Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potential. While the first peak follows a stimulation, the second corresponds to the random arrival over much longer time of ions located in the synaptic terminal to small binding vesicular targets. To conclude, the present multiscale stochastic modeling approach allows studying cellular events based on integrating discrete molecular events over several time scales. Cellular activation is described by the binding of few diffusing molecules to specific small and hidden targets. What is the time scale of a cell response, triggered by rare molecular events? Such a process requires exploring microdomains at a nanometer precision. Examples are vesicular fusion triggered by the binding of calcium ions, detection of a morphogen concentration by a growth cone, molecular events underlying the induction of synaptic plasticity at neuronal synapses or activating cellular check points where molecular events are transformed into a cellular decision.Traditional chemical kinetics231However, none of the approaches described above have been used to model the interaction between a large bath of particles modeled by a continuous dynamic and a stochastic dynamic induced by rare events where few particles bind to small targets to trigger a response.The goal of this report is to introduce a novel hybrid model and to provide an application to synaptic physiology for computing the probability of vesicular release following calcium influx. Calcium ions induce vesicular release when few of them accumulate underneath a vesicle. This accumulation can follow the direct influx at a short time scale or can be due to ions originating from the pre-synaptic terminal with a longer time scale. In all cases, triggering a vesicle release is a rare molecular event described as the accumulation of few ions at a single protein locationR are modeled as Brownian particles, entering a domain Ω through localized point sources with an inward flux J(t) at each single source. The entering Brownian particles can reach any target site to activate them. After particles enter, they can either hit a small target or reach the bulk, where they are lost in the undifferentiated state consisting in many particles. In the bulk, the reactant particles R can either interact with a substrate S, leave the bulk with a rate kes or bind a target site with rate kT, as shown in T particles at a single target is the event that we are interested in, as it models a cellular activation from a molecular event. As we shall see here, the Brownian reactant particles and the small targets can be described by a coarse-grained model, where the mass action description (for the continuum limit) is coupled to a finite state Markov chain  of particles enters the domain at a source point x. The entering particles can reach a small target with a splitting probability ps(x) or go to the bulk with probability 1 − ps. A particle entered at point x that reaches one of the NT target sites, will reach specifically site i with probability q, for i = 1..NT (see the Methods section for the description). Thus the flux of ions arriving at a target site i is the sum of the conditional fluxes over the ensemble of point source locations The flux ps(x) for a Brownian particle to reach the small ribbon below a ball  is the distance between the point source and the closest target site, and ε is the height of the ribbon representing the target site. This probability accounts for the particular geometry of the target and depends on the relative distance between the targets and the source pointswhere So far, we discussed the direct arrival of a particle from a point source. We now consider the arrival of a Brownian particle coming from the bulk to one of the small targets. This arrival to a small ribbon red in  is PoissD is the particle diffusion coefficient.where i and for a given distribution P of source points, the probability Pri{k, t} that k particles are bound at time t is computed from a Markov model: once a particle binds to a target, it cannot unbind, and thus the transition probability from the states k − 1 to k (bound particles), between t and t + Δt, is due to the fluxes of particles from the point sources and from the bulk:We shall now present the set of equations that describe the arrival of a few number of particles to the target either coming directly from the point source or from the bulk. For each target site where i summed over all point sources. It represents the amount of particles reaching target i directly after their entry through a source point. The second term kTNf (t) represents the fraction of particles originating from the bulk that will bind to the target sites. Here Nf (t) is the number of free particles at time t in the bulk, and kT is the arrival rate of particles located in the bulk. The rate kT is computed using the Mean First Passage Time theory5The first term T bound particles. We obtain for each target 1 ≤ i ≤ NT, the Markov chain for the probabilities We shall now described the model of activation. A target is considered to be activated when there are exactly k = T describes the absorbing state for the probability t = 0 iswhere the final equation for and the normalization condition isT for target i, when the distribution of point source is T particles at target i. It is also the last passage time of a particle when T − 1 particles are already at the binding sites. The distribution of time i and is given byWe can now introduce the time hence the probability density function and the mean release time T binding events. We note that the particles originate from two sources: either from the bulk or a transient influx. We shall introduce in the next section a new set of equations to couple the Markov chain and the density of free particles Nf (t) that can further interact with a varying population of substrates S.To conclude this section, we have presented here a Markov chain that counts exactly The reactant particles in the bulk can interact with a substrate according to the chemical reactionk−1 (resp. k0) is the backward (resp. forward) rate. We determine the mass-action equations for the number of free Nf (t), and bound Nb (t) particles. The total number of substrate sites Stot is fixed, and at time t, the number of available sites is Stot − Nb(t). The particles can escape the domain Ω at a Poissonnian rate kes, and bind to a target site with a rate kT. We note that the probability that target i is free, i.e. not activated, is given bywhere Nf and Nb satisfy the mass action equations:In summary, kes is fast compared to the binding rates). Finally the last term accounts for the release into the bulk of the T particles bound to a target, following the target activation. Indeed, after activation, the T bound particles are released into the bulk, leading to an increase of the free particles Nf by a jump event of T particles  is simulated using a simplified Hodgkin-Huxley model for calcium currentIapp(t). The induced calcium current lasts 2.75 ms, with a maximal value of ICa,max = 36.2 nA . We consider that vesicles are located on a square lattice and that channels are uniformly distributed. The probabilities q are estimated numerically using Brownian simulations (Methods section). All parameters used for the simulations are described in The initial influx of calcium ions through a VGCC  36.2 nA . The totTo confirm the result of this novel Markov-mass action model  peak, we tested numerically the effect of considering buffers in the synaptic bulk at various concentrations. Their role is to buffer the calcium ions in the bulk. We found that increasing the number of buffers abolishes the second peak , confirmk−1 = 2 s, at the time scale of tens of ms most ions are still buffered and the second peak disappears (kes = 0.7 s). However, we can still observe rare events in the distribution tail due to the arrival of free ions from the bulk.We conclude this report with the following prediction: the diffusion time course in the bulk , where target binding sites are located underneath vesicles of size 20 nm leads to a residual vesicular release that peaks around 60 ms. However, in the case of a high buffer concentration, because the mean unbinding time to buffer is 1/sappears   induced by the direct entrance of calcium ions, followed by a second peak, which is due to the return of calcium from the bulk to the small hidden targets, a process that also depends on the interaction with buffer molecules and can last hundreds of milliseconds. The emergence of these two phases can possibly explain asynchronous quantal release, without introducing any additional time constant at a molecular level. The present approach could also be used to describe short-term plasticity at a molecular level20Iapp = 50 mV during 1 ms. The equations are summarized belowThe initial influx of particles through a channel following an action potential is computed using a simplified Hodgkin-Huxley model. The membrane depolarization following an action potential is modeled using an applied current whereV0, n0, m0, h0 are the equilibrium solutions of the ODE. They are summarized with all the parameters in ICa,max = 36.2 nA , distributed on a square lattice. There exactly Nc source points (channels) distributed in a square S of length 2H near the targetsIn this section, we describe the numerical simulations that we used to estimate the probability to distributed an ions among one of the S into 8 sub-triangles (si)i=1...8  that the entering particle binds to the closest target i1,  (green or magenta) and so on, with respect to the distance dist(x) to the closest vesicle. The normalization identity is After particles either enter the bulk or bind to one of the targets. In the latter case, using Brownian simulations we determined the target. For that, we subdivide each square )i=1...8 . Using se x ∈ s1 , we esti blue in , to the q, we further decompose the triangle s1 into blocks parameterized by polar coordinates k. We generated 200 runs for each block k and fitted the results using a routine procedure in Matlab  to reach specifically the target site i, when starting from point x. Finally, the fraction of particles entering through a channel positioned at x, that reaches a target i, is ps(x)q, and the fraction of flux coming from a channel located at x and arriving to target i is Ji = J(t)ps(x)q.The exact numerical procedure is the following: To compute the distribution Nc channels, we solved the system using a Matlab solver. To get the results for a uniform distribution of channels .


