The internal noise present in a linear system can be quantified by the equivalent noise method. By measuring the effect that applying external noise to the system’s input has on its output one can estimate the variance of this internal noise. By applying this simple “linear amplifier” model to the human visual system, one can entirely explain an observer’s detection performance by a combination of the internal noise variance and their efficiency relative to an ideal observer. Studies using this method rely on two crucial factors: firstly that the external noise in their stimuli behaves like the visual system’s internal noise in the dimension of interest, and secondly that the assumptions underlying their model are correct (e.g. linearity). Here we explore the effects of these two factors while applying the equivalent noise method to investigate the contrast sensitivity function (CSF). We compare the results at 0.5 and 6 c/deg from the equivalent noise method against those we would expect based on pedestal masking data collected from the same observers. We find that the loss of sensitivity with increasing spatial frequency results from changes in the saturation constant of the gain control nonlinearity, and that this only masquerades as a change in internal noise under the equivalent noise method. Part of the effect we find can be attributed to the optical transfer function of the eye. The remainder can be explained by either changes in effective input gain, divisive suppression, or a combination of the two. Given these effects the efficiency of our observers approaches the ideal level. We show the importance of considering these factors in equivalent noise studies. Under this analysis many psychophysical paradigms in which “thresholds” are measured can instead be thought of in terms of what is happening to the underlying noisy response distributions in, for example, the target and null intervals of a forced-choice task. In fact under SDT there is no special “threshold” stimulus magnitude, and references made to thresholds are a matter of convenience [The neural signals in the human visual system are perturbed by internal noise from a variety of sources . Accordivenience , 5. The venience –12.c is the target contrast and each of the random variables μ and variance σ2. The observer makes their decision by taking the difference between the responses from the two intervalsd′) isd′ = 1 gives the threshold contrast at Pcorrect = 76.02%σext. Where the σext value is given in either the same or at least equivalent units to c, this is the behaviour of an ideal observer with internal noise. Empirically however one very often finds that thresholds in dominant external noise are higher than is predicted by this model. This cannot be due to the internal noise, as it is already established that its effects are negligible when the external noise is dominant. These effects are instead accounted for using a “calculation efficiency” parameter, η, so thatσ values are given in either the same or at least equivalent units to c, this is the efficiency relative to an ideal observer with internal noise . Otherwise the value of η only has a relative meaning . One factor that can affect efficiency is the nature of the integration stage , and then to infer both the internal noise (η). If human vision behaves like the LAM  then differences in performance can be wholly explained by these two parameters. This has been used to investigate contrast detection in normal observers [bservers , 14, in bservers –17, and bservers –21. Howep and q, and the saturation constant z, control the shape of the function. Considering a pedestal masking experiment on a trial-by-trial basis, the observer receives a response from the target intervalt and m are the target and mask contrasts respectively. Therefore the d′ for an observer discriminating between mask (m) and target plus mask (t + m) intervals isσint on the denominator represents the noise across both intervals of the 2IFC task, as is also the case in Studies that use the LAM to fit contrast threshold data and then report sduction –26. The sduction . This mosduction  to introfacilitate detection) can be explained by a model of this type [σint to refer to the internal noise in our nonlinear model  these are abstractions of the level of activity  that is being input into the decision stage. When we talk about d′ we are referring the signal-to-noise ratio at the decision stage . Note that the integration stage plays no direct role in the modelling of our experiments  that are used to justify the PTM are instead due to the use of broadband noise , 44. If In this study we compare pedestal and contrast-jitter noise masking functions using the same stimuli within a set of observers in order to demonstrate that noise masking results that have previously been attributed to internal noise effects may be entirely due to changes in gain control. We chose to make the comparison between two spatial frequencies (0.5 and 6 c/deg) as the loss of sensitivity with increasing spatial frequency is well-established by the many experiments that have measured the contrast sensitivity function (CSF). Although some of this effect can be attributed to the eye’s optics, it is clear that neural factors also play a role . The LAMFive psychophysically-experienced observers took part, including two authors (AB and DB). All observers were tested at McGill University except DB, who was tested at the University of York. Observers either had normal vision, or wore their prescribed optical correction appropriate to the viewing distance. The experiment was carried out with informed written consent in accordance with tenets of the Declaration of Helsinki, and approved by the Centre for Applied Ethics at the McGill University Health Centre.2. These experiments were conducted with natural pupils, however measurements of pupil diameter under the testing conditions were made for each observer. These were within the range of 2.5-3.5 mm. At York the monitor was an Iiyama VisionMaster Pro 510, and the mean luminance was 37 cd/m2. DB had a pupil diameter of approximately 5.5-6 mm.All experiments were conducted using Matlab 2010a. A Cambridge Research Systems Visage was used to provide 14 bits of contrast depth on a gamma-corrected CRT monitor. At McGill the stimuli were presented on a Dell Trinitron with a mean luminance of 83 cd/mL with mean luminance LmeancdB = 20 × log10(cdelta). For convenience we also express some of our model parameters in this same unit. Two spatial frequencies were used in both experiments: 0.5 c/deg and 6 c/deg. Our viewing distance was set to give 48 pixels per degree of visual angle, so the numbers of pixels per cycle were 96 and 8 respectively. The viewing distance at both testing locations was 80 cm.We used cosine-phase horizontal Cartesian-separable log-Gabor , 54 patcPalamedes [d′ = 1).All experiments were conducted using a two-interval forced-choice procedure. The stimulus duration was 100 ms, with both inter-stimulus and inter-trial (post-response) delays of 400 ms. Target contrast was controlled by a pair of staircases. One was three-down one-up and the other two-down one-up, so that the combined data from the two would concentrate sampling at the 70.71% and 79.37% points on the psychometric function (helping us obtain good estimates of psychometric slope). Although the staircases may not actually converge to these points  this is alamedes  and thenThe other properties of the staircases were a 6 dB step size before the first reversal followed by a 3 dB step size thereafter, and a stopping point of 70 trials or 12 reversals (whichever was reached first). In the noise masking experiment each condition was repeated four times. In the pedestal masking experiment there were three repetitions. In both cases the data were collapsed across repetition and psychometric function fits performed on the combined data. Observers were only tested on one spatial frequency in each block. To reduce spatial uncertainty and provide a continuous fixation cue the stimuli were surrounded by a ring (radius of 3.75 carrier cycles), as seen in For the pedestal masking experiments a version of the target with an identical pedestal contrast was added to both intervals in each trial. This pedestal contrast was kept constant in each testing block. The mask levels were chosen based on the observer’s detection thresholds, as the “dip” in these functions typically occurs when the pedestal contrast is equal to the unmasked threshold. Our general method was to test at -12, -6, -3, 0, +3, +6, +12, and +18 dB relative to the threshold measured for each spatial frequency, and also fixed points at the minimum of 0% contrast (no mask) and maximum of 44.7% (33 dB). In practise this resulted in some observers for whom mask levels would either overlap or fall out of range, so for these they were altered slightly.For the noise masking experiments we used the “zero-dimensional” contrast-jitter noise , where ax-axis is the response to the null interval and the y-axis the response to the target interval. In a pedestal masking experiment the expected x and y coordinates on each trial are specified by the target and pedestal contrasts. In a noise masking experiment the contrasts in each interval are chosen randomly . The actual contrasts presented in each interval are not usually used in the analysis of a noise masking experiment (instead the mean and standard deviation are used), however if one were to save this information it would be possible to rearrange data from sufficiently extensive testing in a way that it could be analysed like the data from a pedestal masking experiment. The reverse is also true: by including a wide range of target and pedestal contrasts it would be possible to collect a pedestal masking data set whose trials could be rearranged into those that would be collected in a noise masking experiment. Therefore, any explanation of the results from one experiment should be consistent with the results from the other.It is important to recognise that the two paradigms we use are closely related. In both pedestal and noise masking one can consider the observer’s task to consist of discriminations made in a two-dimensional space where the Palamedes to obtain a population of 1,000 bootstrap samples from which we could calculate a median and 95% confidence interval. We use the median as the central tendency when we plot our data because it is the measure most consistent with the use of the 95% confidence interval from bootstrapping to represent the variability associated with that value. In reality however the use of the median from bootstrapping rather than the single threshold obtained by fitting to the raw data made very little difference. Combining data across all conditions and observers and then subtracting the raw thresholds for each psychometric function from the medians obtained by bootstrapping gives us a distribution of residuals with a mean of 0.01 dB, a standard deviation of 0.05 dB, and a maximum difference of 0.25 dB.When fitting our psychometric functions, we used the parametric bootstrapping routines in Palamedes. For our figures, we simply present the medians and 95% confidence intervals of these distributions. When calculating standard error (the standard deviation of the population of bootstrap samples) for our tables however, the effects of a few outlier bootstrap samples would occasionally exaggerate the standard errors when compared to the confidence intervals. These outliers occur because the bootstrapping procedure will sometimes generate sample datasets that do not adequately constrain the model fit.We