This study aimed to find a more sensitive and systematic behavioral evaluation protocol to evaluate the cognitive impairment in rats with heart failure (HF).An HF rat model was built by ligating the left anterior descending coronary artery. The cardiac function and structure were detected using echocardiography. Myocardial histopathological changes were observed by nitro blue tetrazolium and hematoxylin–eosin staining. The cognitive functions were evaluated using the acquisition task, probe trial, reversal test, and matching‐to‐sample test of the Morris water maze. In the probe trial, the number of times the rats in the model group crossed the platform site significantly decreased compared with that in the sham group. In the reversal test, the average latency was significantly longer in the sham group compared with the model group in the first trial but was shorter in the second and third trials. In the matching‐to‐sample test, the average latency of Trial1 increased significantly in the model group compared with the sham group, while no obvious difference was observed in Trial2. Therefore, the difference in the average latency between Trial1 and Trial2 of the model group was significantly larger.The cognitive impairment in rats with HF mainly reflected in the long‐term and working memory, spatial learning, and reversal learning ability. The probe trial and reversal test in the water maze may be more sensitive and preferred to evaluate cognitive function after HF. These findings would provide a brief evaluation protocol for further studies on the relationship between cognitive function and HF. This study aimed to find a more sensitive and systematic behavioral evaluation protocol to evaluate the cognitive impairment in rats with heart failure (HF).The cognitive impairment in rats with HF mainly reflected in the long‐term and working memory, spatial learning and reversal learning ability. Ltd [Animal license number: SCXK (Beijing) 2012–0001]. The animals were housed in humidity‐controlled (60% ± 10%) rooms at 24°C ± 1°C and maintained under a 12‐hr light–dark cycle. The animals were provided with standard diet and water. All animal experiments were approved by the Animal Care and Use Committee of Beijing University of Chinese Medicine.2.2The HF model of rats was established, as discussed in a previous study  and fixed on their backs on boards with skin cleaned. After electrode needle insertion under the skin of the upper limb, lower limb, and chest of rats, the 12‐lead ECG was performed.The examination of echocardiography was carried out using the Vevo 2100 Imaging System Ultrasonic Diagnostic Equipment . The ultrasonic probe with a 15‐MHz high‐frequency linear array transducer was placed on the left side of the sternum, showing the parasternal long‐axis view. The heart function was measured using the M‐curve, guided by the two‐dimensional ultrasonic image. The main parameters consisted of EF (%) and fractional shortening .2.52.5.1The Morris water maze apparatus was purchased from Shanghai Mobile Datum Information Technology and consisted of a 1.6‐m diameter pool, which was divided into four quadrants . The pool was surrounded by light blue curtains with attached different shapes . The tank was suffused with the 27‐cm‐deep water level, which was mixed with 30 ml of ink to obscure visual cues. The temperature of the water was maintained at 23°C–24°C. A platform 12 cm in diameter was hidden 1–2 cm below the surface of the water. The experimental room was soundproof and without direct light.The rats were firstly pretrained for 1 day. Experiment 1 comprised three phases: acquisition trial, probe trial, and reversal test. In the acquisition trial, the rats were placed on the platform located in the SW quadrant for 5 s and then randomly released into the water from the other three quadrants  with the head toward the wall of the tank. The time was limited to 120 s per trial, and the activities were recorded. If the rats did not find the platform in 120 s, they were guided to the platform and placed on it for 5 s (this adaptation training was performed only once). Three trials were performed per day for three consecutive days with each rat so that each rat underwent nine trials in all for this phase. In the probe trial, 24 hr after the acquisition trial, the platform was removed and the releasing point was similarly to the acquisition trial, while number of times the rats crossed the platform site in 120 s was recorded. In the reversal test, the platform was moved to the opposite quadrant (NE) and the rats were released into the water as done on the first day of the acquisition trial. The swimming time and path were recorded.2.5.2In experiment 2, the water maze apparatus and experimental situation were the same as in experiment 1. The rats were pretrained for 1 day before the official test. Each rat received four pairs of trials every day, for five consecutive days. The locations of platform and entry points were different and randomly changed between each pair of trials. Each pair of trials consisted of Trial1and Trial2. In each pair of Trial1, the rats were placed in the platform for 5 s first and then into the water with heads toward the wall of the tank; the time was limited 120 s to find the platform. If the rats did not find the platform within this time, they were guided to the platform and placed on it for 30 s (this adaptation training was performed only for once). After a 15‐s intertrial interval, the rats were placed in the water again in Trial2, and the location of the platform and entry points were the same as in Trial1. The swimming time and path were recorded.2.6After echocardiography and behavioral examination, the hearts of the rats were cut uniformly into five 1‐mm‐thick transverse sections. Then, they were put in 0.1% nitro blue tetrazolium (NBT) stains, colored for 6–8 min in an incubator maintained at 37°C, and kept away from light. The normal myocardial tissues showed a uniform bluish‐purple stain while those in the infarction area presented a gray‐white stain, which formed a sharp contrast with the normal blood supplying area and made it easy to locate and measure. The stained myocardial tissues were photographed immediately.2.7The heart samples of the rats were fixed in 4% paraformaldehyde solution. Then, 3‐mm‐thick heart tissue was cut from the maximum transverse diameter of the heart. The tissues were dehydrated, cleared, and embedded in paraffin. Then, 4‐μm‐thick slices were cut and stained with hematoxylin and eosin (HE). The changes in myocardial morphology were observed under a light microscope (×400).2.8t test was used, otherwise the Mann–Whitney U test was used. For behavioral data, the significance of differences was assessed by ANOVA for repeated measures. A value of p < .05 was considered statistically significant.All statistical analyses were performed using SPSS version 20. All continuous variables were expressed as mean ± standard deviation. If the distribution of the variable was normal, the 33.1p < .05). The LVIDd and LVIDs in the model group were significantly increased compared with the sham group (C2). And the left ventricular wall thickness of model group was obviously thinner than the sham group (D1 and D2).The results of electrocardiography and ECG revealed the cardiac structure and function. In the model group, the results of ECG showed significant pathological Q waves 24 hr after ligation Figure b2, which3.23.2.1Compared with the sham group, the heart of the model group enlarged and showed significant necrosis of the anterior wall Figure a1,a2.The results of the NBT staining showed that the myocardia were stained bluish‐purple uniformly in the sham group Figure b1. Howev3.2.2As shown in Figure The myocardial fibers lost cross striations, and the nuclei were not clearly visible in most of the cells Figure c2.3.33.3.1p < .05) in the fourth trial.In the acquisition trial, no significant difference in path length, average latency, swimming speed, and percent time of the target quadrant (SW) was found between the model and sham groups Figure a1‐a3,b2.p < .01). Furthermore, the percent path length and time in the target quadrant of model group significantly reduced in probe trial . This evidence indicated that the spatial memory of the model group was impaired.In the probe trial, when the platform was removed, the number of times the rats in the model group crossed the platform site significantly decreased compared with that in the sham group . Further analysis revealed that the percentage time and length in the original quadrant (SW) of the sham group were significantly higher than those in the model group while the results were on the contrary in the new target quadrant , indicating worse memory retrieval of previous information in the model group compared with the sham group. Due to a good memory of the location of the former platform, the rats in the sham group searched for the platform for a significantly longer time in the original target quadrant (SW) and for a shorter time in the target quadrant (NE). However, in the following second and third trials of the reversal test, the average latency and swimming path length of the model group were significantly longer than those in the sham group , and the percent time/length in the new target quadrant (NE) were significantly lower in the model group . These results indicated that the spatial reverse learning and executive function to search for new platforms were impaired in the model group.In the reversal test, some changes happened between the model and sham groups. In the first trial, the average latency and swimming path length of the sham group were significantly longer than those of the model group unexpectedly , the average latency of Trial2 improved significantly compared with Trial1 in both the model and sham groups, indicating that all the rats were learning the matching‐to‐sample problem and had a memory of the location of the platform in Trial1. No significant differences in the average latency of Trial1 and Trial2 were observed between the model and sham groups from the first day to the fourth day . Further analysis found that the average latency of Trial1 increased significantly in the model group compared with the sham group on the fifth day , while no obvious difference in the average latency of Trial2 was found between the model and sham groups, indicating that the rats with HF performed worse in learning the ever‐changing locations of the platform . These pieces of evidence indicated that the short‐term memory of the HF model of rats was not impaired while the executive function to search for a new platform was impaired in the model group.To assess the working memory and short‐term memory of the HF model of rats, the matching‐to‐sample test of Morris water maze was used. As shown in Figure 4The early stage of cognitive impairment in HF is characterized by mild cognitive deficits and subtle changes. This study aimed to find a more sensitive behavioral evaluation method to assess cognitive impairment in HF and detect the damage to learning and memory abilities. The spatial acquisition trial, probe trial, reversal task, and matching‐to‐sample test of the Morris water maze were performed to detect the long‐term memory, short‐term memory, and learning of rats with HF in this study. The probe trial and reversal test in the water maze appear to be more sensitive and specific than the matching‐to‐sample test. The cognitive impairments of rats with HF were manifested mainly in spatial memory and learning ability.In the present study, the HF model of rats was built via ligating left anterior descending coronary artery, which has been widely used in cardiovascular studies (Hou, Huang, Cai, Zhao, & Guo, Consistent with the results of ECG and echocardiography, the myocardial histopathological assessment confirmed the myocardial ischemic injury of the model group.The cognitive impairment in patients with CHF was displayed in different areas of cognitive function, including memory, learning, executive control, attention, processing speed, and fluid intelligence (Hawkins et al., The Morris water maze is the most frequently used technique to detect spatial learning, memory, and spatial navigation in laboratory rats with a wide range of application (Brandeis, Brandys & Yehuda, In experiment 1, the rats in the model group had significantly impaired memory and learning abilities. No difference in the swimming time and length was observed between the model and sham groups in the spatial acquisition trial. However, in the probe trial, the number of times the rats in the model group crossed the original platform site was significantly less than that in the sham group. This indicated that the long‐term memory of the rats in the model group was seriously damaged. This was consistent with the results that the long‐term memory of patients with HF was worse than that of healthy people in clinical studies (Kindermann et al., In experiment 2, the procedures of the matching‐to‐sample test in the Morris water maze were evaluated in Trial1and Trial2 for each pair of trials (Vorhees & Williams, However, in this study, the difference in the average latency between Trial1 and Trial2 of the model group was significantly larger than that of the sham group on the fifth day. Further analysis found that the average latency of Trial1 increased significantly in the model group compared with the sham group, while no obvious difference was found in the average latency of Trial2. The explanation of the significantly longer average latency of the model group in Trial1 was that the rats in the model group could not change their search strategy according to the change in the platform location, and its ability to deal with problems decreased. The working memory of the rats with HF may be damaged by affecting the information processing, including encoding, maintenance, and information processing. However, the model group did not spend more time in Trial2 compared with the sham group, indicating that the short‐term memory of the HF model of rats was not impaired seriously. Potential factors contributing to the different results from the previous studies may be mainly the different animal models. In other words, since that the degree and position of brain damage on HF rats were inconsistent with previous studies; therefore, the characteristic of cognitive impairment was also different and so did the results.However, this study still had some limitations. The language and counting ability of the patients with HF can be detected by screening instrument in clinical studies, which could not be achieved in this study via the animal experiments (Hawkins et al., In summary, the cognitive impairment in rats with HF mainly reflected in the long‐term and working memory, spatial learning, and reversal learning ability. This was consistent with the clinical symptoms of patients with HF. Moreover, we also found that the probe trial and reversal test in the water maze may be more sensitive and preferred although the matching‐to‐sample test can also assess the function of memory. These findings would provide a brief and sensitive behavioral evaluation protocol for further studies on the relationship between cognitive function and HF.The authors have no competing financial interests to declare.Ziwen Lu and Tao Yang should be considered joint first author. Ziwen Lu and Tao Yang conducted experiments, analyzed data, and wrote the article; Lei Wang, Qi Qiu, Yizhou Zhao,Tong Li, Wenkun Cheng, Baofu Wang, Yang Li, and Jingjing Yang conducted experiments; Aiming Wu contributed reagents/materials/analysis tools; Mingjing Zhao conceived and designed the study, wrote the article, contributed reagents, materials and interpretation of results.


