this approach we found that the distribution of ticks on mice may vary across the season, with higher aggregation heterogeneity in periods of low rodent abundance and lower aggregation heterogeneity during the peak of host abundance see . We alsoases see . Shaw anOur primary goal was to help understand the role of tick aggregation across mice on the spread of non-viraemic transmitted diseases through a simple and general transmission model. Other works – such as Text S1Sensitivity analysis of distribution parameters on epidemic spreading.(PDF)Click here for additional data file.Text S2Sensitivity analysis of f, fraction of nymphs among ticks.(PDF)Click here for additional data file.


A new filling-in model is proposed in order to account for challenging brightness illusions, where inducing background elements are spatially separated from the gray target such as dungeon, cube and grating illusions, bullseye display and ring patterns. This model implements the simple idea that neural response to low-contrast contour is enhanced (facilitated) by the presence of collinear or parallel high-contrast contours in its wider neighborhood. Contour facilitation is achieved via dendritic inhibition, which enables the computation of maximum function among inputs to the node. Recurrent application of maximum function leads to the propagation of the neural signal along collinear or parallel contour segments. When a strong global-contour signal is accompanied with a weak local-contour signal at the same location, conditions are met to produce brightness assimilation within the Filling-in Layer. Computer simulations showed that the model correctly predicts brightness appearance in all of the aforementioned illusions as well as in White's effect, Benary's cross, Todorović's illusion, checkerboard contrast, contrast-contrast illusion and various variations of the White's effect. The proposed model offers new insights on how geometric factors , together with contrast magnitude contribute to the brightness perception. Simultaneous brightness contrast, in which a gray target appears brighter when surrounded by black than a gray target surrounded by white, suggests that brightness perception is not determined solely by the luminance of the target but depends on the luminance of the surrounding region as well. The explanation of brightness contrast involves lateral inhibitory interactions that suppress response near the gray side of the gray-white border and enhance response at gray side of the gray-black border. Differential responses to luminance discontinuities are achieved by center-surround antagonism in the receptive fields found in the early stages of visual processing  function. In the proposed model, the recurrent MAX function achieves two computational goals. In the BCS, it supports contour facilitation among collinear or parallel like-oriented nodes. In the FCS, it supports brightness filling-in among un-oriented nodes. The second section describes the model's components, including two separate processing streams: BCS and FCS. The third section describes the output of the model's components when they reach a steady-state. Finally, the fourth section discusses behavioral and neurophysiological data relevant for contour facilitation.The cortical microcircuit capable of computing MAX function is presented in Figure The arrangement of nodes depicted in Figure The proposed neural architecture for brightness perception is depicted in Figure ON and OFF Contrast Pathways compute luminance ratios between two sides of luminance border using shunting or divisive inhibition. Computation of the ratio is implemented by the nodes with balanced center-surround receptive fields simulating the properties of neurons in the retina and LGN. These cells respond strongly to sharp luminance borders but their response is attenuated on uniform luminance areas or on shallow luminance gradients. The nodes in the ON Contrast Pathway respond strongly on the bright side of the bright-dark border while the nodes in the OFF Contrast Pathway provide a complementary signal by providing a strong response on the dark side of the bright-dark border.ON and OFF Luminance Pathways encode input luminance and its inverse, respectively. Sensitivity to luminance is implemented by cells with unbalanced center-surround receptive fields in which the center outweighs the surround, thus creating an approximate luminance detector. This model stage is justified by the analysis of Mach bands, Chevreul illusion and the perception of luminance gradients which cannot be accounted for by the output from the nodes with balanced receptive fields  signals with the output of BCS. The activity of the ON Filling-in Layer is isomorphic to brightness perception while the activity of the OFF Filling-in Layer is isomorphic to darkness perception. Both Filling-in Layers implement the recurrent computation of the MAX function among the nearest neighbor nodes. This slow isotropic spreading of neural activity requires more time to cover larger distances consistent with behavioral  from the white background to the gray targets, but it will not allow filling-in from the gray targets to the black background. In the same way, the OFF Filling-in Layer will produce filling-in (darkness assimilation) from the black background to the gray targets but it will not allow filling-in from the gray targets to the white background.Local Boundary Detection (LBD) receives input from the ON and OFF Contrast Pathways. It simulates the orientation selectivity of simple and complex cells found in the primary visual cortex. The receptive field of the model simple node consists of adjacent excitatory and inhibitory lobes elongated along the preferred orientation of the node. Excitatory lobe receives excitatory projections from the ON Contrast Pathway and inhibitory projections from the OFF Contrast Pathway. On the other hand, inhibitory lobe receives excitatory projections from the OFF Contrast Pathway and inhibitory projections from the ON Contrast Pathway. At each network location, there are two simple nodes with opposite contrast polarities, that is, with opposite arrangements of the excitatory and inhibitory lobes. The receptive field of the model complex node is created by summing output from