Focussed Ultrasound (FUS) combined with microbubbles (MBs) was proven a promising modality for non‐invasive blood brain barrier disruption (BBBD). Herein, two devices for FUS‐mediated BBBD in rodents are presented.A two‐axes robotic device was manufactured for navigating a single element FUS transducer of 1 MHz relative to the brain of rodents. A second more compact device featuring a single motorized vertical axis was also developed. Their performance was assessed in terms of motion accuracy, MRI compatibility and trans‐skull BBBD in wild type mice using MBs in synergy with pulsed FUS.Successful BBBD was evidenced by the Evans Blue dye method, as well as by Fibronectin and Fibrinogen immunostaining. BBB permeability was enhanced when the applied acoustic intensity was increased.The proposed devices constitute a cost‐effective and ergonomic solution for FUS‐mediated BBBD in small animal models. Further experimentation is needed to examine the repeatability of results and optimise the therapeutic protocol. The techniques available so far are not very effective. The BBB, which is the body's defence against toxic substances, also provides resistance to the supply of therapeutic agents. Therefore, the provision of medication to the brain is a main problem to overcome. In this regard, focussed ultrasound (FUS) seems to be an alternative completely non‐invasive method that can enhance treatment against neurodegenerative diseases.It has been shown that opening of the BBB can be achieved with the use of therapeutic ultrasound and the administration of microbubbles (MBs).The application of this method for disrupting the BBB has been tested in various animal models, but mostly evaluated in mice and rats.The team of Konofagou did remarkable work in the field using a 3‐axis robotic system .A manual mounting system was proposed by the team of Hynynen.There are also systems available in the market that were developed for research activities. An example is the PK50 system offered by the FUS Instruments company . The system has 3 degrees of freedom (DOF) for transducer positioning.Image guided therapy manufactures robotic systems compatible with MRI. This company offers 2 different robotic systemsThe company Sonovol focuses on imaging modalities for preclinical applications,Robotic‐assistance was introduced in many studies to improve the accuracy of ultrasonic targeting.There is an increasing demand for preclinical robotic devices, as various FUS applications are continuously being developed and should be investigated to demonstrate the accuracy and repeatability needed for their clinical translation. Preclinical devices are the most cost‐effective solution because medical certification is not necessary. Although numerous devices with different functionalities have been developed and tested so far, more simplistic and ergonomic devices dedicated for small experimental animals would be of great usefulness in accelerating research in the field.In this study, we propose two systems dedicated to manoeuvering a single element FUS transducer for preclinical research in small animal models. The first system had the ability to manoeuver the transducer in two dimensions. The operation of the system is simplistic since all the moving parts are placed in a single water tank that includes an acoustic window on the top. A target supporting platform was specially designed to securely position rodents above the ultrasonic source.A second system was built to simplify targeting given the very small size of the mouse head and offer improved ergonomics. In this version, the mouse is placed in the more stable prone position on a flat platform, with the transducer reaching the head with a top to bottom approach. In fact, the transducer is located inside a cone that is acoustically coupled to the mouse head using ultrasound gel. With this design, the administration of anaesthesia is more flexible.Both devices were made MRI compatible. Even though the two devices were primarily developed for laboratory use, MRI compatibility is important since it allows for treatment planning and accurate targeting in the MRI setting, as well as confirmation of BBBD by contrast agent enhanced imaging directly after treatment.The proposed devices will provide the researchers with means to perform research on FUS applications in small animals. The two devices were engineered in a way that ensures ease of use, with adjustment tools to suit the different species. Especially for very small animals such as mice, the accuracy benefits of the proposed experimental setup are of high importance. Overall, the proposed systems are easy to make at an affordable price and were developed based on the knowledge gained from our previously introduced robotic systems.22.1A custom‐made FUS transducer was manufactured in‐house using a single piezoceramic element , with a radius of curvature of 80 mm, an active diameter of 50 mm, and an operating frequency of 1 MHz. A dedicated housing was 3D printed using Acrylonitrile styrene acrylate (ASA) material on a STRATASYS  printer having a circle‐shaped cavity, wherein the element was soldered. An electric circuit was created and encapsulated with epoxy, which serves as electric isolator and simultaneously as a backing material preventing excessive vibration of the element and improving the acoustic performance of the transducer. The acoustic efficiency of the transducer was experimentally determined at 33% by the radiation force balance method.The transducer is tuned to an RF amplifier  and its actuation is controlled via an in house developed software, which allows selection between continuous and pulsed ultrasound sonication. There is also the possibility to set the sonication parameters, such as the electric power, sonication duration, frequency, and duty cycle.2.22.2.1X and Y linear axes, with a motion range of 60 and 130 mm, respectively. Specifically, the rotational motion of two piezoelectric motors  located outside the water enclosure is converted into linear motion via complex mechanisms located inside the enclosure, as shown in Figure A 2 DOF motorized device was manufactured using a 3D printing machine . Figure X axis angular motion is converted into linear motion by a Jack screw mechanism. The motor rotates the Jack screw that is linked with the X‐plate  or back (upon clockwise rotation) along dedicated guides of the X‐frame, which has also a supportive role increasing structural rigidity. The pitch of the Jack screw is 1.44 cm, meaning that for each complete rotation, the X stage moves 1.44 cm.The e Figure . The rotY axis mechanism involves additional moving parts since the motion has to be delivered at a 90° angle . Bevel gears refers to a type of gears with conically shaped teeth that transmit motion at an angle. The gear rotates the Y axis jackscrew, thus converting rotational motion into linear motion of the Y plate. The angular to linear motion ratio of the X and Y axes is equal, thus establishing uniformity.The e Figure . The motThe entire mechanism operates within the water container Figure , which i2.2.2The second version of the device is shown in Figure The device was manufactured on a polyjet 3D printing machine  using resin, which is cured when exposed to ultraviolet radiation. This technology offers high resolution, thus enabling the production of dimensionally accurate parts. The surface finish is also superior compared to the FDM technology where the layer lines are more visible.This version of the device includes a flat platform where the mouse is positioned. Notably, an absorber was embedded in the centre of the platform for minimising ultrasound reflections. This platform is connected to a frame that includes linear guides for height adjustment via a moving plate Figure . The heiThe height adjustment plate is operated in conjunction with a Jack screw having its first side attached to the platform and its second side connected to the top plate. The jackscrew is rotated by an ultrasonic motor  inducing vertical motion of the height adjustment plate so that the transducer cone can be fixed on targets of different size. Notably, its bottom part is securely sealed with a thin silicone membrane that is held by an O‐ring Figure . Upon opThe transducer was mounted on the upper section of the cone using a special mechanism that enables its manual angulation. Angulation of the transducer is limited by a stop, thus ensuring the alignment of the ultrasonic beam with the acoustic opening Figure . This me2.3The axial and radial power field of the designed transducer operating at its fundamental frequency of 1 MHz was evaluated by FUS field scanning with a hydrophone. A dedicated plastic holder was utilised to accommodate the designed transducer and the needle hydrophone  in an acrylic tank filled with degassed, deionised water. The transducer was precisely moved along the axial and radial directions by a system of stepping motors  while the hydrophone was aligned to the beam axis to record the pressure waves at increasing distance from the transducer's surface. The hydrophone signal was displayed on a digital oscilloscope  and the peak to peak voltage recordings were collected. In total, 65 measurements were acquired with 2 mm intervals, in the range of 3–16 cm from the transducer's surface. At the estimated focal distance, 80 measurements were acquired in radial direction with 0.1 mm intervals. A voltage of 50 mV was applied in each case.2.4The accuracy and repeatability of robotic motion for the two versions of the robot was assessed following a calliper‐based method as previously detailed in the literature.2.5The developed robotic devices were then evaluated in terms of proper operation in the MRI environment. Evaluation was carried out in a 1.5 T MRI scanner. The SNR served as the main tool for assessing the compatibility of the transducer with the scanner.3, matrix = 128 × 128, number of excitations (NEXs) = 2, and acquisition time/slice = 7 s.Imaging of an agar‐based tissue mimicking phantom  was performed using the spoiled gradient recalled echo (SPGR) sequence with the following parameters: repetition time (TR) = 23 ms, echo time (TE) = 16 ms, flip angle (FA) = 35°, echo train length (ETL) = 1, pixel bandwidth (PB) = 45 Hz/pixel, field of view (FOV) = 280 × 280 × 10 mmThe following activation states of the positioning mechanism were tested: motor/encoder cable not connected, motor/encoder cable connected, electronic control system energised but no motion command initiated (referred to as: DC ON), and motion command initiated (referred to as: motor moving). Regarding the FUS system, the following states were tested: RF cable not connected, RF cable connected, amplifier energised (zero power applied), and ultrasonic power applied. Electrical power values of 50–200 W were tested. In each case, the SNR was determined using the following formula2.6Feasibility experiments were conducted in wild type (WT) mice  in collaboration with the Cyprus Institute of Neurology and