A computational sensibility analysis of the transport model reveals that the shared conductance between the ions lowers the limited currents with larger supporting salt concentrations. When the supporting salt supplies most of the conductance, the electric-field-driven transport of the electrochemically active ions becomes negligible so that the limited current drops to the diffusion-limited current that is described by Fick’s first law. The transition from diluted supporting electrolyte to the case of ionic liquids is elucidated with the transport model, highlighting the different physical transport mechanisms in a non-conducting (polar) and a conducting (ionic) solvent.Supporting electrolytes contain inert dissolved salts to increase the conductivity, to change microenvironments near the electrodes and to assist in electrochemical reactions. This combined experimental and computational study examines the impact of supporting salts on the ion transport and related limited currents in electrochemical cells. A physical model that describes the multi-ion transport in liquid electrolytes and the resulting concentration gradients is presented. This model and its parameterization are evaluated by the measured limited current of the copper deposition in a CuSO For example, in industrial copper refining and winning the conductivity of aqueous CuSO4 baths is increased by H2SO4 addition5. Electrolytes with at least three different sorts of ions also emerge when reactive ion types are dissolved with inert ions in for instance aqueous salt solutions8, molten salts11, deep eutectic solvents13, or ionic liquids17.Supporting electrolytes are solvent-based liquids that contain inert salt additives  which are not electrochemically converted. These additive salts can increase the conductivity of the electrolyte and thereby improve the efficiency of electrochemical processes20. In these systems, the electrolyte is thinning out at the electrode at which dissolved ions are electrochemically converted, whereas the ions accumulate at the electrode which introduces ions into the electrolyte. Thus, electrochemical reactions cause concentration gradients in liquid electrolytes23 that ultimately limit the current that electric-field and diffusion-driven ion transport can carry without locally depleting the concentration of the converted ion types24. The limited currents and concentration gradients in multi-ion systems with its relation to the microenvironment at the electrode (such as pH26) display an important design aspect for electrochemical devices for batteries23, the separation of ions28, CO2 reduction30, electrowinning32, electroplating35 and so forth.For binary (one type of cation and one type of anion) solvent-based electrolytes the transport of ions was experimentally characterized and theoretically described in various works24. Numerical time domain modeling of the electrochemical transport differential equations has proven its reliability to represent the concentration dependence of the electrolyte parameterization, while it also can resolve changing boundary conditions such as varying currents24.In binary electrolytic solutions, the electrolyte parameterization is described by the transfer numbers (that describe the different contributions of the anions and cations to the conduction), the mutual diffusion coefficient  and the molar conductivity. These properties depend on the concentration, for which the electrochemically driven concentration gradients require a spatially resolved parameterization for a precise transport modeling38 and numerical41 approaches to solve the electrochemical transport equations. From these studies, only Awakura et al.37 compared model results with experimental data, which is however crucial to understand and describe the complexity of the ion–ion interactions in these systems that cannot be precisely described by ab-initio models. All of these studies were conducted with a constant set of electrolyte parameters that do not take into account the concentration dependence and ion–ion interactions. Most of these studies considered an infinite distance of anode and cathode41, which simplifies the mathematical description and analytical solution of the transport equations. This scenario however does not lead to a steady state with a constant limited current24. A detailed understanding of the mechanisms that influence limited current in supported electrolytes, its correlation to the electrolyte properties and the parameterization of the interaction of different sort of ions is not yet reported.The ion transport in supporting electrolytes was modeled in previous studies with analytical4 and Na2SO4 electrolytes. To understand the physicochemical mechanisms of the ion transport in supported electrolytes and its influence on the limited current in detail, a computationally sensibility analysis of the parameterization is conducted. Moreover, the computer model is adjusted to multi-ion systems in molten salts and ionic liquids, showing similarities and differences of the ion transport in comparison to the solvent-based electrolytes. The source codes of the computational model are provided in the supporting information, so that the community effortlessly can reproduce the presented results and thereon further develop the presented model.The aim of this study is to describe the ion transport in supporting electrolytes with a physical model of the electrochemical transport equations which enables a concentration-dependent parameterization and the description of steady limited currents. The modeled limited currents are compared under different parameterization scenarios to measured limited currents of mixed CuSO4 and Na2SO4 electrolytes serve as an exemplary system of supporting electrolytes to examine limited currents. Hereto, the two polished copper plates are separated by a stamped fluoroelastomer flat sealing with an inner diameter of 14 mm and a thickness of 500 µm (Reichelt Chemietechnik). To assemble the cell, the sealing was laid on one electrode and the copper surface was wetted with approximately 1 ml of electrolyte. The surface of the other electrode was also wetted with the electrolyte and then pressed onto the electrode with the sealing. Thereby, the excess electrolyte floated out of the cell assembly while the sealing between the electrodes was completely filled with the electrolyte. The anode was placed at the bottom to avoid macroscopic density differences that are compensated by gravitational shear forces24. An additional cell with copper electrodes and an electrode distance of 20 mm was used to characterize the conductivity of Na2SO4 solutions. Hereto, the copper electrodes were pressed with flat sealings (same type as above) on a polypropylene body. With 4-wire potentiodynamic alternating current impedance measurements, the electrolyte resistance was determined42.In this study, the copper deposition and dissolution of plane and polished copper electrodes in mixed CuSO24, which included an experimental evaluation and a concentration-dependent parameterization of the molar conductivity, mutual diffusion coefficient and ion transfer numbers. This transport model describes the electric field and diffusion driven motion of dissolved ions in liquid electrolytes and is in the following adapted to an electrolyte with three ion types. This multi-ion system is in the following parameterized on the basis of reported experimental conductivities, diffusion coefficients and transfer numbers on the binary electrolyte systems of CuSO4 and Na2SO4, respectively. The source codes of this approach are supplied in the supporting information.A detailed model on the ion transport in binary electrolytes has been presented previously4 and Na2SO4 electrolyte solutions, respectively, referring to the data reported by Owen et al.43, Bester-Roag et al.44, Emanuel et al.45, Noulty et al.46, Woolf et al.47, Rard et al.48, Pikal et al.49 and Longsworth et al.50. The molar conductivity and diffusion coefficients decrease towards higher electrolyte concentrations, which is a direct result of the ion–ion interaction that is described by the Debye-Hückel theory52. Most of the literature reported values at the standard temperature of 25 °C, whereas the measurements in this study were performed at 20 °C. The effect of temperature on the molar conductivity and diffusion coefficient is discussed elsewhere in detail24. The conductivity and the transfer coefficient of the CuSO4 electrolyte show a more distinct concentration dependence than those of the Na2SO4 electrolyte. The dissolution of CuSO4 acidifies the aqueous solvent, however, the concentration of protons is more than 1000 smaller than the concentration of dissolved copper for which the impact on protons on the transport model is negligible24. The trends of the concentration dependence of the electrolyte properties can be described on the basis of the Debye–Hückel theory, whereas the complexity of the aqueous solutions do not allow a precise theoretical prediction of ion–ion interactions and their impact on conductivities and diffusion coefficients54. Thus, the experimental data is described by analytical non-physical equations which adequately describe the concentration dependence of the literature data in Fig. Figure The transfer number Using Ohm’s law, this equation can also be interpreted as a ratio of conductivities 2SO4, the anion .To calculate the limited currents with the computational transport model, the simulation is started with a current density of 15 mA/cmIn contrast to the copper ion starvation at the cathode and its accumulation at the anode, the sodium ion concentration gradient is converse, with an enlarged amount at the cathode and a reduced amount at the anode. The sodium ions are transported by the electric field in the electrolyte to the cathode where they cannot be converted. In the steady state, the sodium ion current by the electric field towards the cathode is balanced by diffusion into the opposite transition, leading to no net sodium ion transport. As the sulfate ions are transported by the electric field towards the anode, the amount of sulfate ions is decreased at the cathode and increased at the anode. As the sulfate ions are the only anions in this system, their amount reflects the total amount of dissolved ions with respect to the charge. Similar to the sodium ions, in the steady state the net sulfate ion transport equals zero so that the copper ions as the only electrochemical active ion type constitute the total net current. The electric-field and diffusion-driven ion transport of the copper ions point in the same direction from the anode to the cathode.2SO4 concentrations. The four different parameterizations are characterized by the following features:(i)41. The values of Fig. 4 and Na2SO4 serve as model input parameters. When the concentration of copper ions near the cathode is thinning out, their local conductivity, diffusion coefficient and transfer number increase with reference to Fig. 4 electrolytes24. By neglecting these concentration dependencies, the current is up to a Na2SO4 concentration of 0.5 M underestimated (similar to that in binary solutions24), as the locally higher diffusivity and ion transport number 4 and Na2SO4 respectively, without taking their interaction into account. Thus, the molar conductivity, diffusivity and cation transport number of the CuSO4 component decreases towards higher CuSO4 concentrations, whereas it is not affected by the Na2SO4 concentration. Likewise, the properties of the Na2SO4 component are influenced by its concentration and do not interact with the CuSO4 component. The modeled data is overestimating the measured limited current. At Na2SO4 concentrations below 0.05 M the differences between the modeled and measured data is with less than 5% moderate, however, it increases towards higher concentrations. As expected from the Debye–Hückel theory, the interaction of the ions is expected to decrease the molar conductivity and diffusion coefficients, explaining the modeled overestimation of the limited currents.In the second case, the model is parameterized with the individual concentration dependencies of CuSO(iii)4 and Na2SO4 components are calculated as a function of the total concentration of sulfate ions, assuming that the interaction between the sulfate ions and the different cations is equal. However, this parametrization underestimates the measured limited current. Thus, the assumption that the ions influence one another in the same amount does not hold valid. Figure 4 than those of Na2SO4. Thus, the ion–ion interactions in CuSO4 are different from that in Na2SO4 and the influence of the different components on one another is therefore also not that easy to describe.In the third parametrization scenario, the parameters of the CuSO(iv)4 component are calculated for the concentration of CuSO4 plus 20% of the concentration of Na2SO4. Analogously, the parameters for the Na2SO4 component are calculated for the concentration of Na2SO4 plus 20% of the concentration of CuSO4. Thus, an interaction between the different