This work introduces a new method for verifying MLC leaf positions with enough spatial resolution to replace film‐based methods in performing QA tests. It is implemented on a 2D ion chamber array, and it is based on the principle of varying signal response of a volumetric detector to partial irradiation. A PTW 2D‐ARRAY seven29 (PTW‐729 2D) array was used to assess a Siemens OPTIFOCUS MLC. Partial volume response curves for chambers in the array were obtained by irradiating them with the leaves of the MLC, progressively covering varying portions of the chambers correlated with the leaf positions. The readings from the array's chambers are processed with an in‐house program; it generates a reference response that translates readings into leaf positions. This principle allows discriminating errors in pairs of opposing leaves that could combine to cancel their detection with other tools.±1 mm, ±2 mm and ±3 mm, all were correctly determined with the proposed method. The analysis of the same pattern with film using the Bayouth routine in the RIT software resulted in either somewhat low true positives combined with a large fraction of false positives, or a low true positive rate with a low false positive ratio, the results being significantly affected by the threshold selected for the analysis.Patterns of leaf positions, similar to the Bayouth test but with different, purposefully introduced errors, were generated and used to test the effectiveness of the method. The same patterns were exposed on radiographic film and analyzed with the RIT software for validation. For four test patterns with a total of 100 errors of This method provides an effective, easy to use tool for quantitative MLC QA assessment, with excellent spatial resolution. It can be easily applied to other 2D arrays, as long as they exhibit a partial volume detector response.PACS number: 87.55.Qr Accurate positioning of leaves constitutes a critical parameter in treatment delivery, especially in intensity modulated radiation therapy (IMRT). The literature describes different procedures to evaluate the mechanical accuracy and reproducibility of MLCs, which are mainly based on irradiation of radiographic films with fields of various geometries. Recently, several authors have pointed out the current trend to move to digital imaging. This trend has resulted in a decline in the availability of films and chemical processors, which led us to look for alternative methods for this type of control.The use of multileaf collimators (MLC) in radiotherapy calls for quality control procedures that guarantee their correct functioning.1 Accu however, their low spatial resolution limits their applicability in resolving position errors in the order of few millimeters. The following work shows that this limitation can be solved by taking into account the fact that partial coverage of a volumetric detector by a radiation beam gives a response proportional to the irradiated volume, as described by Yang et al. Spezi et al. studied the response of a 2D ion chamber array when radiation fields gradually increase the coverage of the detector area, and found a close correspondence between detector coverage and its response.2D arrays of detectors could be considered a solution for replacing radiographic films;7 howe is a tool developed for the 2D ion chamber array PTW‐729 to detect leaf positioning errors, associated with failures in the positioning of adjacent fields. However, this method does not allow determining which leaf of an opposing pair causes the error, nor does it guarantee that two errors of opposite effects will not go undetected.The MLC_Fastchecker software10 is The aim of this work is to implement a MLC quality control method that allows quantifying the error in individual leaf positioning using a 2D ion chamber array based on the concept of ion chamber partial volume response.27×27 cm2. Detectors are covered with a 5 mm depth PMMA layer. Several authors have studied the sensitivity and reproducibility parameters of this array and the results obtained are comparable with similar, commonly used detectors. The VeriSoft software  was used to record radiation dose readings. The array was optically aligned with the MLC so that each leaf corresponded to one row of detectors.A PTW‐729 2D ion chamber array , which has 729 detectors on a uniform matrix of 27 rows and 27 columns, was used. Each ionization chamber has an active cubic volume of 5 mm side. The chambers are separated by 5 mm septa, establishing a maximum detection area of etectors.,9 ThA 6 MV beam from a Primus linear accelerator  equipped with a 82 leaf MLC OPTIFOCUS  was used. The MLC leaves have a 1 cm wide projection at the isocenter, a 10 cm overtravel over the collimator axis, and a stated inaccuracy of leaf positioning not greater than 1 mm.111cm×27cm with intervening unirradiated bands of 1 cm was generated; the area thus covered is 21×27 cm, similar to the pattern studied by Bayouth et al., as shown in Fig. First, a regular test pattern of 11 rectangular fields of h et al.,4 as sThe response of each detector to different positions of the leaves for a constant number of monitor units in each field was recorded in the dose file returned by the PTW‐729. A calibration file was created from the response of the detector readings under the variable field edge, normalized by the average reading of all the detectors in the adjacent column which is kept under the fixed field edge. As the fixed and variable field edges were reversed, the detectors in both sides were thus calibrated.A software program  was developed in MATLAB environment . The software reads the files containing the dose readings resulting from the irradiation of the calibration patterns. This information is arranged in a suitable matrix that contains the normalized response of the detectors to varying degrees of partial volume irradiation, as described above. For subsequent MLC regular test patterns, AURIL allows evaluating deviations corresponding to individual leaf positioning errors, assuming a linear dependence between position and detector response. Since a strict alignment of the PTW‐729 device with the collimator/leaf axis is critical, a tool was developed in AURIL that calculates the mean readings ratio for the detectors under the left and right sides of the central rectangular field of the regular band pattern Fig. . A ratioFor all the subsequent tests, the PTW‐729 device was irradiated at 100 cm SAD and 15 mm of water equivalent material  as buildup and 90 MU for each field of the patterns described above. Because of the PTW‐729 size, only the 27 central leaves of the MLC were studied; the width limitation was given by the maximum overtravel of the MLC. For validation of the sensitivity of this method and the associated AURIL software program, four verification test patterns were created and irradiated on the PTW‐729 after the calibration process. Each of these verification test patterns included predetermined, arbitrarily chosen leaf position errors of 1 mm, 2 mm and 3 mm, as shown in Table 35cm×43cm, for comparison. Since the absolute position of each leaf in these tests depends on the precision achieved during the MLC leaf calibration procedure, we took an additional step designed to account for the residual errors in the leaf calibration on the Bayouth test with radiographic films. Prior to executing the test patterns, a full MLC calibration was performed following the manufacturer's guidelines. Next, a film was irradiated using the Bayouth test with 50 MU per field, and its results in the area of the 27 inner leaves were taken as reference. The film was scanned using a VIDAR VXR‐16 Dosimetry Pro Advantage Scanner  and analyzed using the RITv5.2 software . In order to avoid errors caused by the field edge in the Bayouth test analysis, the first and last rows were discarded from the comparison and only the 25 innermost ones were analyzed. Based on the analysis of this reference pattern, a reference response matrix was obtained with the values of the initial leaves positions in order to eliminate the residual inaccuracy of the MLC calibration process from subsequent measurements.All these tests were carried out also with X‐OMAT V Ready‐Pack  radiographic films of The four verification test patterns with leaf position errors were then irradiated onto films, scanned, and analyzed using the same procedure. The leaf positions were obtained according to the standard Bayouth procedure and compared with the known predetermined position errors. In order to eliminate the effect of the residual leaf position errors during the MLC calibration, the reference response matrix was subtracted from the leaf position matrix obtained for each one of the four verification test patterns.All response curves to partial volume irradiation were similar to those shown in Fig. ±0.4 mm  to “1 mm” errors, values between 1.5 mm and 2.3 mm (1.84±0.16) to “2 mm” errors, and values of 2.7 mm and 2.8 mm to “3 mm” errors. The threshold for an error to be considered as “detected” was 0.6 mm. This criterion was adopted based on the minimum value obtained for “1 mm” deviations. Seven 0.6 mm deviation values and one 0.7 mm deviation value that did not correspond to predetermined errors were reported. Seven of these eight false errors were located on the field edge. These errors would have been among those discarded in the film‐based test.Analyzing four different verification test patterns, it was found that AURIL detected the total number of intentionally introduced errors, as well as the direction of the deviations, as summarized in Table Table Taking into account the reference matrix and its subtraction in the patterns with errors, the analysis showed higher specificity and similar sensitivity for low threshold values, causing a slight sensitivity decrease for high‐threshold values, as can be seen in Table The ideal MLC quality control method should be able to reveal slight differences between the prescribed positions and the actual positions of the leaves, over all the range of positions. Preferably, it should be simple, automatic, and independent of extraneous factors.The Bayouth test with radiographic films allows a quantification of the leaf deviations, but since it uses the midpoint between a dosimetric peak and the adjacent valley to determine the field edge, it is possible to have opposite errors that do not alter the central position of a peak and the adjacent valleys. Under these circumstances, errors in leaf positioning would not be detected. Besides, the presence of a leaf position error introduces a shift in the dosimetric center of the adjacent peak and valley that may cause a false error report in the opposite side of that particular field or valley. In addition, our experience on the analysis of the Bayouth test using the RIT software indicates that its result is highly dependent on the