According to the American Cancer Society, breast cancer is the second largest cause of mortality among women after lung cancer. Women’s death rates can be decreased if breast cancer is diagnosed and treated early. Due to the lengthy duration of manual breast cancer diagnosis, an automated approach is necessary for early cancer identification. This research proposes a novel framework integrating metaheuristic optimization with deep learning and feature selection for robustly classifying breast cancer from ultrasound images. The structure of the proposed methodology consists of five stages, namely, data augmentation to improve the learning of convolutional neural network (CNN) models, transfer learning using GoogleNet deep network for feature extraction, selection of the best set of features using a novel optimization algorithm based on a hybrid of dipper throated and particle swarm optimization algorithms, and classification of the selected features using CNN optimized using the proposed optimization algorithm. To prove the effectiveness of the proposed approach, a set of experiments were conducted on a breast cancer dataset, freely available on Kaggle, to evaluate the performance of the proposed feature selection method and the performance of the optimized CNN. In addition, statistical tests were established to study the stability and difference of the proposed approach compared to state-of-the-art approaches. The achieved results confirmed the superiority of the proposed approach with a classification accuracy of 98.1%, which is better than the other approaches considered in the conducted experiments. One of the most frequent types of cancer in women, breast cancer, develops in the breast and then spreads to other regions of the body . Breast Several imaging methods exist for diagnosing breast cancer at an early stage. In clinical practice, breast ultrasonography is one of the most often utilized diagnostic tools ,7. BreasUltrasound is a powerful diagnostic technique in dense breast tissue, often detecting breast cancers that mammography misses . UltrasoDeep learning has recently demonstrated significant improvement in several areas, including cell segmentation , skin meWithin the scope of this paper, the following issues are examined: (i) As a model based on a smaller number of images produces inaccurate prediction, the available ultrasound data are insufficient for building a good deep model. (ii) Misclassification often occurs because of the great degree of resemblance between benign and malignant breast cancer cancers. (iii) Incorrect predictions are made because the features retrieved from images include redundant and unimportant data. To address these issues, a novel approach is proposed based on deep-learning-based and metaheuristic optimization for breast cancer classification from ultrasound images.The remaining sections of this article are presented as follows. Researchers have presented several automated approaches for breast cancer categorization using ultrasound images ,45. ThesThe radionics classification pipeline was first presented by the authors in  and is bA contextual level set technique was described for breast cancer segmentation in . A netwoBreast MRI slices can be analyzed using a computerized method developed by the authors in  to find With edge detection and the U-NET model, the authors in  proposedAccording to the methods discussed, researchers often overlook the preprocessing stage. The researchers often began with the segmentation process and then moved on to the feature extraction phase. To enhance their categorization accuracy, several of them tried feature fusion. Unfortunately, they did not put much effort into picking the best features. Computational time is now a significant consideration they did not consider. In this study, we put forth a best practice for classifying breast masses using a combination of several deep-learning features. This section describes the proposed framework for ultrasonic breast imaging breast cancer categorization. For a visual representation of the proposed framework’s structure, see Recent years have seen significant research on data augmentation’s role in deep learning. However, available datasets in the medical sector are considered to be a low resource, which is a problem for deep learning, as it requires a large number of training samples. Because of this, a data augmentation process is required to boost the variety of the primary dataset. When validating these results, the BUSI dataset is consulted. There are 780 images (500 × 500) in the dataset, with 133 “normal” images, 210 “malignant” images, and 487 “benign” images , as showTransfer learning (TL) is a machine learning technique that applies a previously learned model to a new problem. From a practical aspect, a supervised learning agent’s sampling efficiency may be vastly improved by reusing or transferring data from previously taught tasks for the newly learned tasks . Deep feThe proposed feature selection method selects the most significant features that can be used to robustly categorize the breast cancer case. The classification of the selected features is performed in terms of a convolutional neural network (CNN). The performance of this CNN is boosted by utilizing the proposed optimization algorithm for optimizing the parameters of the CNN. The optimized CNN is then used to classify the selected features. The output of the optimized CNN is analyzed and evaluated using several criteria and is finally compared to the recent classification models to demonstrate its effectiveness and superiority.The proposed optimization algorithm is based on two optimization algorithms, namely, dipper throated optimization (DTO) and particle swarm optimization (PSO) algorithms, which swaps between the two algorithms dynamically and is denoted by dynamic DTPSO (DDPSO). The proposed algorithm exploits the advantages of both algorithms to improve the exploration and exploitation of the optimization process and thus finds the best solution optimally. The steps of the proposed algorithm are shown in the flowchart depicted in The feature selection process proposed in this work is based on the proposed optimization algorithm but with converting the resulting solution to binary. Therefore, the proposed feature selection method is denoted by binary DDTPSO (bDDTPSO). The conversion to binary is based on the sigmoid function that converts the result of the continuous DDTPSO into binary. The proposed feature selection algorithm is presented in Algorithm 1. This algorithm is used to select the significant features resulting from the feature extraction process performed using the GoogleNet deep network. The selected features are then used to classify the input ultrasound image of a breast to determine the case of cancer.    Algorithm 1: The proposed binary DDTPSO algorithm.Initialize the parameters of DDPSO algorithm1: Convert the resulting best solution to binary 2: Evaluate the fitness of the resulting solutions3: Train KNN to assess the resulting solutions4: Sett = 15: whiledo6: Run DDPSO algorithm to obtain best solutions 7:  Convert best solutions to binary using the following equation:                           8:  Calculate the fitness value9:    Update the parameters of DDTPSO algorithm10:  Updatet = t + 111:  end while12: Return best set of features13: The specifications of the machine used to run the conducted experiment are: Windows 11 PC with Core(TM) i5-2430M CPU @ 2.40 GHz and 16 GB of RAM and NVidia GPU with 8 GB memory. Python 3.10 is also used to implement the proposed methodology. A freely available dataset on Kaggle is used to train the proposed methodology for classifying breast cancer cases. The dataset’s training, validation, and testing subsets are all assigned identical random sizes. The testing set is used to evaluate the effectiveness of the provided model, whereas validation is employed while calculating the fitness function for a given solution.The experimental setup for the proposed approach is shown in M, the best solution at run j is denoted by N, and the predicted and actual values are denoted by The achieved results are assessed using the criteria presented in The evaluation of the feature extraction was performed, and the results are presented and discussed in this section. Once the features are extracted, the best set of features that can be used to classify the input image are selected. The feature selection is performed using the proposed algorithm presented in the previous section. Eleven other feature selection algorithms are employed for comparison to prove the effectiveness and superiority of the proposed feature selection method. The evaluation of the results achieved by the proposed and other feature selection methods is presented in In addition, a statistical analysis is applied to study the stability of the proposed feature selection methods, and the results are listed in On the other hand, two statistical tests were conducted to study the statistical difference between the proposed feature selection method and the other feature selection methods. The first test is the one-way analysis of variance (ANOVA) test, and the other test is the Wilcoxon signed-rank test. The results of these tests are presented in A more in-depth analysis of the results achieved by the proposed feature selection method is presented in terms of the plots shown in The best set of features selected by the proposed feature selection algorithm are then used to train the classification models. In this work, four classifiers are evaluated to choose the best classifier. These classifiers are convolutional neural networks (CNN), neural networks (NN), support vector machines (SVM), and K-nearest neighbors (KNN). The results of these classifiers are presented in As the CNN model is adopted for the classification of the input images, this model is subjected to optimization using the proposed DDTPSO algorithm to improve its performance. The optimization of this model is performed using four optimization algorithms in addition to the proposed optimization algorithm. The results of the optimized CNN using these optimization algorithms are presented in To further analyze the proposed optimization algorithm’s performance, the optimized CNN’s results using different optimization methods are analyzed statistically to show the proposed algorithm’s superiority and statistical difference. The statistical difference of the proposed optimization algorithm is studied in terms of the ANOVA and Wilcoxon tests, similar to the study performed on the proposed feature selection method discussed in the previous section. The results of these tests are presented in Another in-depth analysis of the results achieved by the proposed optimization method for CNN is presented in terms of the plots shown in On the other hand, the convergence curve is depicted in p value is less than In addition, the linear regression test is performed to study the relationship between the proposed and other approaches. The regression test results are presented in This paper proposes a fully automated technique to analyze ultrasound images for signs of breast cancer. The proposed approach relies on a series of consecutive procedures. At first, a GoogleNet deep learning model is applied to the breast ultrasound data, enhancing and retraining it. Therefore, a novel optimization technique is derived from the dipper throated optimization algorithm and the particle swarm optimization algorithm to select the best set of features. This set of features is used in classifying breast cancer cases. Experimental results showed that the proposed approach achieved the highest accuracy, at 98.1% (using the selected features and CNN classifier). Compared to more modern methods, the outcomes are better when the proposed framework is used. This work’s strengths lie in the enhanced dataset, thereby increasing the training strength. In addition, the irrelevant features were eliminated through the selection of best features using a novel feature selection algorithm. In the future, two main steps can be considered: utilizing a dataset of larger size and (ii) developing a new CNN model specifically for breast cancer classification.