ion types is partly included, however, to a smaller extent than that between the ions of the same type. Using this parameterization, a good fit of modeled and measured data is obtained.The fourth case describes a concentration-dependent parameterization that displays a mixture between the second and third approach. Hereto, the parameters for the CuSOFrom the measurements graphed in Fig. 53, the Debye–Hückel theory based physicochemical models that are used to describe the complex interaction between the ions are non-trivial and typically do not exactly describe the concentration dependence of the electrolyte parameters. However, using such approaches a physicochemical description of the ion–ion interactions for the electrolyte parameterization may be possible. Theoretical works to address the prediction of the ion–ion interaction in multi-ion systems have to follow and may lead to more precise parameterization procedures as the presented approaches that is based on the experimental data of binary electrolytic solutions.The scenarios discussed above are based on the experimental data on binary electrolytes and do not represent a physicochemical approach to characterize the ion–ion interactions in mixed ion systems. Based on these data, however, the ion–ion interaction is shown to crucially impact the ion transport in supporting electrolytes and the related limited currents. In the literature4–Na2SO4 system, where water displayed the polar solvent.Thus far, measured and modeled data showed that limited currents decrease towards higher concentrations of the inert ions. In the following, the modeled limited currents are modeled under a variation of the electrolyte parameters, aiming to display the physicochemical relations that are described by the differential equations of the transport model. Hereto, two cases are considered, a polar solvent in which the salts are dissolved and an ionic liquid (or ionic melt). The first case resembles the above discussed CuSOA simplified test system is considered in the following, in order to focus on the physicochemical interactions of the transport mechanisms rather than the complex parameterization that is discussed above. The test system is characterized by the following properties: (1) The electrolyte is comprised by two different salts, with two different types of cations (denoted as C1 and C2) and one type of anion (denoted as A). (2) Cation type C1 is pushed at the anode into the electrolyte and it is removed at the cathode, the other ions are inert. (3) Both salts have an equal density. (4) The molar conductivity, diffusion coefficient and transfer number of both salts are assumed as concentration independent with constant values of Figure Figure 24. However, as here defined by the conductivity ratio .Figure 5 or aqueous copper/sulfur batteries56. However, the aim of this article is to conclude physicochemical relations that are applicable to a wider scope and which are independent of the parameterization of the presented model system. With the knowledge that the limited current decreases with the amount of supporting ions, the addition of inert ions displays a compromise between an increased conductivity and a decreased limited current. When the electrolyte is mechanically mixed by convectional forces, the concentration gradients formed by the electrochemical current are partly equilibrated. Thus, the diffusion-limited currents in such flowing electrolytes is larger than in the case of static electrolytes. Causes for such convection can be found in: (i) Macroscopic density difference, where the gravitational force leads to shear forces. (ii) Bubble formation and ascending bubbles. (iii) Mechanical mixing of the electrolyte by stirring or pumping.The results on the copper based model system can find direct application in the design of electrochemical processes and devices such as copper refiningIn ionic liquids, the electrode is always in contact with the electrolyte, which reduces with reference to Fig. 4–Na2SO4 electrolytes. The comparison of measured and modeled data shows that a complex concentration-dependent parameterization of the interaction between the different ion types in supporting electrolytes is required to adequately model the ion transport. A computational study on the variation of the electrolyte parameters reveals the ion transport mechanisms and the interplay of electric-field and diffusion-driven ion motion. With an infinite amount of supporting salt in the electrolyte, the conduction-driven transport of the active ion becomes negligible and the limited current drops to the diffusion-limited current that is described by Fick’s first law. The similarities and differences of the ion transport in supporting electrolytes and ionic liquids is examined with the computational model, showing the impact of electrolyte parameters on limited currents.This study examined the ion conduction, current-driven concentration gradients and related limited currents in supporting electrolytes. A computational model is developed to describe the ion transport and the related spatiotemporal ion concentrations in electrolytes with three ion types. This model is equipped with different concentration-dependent parameterization scenarios and evaluated with measured limited currents of CuSOSupplementary Information.


Transcranial static magnetic field stimulation (tSMS) using a small and strong neodymium (NdFeB) magnet can temporarily suppress brain functions below the magnet. It is a promising non-invasive brain stimulation modality because of its competitive advantages such as safety, simplicity, and low-cost. However, current tSMS is insufficient to effectively stimulate deep brain areas due to attenuation of the magnetic field with the distance from the magnet. The aim of this study was to develop a brand-new tSMS system for non-invasive deep brain stimulation.We designed and fabricated a triple tSMS system with three cylindrical NdFeB magnets placed close to each other. We compared the strength of magnetic field produced by the triple tSMS system with that by the current tSMS. Furthermore, to confirm its function, we stimulated the primary motor area in 17 healthy subjects with the triple tSMS for 20 min and assessed the cortical excitability using the motor evoked potential (MEP) obtained by transcranial magnetic stimulation.Our triple tSMS system produced the magnetic field sufficient for neuromodulation up to 80 mm depth from the magnet surface, which was 30 mm deeper than the current tSMS system. In the stimulation experiment, the triple tSMS significantly reduced the MEP amplitude, demonstrating a successful inhibition of the M1 excitability in healthy subjects.Our triple tSMS system has an ability to produce an effective magnetic field in deep areas and to modulate the brain functions. It can be used for non-invasive deep brain stimulation. Transcranial static magnetic field stimulation (tSMS) is a promising non-invasive brain stimulation modality because of its competitive advantages such as safety, simplicity, and low-cost , 2. UsinDeep brain areas such as the basal ganglia and hippocampus are involved in a number of movement, neurological, and psychiatric disorders. Some of these disorders can be treated with deep brain stimulation (DBS) delivering constant or intermittent electricity to a target located in the deep brain areas. Stimulation-induced disruption of pathological brain circuit activity has been proposed as a mechanism by which the DBS operates . AlthougHere, we propose a triple tSMS system, colloquially termed as “SHIN jiba” in Japanese, enabling to stimulate deep brain areas with an effective magnetic field non-invasively. We demonstrated the triple tSMS could produce a magnetic field with a sufficient strength to provoke biological effects in a remote area from it. Further, we confirmed the triple tSMS could inhibit cortical excitability below it like the current single tSMS in healthy subjects.3, the nominal strength was 863 N, and the surface magnetic flux density was approximately 5340 G   NdFeB magnets placed close to each other. The north pole of the three magnets were embedded in a foundation made of non-magnetic material with a diameter of 140 mm and a thickness of 48 mm. The vertical axis of the magnets was tilted 16.5 degree from that of the foundation. Parameters of the magnets were as follows: the diameter was 50 mm, the thickness was 30 mm, the maximum energy density was 406 kJ/mThe strength of the magnetic field produced by the triple tSMS was measured with a HTD18-0604 transverse probe and an FW Bell 5180 Gaussmeter . All measurements represent the strength of the magnetic field vector along the axis perpendicular to the flat side of the probe. The decay of the static magnetic field with distance was measured by increasing the distance between the probe and the surface of the foundation, keeping the flat side of the probe parallel to the surface of the foundation. We performed duplicate measurements at the center of the foundation, that of one of the three magnets, and a point between the centers of the two magnets on the foundation. The strength was measured at intervals of 5 mm (Z-axis) from 10 mm below the surface of the foundation to a depth of 100 mm (Z = − 10 to − 100) at the center of the foundation and the point between the centers of the two magnets on the foundation, and from 15 mm below the surface of the foundation to a depth of 100 mm (Z = − 15 – − 100) at the center of one of the three magnets. For comparison with the current tSMS, we also measured the strength of the magnetic field produced by a single magnet (the current tSMS) which is same as the three magnets in the triple tSMS. The strength was measured twice at intervals of 5 mm (Z-axis) from 10 mm below the surface of the magnet to a depth of 100 mm (Z = − 10 to − 100) at the center of the magnet surface.To confirm the functionality of triple tSMS, we performed a stimulation experiment in 17 healthy subjects ). All subjects were right-handed as determined by the Edinburgh handedness inventory .The subjects were seated in a chair during the experiment. Each subject received both real (triple tSMS) and sham stimuli. The device for the sham stimulation had the same size and appearance as the triple tSMS system except that three non-magnetic stainless-steel cylinders were embedded in the foundation. To avoid carryover effects , the intThe protocol of TMS was same as a previous study  as outliAfter visually removing trials containing significant artifacts, we measured the peak-to-peak MEP amplitudes and calculated the averages. To evaluate corticospinal excitability in the left M1, the mean unconditioned MEP amplitude at Post was normalized to that at Baseline. For parameters of SICI and ICF, the amplitude ratio of the mean conditioned (with preceding CS) MEP to the mean unconditioned  MEP was calculated. All the values were transformed to logarithm.For the measurements at the center of the foundation, the strength–depth curve was unimodal Fig. a. There For the measurements at the center of one of the three magnets and the point between the centers of the two magnets on the foundation, the strength of the magnetic field decreased monotonically as the depth increased , while that in the sham session  did not change significantly   showed a decrease in the MEP after the intervention, while in the sham tSMS session 13 (76.5%) showed a decrease in the MEP. Wilcoxon signed-rank test between Baseline and Post showed that the normalized MEP in the triple tSMS session  significantly decreased after the intervention . Although more efforts are required to investigate the mechanisms of the neuromodulation by the static magnetic field, the proposed system can provide not only the same neuromodulatory effect as that of the current tSMS  but alsoThe measurement of the magnetic field profile showed that the triple tSMS system produced the magnetic field sufficient for neuromodulation up to 80 mm depth from the surface of the foundation. Just below the system, the magnetic field was weaker for the triple tSMS system than the current tSMS due to the interference of the magnetic fields produced by the three magnets. However, considering the distance (approximately 20 mm) between the scalp and the superficial cerebral cortex [The stimulation experiment showed that the triple tSMS inhibited the excitability of the human motor cortex. This neuromodulatory effect is comparable to the current tSMS , 20–22. In this study the triple tSMS showed different effects on the intracortical neural circuits as compared to the current tSMS. The triple tSMS induced no significant changes in SICI or ICF, while the current tSMS over the M1 for 20 min increased SICI but had no effect on ICF . The posAlthough the triple tSMS system has poor focality than the current tSMS, its neuromodulatory effect is comparable to the current tSMS. In addition, it has a capacity to produce an effective magnetic field in deep areas. Expanding the effective range with the triple tSMS can enhance the clinical utility of safe, simple, low-cost tSMS.