choice of the central axis, and that an error threshold of less than 1 mm leads to an increasing number of false errors. Moreover, film dosimetry demands a high level of care, adding a burden that does not contribute to the value of the test. Also, the decreasing supply of film and photographic chemicals makes it necessary to find other alternatives.,6The subtraction of the reference matrix appears to increase the specificity for lower threshold values of errors in the Bayouth test. This is consistent with the hypothesis that the residual leaves calibration errors, while lower than 1 mm, remains quite stable on near consecutive measurements.The detector response dependence as a function of its irradiated volume fraction by a radiation beam allows the implementation of our algorithm to any other type of detector arrays, as long as they display a partial volume response. Although in our work only the 27 inner leaves were targeted, it is clear that the totality of the MLC can thus be evaluated with straightforward shifts of the PTW‐729 in the gun‐target direction. Thus, deviations in leaf positioning are quantified. Since two adjacent fields cover a detector, the method is not able to indicate which bank of leaves is responsible for a particular error. A one‐leaf error could be compensated by an error of the opposite leaf and neither of them would be detected. All 729 detectors are characterized by a unique calibration parameter.The MLC_Fastchecker software uses a calibration somehow similar to ours, based on variations in the position of adjacent fields in order to identify deviations at the field edge. These deviations are seen in the response of the detectors that agree with the field boundaries.10 ThuThe analysis developed with AURIL software to be used with the PTW‐729 responds directly to position variation of the field boundaries being irradiated. Unlike the MLC_Fastchecker, each leaf bank can be evaluated independently, without opposing errors being cancelled. In addition, for each detector, the reading corresponding to the initial independent calibration is registered on a matrix for future use. The few false errors reported were found mostly at the field edges, where scattering conditions are more extreme.The initial system calibration time takes approximately 60 minutes, which includes the device setup and the irradiation of nine patterns with 11 fields. This initial calibration is valid for as long as the MLC calibration does not change. The acquisition time for a control test is about 20 minutes. Considering the preliminary results of ongoing studies, the number of MU for each field could be significantly reduced, shortening these times without affecting the quality of the results.This work proposes a new method for quality control of a MLC using a PTW‐729 ion chamber array. The principle of varying signal response of a volumetric detector to partial irradiation enables this method to correlate the signal with the variations of the radiation beam edges and, therefore, to detect deviations in the expected position of the leaves with increased spatial resolution.The method is easy to implement and does not exhibit many of the problems related to the use of radiographic films. It was possible to detect the total number of predetermined deviations and to quantify them at their correct frequency, with a minimum number of false errors. It is easy to modify to cover the whole MLC by doing the test in two stages. AURIL software may become a useful tool for the routine quality control of MLCs at radiotherapy departments.The authors wish to thank Silvia Zunino, PhD, for her priceless help and encouragement to conduct this research.R. DÍaz Moreno wishes to thank Rodolfo Alfonso, PhD, and Carlos Sánchez Catasús, PhD, for valuable teaching and inspiration. He gratefully acknowledges the support of the Instituto de Neurologia y Neurociencia, Cuba, and of Instituto de Radioterapia ‐ Fundación Marie Curie, Argentina.Part of this work was carried our under the framework of a co‐ordinated research project E.2.40.15 with the International Atomic Energy Agency . All authors would like to thank the IAEA for the support it provided under this project.


Several researchers have recently demonstrated visualization of subsurface features with a nanometer-scale resolution using various imaging schemes based on atomic force microscopy. Since all these subsurface imaging techniques require excitation of the oscillation of the cantilever and/or sample surface, it has been difficult to identify a key imaging mechanism. Here we demonstrate visualization of Au nanoparticles buried 300 nm into a polymer matrix by measurement of the thermal noise spectrum of a microcantilever with a tip in contact to the polymer surface. We show that the subsurface Au nanoparticles are detected as the variation in the contact stiffness and damping reflecting the viscoelastic properties of the polymer surface. The variation in the contact stiffness well agrees with the effective stiffness of a simple one-dimensional model, which is consistent with the fact that the maximum depth range of the technique is far beyond the extent of the contact stress field. Several researchers have recently demonstrated visualization of subsurface features with a nanometer-scale resolution using various imaging schemes based on atomic force microscopy (AFM)12345678910111213141516fc) of the cantilever to enhance the contribution of the nonlinear coupling to the imaging mechanism as well as the signal-to-noise ratio. The technique is referred to as heterodyne force microscopy (HFM) or scanning near-field ultrasound holography (SNFUH). It has been applied to subsurface imaging for various sample systems with a depth range of a few hundred nm, but mainly for buried hard objects in a soft matrix. The imaging mechanism by this scheme has been explained as the amplitude and phase modulation of the surface acoustic standing wave resulting from the interference of the ultrasound waves transmitted through the sample and cantilever3One of the major imaging schemes is to excite two piezoelectric actuators located at the cantilever base and the bottom of the sample at two different frequencies and detect the flexural oscillation of the cantilever at the beat frequency, which is caused by the nonlinear tip-sample interaction3458910fc and detect the flexural oscillation of the cantilever at fc. The technique is referred to as atomic force acoustic microscopy (AFAM)197Another possible imaging scheme is to excite a piezoelectric actuator located at the bottom of the sample at a frequency close to We have also demonstrated visualization of Au nanoparticles buried 900 nm in a polymer matrix using HFM and AFAMfc. We now believe that the contact resonance is playing a major role in producing the subsurface contrasts in the AFAM, at least for the solid nanoparticles buried in a soft matrix. We then raised the question; do we really need to excite a cantilever oscillation? If we just need to measure the contact resonance spectra on the surface for subsurface imaging, it should be possible to do the same thing with the thermal drive of the cantilever. This was the motivation of the study.As already mentioned, most of the subsurface imaging experiments have been based on the detection of the cantilever oscillation close to There have been several reports on the AFM measurements of the tip-sample interactions using thermally driven cantilevers2324252627In this work, we demonstrate visualization of the Au nanoparticles buried 300 nm in a polymer matrix by STNM. Since STNM does not require additional excitation methods of the cantilever base or sample surface, the contact resonance spectrum measured by STNM is free from the spurious peaks that hinder quantitative estimation of the contact stiffness and damping, and the nonlinear tip-sample interaction can be minimized because of a very small oscillation amplitude. We quantitatively evaluated the differences in the contact stiffness and damping of the polymer surface areas with and without the Au nanoparticle underneath using a linear spring dashpot model, and discuss the imaging mechanisms by STNM as well as those by other schemes.μm-thick polyimide sheet (DuPont-Toray: Kapton 500 V). The sheet was dried on a hot plate heated at 105 °C. A photopolymer (Rohm and Haas: S1813G) was spin-coated as the top-coat and the sheet was annealed at 150 °C for 5 min. The thickness of the top-coat layer was determined by a stylus profiler (KLA-Tencor: P-15) to be about 300 nm. More details about the sample preparation procedures and a cross-sectional scanning electron micrograph were published in ref. We used a commercial AFM (JEOL: SPM 5200) after some modifications to the optics and electronics to reduce the sensor noise in the optical beam deflection sensorf0 = 26.1 kHz) and the quality factor (Q0 = 140), from which the spring constant of the cantilever (kz) was calibrated by Sader’s method to be 1.2 N/mWe used a Si cantilever with a backside Al coating (Nanosensors: PPP-ZEILR). We first measured the thermal noise spectrum of the first free resonance in air and it was fitted to the SHO model29We brought the tip into contact with the sample surface at a loading force of 10 nN, and performed AFAM imaging at the first contact resonance using a piezoelectric plate glued to the polyimide sheet and a lock-in amplifier (Zurich Instruments: HF2LI), and found some subsurface Au nanoparticle features (see 314fc) and the quality factor (Qc). Ppeak is a fitting parameter corresponding to the peak noise power density of the angular deflection of the cantilever. As shown in fc and Qc on the area with the Au nanoparticle were shifted to about 104.0 kHz and 77 from the values on the area without it, which were about 102.7 kHz and 53, respectively. We calculated fc and Qc using the same method for all the thermal noise spectra, from which we reconstructed the fc and Qc images as shown in fc and Qc images, as clearly as in fc and Qc are related to the contact stiffness and inverse of the damping. We also performed STNM imaging on the same sample and obtained fc images at different loading forces  by κ1, f0, and Q0 are the wave number (=1.8751/L), frequency, and quality factor of the first free resonance. ϕ(κ) and N(κ) are given by where uth is a fitting parameter corresponding to the thermal noise displacement at the cantilever end. We fitted the thermal noise spectra in k∗ and γ on the area above the Au nanoparticle were 63 N/m and 5.1 × 10−6 Ns/m, respectively, while those on the area without it were 55 N/m and 6.1 × 10−6 Ns/m, respectively. Therefore, k∗ was increased by 15% and γ was decreased by about 16% due to the presence of the Au nanoparticle in the matrix. Thus the imaging mechanism of the Au nanoparticles by STNM is quantitatively explained by the increase in the contact stiffness and damping of the