also used bootstrapping to obtain confidence intervals and standard errors for our model-fitting. For the likelihood-based modelling we performed for our pedestal masking experiments we randomly sampled individual trials (with replacement) from our empirical data to obtain 1,000 bootstrap datasets. Parameter bootstrap distributions were obtained by fitting the model to these datasets. For the noise masking experiments we obtained parameter bootstrap distributions by fitting to the threshold populations generated by σint samples in the 6 c/deg condition for observer AR). In the LAM fitting for the noise masking experiment outliers were slightly more common. The most affected case was the 6 c/deg condition for observer AR where we removed nine out of the thousand bootstrapped η samples. In the fits to the simulated data used to generate the nonlinear model (NLM) prediction, it was only in that same condition for the same observer that outliers were found. Three of the thousand bootstrap samples were rejected for both the η parameters.To prevent outliers inflating the standard error values, we employed an outlier-removal method based on that proposed by Tukey , 60. We d′ = 1 [Pedestal masking functions for each of the five observers are shown in d′ = 1 , 61.t(4) = 2.14, p = 0.10), or the mean handle slope (t(4) = 0.37, p = 0.73). We shall return to these data and explain the fitted curves when we discuss the modelling.Comparing the results between the two spatial frequencies, the dipper functions translate upwards (higher thresholds) and to the right  as the spatial frequency is increased. For all observers except AR this results in equal thresholds for the two spatial frequencies at the highest mask levels. This effect can also be seen in data from previous studies . The aveβ) are plotted in t(9) = 1.62, p = 0.14), however we do not rely on these slopes to support our conclusions. We present them here merely for illustrative purposes.The psychometric function slopes  diagonally upward and to the right. An increase in the σint on the other hand translates the entire curve directly upward.We fitted our data with the nonlinear transducer model described by p and q at 2.4 and 2 respectively. These values provide good fits to the data here, as they have also done in other studies [D) of the fits relative to the saturated model [z than σint between the two spatial frequencies. Over the 12-fold increase in spatial frequency there was an 84-fold increase in z, but only a 1.4-fold increase in σint. As the change in σint was small we considered a model where it was fixed across spatial frequency, however the AICc (corrected Akaike’s Information Criterion) scores of this model were higher and so the inclusion of individual parameters was preferred [z vastly exceed the confidence intervals provided by the bootstrapping. Although the changes in σint are much smaller the confidence intervals only overlap for AB, indicating that the small differences present for the other observers are still significant.Based on previous results  we fixed studies , 66, 67.ed model . Immediareferred , 70. We In our noise masking experiments we obtain the typical result where thresholds increase with the standard deviation of the masking noise . The unmβ). Looking at the data, the mean slope decreased from 2.0 for the unmasked conditions to 1.5 for the conditions with masking noise. This is consistent with Birdsall linearisation [β = 1.3. A two-way within-subjects ANOVA  found no significant effects or interactions however, meaning that this decrease in slopes was not statistically significant.We performed a brief analysis of the psychometric slopes . In order to approximate this value and so generate noise masking predictions, we used c (-18 dB to 40 dB in 0.05 dB steps) and 6 mask levels (-21 dB to 39 dB in 12 dB steps). For each mask level we found the value of c where the difference between the mean and standard deviation of the population of Δr samples was at its minimum. This gave us six simulated data points that in all cases followed the shape expected by the LAM .The dashed curves in z parameters in the nonlinear contrast response function . This is the reason why the fitted LAM σint by decoration with a hat and illustrates one of the key points of this paper: changes in the fitted LAM do not in this case) correspond to changes in the actual σint in a nonlinear system.It is expected that the NLM curves will have a very similar shape to those from the LAM . We areη is close to 0 dB (100%) in all cases apart from the 6 c/deg condition for AR. The efficiency values in The NLM prediction curves in og10(η),1here, whσint parameter used in the simulation process is fixed across the two spatial frequencies . This allows us to demonstrate that the large differences in the fitted z. This comparison can be made in σint are shown by square symbols, and the fixed σint by diamonds. There is little difference between them.We conducted a further analysis based on bootstrapping in order to get an idea of the size of our effects relative to the variability in the data. The thousand sets of thresholds generated during the bootstrapping process were each fitted with the LAM model, allowing us to plot the median value of each parameter here with 95% confidence intervals. We were also able to generate a bootstrapped version of the nonlinear model prediction using the parameters summarised in σint or the saturation constant z. In general however we can account for most of the change in z with a fixed σint, indicating that in this case the result seen in the “internal noise” parameter of the noise masking data is not due to noise.Comparing the nonlinear simulations in z behaves like a change in internal noise. Other studies [z was more likely responsible for individual differences in contrast sensitivity than σint. The work we present here however is the first time that the relationship between the two paradigms has been directly explored, thanks to the use of the “zero-dimensional” contrast-jitter noise paradigm. This allows us to present the same stimuli for our noise and pedestal masking experiments. We show that one can use the contrast response function obtained from a pedestal masking experiment to mostly predict an observer’s behaviour in a noise masking experiment, and that when doing so the human decision stage approaches ideal performance. Demonstrating this result with the more conventional white- or pink-noise masking method would also require a model of how the off-target stimulation from the broadband noise mask serves to suppress the detection of the target [Our results demonstrate that effects which appear to be changes in internal noise when measured by the noise masking paradigm may instead be due to changes in gain control properties. Specifically, an increased saturation constant  studies  have pre studies  showed te target . To our g could be incorporatedz parameter. To show this we set the z parameter in g parameter to fit the output of z parameter. We also set the p and q parameters to 2.4 and 2, as was the case in our experiments. A log-log plot of the best-fitting g values against the values of z used in the generating model gives a straight line . The parameters from a straight line fit then allow us to say that for an x dB change in z, we expect a 0.41x dB translation both upward and to the right in the dipper functions. This can be confirmed by comparing the differences in the z values in Although the primary purpose of this paper was as a proof-of-concept, with the manipulation of spatial frequency chosen as an example, our results still provide a novel insight into why sensitivity declines with spatial frequency. We must first estimate how much of the sensitivity loss can be attributed to optical factors. The lowpass Optical Transfer Function (OTF) of the eye attenuates higher spatial frequencies more than lower spatial frequencies. Attenuation by the eye’s optics will reduce the input gain of the system. In z. For DB the pupil size was 5.5 mm. This would give an attenuation difference of 7.7 dB, equivalent to a 18.8 dB change in z. By comparing these values against the differences in z reported in z). One must take these effects into account, particularly in situations where comparisons are made between groups of subjects in whom differences in OTF may be expected .z should have a neural basis. One possible explanation is that performance at different spatial frequencies is limited by the number of cone photoreceptors contributing to the receptive field [toward scale invariance, but the magnitude predicted for that effect from previous data is far too small to actually reach it [z parameter in our contrast response function can be considered to represent.Once the optical effects are accounted for the remaining difference in ve field , 76. An ve field  which isve field , 77. Thereach it . It is pThe results we report here are the effects seen over only a relatively small distance in the spatial and temporal frequency space. It is possible that comparisons between more remote spatial frequencies or between different temporal frequencies would demonstrate greater changes in internal noise. Another possibility is that there is a single limiting source of noise for all contrast detection tasks, in which case all differences in contrast sensitivity would be attributed to differences in gain.Our key finding is that one cannot report changes in the fitted internal noise parameter of a LAM function as actual changes in internal noise without first establishing that the system being investigated is linear. We also show that the noise masking paradigm itself confounds changes in internal noise with changes in the nonlinearity, meaning that an alternative model that did feature those effects could not be constrained by noise masking data alone. Examples of these nonlinearity effects would be changes in sampling of the input, the gain, or the subsequent divisive inhibition within a contrast gain control process. Where previous noise masking experiments have found effects attributed to internal noise these may in fact be partially or wholly due to changes in these nonlinear aspects of the system being investigated. While it is true that some of these studies were carried out with the knowledge that the effects they are attributing to “equivalent internal noise” differences may have multiple possible explanations  these caveats are often left unexpressed. Where changes in the internal noise in a system are of interest one can use pedestal masking experiments to distinguish between those effects and those due to differences in the nonlinear response. The inadequacy of using the noise masking method on its own to constrain our interpretation of the actual processes occurring in the brain is only supported by Dao, Lu & Dosher , who in tthresh) corresponding to a particular d′ (e.g. d′ ≈ 1.273 if tthresh is the α parameter of a fitted Weibull function) is found for multiple mask levels (the vector m). An iterative search procedure is then used to find the values of the CRF parameters  that minimise the difference between the model’s predicted set of tthresh values and those found in the data. This method has several disadvantages: i) the initial psychometric function fitting stage that finds the empirical tthresh values requires sufficient data to perform a stable fit at each mask level in m, ii) because only the threshold parameter of the psychometric function is used, the information from the slope of the psychometric function is discarded, and iii) the nested search that is used to find the predicted tthresh for each set of parameters slows down the fitting procedure. All these disadvantages can be avoided using a maximum-likelihood fitting procedure [n and correct responses c) for each target level (t) and mask level (m). Using a maximum-likelihood method to choose the best-fitting parameters also allows the data to be weighted by the number of observations made for each condition. In this method, d′ predicted by the current parameter set for the tested m and t. These d′ values are then converted using the normal integral (Φ) to their corresponding percent-correct values for each condition (i)d′ by σint represents the combined noise from both intervals). The log-likelihood of that parameter set is then calculated asP(A ∩ B) = P(A)P(B)Pi(c) = P, we can simplify this  and rewrite The typical method  used to rocedure , 81, 82.fminsearch function in Matlab to minimise the negative log-likelihood , relative to that of an ideal observer. This is shown in m = ∞)y = 0) when the exponent is 1.The greatest nonlinearity is a max operator, where only the response of the mechanism which is most activated by the stimulus in each interval contributes to the decision as to which interval contained the target. We used the stochastic Monte Carlo method to generate efficiency predictions for a system that behaves in this way (with This raises the question of why our results do not show overall lower efficiencies, considering that we find nonlinear signal transduction in our pedestal masking experiment. Our explanation is that we used a small target which was approximately the size of a V1 receptive field. In previous summation experiments , 87 it h