The EPID PSM is a useful EPID calibration method for QA applications. The dependence of the EPID PSM on the photon beam used to acquire it has been investigated in this study for the four available PSM methods. The aim is to inform upon the viability of applying a single PSM for all available photon beams to simplify PSM implementation and maintenance.Four methods of PSM determination were each measured once in a single session on a single TrueBeam ® STx linac using 6 MV, 10 MV, 6 MV Flattening‐Filter‐Free (FFF), and 10 MV FFF photon beams. The resultant PSM was assessed for both intra‐ and inter‐method beam dependence via comparison between PSM of the same method compared to the 6 MV PSM and via comparison between PSM of the same beam with the corresponding Monte Carlo PSM. Comparisons were performed via 2D percentage deviation plots with associated histograms, 1D crossplane profiles, and via mean, median, and standard deviation percentage deviation statistics. Generated beam‐response was compared qualitatively via 1D crossplane profile comparison and quantitatively via symmetry assessment with comparison to the IC profiler device.The Varian method provided the most consistent PSM with varying photon beam, with median percent deviation from the 6 MV PSM within 0.14% for all other beams. Qualitatively, each method provided similar beam‐response profiles. The measured beam‐response symmetry agreed to within 0.2% between the Calvary Mater Newcastle (CMN) method and IC profiler, but agreement reduced to within 0.9% and 2.2% for the Varian and WashU methods. PSM percent deviation with Monte Carlo PSM was within 0.75% for all methods and beams.Results suggest that the PSM may be independent of photon beam to clinically relevant levels. The Varian method of PSM determination introduces the least beam dependence into the measured PSM. For such applications, the image non‐uniformities caused by the patient anatomy in the beam are of interest. As such, correcting out the non‐uniformities introduced by the beam and those introduced by the EPID panel itself are required. This is standardly achieved via the flood‐field calibration procedure. However, correcting out the non‐uniformities introduced by the beam is problematic for many linac and patient quality assurance (QA) applications because the beam non‐uniformities  are the information required for investigation. As such, the flood‐field correction represents a major current limiting factor to the use of EPID for dosimetry and QA applications.GreerBecause of the problems associated with the EPID flood‐field calibration for QA applications a number of authors have attempted to develop alternate EPID calibration procedures where the non‐uniformity of the imager response is corrected without disturbing the non‐uniformity of the incident beam.Yaddanapudi and Cai studies were based upon an adaptation of the Boriano methodBarnes publication is based upon a simplified version of the GreerThree studies have been published which examined the utilization of PSM‐corrected EPID images for linac QA purposes.Similar to the linac QA applications, PSM calibration has demonstrated utility in EPID‐based patient‐specific QA applications.The question as to whether the PSM is dependent on the photon beam used to acquire it has not been definitively answered. In the study of Cai et al.,If the PSM were independent of photon beam then this would make implementation simpler as only a single PSM generated from a single photon beam would need to be determined and maintained, but could be applied to all applicable QA measurements regardless of photon beam. It is the purpose of this Part 2 study to investigate the beam dependence of the PSM and of four available methods for determining it. Analysis using four different photon beams with each of the PSM methods allows for both the intra‐ and inter‐method beam dependence to be assessed.2The PSM methods investigated include an improved Greer method henceforth known as the CMN method, a modified Boriano method henceforth known as the WashU method and a method developed by Varian  henceforth known as the Varian method. A fourth method is also included based on data obtained from Monte Carlo simulations (the Monte Carlo method). Other methods of determining the PSM have been published in the literature,2.12 panel with 40 × 40 cm2 active area in an 1190 × 1190 pixel array used for dosimetry mode resulting in resolution of 0.34 mm at isocenter. The aS1200 EPID also has a backscatter plate to remove backscatter from the EPID support arm, which would otherwise introduce an additional source of non‐uniformity to be corrected by the PSM. Results’ comparison was performed using a custom Matlab script .The measurements in this study were performed on a single Varian TrueBeam ® STx linac with aS1200 EPID. The aS1200 panel utilizes a 43 × 43 cm2.22.2.1Data were collected for all four PSM methods in a single measurement session. Each method was performed once on each of the available photon beams (6 and 10 MV and 6 and 10 MV FFF) so that an assessment of PSM dependence on photon beam could be made. Use of a single measurement is justified by the high short‐term repeatability observed for all methods in Part 1 of this study.2.2.2If the actual PSM is beam independent, it is possible that the methods of determining it introduce a beam dependence into the results. To inform on these questions, the measured PSM per beam were plotted as 2D percentage deviation maps with corresponding histograms relative to the 6 MV PSM. This was repeated for each PSM method. Additionally, 1D crossplane profiles for each beam were all plotted together per method, together with percentage deviation from the 6MV PSM for each method, so that results for all methods could be compared in the same plot.In Part 1 of this study,The beam‐response generated by each PSM method and for each energy was assessed both qualitatively and quantitatively. Qualitatively, 1D beam‐response crossplane profiles were overlaid and visually contrasted. Quantitatively, Sun Nuclear IC Profiler  measurements of beam symmetry using the Point Ratio (IEC 976) metric were performed for each beam. Symmetry of the beam‐response in both inplane and crossplane directions was calculated using the IEC 976 definition of symmetryThe aim of this study is to inform on whether the PSM generated with a single photon beam can be used for other available photon beams. For this to be feasible the PSM would need to be independent of a number of photon beam parameters that differ between beams. Such parameters include, but may not necessarily be limited to, beam spectrum and dose rate. As an initial investigation into the dose rate dependency a simple experiment was performed whereby in a single measurement session the PSM was generated using the CMN method for the 10 MV FFF beam with nominal dose rate set to both 400 MU/min, representing the minimum available nominal dose rate and 2400 MU/min representing the maximum available nominal dose rate. This beam was chosen as the one with the greatest variation in available nominal dose rate. If there were to be a dependency on dose rate than this may manifest in either the beam‐response or PSM. As such, both were investigated in this experiment. Both the beam‐response and PSM were generated for each dose rate using the CMN method and compared via 2D Percent deviation maps and percentage deviation histograms.3Figure 3.1Figure Figure Figure 2 field within the directly measured PSM data points.The top plot of Figure Figure Figure Figures 3.23.2.12 field size. It is worth reminding from Part 1 of this studyFigure Figure Table Monte Carlo results were not presented in Table 3.2.2Similar to the 6 MV results presented in Part 1 of this study,The median percent deviation for the CMN method with the Monte Carlo method as presented in Table The PSM median percent deviation for the Varian method compared to the Monte Carlo method across beams is most consistent of all methods and consistently the smallest magnitude of all methods, ranging between 0.19% and 0.27%. The WashU median agreement is least consistent with FFF results, having a negative value and flattened beams a positive value with magnitude ranging up to 0.74% which is the highest disagreement of all methods.3.3Figure The CMN method measures the beam response and the PSM is then generated by dividing the raw image by the beam response. Therefore, if there was no dependency on the dose rate for the beam response then the percent deviation histogram would be expected to be centered on zero to within the CMN method repeatability uncertainty presented in the Part 1 study.Since the PSM is generated in the CMN method by removal of the measured beam response then if there was no PSM dependency on dose rate then the PSM results of Figure 4The results of Figures The beam‐response profiles of Figure In this study, the measured beam symmetry was used as a quantitative method for assessing the accuracy of the beam‐response generated by each method. The results suggested that in this regard the CMN method is superior and highlighted the drawback of the Monte Carlo method, where perfect symmetry is inherent. Significant disagreement in the measured symmetry was observed for the Varian and WashU methods, which will at least partially be due to the noise inherent in the beam‐response from these methods. A simple solution to this problem is to smooth the beam‐responses prior to applying the symmetry metric, however, using this metric with the noise still included, provided a demonstration as to a potential clinical effect of this noise. Due to the mutual dependence of the PSM and beam‐response (an error in one leads to an inaccuracy in the other) the effect of noise in the beam‐response will be inaccuracy in the corresponding PSM.While symmetry was chosen in this study as a measure of clinical significance, the utility of each method will likely be application specific. As such, other methods of assessment should be considered specific to the application.In general, the PSM generated by the Varian method agrees best with the Monte Carlo method in terms of median agreement, followed by the CMN method and the WashU method. For all methods, the median percent deviation is always within 0.5%, except three out of the four beams with the WashU method in which case these beams are within 0.75%.With multiple beams and multiple PSM methods, there are many relationships within the results that have not been investigated in this study and these are now recommended for further work. One example is investigation of the effect on measured symmetry of smoothing the Varian and WashU beam‐responses. Another is investigating whether methods can be modified to assign dead pixels and the primary collimator correctly to the PSM and beam‐response, respectively. The Monte Carlo method could also be improved with a greater number of histories, but its flaws of assuming ideal beam symmetry and beam energy are inherent. The CMN method could potentially be investigated to see whether changing the number of directly measured data points improved the quality of the fit, particularly in the extrapolated regions at the extremity of the image or conversely whether a reduced number of directly measured points could reduce the required measurement time without affecting accuracy. The effect of dark field calibration has not been assessed in this study, although the WashU and Varian methods utilize the ABDF technique that takes dark field images during the data acquisition process so in theory should be unaffected. Lastly, other clinical significance metrics rather than beam symmetry could be investigated to inform on the performance of each PSM method. A simple way of doing this would be to try each PSM method for any PSM application developed and benchmark the results of the application against an independent system. Since the work was only performed on a single EPID panel then a follow‐up study to verify these studies results on multiple EPID panels is also suggested.Based upon the findings from both parts 1 and 2 of this study, the choice of which PSM method is best for clinical use is likely application specific. The required accuracy should be weighed against the time required to acquire the PSM and consideration should also be given to the EPID panel‐type used, likely field sizes to be measured and to whether multiple photon beams will be utilized.5Strengths and weaknesses of each of the PSM methods available to this study have been expanded upon from Part 1 of this study and the beam dependence of the PSM and of the four available methods for determining it has been investigated. Non‐conclusive evidence is presented that, at least for photon beams, that the actual PSM may be independent of photon beam.The authors declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported.Michael Barnes: Had the original idea for the study, performed data acquisition, and analysis and primarily wrote the manuscript.Baozhou Sun: Provided the WashU and Varian PSM methods and for these methods performed both post processing of data to generate PSM and wrote the relevant methods section of the manuscript. Baozhou also provided scientific input into the study and writing of the manuscript.Brad Oborn: Provided the Monte Carlo simulations, wrote the Monte Carlo related methods sections and provided scientific input into the study and writing of the manuscript.Bishnu Lamichhane: Performed the 2D curve fitting required for the CMN method and wrote the corresponding section in the methods as well as providing scientific input into the study and writing of the manuscript.Matthew Schmidt, Stuart Szwec, Bin Cai, Fred Menk and Peter Greer: All provided scientific input into the study and writing of the manuscript.Supporting InformationClick here for additional data file.