polymer surface due to the existence of the Au nanoparticle. Based on the fitting parameters, the magnitude of the thermal displacement of the tip can also be estimated as about 3.3 pm and 4.2 pm on the area with and without the buried Au nanoparticle, respectively , δHertz is given by aHertz is the contact tip radius given by Rt and E∗ are the tip radius and reduced Young’s modulus, respectively. Using these relationships, E∗ is related to k∗ as Rt = 15 nm and Fn = 10 nN, E∗ on the area with and without the Au nanoparticle were calculated as 16.7 GPa and 13.5 GPa, respectively, from the k∗ value obtained by the STNM measurement. E∗ is related to the effective sample stiffness (Es) by Et denotes the Young’s moduli of the tip (=130 GPa)νt (=0.18)νs (=0.33)Es value on the area with and without the Au nanoparticle were calculated to be 16.7 GPa and 13.5 GPa, respectively. These values are much larger than the Young’s modulus of the top-coat photopolymer film in the literatureEtc = 3.4 GPa)  see . MoreoveδJKR and Fad (=15 nN) is the adhesion force. Based on the JKR model, E∗ on the area with and without the Au nanoparticle were calculated to be 11 GPa and 9 GPa, respectively, from which the Es values were 10.6 GPa and 8.6 GPa, respectively. This calculation suggests that the Young’s modulus on the top-coat photopolymer was increased by about 23%. Note that these values are close to the Young’s modulus of the top-coat photopolymer film in the literatureWe also considered the Johnson-Kendall-Roberts (JKR) contact modelδ1D) under a uniform stress (σ) is given by ttc, tAu, Etc, and EAu denote the top-coat photopolymer thickness, Au nanoparticle diameter, and the Young’s modulus of the top-coat film and Au . Therefore, we interpreted the subsurface contrasts in the experimental results by STNM as well as by AFAM as the variation in the contact stiffness and damping because the stress field extends more than expected from the sphere-plane contact models up to several hundreds of nm. This may be possible due to the anisotropy in the viscoelastic property of the spin-coated photopolymer film and some nonlinear or nanometer-scale effects that have not been considered in the macroscopic contact models. The conclusion is also consistent with the previous studies that explained the subsurface imaging mechanisms using one-dimensional models4546Although the JKR model qualitatively explained the contact stiffness variation, it failed to explain the depth range of the subsurface imaging since the expected elastic stress field was on the order of 10 nm. We finally note here that we found that the effective Young’s modulus could be reproduced by considering a one-dimensional model. We modeled the sample as a two-layer film of the top-coat layer and the Au layer. The variation in thickness of the two-layer film 5254Finally, we discuss the practical applicability of STNM for subsurface imaging and viscoelastic property mapping. First of all, one of the major drawbacks of STNM is its low signal-to-noise ratio. In this demonstration, we recorded the thermal spectra during trace and retrace scans (the tip scan of left to right and vice versa), which required 6 h. If we record the thermal spectra only during a trace scan, it can be shortened to 3 h. We also expect that the measurement time can be shortened by using a small (short) cantilever with a higher free resonance frequency. However, it may still take considerable measurement time for acquisition of full spectra by STNM. Therefore we rather recommend subsurface imaging or viscoelastic property mapping by the contact resonance techniques with excitation or by the resonance tracking techniques2248In conclusion, we experimentally performed the visualization of subsurface features by STNM that simply measures the thermal noise spectrum without additional excitation methods. We realised an ultimate simplification of the measurement scheme and imaged the Au nanoparticles buried 300 nm in the photopolymer matrix in a less invasive manner compared to AFAM and other conventional contact resonance techniques. We have shown that the subsurface features in the STNM images were brought by the variation in the contact stiffness and damping by the fitting of the theoretical equation to the thermal noise spectra. It was also shown, based on the JKR contact model, that the Young’s modulus of the photopolymer surface was increased by 23% due to the presence of the Au nanoparticle. However, the contact models failed to explain the imaging mechanisms because the depth of the stress field in the model was more shallow than the depth of the Au nanoparticle. On the other hand, the simple one-dimensional model also predicted the increase in the Young’s modulus of the photopolymer film by 15%. Therefore, we suggest that the imaging of subsurface features is realised by the stress field extension in a quasi-one-dimensional manner. To investigate the detailed one-dimensional strain model, the relationship between the effective Young’s modulus of the top-coat polymer film and the top-coat thickness will be examined in the near future. As shown by the STNM experiments, the subsurface features could be solely explained by considering the variation in the viscoelastic properties of the area under the tip. Therefore, the subsurface imaging mechanisms of various experimental schemes using the contact resonance might need to be revisited. The STNM technique will serve as a technique to study subsurface imaging mechanisms by the AFM related techniques as well as a method to quantitatively evaluate the viscoelastic properties of the sample surface.How to cite this article: Yao, A. et al. Visualization of Au Nanoparticles Buried in a Polymer Matrix by Scanning Thermal Noise Microscopy. Sci. Rep.7, 42718; doi: 10.1038/srep42718 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


The device consists of an ultra-thin NbxOy solid state electrolyte between an Al2O3 tunnel barrier and a semiconductor metal interface at an Au electrode. It is shown that the device provides a number of interesting features such as an intrinsic current compliance, a relatively long retention time, and no need for an initialization step. Therefore, it is particularly attractive for applications in highly dense random access memories or neuromorphic mixed signal circuits. However, the underlying physical mechanisms of the resistive switching are still not completely understood yet. To investigate the interplay between the current transport mechanisms and the inner atomistic device structure a lumped element circuit model is consistently coupled with 3D kinetic Monte Carlo model for the ion transport. The simulation results indicate that the drift of charged point defects within the NbxOy is the key factor for the resistive switching behavior. It is shown in detail that the diffusion of oxygen modifies the local electronic interface states resulting in a change of the interface properties.In this work we report on the role of ion transport for the dynamic behavior of a double barrier quantum mechanical Al/Al Inherent are initial electroforming procedures and distinct “on” and “off” states. The latter are in fact beneficial for memory applications. However, in the context of neuromorphic applications a wider dynamic range is required, rather than a purely “digital” behavior. To overcome these limitations various kinds of interface-based resistive switching devices have been developed. A profound review of the progress in the field with respect to materials, switching mechanisms, and performance has been provided by Pan The aim of this work is to provide a model which allows to investigate the role of the ion transport for the resistive switching of the double barrier memristive device. We utilize a 3D kinetic Monte Carlo code in order to describe the ion transport within the solid state electrolyte subject to both externally applied and Coulomb fieldsxOy/Al2O3/Al. We assume the NbxOy layer to act as an ionic/electronic mixed conductor. It represents a solid state electrolyte in which mobile oxygen ions (blue circles) drift under the influence of an externally applied electrical field. In order to guarantee for charge neutrality of the simulation domain, the negative oxygen ions are compensated by stationary positive ions (red circles)xOy assuming thermodynamic equilibrium. The NbxOy/Au interface is assumed to be inert to prevent oxidation. It can be regarded as a Schottky contact. The Al2O3 tunnel barriers are electrically high-quality barriers enabling elastic electron tunneling. They are nearly free of defects and highly stable. Both the tunnel barrier and the Au/NbxOy interface represent chemical barriers which confine the ions within the NbxOy layer. Details about the devices fabrication can be found in Hansen et al.The simulation scenario is shown in xOy/Au interface is descibed by the Schottky contact model21Before we describe the details of the model it might be helpful to firstly explain the overall idea of the simulation approach: The physical device is decomposed into distinct lumped elements which are connected in series, similar to an earlier approachxOy layer has found to be amorphousxOy18z direction and and 0.33 nm in x and y direction. This is indicated in xOy. For an amorphous material it might be intuitive to chose equal lattice constants for all direction. However in order to have a better resolution in z direction, we apply a slightly reduced lattice constant, which is realistic and without any influence on the simulation results. The 3D simulation domain consists of a quadratic 9 nm × 9 nm basis area, a 2.5 nm thick solid state electrolyte and a 1.2 nm thick tunnel barrier  barrier between the lattice sites i and j. For the hopping barrier we use k = diffusion, adsorption, desorption). The term xOy layer, the negative ions drift according to the local electric field which itself is a superposition of the field due to the externally applied voltage and the Coulomb field of the remaining ions in the system. When an oxygen ion reaches one of the interfaces a surface interaction takes place, depending on the local electric potential. The simulation parameters, which are mainly extracted from the experiment, are collected in The transport of ions within the solid state electrolyte evolves as follows: After inserting a certain number of stationary positive and mobile negative ions into the Nb2O3 tunnel barrier. We assume that the Al2O3 is a perfect insulator which contains no electric charge carriers. Therefore, the electric potential can be obtained from a simple Laplace equation subject to Dirichlet conditions,The first step of the simulation loop is to calculate the electric potential within the Al2O3 layer is assumed to be homogeneous. This leads of course to a spatially linear potential and a spatially constant electric field. With the voltage drop across the