the pair of like-oriented simple nodes with opposite contrast polarities. Consequently, complex cell loses sensitivity to contrast polarity.Figure Furthermore, the complex node computes the feedforward MAX function among its nearest neighbors  receives excitatory projections from the like-oriented nodes in the LBD stage. The GBD consists of nodes capable of long-range collinear and parallel contour facilitation. As Figure In contrast to the isotropic activity spreading within the Filling-in Layer, orientation-specific activity spreading among GBD nodes is a fast process because they have large extra-classical receptive fields capable of detecting distal input far from their classical receptive field. Consequently, activity spreading within the GBD stage could be achieved in a few steps. It should be noted that the GBD nodes do not have capabilities of bipole cells in the FACADE theory that can generate perception of illusory contours  Interaction represents the output of BCS which is projected to FCS. The L/G Interaction receives excitatory projections from the LBD nodes and divisive inhibition from the GBD nodes. Therefore, it computes the ratio between the corresponding Local and Global Boundary signals at each network location. When the Local and Global Boundary signals are of equal strength, their ratio will be close to 1. This is the case when there is no collinear or parallel contour facilitation among the GBD nodes. On the other hand, when the GBD signal is much larger relative to the LBD, their ratio will be much smaller than 1. The output of the L/G Interaction stage is binary. It will assume value 1 if the computed ratio crosses the threshold and value 0 if the ratio is smaller than the threshold. The threshold is set in a way to favor larger ratios . In this way, Boundary Contour representation of the low-contrast edge that is collinear or parallel with high-contrast edge will be removed from the BCS output. On the other hand, Boundary Contour representation of the low-contrast edge that is not collinear or parallel with high-contrast edge will remain intact in the BCS output.In order to better appreciate the image transformations taking place within different network stages, Figure Finally, the L/G Interaction computes the ratio between the output of the Local and Global Boundary Detection stages. This ratio is close to 1 if there is no contour facilitation and it is much smaller at locations where contour facilitation occurs within the GBD. Consequently, L/G interaction will attenuate spatial positions where the Global Boundary signal is much stronger relative to the Local Boundary signal as it occurs on the horizontal edges of the gray square. On the other hand, it will leave intact those locations where the Global and Local Boundary signals are of the same magnitude as it occurs on the white-black edges and on the vertical edges of the gray square. Threshold for the L/G Interaction removes completely Boundary Contour representation of the horizontal edges of gray square. Such removal of the Boundary Contour signals will produce activity spreading (assimilation) within the Filling-in Layers.In FCS, filling-in enables the brightness signals to spread until they are blocked at the luminance borders by the output of BCS . These Boundary Contour signals are effective in preventing filling-in only when they are complete, that is, when they cover all edges of the surface. In the OFF Filling-in Layer, there is no assimilation because activity spreading is blocked along both horizontal and vertical edges of the gray square. Activity spreading across vertical edges is blocked due to the BCS output. On the other hand, activity spreading across horizontal edges is blocked by the threshold of the Filling-in Layer nodes which prevents activity spreading when they receive weak input. The effect of this threshold is to prevent assimilation across black surfaces. In the ON Filling-in Layer, assimilation occurs from white background to the interior of the gray square due to the lack of the BCS output along the horizontal edges of the gray square. Again, blockage of activity spreading across the vertical edges of the gray square is due to the existing BCS output.Model's collinear projections are consistent with psychophysical findings on contour facilitation . The second part shows that the same assimilation effect arises when contours are arranged in parallel (bullseye illusion and ring patterns). Also, it shows that the model's response is reduced to the brightness contrast when there is no contour facilitation between low-contrast and high-contrast contours. Third part shows that the same computational principles explain illusions where inducing elements are connected with the target . Finally, in the fourth part it is shown that the model is able to explain various modifications of the White's illusions where inducing elements are detached from the target.The dungeon illusion will serve as an example to illustrate all model stages and to explain how contour facilitation might contribute to brightness perception. Figure Figure Interestingly, there is no assimilation for the gray squares on the black background in Figure Figure Output from the LBD is projected to the GBD whose output is shown in Figure Finally, the binary output of the L/G Interaction Figure  shows prFigure In the previous section, it was shown how collinear contour facilitation can account for the dungeon, cube and grating illusion. However, in the bullseye display (Bindman and Chubb, The present model accounts for these effects by the observation that when the high-contrast contour is positioned in parallel with the like-oriented low-contrast contour, it will produce the same excitatory effect as collinear contour will do within the GBD. This is a consequence of the fact that the model's GBD nodes have excitatory connections with like-oriented nodes positioned orthogonal to the preferred axis of orientation Figure . ParalleFurthermore, Figure It is interesting to note that the observed magnitude of brightness contrast is weaker compared to Grossberg and Todorović  because Figure The explanation offered here is closely related to the scission account of the White's illusion proposed by Anderson . HoweverFigure Here, an alternative