Coal mining may lead to ground subsidence in a long term and is widely distributed, which can cause environmental damage and other disasters. Predicting the dynamic process of ground subsidence in real time is very important for offering theoretical or technical guidance to deal with the consequences of mining. In this study, we developed a prediction method for dynamic ground subsidence using a time function model that considers two stages of surface subsidence and reflects the law of surface subsidence in goaf. We applied the model to the Barapukuria mine, and our simulation shows that the prediction results are in good agreement with the monitoring data. Our results suggest that the dynamic development of the ground subsidence basin may be an effective measure to assess the loss of ground and provide early warning of oncoming hazards. Underground mining causes the ground surface to move downward relative to the initial mining position, which promotes subsidence basin6. Surface subsidence is a dynamic process that gradually develops with the advancement of the mining working face9. An arbitrary point on the ground surface continues to subside as extraction is performed within a critical area below that point10. It is important to predict the dynamic development of a surface over time.Coal mining often leads to ground subsidence around mining areas, which can cause problems, such as water accumulation, agricultural reduction, road collapse, and deformation or damage to buildings11. Based on the analysis of subsidence monitoring data, influential functions can be used to describe the influence of the excavation elementary part of the formation subsidence14. The dynamic prediction of mining subsidence can be obtained by multiplying the static prediction results with the corresponding time coefficient16. Double-parameter time functions and prediction parameters have been proposed to improve simulation performance20. Although the Knothe time function can be used to predict the dynamic movement and deformation of the ground surface, it is still difficult to determine the coefficient of the influence function because land subsidence is affected by geological parameters and geomechanical mechanisms.The prediction of mining subsidence is an important issue for the mining industry, government, and the affected people. This is particularly important for towns and engineering projects where mining occursIn this paper, we first present the major contribution of this study—a prediction model developed with the parameters of ground subsidence. Then, with the help of MATLAB programming platform, we simulated the surface subsidence process over time in the Barapukuria mining area in Bangladesh. The results show that the numerical simulation matches the monitoring data well. We hope that our study offers a dynamic prediction of ground subsidence and provides a basis for the early warning of forthcoming hazards.The mechanism of ground movement caused by mining is complex and influenced by the geological environment of the mine and overlying strata. Although an accurate model is difficult to find, an approximate prediction model can also be used to forecast subsidence caused by mining by modifying certain influence parameters. In the process of mining, ground subsidence continues to increase and forms a subsidence basin, as shown in Fig. 21, the formula is expressed as follows:The spatial influence function can predict ground subsidence, which should not only take into account the main characteristics such as the depth of the coal seam, maximum possible subsidence, and time factor, but also involve the evolution of subsidence in space. Here, we introduce a spatial influence function12, assumes that the surface subsidence velocity The subsidence of the surface cannot be completed instantaneously after mining, and always develops over a period of time and even several years to reach a relatively stable state. One of the most widely used time functions proposed by KnotheThe above relationship represents the subsidence expression of the dynamic prediction of surface movement based on the Knothe time function. The accuracy of the Knothe time function depends mainly on parameter 22. The improved function includes two functional expressions. First, the surface subsidence velocity gradually increases from zero to the maximum value, and the surface points gradually bend owing to mining. The second shows that the surface subsidence velocity decreases from the maximum to zero. The functional relationship of the subsidence velocity with time is as follows:To reflect the dynamic change law of surface subsidence, the Knothe time function is improved to meet the need for dynamic prediction of practical projectsFor a near-horizontal coal seam, the surface subsidence reaches the maximum subsidence velocity entclass1pt{minimaAccording to the above analysis, the theoretical subsidence value 23 is given as:Here, an optimized piecewise Knothe time functionWith the optimization of the time function, regardless of parameters 25. The coordinates of the monitoring points in the coordinate system of the working face are The prediction parameters for mining subsidence in the probability integral method have been calculatedn-equal units along the working face before the dynamic prediction of ground subsidence. The mining moment at the open-off cut and speed of the working face of the first mining unit are defined as the initial moments n-th unit is First, the mining area should be divided into n-th units induced after mining can be expressed as follows:The ground static subsidence of the first, second and n-th mining unit is Assuming that the predicted time of surface subsidence is In the actual mining process, the daily excavation speed and mining time remain constant: r is the major influence radius. When the predicted moment is greater than the total mining time, the mine was fully mined. We set According to the above analysis, the formula for the probabilistic integral method is given.During subsidence prediction process of the strike principal section, the subsidence of all the affected surface points can be predicted using the three-dimensional coordinate system, as shown in Fig. To predict the subsidence of an arbitrary point on the surface of the mining area, a coal seam coordinate system is set with the origin and the Figure sing Eq. , the sur26, the capital of Bangladesh, with a geographical location of 25°31′–25°34′ N and 88°57′–88°59′ E. The spans of north–south and east–west are respectively about 4.9 km and 0.3 ~ 1.9 km about covering an area of 5.8 square kilometers.The mine is located in the northwest of DhakaThe coalfield stratum belongs to the Carboniferous-Permian, the 1210 working face is located in the south of the mine, and coal seam is horizontal with an average thickness of 5 m. The 1210 working face only laid a north–south direction observation line on the side of the open-off cut, with a total of 32 measuring points and with an average distance of approximately 25 m. The 1210 working face mining process lasted for 118 days. The average mining depth of the 1210 working face is 414 m, mining length is 349 m, and mining speed is 2.96 m/day. The 1210 working face can be regarded as a near-horizontal coal seam. The position of the mining area and a comparison diagram of the 1210 observation stations are shown in Figs. According to the empirical value of the prediction parameters of the mining area, with the help of Eqs.  and 14)14), we olts Fig. . Figure In both the monitoring data and the predicted value of the strike principal section, the overall subsidence rate first increased and then decreased, and the subsidence curve conformed to the law of the S curve. The average interval of the maximum subsidence value for each monitoring curve is 0.311 m, whereas the predicted curve is 0.317 m. After excavation, the number of days experienced for each increase in a certain subsidence value decreases and then increases, and the monitoring curve is in good agreement with the prediction.t represents the duration from the moment of mining, and the total mining time was 118 days.Based on the above prediction model described for surface subsidence, we solved Eqs.  and 14)14) with Figure Figure Figure The surface subsidence continues to spread after mining, and with the help of our model, we can obtain some more predictions for the subsidence basin shown in Fig. Surface subsidence caused by mining often produces subsequent disasters, the prediction of which may help to assess subsequent disasters. Based on the monitoring data of the Barapukuria mine, we developed a prediction model based on the optimized piecewise Knothe time function and prediction parameters from the actual monitoring results, which can determine the subsidence prediction curve of the strike principal section and subsidence basin at arbitrary points on the surface through simulations.Our simulation shows that the prediction results and monitoring data are very similar, as shown in Fig. In this study, we developed a time influence function to model surface subsidence caused by mining. These subsidence equations are implemented in MATLAB for the numerical prediction of surface subsidence in Barapukuria mining. The results of our simulation allow us to show how the subsidence basin extends at different times during the mining process. Our simulation shows that the predicted results agree well with the monitoring data. Our simulation provided the final shape of the subsidence basin. This may provide an early prediction of ground subsidence caused by mining.The present simulation ignores the influence of the physical parameters of the overburden strata. In the next, we will give more consider the physical parameters of overburden strata and the inflection point offset distance to obtain a more accurate prediction model.Supplementary Information 1.Supplementary Information 2.