tunnel barrier the local electron tunneling current density can be calculated from the Simmons formula,The permittivity of the Al0 is the barrier height of the tunnel barrier .xOy layer cannot be obtained directly from Poisson’s equation as the charge density within the layer is not known a priori. The assumption of an electric charge carrier-free insulator, as used for the tunnel barrier, is not valid in the NbxOy layer due to an electric current which is present here. Instead, we calculate the local electric potential by solving the continuity equation σ represents the electric conductivity of the NbxOy layer, which is assumed to be homogeneous. It is important to note that the displacement current can be neglected because it scales with (L/Tc)2 where c is the speed of light and L and T are the length and the time scales of the system. The displacement current is therefore small compared to the conduction current.The electric potential within the NbxOy/Au Schottky contact, depends mainly on the oxygen ion concentration close to the NbxOy/Au interface. The ions influence the height of the Schottky barrier and the ideality factor. To calculate the electric field across the Schottky contact, the thermionic emission theory is employed. The Schottky contact is described by a set of analytical formulas21The electric field across the third device part, the NbkB and T are the Boltzmann constant and temperature, respectively. n is the ideality factor which describes the derivation from an ideal current. The reverse current JR at forward bias voltages is given bywhere b is the Schottky barrier height and A* = 1.20173 × 106 A/(m2K2) the effective Richardson constant. The reverse current in reset direction is dominated by the lowering of the Schottky barrier. If the apparent barrier height Φb at the Schottky interface is significantly smaller than the conductive band gap of the insulator, the reverse current decreases gradually with the applied negative bias approximately aswhere Φαr denotes a device dependent parameter which is used to describe the experimentally observed voltage dependence of the reverse current. Regarding (5)–(7) the effective current density is affected by both the ideality factor of the Schottky barrier n and the height of the Schottky barrier Φb. The change of the ideality factor is calculated by taking the average distance of the oxygen ions to the Schottky barrier into account,λn is a fit parameter and n0 is the initial ideality factor which has been estimated to be 4.1 for the deviceb0 being the initial Schottky barrier height and ΦM being the average surface potential at the Au electrode. This involves in particular the Coulomb field of the ions within the solid state electrolyte which is superimposed to the local electric field produced by the external voltage. Therefore, for a complete description of the electric field the Coulomb field of the oxygen ions has to be taken into account. The Coulomb potential is calculated using Poisson’s equationwith Φ2O3 or the NbxOy, respectively.where the permittivity xOy/Au Schottky contact. Furthermore, we are able to capture the nonlinear behavior of the I-V curve in which a high resistance at small voltages and a current saturation at higher voltages is obtained. The model shows moreover the gradual change of the device resistance by several orders of magnitudes. The fine structure for small measured currents at negative bias, which is due to the limitation of the current resolution of the experimental set up rather than physically relevant mechanism, is not captured by the model.In To study the dynamics of oxygen ions within the solid state electrolyte under the influence of an external voltage and their impact on the device resistance the spatial ion distribution at four significant positions of the I-V curve are shown in a 3D view graph depicted in The numerical simulation indicates that the oxygen ion movement is strongly voltage dependent and therefore responsible for the gradual change of the device resistance. To study the voltage dependence of the resistance variation in some more detail, the change of the device resistance as a function of the applied voltage is depicted in xOy solid state electrolyte, and the Schottky contact. At low applied voltages the partial voltages across the NbxOy layer and the tunnel layer , (8), and (9) we assume for the model that the spatial distribution of negative charged oxygen ions in front of the barriers influences both the effective tunnel barrier length and the parameters of the Schottky barrier, such as the ideality factor and the barrier height. We find that the effective tunnel barrier width decreases from 1.3 nm to 1.2 nm if the voltage applied to the Au electrode raises from 0 V to 3.0 V. At the same time the ideality factor decreases from 4.0 to 3.4. The Schottky barrier height is lowered from 0.9 eV to 0.83 eV .x and y directions. We find in particular that the Coulomb potential at the NbxOy/Au interface decreases from 0 mV to −70 mV when ramping the external voltage from 0 V to 3.0 V. This means that the lowering of the Schottky barrier height (see As given in (4) and (8) both the effective tunnel distance and the ideality factor are assumed to depend linearly on the average ion position, while the lowering of the Schottky barrier height depends on the Coulomb potential in front of the Au interface (see (9)). The variation of the Coulomb potential as a function of the applied external voltage is shown in ight see ) originaxOy layer is depicted in xz-plane. For t = 10 s the applied voltage is 0 V and the origin of the electric field are the positive and negative charges. This attractive Coulomb field has to be overcome to deflect charges from the stable position. Small setting voltages are blocked by the Schottky barrier . Howeverved see ) althougrved see ). A posiThese observations indicate that the maximum applied voltage has a strong influence on the shape of the I-V curve in set direction. In particular, since for voltages smaller than approx. 1.5 V the directed ionic motion is suppressed. Furthermore, the hysteresis of the I-V curve is expected to disappear for maximum applied voltages smaller than approx. 1.5 V. To verify this hypothesis the positive branch of simulated and measured I-V curves for three different maximum applied voltages  are shown in xOy/Au interface. This mechanism is actually not included in the simulationIn order to investigate the retention characteristics of the device, it is set to the LRS which is the initial state for this study. The change of the device resistance is then mapped over time. To track the evolution the resistance of the device, voltage pulses of 0.5 V are applied every 60 s in order to readout the resistance. 2O3/NbxOy/Au structure where the NbxOy solid state electrolyte is enclosed by a tunnel barrier and a Schottky contact. We present results from a kinetic Monte Carlo simulation of the (atomistic) ion transport, consistently coupled to a lumped circuit element model for the current through the device. The current voltage characteristics which is an important indicator for the dynamics of the device is numerically calculated and compared to experimentally obtained results. We find very good agreement between simulation and experiment. We claim that the model which is proposed captures most relevant physical processes for resistive switching on both, atomistic length scales and experimental time scales. The simulation results identify the transport of charged point defects within the solid state electrolyte as a key mechanism for the resistive switching of the double barrier device, although the charging and de-charging of trap states within the solid state electrolyte and/or at the metal semiconductor interface cannot be completely excluded from the physical picture. The results indicate that the local electric field is the rate determining quantity, particularly during the set process. Finally, we find that the threshold voltage for resistive switching in set direction and an adsorption mechanism is the reason for the long retention time. It is found that the Coulomb field and the concentration gradient are the main reasons for back diffusion of charged point defects. The calculated retention time is in excellent agreement with experimental findings. We believe that with the model we provide a powerful simulation tool that can be used to gain a deeper physical understanding of the resistive switching mechanisms of the double barrier memristive device.We report on numerical simulations of a quantum mechanical double barrier memristive device. The device consists of an Al/Al2  using a standard optical lithography process. The junctions are arranged in 1 mm × 1 mm cells across the wafer, containing 6 different contact sizes ranging from 70 μm2 to 2300 μm2. The devices are fabricated using the following procedure: First, the multilayer (including top- and bottom-electrode) is deposited without breaking the vacuum using DC magnetron sputtering. The Al2O3 tunnel barrier is fabricated by depositing Al which was afterwards partially oxidized in-situ. The NbxOy layer is deposited by reactive sputtering in an O2/Ar-atmosphere. Following the subsequent lift-off, the junction area is defined by etching the top electrode using wet etching  and dry etching . The etched parts are then covered with thermally evaporated SiO to insulate the bottom electrode from the subsequently deposited Nb-wiring to contact the top electrode.Memristive tunneling junctions are fabricated on 4-inch Si wafers with 400 nm of SiOAll measurements are performed using an Agilent E5260 source measurement unit. Current-voltage measurements are obtained by sweeping the applied voltage and measuring the device current simultaneously.xOy/Au interface is descibed by the Schottky contact model. The solid state electrolyte is modeled by an Ohmic resistance which depends on the inner atomic structure. The transport of ions within the solid state electrolyte under the influence of the externally applied electric field and the Coulomb field due to the ions themselves is described in the frame of a 3D kinetic Monte Carlo model. The lumped element circuit model is consistently coupled with a 3D kinetic Monte Carlo model in such a way that Kirchhoff’s voltage and current laws for the circuit model are satisfied at all instances of time. Within an inner loop the dynamical state of the solid state electrolyte is calculated subject to the electric field acting on the ions.The physical device is decomposed into distinct lumped elements which are connected in series. The tunnel barrier is mimicked by a voltage controlled current source based on the famous Simmons formula. The NbHow to cite this article: Dirkmann, S. et al. The role of ion transport phenomena in memristive double barrier devices. Sci. Rep.6, 35686; doi: 10.1038/srep35686 (2016).