During inhalation, progeny nuclides accumulate in the respiratory tract while most of the radon gas is exhaled. The decay of progeny nuclides in the lung together with the high radiosensitivity of this tissue lead to equivalent doses implying a significant cancer risk. Here, we use gamma spectroscopy to measure the attachment of radon progeny on an air-ventilated filter system within a radon enriched atmosphere, mimicking the respiratory tract. A mathematical model was developed to describe the measured time-dependent activities of radon progeny on the filter system. We verified a linear relation between the ambient radon activity concentration during exposure and the amount of decay products on the filter system. The measured activities on the filters and its mathematical description are in good agreement. The developed experimental set-up can thus serve to further investigate the deposition of radon progeny in the respiratory tract under varying conditions for determination of dose conversion factors in radiation protection, which we demonstrate by deriving dose estimations in mouse lung.Radon ( As 222Rn is an inert gas, it does not attach to aerosols and the walls of the respiratory tract. Therefore, most of it is directly exhaled and simulations show that only about 1% of the inhaled gas dissolves in blood from where it is distributed all around the body5. In contrast to 222Rn, its decay products are solids under normal exposure conditions so that they may attach to aerosols they get in contact with6. Directly after decay, the α-emitting decay products 218Po and 214Po are highly charged8 but get rapidly neutralized via mechanisms as electron scavenging, electron transfer and ion recombination12, so that most of them carry no charge at the end of their recoil path13. During inhalation the progeny radionuclides are deposited in different regions of the respiratory tract depending on their size and shape as well as the physiological properties of the respiratory tract as e.g. morphology and air-flow velocity in different regions14. Larger particles are more likely to be exhaled compared to smaller unattached particles that get nearly completely adsorbed. Once deposited in the respiratory tract, the radon progeny radionuclides decay there because the clearance processes  are much slower than the half-life of all radon progeny until 210Pb15. Therefore, no efficient clearance from the respiratory tract occurs and the decay energy of the nuclides that is released until they decay to 210Pb is deposited in the respiratory tract.The radioactive noble gas 222Rn decay chain is shown in the following16:The relevant part of the 17, which needs to be taken into account when calculating the equivalent dose. In good approximation only α-emitting particles are accounted for the calculation of the absorbed dose. All decay products following 210Pb are neglected due to the long half-life of this nuclide18.During decay, the α-emitting isotopes are responsible for most of the deposited energy while the β- and γ-emitting isotopes are responsible for about 10% of the cumulative decay energy. Moreover, α-particles with a high linear energy transfer (LET) exhibit a higher biological effectiveness than β-particles or γ-radiation. This is also represented by the higher radiation weighting factor of 20 for this radiation type, compared to a radiation weighting factor of 1 for β-particle or γ-radiation222Rn exposure, the progeny radionuclides account for more than 95% of the effective dose , whereby the 222Rn gas itself accounts for less than 5%. In addition, the lung equivalent dose makes up for over 95% of the effective dose18, which explains why radon and its progeny are classified as carcinogenic for the lung19. Thereby the lung is defined as the part of the respiratory tract starting from the trachea14.With each breath, further radon progeny radionuclides accumulate in the respiratory tract and deposit their decay energy there. Simulations show that following 21. They are validated by some experimental data on humans for different exposure scenarios22. But still no experimental set-up exists in which parameters such as breathing rate, geometry and air-flow velocity in the respiratory tract as well as the radon concentration and particle size distribution in air can be controlled to experimentally investigate the distribution of radon progeny in the respiratory tract. Therefore, our aim is to build an experimental set-up in which a simple mechanical surrogate of the respiratory tract is exposed in a well-defined adjustable atmosphere. This would allow to systematically test the theoretical models with a high number of experiments under the same, controllable conditions, which are not affected by e.g. the individual morphology of the respiratory tract. In a next step, readjustments of model parameters could be introduced to reflect individual variations.Nowadays, detailed theoretical models on the deposition of radon progeny in the respiratory tract exist to calculate the dose-distribution and the corresponding riskThis manuscript presents a first step to such a mechanical set-up. Here, radon containing air is pumped through a filter system, on which progeny radionuclides get deposited like they do in the respiratory tract. First measurements were conducted under well-defined exposure conditions where only the radon activity concentration and relative humidity in the exposure atmosphere were varied, whereas the other parameters were kept constant. This allowed us to develop a mathematical model to consistently describe the time-dependent distribution of radon and its progeny in the overall experimental set-up and especially on the ventilated filter system.23 at different controllable radon activity concentrations for one hour, during which the radon activity concentration, relative humidity, temperature and air pressure were recorded. Afterwards, the activity of the γ-emitting isotopes 214Pb and 214Bi on the filter system was measured until the background level was roughly reached again. The time dependent activity curves allowed us to determine the amount of deposited progeny on the filter system and correlate it to the radon activity concentration and other impacting factors during exposure . Using a set of differential equations, the distribution and dynamical evolution of all decay products in the radon chamber were analysed including the concentration of progeny in the atmosphere, the attachment on the air-flowed filter system and the attachment on the chamber walls. To further verify the mathematical model, activity measurements with a filter system attached to the chamber walls were conducted to independently measure the wall attachment and compare it to the results suggested by the measurements of the air-flowed filter system.During the experiment, the filter system adsorbs progeny radionuclides that are pumped through with a defined air-flow which reflects the very basic function of the adsorption of progeny in the respiratory tract during breathing. Still, many characteristics of the respiratory tract are missing in this very rudimentary mechanical surrogate. It does not account for the breathing cycle and changing air-flow velocities in combination with the geometry of the respiratory tract. Instead, all radon progeny nuclides are deposited on the filter system. The filter system was exposed within an in-house designed radon chamberThe model allows to consistently describe and understand the experimentally gained data for progeny deposition on an air-flowed filter system in a fully characterized closed system. Here, all radon progeny nuclides are sampled together on the filter system. Therefore, overall energy deposition (given in Gy) on the filters instead of locally applied doses, which would depend on activity size distribution, the respiratory tract morphology and the radiation sensitivity of different cell types, is considered throughout the manuscript.24, but via the complete mathematical description of our experimental system, we have access to all related quantities. This allows us to also determine the time-dependent distribution of radon progeny radionuclides in the experimental set-up  and thus a rigorous analysis of the dosimetric data. Therefore, we can determine what part of radon in air arrives on the filter system and how it depends on impacting factors.The model is a first step for experimentally measuring deposition of radon progeny under varying exposure conditions in the respiratory tract and, in a next stage of development, may complement theoretical simulations. So far, this manuscript deals with overall energy deposition on an air-flowed filter system and the comprehensive characterization of the exposure system. Employing aerosol filters to sample radon progeny is the current gold standard−1 from the upper to the lower end of the centrifuge tube through the filter system, which is in the same order of magnitude like the respiratory minute volume of a mouse. A schematic drawing of the set-up is shown in Fig. An air-flowed filter system was exposed in an in-house constructed radon chamber. The filter system consists of a 200 mesh stainless steel grid with a wire strength of 0.053 mm  positioned over a 0.4 mm thick glass fibre filter with a pore size of 500 nm . The two filters have a radius of 27.2 mm each and are separated by a thin wire with a diameter of 0.8 mm. The system was positioned at the upper end of a 50 ml centrifuge tube , on whose lower end a 6 mm wide hole was drilled to connect it to a pump  via silicon tubes . The pump produced a defined air-flow of 193.4 ± 2.8 ml min222Rn containing air, so that pure radon gas was induced in the otherwise sealed chamber. The filter system was exposed for 1 h at constant radon activity concentrations at a preselected level between 0.3 and 6 MBq m−3. For experiments with a lower relative humidity during exposure, the radon chamber was flushed for 15 min with dry compressed air before the radon was introduced and the pump was activated. The radon activity concentration and relative humidity in the chamber were tracked during the time of exposure .The prepared centrifuge tube was placed in a rack in the cylindrical radon chamber that has a height of 14.6 cm and radius of 8.5 cm. Afterwards, the chamber was sealed and the voltage applied to the pump, so that air was pumped through the system and recycled in the chamber. In parallel, the chamber was once flushed with 0.7 l of filtered 214Pb and 214Bi at different time points after exposure with a high purity Ge-detector (BE3825 Mirion Technologies (Canberra) GmbH, Rüsselsheim, Germany). Therefore, the filters were placed in a petri dish (ø 6.0 cm) to avoid surface contamination of the detector. Afterwards γ-spectra were recorded for up to 4.5 h after end of exposure with varying measurement intervals between 2 and 20 min, depending on the γ-activity.At the end of the exposure, the radon chamber was flushed with fresh air for 5 min and the filter system (mesh and glass fibre filter) was removed from the centrifuge tube to record γ-spectra of 214Pb and 214Bi was simultaneously measured for all filters with the same detector as for the air-flowed filter system. From this, an average value for the attachment of progeny to the chamber walls was determined.For an additional consistency check of the mathematical model that fully describes the closed exposure system, filter measurements were conducted at the chamber walls. For this purpose, the same filter system that was placed in the centrifuge tube but with a larger diameter of 55 mm was stuck to the bottom, side wall and lid of the radon chamber during exposure. Afterwards, the filters were removed from the chamber and the γ-activity of In total, 13 experiments were conducted at defined radon activity concentrations, thereof 11 with a high relative humidity in the range between 57 and 75% and 2 at lower relative humidity of ~ 20%. In three cases the aforementioned wall exposure was measured in parallel.214Pb and 214Bi on the exposed filter systems, the area underneath the peaks (at 295 keV and 352 keV for 214Pb and at 609 keV for 214Bi) in the γ-spectra were determined using the Genie 2000 peak analyses software . Afterwards, these areas were background adjusted (step continuum substraction with 12 continuum channels) to get the net peak area Nn, which corresponds to the number of decays. Then, the activity To determine the time-dependent course of activities of −3 and an absorber  with the height of 1 mm was assumed. The same accounts for the pile-up correction, which was negligibly small for all recorded spectra  term, reflecting the decay of previously adhered mother nuclides. For the atmosphere, the isotopes may attach to the chamber wall . The scaling factor is the ratio of the two areas given by from Eq.  scaled w214Pb and 214Bi recorded for single experiments with different radon activity concentrations in the chamber. Assuming a linear relation between the radon activity in the radon chamber and the activity on the filter system, all data were linearly scaled to a reference