Genetics to obtain proof of concept for the first version of the device. All the experimental procedures were approved by the Cyprus Veterinary Service under the protocol number CY/EXP/PR.L05/2021.Initially, the transducer's location was adjusted to coincide with the circle‐shaped opening of the mouse holder (where the mouse head is fixed) through the motion commands of the interfaced software. The mouse head was shaved using hair removal cream. The mouse was then anaesthetized with isoflurane  following administration of 10 or 20 μL of SonoVue MBs  intravenously through the tail vein with a 30G syringe. Once the mouse was sufficiently anaesthetized, it was mounted on the device above the FUS transducer in the supine position and immobilised by properly adjusting the holder's handles. The container was filled with degassed‐deionised water up to the mouse head to ensure efficient ultrasonic coupling. It is essential to mention that before fixing the mouse to the holder, the transducer was energised enabling visual localization of the beam at the water surface, thus providing an additional reference for mouse positioning. Each mouse received a single sonication using FUS pulses of 10 ms length, applied at a repetition frequency of 1 Hz, for a total duration of 60 s using electrical power of 20 or 30 W.In total, 6 mice were included in the study. Four (4) mice were treated using MBs‐enhanced FUS. The Evans Blue (EB) dye method was used to assess the success of BBBD. Specifically, 5 μL/g of body weight of a 4% EB stain solution  was injected intravenously into each mouse immediately after sonication; 30 min before they were sacrificed. One mouse received EB only and another mouse served as the control mouse and received no treatment or EB.All mice were sacrificed approximately 30 min after the sonication or/and EB administration. Slides containing brain sections were directly visualised using a Nikon eclipse‐Nἱ  fluorescence microscope to examine the EB extravasation. Furthermore, cryosections from brain were immunostained for fibronectin  and FITC‐labelled polyclonal fibrinogen antibody  to assess the protein leakage into the parenchyma. DAPI staining  was used for nuclear localization (blue).33.1Ultrasonic pressure field characterisation was performed using a hydrophone. The voltage recordings show a maximum pressure at 7.5 cm indicating that the actual focal spot is slightly shifted towards the transducer's surface. The axial pressure profile follows a Gaussian distribution with a full width half maximum (FWHM) of about 10 mm around the focus location . Accordingly, the radial pressure profile at the estimated focal distance of 7.5 cm also follows a Gaussian distribution around the central axis, which is characterised by a FWHM of about 4 mm . These measurements provide a good indication of the size of the focal spot.3.2X and Y directions, respectively. Regarding the second version of the robot, the Z‐stage was found to move with a speed of 8.65 ± 0.08 mm/s.The results on motion accuracy as obtained by the calliper based method are summarised in Table 3.3The bar charts of Figures 3.4BBB opening was evidenced in all cases (4/4). Representative microscopy photos of EB extravasation in the brain parenchyma adjacent to the lateral ventricles are shown in Figure The BBB permeability was also characterised using Fibrinogen and Fibronectin immunofluorescent staining. The mice treated with FUS plus MBs showed higher levels of the protein in all examined brain areas compared to the control mice. Images of fluorescence microscopy from the corpus callosum are presented in Figure 4The current study presents two robotic devices intended to facilitate preclinical research on transcranial applications of FUS in small animal models, such as mice. The specific application of the system is the FUS‐mediated BBB opening for the delivery of therapeutic drugs that are normally hampered by the BBB into the brain parenchyma.The first version of the robotic system was developed with two piezoelectric‐actuated motion axes. The mechanical parts and FUS transducer were arranged in a single water enclosure. The rotational motion of the motors located outside the container is converted into linear motion of the respective stages inside the enclosure by Jack screw mechanisms. The system incorporates a custom made single element FUS transducer operating at a frequency of 1 MHz. Note that MBs‐enhanced pulsed FUS around 1 MHz was predominantly selected for similar applications in mice by numerous studies.The FUS transducer was also manufactured in‐house using a purchased piezoelectric element that was housed in a plastic case and covered by an epoxy encapsulant. The acoustic efficiency of the transducer was experimentally determined at 33% by the radiation force balance method. The produced FUS field was scanned using a hydrophone. The collected sound pressure signals were displayed on a digital oscilloscope, thus allowing assessment of the pressure field distribution. The obtained results revealed an actual location of the focal spot shifted at 7.5 cm, compared to the focal distance of 8 cm reported by the manufacturer for the element. This method also provided good indication of the size of the focal spot.The most parts of the device were developed on a rapid prototyping machine using plastic to avoid interference with the scanner. The MRI compatibility of the developed system was assessed in a 1.5 T MRI scanner by comparing the SNR of SPGR images of an agar‐based MRI phantom obtained under different activations of the system. Regarding the positioning mechanism, noticeable SNR reduction was observed when the motion command was initiated (motor moving). Regarding activation of the FUS transducer, the image quality was getting degraded as the output power was increasing, thus resulting in some loss of detail. However, the induced SNR reductions were not considered significant. In other words, all tested activations resulted in SNR values sufficiently high for proper imaging, and thus, the efficacy of anatomical targeting and MR thermometry are not influenced. It should be though noted that since activation of the various components requires the use of electricity the system is classified as MR conditional  standards).The feasibility of the system in opening the BBB of small animal models using pulsed FUS in synergy with MBs was examined in WT mice. The mouse platform provided proper immobilisation of the mouse in the supine position. Targeting was though proven challenging due to the inability to directly visualise the exact location of the transducer relative to the mouse brain. However, promising results were obtained indicating successful opening of the BBB. Specifically, EB leakage in the brain parenchyma was clearly evidenced in microscopy images of brain cryosections only in the case of mice treated with FUS in synergy with MBs. It is interesting to note that the mouse treated with higher acoustic power showed higher levels of EB dye diffusing through a larger brain area. The BBB permeability was also confirmed by Fibronectin and Fibrinogen immunofluorescent staining. Again, the FUS treated mice showed higher levels of the protein in all examined brain areas, whereas for the control mouse the protein remained in the extracellular matrix.Some issues identified during these preliminary experiments led to the development of a second improved version of the system. The first system comprises a relatively large water container that has to be filled up to the top so that the animal's head is in direct contact with the water and efficient ultrasonic propagation is achieved. However, the large water volume needed to achieve acoustic coupling makes the device heavy and less ergonomic. It was also observed that this design is prone to water leakage from the acoustic opening. Additionally, targeting the animal's brain in the laboratory setting was proven challenging due to the inability to directly visualise the transducer's location. Another identified limitation relates to the intravenous injections and administration of anaesthesia, which cannot be performed properly without removing the mouse from the device.The second version was designed to address these issues, thus facilitating mice experiments even more. This device uses a top to bottom approach and features motion only in the vertical direction. To be more specific, the FUS transducer was integrated in a coupling cone that can be moved vertically and tightly fit the mouse head. Accordingly, the dimensions of the system were reduced considerably making the device even more compact, lightweight, and ergonomic in its use. A silicone membrane was used to seal to bottom opening of the coupling cone. The membrane unavoidably reduces the efficacy of acoustic coupling. For this reason, it was selected to be thin (0.2 mm) to minimise ultrasonic attenuation. Also, ultrasound gel was applied to displace air and maximise ultrasonic transmission. It is noted that this is a simplified device suitable for single‐shot FUS applications. A more advanced device could be developed in the future with the addition of horizontal motion stages, thus enabling sequential placement of the transducer at multiple brain locations, but at the cost of increasing size and complexity.Additionally, the top to bottom approach allows the placement of the animal in the prone position that is much more stable, simultaneously offering better immobilisation of the mouse and visual confirmation of proper acoustic coupling. Furthermore, there is no possibility for water leakage from the cone. Finally, since the animal lies in a flat platform, there is direct access for the administration of anaesthesia, MBs and contrast agents through needles. An absorbent material was incorporated into the animal platform, thus reducing ultrasound reflections.It is important to ensure that no bubbles obstruct the beam path. In this regard, the manual rotational mechanism of the transducer incorporated in the second version of the system is extremely useful. A simple method to remove air bubbles is to rotate the transducer at 90°, and then, once the coupling cone is filled with degassed water, rotate it back in its horizontal position. An elastic band was included in the mechanism to stabilise the transducer.The motion accuracy of both systems was assessed following a calliper‐based methodology as previously detailed in the literature.The single‐element spherically focussed transducer of 1 MHz that was developed in‐house was proven suitable for the specific trans‐skull application of FUS‐induced BBBD in mice, most probably due to their small skull thickness. Although very promising results were obtained, further experiments should be performed using the second version of the device, which is expected to address all the difficulties faced during the feasibility studies of the first version.Despite the fact that the systems are mostly intended to be used in the laboratory setting, their MRI compatibility