There are sometimes cost, scientific, or logistical reasons to allocate individuals unequally in an individually randomized trial. In cluster randomized trials we can allocate clusters unequally and/or allow different cluster size between trial arms. We consider parallel group designs with a continuous outcome, and optimal designs that require the smallest number of individuals to be measured given the number of clusters. Previous authors have derived the optimal allocation ratio for clusters under different variance and/or intracluster correlations (ICCs) between arms, allowing different but prespecified cluster sizes by arm. We derive closed-form expressions to identify the optimal proportions of clusters and of individuals measured for each arm, thereby defining optimal cluster sizes, when cluster size can be chosen freely. When ICCs differ between arms but the variance is equal, the optimal design allocates more than half the clusters to the arm with the higher ICC, but  less than half the individuals and hence a smaller cluster size. We also describe optimal design under constraints on the number of clusters or cluster size in one or both arms. This methodology allows trialists to consider a range for the number of clusters in the trial and for each to identify the optimal design. Except if there is clear prior evidence for the ICC and variance by arm, a range of values will need to be considered. Researchers should choose a design with adequate power across the range, while also keeping enough clusters in each arm to permit the intended analysis method. An expression is available to identify the optimal allocation ratio in this case, for given cluster sizes in each arm.3 A related expression for individually randomized trials where only one arm is clustered due to treatment has been derived,4 but this setting is not considered further in this article. Besides consideration of efficiency, unequal allocation in trials may be chosen because the intervention is more expensive to provide and/or there is a fixed amount of equipment or staff available to provide the intervention. Fewer clusters were allocated to the intervention in the PARAMEDIC trial that randomized ambulances where the intervention was provision of a mechanical compression device for cardiac arrest.5 In the ROPE trial, where clusters were villages, exactly 26 villages were allocated to the intervention because there were resources available to train and support 26 teachers to deliver the intervention, one per village.6 A potential reason to conversely allocate more clusters  to the intervention arm is to improve learning about its implementation.In individually randomized trials it has long been known that it is more efficient to randomize to arms unequally when the variance of the outcome differs between arms.5 Such an intervention could cause the ICC and/or variance to decline relative to current care. Conversely interventions may potentially increase the ICC and/or variance if they are not fully implemented in all clusters, or involve adaptation to each cluster such as participatory learning and action interventions that develop local solutions to local challenges as in the ongoing SNEHA-TARA and JIAH trials.8In many cluster randomized trials it is possible for the ICC and variance to differ between arms due to the effect of the intervention(s). We note this can in particular be expected where an intervention standardizes care, for example, through use of an algorithm in medical care, or a device as in the ongoing PARAMEDIC trial.3 we here investigate optimal design in which not only the allocation of clusters is allowed to vary but also the allocation of individuals to be measured to the trial arms. In other words while we assume a common cluster size within trial arms the cluster size is allowed to differ between arms and is selected freely. Hemming et al present methodology for sample size calculation with different ICC and cluster size between arms.9 In some trials the number of individuals recruited or exposed per cluster is determined by the setting, for example, because the intervention is delivered at the level of a health facility and all individuals in the local area are affected. Nevertheless our methodology may still be helpful in this case because it allows trialists to see how to minimize the number of individuals that need to be measured in the trial, where outcomes are not routinely collected and only a random sample of those exposed are measured. Such a design is common in community randomized trials where the number of individuals exposed per cluster may be very large as in the SNEHA-TARA trial.7 We use the term cluster size in this article to denote the number of individuals measured in a cluster, and we assume all clusters provide some measurements. Identifying an optimal design, meaning one with the minimum number of individuals measured for a given number if clusters, is particularly important if the data collection is burdensome or expensive, such as in the PA4E1 school randomized trial where the student-level data collection includes 7-day accelerometer measurements, anthropometry, and a survey.10In contrast to earlier research,We restrict our attention in this article to parallel group trials, without baseline measurement, and a continuous outcome. We first establish how to identify the optimal allocation of clusters and individuals measured without constraints, and then when the number of clusters or cluster size is constrained in one or both trial arms. We show how trialists could investigate alternative suboptimal (less efficient) designs which could be nevertheless be preferred for logistical or other reasons. We also provide an approach to considering trial design in practice under uncertainty in the ICC or other values required to calculate sample size. We show how to calculate sample size, and illustrate our approach through considering how the PA4E1 trial might have been designed under a range of hypothetical  alternative scenarios leading to unequal allocation.2j in cluster i, where iX denotes the trial arm for cluster i (coded 0 for control and 1 for intervention). We assume the random terms are Normally distributed with mean zero, but with potentially different variance according to the trial arm. The individual variability term is denoted εij0 or εij1 depending on trial arm and is assumed independent of the cluster random effect denoted ui0 or ui1. We denote the variance of the random terms thus The data are assumed to follow this model: Y by We denote the overall variance of N, and the total number of clusters randomized  by K. We assume a common cluster size of m0 for clusters in the control arm and m1 in the intervention arm. We denote the proportion of measured individuals in the intervention arm by p and the proportion of trial clusters allocated to the intervention arm by g. When design choice is unconstrained we consider designs across all possible values of p and g between 0 and 1, given values of N and K. These in turn define the cluster sizes because To describe different designs we denote the total number of individuals measured by Y to detect as d. We define the power function, based on a Normal distribution for large sample sizes, thus: In order to consider power we define the target difference in m0 – 1)ρ0 and 1 + (m1 – 1)ρ1 take the form of the design effect commonly used in sample size calculations, we can define the arm-specific effective sample size (ESS) for the two trial arms in terms of either p and N or g and K as Noting that 1 +  if and only if γρ1 > ρ0, and fewer than half the individuals measured (optp < 0.5) if and only if (1 – ρ0) > γ(1 – ρ1). If the two ICCs diverge, for example, ρ1 → 1 and ρ0 → 0, then progressively more of the clusters and fewer of the individuals are allocated to the arm with the higher ICC. This is intuitive because as the ICC tends to zero the clustering of the data becomes irrelevant and a few large clusters are as informative as many small ones, conversely as the ICC tends to 1 then many clusters are required and the size of these becomes unimportant.11We see the optimal design allocates more clusters to intervention than control  will be fixed, though the methodology can be adapted to either arm. With cluster size fixed in one arm then we need only consider varying one allocation proportion, we choose to vary g. We note that we can write m0 in the expression for ESS0in N, K, and m1 as in We suppose that the cluster size in the intervention arm  is given by β indicates the desired power. Expressions for m0 and m1 can be substituted, based on N, K, p, and g, following From N > 0) provided the expression in square brackets is positive, and therefore This has a valid solution  are fixed. N only thus  designs , express5N and K to be identified that will provide the desired power. To search for suitable designs it can be convenient to choose a range of values for either N or K and for each value solve for the other. In most settings it will be more appropriate to select a range of values for K because the number of clusters that can be included in the trial is often within a particular range, for logistical or cost reasons. There is also a lower bound for K at which even if N approaches infinity the desired power cannot be attained, as demonstrated by the inequalities in K we presented in the previous section.The formulas in the previous section allow designs with different pairs of K = 30 in total, 15 per arm) nested within the trial . In total then outcomes will be obtained from N = 1200 students. We focus on the outcome minutes of physical activity within school hours per day, which is measured over a week based on each student wearing an accelerometer. No basis of the sample size for the nested student level data collection is provided in the published protocol,10 but we can calculate that hypothetically assuming an ICC of 0.05 in both arms and equal variance then the design provides 80% power to detect a standardized effect of 0.278. We assume that this power for this effect is desired, and look into alternative designs that could have been chosen under different hypothetical assumptions about the ICC and variance by arm, with and without constraints. We imagine it has been decided to minimize N due to the measurement burden, and therefore consider a range of values for K from 30 upward to 50.The ongoing Physical Activity for Everyone (PA4E1) school randomized trial in Australia assesses the effectiveness of an intervention to promote physical activity in school students compared with routine practice. The primary outcome is assessed at the school level, but important outcomes are assessed at the student level. Because of the measurement burden and cost the student outcomes are collected from only a subset of students (40) within each of a subset of schools  m0 = 28 and so the total number of measurements in practice is N = 1010. This further constraint has increased N by only 20, compared with N = 990 seen in Here we suppose that the expected maximum feasible size for each cluster is 45 because of concerns over the proportion of students likely to consent to data collection. Considering designs with at least 10 clusters per arm, we see in 5.4p and g) for logistical or other reasons. If for example there are additional costs or resources associated with allocating clusters to the intervention arm then a lower value of g than optg may be selected if this causes only a modest increase in N, the number of individuals to be measured. In the PA4E1 trial this is perhaps unlikely but we expand on our example to illustrate our methodology.Trialists may wish to also investigate “suboptimal” designs  to 0.40 (K1 = 16 and K0 = 24) increases N by around 70. We also see that while holding g at optg, reducing p from optp