activity value of 1 MBq m−3 to allow for a joint analysis and to obtain one representative average constant for the wall attachment. The error of the scaled activities is given by Gaussian error propagation concerning the uncertainty of the radon activity concentration given by the accuracy of the measurement device and the uncertainties for the non-scaled activities from the single spectra  is in good agreement after the scaling. In the first hour during the exposure, the activities of all nuclides rise, whereby 214Bi because of the decay of 214Pb. This delay phenomenon is more distinct for 214Bi than for 214Pb as the half-life of the corresponding mother nuclide, 218Po and 214Pb, respectively, is longer for 214Bi than for 214Pb. After about 4 h most of the 214Pb has decayed, so that only a small amount of 214Bi is delivered and the 214Bi activities also approximate an exponential decay. The measured activities of 214Pb and 214Bi are adequately described by the developed fit model. In particular the model describes the shape of the activity course well, justifying that the model henceforth can be used to describe the experimentally gained data. As the air-flow rate through the filter system just as the radon activity concentration during exposure are known and the amount of progeny at the beginning of exposure is negligibly small, the only free fit parameter of the model is given by the wall attachment rate −1 is representative for all experiments.A more pronounced delay and even a built-up in activity is observed for Nevertheless, fluctuations of the scaled activities exceed their error. For one experiment the calculated errors explain about 70% of the entire fluctuations, but the errors of the scaled activities do not account for additional factors that change between the experiments with different radon activity concentration and have an impact on the wall attachment constant entclass1pt{minima−3 during exposure and pooled afterwards. In this section the unscaled measurements are considered and we analyse the relation between the amount of attached progeny on the air-flowed filter system and the ambient radon activity concentration in the radon chamber during exposure in more detail. Therefore, the mathematical description of the measured activity values of 214Pb and 214Bi was fitted individually to each non-scaled data-set. From these fits the activities of 218Po, 214Pb and 214Bi right after exposure  on the air-flowed filter system were extracted and plotted against the independently measured radon activity concentration  are observed for radon activity concentrations higher than 4 MBq m−3 during exposure . In this model only the inner surface of the radon camber is accounted for, but not the surfaces of all items of the experimental set-up, including the mount of the filter system and various tubes. Therefore, the amount of progeny that attaches to the surface is estimated from a smaller boundary surface than is actually present and thus results in a higher calculated surface activity, i.e. an overestimation of activity per wall area. Second, the filter system was attached to smooth areas of the walls, so that edges of the chamber, where the progeny radionuclides tend to accumulate in higher concentration, were not accounted for in the wall measurements. Therefore, the measured activities with the wall-attached filter system show a lower amount of progeny than is actually expected including the edges. As we did not account for these factors in our model, the discrepancies reflect sources of expected model uncertainties, apart from which the model prediction agree fairly well with the actual measured activity curves of 214Pb and 214Bi on both the walls and the air-flowed filter.The general course of the expected 214Bi curve is the largest as it contains 214Bi decays following the decaying 218Po and 214Pb, which is produced on the filter in addition to the decays of 214Bi nuclides directly deposited from the chamber atmosphere. Still, the area underneath the 214Pb curve is just marginally smaller. This is reasoned as most of the 222Rn progenies 218Po and 214Pb are already deposited to the chamber walls and filter system before their decay, so that only a very small amount of 214Bi atoms is present in the chamber atmosphere and directly attaches to the filter system. The area underneath the 214Pb curve reflects 218Po nuclides that have decayed while already being adherent to the filter and the directly deposited 214Pb from the chamber atmosphere. Finally, the area underneath the 218Po curve is the smallest, consisting solely of directly deposited polonium.To determine the energy deposited on the air-flowed filter system, first the integral of the activity curves, which represents the number of decays of the corresponding nuclide, are calculated from the model fit. Here, the area under the −3 and 1 h exposure time the activity integrals can be used to determine the corresponding energy depositions, allowing for further dosimetric considerations. By multiplying the numbers of directly deposited nuclides with their potential alpha energy 218Po the second part of the equation is given by 0 because it is the first progeny radionuclide in the decay chain.For the reference activity concentration of 1 MBq mentclass1pt{minimaentclass1pt{minima214Po can be neglected. In sum, a total deposited energy of about 2341 GeV is determined.Notably the contributions of directly deposited nuclides get rapidly smaller along the decay chain. Therefore and due to its very small half-life further contributions of Here we presented a prototype of an experimental mechanical surrogate system to simulate how the overall deposition of radon progeny in the respiratory tract depend on external environmental factors. We developed a mathematical model to describe the deposition of radon progeny on an air-flowed filter system, which is placed inside a radon chamber. Besides the progeny attachment on the filter, the model includes the deposition on the chamber surface and the radioactive decay of each nuclide.−3, so that the wall attachment constant tends to higher variability at higher radon activity concentrations. Also, the influence of changing relative humidity on the wall attachment seems to be higher at higher radon activity concentrations without an apparent explanation, making further investigations necessary  stay the same. This assumption proofs consistency with current radiation protection models and we can verify this fact with our simple model, which is less affected by internal or external factors than human or animal studies.The worldwide average indoor radon activity concentration was estimated as 39 Bq m26 and stay there during exhalation18. Only the consideration of these processes would allow for a detailed model of dosimetry in the airways14. Moreover, not only the respiratory minute volume determines the number of deposited particles in the respiratory tract like assumed in our model, but also the breathing rate, because it determines, where particles are deposited and which amount will be exhaled again.For dosimetry in a real respiratory tract or a mechanical surrogate system including bifurcating airways, in addition to the ambient activity concentration also aerosol size distribution and breathing rate play an important role, as this determines the location of energy deposition. Inhaled aerosols can deposit in the respiratory tract via three distinct mechanisms But already from the findings in the present study, in which we consider the respiratory tract as one compartment in which all inhaled progenies are deposited, dose values for the respiratory tract of a mouse can be estimated. Therefore, the parameter of the air-flowed filter system are adapted to anatomical values of a mouse. The obtained dose values can then be compared to the literature.−3 and 1 h exposure time) and the approximate mass of a mouse lung 27. To scale the deposited energy from the filter system to a mouse lung, the ratio of the ventilation rates appear in the equation as well, where the rate for mouse lung is just the breathing rate of a mouse −1 (mean ± standard error of the mean)28, and the rate for the filter system is the air-flow rate −1. Evaluating this equation and normalizing it to the reference conditions mentioned above, a dose rate of 0.76 ± 0.08 nGy (Bq m−3)−1 h−1 is determined. The error was calculated by Gaussian error propagation.Based on our experimental and mathematical model, different parameters that influence the applied dose to the whole respiratory tract following exposure can be investigated. The dose −3)−1 h−1 for exposure to radon progeny for conditions similar to mine sites29, in which in humans (not mice) only about 12.5% of the inhaled particles are deposited in the lung and excludes the fraction of progeny being exhaled again or deposited in the upper airways18. Furthermore, an equilibrium factor of 0.4 is assumed, meaning that the concentration of radon progeny in air is 40% of the concentration expected in equilibrium with radon. In our setup, a deposition of 100% (sticking probability of 1) and an equilibrium factor of around 0.01 was estimated, as pure radon gas is induced in the radon chamber and its progeny radionuclides start to slowly build up during exposure. Although it is only a rough estimate motivated by a measurement of the equilibrium factor in a bigger radon chamber (50 l), the order of magnitude for this factor is well represented by this assumption. When considering this −3)−1 h−1. Thus, our obtained dose values are slightly lower than given by Sakoda et al., probably due to a slight overestimation of the F-factor from the bigger compared to the smaller chamber. Nevertheless, it should be noted, that this does not account for the inhomogeneous distribution of radon progeny in the airway system, but is only the average dose over the whole lung. It also underlines the importance of the equilibrium factor for radon dosimetry.Simulation studies by Sakoda et al. obtained a dose rate for the whole mouse-lung of 34.8 nGy (Bq m−3)−1 h−1 was determined. These data are useful for places with a very low equilibrium factor, meaning that the concentration of radon progeny in air is expected to be low30.The same model simulation for exposure to radon progeny was done by Sakoda et al. for exposure to pure radon gas, where a dose rate of 25.4 pGy (Bq m31 or spatial attachment at different anatomical regions in the lung and their biological effects on cellular level33, our experimental and mathematical model complement these data.While other publications are only focusing on human exposure34, in which a dose in the order of single digit µGy was deduced. In this experiment, the radon activity concentration was 55 kBq m−3 and radon progeny radionuclides were filtered. Therefore, the conditions were comparable to the simulations done by Sakoda et al. for pure radon gas30 and dose values are in good agreement to these results.The here presented measurements and models are further validating our method used for dose determination in a voluntary patient after radon therapy−1 instead of 10 mSv WLM−118.Our set-up enables to experimentally investigate different exposure scenarios, e.g. aspects of higher breathing rates during exposure, and thus verify current simulations. This is important as also the ICRP suggests higher applied doses for an increased physical activity and the accompanying higher breathing rate of a person during radon exposure, so that they recommend a dose conversion factor for worker with high physical activity of 20 mSv WLMThe here presented model provides the following extensions to currently existing publications:However, it should be noted, that in the exposure scenario assumed by ICRP there is a higher radon progeny concentration and attachment to walls is reducing it negligibly. This is different to our exposure scenario, in which wall attachment is much higher and must be considered.Considering the 3rd aspect listed above, to simulate the influence of a higher breathing rate, the throughput of air through the exposed filter system could be enhanced and the influence on the amount of attached progeny determined, although the effect of changing airflow velocities in the respiratory tract cannot be investigated with the current model. Nevertheless, our developed experimental setup and theoretical analysis allow the investigation of deposition of radon progeny on a basic level. It could be expanded to a more sophisticated setup in order to distinguish between different deposition mechanisms and more anatomical details as e.g. bifurcation of airways. In consequence, the deposition processes of progeny in the respiratory tract could be traced and used to determine spatially resolved dose distributions and validate the calculated absorbed doses.This work is the first step for the development of an experimental surrogate system to investigate the deposition of radon progeny under varying exposure conditions in the lung of organisms, applicable to e.g. mice in animal experiments and humans for radiation protection purposes.