explanation is given because the effect is attributed to the assimilation of surface color from the occluding squares. More precisely, brightening of the gray target on the left is a consequence of the brightness assimilation arising from the white occluding squares and the darkening of the gray target on the right is a consequence of the darkness assimilation arising from the black occluding squares. Güçlü and Farell  providedSeveral variations of White's illusion have been created in order to show that the explanation based on T-junction or transparency is not sufficient to explain the illusion. Simulations of these effects are presented in Figure The importance of collinear contour facilitation is illustrated by the variants of White's illusion devised by Anderson  and HoweHowever, when the gray target is positioned in a way that all of its borders are subject to collinear contour facilitation Figure , both blA novel filling-in model is developed in order to explain challenging brightness illusions listed in Table Computer simulations showed that the combined neural activity from the ON and OFF Filling-in Layers correctly predicts the appearance of gray patches in the dungeon, cube, and grating illusion, bullseye display and ring patterns. These illusions are beyond the scope of the previous filling-in models (Kelly and Grossberg, Importantly, the same mechanism is also able to account for other brightness illusions such as White's effect, Benary's cross, Todorović's illusion, checkerboard contrast and second-order contrast. Moreover, the model can explain variants of White's effect which do not contain T-junctions such as Yazdanbakhsh et al. . It shouFinally, when the background is homogenous, that is, when there are no inducing elements present in the background, the model generates a simultaneous brightness contrast. This is not the case with the contrast-contrast model which predicts only the assimilation effects Barkan et al. . AlthougAlthough the present model is able to account for a wide variety of brightness illusions it has several shortcomings. First, it provides only a qualitative prediction of the direction of the target brightness because the output of BCS is binary. Depending on the stimulus conditions, BCS either allows or prevents assimilation but it cannot modulate its strength. In other words, the model predicts the same magnitude of the assimilation effect for all illusions listed in Table Finally, the model of the global boundary network includes only excitatory lateral connections although it is known that inhibition plays an equally important role in mediating lateral interactions (Adini et al., The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Attention placebo control (APC) is considered a highly valid control condition when conducting trials of social interventions. Unfortunately, an appropriate APC condition is rarely used. This letter discusses the tension between methodological and ethical requirements of an APC group in psychosocial interventions based on our experiences with a randomized controlled efficacy study of a parent training program. To prevent negative side effects and high drop-out rates, feasible and accepted attention control conditions are discussed. The paradigms of placebo research must be adapted to the special challenges of psychosocial intervention research.Trial registration: Clinicaltrials.gov NCT02313493: registered 10 December 2014 Several researchers claim that psychosocial intervention research should not only rely on the classical design of active treatment versus waitlist control group, but should also include an attention placebo control (APC) arm to test the specific effect of the psychosocial treatment . HoweverResearchers rarely use APCs in the field of parent training. A review of the effectiveness of group-based parent education programs on behavioral problems of 3- to 10-year-old children found that out of 255 such studies none included an APC condition . To our In the study described here, the experimental condition was a parent training to improve parenting skills and the psychological well-being of expecting first-time parents and their babies. A discussion group moderated by a psychologist was chosen as the APC condition. Here, the participants were encouraged to share information and exchange experiences and worries about becoming a parent. The intervention group and the APC discussion group were equivalent concerning the number of contacts, time of start and duration, peer support and presence of a professional, but not regarding the content of the specific parent training under study. When we developed the study, four studies were already running in UK and Australia comparing prevention-oriented parent training with care as usual or waitlist. To deepen the understanding of the effectiveness of the parent training program, we wanted to learn how the so-called non-specific (placebo) factors like social support/social attention affect the success of the program. At this point, we were not aware, and more importantly, did not expect that a pure APC arm would result in the problems described here. We questioned whether both the APC and the parenting training group would improve the well-being of becoming first-time parents and therefore would be comparable in regard to clinical equipoise. As far as the additional benefit of one group over the other is not evident, clinical equipoise can be assumed in randomized controlled trails . ProfessVotum 036). Prior to the training, we informed the participants about the purpose of the study and the voluntary nature of their participation. They gave written informed consent before participating. After randomization, 19 couples were allocated to either the parenting training (11 couples) or the APC (8 couples) group. Disproportional drop-out numbers after randomization posed the first methodological problem, which eventually led us to discard the APC group. Specifically, 4 couples (50%) in the APC group and 2 couples (18.2%) allocated to the parent training group dropped out after randomization. Also, the cited reasons for dropping out differed between the two groups. The couples within the APC group dropped out without a reason or because they wanted to participate in the parent