Discussions about limiting anthropogenic emissions of COThe numerical experiments show that under a hypothetical scenario of globally sustainable forestry the world’s forests could provide a large carbon sink, about one gigatonne per year, due to enhancement of carbon stock in tree biomass. In addition, a large amount of wood, 11.5 GT of carbon per year, could be extracted for reducing COThe results of this study indicate that carbon harvest from forests and carbon storage in living forests have a significant potential for CCS on a global scale. According to the intergovernmental panel on climate change (IPCC), a reduction of the anthropogenic emissions of COmentclass2pt{minimestments . For CCSestments . The coschnology .The scale of the problem should not be underestimated: to reach the less than two degree goal of IPCC, the annual COor above , or to ior above .The annual sink of the world’s forests has been estimated to be about 2.4 GtC . Taking Storing carbon as standing forests or from harvested wood has long been recognized as a CCS option: for example, Schroder et al. estimated that 15–36 GtC could be stored in tropical plantations and 50–100 GtC sequestrated on a global scale . A detaiHere, we attempt to address this problem by modeling global potential for carbon storage in biomass based on a plant-harvest forestry program. It is assumed that a fraction of the forest is harvested and replanted every year. As a starting point we assume that forest growth in the boreal, temperate and tropical regions is latitude-dependent. Reasonable assumptions are also made regarding future reforestation and deforestation for different zones. The results are then directly based on non-linear forest growth and the instantaneous status of the world forests.We here demonstrate four applications of our model , as a background, we are now ready to model forest development under four alternative harvest-replanting scenarios. All harvesting strategies assume immediate replanting so that the land remains functioning as forest land. We also assume that tropical deforestation is alleviated from 0.44–0.3 % during the whole simulation period. The first two simulations assume harvesting parameters of 0.3 and 0.45 %, respectively, for all three zones. In the third strategy, we reduce the harvesting parameter to 0 in the tropical zone, and increase it to 0.8 % in the two other zones. The reduced harvesting rate in the tropics is motivated by the special soil feature in tropical areas. Due to relative high temperature all year round, the decomposition of forest residues happens fast, and this results in a rather thin layer of soil. Harvesting and storing wood away under these conditions may cause significant reduction in ground soil, motivating the non-harvest strategy. In the final simulation an extra plantation program is introduced so that every year a specified fraction of new forest area is added into the model. This is to explore the potential under a large-scale policy change of using forests as a CCS method.In simulation 1 with 0.3 % harvest rate the total forest carbon increases from 372 to 447 GtC over 100 years  may not be sustainable Fig. . Here, mIn the final two simulations we extract carbon only from temperate and boreal zones to protect the tropical forest. After the simulation period, boreal and temperate zones retain almost the same amount of forest carbon as today, in the regime of annual harvest rate of 0.8 % Fig. . In totaIn simulation 4, storage may be raised further if an additional planting program adds 0.05 % of the original area in boreal and temperate zones every year while in tropical zone the deforestation rate is reduced from 0.3 to 0.25 %. The forest area then increases by 80 million ha. Under these assumptions the total harvested wood remains the same while the carbon content of the standing stocks increases up to 526 GtC, or 1.5 GtC per year. The total amount of sequestration is about 2.8 GtC annually.The uncertainty in the estimates above stems partly from the model itself and partly from external factors. The model error bars are mainly determined by the deviation of the applied growth curves from the real average growth characteristics of global forests. Comparison with available growth data indicates that this uncertainty is in the order of 20 % or less. Additional caveats come with external factors: future technology improving the growth may occur on one side; deterioration of the soil or lack of nutrients or water supplies hindering growth may occur on the other. Regional catastrophic events such as wildfire, insect attacks, wind throw or volcano eruptions and the like may also happen. However, considering the annual global forest area change rate of  to 2010 , we beliWe have developed a dynamic model for carbon storage in forests and harvested wood as an active CCS strategy. With harvest parameters limited by the need to conserve the forests, applications of the model show that in a 100 year perspective the capacity of harvested wood is 1–1.5 GtC per year, and the total sequestration including storage in living trees is on average more than 2–2.5 Gt carbon per year. This is in fair agreement with the previous estimate of Zeng , but it Our model also shows that the amount of stored carbon depends critically on the strategies for harvesting and planting. As compared to pure forest conservation with no harvest, the advantage of an active harvest strategy is that it may be applied at a constant rate on a timescale of several hundred years, not being constrained by maturing forests that cannot store more. Also, this proposal does not change the albedo since the small percentage areas of harvesting are rapidly becoming green again after the replanting. Our obtained numbers are a factor of five smaller than Zeng’s  estimateA main advantage of implementing the proposed approach is storage at low costs. For industrial CCS, estimated costs are in the order of 100 USD per tonne of COcument}2 . In concIn this section we derive the plant-harvest (PH) model used in the simulations and assess its validity in comparison with tree growth data. The idea in our approach is to develop a characteristic average growth curve of wood at a latitude and to discretize the forest area at each latitude. The PH-model associates forest growth potential worldwide with different temperature and latitude characteristics in three zones: tropical, temperate and boreal. Within each zone the wood volume growth follows this characteristic curve after planting. Every year a certain area is harvested and immediately replanted. Additionally, new areas may be opened up for afforestation.i.The global forest volume in cubic meters is computed as a function of time,The growth functions are non-linear and determined mainly by the incoming radiation, the COequation . Other aequation . For a gT be the age at which planted trees within a large area start to spend all of their energy on maintaining the total mass, so that volume growth after T is effectively zero within the area. During the time interval  the wood volume reaches its maximum size, i.e., A(t) set up by the leaves of all trees within the given fixed region,A and the proportionality factor are time-dependent: A(t) increases with the volume growth of the trees and is taken in the following to be proportional to the total wood volume, Let T for each zone to be 200, 150 and 140 years [According to the World Energy Assessment 2000, the net energy yield (E/ha/year . E\documT taken from Ref. [As a consistency check of the present numbers we compare the computed rom Ref.  are in trom Ref. . The othmentclass2pt{minimThe resulting growth curves of each zone to be applied in the PH model Fig.  may be cSimilar extensive forest data could not be found in the two other regions. However, we may compare the regional growth curve with data for single stands. This is a smaller problem in boreal forests than in the other regions, because boreal forests are often dominated by only a few species. However, local environmental conditions will always have impact on growth. As an example, we compare stand growth data for Norwegian spruce with the boreal growth curve from . Typicalasonably . With thIn summary, the comparison with average wood growth from the regional USA data indicates an uncertainty in the growth model of less than 20 %. The model performs well with individual stands and tree data samples in the boreal and tropical region as well. However, we cannot deduce an absolute model error unless large data sets over a 100 years period from all regions had been available. The fact that the growth curves agree well with the data actually available supports the assumption of an accuracy of the order 20 % which induces a similar uncertainty in the simulation results.With the growth functions at hand, the model propagates in time, year by year according to different assumptions of harvest rate, deforestation rate and expansion rate. In the start each discretized forest area has the same fraction of the total known carbon content of each of the three forest zones. This automatically sets the initial age where each area continues to grow from. The expansion rate of each forest zone decides the number of added area units being created every year. Once created, the new area will start accumulating carbon according to our growth function from zero time. Deforestation rates, only valid for tropical zone, determine how many areas will be deleted from the model each year. It is assumed that the carbon stored in these areas will be released immediately since most wood from deforested areas are burned as fuel directly. Harvest rates determine the areas in which the carbon is harvested and stored as wood. After harvesting from one area unit it is assumed that the unit is replanted and continues to grow according to the growth curve from time zero. The total dynamic forest carbon is calculated by summing up the carbon content in all active growing areas of each region each year.