constitutes a great benefit since it allows for treatment planning and accurate targeting based on high resolution anatomical images, as well as confirmation of BBB opening by contrast agent enhanced imaging directly after treatment without moving the device from the scanner. Therefore, subsequent experiments may be benefited by treatment planning and post‐treatment BBBD assessment in the MRI setting. Note that MRI has been already employed in numerous studies mostly for assessing whether the BBB was successfully disrupted,It is essential to clarify that the current study focuses on the development of the two FUS robotic systems while a feasibility study on a small number of mice was only included to provide proof of concept for their intended application. Therefore, a dedicated targeting method such as the use of a stereotactic frame was not adapted. Instead, a global approach was followed, where the transducer's location was adjusted so that the FUS beam targets the skull centrally roughly focussing at the level of the hippocampus. This approach was efficient to obtain proof of successful ultrasonic coupling and disruption of the BBB. Follow up studies will focus on evaluating the second optimised version in a large number of mice accounting for specific parameters affecting the location and extent of the BBBD, as well as on assessing the ability of delivering chemotherapeutic drugs through the opened BBB.5Overall, the proposed devices constitute a cost‐effective and ergonomic solution for FUS mediated non‐invasive and reversible disruption of the BBB in small animal models, such as mice and rats. It should be though noted that both devices could also be used for other brain or body applications in various types of rodents, provided that their size is appropriate. The preparation of the experimental setup can be completed within a few minutes taking up minimal space. The user can remotely adjust the transducer's position and initiate sonication through a dedicated user‐friendly software. Such ergonomic devices are expected to facilitate research in the relevant field, thus accelerating clinical translation of the technology to offer an alternative therapeutic solution for neurological diseases.Marinos Giannakou contributed to the development of the robotic devices and draughting of the manuscript. Anastasia Antoniou contributed to the draughting of manuscript and implementation of the scientific methods. Elena Georgiou and Kleopas Kleopa contributed to the execution of the mice experiments. Christakis Damianou supervised the overall study, as well as the draughting of the manuscript.All authors declares no conflict of interest.


There is a growing but mixed literature on the health effects of minimum wages. If minimum wage changes have a statistically significant impact on health, this suggests health effects should be incorporated into cost‐benefit analyses to capture wider policy impacts. Whilst most existing UK based literature examines the introduction of a minimum wage, this paper exploits the 2016, 2017 and 2018 UK National Minimum Wage (NMW) increases as natural experiments using a series of difference‐in‐differences models. Short Form‐12 (SF‐12) mental and physical component summary scores are used as dependent variables. In the base case and all sensitivity analyses, the estimated impact of NMW increases on mental and physical health are insignificant. The policy implication is that health effects should not be included in cost‐benefit analyses examining the NMW. Mental and physical component summary scores from the Short Form‐12 (SF‐12), a widely used self‐reported health measure, are used as dependent variables. If the NMW has a statistically significant positive impact on health, this suggests health effects should be incorporated into cost‐benefit analyses as to capture the wider effects of the policy. The motivation stems from the fact that cost‐benefit analyses examining the uprating of the UK NMW do not examine the potential impact of the policy on health  and ta (after the policy change). By only considering employed individuals, the analysis removes potential adverse effects of unemployment on health which may (downwardly) bias the results.The sample was restricted to individuals aged 25–64 at the time of their interview. Individuals aged below 25 are excluded as from April 2016 this is the eligibility age for the top NMW rate. Those aged 65 and above are excluded as this is the age at which individuals become eligible for pension benefits, such as the state pension. This increase in income may be a confounding factor affecting health, so was removed. Individuals must be employed in both periods before period must be equal or up to 120% of the April 2017 NMW in the base case analysis. This condition means the control group are not affected by the NMW but are similar in their earnings to the treatment group. There is a trade‐off between the quality of counterfactual and sample size . The higher the control groups wages are permitted to be, the further they may diverge from the treatment group in their income and characteristics, although this permits a larger sample. Therefore, a sensitivity analysis using a 140% condition was also implemented in line with Kronenberg et al. . If higher incomes lead to improved health, the control individual's health will increase following a large pay increase. The Average Treatment Effect for the Treated (ATT) estimate will be downwardly biased, as the ATT estimate also captures increasing health in the control group. Treatment and control group sizes for the base case and presented in Table Using the natural experiment created by the 2017 NMW change as an example, individuals earning below the April 2017 NMW (£7.50) before April 2017 and earning equal to or above that rate after April 2017 are in the treatment group. The control groups wages in the 2.2The dependent variables are the SF‐12 mental and physical component summary scores (MCS and PCS respectively). The SF‐12 is a psychometrically tested generic non‐preference‐based measure of health which contains eight dimensions, such as questions on depression and physical functioning, which are common in most generic health instruments. In the UK general population, SF‐12 scores are transformed to be on a 0–100 scale with a mean of 50 and standard deviation of 10 , which were informed by the existing literature. A fixed effects specification is used, meaning εit is the composite error term, defined as εit=ai+uit where ai accounts for time‐invariant unobserved heterogeneity. For example, this might be the unobserved effect of readily available stop smoking services, access to which differs by individual but not between tb and ta. This factor may affect health, but data is not available in Understanding Society to include it as a covariate. The fixed effects specification was selected in order to eliminate the unobserved effect ai. This is desirable as when using ordinary least squares (OLS) on panel data it must be assumed that covariates and ai are uncorrelated. If this does not hold then pooled OLS estimates will be biased and inconsistent, giving misleading results of the ATT estimate. Importantly, the fixed effects specification means that time invariant covariates, such as gender, will be omitted. However, this is not problematic because the DiD coefficient, β3, is still analysable as Postt∗Treatedi is time variant. Two assumptions must hold for DiD to produce an unbiased ATT estimate. Firstly, there must be common trends meaning that were the NMW not introduced, the health outcomes of the two groups would follow the same trend. Secondly, there must be no spill overs, meaning NMW increases must not affect the control group. Spill overs would constitute a violation of the stable unit treatment value assumption (SUTVA). These assumptions are discussed later.44.1To estimate the impact of the NMW, the treatment and control groups must be statistically similar except for their exposure to the NMW. This means the treatment group should experience an increase in wages above any wage increases that the control group receive. To establish the wage effect, we run Equation :(2)waTable 4.2before and after periods for the treated group. The model predicts that the 2016 NMW increase led to a 0.274‐point decrease in SF‐12 MCS scores for the treated group, holding other factors constant, which is statistically insignificant at all conventional levels of significance. This suggests there was no significant impact of the 2016 NMW increase on the mental health of individuals in the sample who received the NMW increase. The models also predict insignificant impacts of the 2017 and 2018 NMW increases on mental health. Furthermore, the fixed effects DiD coefficients when using the SF‐12 PCS as the dependent variable, in the 2016, 2017 and 2018 models, are also insignificant at all conventional significance levels. This suggests the NMW changes in all years analyzed had no significant impact on physical health.Table 4.3εit and Postt∗Treatedi are correlated which violates the classic linear regression model assumption of no multicollinearity. If there are common trends, it is not essential that the treatment and control groups have the same average outcomes before the policy, as any selection bias is removed by the differencing operation. Figure There is no formal test for common trends, but the validity of the assumption can be assessed , whilst justification is provided to argue that common trends hold.In the base case and all sensitivity analyses, the ATT estimates for the impact of the 2016, 2017 and 2018 NMW increases on mental health are insignificant. These findings align to those of Kronenberg et al. (A limitation of the analysis is that the common trends assumption may not hold, particularly in the pre‐treatment trends of mental and physical health for the 2016 NMW change Figure . The issThere are several potential avenues for future research. Firstly, an exploration of within‐household spill over effects may prove to be an important factor affecting ATT estimates. Secondly, analysis of the long‐term health effects of the NMW may provide interesting results that are not captured in this paper or in the literature. Thirdly, there may be heterogenous treatment effects across sub‐populations, which may be of future interest. Finally, the introduction of the National Living Wage in April 2016 also entailed changes in the eligibility age for the top wage rate. This provides an exogenous age cut‐off for which regression discontinuity design could be applied to examine the impact of differing NMW rates on young people (Dickens et al., The wider societal impacts of the NMW are still not fully understood. Given the findings of this analysis, and the mixed results found in the literature, at present the policy implication of this work is that health effects of the NMW should not be included in future cost‐benefit analyses examining the NMW.There are no conflict of interest.