to 0.4 increases N by around 40, and increasing p from optp to 0.6 increases N by around 25.We illustrate a graphical approach to investigate suboptimal designs by extending the unconstrained design presented in the previous section, for 6We have previously focused on scenarios where researchers are happy to select single values for the ICC and variance in each trial arm, but uncertainty in these parameters is common in practice and could be expected for settings such as the PA4E1 trial. In this section we address optimal design where the parameters are considered to lie in plausible ranges. We seek to identify the design which, for a given number of clusters, requires the smallest number of individuals measured to achieve a specified power across all values in the ranges.K = 40) to consider how best to design a trial if there is uncertainty in the values of ICC expected for each trial arm, as there could well be in the PA4E1 trial. We assume ρ0 lies between 0.075 and 0.1 and ρ1 lies between 0.01 and 0.025. In N varies with g at the four combinations of these boundary values, while holding p = 0.51 which is very close to optp for every combination (optp varies between 0.507 and 0.512). The values of N are derived from N is larger for larger values of the ICC. While a total sample size of around 750 together with g in the range 0.3 to 0.4 would provide adequate power in three of the four scenarios considered, at the extreme where both ICCs are the largest considered, that is,  is  the required sample size increases to at least 880. Choosing N = 900 and setting g to 0.325 or 0.350 (K1 = 13 or 14) is a conservative choice proving power across all values of the ICC considered.We next extend our example based on the PA4E1 trial ). This is because any design that achieves the desired power (say 80%) at the highest parameter values will have higher power should their values be lower, and by definition of optimality no alternative design can achieve the desired power with fewer individuals at the highest parameter values. Some further issues around trial design in practice under uncertainty are however discussed in the next section.Thinking more generally it is intuitive that when considering a range for the ICC and/or variance within each trial arm that the design that requires the smallest number of individuals measured given a total number of clusters is the optimal design for the highest values of the parameters  for  which would be very inefficient if both ICCs were 0.01. An area of further work is to explore more sophisticated strategies for choosing a design in this case, for example, a Bayesian approach based on priors for the ICC parameters in which we identify sample size to achieve adequate power across ranges for the ICCs well supported by the priors.In the design of cluster randomized trials there will often be uncertainty in the ICC and/or variance parameters. This uncertainty is compounded if it is suspected that the intervention itself might affect the ICC and variance. Given plausible ranges for the parameters in each trial arm it is straightforward to design an “optimal” trial that minimizes the number of measurements for a given number of clusters, with at least a specified level of power across all values in the plausible ranges. As discussed in the previous section this optimal design assumes the highest plausible parameter values in each arm. This design may not perform uniformly well over all plausible parameter values, however. Suppose we are confident that the ICC is 0.01 in the control arm but in the intervention arm the plausible range is anything from 0.01 to 0.10 (to keep things simple let us suppose the variance is unaffected by the intervention). The optimal design in this case, based on ICC values of 0.01 and 0.10, allocates clusters in an unbalanced way . We recommend that both the variance and ICC should be reported separately by arm as we argue it will be rare that it can be assumed with any certainty that the intervention does not affect these.It is difficult to know how often values of the variance and ICC differ between arms because they are infrequently reported separately by arm and the CONSORT guidance does not recommend doing so.Supplementary Appendix


Ostomy barriers are adhesive devices designed to hold pouching systems to the abdomen and protect the peristomal skin from stoma effluent. The objective of this study was to determine differences in the extent of skin trauma resulting from serially applying and removing two types of ostomy barriers.TEWL was measured in a designated site and again in the most visually traumatized location at termination.The study was a randomized, prospective, repeated measure trial involving healthy volunteers. The ostomy skin barriers were applied to the abdomen and changed every 3‐4 days over a 17‐day period. Skin observations  were completed by a trained (blinded) observer. Transepidermal water loss (TEWL) measurements were completed by a separate (blinded) technician. TEWL were found between the test products when measured at termination from the most visually traumatized sites.Statistically significant differences were found between the two test devices in all assessments but visual observation of erythema. Highly significant differences in TEWL measurements were more sensitive to changes in the barrier function of the skin than visual observation of erythema.The ostomy barrier with ceramide was significantly less disruptive to the epidermis than the ostomy barrier without ceramide.  Computerized evaporimetry is considered the “gold standard” for assessing the extent of stratum corneum barrier disruption.Measuring TEWL after test strips are removed from the surface of the volar (inside) forearm is a common practice in adhesive tape studies. However, several factors need to be considered when studying the effect of removal of various types of adhesive medical devices to make them relevant to their actual clinical use. Duration of use (dwell time) and the preferred application site are the most critical of these factors.Study methods were slightly modified from those typically used to study the skin effects of adhesive tape removal. Modifications were made to account for use of the ostomy skin barriers on the abdomen, and also for the larger size of ostomy skin barriers in comparison with the typically small test product sizes used in tape removal studies. In prior work, we have observed that variability occurs in the appearance of redness and irritation under ostomy skin barriers which may not be reflected from using a single site of measurement. A typical pattern showing irregularly distributed irritation is shown in Figure 22.1The study was a randomized, prospective, repeated measure trial involving healthy volunteers without a stoma. It was conducted at a single site in the northeastern United States. Institutional Review Board approval was obtained  and the study was conducted in accordance with ICH‐GCP. Participants were randomized to type of adhesive ostomy barriers, and they came to the study site every 3‐4 days for a total of six visits over the study period of 17 days. Each subject wore two marketed ostomy skin barriers in a paired fashion with a total of five applications and removals during the 17‐day study period. This wear schedule was selected to reflect that commonly followed for ostomy skin barrier change in North America. Ostomy barriers were applied and removed by study staff. Skin observations were completed by a single trained observer while TEWL measurements were completed by a separate technician; each was blinded to the identification of the study barriers and did not see the application or removals of the products. Digital images were taken of participants’ skin following discontinuation or completion of the study.2.2Two ostomy skin barriers which are currently marketed in North America  were selected for use in the study, as shown in Table 2.3Twenty‐three healthy volunteers with Fitzpatrick scale phototypes I‐III were enrolled into the study. Twenty subjects completed the study; two subjects withdrew consent for further participation and one subject was discontinued from the study after experiencing an adverse event. The 6 male subjects ranged in age from 28 to 60 years with a mean age of 45.3 ± 14.2 years while the 14 female subjects ranged in age 23‐62 years with a mean age of 45.3 ± 11.5 years. Additional details of inclusion and exclusion criteria are listed in Table Written consent was obtained from participants prior to their enrollment. Each candidate was instructed to stop the use of all topical products other than their normal cleanser on the abdomen for the 3 days prior to the start of the study. They were also instructed to not wash the test sites or apply any other products to the test sites during the course of this 17‐day trial.2.4One expert grader made all skin assessments in this study. The assessments were made prior to the first application of the ostomy skin barriers at baseline and approximately 30 minutes post removal of ostomy skin barriers on Days 4, 7, 10, 14 and 17. The skin grader was blinded as to product applications and was not allowed to compare any previous scores. In order to qualify, all assessments at baseline must have been zero. If any of the barriers were partially‐adhered or had fallen off at subsequent study visits, it was recorded and assessments were still made and the barriers were reapplied on schedule.. Erythema and denudation grading were per‐zone  excluding the area at and under the very edge of the device. Edge Irritation grading was per‐zone , exclusively for the area at and under the very edge of the device. In addition, the expert grader used a 4 point ordinal scale to provide an overall comparison based on the overall differences in erythema, skin stripping and irritation as a pairwise comparison of two devices. The device considered to be the least traumatic to the skin was given a score of 0 while the opposing test site was given a grade of +1,+2 or +3 if the differences were respectively either slight, moderate or dramatic in comparison.All subjects were visually evaluated using the five point ordinal scales for erythema, denudation (skin stripping) and edge irritation where grade 0 was none and grade 4 was severe, with intermediate scores of 1, 2 and 3 representing mild, moderate and marked conditions respectively. Half grades were allowed so that finer distinctions could be made. Zonal grading was performed as per the diagram in Figure If any test site zone reached a grade 3 or greater for erythema, 2 or greater for denudation or 4 or greater for edge irritation during the study, treatment on that site was discontinued. Once a site was discontinued, all product application and study assessments were discontinued for both sites with the exception of capturing adverse event information until the irritation was resolved.2.5Transepidermal water loss measurements were obtained with a computerized cyberDERM RG‐1 Evaporimeter2.6Scores from the four zones within each test site were summed to yield a cumulative score for each of the three parameters . If the treatments had been terminated due to severity of irritation, the data from the last observation was then carried forward for that individual in subsequent sessions. In addition to the TEWL measurements obtained from the designated zones of each of the paired sites, any early termination measurements were also taken from the site that showed the most visual signs of irritation regardless of its location.P‐values < 0.05 were considered statistically significant. Statistical analysis was performed using GraphPad InStat for Windows . The Mann‐Whitney test was used for categorical data such as the expert grader's assessments. The Student's paired t test was employed for continuous