EQ-5D-3L valuation studies continue to employ the MVH protocol or variants of MVH. One issue that has received attention is the selection of the states for direct valuation by respondents. Changes in the valuation subset have been found to change the coefficients of the utility function. The purpose of this study was to test the performance of valuation subsets based on orthogonal experiment designs. The design of the study also allowed a comparison of models based on raw or untransformed VAS values with values transformed at the level of the respondent and at the aggregate level.Two different valuation subsets were developed based on orthogonal arrays. A VAS elicitation was undertaken with two groups of similar respondents and the resulting utility functions based on the valuations of the two different valuation subsets were compared using mean absolute errors between model and observed values, and by correlation with values in and out of sample. The impact of using untransformed versus VAS values transformed at the level of the individual and at aggregate level and the inclusion of a constant term in the utility functions were also investigated.The utility functions obtained from the two valuation subsets were very similar. The models that included a constant and based on raw VAS values from the two valuation studies returned rank correlation coefficients of 0.994 and 0.995 when compared with respective observed values. MAEs of model values with observed values were 2.4% or lower for all models that included a constant term. Several models were developed and evaluated for the combined data . The model that included the N3 term performed best.The finding that two very different valuation subsets can produce strikingly similar utility functions suggests that orthogonal designs should be given some attention in further studies. The impact of rescaling VAS values at the level of the individual versus at aggregate level had minimal impact on the performance of the models when compared to models based on the raw VAS values. Health states defined by EQ-5D and other health status classification systems such as HUI  and SF-6Valuation studies have taken several approaches when selecting a subset of EQ-5D states for direct assessment. The first large EQ-5D valuation study was the Measurement and Valuation of Health (MVH) study in the United Kingdom carried out in 1993 [The MVH protocol used a subset of 43/243 EQ-5D states plus unconscious and immediate death . Valuation of all states in this subset was considered to be too much by way of respondent burden and a block design was used so that each respondent evaluated a total of 15 states. The reduction of respondent burden in this way necessitated an increase in the size of the study sample. Subsequent interest in identifying efficient subsets for EQ-5D valuation studies has yielded a number of alternative designs.The valuation subset used in the MVH study comprised 43 states that were selected to cover a wide range of severity, to maintain consistency with an earlier study that had been conducted in Finland, and to include only states that would be considered by the researchers to be ‘plausible’ to the average respondent [One study  that speIn another study that was based on MVH data, Lamers et al.  used simZarate and Kind  attempteOther EQ-5D valuation studies have used the Macran and Kind subset combined with 8 other states drawn randomly from the rest of the MVH set .A large valuation subset comprising 101 states was used in South Korea [Plausibility: by examining large empirical data sets to find states that are observed in the population for which the value set is being developed.Relevance: the states selected for direct valuation should be those most frequently reported by the population for which the value set is being developed.Coverage over severity range: This is related to the ‘code score’ of an EQ-5D state which is obtained by adding the value of the level of each dimension in the state. Thus state 11111 has a code score of 5 × 1 = 5, and state 12223 would have a code score of 1 + (3 × 2) + 3 = 10. The state that lies furthest from 11111 is 33333 which has a code score of 5 × 3 = 15. This measure gives a general indication of severity, so a valuation set based on this approach would include states covering all possible levels of code score from 5 to 15.Simple severity increments: valuation subsets should comprise states that represent single ‘adjacent steps’ (i.e. states having a difference in code score of 1) in progressing from 11111 to 33333. It is argued that this would allow direct measurement of the lowest level of differentiation that can be obtained from the EQ-5D-3L system.Bagust  attempteThis approach produces a set of 55 states in 5 blocks, so that each respondent values a sub-set of 11 states. The study developed a valuation subset based on MVH data, but there is no application or empirical data regarding the performance of this valuation set. The approach would require the self reported EQ-5D states for thousands of citizens of the country for which a value set is being developed in order to identify the states that meet criteria 1 and 2. Most developed countries now have EQ-5D Value Sets . Moving The purpose of our study was to test the performance of valuation subsets based on orthogonal experiment designs. An orthogonal design is one in which the columns of the independent variables are orthogonal to each other. For the design of an EQ-5D valuation subset, this would mean that in each replicate, each level of every dimension would appear an equal number of times. Historically, orthogonal experiment designs have been used extensively in many fields . For thiThe design of this study also allowed the opportunity to test two further issues involved in modeling EQ-5D valuation data. These are 1- the question of whether to transform the VAS values  at the level of the individual, or at the aggregate level, and 2- the effect of the inclusion of a constant term and additional dummy variables in the regression model.In order to derive weights that would enable EQ-5D states to be used as quality-adjustment scalars in QALY calculations, the data must be rescaled using a monotonic transformation to map the Visual Analogue Scale (VAS) values of states on a 0 to 1 scale, corresponding to the states dead and full health respectively. One approach is to carry this transformation out at the level of the individual respondent using an adjustment:The same form of transformation could be applied to aggregated observed data taking the mean value, for example, as the measure of central tendency. The advantage of this approach is that it effectively dampens the effect of variability within an individual respondent’s data thereby introducing a degree of smoothing and potentially giving rise to a simplified estimation model. On the other hand, this approach could be criticized for losing some of the individual data. To compare these two approaches, regression analyses were run on VAS values transformed at the level of the individual and at aggregate level. The regression analyses were also run on the raw or untransformed VAS values to allow for comparison with the models based on transformed VAS values.A further element of consideration in developing estimation models was the use of a constant term. Many EQ-5D valuation studies include a constant term which is interpreted behaviorally as representing the value decrement accounted for by any departure from full health . HoweverTwo valuation subsets were designed, the first of which (labeled ‘Green Set’) was created using a pre-existing orthogonal array  and is sA sample of 230 university students took part in a valuation exercise conducted at the St. Augustine campus of the University of the West Indies. All of the elicitations were conducted in a 1:1 office setting and respondents received TT$50.00  at the start of the interview. Respondents were randomly assigned to the Green and Blue valuation sets.Respondents were first asked to complete the standard EQ-5D self-classifier that records their own assessment of their health status and was designed as a ‘warm up’ task to build familiarity with the descriptive system in original EQ-5D valuation studies. Upon completion respondents were handed a set of cards containing descriptions of EQ-5D health states. The cards were 4 cm × 12 cm in size with protruding rhomboid edges that made them hexagonal as is shown in Figure Each card had a two letter code printed in the bottom right corner so that the interviewer could record the rank data and VAS valuations. It was explained to the respondents that these codes were generated randomly and had no significance.The cards were ranked from best to worst along the edge of a desk with respondents first being handed two randomly selected cards and instructed to place one card on the desk and decide whether the second was better or worse than the first, placing it above or below accordingly. A third card was then introduced and the respondent was asked to decide whether this should go above, below or in between the other two. This process was repeated until all 23 cards for that respondent were ranked. Tied ranks were permitted.Once this ranking task was complete the interviewer noted the order of health states and then placed a 1-metre version of the VAS alongside the ranked cards. Respondents adjusted the location of each card so that the rhomboid edge pointed to the VAS rating corresponding to their assessment of the value of each state on the 0 – 100 scale. This allowed the respondent to see all of the cards on the VAS at the same time and to adjust their positions and values. Respondents were reminded that ties were permitted and that they had the freedom to change the order of states if they so chose. Interviewers had been instructed that if a respondent raised the issue of an implausible state, they were to respond with a statement explaining that some people do find that some of the states are difficult to imagine and to encourage respondents to carry out