The authors have retracted this article. After publication, it was noted that Figures 6 and 7 used incorrect data from a different study. This has led to the authors having a loss of confidence in the results of their article.All authors agree to this retraction.


Postovulatory aging is a process occurring in the mature (MII) oocyte leading the unfertilized ones to apoptosis. The optimal time window of fertility for different mammalian species after oocytes maturation depends on its timeliness: the higher the time elapsed from the accomplishment of the MII stage, the lower are the chances of fertilization and of development of a viable embryo. In the in vitro fertilization, the selection of competent oocytes for intracytoplasmic sperm injection (ICSI) is mostly made by the visual inspection of the MII oocyte morphology, which does not allow to determine the oocyte postovulatory age. On the other hand, more specific tests usually involve some kind of staining, thus compromising the viability of the oocyte for reproductive purposes. Hence, the need of a noninvasive analysis of oocyte aging to improve the success rate of in vitro fertilization procedures. Here, we exploit atomic force microscopy to examine the evolution of the mechanical properties of mouse oocytes during in vitro postovulatory aging. Three hours before the occurrence of any visual morphological feature related to degradation, we observe a sudden change of the mechanical parameters: the elastic modulus doubles its initial value, while the viscosity decreases significantly. These mechanical variations are temporally correlated with the release of the cortical granules, investigated by fluorescence microscopy. Interestingly, the oocyte mechanics correlates as well with the yield of embryo formation, evaluated up to the blastocyst formation stage. These results demonstrate that minimally invasive mechanical measurements are very sensitive to the aging of the oocyte and can be used as a label‐free method to detect the age of the postovulatory oocytes. At birth, oocytes are arrested at the first meiotic prophase and are characterized by the presence of the germinal vesicle (GV). The nuclear envelope breakdown occurs only at the time of puberty when oocytes enter the first meiotic division (MI). At ovulation, mature oocytes (MII) are released from the ovarian follicle. After release, in the absence of fertilization, the mature oocytes go through a process of slow degradation culminating in apoptosis.2+ channels and ATPases that affects Ca2+ homeostasis, and variations in the dynamics of actin‐tubulin assembly that are related to the formation of the meiotic spindle.This phenomenon is called “postovulatory aging” and its duration varies according to species: in humans, the useful time window for fertilization is lower than 24 h, while in mice is lower than 8–12 h.A further key event related to postovulatory aging is the occurrence of a spontaneous cortical granule (CG) exocytosis.The clinical implications of postovulatory aging include decreased rates of fertilization, as it occurs in “rescue” ICSI performed on failed‐to‐fertilize oocytes, loss of the embryo uterine implantation capacity, and impaired development during embryogenesis. Moreover, dysfunctional mitochondria and altered epigenetic profile can cause abnormalities in offspring .To increase the number of competent oocytes during the in vitro fertilization (IVF) practice, women are treated with different gonadotropin stimuli to induce superovulation; therefore, the retrieved oocytes can have different maturation stages. The embryologist selects competent MII oocytes looking at those visual morphological features that are commonly related to mature healthy oocytes. The presence of the first polar body (PB) identifies a meiotically mature MII oocyte, while an immature oocyte is characterized by the absence of PB (MI) or the presence of the germinal vesicle (GV), the egg nucleus with the condensed chromosomes. The regular structure and thickness of the ZP, and the absence of cytoplasmic granularity are some of the key parameters associated to a good quality oocyte.Further analytical approaches beyond visual inspection have been proposed to determine the stage of MII oocyte such as genetic screening, spectroscopy‐based metabolomic profiling, enzymatic activity assays, and protein expression analysis on follicular fluidsRecently, there is a growing attention to the cellular mechanical properties for their relation to the physiological or pathological cell status.In this article, we examined the mechanical properties of mature (MII) mouse oocytes by AFM indentation. An alteration of the mechanical features of the aged oocyte can be detected few hours before the morphological changes related to apoptosis become evident by visual inspection. This event is temporally anticipated by a CG exocytosis, which prompts us to assume the occurrence of a CG‐induced cross‐link reaction in the ZP.This could allow the identification of a more reliable parameter to classify the quality of the oocyte that could be exploited for increasing the yields of IVF.22.1To identify the suitable mechanical parameters to study the oocyte aging, we investigated the mechanical properties of the whole mouse oocyte by performing AFM indentation measurements on a population of denuded MII mouse oocytes retrieved from superovulating mice Figure . We usedE2) associated with the more internal part of the ZP  and (160 ± 10) Pa and are comparable with those obtained for freshly retrieved oocytes, respectively (43 ± 4) and (148 ± 7) Pa in agreement with what observed for human oocyte.Moreover, to increase the sample size by reducing, at the same time, the number of sacrificed animals, we investigated the effect of the freezing procedure on mice oocytes. Oocytes were frozen according to the protocol described in the supplemental material. The rocedure . To comp2.2To rule out the possibility that the indentation measurements themselves can have an effect on the dynamics of the postovulatory aging, we used cryo‐conserved oocytes to investigate is the possibility of a correlation between degradation time and indentation force. Indeed, the mean elapsed time between thawing and the onset of the visually detected morphological alterations did not change significantly, and all the tested conditions were similar to the control group, where no force was applied Figure .To better monitor in‐vitro the effect of the AFM indentation on the health and postovulatory evolution of freshly retrieved oocytes, we investigated the correlation between CG exocytosis and the force applied performing the AFM indentations. For this purpose, we added to the culture medium a solution of FITC‐LCA , a lectin‐conjugated fluorophore that binds to the α‐mannose residues which are released by GCs during the exocytosis process. Initially, a background fluorescence can be observed everywhere; after the occurrence of spontaneous GC exocytosis, the α‐mannose concentration in the PVS peaks, and so do the bound fluorophores, resulting in a weak, but detectable, local increase of the fluorescence, as shown in Figure 2) and extracted only for the time needed for image acquisition. Their morphology was monitored by bright field microscopy, considering healthy specific visual features, such as the presence of a round‐shaped ooplasm, a regular ZP, and the presence of the PB. Oocyte degradation was identified when anomalous morphological features appeared, such as an increase in cytoplasm granulometry, a visual deformation of the ooplasm, and the oolemma break down resulting in the disappearance of the PVS.Then, different forces were applied on the oocytes by AFM with a bead‐modified cantilever. Starting from the thawing time, up to oocyte visible degradation, forces of 1, 10, and 20 nN were applied to different oocytes groups, and epifluorescence images were taken every hour. During this interval, the oocytes were kept at 37°C in the incubator , as depicted in Figure E2 of the ZP‐surrounded oocytes (ZP‐Oo) is significantly higher than that of the Ooplasm (Oo), (280 ± −80) and (90 ± 30) Pa, respectively. At the same time, the energy dissipation is much lower on ZP‐Oo than on Oo, indicating that the ooplasm is a more viscous and softer structure.To further confirm that the observed effects are not linked to local properties but reflect the status of the whole oocytes we performed whole‐oocytes stress relaxation measurement using macrocantilevers fabricated on purpose.τ1, to the ZP and τ2 to the ooplasm, which relaxes over a longer time interval. With this assignment, the decrease in time of τ1 3 h after the retrieval  able to directly induce a fast crosslinking of this glycoproteic layer.To understand whether the release of GC is involved in the observed increase in stiffness, we repeated the AFM indentation measurements in combination with epifluorescence microscopy to monitor GC exocytosis during in vitro oocyte aging. In Figure 2.62. The main effect of SrCl2 is the Ca2+ release from the internal compartments of the cell. Ca2+ oscillations involve the activation of the meiotic resumption and eventually the formation of the two pronuclei of the parthenogenetic embryo. This chemical activator was already proved to also elicit the cortical granule reaction in the MII oocyte.To further understand the effect of CG exocytosis on ZP mechanical properties, we chemically induced the CG exocytosis adding to the medium a well‐known parthenogenetic activator, SrCl2 and the change in the mechanical properties as well as the variation in the FITC‐LCA fluorescence intensity were continuously recorded for up to 90 min. Few minutes after the addition of the activator, CG exocytosis was detected by a sudden increase of the fluorescence signal, which reached the maximum intensity within 30 min and then it gradually decreased. This behavior was consistently observed for all investigated oocytes. On the contrary, although the activator had a clear influence on the ZP stiffness, a regular and simple behavior was not identified. The activator determined strong oscillation on the stiffness with time, frequency, and intensity strongly dependent on the investigated oocyte, which did not allow to extract a common trend , as already observed by our group on human oocytes.E1 values show highly inhomogeneous values from cell to cell, but also within the same cell, just varying by a few micrometers the indentation position. On the contrary, the inner layer is more homogeneous and the results are consistent within the same cell, no matter the indentation position. Hence, we focused on E2 to investigate the evolution in time of the oocyte mechanical properties during oocyte in vitro postovulatory aging from the thawing to the occurrence of the visual change due to degradation.We identified the presence of two, mechanically distinct layers on the mouse ZP characterized by different values of the Young's modulus  in the fertilized oocyte. Ovastacin, one of the substances inside the CG, is thought to be responsible for this change in the mechanical properties, as it cleaves ZP2 (one of the three glycoproteins of murine ZP) causing a permanent change in the structure of the fibrils. This is normally a slow process occurring over 2/3 h from fertilization. Evidence of cortical reaction occurrence during oocyte postovulatory aging has already been observed and considered as one of the hallmarks of the aged oocyte.Apoptosis is a well‐known process that begins with oxidative stress and brings to the damage of the mitochondrial DNA, a reduced ATP production and the failure of the mechanisms that regulate the ionic transfer and therefore to the impairment of CaTo prove that indentation measurements do not affect the cell viability inducing a premature aging of the oocytes, the possibility to trigger the CG release with the application of different forces was