The atmospheric water vapor is commonly monitored from ground Global Navigation Satellite System (GNSS) measurements, by retrieving the tropospheric delay under the Zenith Wet Delay (ZWD) component, linked to the water vapor content in the atmosphere. In recent years, the GNSS ZWD retrieval has been performed on shipborne antennas to gather more atmospheric data above the oceans for climatology and meteorology study purposes. However, when analyzing GNSS data acquired by a moving antenna, it is more complex to decorrelate the height of the antenna and the ZWD during the Precise Point Positioning (PPP) processing. Therefore, the observation modeling and processing parametrization must be tuned. This study addresses the impact of modeling on the estimation of height and ZWD from the simulation of shipborne GNSS measurements. The GNSS simulation is based on an authors-designed simulator presented in this article. We tested different processing models  and simulation configurations . According to our results, we recommend processing shipborne GNSS measurements with 3° of cut-off angle, elevation weighting function square root of sine, and an average of 5 mm·h The Global Navigation Satellite System (GNSS) measurement is based on an electromagnetic signal emitted in the L-band by GNSS satellites around the Earth and received by GNSS antennas at the Earth’s surface . From thDifferent aspects must be taken into account to obtain an accurate PPP positioning. First, the receiver and satellite clocks must be well-synchronized to obtain precise positioning, but they are subject to some errors. Contrary to the satellite clock continuously monitored by ground reference stations, the receiver clock errors are unknown, so they have to be estimated. On the other hand, the GNSS signals are disturbed by the medium through which they pass: the ionosphere at higher altitudes , and theSeveral studies focused on the precise extraction of ZWD from raw GNSS measurements ,21,22,23The vast majority of studies on GNSS for atmospheric water vapor measurements are based on fixed ground reference stations ,35. ThesGNSS PPP processing results are sensitive to the processing modeling , mainly Processing GNSS data with appropriate modeling is especially relevant at sea. Indeed, the carrying vessel is moving, so many parameters have to be estimated simultaneously with low constraints. A previous study has been carried out to investigate the impact of modeling on the estimation of height and ZWD using GNSS measurements from a shipborne antenna . In thisThis study aims at recommending a processing model for the systematic analysis of GNSS raw data acquired by shipborne antennas. Indeed, hundreds of research vessels (R/V) carrying a GNSS antenna travel the oceans across the World, acquiring GNSS raw data. The potential of these data is significant if their systematic analysis is possible. In order to test a series of processing modeling to a more typical dataset, we simulated a GNSS signal that would correspond to the signal acquired by a GNSS antenna as those mounted on R/V. We estimated the GNSS variables from this signal through a Kalman filter with different processing parameters. We compared the estimated height and ZWD to the simulated quantities. The realization of several simulations made it possible to determine statistically whether a configuration should be preferred. Using simulations also enables the data processing as many times as needed in a short period to test all the configurations altogether, as changing a processing parameter could affect the behavior of others . TherefoC denotes the receiver clock error, H denotes the simulated height, i-th satellite, respectively.The simulated acquisition is made up by adding different simulated components, as explained in the following sections, such as in Equation .(1)ϕIFifree IF,  combinatC, resulting in the first three terms of the simulated carrier phase of Equation . Other real broadcast orbits have been tested, which show no significant impact on the simulation. Thus, as for the King et al.  simulatiEquation  come froC term, it has been set to zero throughout the day for this study, reproducing the choice of Elosegui et al. [Although it is possible to implement a clock error in this simulator through the i et al.  to not sH integrates the simulated tide and heave to the mean sea level (MSL), as well as a constant height positioning A change in antenna height results in an additional signal path stretch expressed as H·sinϵ . The simThe angular motions of the boat are neglected in this study. It could be interesting to study the impact of such movements on GNSS signal PPP processing because these movements can be very heavy on boats, especially during rough sea states.The horizontal displacement of the antenna carried out by an R/V is not studied here, so its effect is not simulated for simplification purposes.Our simulated GNSS carrier phase is based on a linear IF combination of two frequencies from each GNSS constellation, such as Equation .(2)XIF=The available frequencies depend on the constellation, as in The frequency we chose to select in Using the linear combination of Equation , it is aBecause the troposphere hydrostatic delay is usually computed aside the estimation of the parameters, as explained in The measurement of the troposphere wet delay at the zenith of the antenna is simulated by setting a first ZWD value of about 0.15 m, and a random walk variability depending on the latitude of the study.The water vapor delay at the zenith of the antenna is mapped to the GNSS signal path between a satellite at elevation  or VMF3 . These m or VMF3 , empiric or VMF3  recently or VMF3 , or deri or VMF3 ,60. All rks well . This isThe antenna phase center variation (PCV) was simulated by adding a Trimble TRM105000.10 PCV offset to the signal. This antenna was selected because it can be mounted on R/V. The PCV effect for the Trimble antenna is found in the antenna calibration file ngs14.atx provided by the National Geodetic Survey (NGS) . A cubicz the angle of the observed satellite to the zenith. To implement the right-hand circular polarization of the GNSS signal, the Fresnel equation implemented becomes the following:Our multipath effect model is inspired by the model used by King et al. . In EquaEquation  computedThe precision of the carrier phase measurement is 0.01 cycles . The noiEquation .(7)ση2=Different parameters such as receiver clock error, 3D positioning, ZWD, and tropospheric gradients are estimated from the processing of the carrier phase measurement simulated as in Equation , but we Equation  is linea00σGN,E2 .the cut-off angle;the weighting function of the elevation of the observed satellites;the random walk on the ZWD.The implemented Kalman filter has several features developed in the following sections that can be set up as processing options:It is essential to remove signals from the satellites that are too low above the horizon of the observing antenna. It allows fewer multipath errors to affect the results.It is also important to choose an elevation cut-off angle low enough above the horizon. A small angle elevation satellite will permit to keep more data coming from the satellites, giving more observations to the Kalman filter. Height and ZWD can also be more easily decorrelated due to the low-elevation satellites than with the satellites near the zenith of the antenna . TherefoHere, we studied the commonly used values of 3°, 7°, and 10° of elevation cut-off angle. The cut-off angles of 3°  and 7°  have beeFor the same reason as for the elevation cut-off angle, it is also possible to implement a weighting function applied according to the elevation of the observed satellites. This method permits taking the low elevation measurements into account but giving them less weight in the estimation process than the zenithal observations. Weighting is involved in the uncertainty of phase measurement in the Kalman filter ,70.uniform, which applies a constant weighting to all satellite observations, regardless of their elevation.sine, which modulates the uniform weighting by dividing it by the sine function applied to the elevation of the observed satellite. In this way, the measurements coming from low-elevation satellites have greater uncertainty. They are less taken into account.sqrtsin, which modulates the weighting of sine by applying the square root function to the sine function of elevation.cos4, which modulates the uniform weighting by multiplying it by the elevation weighting proposed by Hadas et al. [s et al. : , but this could affect the height of the antenna. However, it is a slow motion and we can consider that slow vertical motions are already studied within the tide modeling.The simulation provides 200 simulated tropospheres. This number is optimal, so the statistics on the estimated variables show little bias compared to a smaller number of simulations, but we noticed no significant changes when increasing the number of tropospheres. The 200 reference study ZWD are simulated with a 5 mm·hlatitude .The PCV of the antenna that affects the measurement of the GNSS signal is supposed to be perfectly corrected for the reference study. To simplify the simulation we did not add any PCV effect to the simulated carrier phase, which means that From the reference study, we conducted a complementary survey on the acquisition setting. The aim is to study the impact of the choice of the constellations used, the time resolution, and the location of the carrying R/V on the data processing results. Each of these three aspects constituted a new study with all other acquisition settings than the one studied similar to the reference study of To evaluate the contribution of multi-constellation use compared to only one constellation, we conducted another study of the processing parameters on GPS signals only, from the reference simulation.We studied the impact of time resolution considering only one datum out of ten within the reference study during another processing. This results in a new estimation with a 300 s time resolution instead of 30 s. We will then be able to discuss the importance of the time resolution choice.The impact of the location of the R/V carrying the GNSS antenna on the processing results is studied by changing latitude. Two new simulations have been carried out with a +10° N and +80° N latitude, respectively.The latitude of the antenna has an impact on the