An increasing number of ion channel structures are being determined. This generates a need for computational tools to enable functional annotation of channel structures. However, several studies of ion channel and model pores have indicated that the physical dimensions of a pore are not always a reliable indicator of its conductive status. This is due to the unusual behavior of water within nano-confined spaces, resulting in a phenomenon referred to as “hydrophobic gating”. We have recently demonstrated how simulating the behavior of water within an ion channel pore can be used to predict its conductive status. In this addendum to our study, we apply this method to compare the recently solved structure of a mutant of the bestrophin chloride channel BEST1 with that of the wild-type channel. Our results support the hypothesis of a hydrophobic gate within the narrow neck of BEST1. This provides further validation that this simulation approach provides the basis for an accurate and computationally efficient tool for the functional annotation of ion channel structures. Ongoing advances in the determination of ion channel structures now clearly necessitate the development of accurate computational tools to aid the functional annotation of both new and known structures.hydrophobic gating.To date one of the most widely used methods for predicting whether a channel structure is conductive or not has been to evaluate the physical dimensions of the pore, often via the use of HOLEIn a recent paperIn the previous paperKlebsiella pneumoniae) homolog KpBestEukaryotic bestrophins are calcium-activated chloride channels with a broad tissue distribution.The BEST1 channel is a symmetric assembly of 5 subunits surrounding a central pore . There iWT) and triple alanine mutant (BEST1AAA) structures differ in the radius of the proposed gate in the hydrophobic neck region, this channel structure provides an excellent test for further examination of this method for the functional annotation of ion channel structures.Interestingly, the narrow neck region has been implicated in the gating mechanism of BEST1. A structure has been determined for a “triple A” mutant, in which the 3 bulky hydrophobic residues lining the neck were replaced by alanine.in silico within a phospholipid  bilayer (− and Na+ ions (at a concentration of 0.15 M) on either side. To retain the exact conformation of the experimentally determined structure, the positions of the protein atoms were restrained. Upon simulation at 37°C, water molecules were observed within the pore . This structure of BEST1 can therefore be clearly assigned to a closed, non-conductive conformation. There is also a smaller energy barrier in the vicinity of the V205 aperture.The water density may be used to estimate the free energy profile for water along the axis of the pore . This reAAA) structure of the channel appears to correspond to a constitutively open stateAAA structure is predicted to have a functionally open gate. Interestingly, the results provide a more complex example of a hydrophobic gating motif than previously observed in e.g., the L9' sidechain ring of pLGICs and further demonstrate the capability of our simulation method to allow annotation of conductive state of new ion channel structures.The triple alanine mutant  side-chain flexibility. However, despite the increased degree of conformational mobility and resulting shifts in pore radii (changes of < 1 Å), the large energetic barrier to water permeation within the neck remained  to chloride ion permeation  were applied to either to all protein atoms or to the backbone atoms. Post-processing of the simulation trajectories was performed using Gromacs. Molecular graphics were created with VMD.Starting from the experimentally determined protein structure , the simulation system was prepared using a sequential multi-scale procedure as described previously.n(z), is related to the free energy at this position, E(z), throughz is the Cartesian coordinate normal to the plane of the membrane, k is Boltzmann's constant, T is absolute temperature, and C is a normalization constant related to the system's partition function. Inverting the above relation yieldsz, which we determine by setting the free energy in the bulk outside the pore to zero. The number density of water particles can be determined by dividing the water count at a given position by the local cross-sectional area of the pore (approximated as circular) and calculated using HOLE.Since the atomistic simulations reflect equilibrium conditions, the number density of water molecules at a given position along the main axis of the BEST1 pore, z coordinate of the chloride ion with a force constant of 1000 kJ mol−1 nm−2. Each window was simulated for 5 ns, during which positional restraints (force constant 1000 kJ mol−1 nm−2) were applied to backbone atoms of the protein. PMFs were computed using the weighted histogram analysis method (WHAM), and errors on each free energy profile were estimated using the Bayesian bootstrapping method.Umbrella sampling simulations were initiated using an equilibrated atomistic system containing the BEST1 TM domain embedded in a lipid bilayer and surrounded by water and ions, as described above. In 36 consecutive sampling windows, a single chloride ion was placed at successive z positions along the central pore axis, spaced at 1 Å intervals. The sampling windows covered the neck region and extended approximately 10 Å either side. A harmonic biasing potential was applied to the


VMAT) treatment delivery requires three key dynamic components; gantry rotation, dose rate modulation, and multi‐leaf collimator motion, which are all simultaneously varied during the delivery. Misalignment of the gantry angle can potentially affect clinical outcome due to the steep dose gradients and complex MLC shapes involved. It is essential to develop independent gantry angle quality assurance (QA) appropriate to VMAT that can be performed simultaneously with other key VMAT QA testing. In this work, a simple and inexpensive fully independent gantry angle measurement methodology was developed that allows quantitation of the gantry angle accuracy as a function of time. This method is based on the analysis of video footage of a “Double dot” pattern attached to the front cover of the linear accelerator that consists of red and green circles printed on A4 paper sheet. A standard mobile phone is placed on the couch to record the video footage during gantry rotation. The video file is subsequently analyzed and used to determine the gantry angle from each video frame using the relative position of the two dots. There were two types of validation tests performed including the static mode with manual gantry angle rotation and dynamic mode with three complex test plans. The accuracy was 0.26° ± 0.04° and 0.46° ± 0.31° (mean ± 1 SD) for the static and dynamic modes, respectively. This method is user friendly, cost effective, easy to setup, has high temporal resolution, and can be combined with existing time‐resolved method for QA of MLC and dose rate to form a comprehensive set of procedures for time‐resolved QA of VMAT delivery system.Volumetric‐modulated arc therapy ( Adamson et al. 2012) proposed the use of a custom‐built phantom with five gold coils of 0.8 cm diameter embedded in Styrofoam. Gantry angle determination was performed by acquiring cine‐EPID images and extracting the projection of the gold coils to determine the gantry angle. The accuracy of this technique was characterized to be 0.0° ± 0.3° for static and 0.2° ± 0.2° for dynamic gantry rotation. proposedA fast and accurate method for dynamic gantry angle measurements was developed by Rowshanfarzad et al. 2012Time‐resolved commissioning and QA of VMAT delivery systems have been demonstrated by a number of groups.In order for these systems to be fully independent and sensitive to all types of delivery errors (including gantry angle errors), a method is required which can accurately and easily measure the dynamic gantry angle as a function of time during acquisition of EPID images or phantom measurements. In this work, we developed a simple, inexpensive, and fully independent gantry angle measurement methodology that allows quantitation of the gantry angle accuracy as a function of time. Our proposed method is inherently independent of the linear accelerator system and does not impede phantom or EPID‐based QA of MLC and dose rate, which can be performed simultaneously with this measurement. The accuracy of this novel method was evaluated for both static and dynamic gantry angle plans and for test plans designed specifically for dynamic gantry angle QA. The procedures and techniques developed in the work can be used to complement the existing time‐resolved MLC and dose rate QA methods for VMAT control systems.22.AThe gantry angle measurement technique is based on the analysis of video footage of a “Double Dot” pattern