also investigated. The increase of the fluorescence associated with the CG exocytosis inside the PVS was evaluated during the lifespan of the oocytes, from right after retrieval to the occurrence of visual degradation. The force loading applied up to 20 nN does affect the dynamics of the CG release and we concluded that the mechanical measurement does not interfere with the aging progression.E2 during the oocyte lifespan highlighted a feature common to all the measurements performed consisting in a statistically significant increase of the ZP stiffness accompanied by a decrease of the viscous dissipation, which is linked to the ZP viscosity, 2 h before any visual change due to degradation. This effect is immediately followed by a ZP softening and recovery of the ZP viscosity as the degradation occurs. In general, when the stiffness of this layer increases, the viscosity decreases, and vice versa.The evaluation of the variation of This suggests the presence of a dynamic cross‐linking of ZP glycoproteins in the aged oocyte. The phenomenon known as “zona hardening” (the increase in the stiffness of the ZP from the mature oocyte to the zygote) has been already reported to occur in hours from a fertilization event,To demonstrate that this effect is independent of the adopted measurement strategy, we investigated the stress‐relaxation properties of aging oocytes. To this purpose, we used homemade macroprobes that, when mounted on the AFM head, allow the implementation of microplate rheometric measurements with pN sensitivity. Stress‐relaxation measurements provide one or more relaxation time constants, depending on how many different mechanical contributions are involved. Here, we identified two main players, the ooplasm, and the ZP, whose Young's modulus we measured separately by AFM indentation with and without ZP, finding the former more viscous and softer and the latter less viscous and stiffer.In this way, we were able to assign the faster time constant to the ZP and the slower one to the ooplasm. The former, which is a measure of the ratio between the ZP viscosity and elasticity, decreases in time during the postovulatory aging, reproducing the behavior previously highlighted with indentation measurements.2, a known parthenogenetic activator. It has already been shown that this salt induces a structural change in the oocyte ZP as well as a cortical granule reaction over time.2. We observed a sudden increase in the CG‐related fluorescence after the addition of the activator, reaching the maximum intensity over 30/40 min from that point. The dynamics of this induced exocytosis are the same in all the tested cells. Interestingly, also the ZP stiffness increases after the addition of the activator. Nevertheless, the high variability in the E2 values does not support a clear triggering effect caused by the cortical reaction on the ZP stiffness increase. One of the reasons for the observed variability could be found in the local nature the GC release induced by SrCl2 that is higher in some specific location of the oolemma; as a consequence, also the ZP hardening could significantly vary depending on the position and the measurement; the adopted instrumental approach does not allow to select the measurement point where the exocytosis effect is maximum. A more precise evaluation of the fluorescence limited to the indentation area could be implemented to address this problem.The cause of the observed change in the ZP mechanical properties is a spontaneous GC exocytosis as a consequence of oocyte aging, in a mechanism similar to that of the Zona hardening after fertilization. Here, the oocytes were chemically activated with SrCl2+ release within minutes from fertilization together with his role as an important metalloprotein cofactor in the catalytic active site of some enzymes, the variation in ZP fibrils thickness after Zn2+ exposure, and the decreasing amount of sperm binding makes this ion one of the possible candidate for this induced variation of the ZP structure and mechanical properties.Other possibilities are related to a dynamic cross‐linking, triggered by some other factors released from the cell, that act in a way similar to ZP1, the ZP glycoprotein that mediates the binding between the fibrils. The detection of ZnFinally, we wanted to understand how the observed change in the oocytes mechanical parameters affects the yields of embryo development. For this reason, two groups of oocytes were considered: the “freshly thawed” one was mechanically measured 1 h after the thawing, while the “aged” group was measured after 6 h from the thawing. Immediately after the mechanical measurement oocytes were subjected to an IVF procedure and the embryo yields were evaluated. We show here that the yields of 2‐cell embryos were more than halved in the “aged” group compared to the “freshly thawed” one. And the yields related to the blastocyst development are even lower.The decreased yields of embryo development in the “aged” sample correlates with the mechanical data as after 6 h from the thawing we can see a statistically significant increase in the oocyte stiffness and a statistically significant decrease in the dissipated viscous energy. This is an important information because we established a direct correlation with the observed change of the mechanical parameters and the yields of in vitro fertilization. Moreover, the yields of embryo development of the “freshly thawed” oocytes previously measured, are very close to the one obtained in the control group. This result further confirm that this method of oocytes analysis does not affect the oocytes quality and probability to be fertilized.In conclusion, we found out two mechanical parameters (viscosity and elasticity) that can be related to the aging status of the oocyte before any visual feature of degradation can be observed. The measurement of these parameters can be performed with a noninvasive approach which involves the application of forces 6 order of magnitude weaker than those applied in the ICSI procedure.Moreover, the occurrence of a ZP dynamic cross‐linking in the aged oocyte temporally correlates with cortical granule exocytosis, although we did not address in this paper the molecular mechanism behind this effect, which would require further studies and be the subject of a separate publication.Other than the investigation of postovulatory aging, the same methodology can be applied to the development of more efficient protocols for oocyte in vitro maturation (IVM), for the screening of drugs able to induce the ovulation. Moreover, ZP mechanical properties might be predictive of oocyte chromosomal abnormalities. Although the clinical use of AFM is limited by the complexity of the experimental setup, its recent evolution is pointing toward automation and easy‐to‐use approaches, so that their implementation in clinics is probably closer than it may appear. Besides, many alternative devices based on force sensing suitable for the use in clinics have been developed in which the experimental setup are much simplified and easy to handle. Moreover, a carefully designed microfluidic system could allow to solve the problem of the oocyte immobilization and sorting, improving the standardization of the clinical procedures. Different devices based on micropipette aspiration and indentation and systems based on hydrodynamic cell stretching have been developed and used for the measurements and sorting of different cellular systemsFinally, our findings put into evidence that a mechanical essay, based on AFM, represents a very sensitive tool able to detect physiological changes associated with the oocyte status before the occurrence of the visible morphological changes and help to improve the yield of IVF protocols.44.1MII oocytes were obtained from the oviducts of 7–weeks‐old female mice (C57BL/6) superovulated by intraperitoneal injection of 7.5 IU of PMSG  followed 48 h later by injection of 7.5 IU of hCG . All experiments were performed under the project #509LAZ19, which was approved by the Administrative Panel of Laboratory Animal Care at the University of Trieste and by the Italian Health Ministry.Mice were sacrificed by cervical dislocation and oocytes were recovered from ovaries 16 h after the hCG injection into α‐MEM (Sigma) supplemented with bovine serum albumin (BSA) (4%). Cumulus cells were removed by means of a mechanical treatment by pipetting cumulus oocytes complexes with 100 μm inner diameter sized flexipets  in α‐MEM supplemented with 0.03% hyaluronidase (Sigma). Approximately 1 h from the retrieval, oocytes were either immobilized on the surface of petri dishes in α‐MEM supplemented with N‐2‐Hydroxyethylpiperazine‐N′‐2‐ethanesulfonic acid without BSA or frozen according to the protocol described in the supplementary material.4.22 at 37°C. MII oocytes were selected by visual inspection for the presence of the first PB. Only MII oocytes with a round‐shaped ooplasm, a regular ZP and PVS were considered for the analysis. AFM‐indentation measurements were performed after 1 h from the retrieval with a Nanowizard II AFM  equipped with an inverted optical microscope. The indenter was obtained by attaching a silica microbead (4.5 μm diameter) to a silicon triangular tipless cantilever of nominal spring constant k = 0.32 N/m (Nanoworld with Cr/Au back‐side coating) by using UV sensitive glue . Before each measurement, the spring constant of bead‐mounted cantilevers was calibrated by using the thermal noise method, on the surface of glass slides in milli‐Q water. Measurements were performed directly in the petri dishes, on a squared grid of 3 μm × 3 μm at the center of the oocyte. For each point, three force‐distance curves were acquired, for a total of 27 curves for each oocyte. Between one measure and another a recovering time of 5/10 s was used. A maximum force load of 1 nN at a rate of 5 μm/s in z closed‐loop feedback mode was used. The measurement takes no more than 5 min for each cell.After removing the cumulus cells, oocytes were immobilized on the surface of petri dishes in α‐MEM medium, without BSA, with incubation of 1 h in 5% COE1 and E2.Force distance curves were converted into force‐indentation curves with JPK DP software by subtracting the cantilever bending from the measured height to calculate indentation. The resulting curves were fitted by using a modified Hertz model that considers the contribution of layers with different elasticities. By using this model, two contact points were identified and used to calculate 4.3E the Young's modulus. An Igor procedure was used to fit the data and calculate the relaxation time.The spring constant of macrocantilevers was calibrated by the spring‐on‐spring method.4.4CG exocytosis was evaluated in real‐time after the addition of 25 μg/mL FITC‐LCA  in α‐MEM medium without BSA. The fluorophore was not washed during the experiment, as α‐D mannose is continuously released inside the PVS, and a dynamical staining, proportional to the instantaneous α‐D mannose concentration, is required. Therefore, a high concentration solution of unbound dye should be maintained for the whole duration of the experiment. Images were taken with an inverted microscope , a 40X objective , a DVC camera (Thorlabs) and an X‐Cite fluorescence lamp illuminator (Excelitas Technologies) every hour, with an exposure time of 500 ms. After the image acquisition, the oocyte was put again in dark condition inside the incubator. The overall exposure of the fluorophore to the UV light is less than 10 s for the whole experiment: under this condition, we do not expect a significative fluorophore photobleaching.2 addition, images were taken every 5 s for the whole duration of the experiment (90 min) while keeping the UV illumination continuously on. Under this second condition, we evaluated the possible effect of fluorophore photobleaching. Indeed, in a control experiment, shown in Figure