training and not in the discussion group. The parents in the training group dropped out because of scheduling difficulties.The study was approved by the Ethics Committee of the Faculty of Psychology at the Ruhr-Universität Bochum on 4 September 2012  called for simply asking the parents what they would be interested in and then encouraging the participants to discuss among themselves. Yet, the participants wanted the psychologists to tell them what they should deal with.Furthermore, ethical reasons prompted us not to continue the study as originally planned. In particular, we were confronted with parents’ comments and questions that showed risky misunderstandings of childcare, which could have exposed a child to dangerous parenting behavior. For example, some parents had misleading ideas about settling strategies like settling a baby on top of a shaking washing machine. One mother had lost a baby due to sudden infant death (SID) and asked for confirmation regarding advice given in a brochure. We felt ethically obligated to correct false understandings of childcare and to reassure the parents that they had received correct information on SID. We felt that we would be responsible in case parents would leave the group with false and dangerous beliefs discussed within the group but not corrected by a psychologist. Moreover, it was difficult to differentiate between mistaken ideas about parenting that would still be acceptable versus ideas that needed to be commented on and dealt with.Our experiences demonstrated the contradiction between the ethical and methodological requirements of a placebo control group for psychosocial training interventions like our parenting program. Although we expected that parents would benefit from the social support of other parents and from the monitoring function of the psychologist, it became evident that an undirected discussion group as a placebo control group is neither a feasible nor an ethical alternative to the parenting training for expecting first-time parents. We detected different causes for this outcome.First, parents were confronted with the randomization of the two intervention arms which in our study design were considered equally attractive. Researchers are ethically required to inform participants about study design and to describe the intervention arms under study. When parents were asked about their motivation to participate in the study, the majority explained that they felt insecure in their future role as parents. Thus, contrary to prior expectations, the APC design did not meet the participants’ expectations of receiving information about parenting. Therefore, the discussion group without active guidance was not as attractive as the parent training group. Second, the APC did not provide a convincing therapeutic rational compared to the experimental group, even though we introduced the APC as a promising intervention with its social support and attention aspects. Furthermore, the disproportionally high drop-out rate within the control condition demonstrates a methodological problem in the group selection. Third, an APC within a parenting program poses an ethical problem: parents might exchange false and harmful information in the discussion group, which the psychologist leading the group must amend.What are the alternatives? A more appropriate APC should meet the expectations of the target group and must provide a convincing therapeutic rational. For the participants in the present case study, the therapeutic rational would be: (1) social support of other participants and (2) collectively working on solutions for difficulties that can emerge during the transition to parenthood. An agenda based on the participants’ expectations, fixed time frames per topic and communication rules would provide a more clear and conclusive structure for group discussions. To control for attractiveness of APC versus experimental treatment, the program’s credibility before and after the first session should be assessed.To deal with the contradiction between the ethical and methodological requirements of a placebo control group for psychosocial training interventions like parenting programs, we should look back at the beginning of placebo conditions in research, even drug research. Psychosocial research adopted the use of a placebo condition from drug research except for one important detail - blind participation. If participants would not be aware of the different ingredients of the treatments under comparison , drop-out after randomization would decline. In fact, common recruitment strategies where treatment conditions are revealed are not suitable for blind randomization. However, instead of randomizing individual participants, a randomization of groups of participants might ensure blinding without inducing unequal drop-out rates. In the case of prevention trials , researchers may randomize whole institutions instead of individuals through existing prevention infrastructure, such as birth preparation classes or gynecological practices. This type of cluster random allocation may be an ethical and methodologically adequate compromise to maintain blindness.Although scientific advantages of an APC group are obvious, the design of a control group for a prevention-oriented parenting program calls for alternative methods. One solution might be a dismantling strategy where specific elements of a treatment program are studied separately. For example, the parent training program under investigation includes parent communication skills training and baby-calming techniques. A design with three arms  would help us to evaluate how such components impact the success of a parent training program in expecting first-time parents.In conclusion, intervention researchers should think out of the box: first, they should consider dismantling strategies to offer more attractive treatment conditions. Second, study designs with cluster randomization might help to avoid drop-outs caused by less desirable placebo conditions. This way more researchers would be encouraged to test for placebo effects and shed light on specific treatment effects as well as on the feasibility of treatments in clinical interventions.In theory, theory and practice are the same. In practice, they are not.- Albert Einstein