data obtained from TEWL measurements. In those situations where one or both of the sites had been discontinued due to irritation, the last observation was carried forward for both sites for subsequent days.Data are presented as mean ± SD. 3. Erythema scores progressively increased over time but in a similar fashion with both test products as shown in Figure The Expert Grader's Skin scores at the 5 follow‐up observation sessions are displayed in Figures P = 0.027 and P = 0.006) but only directionally thereafter. In striking contrast, highly significant differences were found to exist between the two test products when the analysis was based on TEWL rates measured at the time of termination from the most visually traumatized sites (termed “worst”), as shown in Figure TEWL rates progressively increased over the 17‐day wear period in the designated test sites as shown in Figure 4Skin trauma following repeated removal of adhesive medical devices is often measured using visual observation; however, other methods such as TEWL may be more sensitive for the measurement of skin trauma effects. This clinical study was designed to reflect actual use conditions with regard to wear time and application site with healthy individuals. Modifications were made in measurement and analysis to account for size of the product and the potential for irregular patterns of irritation.Product A was less likely to cause irritation that would lead to an early termination compared to product B. As expected, TEWL rates increased with each of the five device changes that occurred during the 17‐day trial. The TEWL findings are in good general agreement with the Expert Grader's ratings, particularly stripping/denudation. In the case of skin stripping/denudation, the Expert Grader's rating increased progressively over time but much more so in those sites assigned to product B than product A. In the case of Edge scores, the differences are only directional at Day 7 but become significant at all later time points and indicate that this trauma is much more pronounced as time goes on. The overall comparison scores also indicated that there was less irritation with product A than product B and that these differences can be appreciated fairly early on.Our findings are generally consistent with our understanding that removal of an adhesive device is a form of mechanical insult to the stratum corneum and can result in increased TEWL. The findings of this study suggest the product with ceramide provided some level of protection against the potentially damaging effects of ostomy skin barrier removal in relation to the comparator product. This may be due to the fact that ceramides have dual action: they can bind water and can also act as a lubricant, which may help prevent injury over time.Some limitations inherent to product study with healthy volunteers are noted. Study participants were naïve to ostomy skin barriers and did not have stomas; thus, their response to the products may not represent what would be expected in actual use of the products. The design did not include a sham control; thus, the cause of the difference between groups may be factors other than the presence or absence of ceramides in Product A. The practice of using LOCF also allows for underestimation of the effects of the worse product.5Product A (CeraPlus) was significantly less disruptive to the underlying epidermis when compared to Product B as demonstrated by skin stripping, edge irritation, TEWL and overall comparison grading. This suggests that of the ways to improve ostomy skin barrier function, a particularly good one may be the addition of ceramide.We feel that applying the ostomy skin devices in a paired wise fashion at the body location where they are intended to be used and monitoring the changes in skin conditions in a standard fashion after each change as was done in this study provides a more accurate measure of skin trauma than previous methods. These modified methods, which take into consideration the heterogeneity of the injury, may be helpful to other researchers conducting skin trauma studies on adhesive devices.


We have shown that spectrum feature presented as a “split alpha” can be the result of applying improper means of analysis of the spectrum of the EEG signal that did not take into account the significant properties of the applied Fast Fourier Transform (FFT) method. Analysis of the shortcomings of the FFT method applied to EEG signal such as limited duration of analyzed signal, dependence of frequency resolution on time window duration, influence of window duration and shape, overlapping and spectral leakage was performed. Our analyses of EEG data as well as simulations indicate that double alpha spectra called as “split alpha” can appear, as spurious peaks, for short signal window when the EEG signal being studied shows multiple frequencies and frequency bands. These peaks have no relation to any frequencies of the signal and are an effect of spectrum leakage. Our paper is intended to explain the reasons underlying a spectrum pattern called as a “split alpha” and give some practical indications for using spectral analysis of EEG signal that might be useful for readers and allow to avoid EEG spectrum misinterpretation in further studies and publications as well as in clinical practice.This paper attempts to explain some methodological issues regarding EEG signal analysis which might lead to misinterpretation and therefore to unsubstantiated conclusions. The so called “ For example, why the “split alpha” in consecutive publications on the topic of EEG analysis.Explanation of errors is necessary for two reasons, one is an education purpose and the second one is to avoid further propagation of errors and wrong conclusions regarding “Fast Fourier Transform (FFT) analysis , even thFrom the signal analysis point of view spontaneous EEG activity is classified as non-deterministic, stochastic process recorded as a low-voltage band limited (pink) noise and non-stationary one. The characteristic of EEG signal is influenced by various simultaneous psychophysiological processes and physical factors. Therefore, interpretation of frequency spectrum of spontaneous EEG activity should be made very carefully.Fourier transform is an exact method only when applied to an infinite time or, at least to very long epochs in comparison to the period analyzed, and stationary signals. Otherwise, spectral analysis provides only an estimation of power spectrum. Spectral analysis is a powerful analytical tool with good statistical properties as long as certain assumptions about the nature of the data, especially normal distribution of the amplitudes and stationarity are not grossly violated. It is important to note this restriction since EEG data are rarely a Gaussian noise. Rather EEG data in many cases may look like a random noise due to EEG signal nature. This means that one must carefully examine both EEG recording as well as the resulting spectra as the error estimates of obtained spectra are difficult to obtain without the knowledge of actual frequency content. Moreover, the assumption of stationarity is valid only for relatively short epochs of EEG data. Spectrum stability and statistical significance decrease with the decrease of duration of EEG epoch under analysis.In practice, the spectral analysis is applied to epochs (data segments) of finite and shortest possible duration (T). With short epochs one can try to minimize the effect of the EEG signal being non-stationary. However, this leads to two different sources of difficulties: spectral resolution limitation: the frequency resolution of the obtained spectrum is limited to 1/T and truncation error. In such a case the resultant spectrum is a convolution of the spectra of the epoch of EEG signal and of the time window function . In consequence, each frequency peak is broadened into a band of 2/T width and has a series of lateral lobes, and due to truncation error harmonic frequencies may appear in the spectrum that result in spectral aliasing. Procedures of overlapping of analyzed signal epochs or spectrum smoothing might reduce spectrum alterations and increase statistical reliability of results .However, despite of objections from theory of time series analysis, spectral analysis of non-stationary EEG epochs may provide useful information and is widely used. The spectral analysis of EEG signal requires rational choice of parameters mentioned above and a large experience in the interpretation of EEG signals. Otherwise, it is easy to obtain wrong results and misinterpret the spectral content of the EEG signal. This is why automatic methods available in standard packages of numerical procedures can not be “blindly” used for calculations and making automatic inferences about the underlying brain activity.split alpha” phenomenon  over a range of frequencies, from fa to fb. The range of frequencies considered fa ≤ f ≤ fb may be considered as corresponding to the frequency band contained in the segment of the EEG signal  corresponding to angular frequency ω0 is calculated for a finite segment of the signal of length T as:The Fourier transform of the We are thus calculating Fourier transform of a windowed signal, just as is the case in case of EEG FFT analysis.The formula for the Fourier transform may be rewritten into the following form enabling further analysis:G is given by:where F(ω0) the following equation:In order to calculate the Fourier transform corresponding to a band of frequencies the expanded formula for G is used giving for x)/x or sin(x)/x, and, because the integral defining F is a definite one, the F is calculated as the difference between the value for the integral at the upper limit and the value at the lower limit of ω. The resulting equation for F is quite long, however, it can be easily calculated using mathematical libraries for the calculation of sine and cosine integrals.Here Ci and Si are cosine integral and sine integral, respectively. They result from the integration of expressions like cos.In order to find out how windowing affects the shape of the spectrum a simulation was performed in which a sum of 22 sinusoids was calculated with the frequencies of the sinusoids spaced evenly in a range 8–13 Hz. The signal was sampled with a frequency of fThe analyzed model signal used may be described using following formula:fi = fa + i⋅δf, with δf being the frequency step (in Hz), fa the lower frequency of the range, the fb the upper frequency range and i = 1..n, such that fa ≤ fi ≤ fb, and where n can be selected (here n = 22). The tj = j/fs, with fs being the sampling frequency, and j = 0..N−1.where Before submitting the signal to FFT analysis it was passed through either a rectangular window  or a Blackman-Harris, Triangle, Parzen or Hann windows. The results are presented in As can be seen from By filtering the signal using triangular window before applying FFT only leads to amplification of the magnitude of the peaks appearing at the edges of the frequency interval. The same effect occurs for other windows that we have tried. Thus, by windowing the signal only the amplification of spurious peaks occurs.If on the other hand one uses a long segment the power spectrum of the same signal as used in With a long signal segment  is used.It may also be interesting to examine what should be the number of frequencies present for the double alpha to appear in the spectrum. It turns out that for a ff1 = 10.48Hz and f2 = 11Hz. With a sampling frequency fs = 100Hz and segment length of: 2.048, 4.096 or 8.192 s. Even with the shortest segment length the frequency resolution is sufficient to resolve the two main peaks. Each of the groups of frequencies was accompanied by ±5 accompanying frequencies, spaced 0.41 Hz apart so that in the two groups the frequencies were: f1i =10.48+0.41i, and fi2 = 11 + 0.41i, with −5≤i≤5. Altogether then there were 21 frequencies present covering a range of 5.89–12.53 Hz for the first group, and 8.59–13.05 Hz for the second group. The amplitude of the sinusoidal components was not constant it decreased from 1 for i=0 to 0.2 for i = ±5. As can be seen the frequency ranges of the two groups were overlapping and were sufficiently close together to result in a double alpha peaks.Up till now we have analyzed the power spectra obtained from a continuous or discrete set of frequencies with same amplitude sine waves. It is also worthwhile to examine the power spectrum obtained for a short duration segment when there are two dominant frequencies as this is what was expected when the double alpha spectra were discovered. Since in order for the double peaks to appear several (>10) frequencies are necessary we have computed a simulated signal that was composed of two sets of frequencies: The power spectrum obtained for this case is seen in When in an epoch of EEG signal several closely spaced frequencies appear so that a frequency band emerges this forms the conditions for the formation of characteristic double peaks spectrum.The double peaks appear as a result of interference from the spectra from individual frequencies which are widened by the finite epoch duration. And they appear at the boundaries of the frequency band because of Gibbs phenomenon .The emergence of double peaks depends sensitively on quantities like relative phases of the frequency components, amplitudes of these components and other parameters. This means not for every multifrequency signal will the double peaks appear. However, when they appear close to the ends of the band it is a strong indication that these are not due to real frequencies.T Hz, although the actual width depends on the used window.A single frequency for an epoch of duration T seconds contributes to power spectrum with a peak of width of about 1/fi = 1/T Hz.Two closely spaced peaks will result in power spectrum that will be the sum of their spectra, and if they are spaced closer than about half-width of their peaks their combined spectrum will be affected by interference. Hence, a simple criterium for the appearance of interference is that the frequencies are spaced closer than: ΔF(ω0) in Section “Power Spectrum for a Signal With a Frequency Band.” The primary fluctuations of Si or Ci have a half width of about 6. If we assume that the primary fluctuations of these terms are responsible for the formation of the side peaks located at the edges of the band then the width of the side peak (Δfw) may be related to epoch duration as: ΔwT = 2πΔfw ≈ 6.The peaks around 8 Hz and 13 Hz seen in fw) is: T), although somewhat narrower.The resulting frequency width (ΔfB Hz) must be larger than twice the side peak width: ΔfB = 2Δfw≈ 1.9/T Hz.For the two side peaks not to merge the minimum band width  that need to occur in a band ΔfB for the split alpha to emerge in the spectrum may be estimated from: N = On the other hand, if there are sufficiently many frequencies and they are spread over a band of width larger than ΔPlease note how narrow is the minimum band width. In EEG the split-alpha bands have much larger width, implying presence of much larger number of frequencies than the minimal 2.fi Hz apart.If there are more frequencies they may be spread over a wider band provided they remain spaced no more than ΔfB or they are spread over broader frequency range than ΔfB the split-alpha effect will not appear.If there are fewer frequencies than N in a band of width ΔB Hz and B < ΔfB then one can suppose that the peaks are due to two frequencies and are not a manifestation of a multi-frequency EEG event.On the other hand if one observes double peaks in an EEG segment and the side peaks are separated by From the above it follows that in order to check if an observed double peaks is due to a multiple frequency EEG or due to two frequencies it is necessary to compute power spectrum with a four times longer epoch.If we take a four times longer EEG segment then the minimum frequency band for such longer segment is four times narrower. Since taking four times longer segment does not increase the number of frequencies present  then it follows that in a four times narrower band there will be approximately four times less frequencies present and hence there will be too few frequencies to produce “split-alpha” like spectrum.Of course, it may so happen that the EEG will contain large number of frequencies and taking a four times longer epoch will not be sufficient, but in practice it is found that comparison of power spectra from the original and two times longer segment already provides clues to the nature of the observed double peaks event, and usually four times longer segment is sufficient to verify whether double peaks are due to multiple frequencies or two.T = 2.56 s . For short data segments both the frequency resolution of the spectrum is low  and there appears distortions in the calculated spectrum at the end of frequency band that are a result of spectrum leakage. These two factors work together to obliterate the real nature of the spectrum. In order to obtain spectrum free of this distortion care has to be taken that the FFT provides real information .split alpha” does not in fact enable any deeper insight into the nature of the examined EEG recording, it merely is a result of power leakage due to low resolution and properties of the Fourier transform. It thus has no diagnostic meaning to analyze double alpha other as a precaution against using too short data segment for the analysis or as an indication that the analyzed EEG signal contains multiple closely spaced frequencies (or a frequency band).The reported in the literature by split alpha” is a result of serious methodological errors, as it was shown in Section “Analysis of the Factors Leading to the Emergence of Double Alpha Feature in FFT Power Spectrum.”The misinterpretation by the authors  of EEG sthe split alpha spectrum can be generated by two or more independent and interconnected alpha wave generators located in different regions of the cerebral cortex, but not necessarily in the occipital cortex” and “a window size of 2 s was found to be optimal for this purpose”  and moreover postulate that “the localization of generators depends on the choice of the reference electrode.”In conclusions the authors stated that “Unfortunately, these conclusions might sound attractive and therefore might be repeated and propagated by readers which are not critical enough .Both cases discussed above illustrate the existence of generators localized in posterior areas, particularly at derivations O1 and O2. Alpha rhythms can be also generated in other parts of the brain. The coexistence of several generators was demonstrated in the third patient, a 54-year-old woman [see Figure 4 in .” and more: “In addition, other generators were identified when the reference was placed on the neck, with one at P8 (with maximum strength at 9–10 Hz) and another at O2 (with maximum strength at 11–12 Hz). These DTF results changed dramatically when the signal was rereferenced to the linked earlobes [cf. Figure 6B in .”To illustrate above some citations from the paper split alpha” made without the examination of the sources of such double peaks emergence can lead to incorrect conclusions.This illustrates that the attempts to assign physiological meaning to the events of “split alpha” generators localization as well as other methodological bugs are out of the scope of this paper. False conclusions such as, i.e., “influence of reference electrode on generator localization” are more than obvious since understanding the role of reference electrode is a fundamental to anyone attempting electrophysiological measurements in biomedical engineering. In any case the reference electrode can not influence localization of generator in the brain.We do not comment on any statements provided in the cited paper regarding neurophysiological interpretations of results. Also, the issue of property of application of DTF method for “The above analysis and conclusions authorize us to some general remarks on EEG analysis. Visual inspection of EEG recordings in the time domain is an empirical science and requires a considerable amount of clinical and neurophysiological knowledge. Any methods of automatic analysis can serve as a support which might be helpful in EEG recording evaluation but only in case when all shortcomings and properties of this method are very well understood. FFT analysis is a good example and from the very beginning an assumption that EEG is a phenomenon to which Fourier transform can usefully be applied was questionable and spectral analysis of EEG has to be applied and interpreted very carefully. It is not possible to assume that the spectra show “true” EEG features without a deeper analysis of the EEG signal and the conditions in which the spectra were obtained. In a sense the EEG signal is not a good candidate for a fully automatic spectral analysis as it is easy to obtain completely incorrect results (as we have shown above).split alpha” is not an exception in the area of incorrect use of automatic EEG signal analysis, however, it is strongly worth to clarify these errors because definition of “new phenomena” such as “split alpha” and identification by authors of “new generators” in the brain the localization of which may change due to a change of electrode selected for reference does not progress the understanding of the nature of EEG and may easily lead others to pursue non-existing phenomena.The paper on “split alpha” described in We have shown the rationale behind a “new phenomenon” of so called “Therefore, a power spectrum of a signal which contains a band of frequencies results in the emergence of peaks in the spectrum at the edges of the frequency band. These peaks have no relation to any frequencies of the signal and are an effect of spectrum leakage. Any attempt to use it to localize generators of alpha activity in brain is pointless.Hence, the emergence of peaks at the ends of a frequency band is a spurious effect caused by the leakage of power in the spectrum obtained from a discrete, short epoch EEG recording. It is important that there should be multiple frequencies (or a continuous frequency band) present in the recorded segment as this is the factor that leads to the emergence of double peaks located off-center, close to the ends of the band. The same effect of double peaks emergence is not a feature of the alpha frequency band, it may appear for any other band too, provided that there is concentration of frequencies sufficiently close together (a band of frequencies).At the end one might point the following highlights:split alpha” can appear in the form of two spurious peaks with no relation to any frequencies of the signal and is an effect of spectrum leakage.1. The double alpha EEG spectra called as “2. Double peaks like spectrum in any frequency band may be a result of FFT method properties when applied to short time signal of multiple frequencies, i.e., Gibbs phenomenon.3. The automatic methods available in standard packages of numerical procedures, even dedicated for EEG analysis, can not be “blindly” used for calculations and making automatic inferences about the underlying brain activity.ewa.zalewska@ibib.waw.pl.The datasets presented in this article are not readily available because the manuscript contains theoretical calculations and analysis on simulated data. Requests to access the datasets should be directed to EZ, The author confirms being the sole contributor of this work and has approved it for publication.