geometry distribution of the satellites above the antenna and it also affects the water vapor content variations in the troposphere .For this reason and to adapt the simulation to this situation, we implemented simulations of 200 new tropospheres with a random walk of 2 mm·han antenna that is always well oriented to the North, such as a well-positioned ground-based antenna or a vessel going constantly northward;an antenna that has a constant bias of orientation from the North, such as a constant heading vessel;an antenna that is moving through time, such as the boat turning around, performing a 360° over 24 h.Different antenna orientation effects have been implemented for the PCV simulation and are studied here:no PCV correction is applied at all;the PCV correction is applied considering that the antenna is well oriented toward the North;the azimuthal mean of the PCV map in The estimator can correct the antenna PCV effect by three different means listed below, by adding the antenna correction to the carrier phase measurement before the Kalman filtering:The PCV values implemented for simulation and correction purposes are from the Trimble antenna presented in This additional study proposes a correction of the antenna PCV effect that would be suitable for a shipborne antenna whose orientation is unknown because of the displacement of the antenna. Only the antenna yaw is studied here, but implementing the other angular movements would have been interesting to study their effects.The results presented here will focus on the height and ZWD estimation match with the simulated quantities, as well as the correlation between both estimated variables.The correlation coefficient between height and ZWD has been calculated for each of the GNSS signal processing models in the 200 different tropospheres. The mean height and the ZWD correlation coefficient were then calculated from the 200 resulting correlation coefficients for each processing model. Therefore, there remains a mean correlation coefficient between height and ZWD and its standard deviation for each of the processing models. The standard deviations of the correlation coefficients are all lower than 0.1. In the following, we will focus on the mean correlation coefficient between ZWD and height presented in sine and sqrtsin, which corroborates the fact that height and ZWD are better decorrelated when embedding the signals coming from the low elevation satellites above the horizon.As expected, uniform and cos4 elevation weighting functions. As shown in uniform and cos4 give more weight to measurements of very low elevation angles than sine and sqrtsin. cos4 weighting reaches sqrtsin around 7° of elevation angle, and the weight of cos4 is twice as high as sqrtsin at 3° of elevation angle.However, we observe the opposite behavior on correlation and height estimation with sine weighting function, and 1 mm·huniform weighting function, and 20 mm·hsine is the best weighting for decorrelating height and ZWD, while uniform appears to be the worst. sqrtsin appears to decorrelate height and ZWD slightly better than cos4 at 7° and especially at 3° of cut-off angle, and both at 10° of cut-off angle give the same correlation coefficient. We can notice that the change in random walk value impacts the correlation coefficient more than the cut-off angle. This might be because a tight constraint on ZWD will force this variable to absorb a limited amount of errors coming from the antenna movement, particularly the change height that could be wrongly assimilated to ZWD in the case of loose random walk value. The height part thus wrongly assimilated to the ZWD could be responsible for its correlation being increased with the height estimate.The biases between the estimation and the simulation on height and ZWD have been calculated for each of the GNSS signal processing models over the 200 different tropospheres. The average height and ZWD biases were then calculated from the 200 resulting biases for each processing model, as well as the associated dispersion. From this, the root mean square error (RMSE) of the height bias and ZWD have been calculated for each of the processing models and are presented in sine weighting function. This processing modeling also gives the highest ZWD bias RMSE of 1.3 mm, with , we modified the reference simulation by considering only GPS observations. This change impacts the number of data available at each processing time and the geometry of the observed satellites. Using only GPS satellites induces a degradation of the estimation. Indeed, the average standard deviation increases by +59.8% for the height estimate and +51.1% for the ZWD for a cut-off angle of 3°, weighting function uniform weighting function and 5 mm·hGPS-only height bias is almost twice better than multi-constellation with Then, if several constellations are available, it is very important to use all of them to reduce the estimation error, with an improvement that can reach a factor of 2. On the other hand, the mean correlation coefficient between ZWD and height is slightly better when using only GPS, with an improvement of +12.8% compared to multi-GNSS processing. This effect seems to be contrary to common sense, so it might be the first evidence of some weaknesses of our simulation.To North: the vessel is heading North all the time during the 24 h of the simulation;45° North: the vessel is heading 45° towards the West during the whole time;24-h turn: the vessel is turning at constant speed, completing a 360° turn in 24 h.The impact of the PCV of the receiver antenna has been added to the reference simulation of GNSS observation. Three different movements of the boat have been simulated:No correction: the antenna effect is not corrected, so it still affects the signal during estimation;North correction: the PCV correction is applied to the signal assuming that the antenna was well oriented to the North, as would have been the case with a fixed ground GNSS antenna;Azimuthal mean: the PCV correction applied is an azimuthal mean of the antenna PCV map so that the correction depends only on the elevation of the observed satellite.These three simulated observation sets have been processed using three different ways of correcting the antenna effect before the estimation of the variables:sqrtsin weighting function and 5 mm·hHere, we study the impact of the change in the latitude of the R/V.Now we consider the simulation of 200 tropospheres using different locations than the mid-latitude of the reference processing.The multipath has been computed for these latitudes, as the geometry of the satellites above the antenna changes depending on the latitude of the location. At high latitudes, the satellites will stay at low elevations, whereas at low latitudes, the satellites will cover the entire sky above the antenna.sqrtsin weighting function, and 5 mm·hEstimating the ZWD and height at these latitudes with 3° of cut-off angle, latitude .Changing the latitudes does not appear to have a significant effect on the mean correlation coefficient.A more chaotic ZWD is more difficult to predict. This may explain why the results are better for low random walk simulated GNSS signals. It is relevant to use a processing random walk as close as possible to the ZWD variations at the location of the study. If possible, models or reanalysis could be used to determine an approximate value of the random walk ZWD at the antenna location. However, 5 mm·hAn accurate estimation of tropospheric delay is essential for the analysis of kinematic PPP GNSS data such as those acquired from shipborne antennas. This is especially critical as the troposphere delay is highly correlated with the height during the estimation process. In this study, we simulated shipborne GNSS measurements to assess the impact of the modeling strategy on the estimation. We applied a Kalman filtering of the simulated GNSS measurements to highlight a standing-out processing configuration for PPP shipborne GNSS.sqrtsine of the elevation, and 5 mm·hThe results corroborate previous observations made on a real dataset under simple acquisition conditions . Indeed,The use of a low cut-off angle such as 3° is shown to provide rather conclusive results, since the use of low elevation measurements permits decorrelating ZWD and height estimates, then improving the whole estimation process.sine gave, slightly, the best estimates of ZWD and height, it appears that sqrtsin better describes the physical behavior of the ZWD. Indeed, the processing random walk needs to be raised compared to the simulation, to obtain the best ZWD estimate with the sine function. The sqrtsin function then appears to be the best compromise between representing physical processes and obtaining a suitable estimation in PPP processing.Although the weighting function sqrtsin weighting function will require the use of a random walk of 5 mm·hsine function will require doubling the random walk to obtain a better estimation, according to the simulation results. We will then require to use the sqrtsin function.The use of a The processing of the simulated shipborne GNSS gives a +22% better estimation of the ZWD when using GPS, GLONASS, and Galileo, instead of GPS only. It is worth processing all the available constellations to obtain a broader dataset and a wider satellite geometry.If the time-dependent orientation of the antenna is not known, we also recommend applying an azimuthal mean antenna PCV correction, instead of the usually applied PCV map. As the vessel does not face North, such as a ground GNSS antenna, this method allows adaptation of the antenna effect correction to any heading of the boat, improving the ZWD estimate of +7% compared to the usual PCV correction.Finally, reducing the temporal resolution gives better results in the estimation. We would then recommend using at most 30 s of resolution for processing the shipborne GNSS data.The whole simulation relies on a simplified model of the shipborne GNSS carrier phase measurement. For example, no horizontal movement of the boat was simulated. This could be implemented for further study.In future work, the recommended processing modeling will be applied for the routine analysis of the GNSS raw data acquired by R/V from the French Oceanographic Fleet. This analysis will likely result in an estimate of the ZWD over the course of the boat, suitable for studying the space and time distribution of atmospheric water vapor over open seas.