attached to the front cover of the linear accelerator. The pattern consists of red and green circles of different size printed on an A4 sheet of paper using a conventional printer. Placement on the linear accelerator should be approximately near the axis of rotation but exact position is not critical. A standard mobile phone camera is placed on the couch to record the video footage during gantry rotation. The video file is subsequently analyzed and used to determine the gantry angle from each video frame using the relative position of the two dots see Fig. .2.BDetermination of the gantry angle is based on measurement of the relative angle between the red and green dots see Fig. . The met2.B.1Following acquisition of the video footage, the colourmap matrix  is extracted from each frame. Image frames corresponding to the red and green channels are used to localize the two dots separately. This effectively filters out other features of the image to maximize the accurate detection of each of the dots. For each image (red and green), the image noise is reduced by applying a median filter with 5 × 5 pixels2.B.2θ and the angle θ + 180°. Second, the angle between the centroid of the red and green circles is calculated using eq. x is the x‐coordinate of the red circle, Ry is the y‐coordinate of the red circle, Gx is the x‐coordinate of the green circle and, Gy is the y‐coordinate of the green circle. An example of the output of the system for a single frame is given in Fig. This process outlined above is repeated for both the red and green images. The relative locations of the centroids are first used to determine which of the four quadrants the gantry is in, to differentiate between the actual gantry angle 2.B.3θ0), which is the angle between the two circles when the gantry is at absolute zero. This technique enables the method to be independent of the absolute positioning of the A4 paper on the gantry. The gantry is initially set to absolute 0° using a spirit level rather than relying on the readout of the linear accelerator gantry angle.After extracting the relative angle between the red and green circles, this angle is then converted into the actual gantry angle. To do this, image frames from the first 10 s of the video footage are used to calculate the calibration angle . The linac control systems relies two encoding potentiometers (one primary and one secondary) that replicate each other and provide signals linearly proportional to the gantry angle.To test the accuracy of the gantry angle measurement method, three independent methods for gantry angle determination were used: (a) gantry angle from the linac control system recorded within machine log files (DynaLog files), (b) gantry angles from the on‐board imager (OBI) gantry angle encoder, and (c) and independent digital inclinometer.The DynaLog files are generated by the Varian MLC control software with updated information every 50 ms, from which the gantry angle can be extracted as a function of time. The OBI gantry angle encoder signal is very precise (±0.05°)The mobile camera used in this experiment to collect the video footage of the Double Dot pattern was a standard Samsung Galaxy S6 mobile phone . This device has a 16 megapixel rear camera and contains optical image stabilization and autofocus hardware features. The dimensions of the video are 3840 × 2160 pixels and the frame rate is 30 frames per second.2.DTo assess the accuracy of the Double Dot method for gantry angle determination, the gantry was positioned at 10° intervals from −180° to +180° using the linac readout system. At each gantry angle, while the gantry was static, the gantry was measured using the Double Dot method, OBI gantry angle encoder and digital inclinometer (NG360).2.EThree VMAT test plans were designed for gantry angle QA; constant gantry speed, gantry speed transitions, and maximum gantry speed tests see Fig. . These pThe first test plan, [Fig During delivery of these plans, gantry angle versus time data was acquired using DynaLog files, the OBI gantry angle encoder and, the Double Dot method. Note that, in dynamic‐gantry mode, inclinometer measurements were not performed due to (a) the low sample rate of the inclinometer (1 Hz) and (b) the interference between the wire connection from the inclinometer and the video.33.AFigure 3.BFor dynamic gantry deliveries, the Double Dot method was compared to the gantry angle from the DynaLog files and OBI gantry angle encoder for the three QA tests plans. The mean absolute gantry angle difference between the Double Dot Method, DynaLog and encoder is given for each arc in Table 4A comprehensive time‐resolved VMAT QA using EPID is still associated with some critical issues, one of which is an independent gantry angle check. In our previous studies,The proposed method is practical and the associated cost is very low as it only requires a small camera (phone) and paper. This method is user friendly, easy to setup, and has high temporal resolution equal to the frame rate of the camera. Here, 30 frames per second were used, but the method can also utilize any higher frame rate resulting in a correspondingly higher temporal resolution. With the acquisition rate, the system can easily be synchronized to EPID images using a linear interpolation method. A limitation of synchronization between EPID and the proposed system, however, still exist in identifying the first frame of beam‐on status. In our system, we assumed that the first frame of gantry rotation represents beam‐on. The accuracy in synchronization between the EPID images and the Double Dot system can be improved by, for example, placing an additional dose rate meter, such as Automess Dose Rate Meter—6150 AD5/6  next to the mobile phone. Once the radiation is on, the dose rate meter will alarm while video is recoding. This alarm sound can be processed to identify which frame represent “beam‐on” status for synchronization.The ability to accurately synchronize the video signal with the Dynalog or Encoder signal is difficult. Figure In this study, the double dot with red and green colours are used, however, different patterns can also be used. We tested on a green arrow pattern and developed an algorithm to determine the gantry angle based on Hough transform algorithm.The robustness of image processing techniques in this method is dependent on the camera position. While the exact camera position is not critical, the camera should be roughly aligned with the center of the two dots. Small deviation in this alignment did not result in significant errors. The uncertainty of the video camera signal could also influence the accuracy of gantry angle determination from the system. Higher camera resolution or reducing the framerate could reduce the noise. However, lower framerate will introduce the issue of image blurring from dynamic tests. The systems used for video recording in this study were found to offer adequate image quality for these tests., (2012). The maximum of deviation between Double dot and Encoder was 2.1° which occurred during Test 2. It is likely that this difference was due to the low temporal resolution of Encoder, which is read out at 10 samples per second, while Double Dot has a higher temporal resolution of 30 samples per second.In Figs. It should also be noted that our method is not limited to using a mobile camera, but any other cameras  can be used. In this study, we proposed the mobile camera for its practicality; (a) it is easily accessible, (b) it can record high‐resolution video, (c) the output video file can be easily transferred to a computer. However, it is not recommended to put the mobile camera close to the radiation beam. When using Double Dot, the room light should be turned on to increase the image contrast and to reduce image noise.5A low cost and independent gantry angle measurement tool using a mobile camera and double dot pattern was developed and its accuracy was evaluated in this paper. The advantage of our method is that allows a simultaneous independent measurement of EPID dosimetry, geometry and gantry angle in a single delivery. The Double Dot pattern is placed on the linac, and its motion due to gantry rotation was recorded using a mobile camera on the treatment couch. The gantry angle can be automatically measured offline from the video file using image processing techniques. The accuracy of this method in static mode was 0.26° ± 0.04° on average compared to inclinometer and encoder. The proposed three test plans were used to evaluate the system performance for dynamic gantry rotation, and an accuracy of 0.46° ± 0.31° was found when comparing to DynaLog file and encoder. Our proposed gantry angle measurement tool is an accurate and practical solution for VMAT QA as it provides a fully independent gantry angle measure while still allowing dosimetric testing using EPID, using low‐cost equipment, and an easy setup.The authors declare no conflict of interest.