The paper “A review of center of pressure (COP) variables to quantify standing balance in elderly people: Algorithms and open access code”  or a standard ellipse area (SEA) is calculated, as these do not depend on the number of the points of the sway Duarte, . GeneralThese three ellipses  are centered at the sample mean and have common major and minor axis directions. In my opinion, the parameter of choice in an approximation of COP sway by ellipse areas should be the prediction ellipse area. Also, it should be noted that the way to report the orientation of the ellipse in the medial‐lateral (ML) and anterior–posterior (AP) coordinates has not yet been standardized. Currently, it is done by giving the angle by which the major axis of the ellipse is inclined versus either the ML‐axis (Rocchi et al., The author declares no conflict of interest.


Homogeneous hydrogenation catalysts based on metal complexes provide a diverse and highly tunable tool for the fine chemical industry. To fully unleash their potential, fast and effective methods for the evaluation of catalytic properties are needed. In turn, this requires changes in the experimental approaches to test and evaluate the performance of the catalytic processes. Design of experiment combined with statistical analysis can enable time‐ and resource‐efficient experimentation. In this work, we employ a set of different statistical models to obtain the detailed kinetic description of a highly active homogeneous Mn (I) ketone hydrogenation catalyst as a representative model system. The reaction kinetics were analyzed using a full second order polynomial regression model, two models with eliminated parameters and finally a model which implements “chemical logic”. The coefficients obtained are compared with the corresponding high‐quality kinetic parameters acquired using conventional kinetic experiments. We demonstrate that various kinetic effects can be well captured using different statistical models, providing important insights into the reaction kinetics and mechanism of a complex catalytic reaction. Statistical modelling: A rapid and powerful approach to assess the catalytic reaction kinetics is developed by combining the design of experiments with statistical modelling. Equating the regression equations and derived coefficients of resulting statistical models, we are able to measure the activation energy, to capture different reaction regimes, and to map the response of the observed reaction rate to condition parameters. Rapidly increasing demand in chemicals and fuels puts forward new challenges for chemical industry and chemistry in general. The fast implementation of novel catalytic processes is therefore becoming crucial as it enables more sustainable and effective chemical transformations.A,‐B,CE,F,G[D]14, HReduction of carbonyl compounds is an important process widely applied in the fine and bulk chemical industry. In contrast to conventional stoichiometric reactions yielding vast amounts of inorganic waste, catalytic hydrogenation utilizing molecular hydrogen represents an environmentally‐friendly and atom‐efficient alternative.Modern synthetic protocols allow obtaining well‐defined catalytic complexes with nearly any given ligand environment. In contrast, the testing procedures used to evaluate the catalyst performance are less defined. The limited scope of conditions used during the initial catalyst screening phase often result in a situation when important effects including the catalyst activation, its stability under reaction conditions and different deactivation pathways are overlooked. This may lead to a limited understanding of the intrinsic catalyst activity and therefore hamper the establishment of solid predictive structure‐performance relationships. The availability of kinetic data and its accurate modelling would provide a comprehensive insight in the behavior and mechanisms of catalytic reactions and therefore facilitate further development and optimization of highly efficient hydrogenation catalyst systems.The modelling of homogeneous catalytic reactions can be based on different approaches ranging from a purely empirical description to formal kinetics to theory‐assisted micro kinetic modelling.2 pressure, concentration of the catalyst and concentration of the base) and kept un‐coded. Due to uncertainty in measuring initial reaction rates, the chosen regress and was the average reaction rate (measured as product*t−1). The average rate was calculated as the concentration of produced alcohol divided by the reaction time in hours. No blocks were used and all runs were randomized save for the temperature due to the home‐built autoclave heating six reactions at a time in unison. With all the cube points, axial points and replicates, a total of 30 runs were performed. The reaction loadings and conditions are summarized in Table S1.The experimental setup was designed according to the Box‐Wilson methodologyA central composite face‐centered design was used to obtain a multiple polynomial regression equation that would take the same form as an adjusted Arrhenius equation describing the kinetics of the reaction.simplest first order version with no quadratic terms and no interaction terms takes the following form:A multiple polynomial regression analysis takes the form of a linear equation where each separate factor is included. In this sense, the 0 is the coefficient corresponding to the intercept, βi is the coefficient corresponding to the i‐th iteration of the regressor xi.Where ŷ is the actual (or expected) response, βW can be defined in a differential and logarithmic form:A physical meaning for a linear regression model can be established from the generalization of the formal reaction kinetics. Thus, in a general form for a given chemical process, the reaction rate The temperature dependence of the reaction rate constant is described by the Arrhenius equation:Overall, the expansion of the rate constant in the rate equation leads to a full linear equation as such:0 can be denoted as the frequency factor, and the rest are similar first order terms. Besides, one regressor (xi) may be seen as 1/T, leaving one coefficient βi as −Ea/R.Via the comparative analysis of Equations (1) and (5), intercept βgoodness of fit. Additional values for assessing the model are the R2 value, adjusted R2 value, the predicted residual error sum of squares (PRESS), the predicted R2 and the p‐value assessing the statistical significance of each term in the model.A second order polynomial regression of multiple variables includes square terms and interaction terms, each with its own coefficient.quadratic and interaction terms showing the joint effect of couples of parameters. If the addition of these terms is properly justified, it can be indicative to some actual physical effects. The eventual full regression equation will take the form ofA potential benefit of attempting to approximate a physical equation with an abstract statistical model is with the inclusion of normally excluded factors or terms, which might have a more complex effect on the reaction kinetics. This is exemplified by our addition of pressure as a factor, or the inclusion of Following this approach, the first step is to construct a full multiple polynomial regression with all quadratic terms and interaction terms. The resulting model is then examined and statistically insignificant terms or factors are removed using a stepwise elimination algorithm. To further justify the resulting model, the linearity of the corresponding main effects plot should be assessed along with the p‐value for the regressor.). Additionally, the corresponding responses are shown as the logarithm of the concentration of the reaction product divided by the reaction time which represents an averaged reaction rate (Table ). It is worth noting that the average rate is different from the initial reaction rate conventionally used in kinetic experiments. The initial reaction rate is often preferred as it makes it easier to extract formal kinetic parameters. However, for fast processes and for processes with a more complex behavior extracting the initial rates can be problematic and the resulting values can be heavily impacted by the reaction initiation procedure. Besides, it does not provide information about the overall process kinetics which can change during the process. In contrast, the average reaction rate can be a good descriptor for obtaining the formal kinetic parameters and capturing more complex behavior. For the formal kinetic parameters, the assumption can be made that the rate throughout the reaction is either linear or in correlation with the initial reaction rate of the target process.The key process variables including temperature, hydrogen pressure, concentration of the catalyst and concentration of the base are modified into a logarithmic form to fit the physical equation Table . Additite Table . It is fitlm) based on a least squares methodology. The data is