Instead, during the analysis of CG‐related fluorescence after the SrClAnalysis of the fluorescence intensity profile associated with the region of the PVS space was performed by a MATLAB routine. The fluorescence intensity profile was drawn and the area underneath the peak corresponding to the PVS was calculated for five different profiles of the same cell for a given time. The background fluorescence was subtracted and the averaged values were plotted.4.52 was used in which 0.1% methyl‐β‐cyclodextrin (Merck Life Science) was added. This molecule, together with Ca2+ are needed for the sperm hyperactivation that consists in the change in sperm motility from straight trajectories to circular ones.The 7‐ to 8‐weeks‐old male mice were sacrificed and sperm cells were recovered from the cauda epididymis and transferred in a drop of medium (90 μL/mouse) under paraffin oil. The medium was prepared according to the protocol described by the European Mouse Mutant Archive organization.2.After the addition of the gametes, the fertilization drop is stored in the incubator at 37°C, 5% COAfter 3 h oocytes are removed from the droplet and moved to a 100‐μL drop of HTF medium (Cosmo Bio) without reduced glutathione in order to remove the excess of sperm cells and the cell debris. The development of 2‐cell embryos was evaluated 24 h later by visual inspection and the embryos were moved to a 100‐μL drop of KSOM Embryo Medium (Merck Life Science). Forty‐eight hours later the development of the 8‐cell stage embryo was evaluated by visual inspection, and 8 h later, the early blastocyst was observed and, about 15 h later, few of the embryos reached the late blastocyst stage.4.6p value <0.05 was considered to be statistically significant. For the mechanical data related to postovulatory aging of fresh and thawed oocytes ; investigation (lead); methodology (lead); validation ; visualization ; writing – original draft (lead); writing – review and editing . Laura Andolfi: Data curation (supporting); methodology (supporting); project administration ; supervision (supporting); validation ; visualization ; writing – review and editing . Michele Zanetti: Investigation ; methodology ; visualization ; writing – review and editing . Simone Dal Zilio: Data curation ; methodology ; validation ; visualization ; writing – review and editing . Marco Stebel: Methodology (supporting); writing – review and editing . Giuseppe Ricci: Funding acquisition (supporting); resources (supporting); validation ; visualization ; writing – review and editing . Marco Lazzarino: Conceptualization ; funding acquisition (lead); methodology (supporting); project administration (supporting); supervision (lead); validation ; visualization ; writing – review and editing (lead).The authors declare no competing financial interests.5https://publons.com/publon/10.1002/btm2.10294.The peer review history for this article is available at AppendixS1: Supporting InformationClick here for additional data file.


Years of life lost (YLL) is a preferable indicator to assess the mortality impact of COVID‐19. This indicator still has limits, however. Therefore, a new approach and its early‐death weeks (eDW) index has been recently proposed to alter YLL. This study aims to add a new approach, the moving excess‐deficit mortality model, and its method, the weeks of life lost (WLL) index. The new method was then used to measure WLL associated with COVID‐19 in the United States (US).The natural mortality law and the random pattern of spreading COVID‐19 were employed to support calculating WLL. The natural mortality law implied that under the same living conditions and the weaker would die earlier. The random spreading of COVID‐19 assumed that COVID‐19 causes the weekly number of early deaths in equal proportions from all of those who would have died eventually distributed through the pandemic.From Week 02 of 2020 to Week 44 of 2021, we found that the US population has lost 56,270,300 weeks to COVID‐19; the average WLL per COVID‐19‐related death is 74 or 1.4 in the unit of years.The results do not depend on the high heterogeneity of deaths  and on whether COVID‐19 is the main cause of death. The moving excess‐deficit mortality model and WLL index can be applied promptly at any time and anywhere once excess deaths occurred during the pandemic. The index also provides critical insights into COVID‐19, which can support making public health policies and decisions. A new approach, the moving excess‐deficit mortality model, and its method, the weeks of life lost to measure the mortality burden of COVID‐19 in the United States. To do so, we first develop a new model, named the moving excess‐deficit mortality model and distinguishes its analysis of mortality of the COVID‐19 pandemic from others by focusing on its ongoing manifestation and two crucial terms: early deaths (was first used by Cuong)deficit deaths, especially elaborating the relationship between these terms and excess deaths. While the early deaths mean people who died earlier due to COVID‐19,excess‐deficit mortality pattern to support measuring and assessing the mortality associated with COVID‐19, especially valuing the average number of the WLL of early deaths. Finally, this new method is used to estimate the COVID‐19 mortality burden in the United States.This study aims to add a new method to the calculating of the eDW index now called the 22.1natural‐mortality law that was also first mentioned by Cuong meaning that under the same living conditions, the more vulnerable people would die earlier once infected with COVID‐19.We first exploit the statistical analyses on the COVID‐19 associated deaths which are majorly from the most vulnerable people (see Supporting Information for more details) to recall the moving inflationary period to a latter one called the moving deflationary period regardless of whether COVID‐19 causes a single wave or multiple waves. We also argue that due to COVID‐19, the actual weekly number of deaths is fewer than the predicted number in the moving deflationary period, so, this deficiency can be referred to as deficit deaths implying those deaths died earlier than expected (see Supporting Information for more details).Logically, the COVID‐19 pandemic would endure from the k may be defined as the ending week of a certain wave while it is still in the moving inflationary period of other waves, and week k, in this case, can be referred to as a moving observed week. Naturally, the longer the moving inflationary period, the longer the moving deflationary period and the higher value of number k, regardless of whether there are several weeks or short periods without excess deaths. Logically, the moving inflationary period will also end at 1 week called kth (see Supporting Information for more information) that can be defined for several situations, such as the ending week of the pandemic or of a specific wave in a certain country or of the world. Figure In a global context, the current pandemic is not actually ending its moving inflationary period at a specific week due to the spread of the new variants of COVID‐19. Thus, a specific week that is denoted by k, Ekvirus, gradually declines to zero, such as at the end of this week for simplicity and indexed by K before shifting into the moving deflationary period. In reality, this K‐point varies from country to country and drops at any week during the pandemic; it depends not only on the levels of nonpharmaceutical interventions (NPI) but also on the timing of the imposition . For example, countries with a higher ratio usually enter the deflationary period earlier, such as Italy with 99.2%.The graphic above shows several main points that require further explanations. First for this specific case, the number of excess deaths in Week k + 1 to n is fewer than that from Week 1 to k in many situations, such as when NPIs are strictly followed, herd immunity is widespread, and the vaccine is available. Conversely, the moving deflationary period will be longer than the moving inflationary period. And third, although the model can be applied to any country in the world, its shapes and features are not the same. For instance, the older population of Italy will be different from the younger population of the United States. Further, the model can also be applied in multiple simultaneous outbreaks, such as seasonal flu.Second, while both the numbers of excess deaths and deficit deaths are equal, their respective time periods during which the deaths occur may not be the same. In particular, the number of weeks from Week Understanding the COVID‐19 early deaths requires the incorporation of the natural mortality law into a given random spread of COVID‐19. Logically, this incorporation leads to an assumption that COVID‐19 causes the weekly number of early deaths in equal proportions among all those who may be weekly predetermined deaths through the pandemic periods. From which we use the moving inflationary‐deflationary periods of the pandemic to constitute a distribution of early deaths, the excess‐deficit mortality pattern. The additional details on this pattern are available in Supporting Information. Subsequently, we used the methodology above combined with the data related to COVID‐19 in the United States to calculate the average WLL of early deaths.2.2To calculate WLL we first have to estimate the total number of early deaths from the data on excess deaths associated with COVID‐19. These data were retrieved from the Center for Disease Control and Prevention (CDC) of the United States from Week 13 of 2020 to Week 44 of 2021.K‐point was defined at the end of Week 44 of 2021 and takes the value of 85 for the entire ongoing pandemic, which means that Week 85th is also the observed week (see Supporting Information for more information).Although data on both excess deaths and COVID‐19 deaths were retrieved from the same source and as of Week 4, 2022, there are some minor differences between the two. First, while the first death involving COVID‐19 was confirmed in Week 2 of 2020, the excess deaths were only estimated since Week 13 in the same year. Second, the total number of deaths by all causes, from which the estimated weekly number of excess deaths (Supplementary Data_S1) is higher than that of the other source (Supplementary Data_S2), with 5,615,826 compared to 5,608,279 deaths, respectively. The difference of 7547 deaths accounts for 0.1% of the total deaths. Third, the data were collected through Week 4 of 2022, but the calculation was only used till Week 44 of 2021  because the data for the last 11 weeks are incomplete at the time this study was conducted.3From Week 2 of 2020 to Week 44 of 2021 in the United States, COVID‐19 has caused 56,270,300 WLL of 882,886 early deaths. The former reflects the overall mortality burden of the COVID‐19 pandemic in units of weeks or the cumulative WLL of the population while the latter is a proper result than the number of death counts and excess deaths. And each of the COVID‐19 early death has lost an average of 74 WLL. These results together with other conventional metrics were tabulated in Table Esum → 85virus and 87.8% of the cumulative number of early deaths denoted by eDsum → 85virus. This probably has two situations where there were no adequate records of all deaths associated with COVID‐19 or the weekly number of excess deaths was overestimated. Otherwise, the difference between eDsum → 85virus and the number of COVID‐19 deaths is quite significant with 107,766 cases. This, in turn, implies a critical problem in tracking the COVID‐19 deaths of those who did not show the symptoms of COVID‐19 disease.Table eDWsum → 85virus is another goal of this study, which reflects the mortality effects of COVID‐19. Accordingly, the table above shows that the value of this index is 56,270,300 weeks, which provides more insights than the values of Esum → 85virus and YLL. First, this value is