The impact of salt crust formation over porous media on water evaporation is an important issue in relation with the water cycle, agriculture, building sciences and more. The salt crust is not a simple accumulation of salt crystals at the porous medium surface but undergoes complex dynamics with possible air gap formation between the crust and the porous medium surface. We report on experiments that allow to identify various crust evolution regimes depending on the competition between evaporation and vapor condensation. The various regimes are summarized in a diagram. We focus on the regime where dissolution–precipitation processes lead to the upward displacement of the salt crust and the generation of a branched pattern. It is shown that the branched pattern results from the crust upper surface destabilization whereas the crust lower surface remains essentially flat. We show that the resulting branched efflorescence salt crust is heterogeneous with a greater porosity in the salt fingers. This leads to the preferential drying of the salt fingers followed by a period in which the crust morphology change only occurs in the salt crust lower region. The salt crust eventually tends toward a frozen state where no visible change occurs in the salt crust morphology, but without blocking the evaporation. These findings provide in-depth insights into the salt crust dynamics and pave the way for the better understanding of the impact of efflorescence salt crusts on evaporation and the development of predictive models. The salt crusts often form as a result of evaporation and in many cases, they represent a nuisance for buildings. Evaporation induces upward flow in the porous medium directed toward the evaporative surface. Dissolved salts are transported through the flow and tend to concentrate at the porous medium surface where evaporation takes place. When a sufficient ion concentration is reached, salt crystallization occurs and salt efflorescence develops. Associated important phenomena are the salt crust impact on evaporation and the ions transport in the underlying porous media as well as on the possible superficial degradation of the porous substrate. In this context, the salt crust morphology and its dynamic evolution are among the most important open questions since they reflect the whole complexity of the various processes at play. Sometimes, the crust is compact, almost flat10, but it can be also quite rough11 with occasionally bulges in some places12. In some cases, the crust is characterized by very-well defined patterns13, such as the polygonal cell pattern at the surface of some salt playas14. Under other circumstances salt domes form15. Since salt crusts can be submitted to relatively harsh conditions, such as high temperature variations and intense solar radiations, one could expect that the salt crust evolution at a soil surface or on a building material and the associated change in its morphology are essentially due to mechanical effects, such as underneath gas pressure generation or thermal expansion and shrinkage. Although these effects might play a role under field conditions, we report in this article on an experiment where the salt crust morphology change is quite important but not due to mechanical effects. The observed evolution in the crust morphology is analyzed and explained by coupled transport and dissolution (deliquescence)–precipitation processes. The experiment is performed under quasi-isothermal laboratory conditions at room temperature. It is expected that the processes involve in the observed morphology changes are also key processes in salt crust evolution in nature. In the reported experiment, the salt crust morphology changes from compact to branched.Salt crusts have emerged as a specific and important research topic in the area of soil sciences17. As illustrated in Fig. 16, the only difference lies in the initial positions of the crust and the water table within the cell. Whereas these positions in16 led to a regime in which no significant change in the crust morphology could be observed, the crust morphology change is tremendous in the present experiment. This sensitivity of the crust morphology to these parameters finally led to change them more significantly in two additional experiments briefly described in the last part of the present paper. Combined with the experiment reported in16, this led to identify various crust dynamics regimes, depending on the evaporation rate from the crust and the water absorption rate by the crust, which are summarized in a phase diagram presented also in the present paper. It can be also noted that the crust morphology and associated dynamic regime in17 was the same as in16, a regime referred to as stable. The important difference in17 lies in the observation and analysis of the detachment of the crust from the porous substrate over which the crust initially forms. In the experiments discussed here and in16, the focus is on the crust dynamics. Contrary to17, there is no porous substrate left in the cell in these experiments. The experiment is performed in the same set-up as the one used in two previous studiesT≈22 °C), which are recorded all along the experiment.A 18 days experiment is performed, in which the evolution of a NaCl salt crust can be observed accurately and the factors controlling its dynamics can be assessed. As shown in Fig. 17, where the upward crust displacement was analyzed as a coupled process of transport phenomena and dissolution–precipitation mechanisms.The salt crust evolution is displayed in Fig. RH≈0.7518) and the top of the water head in the cell (RH = 1). The relative humidity difference induces water vapor transport by diffusion between the pure liquid water surface in the cell and the crust bottom surface. Hence, the crust absorbs pure water from the reservoir as a result of water vapor condensation, causing dissolution of the crust bottom. Simultaneously, the crust top loses water by evaporation. Dissolved species at the crust bottom, i.e., Na+ and Cl−, are transported upward in crust pore network, until they reprecipitate at the crust top. As a result, new layers of crystals form at the crust top while dissolution progresses at the crust bottom. It is important to notice that this analysis and description of the salt crust upward migration is purely based on transport phenomena and dissolution—precipitation processes and do not involve mechanical considerations, i.e. stress generation. In particular, although the cell walls are hydrophobic , this description does not require the consideration of interactions between crystals and hydrophobic surfaces20 in order to be representative of most applications, which usually do not involve hydrophobic surfaces.The upward migration results from relative humidity difference between the NaCl-saturated solution at the surface of the crust , from day 10 to day 18, but contrary to the third stage, the crust bottom surface is immobile and no change in the crust morphology is visible Fig. .21), 322). Expressing that the salt mass is constant, i.e. The initial stage stage 1) of increasing salt crust thickness can be first discussed from simple mass conservation considerations. The salt mass in the crust is expressed as  of incret ≈0.9 days, thickness increases and the absorption rate is indeed greater than the evaporation rate, i.e. t≈0.9 days and t≈1.5 days) the crust thickness continues increasing and the branched pattern continues developing whereas As can be seen, these considerations do not match with the results in Fig. t = 0.9 days. Consequently, the net mass of water inside the salt crust increases. Water absorption takes place at the salt crust bottom, but is limited by the evaporation rate. As a result, a layer of solution forms at the crust bottom. This liquid layer is visible in Fig.  Figure pvsA is the cell cross-section surface area (A = 0.004 m2), Dv is the water vapor molecular diffusion coefficient , R is the universal gas constant, Mv is the vapor molecular weight,24 indicating that 25. Here, the potential evaporation is the evaporation assuming that the salt crust top surface is covered by a liquid film of NaCl saturated solution. This leads to the result depicted in Fig.  The liquid layer underneath the crust forms a water reservoir in addition to the water present in the salt crust pore space. This reservoir gradually disappears as the liquid layer is absorbed into the salt crust as a result of the evaporation in excess. The results plotted in Fig. mentclass2pt{minim16, namely 16. Thus 26 26. This situation is sketched in Fig. t = 1.5 days and t = 1.6 days is characterized by the preferential drying of the salt fingers. Also, as a result of the salt finger desaturation, the crust top surface stops moving whereas the crust bottom surface continues to moves upward  the evaporation rate at the crust top is much greater than the absorption rate at the crust bottom. Then the evaporation rate drops significantly in less than 3 h  the immobile region and (ii) the active region Fig. .Figure 7No change is visible in the salt finger region, i.e. the salt crust upper region, which is therefore referred to as the immobile or “frozen” region. The salt crust morphology change occurs in the lower region, referred to as the active region in Fig. pvs = 0.75 pvsat over the salt crust bottom surface, i.e. computing pvsat, over the salt crust bottom surface, consistently with a liquid saturated salt crust active region.As can be seen from Fig. mentclass2pt{minim29 whereas flat interfaces are rather expected in dissolution region) . Thus, the most likely scenario is that the water saturation is quite low in the crust, most probably close to zero (dry crust). Assuming that the crust is dry, the mass transfer rate between the crust bottom surface and the cell top can be expressed as J over the considered period) is shown in Fig. This stage is characterized by the salt crust full frozen state. No change in the crust morphology is visible but evaporation still occurs Fig. . It can mentclass2pt{minim30, this gives To get further insights into the crust porosity, suppose that the crust diffusive resistance is essentially due to the lower layer resulting from the dissolution–precipitation process occurring in the active region in the previous stage (stage 3). Then, if the salt finger resistance is neglected, the diffusive conductance of the lower layer  salt crust in Hele-Shaw cell during which a branched pattern develops. Branched patterns are observed in many areas of physics, material science, biology and the earth sciences and have been the subject of many studies, e.g.17 using the same experimental set-up. All these experiments put forward the key role played by the relative contribution of water absorption and evaporation rates in the salt crust dynamics. The present experiment is characterized by an initial period where the absorption rate is higher than the evaporation rate, resulting in the accumulation of liquid water in excess at the crust bottom. The condensation layer at the crust bottom is a key factor for the destabilization of the crust during its upward displacement and the branched pattern generation. The liquid layer together with the branched pattern development induce a higher evaporation rate than the water vapor condensation rate (absorption). Once the condensation layer has been entirely absorbed into the crust as the result of evaporation in excess, the salt crust tends toward a quasi-equilibrium state where no further evolution of the crust morphology is noticed. This quasi-equilibrium state is reached via a relatively complex sequence of preferential drying of the salt fingers and rearrangement of the salt crust bottom part.The branched pattern reported here is significantly different from the compact crusts observed in previous experiments16 or17, it is interesting to investigate further the various regimes that can be expected from our experimental set-up. It can be first recalled that the evaporation and absorption rates are comparable over a long period and the crust moves upward without significant morphology change in17. This displacement regime can thus be considered as stable. In the present experiment, the absorption rate is sufficiently larger than the evaporation rate over a sufficiently long initial period for the branching pattern to occur. This clearly indicates that the ratio between the evaporation rate from the crust and the water absorption rate by the crust, i.e. the net balance between evaporation and absorption, is a key parameter.Since the crust morphology evolution is markedly different in the present experiment compared to the evolution reported inThe initial value of this dimensionless ratio estimated from Fick’s law at the beginning of the experiments is reported in Table This is illustrated with an additional experiment where mentclass2pt{minim40 (18). When the liquid level is sufficiently far below the crust and the relative humidity at the cell top is low, the