the valuation (or ranking task) for the state to the best of their ability. Once the VAS task was finished the interviewer recorded the rating scores for all health states.The use of orthogonal subsets can present special challenges to the respondent when compared to subsets designed in other ways, such as those used in the MVH study. The MVH study sought to avoid implausible states, however these are an inevitable feature when using an orthogonal array that brings every level of every dimension together with every level of every other dimension. Here implausible states cannot be avoided—for example states combining ‘confined to bed’ with ‘no problems’ on the ‘Self Care’ and ‘Usual Activities’ dimensions were observed in both the Green and Blue valuation subsets. Further, the MVH valuation subsets are balanced with 2 or 3 states in progressively more “severe” categories . The orthogonal sets are more concentrated with more than half of the states in the moderate code score range of 8–11, so that preferences among the states are less obvious to respondents using the orthogonal sets  regression produces identical coefficients to fixed and random effects models . Given tIn the absence of having access to a ‘true’ underlying utility function, the models obtained in EQ-5D valuation studies are usually evaluated on such criteria as internal validity, Mean Absolute Error (MAE) versus observed values, R-Squared etc. In addition to these criteria, this study design allowed for a comparison between the utility functions based on valuations by two groups of similar respondents, using two completely different valuation subsets (with no states in common) that were both developed from orthogonal arrays.Model 1: with the dependent variable as 100 – raw VAS value with no constant term in the model.Model 2: with the dependent variable as the raw VAS value with a constant term in the model.Model 3: with the dependent variable as 1 –VAS value rescaled at the level of the individual respondent with no constant term in the model.Model 4: with the dependent variable as the VAS value rescaled at the level of the individual respondent with a constant term in the model.Model 5: with the dependent variable as 1 –VAS value rescaled at aggregate level using mean values with no constant term in the model.Model 6: with the dependent variable as the VAS value rescaled at aggregate level using mean values with a constant term in the model.Statistical analysis was conducted in two stages. In the first stage, 6 different model specifications were used to analyse the two respondent data sets (Blue and Green) as follows:2, within-sample correlation, correlation with out-of-sample values, MAE of estimated and observed values, and the percentage of model versus observed residuals that were above 5% .Testing models 3 through 6 allowed a comparison of the performance of models with and without the constant term, as well as with VAS values transformed at the level of the respondent and at aggregate level. Including models 1 and 2 allowed a comparison of the models with equivalent analyses based on untransformed VAS values. Each model was evaluated using the following criteria - adjusted RIn the second stage of the analysis, the best performing model using rescaled data based on these criteria was used to develop a model for the pooled data . The performance of this model was compared with variants of this baseline model that included dummy variables which had previously been specified in the other valuation studies. These dummy variables indicated the presence of any 1’s, 2’s and 3’s in a state . In addition to these, regressions were also run with dummy variables giving the numbers of 1’s, 2’s and 3’s in a state  and the squares of these counts . These regressions were run to test whether these additional variables would improve performance over the baseline model.2, correlation of model values with observed values, and MAE of model values and values observed for the sample and hold out states.These models were compared based on adjusted R230 individuals participated in this study. The median age was 20 and 40% were male. The rates of self-reported problems as shown in Table Valuation data for the two sets of 23 states were obtained from 112 (Blue) and 117 (Green) respondents respectively. VAS values were obtained for 38 EQ-5D states plus dead. The mean observed values and corresponding transformed scale values are given in Table 2 values than the other models. However on the criteria that deal with predictive ability (MAE and correlation measures) the models that included the constant term outperformed those that exclude it for both the green and the blue set. Comparing the models based on the VAS values transformed at the two levels that include the constant term, Model 6 has a higher adjusted R2, but Model 4 has better MAE and correlation measures. These differences are very small.Results of the first stage are presented in Table Figures The models based on the green and blue data sets comprise very similar coefficients. This similarity is displayed in Figure 2 as well as the predictive measures). The magnitude of these improvements in performance is however small.The effect of including additional dummy variables was investigated using Model 4 for the combined data set (green plus blue). Table The challenges associated with the orthogonal design (inclusion of implausible states and the concentration of states in the moderate range) would have contributed to the relatively low Spearman’s rank correlation coefficients between the results of the ranking task and the ranks of VAS scores of 0.8880 and 0.8884 for the orthogonal valuation subsets (versus 0.94-0.96 for most of the studies that use the MVH protocol). Only 4 respondents in our study 1.7%) preserved the rank order of the states in moving from the ranking task to the VAS task (versus 19% in the MVH study). If it is accepted that the ranking task produces the ordinal preferences of the respondent, then the transfer of cards to the VAS allows the respondent an opportunity to correct any mistakes made during the initial ranking task. Such errors would be most likely among states perceived to be very similar in terms of preference level to the respondent . This is.7% preseThis study also demonstrates the performance of VAS as a valuation method for EQ-5D studies, and adds to the literature in support of the VAS as an elicitation instrument ,19. OverThe studies by Lamers , and ZarThis study employed orthogonal arrays with 18 rows . Further research should be undertaken to test smaller orthogonal designs that can used to produce main effects models. This would allow for smaller samples thus reducing the cost of conducting valuation studies in developing countries. Small orthogonal designs may also permit valuation subsets for TTO studies that do not require blocking, such that each respondent can provide one replicate.This study found small differences in performance of the models based on data transformed at the level of the individual and at the aggregate level. Differences in performance between the models based on raw VAS data and the models based on transformed data were also very small. The inclusion of the constant term improved the performance of all of the models.aIn Table bIn Table


In Norway, it is usually GPs that refer patients to involuntary admission. A high proportion of such referrals come from out-of-hours clinics. Little is known about who first initiate the contact between the patients and the referring doctors and which expectations the referring doctors have with respect to the involuntary admissions. The aim of the study was to examine who first detected the patients who were subsequently involuntarily admitted, and to examine the referring doctors’ expectations for the admissions.Semi-structured interviews with 74 doctors that had referred patients for involuntary admission at a psychiatric hospital.Patients who were involuntarily admitted were detected by other branches of the health service , family , and the police . The doctors mentioned these expectations for the admission (more than one expectation could be given): start treatment with neuroleptics: 58 % (n = 43), take care of the patient: 45 % (n = 34), extensive changes to the treatment regime: 37 % (n = 28), solve an acute situation: 35 % (n = 26), and clarify the diagnosis: 22 % (n = 17). Female doctors significantly more often expected that the patients would be examined and treated, while the male doctors significantly more often expected that the patients would be cared for.Involuntary admissions are typically complex processes involving different people and services and patients with various needs. More knowledge about the events preceding hospitalization is needed in order to develop alternatives to involuntary admissions.The online version of this article (doi:10.1186/s13033-016-0048-8) contains supplementary material, which is available to authorized users. The involuntary admission of a psychiatric patient will often entail numerous evaluations and actions on several levels , 2. WhilIn Norway, the process of involuntary admission will typically start with someone close to the patient, who sees that the patient is in need of help, and makes the decision to contact the patient’s GP or an out-of-hours clinic . In someWhen a patient is brought to the attention of the GP, the GP will evaluate whether there is a need and a legal basis for involuntary admission to a psychiatric institution. If the patient is admitted involuntarily, a legal evaluation of the involuntary admission will subsequently be made by a psychiatrist or clinical psychologist at the relevant psychiatric institution . AccordiThe legislation regarding involuntary admission varies between different European countries. Some countries, including Norway, have a system where the decision to admit involuntarily is taken by health professionals and where judges and other legal professionals become involved when these decisions are monitored or appealed , 21. In While the GPs may