expressed in units of weeks and reflects the loss of life expectancy in weeks rather than in years of all COVID‐19 deaths. Second, the value does not depend on the heterogeneity of COVID‐19 deaths  and whether COVID‐19 was the main cause of death to estimate the total WLL of a population. Thus, the index can be used efficiently to assess and compare the damages caused by pandemics among states or countries.Measuring the cumulative total number of WLL through Week 85 denoted by W¯→85earlydeath with the value of 74 weeks. This value implies that each COVID‐19 death in the United States has lost 74 weeks of life expectancy or 1.4 years, which is fewer than 11 times compared to the average YLL in 81 countries (including the United States) of 16 years.Finally, the key metric for directly comparing to YLL in Table 4This study follows the early‐mortality approach that was proposed by Cuong to further seek an accurate and insightful measurement of life lost to the pandemic as well as the method of calculating WLL, then used it to measure the mortality impact of COVID‐19 in the United States. We found that from Week 2 of 2020 to Week 44 of 2021, COVID‐19 has caused at least 882,886 early deaths with a total of 56,270,300 WLL. The former number is significantly higher than the number of death counts and at least nearly equal to the number of excess deaths. From a statistical analysis aspect servicing health policies, the number of early deaths is crucial in that it exactly reflects how many lives have been lost associated with COVID‐19 regardless of whether COVID‐19 was the main cause of death or not. This indicator also provides a comprehensive assessment of the overall mortality effects of COVID‐19 in units of weeks to avoid the different discounting life expectancies among deaths.The main goal of the study is to estimate the average number of WLL of early deaths by the new method. This indicator can provide more accurate and rapid metrics for accessing and disseminating information during any week of the COVID‐19 pandemic anywhere. In the United States, we calculated her average COVID‐19‐related WLL is 74 or 1.4 in the unit of years. This value is a particularly low level if compared to the value of 16 years calculated by the YLL method,value of a statistical lifeFrom the pathology perspective, the average WLL critically conveys a maximum shortfall in life expectancy due to COVID‐19 disease; hence, it can compare to other causes of premature mortality . This indicator goes beyond the epidemiological questions and implies a more important social issue in ethnographic and moral aspects. Employing the WLL index provides more comparable and insightful results that could better guide public health decisions. Further, both the total WLL and average WLL can assist the assessment of the There is one potential source that may cause up‐or‐down bias to our results, the accuracy of the predicted number of total deaths in the case of no COVID‐19. This number may be an undercount due to not taking into account the different mortality effects of seasonal influenza over years,The author declares no conflict of interest.Supporting information.Click here for additional data file.


Various factors contribute to the pathogenesis of a disease. These include genetic factors, family history, and some idiopathic causes. Genetic makeup has an important role in the progression of disease. This is due to mutations in genetic material, that is, deoxyribonucleic acid (DNA).This is a cross‐sectional study that involved 5000 participants distributed across 250 countries. All the participants were randomly selected and asked to fill out the online survey. All the participants were fully informed about the study's purpose before providing their consent.The participants were distributed among 250 countries. Their age mean (standard deviation) is 46.7 (12.4). We discovered a significant difference between those who have genetic or congenital diseases and those who have a family history of the disease. Also, there is a statistically significant difference between the recurrence of the disease and the duration of the visits of close relatives who have the same disease.The study suggests that there might be some ways, through gene waves or the environment, in which a gene changes the expression of other genes of similar sequence in different individuals when the required period of contact is provided. In the future, this theory might explain the idiopathic nature of some diseases. These include genetic factors, family history, and some idiopathic causes. Genetic makeup has an important role in the progression of disease. This is due to mutations in genetic material, that is, deoxyribonucleic acid (DNA). Differences in DNA can make an individual more susceptible to some diseases for example, a certain type of cancer.22.1We have undertaken a cross‐sectional, international, multicenter study, using an online self‐administered questionnaire, on the cohort composed of participants who were randomly chosen from 250 countries.2.2The survey was conducted in each country had a center, and there was an administrator for each country to select the cases.2.3An online survey was conducted randomly among the general population and included only those who completed the survey properly. There was a consent form for participants at the beginning of each survey and an explanation of the study. Ethical approval was obtained from the ethical committee of the University of Baghdad, College of Medicine.2.4The questionnaire consisted of 30 questions divided into two sections. The answers were divided into single answers and multiple‐choice answers for both quantitative questions and qualitative questions.2.5The study involved 5000 participants distributed in 250 countries.2.6χ2 and Fisher's tests were used.We used SPSS version 24 in finding a relationship between our variables for significance and correlation. In the analysis, the 3The participants were 5000 distributed among 250 countries. Their age mean (standard deviation) is 46.7 12.4). Table 2.4. TablThe questionnaire involved 16 questions about the role of genes in the disease's transmission and the cofounders; Table In Figure We found a significant difference between those who have genetic diseases or congenital diseases and the incidence of the disease in their families Table . Also, t4p value between 0.01 and 0.00), which means that there are higher chances that such genes are present in their family. These genes, controlling the internal environment as well as the external environment through their expression, might have created such an environment that when an individual with disease has a long period of contact with their family members, their genetic expression is modified and disease recurs in them, considering only the genes having similar sequences.Our study seeks to discover the relationship between the period of stay with the family having or not having genetic disease and the recurrence of disease after appropriate management in an international population sample to determine whether genes communicate with each other after birth between individuals. This study only emphasizes the degree of association between the length of stay with families and disease recurrence and has nothing to do with a causal relationship. We recruited a large sample of individuals of varying ages with a history of genetic disease in them or family members living away from the family and found that whether visiting and staying close to your family members has an impact on disease behavior and how long disease recurs in subjects. There is a significant association between the individual having a congenital or genetic disease and the family history of disease. First‐ and second‐degree relatives can be found in a family tree. Structural and functional abnormalities that happen during intrauterine life result in congenital disease. It can appear during the perinatal period or later in life. Genetic diseases are under the umbrella of congenital diseases.p value of 0.01). Studies suggest that persons with improved living status and social support have been shown to have a better outcome, decreased mortality, and an increased disease‐free interval.Duration of time is also very important for both the period of contact and the time after a disease recurs. Our study also has strong evidence for this argument. Individual disease incidence increases with the length of stay with family. This is particularly important when an individual has a period of contact stretching over weeks, months, or years. When the period of contact is encompassed over several days, it doesn't have a significant effect. It means that there is no significant relationship between disease recurrence and period of contact when stay is limited to a few days. It may be due to the fact that genes require a considerable amount of time for their expression or that their expression is influenced by environmental factors. A specific time is required for genetic expression. It is different for different genes. So, genes require a certain amount of time to influence their effect on other genes, and these genes require a certain amount of time to alter their expression.5We simply wanted to find a relationship between genes with similar sequences and each other in different individuals by considering family history of inherited diseases in this study. We have listed some evidence that supports our hypothesis. We think that there may be some types of communication signals—we called them “gene waves”—through which genes communicate with each other. We have considered the distance of separation, the period of contact, and the duration after which recurrence occurs. The study suggests that there might be some ways, through gene waves or the environment, in which a gene changes the expression of other genes of similar sequence in different individuals when the required period of contact is provided. In the future, this theory might explain the idiopathic nature of some diseases.Hashim Talib Hashim: Conceptualization; data curation; formal analysis; methodology; project administration; resources; supervision; validation; visualization; writing – review and editing. Ali Talib Hashim: Conceptualization; methodology; writing – original draft. Abubakar Nazir: Formal analysis; software; writing – original draft. Usama Afzaal: Data curation; software; writing – original draft. Awais Nazir: Data curation; software; writing – original draft. Ahmed Dheyaa Al‐Obaidi: Formal analysis; methodology; validation; writing – review and editing.The authors declare no conflict of interest.Ethical approval was obtained from the ethical committee in the University of Baghdad, College of Medicine. Patients' consents were given before recruitment.The lead author Hashim Talib Hashim affirms that this manuscript is an honest, accurate, and transparent account of the study being reported; that no important aspects of the study have been omitted; and that any discrepancies from the study as planned  have been explained.


Mathur et al.  point ouP < 0.05 and hypothesis-consistent direction correlate at 0.55 (0.66 with not achieving significance and rejecting the hypothesis). This suggests that statistical significance testing was a key aspect in the teams’ own conclusion formation processes. The rate of significant results per team explained 25% of the variation in subjective conclusions, the largest predictive variable by far. It is problematic that conclusions like those found in each team often become the headline findings of individual publications. Headlines often promoted reliant only on p values and without justification or recourse to the size and meaning of effects  held that the hypothesis was supported—despite the consistently small effect sizes. Support of this hypothesis by the team and the number of their models with a  effects , 4. And