relative humidity in the vicinity of the crust is less than 0.75 and no deliquescence occurs. The crust remains dry . This is the stagnant regime  up to certain level, saturated with a NaCl aqueous solution  and submitted to evaporation. As a result of evaporation, a salt crust forms within the Hele-Shaw cell on top of the beads. After a certain time, the beads are carefully removed from the Hele-Shaw cell and a suspended layer is obtained. As detailed in17, this layer is actually a composite system formed by the assembly of two porous layers. The top layer essentially consists of NaCl crystals whereas the bottom layer is a mixture of glass beads and NaCl crystals. Then pure water is introduced at the bottom of the cell and the crust is exposed again to evaporation. As analysed in17, introduction of a water head below the crust causes the upward migration of salt crust up to the detachment of an essentially crystalline layer from the remaining glass bead layer. Then the remaining glass beads are removed from the Hele-Shaw cell, which therefore now only contains a salt crust, i.e. a porous layer whose matrix is essentially formed by halite crystals . The cell is rendered hydrophobic by silanization so as to avoid salt creeping on the cell inner walls17, in the experiment reported in43, as well as in several pre-test experiments. Furthermore, the various regimes summarized in the phase diagram also illustrates the overall consistency of all the experiments performed.In the present paper, three experiments have been presented; the one leading to the crust full dissolution, the one corresponding to the stagnant regime and the one leading to the branched pattern, which was analysed in much more detail. First, it can be noted that the branched pattern was observed in a separate pre-test experiment, which was a strong motivation for performing the more instrumented experiment analysed in the present paper. Also, the stable regime regime has been observed in two separate experiments−5 g was used) adapted in order to transform it into an environmental cell. This consists in inserting two medium petri dishes, filled with a saturated 18), that are suspended in the enclosure, in order to control the relative humidity, and the insertion of a humidity and temperature sensor (Rotronic Hygroclip SP05 probe). The temperature in the room is kept constant at about T ≈ 22 °C.The Hele-Shaw cell is set in the balance proprietary enclosure  the mass of the set-up is measured every 100 s with the precision scale, (ii) the relative humidity in the enclosure and the temperature are measured every 1000 s and (iii) photographs of the set-up are taken every 1000 s in portrait mode with a Nikon D800E camera at a resolution of 7360 × 4912 pixels set outside of the enclosure.17 for details on the used image processing techniques. Distances in the cell, mean distance between the crust top (bottom respectively) surface and the cell top for instance, position of the water table in the cell, are averaged distances over the 13 vertical lines of pixels defined in Fig. Dedicated image processing techniques are used to determine distances in the cell and the adjacent cylinder with the aid of ImageJ Fiji software. One can refer tom(t) by a simple finite difference as “Evaporation–100” in Fig. Absorption-30” in Fig. Absorption-fit” in Fig. The evaporation rate at the crust top is computed from the set-up weight variation whereas the water absorption rate at the crust bottom is computed from the liquid level variations in the cell and the adjacent cylinder Fig. . The evamentclass2pt{minimSupplementary Information 1.Supplementary Video 1.Supplementary Video 2.


Objects in one's environment do not always move at a constant velocity but often accelerate or decelerate. People are very poor at visually judging acceleration and normally make systematic errors when trying to intercept accelerating objects. If the acceleration is perpendicular to the direction of motion, it gives rise to a curved path. Can spatial contextual cues help one predict such accelerations and thereby help interception? To answer this question, we asked participants to hit a target that moved as if it were attached to a rolling disk, like a valve (target) on a bicycle wheel (disk) moves when cycling: constantly accelerating toward the wheel's center. On half the trials, the disk was visible such that participants could use the spatial relations between the target and the rolling disk to guide their interception. On the other half, the disk was not visible, so participants had no help in predicting the target's complicated pattern of accelerations and decelerations. Importantly, the target's path was the same in both cases. Participants hit more targets when the disk was visible than when it was invisible, even when using a strategy that can compensate for neglecting acceleration. We conclude that spatial contextual cues that help predict the target's accelerations can help intercept it. Objects in the environment do not always move at a constant velocity. An approaching tennis ball, for example, will accelerate and decelerate as a result of gravity, of hitting the ground, and of any spin that the opponent used. Despite acceleration being an essential feature of most moving objects, people are very poor at visually judging it e.g., . It is tInterception errors decrease through practice if there is regularity in the acceleration over repeated trials. This might suggest that people learn to anticipate certain accelerations of the target and control the timing of their interception accordingly e.g., . HoweverA ventral visual pathway that connects the primary visual cortex with the inferior temporal cortex processes information that is needed for recognizing objects. A dorsal visual pathway running from the primary visual cortex to the posterior parietal cortex processes information that is needed to guide ongoing actions. The influential two visual streams hypothesis proposes that these two cortical pathways use different visual reference frames . The venMore recent evidence argues against such a strict functional segregation and suggests that allocentric and egocentric reference frames are used by both the dorsal and ventral stream see .In this experiment, we examined whether interception performance improves when one provides spatial contextual information that helps predict a target's accelerations and the resulting complicated trajectory. We asked participants to hit a target that moved with a disk rolling down a slope, similarly to how a valve moves on a bicycle wheel as the wheel rolls along its path. On half the trials, the disk was visible such that participants could use the spatial relation between the target and disk to see why the target was accelerating or decelerating. On the other half of the trials, the disk was not visible. Importantly, the target always followed the same path. According to the functional segregation proposed by the two visual streams hypothesis , providiconstant-phase strategy. For a target attached to a rolling disk, the direction of the target's instantaneous acceleration is determined by the phase of the rotation. As already mentioned, if targets accelerate in the same way across multiple trials, people learn to compensate for the systematic errors that arise from ignoring the acceleration by simply aiming further to one side . Participants either volunteered to take part or took part in return for course credit. The study was approved by the local ethics committee in accordance with the Declaration of Helsinki.The experiment was conducted in a normally illuminated room. The stimuli were back-projected at 120 Hz with a resolution of 800 × 600 pixels onto a 1.25-m × 1.0-m acrylic rear-projection screen  tilted backward by 30°. An infrared camera  that was placed at about shoulder height to the left of the screen measured the position of a marker (an infrared light-emitting diode) attached to the nail of the index finger of the participant's dominant hand at 500 Hz.In order to synchronize the timing of the movement data  with the stimulus presentation, the camera also recorded the position of a second marker attached to the side of the screen. This marker did not move, but it stopped emitting infrared light so that its position was registered as “missing” when a flash was presented at the top left corner of the screen (where a light sensor was placed to detect the flash). We used a simple 4-point calibration to relate the position of the fingertip to the projected images, automatically correcting for the fact that the marker was attached to the nail rather than the tip of the finger.Participants stood in front of a large screen and were free to move as they wished. They were instructed to try to intercept the black target (a 2-cm diameter dot) and were free to hit it at any point before it left the screen. To start a trial, participants placed their finger within the green starting point (a 3-cm diameter dot) that was presented 28 cm below the screen center. Between 600 and 1,200 ms after they did so, the target appeared in the top-left corner of the screen. The black target was attached to a white disk (20 cm diameter) that rolled down a blue slope. On half of the trials, these items were presented on a gray background, so the disk was clearly visible. On the other half of the trials, the background was white, such that the white disk was not visible, and the target disc appeared in isolation. We chose to vary the background color rather than that of the disk so that the contrast at the edge of the target was always the same. The starting position of the center of the disk was always 40 cm left and 19 cm above the screen center, at the top of a blue downward slope . The disk rolled down the slope at a constant velocity of 61 cm/s. The center of the target was attached to the disk at 7.5 cm from its center, such that it followed a curtate trochoid. The initial orientation of the disk was chosen at random on each trial, so that the target's trajectory varied across trials so intercepting the target at the same phase does not correspond with intercepting it at the same position. Participants received feedback if they correctly intercepted the target : They heard a sound and the target remained at that position for 500 ms. If participants missed the target, they heard nothing, and the target deflected away from their finger at 100 cm/s. Participants chose when to begin the next trial by placing their finger in the starting point such that it was a self-paced task. The experiment used a within-subject design with one independent variable: disk visible or invisible. Each participant completed one block of 400 trials  in a single session that took approximately 20 min. The two conditions were randomly interleaved. We were interested in three dependent variables: the fraction of targets hit, the phase of the target's motion when the screen was tapped, and the position of the tap with respect to the target.T = 107, p < 0.0001). This shows that having spatial contextual cues aids interception performance. The time between the target's appearance and it being tapped (mean ± standard error) was similar in both the disk-invisible (772 ± 25 ms) and disk-visible (763 ± 23 ms) conditions.Participants hit more targets when the disk was visible (blue bar in where participants tapped on the screen with respect to the moving target. To do so, we determined the mean tapping error across all trials for each participant in both conditions (To investigate our proposal that the spatial contextual information available in the visible-disk condition helps predict the target's accelerations, we investigated nditions . If partnditions , they winditions . Figure To determine whether participants used a constant-phase strategy and whether doing so improved performance, we looked at the consistency in the target's rotational phase when the screen was hit (see examples in The rightmost example participant in This experiment shows that providing spatial contextual cues can help participants intercept accelerating targets: Participants hit more targets when the rolling wheel that the target was mounted on was visible than when it was invisible . This fiEven when the wheel was invisible, participants compensated for some of the acceleration of the target (red dots in Since the precision of interception is better for slower targets, because any timing errors matter less when the velocity is low , one migSpatial contextual cues improve interception performance by helping participants predict the complicated accelerations and decelerations of the target. In addition, participants who consistently hit the target at the same phase of its rotational movement hit more targets, presumably because it allowed them to use their errors on previous trials to adjust their movement. We conclude that goal-directed movements use any visual information that is relevant for the task and can be judged well enough to be useful.