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Bioelectromagnetics published by Wiley Periodicals, Inc.The expected imminent widespread use of electromobility in transport systems draws attention to the possible effects of human exposure to magnetic fields generated inside electric vehicles and during their recharge. The current trend is to increase the capacity of the battery inside the vehicles to extend the available driving range and to increase the power of recharging columns to reduce the time required for a full recharge. This leads to higher currents and potentially stronger magnetic fields. The Interoperability Center of the Joint Research Center started an experimental activity focused on the assessment of low‐frequency magnetic fields emitted by five fast‐charging devices available on the market in recharge and standby conditions. The aim of this study was to contribute to the development of a standard measurement procedure for the assessment of magnetic fields emitted by direct current charging columns. The spectrum and amplitudes of the magnetic field, as well as exposure indices according to guidelines for the general public and occupational exposure, were recorded by means of a magnetic field probe analyzer. The worst‐case scenario for instantaneous physical direct and indirect effects was identified. Measurements within the frequency range of 25 Hz–2 kHz revealed localized magnetic flux density peaks above 100 μT at the 50 Hz frequency in three out of five chargers, registered in close proximity during the recharge. Beyond this distance, exposure indices were recorded showing values below 50% of reference levels. Bioelectromagnetics. 2020;41:308–317 © 2020 The Authors.  This study specifically focuses on the assessment of low‐frequency magnetic fields emitted by devices used for the fast charging of electric vehicles (EVs). The Joint Research Center (JRC) conducted a measurement campaign on five direct current (DC) fast chargers in standby condition and during the quick recharge (up to 50 kW). Measured values of the magnetic flux density (B‐field) were compared with reference levels (RLs) and action levels set out, respectively, for general public exposure with the Council Recommendation 1999/519/EC EC, . The EurBiological effects related to chronic exposure to EMFs have been reviewed by several international bodies that agree with the World Health Organization in recognizing that the scientific evidence could not confirm any correlation between exposure and long‐term adverse health effects WHO, . The IntOn the contrary, low‐frequency magnetic fields may represent potential electromagnetic compatibility (EMC) threats to equipment such as passive medical devices that are worn on the body or active implanted medical devices (AIMD) [Ruddle et al., The scientific literature includes some studies regarding the electromagnetic environment inside conventional, hybrid, and EVs [Moreno‐Torres et al., 3 circa and the declared resolution is 1 nT. It is capable of performing measurements both in the frequency domain and in the time domain. When the probe is used for spectral measurements, the samples are collected and processed by fast Fourier transform. Its internal software automatically calculates the total integration of the field over the selected frequency range and compares the result with the threshold set by the 1999/519/EC recommendation [EC, jX is the field strength at frequency j, and AL(jX) is the field strength RL at frequency j [ICNIRP, The test was conducted by means of a low‐frequency electric and magnetic isotropic tri‐axial field probe , which is designed according to the requirements of the IEC 61786‐1 standard IEC,  for meas ICNIRP, . This fo ICNIRP, . The WPMt is time, iA is the amplitude of the ith harmonic component of the field, iEL is the exposure limit at the ith harmonic frequency if, and θi, φi are phase angles of the field and phase angles of the filter at the harmonic frequencies, as indicated in ICNIRP [In Equation , t is tin ICNIRP . Equation ICNIRP  recommenn ICNIRP  for geneFive DC fast charging columns, available on the market, were tested inside the Interoperability Laboratory of the Joint Research Center . The chargers were equipped with combined charging system and CHAdeMO charging options and they were connected to the JRC electricity grid providing 400 V AC by means of a max 125 A, 50 Hz wall socket [Trentadue et al., A full characterization of the space around the chargers was accomplished, assessing the background environment as well. Background measurements were performed for both electric and magnetic fields. Electric fields are very easily perturbed by humidity variations and by the presence of conductive objects, such as poor electrical conductors, buildings, trees, and people. A minimum distance of 2 m between the operator and the probe is required IEC, , leadingThe measurements were conducted in two different operating conditions: standby and during the recharge at full load. To capture the worst‐case scenario with high currents and high values of B‐field, measurements were performed within a time interval during which the delivered power is stable and close to 50 kW. This condition was reached during a recharge between 10% and 50% of the state of charge, depending on the vehicle. The vehicle was placed at a distance of 1 m from the charging column. The adopted strategy foresaw a frequency domain assessment, which searched for maximum magnetic field points or “hot spot” identification as a rapid scan of the device under test (DUT) and a spatial assessment of the spectrum with a fixed maximum threshold at a fixed distance. This measurement methodology was necessary to detect direct and indirect effects with a possible instantaneous impact on human health, such as interference with electronic medical devices. Field strengths above the RLs at the position of the device or its sensing leads (when present) may result in a malfunction, which would represent a risk to people wearing them. In such a case, the spatial average foreseen in the IEC 61786‐2 standard (see Appendix) would not be an effective constraint, while the proposed approach, albeit conservative, would be more adequate. Therefore, a grid of measurement points was defined to take into account the spatial non‐uniformity of the field and to simulate a possible exposure situation for generic users, workers, and any person located within the vicinity of the charging column. Measurement points were distributed according to the geometry of the charger's shell, with more being placed in close proximity of the charger. The measurements were performed on each side of the charging column at three different distances between the surface under test and the center of the probe . The number of measurement points varied with the size of the column and detected field levels. Thus, at a distance of 7.5 cm, more linearly distributed points were considered, while fewer points were considered for greater distances where the field intensity decreased. Figure The set frequency range (from 25 Hz up to 2 kHz) was considered a good compromise between the limitations of the available probe and range of interest for the measurement for both operating conditions (standby and recharge at full load). A first rapid scan of the DUT was performed with the probe placed at a minimum distance of 7.5 cm from the charger. Although these measurements were not representative of the calculated average over the human body because the distance between probe and DUT was too short, they revealed the maximum values of B‐field that a generic user could experience during fast charging.For each charger, background measurements of magnetic and electric fields were performed with the DUT switched off. Recorded wideband values of B‐field did not exceed 40 nT while the electric field showed values below 0.6 V/m.In all chargers' assessment in the frequency domain, the highest peaks of B‐field were recorded at a frequency of 50 Hz followed by the harmonics of this fundamental frequency, confirming that the predominant magnetic field waveform for these devices was the sinusoidal waveform at the power frequency. Depending on the charger, the harmonic content was very different as well as the point where the highest peaks of the magnetic field were recorded. This was mainly due to the internal design of each charger, but it was also related to the materials used for the outer shell. Figure Figure In the standby condition, the B‐field was measured at the same worst‐case positions identified during the recharge at full load. Figure Table At the time of the test campaign, the probe for static magnetic fields was not available. Nevertheless, the resulting stray magnetic field produced by the DC current along the charging cable was considered to be far below the RL reported in the 1999/519/EC recommendation [EC, Spot measurements with the WPM were performed, especially at points of the maximum magnetic field. The results, reported by the instrumentation's software as a percentage, refer to Equation  and to RA reproducible measurement procedure was developed as an approach for the assessment of magnetic fields emitted during fast charging. Our measurement protocol takes into account the worst‐case scenario for instantaneous physical direct and indirect effects, particularly in relation to vulnerable users . It also provides a robust test procedure for general public exposure. Indeed, the identification of the point of maximum field and its comparison with a fixed maximum threshold at a fixed distance is proposed to be effective in avoiding potential EMC threats to medical equipment that can happen instantaneously. The spatial assessment of the emitted spectrum takes into account spatial non‐uniformity. Measurements with WPM executed at fixed points, considered representative after the “hot spots” assessment, take into account temporal variations over an extended time interval, and they could be useful for determining if RLs of the 1999/519/EC recommendation [EC, All the chargers were tested according to the principles of measurements for a magnetic field defined in the IEC 62110 and IEC 61786‐2 standards. The B‐field values measured at a distance of 20 cm were far below the RLs of the 1999/519/EC recommendation EC,  for workSpatial averages and temporal monitoring with combined use of dosimeters may be appropriate for the development of a measurement protocol for full characterization of the electromagnetic environment and for exposure assessment. Considering possible future scenarios, workers and/or ordinary users may be in recharge stations with hundreds of fast chargers. Hence, spatial and temporal combinations of fields should also be evaluated over an extended time frame in order to detect any peak during prolonged exposure. New legislative developments are expected soon. Associated technologies for battery charging such as DC fast charging columns  are continuously and rapidly evolving. A new generation of high power charging (HPC) is about to enter the market with power levels up to 350 kW to reduce the recharging time and concern about limited driving range. Higher power requires less time required for a full recharge, but also higher voltage and higher variable currents can lead to possible intense and time‐varying fields. A more extensive test campaign has just begun on HPC prototypes currently available at the Interoperability Center in Ispra in cooperation with ENEA, the Italian National Agency for New Technologies, Energy and Sustainable Economic Development. Exposure scenarios related to vehicles will be the subject of further studies. Moreover, tests in real outdoor conditions are under discussion to increase knowledge and trust in a possible future scenario with a higher concentration of fast chargers, even in urban areas.Supporting information.Click here for additional data file.Supporting information.Click here for additional data file.