weighted with the RobustOpts function which uses an iteratively reweighted least squares methodology. The analysis of variance was done using the ANOVA procedure.The full quadratic fit was done in Matlab using linear regression model fit function (where one is subtracted by PRESS (the prediction error sum of squares)The data obtained from the catalytic tests were processed using four different statistic models schematically shown in Figure To describe the experimental kinetic dataset, we first introduce kinetic model (I) based on the full multiple polynomial regression, which includes all the quadratic terms and interaction terms [Eq. (2)]. In this model the reaction rate (system response) can be defined as follows:a shows the goodness of fit of the experimental data points with model (I). The results point to the substantial predictive power of this indiscriminately constructed multiple polynomial model as evidenced by pred‐R2=0.9003 (see Table S3). Further validation can be done via a p‐value test that gives the probability of new data deviating from model prediction (see Table S4). The p‐value of 1.29e−10 suggests a good predictability of this model based on the data provided. The F‐statistic vs. constant model was 60.7 showing the significance of the model against the model consisting of only a constant term. However, the analysis of the individual p‐values for each term in the model reveals many instances far larger than an α of 0.05 indicating that many of the term effects are to be deemed insignificant, or within the “noise” (see Table S5). The only terms deemed significant are x1, x2, x3, x4, the interactions x1 : x3 and x2 : x4, as well as the x42 quadratic term. Furthermore, the p‐value for the lack of fit is 0.015 (see Table S4). These data show that the inclusion of excess  terms in model (I) renders it over‐fitted.Figure To remove the redundant factors, a new model was derived using the stepwise regression methodology. This methodology iteratively adds terms and keeps them if they meet a pre‐defined criterion, or removes them otherwise. The criterion used was the p‐value for the F‐test of the change in the sum of squared error when a term is added or removed. Additionally, outliers were removed by assessing whether the standardized residuals were larger than 1.25 or smaller than −1.25. In our case, 4 outliers were determined, leaving a dataset of 26 observations. Accordingly, a model with significant terms only was obtained:2 of 0.9696 and an adjusted R2 of 0.978 .This model has a predicted Rt Figure b.a show that the terms with the largest weight are the temperature, the base concentration and the 2nd order term for the base concentration.To further evaluate the models, the effect of model parameters was examined using z‐score and DoE t‐statistics methods. Upon conversion of each term value (including the response) to a “standard score”  or z‐score, with the same unit, we are able to compare the effects of those catalysis parameters.a show that all the terms are significant, with the terms for the base concentration, the 2nd order base concentration and the temperature having the most significance to the change in response being from these terms.The interaction terms have the lowest impact on the reaction rate. Next, by codifying the used factors as 1 and −1 for highest level and lowest level value respectively, the corresponding t‐statistic may be interpreted as the amount of influence of the term on the response in a standardized form, though the technical definition is it being a test of the null hypothesis that the effect is zero. The added value of this method is that the significance of such a standardized effect can be verified with a two tailed test using the error degrees freedom (df) and the chosen significance level α. For a df of 20 and an α of 0.05 the significance level is 2.086. In this case the response does not require standardization. The DoE t‐statistic results in Figure 2 is excellent, the currently abstract statistical model must bear resemblance to reality. The interaction terms between temperature and the catalyst ]), and the interaction term between the pressure and the base ]) are not explained by the generalized rate equations. A new model was constructed by removing these interaction terms. The square term for the base however was kept due to the high weight of its effect. Whereas the first three primary parameters may be well fitted with a linear equation, the fourth parameter (the base) is undeniably second order. Interestingly, constructing the same stepwise model from this hypothetical rate normalized by the concentration of catalyst used (TOF) obviously eliminates the catalyst term and produces a model featuring only the main linear terms and a quadratic base term, and naturally excludes interaction terms. The regression equation for model III is similar but includes the catalyst term:The stepwise eliminated model also runs the risk of overfitting. Though the predicted RTable S13). Next, all experiments with standardized residuals higher than 1.25 and lower than −1.25 were removed from the model. This left 24 observations as 6 observations were identified as outliers. The residual plots for the resulting model . The main effects of each parameter are presented as the prediction slice plots in the supporting information . The prediction plot for the base concentration shows that at a high enough base concentration the corresponding effect saturates and reaches a plateau of a certain maximum rate.All p‐values, except for that of the base term, are sufficiently low to refute the null hypothesis (see b) show that the base concentration has the most significant effect on the reaction rate. Compared to the z‐score, however, we see that the quadratic term for the base concentration and the temperature have now exchanged places in the effect weight. With a df of 21 and an α of 0.05 the significance level is 2.080 (t‐test table).Because the current model only leans on the validity of 24 remaining experiment data‐points, the p‐value for the lack of fit is only 0.0448 Table b show tThe linear regression models presented above imply that a kinetic equation, in which a linear product of the concentrations of the catalyst and the base produce the rate of alcohol production, which makes little sense from the chemical kinetics perspective. To understand why these variables give rise to such a good linear fit, the kinetics of the reaction were revisited. Though the exact reaction mechanism is not fully known, the basic process of catalyst activation and carbonyl compound hydrogenation can be explicitly considered. Following prior mechanistic analysis,−] stands for the concentration of catalyst precursor and [CAT] is the concentration of the activated catalyst. Catalyst activation proceeds via the base‐assisted hydride formation step. Given the assumption of the semi‐batch catalytic experiment (p(H2)=constant during the reaction) with the solution saturated with H2, this component is left out of the reaction rate equation. The rate of the catalytic hydrogenation reaction can be written aswhere , but with a few additional factors. The additional factors in this equation include ln[S] which is the natural logarithm of the substrate concentration, and The nonlinear model was set up as:2 being pressure in bar, x3 being the natural logarithm of the catalyst concentration, x4 being the natural logarithm of base concentration, x5 being the natural logarithm of the substrate concentration at the end of the reaction (note there is no coefficient for this factor) and x6 being the reaction time in seconds and the corresponding coefficient β5 being the rate constant for catalyst activation.with x2 values cannot be used for nonlinear regressionThis model is set up with six initial values of 1 for the coefficients, and with robust fitting options2 of 0.9497 .A nonlinear regression model is generally more difficult to validate. One of the possible validation methods is “leave‐one‐out‐cross‐validation” (LOOCV). Upon analyzing the model using LOOCV, an RMSE of 0.732 is calculated and an R0 Figure a.Table S20). The expansion of the model with an added coefficient for the substrate variable results in the respective p‐value of 0.24403 which is not significant. Importantly, the coefficients for most terms are comparable to the coefficients from the interaction eliminated model, saving for the obvious addition of the fifth coefficient related to the time term, and the base term which is now ∼1 potentially due to the lack of a second order term. The residual plots show a good distribution with a slight tailing in the histogram. The normal probability plot shows a good normal distribution and no residual sticks out in the residual vs fitted value plot or in the residual vs lagged residual plot .All the p‐values for the coefficients in this model were found significant . The high multicollinearity of these terms is due to the fact that the reaction time