The Collective Thomson scattering technique has been implemented to study the stagnation of a single liner gas-puff. The plasma parameters are determined by theoretically modelling the scattering form factor in combination with Bayesian inference to provide the set of the most probable parameters that describe the experimental data. Analysis of the data reveal that incoming flows are able to interpenetrate partially. Estimation of the mean free path shows a gradual transition from a weakly collisional to a collisional regime as the plasma gets to the axis. Furthermore, we find that the ion energy at  When the generator’s current ionizes and flows through the gas, an azimuthal magnetic field is generated that compresses the column radially until it reaches stagnation (the moment of maximum compression). Gas-puffs have been studied as potential sources of X-ray and neutrons6. However, in this work we show that this classic picture is not always the case and the physics at stagnation is more complex.It is commonly believed that at stagnation the imploding plasma kinetic energy is rapidly thermalized (at the ion-ion energy equilibration time), and a big fraction of the kinetic energy is converted to thermal energy. Then, if the ion temperature is high enough, fusion reactions are produced (when deuterium is used as a working gas) and the thermal energy is converted to kinetic energy of the fusion product. In the case of radiation sources, the ions transfer their thermal energy to the electrons (at the ion–electron energy equilibration time), which in turns lose their energy through ionization and radiation7. Also, the true ion temperature have been found difficult to measure. Maron et al.8 showed that the value obtained with Doppler spectroscopy can be several times higher than the real value, and that it represents all the hydrodynamic motion in the plasma rather than its thermal motion. This shows that more diagnostics and accurate data analysis are needed to fully understand the physics at stagnation.Furthermore, there are other processes at stagnation that are not fully understood. For example, acceleration of ions to energies larger than the driver voltage are usually observed; many theories have been suggested, but the acceleration mechanism still remains a source of controversy11. This technique collects light scattered by the electron density fluctuation at a certain volume when a probing laser interacts with the plasma. The collected spectrum shape carries information about the plasma parameters. Its main advantage over other spectroscopy techniques is that it can measure locally from a well determined volume and is independent of broadening mechanisms such as the Stark or Zeeman effect. However, the large number of parameters 12. However, this point-estimate approach does not guarantee to reach the global minimum, especially in cases when the fit is multimodal or when different combinations of parameters can fit well the experimental data (resulting in a similar chi-squared), which is called in the literature as ‘unstable function’13. To deal with these cases is important to have a more general view of the parameter distribution allows us to determine how much each parameter influences the spectrum's shape and the correlation between parameters14.The Thomson scattering (TS) technique has proven to be a powerful tool for diagnosing high energy density plasmas. With this technique, it is possible to estimate the electronic temperature  was modeled as two identical counterstreaming plasmas (red and blue lines) with an electron drift velocity of 500 km/s. The sum of these counterstreaming signals is closely to the experimental data confirming the interpenetration of flows from opposite directions.Finally, for fibers 13 and 14 we observe the following: first, the TS signal presents a tail closer to the laser wavelength indicating a plasma moving at a slower speed; second, the IAW peaks are not symmetric indicating an electron drift with respect to the ions. Considering the last point, a drift velocity of ~ 500 km/s was necessary for most of the modeled spectrum to be within the band of the given uncertainty. In this case (fiber 13 and 14), the changes in the spectrum's shape are attributed to the MRT instability. However, further analysis of the MRT instability using Thomson scattering is outside the scope of this paper and will poste be addressed in future work. Therefore, in the following discussion, we will only focus on analyzing the most central fibers where no instabilities are observed.An example of the Bayesian analysis output is shown in Fig. Applying the procedure mentioned above for each fiber, the radial variation of the inferred parameters can be obtained as shown in Fig. As shown in Fig. ined see . The resentclass1pt{minimaentclass1pt{minima20, where the magnetic field is advected by the incoming plasma flows and it deflects the ions axially. Magnetic field advection has also been measured in gas-puffs using Zeeman spectroscopy, values of ~ 4 T were detected inside the plasma21. This evidence supports the conjecture presented above. Assuming this was the case here, the magnetic field necessary to deflect the ions can be estimated by Therefore, we conjecture that the missing energy may be stored in an axial component of the velocity, which in our configuration cannot be detected because the k-vector lies on the radial plane. Notice that this behavior has been observed previously in tungsten wire arrays22. Also, to evaluate the advection of a magnetic field suggested above, the magnetic Reynolds number was estimated as 5. The results are summarized in Table To evaluate the interpenetration, we computed the ion-ion mean free path . Plasma velocity and density were validated with MCP imaging and interferometry measurements. This procedure reveals an anti-correlation between temperature and electron density. In future works, the electronic feature of the Thomson scattering to be measured to determine electron density. In this way, it becomes possible to choose prior distribution better to obtain electronic temperature results with more precision.The Analysis of the inferred parameters reveals important new information about the implosion dynamics for times close to stagnation. The measurements show a substantial change in the plasma collisionality within a few millimeters, changing from a weakly collisional regime at the periphery to a collisional regime on approaching the axis. In addition, data suggest the existence of an azimuthal magnetic field inside the pinch formed by the advection of the induced field, which deflects the ions in the axial direction. To allow this effect, a field of 4.7 T would be sufficient to deflect the ions.More experiments are underway to unravel the dynamics of interpenetration and deflection of ions in a gas-puff. In future experiments, multi-angle Thomson scattering and Zeeman spectroscopy techniques will be used simultaneously to infer the radial and axial plasma velocity components as well as the distribution of the magnetic field. These studies will help delve deeper into the processes governing the implosion of the gas-puff.24 located at the Instituto de Física of the Pontificia Universidad Católica de Chile. Llampudken is capable of delivering a peak current of ~ 400kA at ~ 200 ns rise time (10% to 90%) when charged to 22 kV per capacitor. A characteristic current trace is shown in Fig. The experiment was carried out on the Llampudken pulsed power generatorA Thomson scattering diagnostic was implemented using a 532 nm Nd-YAG laser (EKSPLA NL310) which can produce a pulse up to 1 J with 4 ns full width half maximum (FWHM). The polarization was oriented vertically by a half-wave plate to maximize the scattered light in the collection direction  self-emission imaging is performed using unfiltered 100 µm pinhole and a four-frame micro-channel plate camera (MCP) with ~ 4 ns temporal resolution. Mach–Zehnder interferometry is performed using a second laser (1 mJ at 532 nm and 4 ns FWHM) to estimate the electron density at early times. The interferograms were recorded digitally on a canon camera (EOS Rebel T3i). We also used a 25 µm Be filtered diode (AXUV HS5) to measure the stagnation time and X-ray yield (> 1kev).25. Nevertheless, the electrons' response is determined not only by the laser's electric field but also by the presence of more electrons and ions that shield each other. Specifically, we need to compare the wavelength associated with the scattering wavevector  by free charged particles present in the plasma. However, since the electrons are much lighter than the ions in the plasma, the measured Thomson spectrum is mainly produced by the electrons as their acceleration in the laser field is much larger compared to the ions26.In the non-relativistic and collisionless limit, the total scattered power . In our case, for a first approach to the Bayesian analysis applied to Thomson cattering data, we consider a normal distribution described by Eq.  method with starting point the set of parameters obtained from a nonlinear least squares optimization.Before implementing the Bayes code, the model for the scattering form factor Supplementary Information.