refer seriously ill patients to involuntary admissions because they consider that the patients meet the required criteria, little is known about which expectations GPs have when referring this group of patients. In order to better understand why patients are referred to involuntary admission, we need to examine the GPs’ expectations. In one study of mainly involuntary admissions, reinstatement of medication, intensive observation, and risk to self or others, were the main reasons for referral . StudiesThe aims of the present study were to find out who first noticed or detected the patients that were subsequently involuntarily admitted to a psychiatric hospital and to examine which expectations the referring doctors had with regard to the involuntary admissions.This was an interview-based study. The interviews were semi-structured and drew on a tailor-made questionnaire with altogether 19 items  of the participants were male and 28 (38 %) were female. Thirty-nine (53 %) worked at an out-of-hours clinic and 35 (47 %) worked elsewhere. Twenty-four (32 %) had worked more than 10 years, 11 (15 %) had worked between 5 and 10 years, and 39 (53 %) had worked less than 5 years. Twenty of the respondents (27 %) were the patient’s family doctors and 45 (61 %) had some prior knowledge of the patient. The characteristics of the participants have been described in a prior publication . The docAlmost all the doctors’ responses could be classified in the preformulated response options and very few responses were coded in the open response options. The data concerning who the GPs believed detected the patients and concerning the doctors’ expectations were summarized in tables . Due to the relatively small sample size and some table cells with a resulting small n Table , we subsThe Regional Committee for Health Research Ethics approved the study (reference P-REK-Nord-2009/1734). No information that could identify patients was collected. The doctors who chose to participate did so after they had received information about the study.An overview of who first detected the patients in question is presented in Table An overview of the referring GPs’ expectations for the admission and characteristics of the GPs is presented in Table When examining the responses according to characteristics of the doctors and their relationships with the patients in question, the biggest difference between the male and the female respondents related to the expectation that extensive changes in treatment and follow-up would be implemented . A higher proportion of the men than the women expected an acute situation to be solved  and the patient being taken care of . With respect to work place, a higher proportion of doctors at the out-of-hours clinic expected an acute situation to be solved  and a higher proportion of the other doctors expected extensive changes in treatment . When considering the expectations of the patients’ family doctors, we find that while 16 (15 %) of those who were not the patients’ family doctors expected the diagnosis to be clarified, this was the case with only 1 (2 %) of the family doctors. With respect to the prior knowledge of the patient, a higher proportion of those who lacked such knowledge expected the diagnosis to be clarified (18 vs. 7 %) and a higher proportion of those with prior knowledge expected extensive changes in treatment (24 vs. 12 %). A higher proportion of the more experienced doctors expected extensive changes in treatment (27 vs. 13 %) and a higher proportion of the less experienced doctors expected the patient to be taken care of (26 vs. 18 %).2 = 3.87, p < 0.05).We grouped the doctors’ expectations into two main categories, ‘Examining and treating’ and ‘Giving care’ Table , and calWe may assume that most of the patients that were later involuntarily admitted had not sought help on their own, but were detected by others. Some prior studies have examined which agencies that helped patients before they were admitted to psychiatric hospital, and described different ‘pathways to care’ for patients suffering from serious psychiatric illness , 18. In The high number of patients detected by the health service is probably a result of the fact that this is a group with serious illness and that the group is responsible for a high proportion of re-admissions to hospitals . ConsequWe chose to group the five types of expectations in two main categories, the category of ‘Examining and treating’  and the category of ‘Giving care’ (including the expectations ‘Take care of the patient’ and ‘Simply solve an acute situation’). While the referring doctors could have several expectations, we believe this categorization is useful in illustrating that other aspects than the purely medical may be important to the referring GPs when considering the involuntary admission of patients .The present study addresses a gap in knowledge regarding GPs’ expectations for involuntary admissions. When looking at the expectations of the group as a whole, the most expected action at the hospital was treatment with neuroleptics , which was also found to be the main expectation in a different study . Many inIn 37 % of all cases of involuntary admission, the referring doctors wished the hospital to make extensive changes in the treatment and follow-up of the patients. Here one must take into consideration the fact that a high number of involuntarily admitted patients are rapidly readmitted to hospital after first being discharged . This crOf the GPs that were interviewed, 22 % (n = 17) stated that they expected help with resolving an unclear diagnosis. This finding may be understood in light of a study that showed that as many as a third of the patients that were involuntarily admitted to another Norwegian psychiatric hospital had never been admitted before, and might therefore be more in need of a thorough diagnostic evaluation .In 45 % n = 34) of the interviews, doctors wanted the hospital to take care of the patient. This may seem obvious, however, we think this is particularly relevant in those cases where the patient has been involuntarily admitted. Studies show that involuntarily admitted patients often have low social functioning, a poor social network with little support, and tend to live alone 4 of the –40. ConsA total of 35 % (n = 26) replied that they wanted to resolve an acute situation when they involuntarily admitted the patient. We believe that such a need may occur in situations where there is a crisis, and the patients are overcome by worry and perhaps aggression. In such a situation, it may be difficult to focus on anything but the patient’s behavior .When examining the responses according to characteristics of the doctors and their relationships with the patients in question, we find some interesting differences. While the female doctors more often expected extensive changes in treatment, the male doctors more often expected the patient to be taken care of. This was also the only statistically significant between group difference (see Table There was also a non-significant tendency that a higher proportion of doctors at the out-of-hours clinic expected the patients to be given care and a higher proportion of the other doctors expected the patients to be examined and treated, a finding that may reflect the role of the out-of-hours clinic doctors as emergency doctors that are expected to prioritize the acute care of patients. Prior studies have suggested that doctors working at out-of-hours clinics have an increased chance of encountering psychiatric patients that are gravely ill , 43.Family doctors know their patients better than doctors who are not the patients’ family doctors, which was reflected in the finding that almost none of the family doctors expected an unclear diagnosis to be resolved during the hospital stay Table . In lineAs early as 1968, Bittner commented that a lack of proper alternatives remained an important reason for why the police used coercion against the mentally ill . Do doctFew prior studies have examined the considerations and expectations of GPs that have referred patients to involuntary admission. The study was based on phone interviews with the referring GPs, allowing the GPs to elaborate on, discuss, and clarify their ideas and thoughts. The interviewer was a psychiatrist. This may have affected the interview in a positive way because he could ask for clarifications based on his knowledge of the subject. At the same, time, we are uncertain whether the doctors adjusted their answers to comply with what they thought were expected of them by a figure of professional authority, rather than providing their own assessments.We have interviewed 74 doctors, a relatively small number in statistical terms, and we must therefore be cautious about generalizing our findings. With this relatively small sample, the possibility of type II errors should be considered. About a third of the doctors we contacted chose to call back in order to participate in the study. It remains a limitation of our study that we have little knowledge of the group that chose not to participate. However, the participants in our study were representative of Norwegian GPs in terms of gender and work experience.A majority of the GPs stated that other branches of the health service had detected that the patients were in need of hospitalization. Most of the GPs expected that therapy with neuroleptics would be initiated during the stay at the hospital. Some, however, replied that they wanted the hospital to take care of the patient or help solve an acute situation. Involuntary admissions are typically complex processes involving different people and services and patients with various needs. We need more knowledge about the events preceding hospitalization in order to develop alternatives to involuntary admissions. We believe there is a need for studies that examine possible alternatives to involuntary admission, including more studies that systematically assess the effect of psychiatric home nursing services and assertive community teams on rates of involuntary admission .