The aim of this quantitative experimental study was to examine which of three instructional methodologies of traditional lecture, online electronic learning (e‐learning) and self‐study take‐home packets are effective in knowledge acquisition of professional registered nurses.A true experimental design was conducted to contrast the knowledge acquisition of 87 registered nurses randomly selected.ACS) true/false test was used to measure knowledge acquisition. Based on 0.05 significance level, the ANOVA test revealed that there was no difference in knowledge acquisition by registered nurses based on which of three learning instructional method they were assigned. It can be concluded that while all of these instructional methods were equally effective in knowledge acquisition, these methods may not be equally cost‐ and time‐effective.A 40‐item Acute Coronary Syndrome (The study was able to determine that there were no significant differences in knowledge acquisition of nurses between the three instructional methodologies. The study also found that all groups scored at the acceptable level for certification. It can be concluded that all of these instructional methods were equally effective in knowledge acquisition but are not equally cost‐ and time‐effective. Therefore, hospital educators may wish to formulate policies regarding choice of instructional method that take into account the efficient use of nurses’ time and institutional resources. All potential participants will complete the survey instrument developed for this proposed study. All completed surveys were used as data for this proposed research. In the case of this study, the focus is on the knowledge acquisition of nursing students after using audio recording in their online class. The first group considered in this study were those who undergone the learning instructional method of lecture. The second group considered in this study were those who undergone the learning instructional method of teacher‐guided e‐learning. The third group considered in this study were those who undergone the learning instructional method of self‐study take‐home packet.Quantitative approaches are employed when the focus of the study is to determine relationships or differences between two or more variables Babbie, . QuantitAs opposed to a quantitative approach, the qualitative approach is focused on establishing “the meaning of a phenomenon from the views of participants” Cozby, , p. 20. Two strategies for quantitative research were considered for this study. These two strategies involve the experimental and non‐experimental designs Bryman, . Experim2.2n = 87) was randomly assigned into three cohorts, each consisted of 29 registered nurses.The sample population was comprised of 87 registered nurses in a Southeastern U.S. hospital specializing in acute care and chest pain accreditation, which totalled 200 registered nurses. G*Power was used to calculate the total sample size of at least 44, based on a medium effect size with 80% power. The sample  quiz is an existing quiz questionnaire that will look at acute coronary syndromes and will test the respondents’ knowledge of the pathophysiology of these syndromes, the risk factors of these syndromes, the clinical presentations of these syndromes and the treatment and management of these syndromes. It is developed by the ACLS certification institution. The scores are obtained by counting the number of correct answers in the 40‐item questionnaire.As the first part of the programme, before the groups started the classes, the participants signed the consent form before the data collection process commenced. This consent form addressed confidentiality issues that the registered nurses may have had regarding the research project. Signing the form served as an agreement to participate in the programme, given the assurance that no individual information would be disclosed to anyone else other than the researcher and the director of education. The informed consent form (Appendix S2) included the purpose of this research study, the expected participation, as well as the contact information of the researcher. The researcher was available to answer any questions the potential participants had regarding the study conduction. The researcher also emphasized that refusal to take part in the study would not have any negative consequences to the participant.Moreover, if the participant felt the need to withdraw at any point during the course of data collection and analyses, he/she could have done so without any associated penalties. In the case of withdrawal, the participants’ initial responses were not considered in this study and they were treated as prospective participants who refused to participate in the study. Participants were also informed that there were no associated risks for participating in the study. Their responses used for research purposes were handled cautiously to ensure that these are kept confidential at all times. After all relevant information had been disclosed to the potential participants, they were presented with a consent form. If they chose to participate in the study, they were informed that they needed to return a signed copy of the consent form. If a signed copy of the consent form was not returned to the researcher, it was be assumed that the person did not wish to participate and he/she was no longer considered for the study.All prospective participants who agreed to participate in the study were considered as part of the sample. Following the coursework, these nurses took a 40‐item test (Appendix S1) designed to evaluate knowledge acquisition using a true or false response scale. Each question was obtained directly from the course material. The test was distributed at the completion of each course under the supervision of a nurse educator. The exam for the lecture course was proctored by a hospital human development officer and administered immediately following the lecture. Each registered nurse was given one hour to complete the exam. The exam for participants using teacher‐guided electronic learning was taken as part of their last electronic lesson. These registered nurses were also allowed one hour to complete the test. The registered nurses who studied the take‐home packet took the exam under proctored settings the day after the packet was dispensed, and were allowed one hour to complete the test. The exam for each instruction methods was corrected by hand by the researcher using a template. An additional collection tool was used to collect demographic of job position of the registered nurses to display descriptive statistics contrasting the demographics of the three groups.2.3To analyse the data gathered, descriptive statistics and inferential statistics were conducted. Descriptive statistics were conducted to describe the samples and study the variables obtained. Frequencies and percentages were used to describe categorical data such as demographic characteristic of job position and the independent variable of method of instruction while measures of central tendencies such as mean and standard deviation were used to describe continuous variables such as the dependent variable of knowledge acquisitions. Normality testing of the study variables was also conducted using Kolmogorov‐Smirnov test.p‐value is less than or equal to the level of significance value. In instances wherein the ANOVA determined significant relationships between independent and dependent variables, a post hoc Tukey's test of multiple comparison was also conducted to further identify the relationships between independent and dependent variables.To answer the research question in this study, Analysis of Variance (ANOVA) was conducted. ANOVA was conducted to determine if there is significance difference in the knowledge acquisition in the use of different instruction method. ANOVA was used since the independent variables are categorically measured variables that have more than two identified groups and there is only a single dependent variable Babbie, . Roberts33.1n = 80, 92%). There was one participant who was a nurse manager (1.1%) and one other participant who held a clinical position (1.1%).The target population for this research study was registered nurses in a Southeastern U.S. hospital specializing in acute care and chest pain accreditation. For this study, a total of 87 participants were sampled with professions ranging from registered nurses to nurse managers. Each of the three cohorts had 29 participants. The frequency and percentages of participants’ job positions are presented in Table n = 29).Table SD = 6.51). It can be observed that the lowest score was 80, while the highest 100. This shows that participants in general had high scores in the ACS quiz.Table To explore the distribution of participants’ job positions according to the three instructional methodologies, cross‐tabulation of data was performed. The results of the cross‐tabulation are presented in Table 3.2K‐S = 1.029, p = 0.240), lecture method  and self‐study method . None of the tests reached significance, indicating that the data for each group were normally distributed.In order to examine whether parametric tests were appropriate for this research study, it was necessary to test whether the data followed a normal distribution. Table SD 6.42), the mean score for the lecture method as 91.00 (SD 6.09) and the mean score for self‐study as 89.17 (SD 7.04). From this table, it is observed that the lecture method resulted in the highest mean score while the teacher‐guided e‐learning method resulted to the lowest mean score. It should be noted that the difference between the highest and lowest score was minimal (1.86).Table 3.3F = 0.77, p = 0.47). Thus, there is insufficient evidence to reject the null hypothesis, which states that there is no difference in knowledge acquisition by registered nurses, regardless of which of three learning instructional method they are assigned .Since the data were found to follow a normal distribution, a parametric test was selected. For the purpose of comparing the three cohorts of instruction method, a one‐way ANOVA test was performed. As observed in Table 4To improve the use of existing knowledge and to facilitate more effective acquisition of new knowledge, nursing educational organizations require research in curricular models and pedagogies that depart from traditional lecture‐style learning paradigms. New methods of instruction have emerged, with many learning institutions embracing advanced technology and modern instruction models (Abdelaziz et al., The conclusions made in this study may only be applicable to the registered nurses in the selected hospital, in short‐term certification courses and when comparing these three instructional methods. Adults display many learning styles in various situations (Cha & Kim, It is advised that future researchers include nurses in other hospitals and other practice settings, contrast other instructional methods, analyse finding with learning gain computed by giving a pretest as well as a posttest to nurses, and/or contrast these instructional methods in longer term courses. In addition to these suggestions, it is also advised that technician and other health professionals should be included in future studies regarding the optimal instructional method for learning acquisition in short term certification courses. It is also recommended that future studies examine not only immediate knowledge gain but retention of knowledge over a more extended period of time. Future studies should also include age demographics and test for generational differences.It is advisable for future researchers to explore additional instructional approaches like DVD tutorials and stand‐alone video presentations that are known to facilitate acquisition of knowledge in a more cost‐effective and shorter period of time. Including these approaches in future research would help to determine whether these low cost instructional methods are equally efficient teaching methods for knowledge acquisition in short‐term certification courses.It is further recommended that future researchers consider conducting qualitative studies exploring the thoughts and feelings of registered nurses in terms of their satisfaction with each of the methods. Although each of the three instructional methodologies resulted in the same knowledge acquisition to the registered nurses, it is presently unknown whether nurses had positive feelings towards each of the instructional methods. This might have effects on learning in future courses, should the administration move to a more cost‐effective method than presently used, which may not be well‐received by nurses.5The purpose of this quantitative study was to determine which of the three instructional methodologies of lecture, teacher‐guided e‐learning and self‐study take‐home packets provided the greatest knowledge acquisition in a short high‐stakes course for nurses. The study was able to determine that there were no significant differences in knowledge acquisition of nurses between the three instructional methodologies. The study also found that all groups scored at the acceptable level for certification. It can be concluded that all of these instructional methods were equally effective in knowledge acquisition, but they are not equally cost‐ and time‐effective. Therefore, hospital educators may wish to formulate policies regarding a choice of instructional method that takes into account the efficient use of nurses’ time and institutional resources. Click here for additional data file.


We welcome this letter to the editor in reaction to our article ‘A fatal combination of situs inversus, pregnancy and cardiac arrest treated with an automated external defibrillator’.The author correctly points out the importance of left lateral tilt and early perimortem delivery of the foetus via Caesarean section. As the length of a Rhythm Puzzle is limited, the scope of our article was restricted to the use of the automated external defibrillator.We only want to add that the European Resuscitation Council elaborates on this issue in its Guidelines for Resuscitation 2015 .