and substrate at the end of the reaction can be considered dependent variables.The Variance inflation factor (VIF) is a value that determines the multicollinearity of a term with other terms. Generally, a VIF of 4 would indicate strong multicollinearity, and require a term to be removed from the model. In the nonlinear model we see high VIF values for the substrate and the time terms, but low enough that one could argue they should remain Figure b. The hThe main statistical characteristics of the different models constructed above are listed in Table Stepwise eliminated model (II):Interaction‐term eliminated model (III):Nonlinear regression model (IV):−1 are similar for the interaction‐term eliminated model (III) and the nonlinear model (IV), but are distinctly different from that in the stepwise eliminated model (II). This is due to the fact that T−1 in the latter case is also accounted for the ln[CAT]⋅T−1 interaction term. Considering the coefficient for T−1 can represent activation energy Equations (16) and (17), the above result implies that the apparent activation energy is affected by initial catalyst concentration. Similarly, ln[CAT] has a decidedly higher coefficient in model II as compared to the other models (III and IV) because of the ln[CAT]⋅T−1 interaction term, suggesting effective catalyst concentration is limited by temperature. In both models II and III, the ln[BASE] is present with a negative coefficient. Model IV instead has a positive coefficient for ln[BASE], arguably due to the negative coefficient related to the reaction time t. This indicates a potentially negative coefficient for a parameter still missing in the equation IV. The coefficient for ln[BASE] thus can be interpreted as a potential catalyst deactivation path induced by base, as the reaction rate is seen to diminish at the higher [BASE] . It is also worth noting that interaction term [P]⋅ln[BASE] with a positive coefficient compensates for the negative effect of ln[BASE], suggesting high H2 pressure can suppress the aforementioned deactivation. The coefficients for the (ln[BASE])2 are equivalent between the linear models I and II. Finally, the coefficients for P are comparable in the three models.Although the exact values of the main coefficients in the three considered model equations  vary significantly, pronounced similarities and common trends can be noted in the obtained parameters Table .[29] MSI). The initial reaction rates for two different catalyst loadings were measured at varied temperature to assess the apparent activation energy, while kinetic runs at varying [BASE] and [CAT] were used to estimate the respective reaction orders. The results of the kinetic experiments are summarized in Figure The statistical analysis results were then compared to the reaction parameters obtained via conventional kinetic measurements. In formal kinetic experiments, the reaction parameters are extracted from the initial reaction rates  catalyst concentration. The change in the catalyst reaction order at higher loading also supports this . Our data strongly imply that, with mass‐transfer limitations, the intrinsic activity of catalysts can be missed when screening them even at a relatively low loading amount (e. g. 200 ppm). In the intrinsic kinetics regime, the reaction order in the catalyst was close to 1.5, while the reaction order for the base changes from ca. 2.5 at low base concentration to 0 at high concentrations  reveal a close coherence of the T−1 coefficient of ∼41 kJ/mol and ∼39 kJ/mol with the Arrhenius barrier  was found. The coefficient of ∼1 could be due to the lack of a quadratic term, whereas the fit remains acceptable due to the (over)abundance of terms in the form of time and substrate concentrations. This potential overabundance is indicated by an ill‐conditioned Bayesian.The kinetics of homogeneous hydrogenation of benzophenone ketone substrate catalyzed by a recently developed highly active Mn(I)‐CNP catalyst has been investigated and analyzed in the framework of formal kinetics as well as by using a response surface Box‐Wilson statistical methodology. In addition to gaining deeper insights into the behavior of this highly potent catalytic system, the study aimed at investigating the possibility of enhancing the data output from high‐throughput catalyst screening/optimization procedures. The results presented highlight the critical role of the secondary effects such as the reaction temperature and the presence and concentration of base activator/promotor on the performance of the homogeneous carbonyl hydrogenation catalysts.Equating the regression equations and the coefficients derived from it with statistical values has to be treated with strong skepticism and must therefore require rigorous statistics to validate this kind of method. The exact relation of the statistical models to the intrinsic reaction kinetics is often difficult to evaluate. However, having found significant models, we are now able to speculate on the relations of certain factors to the observed reaction rate. In this work the stepwise eliminated model (II) is found to be the most statistically significant. The interaction terms between temperature and catalyst concentration and between the pressure and the base concentration indicate some complexity worth further investigation. The interaction terms eliminated model (III) retains a quadratic term for the base concentration, which may be related to the complex role that the base plays in the reaction. For both of the models II and III we consistently find that the base concentration holds the strongest effect on the reaction rate. The limited effect we observe from the pressure is explainable by the increase in molecular hydrogen availability within the reaction medium. We have clearly demonstrated the ability of the statistical model to measure the activation energy of the reaction and to capture different reaction regimes. The coefficients resulting from the stepwise model correlate with the kinetic parameters from classically obtained kinetics. Additionally, the nonlinear model (IV) can be compared with the addendum that an argument could be made for the removal of substrate and time due to the fairly high VIF value, which in turn explains why models II and III are valid.The statistical methodology described in this paper may prove a reliable method to further understand complex and seemingly chaotic reactions. An apparent advantage of such an approach is that no initial assumption for the kinetics or the reaction mechanisms are required. This provides an opportunity to construct descriptive yet unbiased models. Besides it allows for the simultaneous testing of multiple factors allowing understanding of how one factor may influence the other, the addition of terms that usually do not belong to a “default” kinetic rate equation in order to understand the effect this term has, the statistical validation of the data and any coefficients or conclusions taken thereof and allowing extensive interpolation and predictability (effectively mapping a response to multiple factors of interest). Additionally, once the model is made it can be used for both optimization and for mechanistic studies. A careful marriage between reaction kinetics and statistical modelling could prove useful for combining the chemical fundamentals of the reaction mechanism happening in reality with our theoretical understanding of the reaction mechanism, usually supported by computational chemistry and through the avenue of microkinetic modelling.tBu), catalyst (MnCNP), solvent (dioxane) and an internal standard (dodecane) were charged in the autoclave inside a moisture‐ and air‐free glove box. Prior to experiments, all liquid chemicals were treated with basic alumina, degassed in a Schlenk line and dried over 3 Å molecular sieves. The autoclaves were then sealed inside the glovebox and connected to the gas feeding system of the catalytic setup. All gas lines were purged with compressed Ar to remove air, and then the reactors were pressurized to a target pressure with hydrogen gas. The reaction mixtures were stirred with Teflon‐coated magnetic stirrers and rapidly heated to a target reaction temperature. Prior to experiments, the temperature in the reactors was calibrated using an external thermocouple. Molar hydrogen consumption during the course of the reaction was followed with parallel pressure sensors volumetrically calibrated prior to catalytic experiments. After the reaction, products were analyzed with a gas chromatograph equipped with an FID detector.Acetophenone hydrogenation was chosen as a model reaction. The reaction schematics, catalyst structure and the experimental setup are shown in Figure The authors declare no conflict of interest.As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re‐organized for online delivery, but are not copy‐edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors.Supporting InformationClick here for additional data file.