We study the continuity of many channel parameters and operations under various topologies on the space of equivalent discrete memoryless channels (DMC). We show that mutual information, channel capacity, Bhattacharyya parameter, probability of error of a fixed code and optimal probability of error for a given code rate and block length are continuous under various DMC topologies. We also show that channel operations such as sums, products, interpolations and Arıkan-style transformations are continuous. This paper is an extended version of our paper that is published in the International Symposium on Information Theory 2017 (ISIT 2017) (o) . TherefoNoisiness metric: For every W (see [The quantity f W (see ). TherefDefine the noisiness distance We have shown in  that (DMThe space of channels with input alphabet We define the equivalence relation The space of equivalent channels with input alphabet W with the For every Since any two equivalent channels have the same Blackwell measure, we can define the Blackwell measure of We have:A topology Every natural topology is onnected . On the anywhere . This imStrong topology on We associate -compact .The strong topology A is a subset of A is strongly open if and only if A is strongly closed if and only if We call open and closed sets in We have shown in  that Ts,d and T4 . On the anywhere ; hence, Noisiness metric: Define the noisiness metric on The metric topology on shown in  that TX,Topologies from Blackwell measures: The mapping Since In , we studThe total-variation metric distance The total-variation topology roved in  that if X is distributed as p and Y is the output of W when X is the input. The mutual information is computed using the natural logarithm. The capacity of W is defined as Let W under prior p is defined as:For every Clearly, W as:For every It is easy to see that It was shown in ,11 that n is the block length of M is the size of the code. The rate of An W is given by:The optimal error probability of The following proposition shows that all the above parameters are continuous:Proposition 2.We have:For every code For every Proof. I, its concavity in p and its convexity in W [C is the supremum of a family of mappings that are convex in W, it is also convex in W. For a proof of the continuity of C, see Z, p and in W can also be easily seen from the definition. ☐These facts are well known, especially the continuity of ity in W . Since CW and V as follows:If For every function It is easy to see that if For every two channels We define the channel product annon in .For every Channel interpolation arises when a channel behaves as  used in  to constNow, fix a binary operation ∗ on These operations generalize Arıkan’s polarization transformations .Proposition 3.We have:The mapping The mapping The mapping The mapping For any binary operation ∗ on For any binary operation ∗ on Proof. The continuity immediately follows from the definitions. ☐W. Therefore, we can define those parameters for any It is well known that the parameters defined in Proposition 4.We have:For every code For every Proof. I and Z. We will only prove the continuity of I since the proof of continuity of Z is similar.Since the corresponding parameters are continuous on R on Define the relation R-equivalence class of I is continuous on I is continuous on I is continuous on It is easy to see that With the exception of channel composition, all the channel operations that were defined in Let annon in .Therefore, if With the exception of channel composition, we can “quotient” all the channel operations of Proposition 5.We have:The mapping The mapping The mapping For any binary operation ∗ on For any binary operation ∗ on Proof. We only prove the continuity of the channel sum because the proof of continuity of the other operations is similar.f is continuous.Let R on Now, define the equivalence relation R-equivalence class of f defined on The discussion before the proposition shows that f on Notice that f on Now, since the mapping The following lemma provides a way to check whether a mapping defined on Lemma 6.Let Proof. I, C, Z, Since the channel parameters  n≥1 see , they arProposition 6.Let For every code For every Proof. I and Z are similar, we only prove the continuity for I.The continuity of Due to the distributivity of the product with respect to disjoint unions, we have:I is continuous on I is continuous on Therefore, R on R-equivalence class of I is a continuous mapping from I is continuous on Define the relation It is also possible to extend the definition of all the channel operations that were defined in Proposition 7.Assume that all equivalent channel spaces are endowed with the strong topology. We have:The mapping The mapping The mapping For any binary operation ∗ on For any binary operation ∗ on Proof. We only prove the continuity of the channel interpolation because the proof of the continuity of other operations is similar.Let Therefore, the space For every n is the unique integer satisfying Define the mapping f is continuous on f is continuous on Due to Proposition 3 and due to the continuity of R on Let R-equivalence class of f is continuous on Since Since Corollary 3.Proof. H is continuous by Proposition 7. We also have Fix The reader might be wondering why channel operations such as the channel sum were not shown to be continuous on the whole space R be the equivalence relation on One potential method to show the continuity of the channel sum on It was shown in  that theWe need to express the channel parameters and operations in terms of the Blackwell measures.The following proposition shows that many channel parameters can be expressed as an integral of a continuous function with respect to the Blackwell measure:Proposition 8.For every where Proof. By choosing any representative channel Proposition 9.Let For every code For every Proof. I is continuous on Z similarly.We associate the space Now, define the mapping Fix C is continuous on Similarly, we can show that For every Now for every Clearly It is worth mentioning that Proposition 6 can be shown from Proposition 9 because the noisiness topology is coarser than the strong topology.Corollary 4.All the mappings in Proposition 9 are also continuous if we replace the noisiness topology Proof. This is true because In the following, we show that we can express the channel operations in terms of Blackwell measures. We have all the tools to achieve this for the channel sum, channel product and channel interpolation. In order to express the channel polarization transformations in terms of the Blackwell measures, we need to introduce new definitions.Let o itself . For eveshown in  that a bBinary operations that are not uniformity preserving are not interesting for polarization theory because they do not preserve the symmetric capacity . TherefoLet ∗ be a fixed uniformity preserving operation on The probability distribution Clearly, gies see . For eveSince the product of meta-probability measures is continuous under both the weak-∗ and the total variation topologies , the (−,For every The probability distribution Define the mapping If For every Since the product of meta-probability measures is continuous under both the weak-∗ and the total variation topologies , the (+,Proposition 10.We have:For every where For every For every For every uniformity preserving binary operation ∗ on For every uniformity preserving binary operation ∗ on Proof. See Note that the polarization transformation formulas in Proposition 10 generalize the formulas given by Raginsky in  for binaProposition 11.Assume that all equivalent channel spaces are endowed with the noisiness/weak-∗ or the total variation topology. We have:The mapping The mapping The mapping For every uniformity preserving binary operation ∗ on For every uniformity preserving binary operation ∗ on Proof. The proposition directly follows from Proposition 10 and the fact that all the meta-probability measure operations that are involved in the formulas are continuous under both the weak-∗ and the total variation topologies. ☐Corollary 5.Both Proof. We can use the same proof of Corollary 3. ☐The continuity of the channel sum and the channel product on the whole product space


This study proposes a new method of visualizing the ambient dose rate distribution using artificial neural networks (ANNs) from airborne radiation monitoring results. The method was applied to the results of the airborne radiation monitoring which was conducted around the Fukushima Daiichi Nuclear Power Plant by an unmanned aerial vehicle. Much of the survey data obtained in the past were used as the training data for building a network. The number of training cases was related to the error between the ground and converted values by the ANN. The quantitative evaluation index (the root-mean-square error) between the ANN-converted value and the ground-based survey result converged at 200 training cases. This number of training case was considered a rough criterion of the required number of training cases. The reliability of the ANN method was evaluated by comparison with the ground-based survey data. The dose rate map created by the ANNs method reproduced ground-based survey results better than traditional methods. Nine years after the accident, the ambient dose rate (air dose rate) has been decreased by radioactive decay, decontamination work, and weathering effect within the 80-km radius zones from the FDNPP2. As a quick and efficient survey method, manned helicopters and unmanned aerial vehicles (UAVs) have been developed to visualize the environmental distribution of the air dose rate in the airborne radiation survey (UAV-survey) after the FDNPP accident4. UAVs are effective tools for data collection over wide areas that are located around FDNPP because a person does not have to approach a dangerous place6. However, a UAV-survey is less accurate than a ground-based radiation survey using a handheld survey meter because it has a long distance from the ground surface source.Large quantities of radionuclides were released into the atmosphere after the Fukushima Daiichi Nuclear Power Plant (FDNPP) accident in March 20117. Improving UAV-survey accuracy requires accounting for the topographic features in radiation survey areas. Some reports suggested that the topographic effect was corrected by published big topographical data, such as the digital elevation model (DEM) and the digital surface model (DSM)9. A conversion method using the maximum-likelihood expectation-maximization (ML-EM) method was recently proposed to convert the value measured from the sky into an air dose rate of 1 m above the ground level (agl.)11. The conversion using the ML-EM method requires the creation of many types of attenuation parameters to improve the conversion accuracy. This method is effective for conversion in complex terrain areas, such as mountains or forests, which could not be reproduced by conventional FSM methods. However, the decision on the parameters needs many on-site measurement experiments or simulation work.In a conventional approach, the count rates and the pulse height distributions collected by the UAV-survey are converted into air dose rates and deposition of radioactive cesium on the ground. In this approach, the ground is assumed to have a flat form, and this is called the flat source model (FSM)13. Simple and easy ANN software was recently published15. Moreover, the ANN method was applied to search for radiation sources for nuclear security16. Compared to the ML-EM method, the conversion by an ANN is expected to reduce both the workload of creating many parameters and the calculation time . The ANN is applied to the study fields of medicine, physics, etc. as a kind of deep learningWe developed herein a new conversion method using the ANN to improve the accuracy and the analysis time of the UAV-survey. This ANN method was optimized by evaluating the number of hidden layers constituting a network. In addition, we also evaluated the relationship between the number of data cases used