Operant behavioral tasks for animals have long been used to probe the function of multiple brain regions (i.e., understanding the role of dopamine in electrical brain stimulation reward •We provide a low cost alternative to commercially available nose poke system.•Our custom made apparatus is open source and TTL compatible.•We validate our system with optogenetic self-stimulation of dopamine neurons. Operant behavioral tasks designed for rodents are often used to probe the involvement and function of different brain regions linked to a variety of physiological and pathological brain states. The systems used to perform these experiments are often very expensive and beyond the reach of small labs or low budget projects.Here we recapitulate the steps taken to construct a custom-made nose poke system designed for mice, taking advantage of open source technology and inexpensive materials.Arduino boards are becoming increasingly popular due to their versatility and low cost. They have dedicated software and hardware that allow them to be programmed and therefore be applied to suit any need.Starting from a freely available sketch (Supl. Ref. 1) containing source code designed to make a laser tripwire, we applied the same principle to detect the nose entries to a port and built a nose poke system around it.The circuit is composed of a light dependent resistor (LDR) that gets exposed to a light source, in our case a red LED, a second LED (here green) that turns on every time the light beam onto the LDR is interrupted and an output BNC connector that drives the laser (GMP S.A. MBL-F-473-500 mW) for optogenetic stimulation.For a list of all the necessary electronic components to build the Arduino based four-port nose poke system see Our system includes four different ports that have separate circuits connected in parallel. The ARDUINO UNO board processes all of the inputs and outputs.As schematized in The green LED (LED2) circuits are formed connecting a 120 Ω resistor (R2) between DIGITAL ports D8 to D11 and the LED2s, which then are connected to ground .Finally the DIGITAL port D13 is connected to the live contact of the BNC connector and the shielding to ground .We designed the frame that would hold all the electronic components to fit a rectangular PVC box normally used for open field experiments with mice E and F. On the back compartment, surrounding each nose port, there is a structure with 5 mm holes directly above and below the port designed to be aligned vertically and hold the red LED1 above and the LDR below. Thus, when the mouse snout gets into the port it creates a shadow over the LDR changing the value of the resistance .To facilitate the assembly of the electronic components onto the frame we used a breadboard to hold all resistors and used a 3D-printed case that holds the Arduino board  could be loaded on the Arduino board allowing the system to be used. For a detailed guide on how to upload sketches on Arduino boards see Supl. Ref. 2.The Arduino board must be connected to a computer in order to communicate the nose pokes. Power can be supplied to the Arduino Uno either via USB cable or an external power adapter. To initialize an experiment once the board is connected to the PC, the Arduino IDE needs to be launched. Once the serial port monitor window is opened, the board is reset and starts executing the code. The first header line will be transmitted through the serial port, listing the port number, poke number and a time stamp. From that point on, every time there is a nose poke, its information will be transmitted as a new row of text with comma separated values. At the end of the session the list must be manually copied to a text file, which will then be saved in a comma separated values format. Closing and opening the serial monitor window of the Arduino IDE will reset the board and prepare it for a new session.The serial port can be also monitored through third party software and/or a secondary code can be implemented to automatically copy and store the data transmitted by the Arduino board as an alternative to the manual process.To test the functionality of our system we decided to use DAT-CRE transgenic mice (Jackson Laboratory stock number: 006660) injected with DIO-ChR2-EYFP in the VTA and implanted with an optic fiber Six to eight weeks old DAT-CRE transgenic mice (n = 3) underwent stereotactical surgery during which 300nl of AAV5-EF1α-DIO-ChR2-H134R-EYFP bilaterally with the following coordinates from bregma . During the same surgery a single optic fiber implant was placed with a 10° angle above the VTA to deliver light stimulation.Three weeks after the surgery all animals were placed in the nose poke system for a daily 60 min session for a total of six days. The behavior of the animals during each session was recorded and tracked  in all the animals confirming the validity of the preparation and the nose poke system. After the sixth day of testing all animals were intracardially perfused and fixed, the brains were slices and the infection and optic fiber placement were verified (As displayed in verified A and B. Here we provide a recapitulation of the making and testing of a custom-made Arduino-based nose poke system that allows for operant behavioral testing in mice at a fraction of the cost of commercially available systems. Due to the versatility of its microcontroller, this system can easily be modified to modulate any external device that is TTL compatible, and adapted to other types of operant switches such as lever presses or pressure plates.


It has been observed clinically that the Z-effect is a potential cause of failure of an intramedullary nail with two cephalic screws. It describes the migration behavior of the cephalic screws in the femoral head. The primary objective was to examine different cephalic screw configurations and test the load distribution between them as a function of their relative placement and their relative movement in the nail. It has been hypothesized that different cephalic screw positions may have an influence on the stress in the implant and bone and therefore on implant failures, such as the Z-effect.To quantify the load distribution of a dual cephalic screw intramedullary femoral nail , a finite element model of the femur, focusing on the loading of the cephalic screws, was prepared. Four different screw lengths (90–105 mm) were examined. The investigation considered the stresses and strains in the bone and implant as well as the relative movement of the screws.If the inferior cephalic screw had a shorter length, then the superior one and the femoral nail had to bear higher loads. In that case, the “equivalent von Mises stress” increased up to 10 % at the superior cephalic screw and up to 5 % at the femoral nail. The analysis of the relative movement showed that sliding of the inferior cephalic screw occurred in the nail. The total movement ranged from 0.47 to 0.73 mm for the different screw configurations.The stresses were distributed more equally between the two cephalic screws in the bone and the implant if a longer inferior screw was used. The stresses in the bone and implant were reduced with a longer inferior cephalic screw. Therefore, a configuration using a longer inferior cephalic screw is preferable for trochanteric fracture fixation with a dual cephalic screw intramedullary device. The reported number of proximal femoral fractures has increased steadily and due to aging populations, a further increase can be expected , 2. The Intramedullary devices for the fixation of proximal femur fractures are available with single, dual, and two integrated lag screws. Clinical experience with single and integrated screw design is most favorable for intertrochanteric fractures and subtrochanteric fractures. Dual lag screw designs may have a role for medially located trochanteric fractures or lateral fractures of the femoral neck and have demonstrated sufficient mechanical stability , 11. HowOne important factor affecting failure of implants in the femoral head is their localization within the head. For extramedullary implants, the tip to apex distance (TAD) has been identified as an important factor predicting cut-out through the femoral head. It has been shown that cut-out is more likely with an increasing value of TAD –17.Also for intramedullary implants, the location of the cephalic screw within the femoral head has been suggested as an important factor influencing the failure of implant fixation , 19. TheTherefore, the hypothesis of our study was that the cephalic screw positions in a dual cephalic screw design affect the load distribution in the implant and the surrounding bone. The specific aims of this computational analysis were to determine the local stress distributions and micro-movements under load application for different cephalic screw configurations.2 intramedullary femoral nail . The reaction loads at the support of the cephalic screws in the nail, and the maximum strain/stress on the cephalic screws as a response to the applied hip joint force and the fixation of the shaft, were both assessed for different positions of the cephalic screw tips.To quantify the load distribution, a finite element (FE) analysis of the proximal femur was prepared with emphasis on the loading of the two cephalic screws in a cephalomedullary implant for proximal femur fracture fixation. The model comprised a proximal fracture of the femur fixed with an EBAThe study was divided into two parts. In the first part, a mechanically stable configuration representing ideal repositioning of the fracture fragments was modeled. In the second part, an unstable configuration representing inadequate repositioning, reduced bone quality, and sliding of the cephalic screw was investigated.2 nail system. The implant was inserted according to the surgical manual, with no interfragmentary gap. The implant material was modeled as Titanium Alloy Ti6Al4V with material constants: Elastic Modulus E [MPa] 115,000; Poisson’s ratio μ 0.342.The FE model in this study was based on a standardized femur geometry with homogenous bone material properties for cortical and cancellous bone  which has been previously described in detail . The modThe boundary conditions of the FE model mimicked a physiological load in stance. The knee joint was simulated as a cardanic joint and the hip as a ball and socket joint. A force of 1900 N was applied at the center of femoral head, which represents the physiological load of the hip joint during walking for an 80 kg person .The model of the femur including the fracture and the intramedullary nail was created using FE software . Full models were designed with different contact types to determine which contact behavior was the most suitable. For further studies, the “simplified friction multipoint constraint contact (MPC)” model was used. This means that the threads of the cephalic screws are simplified and bonded by a multipoint constraint formulation. Thus in the stable