To study the effects of the control temperature, ablation time, and the background tissue surrounding the tumor on the size of the ablation zone on radiofrequency ablation (RFA) of osteoid osteoma (OO). Finite element models of non‐cooled temperature‐controlled RFA of typical OOs were developed to determine the resulting ablation radius at control temperatures of 70, 80, and 90°C. Three different geometries were used, mimicking common cases of OO. The ablation radius was obtained by using the Arrhenius equation to determine cell viability. Ablation radii were larger for higher temperatures and also increased with time. All geometries and control temperatures tested had ablation radii larger than the tumor. The ablation radius developed rapidly in the first few minutes for all geometries and control temperatures tested, developing slowly towards the end of the ablation. Resistive heating and the temperature distribution showed differences depending on background tissue properties, resulting in differences in the ablation radius on each geometry. The ablation radius has a clear dependency not only on the properties of the tumor but also on the background tissue. Lower background tissue's electrical conductivity and blood perfusion rates seem to result in larger ablation zones. The differences observed between the different geometries suggest the need for patient‐specific planning, as the anatomical variations could cause significantly different outcomes where models like the one here presented could help to guarantee safe and successful tumor ablations. How does the background tissue affect the outcome of radiofrequency ablation of osteoid osteoma for typical configurations and treatment protocols? To study their effects, computer simulations using the finite element method for three different geometries and control temperatures of 70, 80, and 90°C were used to obtain the resulting ablation radius. The ablation radius showed a dependency not only on the properties of the tumor but also on the background tissue. These parameters have a direct impact on the extension of the ablation zone and therefore on the clinical outcome but testing on patients carries the risk of unsuccessful ablations, which could be detrimental to the patient's health. Therefore, we implemented computer models using the finite element method  to approximate common cases of OO and (2) to explore the effects of different anatomical configurations of RFA on OO. Examples of common cases can be seen in Figure  to appro2.2h is the enthalpy, and ki is the thermal conductivity (w/m∙K). These properties are temperature dependent, as described by the piece‐wise functions below. T is the temperature (K), t time (s) and QRF the heat source (W/m3). Qp is the blood perfusion heat loss (W/m3) and is defined as:ρb is the density of blood (kg/m3), cb the specific heat of blood (J/kg∙K), Tb the temperature of blood (K) .ωi is the tissue‐dependent perfusion coefficient (s−1) as a function of the cell viability Ω. The perfusion of each cell is kept constant and becomes zero when it dies, as specified by the cell death model.In RFA, heat is generated due to Joule heating which then propagates through the body. The simulations thus consisted of solving a coupled electric‐thermal problem, in which the thermal problem was governed by Pennes' bioheat equationQRF is given by:E is the electric field intensity (V/m) and σi is the electrical conductivity (S/m) of each tissue. The electric problem is then stated by the Laplace equation:V is the root mean squared value of the applied voltage (V).A quasi‐static approach was used for the electrical problem as it is known that tissues in the area of interest can be seen as totally resistive to the RF ablation frequencies (≈500 kHz).The following boundary conditions were set: a Neumann boundary condition of zero thermal flux at the symmetry axis and a Dirichlet boundary condition of constant temperature of 37°C at the outer boundaries for the thermal problem. Also, a Dirichlet boundary condition of zero voltage at the outer boundaries to mimic the grounding pad, a Neumann boundary condition of zero flux at the symmetry axis, and a Dirichlet boundary condition with a value equal to the applied r.m.s. voltage at the electrode surface were employed for the electric problem.Vr.m.s. is the r.m.s. voltage (V) set at the electrode boundary, Ttarget the desired control temperature, Tt the temperature at the tip at time t, Kp the error proportionality constant, and Ki the integral proportionality constant. The initial voltage was set to zero. Then the Kp and Ki values had to be found with similar behaviors as in the ex‐ Bitsch et al experiments.Kp at 1.15 V/K and Ki at 0.06 V/K/s.To mimic the clinical setting, the voltage was regulated such that a pre‐defined temperature at the tip of the electrode was reached, and subsequently maintained, which can be modeled by using a PI‐controller, i.e.For most of the model, the Trujillo and Berjanoσi is the baseline electrical conductivity (S/m) of each tissue at 37 °C, ∆σ is the 1.5% temperature dependent rate of change in electrical conductivity per degree Celsius, and σvap is the modeled electrical conductivity of vaporized tissue where σvap=10x10−3 (S/m).Regarding electrical conductivity, a linear increase of 1.5% per degree Celsius until the point of vaporization was used. Then, vaporization is characterized as a sudden drop in the electrical conductivity, with a linear decrease up to a factor of 10,000, as described in Equation .(6)σiT°C:ki is the baseline thermal conductivity of each tissue at 37°C and ∆ki corresponds to a 0.003 change in thermal conductivity per degree Celsius.The thermal conductivity was considered as having a linear increase until the point of vaporization where a maximum value was set for any temperature beyond 100 °C, tissue vaporization was modeled using the enthalpy methodρici represent the baseline density kgm3 and specific heat JkgK of each tissue, ρvap(370 kgm3) and cvap (2156 JkgK) are the density and specific heat of vaporized tissue,hfg is the latent heat of vaporization (2.25 x 106Jkg) and Ci is the water fraction of each tissue.When water starts to evaporate there is a sudden change in the heat capacity during the phase‐change. Although tissue vaporization is not expected because the PI controller will regulate the output current to maintain a maximum target temperature of 90 FEniCS,2.3Most of the tissue properties were obtained from,2.4R is the universal gas constant, A (a frequency factor), and ∆E (the activation energy for the irreversible damage reaction) the cell‐line dependent parameters. Since the treatment is on bone tumors, and Tillotson et al found that cortical and trabecular bone have roughly the same susceptibility to heat,A=8.99x10133s−1 and ∆E=838kJ/mol.To assess the tissue damage caused by the heating process we used the Arrhenius damage model.Cell death (Ω) is given as a probability of cell viability, where exposure to higher temperatures for longer periods increases the likelihood of a given cell dying. A value of Ω = 4.6 was chosen as the threshold, corresponding to a 99% probability of cell death. Once a cell reached said threshold, it was considered dead and the perfusion was stopped. To calculate the outcome for our studies, a radius from the center of the electrode in directions perpendicular and parallel (upwards) to the electrode was used to calculate the resulting cell death radius in both directions. Additionally, we allowed the simulations to cool down for 5 min (chosen arbitrarily based on preliminary results) after the active electrode was turned‐off to capture the thermal damage more accurately over time while the heat was still dissipating, as shown in Reference 2.5Our model is based on the computer model by Irastorza et al,Bitsch et al created three OO models using bovine long bone specimens, categorized depending on the thickness of the cortical bone lamella separating the nidus from the periosteum. A hole was drilled and filled with 0.8% agarose gel to model the nidus. In the soft tissue surrounding bone, three thermocouples were placed at distances of 0, 5, and 10 mm from the periosteum. The specimens were heated to an internal temperature of 35°C, and RFA was performed for 400 s with a control temperature of 95°C. The temperatures measured by the thermocouples were reported in graphs. The ex‐vivo setting was then replicated by Irastorza et al using the temperature profiles obtained from the temperature probes to validate and optimize their OO model. Of the three Bitsch et al models, the one with a 3 mm lamella thickness was chosen arbitrarily here, but our model was compared against all their configurations. For a more detailed explanation of the ex‐vivo experiments and the assumptions to replicate them, please refer to Bitsch et al33.1The results were within 1°C degree of difference to the ones obtained by Irastorza et al for most of the ablation time with a maximum absolute error of 2.2°C, encountering the largest differences for the probe closes to the tumor and almost identical results for the other two. Against the Bitsch et al results, a maximum absolute error of 4.3°C of difference was found. Figure 3.2°C, and there was no tissue vaporization.Figure X and Y indicate the directions in which the temperature isotherm was obtained: X, perpendicular to the electrode; Y, parallel to the electrode. Both measurements start at the center of the electrode, and the Y direction was measured from the center to the top.Figure The ablation radii were larger at higher temperatures, and also increased with time, as expected. The ablation radii of all the tested geometries and control temperatures were larger than the tumor at the end of the ablation. The ablation radius developed rapidly in the first few minutes and then slowed down by the end of the ablation. The ablation radius was smallest for geometry (b), followed by geometry (a), and largest in geometry (c), when compared at the same control temperature. The radius was almost identical in both directions for the first two cases, whereas in geometry (c), the ablation radius increased considerably more in the direction perpendicular to the electrode after a couple of minutes for all the tested control temperatures.10−4s−1 and 26 x 10−4s−1) values in the nidus. These parameters were chosen because they are the most influential factors defining the size of the ablation radius.To test the sensitivity of the models further to changes in the tissue parameters, we performed simulations with four combinations of maximum and minimum electrical conductivity  and blood perfusion  but on the surrounding tissue as well. This is particularly clear in the peak at the electrode‐tumor