for the training and the error between the ANN-converted UAV-survey and ground-based survey values. Finally, the ANN method validation was evaluated by comparison with the FSM and the ML-EM method.18. This learning is classified as a regression problem of supervised learning. The cascade correlation is a constructive learning rule and a supervised learning algorithm that constructs a feed-forward network. Learning starts with a minimal network consisting only of the input and output layers. Minimizing the overall error of a network, new hidden layers are then added step by step. The cascade correlation builds a network in which one hidden layer has one neuron. Figure In this study, the ANN was constructed using NeuralWorks Predict , a software that uses cascade correlation to determine the optimal network structure with a simple graphical user interfaceConversion of the input variable: The input variable is represented by some functions. The data with a high correlation between the input and target variables are normalized and added as the input data.Learning of the input and output layers: Training is first implemented only on the input and output layers without the hidden layer. The output layer is a sigmoid function recommended from NeuralWorks Predict.Addition of a hidden layer: If the index of the reliability (the correlation coefficient) of the output value in the training of former procedure 2) was not enough, one hidden layer would be added automatically. All hidden layers are tanh functions recommended from NeuralWorks Predict.Re-learning: Learning will be performed again with the added hidden layer. The connection is fixed between the hidden and input layers, and the weight values are not updated. One hidden layer will be added again if the output vale is not improved. When learning is judged to be sufficient, the hidden layer addition is stopped, as well as learning.The training set was randomly divided into two cases depending on the purpose of this method. In the ANN construction, 70% of all the training cases were randomly selected. The other training case was used to evaluate the calculation of the correlation coefficient with the target variable. The changes in the evaluation were observed each time the learning was repeated. Learning was stopped when the correlation coefficient stopped improving. The construction flow of the network is presented below and in Fig. r) which is defined as a criterion for sufficient learning. The learning was continued until no improvement of r was observed. r can be expressed as follows:n is the total number of data; x is the converted value; y is the ground-based survey value ; and 19. The objective function was cross-entropy with added ridge regression.The neural network was constructed with simple input variables and one hidden layer function for judging whether the UAV-survey data can be converted by the ANN. The output value of the network was compared with the target variable using the correlation coefficient (5. The dedicated radiation detector consisted of a LaBr3 (Ce) scintillation detector  around the FDNPP at the fiscal year of 2018 and 2019. The UAV was originally developed for spraying pesticides but was later adopted for radiation measurements. This UAV is operated manually during takeoff and landing and has a program operator for autonomous flight and an operator for the radiation detector. The UAV can conduct a programmed flight with the help of detailed self-localization using a real-time kinematic global positioning system. Its flight waypoints and altitude can be set. The detailed specifications of the UAV are given in a past researchTable −1, and 50 m agl., respectively. For the output value validation, the ground-based survey data (V1) were obtained using a handheld survey meter at the same time as the UAV flight. All data were obtained for less than 8 h on August 19, 2018. Each datum was averaged over a 10 m mesh.The test set different from the training set was used to evaluate the constructed ANN. The test set was obtained from Futaba-machi, which is located 3 km northwest from the FDNPP. This study area (1 km × 2 km) is still acknowledged as an evacuation area by the Japanese government. The flight line space, flight speed, and flight altitude of the UAV used were 50 m, 5 m sThe test set had 3442 cases Table . For comThe accuracy of the ANN method was expected to depend on the neural network condition . We conducted some verification tests to determine the effectiveness of the output validation by the neural network condition.r) value. This software has the option for which the maximum layer is limited. Nine different types of networks  were constructed by the training set to optimize the number of hidden layers of a network. The test set was converted using each network. We calculated the root–mean–square error (RMSE) for nine types of network as follows using Eq.  of the UAV-survey data in mesh i (−1: air dose rate at 1 m agl.); and Gi is the ground-based survey value (V1) in mesh i (−1).First, the output value validation was evaluated by limiting the number of hidden layers. NeuralWorks Predict automatically creates a hidden layer based on the correlation coefficient  Table a and tes11. The ML-EM method is a type of inverse estimation method that employs radiation information from various directions. The ML-EM method is theoretically expressed as follows by Eq. s by Eq. :3\documeFx is the attenuation rate due to air Fx and is calculated from the distance x (m) between i and j by using the particle and heavy ion transport code system (PHITS) developed by the Japan Atomic Energy Agency20. Fx was obtained from the decrease in the number of incident photons according to the distance from the point source of 137Cs. The calculation result yielded 1.97 and 0.010 as parameters Fθ is the attenuation rate due to the effect of the soil scattering calculated from the angle θ (deg) formed by i–j and the soil surface. Parameters A, Fθ was evaluated using the PHITS from the decrease in the number of incident photons when the angle between the soil surface and i–j was changed upon centering on the point source of 137Cs. Fh is the attenuation rate due to forest shielding calculated from the distance h (m) that passes through the forest area between i and j. h is calculated using the DEM and the DSM. Accordingly, 0.061 was used for parameter 11 showed that Fh depended on the tree height.Call: 50–2800 keV) was converted into the air dose rate (Y) using a conversion factor (CD: 0.00028 −1 cps−1) and an attenuation factor (AF: 0.0061 m−1). The CD was obtained in advance by comparing the count rate in the calibration area at altitude Hstd (m) with that measured using a survey meter on the ground. The AF was calculated from the data obtained by varying the flight altitude on the ground from 20 to 150 m. Equation  is the flight altitude above the ground.The count rate obtained by a dedicated UAV-survey detector . The spatial resolution of the resulting contour map for the air dose rate was 10 m × 10 m.Mapping was performed by supplementing unmeasured areas via the interpolation of the measured results. Various methods  were proposed for the interpolation, but the kriging method, which linearly assigns weights to the values of the measurement points and in inverse proportion to the distance, was applied herein to the UAV-survey data. The kriging method is easy to use when analyzing a large amount of data because its parameter setting is simpleG) were compared with the air dose rate calculated using the UAV-survey (Y). Both data were compared by visualizing the unevenness using a scatter diagram. The relative deviation (RD) of each measurement cell was calculated as follows to evaluate the accuracy of the scheme used in this study:The ground-based survey data  and the output values under the condition of hidden layers in the network. The RMSE value tended to decrease with the layer increase, although some variation exists. This result suggests that the conversion accuracy improved as the number of hidden layers increased. In the case herein, a network with 12 hidden layers was most suitable for conversion from the UAV-survey data to the air dose rate on the ground. From this result, the network shown in Fig. Figure RMSE was calculated by comparing the air dose rate with the ground-based survey data that differed from the random training set as an evaluation index. Figure RMSE variation with an increasing number of random training cases. Both RMSEs converged when the number of training cases was approximately 200 or more in random training. The RMSE with two types of different training data sets saturated at 200; thus, this number of training case was considered as a rough criterion for the required number of training data set. In addition, the RMSE values were saturated with a different value, which was expected to affect the statistics error depending on the radiation intensity.Two types  of the random training set were created to evaluate the relationship between the number of training cases and the error between the output value by the ANN and the ground-based survey value. The 6. The east side used as a residential region of this study area had a relatively high air dose rate of 2.0–10 −1), while the forest region in the western area had a relatively low air dose rate of 0.5–3.0 −1. The incline of the air dose rate for this study area was large compared with those from the other regions surrounding the FDNPP.Figure 21. On the contrary, the ML-EM method used the surrounding topographical and multiple measurement information. Therefore, the bias expressed as the RMSE or RD was better than the FSM. The ANN bias was reduced in the learning process to improve the error between the ground-based survey and output values. Figures RD histograms for quantitatively evaluating this tendency. Table Figure RD of the ANN and ground-based values. The number of training cases was classified and counted every 10 m at altitude, every 5000 cps of the total count (P1 + P2 + P3 + P4), and every 1 μSv h−1 of the ground-based survey value (T1). The histograms show a few changes in the RD and RMSE with the change of the number of training cases. Table RMSE between the ground-based survey value and the ANN value, and the interquartile ranges of 25%, 50%, and 75% to quantitatively evaluate this tendency. The RMSE decreased as the number of training cases increased. As a result, the training case number which is necessary to calculate reliable converted value was 200 as well as the simulated verification as shown in Fig. For a detailed evaluation of the ANN accuracy, the correlation with the ANN result and the number of training cases were evaluated and shown in Fig. In this study, we attempted to establish a new conversion method of the UAV-survey using published ANN software. The big data of the UAV-survey that we acquired after the FDNPP accident was used as the ANN training set. Constructing an ANN using the training set around the FDNPP resulted in an optimized hidden layer with 12 layers. The number of training cases was related to the error between the ground value and the ANN-converted value. The evaluation index between the ANN-converted value and the ground-based survey converged at 200 training cases; hence, this number was considered as a rough criterion of the required minimum number. It is thought that the number of training cases can be used as an index to evaluate the reliability of the ANN-converted value. The dose rate map made by the ANN method reproduced ground-based survey results much better than the traditional methods. However, this study used only the basic input variables in the radiation measurement and did not use terrain and photographic data as the input variables. The conversion accuracy is expected to be improved when these input variables are added. Future research will focus on the application of ANN conversion using terrain and photographic data and evaluate the effect of each input variable on conversion.