configuration simulation, no sliding of the cephalic screws could occur in the proximal fragment of the bone. All FE analyses were conducted with ANSYS .For validation purposes, the FE model of the stable trochanteric fracture was constructed as a mechanical model using a composite adolescent-sized femur . The simulated models were validated by four mechanical tests. One test was performed as a reference on the intact surrogate femur. Three further tests used different lengths of cephalic screws .An experienced surgeon performed the surgery and created a fracture with a bone saw. The femoral head was embedded in a hemisphere with casting resin  to ensure adaption to the test machine. Thereby, the hemispherical shape represented the hip-like ball joint. The distal part of the femur was embedded to fit into a custom made cardanic joint. The mechanical tests were conducted with a servo-electric testing machine . A quasi-static axial compression test with a load ramp up to 1000 N was performed. For the validation, the experimental and simulated results were compared for axial stiffness, bone deformation, and strains at the bone and the implant.2 nail was fitted with four SGs: one posteriorly above the cephalic screw holes and one anteriorly below the screw holes. Additionally, one SG was fixed at every cephalic screw. The SGs were coupled to an amplifier . The recording and the evaluation of the data was performed with additional software . Local displacements were detected by optical markers on the bone surface and an optical tracking system  which recorded the displacements of optical markers on the bone surface with an accuracy of 0.025 mm.The strains were measured by strain gauges (SG) . The bone was fitted with four SGs. One SG was fixed superiorly and one inferiorly on the femoral neck. The other two SGs were fixed medially and laterally on the femur shaft. The EBA2 femoral nail as a function of their relative placement. Strains and stresses were examined at the bone and the implant with emphasis on the stresses at the cephalic screws and in the surrounding bone. The stresses were recorded from the straight part of the screw before the chamfer, and the relative movements of the cephalic screws within in the nail were investigated. Four different insertion lengths with a range of 90 to 105 mm were examined for each cephalic screw, so there was a total of 16 different screw configurations.The primary objective of the study was to examine different cephalic screw configurations and determine the load distribution between the two cephalic screws in the EBAThe computational model for the unstable configuration was an extended version of the validated model of the stable configuration. Compared to the stable model, it contained modification of the fracture, the bone quality, and the screw geometry.The unstable model was created with a fracture without any bone contact Fig. . The fraThe quality of the bone was changed. In the unstable model, the Young’s modulus of the cancellous bone was reduced to 80 MPa, which represented a bone with low bone quality. The unstable fracture with low bone quality represented a worst-case scenario.f 0.08 [While in the stable model a simplified screw model without threads was used, the unstable model included simplified circular threads. Additionally, the contact between the screw and the bone was changed. This allowed for the screws to slide with a resistance proportional to the frictional coefficient of f 0.08 . This coThe examined stresses are equivalent von Mises stresses. Only partially and specifically indicated normal stress was examined at the screws.The percentage error between numerical and experimental result was largest for the strain measurements (−36 % ± 27 % (mean ± SD)) and smallest for measurements of axial stiffness (−10 % ± 12 %). While strain and stiffness appeared to be underestimated by the FE analysis, local displacements were overestimated by about 25 % ± 21 %.Comparing the stress on the implant including the cephalic screws, it could be observed that across all combinations of screw lengths, the difference between the stresses in the implant was less than 3 % Fig. .Fig. 2“EThe maximum stress on nail was always observed in the area around cephalic screw holes of the intramedullary nail Fig. . The strThe largest stresses on the screws occurred around the chamfer and reached a maximum of 1168 MPa at the superior screw and 1078 MPa at the inferior screw Fig. . On averThe stress in the cortical bone of the femoral neck changed for different cephalic screw configurations. With decreasing length of the inferior cephalic screw, the stress increased, especially in the inferior cortex and also at the anterior aspect of the transition between neck and head Fig. .Fig. 4“EThe stress maxima in the cancellous bone of the proximal fragment were found in between and above the two cephalic screws. As the length of the screws decreased, the maxima shifted from the head to the neck area Fig. . AnotherThe stress distribution at the nail in the unstable configuration was similar to that of the stable fracture situation. The stress maxima were located around the bore holes and reached values of up to 1748 MPa at the nail Fig. . In the The maximum stress in the cephalic screws occurred at the posterior surfaces of both screws. With a shorter inferior screw, the superior cephalic screw had to bear higher loads. This resulted in increased tensile normal stress for the superior screw and reduced compressional normal stress for the inferior screw Fig. .Fig. 7NoTherefore, the normal stresses were the highest at the superior screw for the 105/90 configuration at 794 MPa and for the configuration with the smallest screws (90/90) at 793 MPa. For those two configurations, the stresses at the inferior cephalic screws were lowest. The normal stresses at the inferior screw were 432 MPa for the 105/90 configuration and 439 MPa for the 90/90 configuration.The stress difference between the superior and the inferior screw was smallest for configurations with longer inferior screws. The normal stress difference was 252 MPa for the configuration with the longest screws and 233 MPa for the 90/105 configuration.Similar to the stable configuration, stress in cortical bone concentrates in the inferior location of the neck to head region. The stress increases when the length of the inferior cephalic screw decreases Fig. .Fig. 8“EThe stress distribution within the cancellous bone is similar for the stable and unstable configurations. The stress maxima occurred between the two screws and above them Fig. . HoweverThe relative movement of the screws within the nail was calculated to determine possible sliding of the screws. A lateral sliding of the inferior screw was observed for all screw configurations. The largest sliding of the inferior screw was 0.7 mm. This was observed in the configuration with both screws having the smallest length (90 mm/90 mm). In contrast, the sliding of the superior screw remained below 0.03 mm for all of the configurations Fig. .Fig. 10SThe objective of this study was to analyze the effects of using different configurations of lag screw placement on the mechanical behavior of a dual lag screw trochanteric nail. Our findings indicate that by using a longer inferior lag screw, stress within the bone, the nail and the superior lag screw can be reduced and the difference in stress between the superior and inferior screws was smallest with a longer inferior screw. The length of the superior screw had minor influence on the stress in the bone and within the implant. The analysis of screw displacement within the nail demonstrated a lateral migration of the inferior screw during loading.Due to the fact that our study represents a FE study, the preferred cephalic screw configuration is a suggestion and has to be proved by further mechanical tests and clinical investigations. Computational models require simplifications of real-world situations and thus always have inherent limitations. Our FE model simulated only one type of fracture with two variations of bone density and two qualities of fracture reduction and therefore represents only a limited part of the large clinical variety of trochanteric fracture situations. The bone model used in the simulation was based on a simplified biomechanical bone model which has been previously validated . While tTwo different FE models were used in this study to analyze implant loading for different lag screw configurations. While the stable model simulated an ideal fracture reposition in a healthy bone, the unstable model simulated a worst-case scenario with imperfect fracture reposition and reduced bone quality. In the stable model, the effect of different lag screw configurations on the load distribution in the implant bone construct was rather small. This would indicate that the treatment of trochanteric fractures is not sensitive to the placement of the lag screws within the limits investigated in this study. In the unstable model, the effect of cephalic screw placement on the load distribution of the implant bone construct became more pronounced. All of the parameters assessed in the FE study were affected by lag screw placement. The most dominant effects were found for screw displacement and stress within the bone.The values of stress within the bone and the implant material can indicate potential locations of failure or fatigue. Stresses in the proximal bone fragment were largest at the inferior location of the femoral neck and reached values of up to 50 MPa. Although these stress values were still below the strength of femoral cortical bone (180–209 MPa) , the locIn our study, the lateral sliding of the inferior lag screw during loading is consistent with the description of the clinically observed Z-effect in dual lag screw implants, in which the inferior lag screw migrates laterally, and the superior lag screw migrates medially during physiologic loading. The lateral sliding was largest if the inferior screw had the shortest length. This indicates that a short insertion depth of the inferior screw would support the occurrence of the Z-effect. It has to be noted, however, that in this study the model was tested under a static load, while the Z-effect is assumed to be a phenomenon which occurs under cyclic loading . The cliIn conclusion, our results demonstrate that the configuration of cephalic screw placement in dual cephalic screw implants influences the load distribution at the implant and the bone. The size of the effect depends on the stability of the osteosynthesis and becomes more relevant in osteoporotic bone and imperfect fracture reduction. The most favorable load distribution with reduced overall stress was achieved using longer inferior cephalic screws. This could potentially decrease the likelihood of implant failure, varus collapse, and occurrence of screw migration. These biomechanical findings confirm clinical recommendations for this implant type.