interface (at 0.75 mm) and at the tumor‐bone interface (at 5 mm). The amount of induced heat varied with time as a function of the voltage applied but its distribution remained more or less the same all the time. Hence, only one graph of the 15 min measurement is shown.The temperature profile also shows the effects of the differences on the distribution of induced heat. At the beginning of the ablation, the case with the tumor surrounded by cortical bone seems to induce less heat around the tumor, but creates an additional peak of heat at the tumor‐bone interface, which, with time, increases the maximum temperatures reached deeper in the tissue. It is also interesting to note that all the cases seem to have similar heat transfer rates after the tumor (at 5 mm), as shown in the slope of the temperature profile.4RFA is a technique that has been consolidated as a standard clinical practice for the treatment of OO due to its effectiveness and low complication rates. However, neither the effects of the ablation time, nor the control temperature, nor the effects of the background tissue surrounding the tumor on the resulting ablation zone are well understood. Some studies have used ablation times as short as 4 minIn some of the first RFA studies with OO, Rosenthal et al concluded that little to no change was achieved in the extent of the ablation zone after approximately 3 min but that nevertheless, in clinical practice, the patients seemed to experience less recurrences when the duration of the RFA was increased to 6 minA possible explanation for the different radii obtained with each model may be due to the effects of blood perfusion. Schutt and HaemmerichHowever, we think that a more plausible explanation for the overall results may be due to the differences in the electrical conductivity of the tumors and their surrounding tissue. It is known that the electrical conductivity of the target tumor is crucial in defining the volume of the ablated tissue, with higher electrical conductivities allowing for more energy deposition and thus larger ablation volumes. Yet, Solazzo et alIrastorza et al mentioned a similar trend in their computer models of OO, where they studied the presence of the layer of sclerosis using various degrees of vascularization and bone density. In their study, the ablation radius increased with decreasing electrical conductivity of the reactive zone, and an additional peak in the temperature distribution, which is similar to what Solazzo et al found.The effects of this mismatch in electrical conductivity were stronger when the electrical conductivity of the nidus was increased further, resulting in even larger ablation radii than the ones produced with the original settings. These variations in tumor properties, however, also showed that the blood perfusion of the tumor had little impact on the heat distribution in comparison to the electrical conductivity. This lack of dependency on the blood perfusion seemed to be because of how quick the ablation zone encompassed the nidus, stopping the nidus's blood perfusion in the first seconds to a minute of the procedure. This insight could be particularly important in cases where RFA is used to treat a malignant bone tumor because tumor tissues, especially malignant ones, seem to demonstrate much higher electrical conductivity compared to healthy tissue.Our experiments show that ablation outcomes are highly tissue dependent, and not only on the properties of the target, but also on its surrounding tissues, which suggests the need for accurate patient specific imaging and treatment planning. This could be particularly important for tumors close to structures at risk, and considerations should be made based upon both the tumor properties and its surrounding tissue. Computational modeling for patient specific planning could play an important role to guarantee the success of the procedures.A limitation of this study is the lack of validation of the model against clinical or in‐vivo models; it could only be validated against ex‐vivo OO experiments. However, since the model correlated accurately to the ex‐vivo experiments, one can assume that the model demonstrates the effects and importance of the tested parameters with clinically useful levels of agreement.5The ablation radius of RFA on OO is clearly dependent on the target temperature and ablation time, where higher temperatures and longer ablation times produce higher ablation radii. The ablation radii grow rapidly during the first few minutes and continue to grow, although slowly, until the electrode is turned off after 15 min. The size of the ablation radius clearly depends on the background tissue surrounding the tumor, where tissues with lower electrical conductivity led to an increased ablation radius, and this effect increases when the electrical conductivity of the tumor is increased as well. The blood perfusion of the tumor does not seem to have an important effect on the resulting ablation radius. This suggests the need for patient specific imaging and planning of the procedures, where computational models like the one presented here could help to give more accurate and personalized patient treatment.


The proportion of the population with immunity because of natural infections has increased significantly due to the spread of the Omicron strain, reaching more than twice the number confirmed and well over 20% of the general population. The proportion of those who have at least partial immunity, including from vaccination, is close to 90%, even when the waning of immunity after vaccination is considered. The peak of the current seventh wave of the epidemic is expected in August, and cases should begin declining rapidly thereafter. What is required in effectively controlling the seventh wave is the rapid testing of high‐risk individuals who have developed symptoms and the administration of antiviral drugs to those testing positive, as well as updating the vaccine profile of those who have not yet received third or fourth shots. For highly infectious but less pathogenic variants like the Omicron, a significant supply of rapid antigen testing and further shortening of the current quarantine period are needed to maintain adequate medical and long‐term care and promote socio‐economic activities.As of July 25, 2022, the number of reported cases of COVID‐19 infection in Japan exceeds 10 million,2Similar to the previous approach,3Figure In the previous estimate,Among those in the “Vaccine (with waning)” category, the proportion of those immunized through one or two vaccines is called “first and second,” and the proportion of those immunized with three or four doses is called “third” and fourth.” Figure 4Figure When considering the waning of immunity, however, the proportion of the vaccine‐immunized population (in purple), which was close to 50% at the peak in November 2021, fell below 40% in July 2022. In particular, in December 2021 and June 2022, just before the beginning of the sixth and seventh waves, the proportion of the vaccine‐immunized population clearly decreased. Therefore, it is possible that factors triggering each wave included not just increased infectiousness and the immune escape properties of the variants but also a decline in vaccine‐related herd immunity.In Figure On the other hand, the overall herd immunity ratio (green in Figure When the basic reproduction number of 2.5However, if the basic reproduction number is >2.5, the critical immunization rate will also be >60%. In addition, it has been reported that an Omicron infection without vaccination increases the risk of reinfection when compared with breakthrough infectionsThe authors have stated explicitly that there are no conflicts of interest in connection with this article.


The latest edition of the Basic Safety Standards, entitled the International Basic Safety Standards for Protection Against Ionizing Radiation and for the Safety of Radiation Sources, is the product of extensive global cooperation. The BSS are jointly established together with five other organizations, including the International Labour Organization and the World Health Organization. González : 2Bulletin dedicated to the development of nuclear and radiation safety standards. As Abel González, the then director of the IAEA’s Division of Radiation and Waste Safety argued, the 1990s had seen the “emergence of […] an ‘international regime on nuclear and radiation safety’” (ibid.). In the wake of the Chernobyl nuclear accident, revisions of radiation safety standards and the introduction of the concept of safety culture were a response to a crisis situation in the nuclear industry. This new “international regime” concerning radiation protection and nuclear safety has been projected legally binding undertakings among member states, globally agreed-upon international safety standards, and provisions for facilitating the application of those standards.In 1998 the International Atomic Agency (IAEA) published a special issue of its This special issue focuses on those organizational structures, material resources, diplomatic practices, and national ideologies that facilitated the social and political shaping of the scientific field of radiation protection in the 1960s and 1970s.Historians have highlighted scientists’ struggles to define the appropriate unit of radiation and their long-standing efforts to invent suitable measurement devices and improve instrumentation, to detect and agree on the effects of radiation on biological systems, to identify the acceptable level of risk with regard to radiation exposure and to agree on safety radiation standards in both medicine and industry. The scientific controversies that emerged through the above processes reflect the complexity and messiness of scientists’ collaborative production of what eventually comes to be considered as reliable knowledge. They also reveal the powerful role of those scientific institutions that assumed the task of regulating radiation and enforcing acceptable standards.3Until 1934, the recommendations on radiation protection referred to medical operating procedures for the use of X‑rays and radium, with a particular focus on equipment design, shielding from radiation sources, and shielding of rooms and enclosures with lead. In parallel, research into the genetic effects of radiation exposure was getting underway: Hermann Joseph Muller’s genetic research highlighted the pressing need to better understand the biological effects of radiation and to regulate exposure to it.As powerful institutions started to take up the elaboration of radiation standards and protection practices, as well as their legal requirements, the field of radiation protection as a whole was characterized by disagreement and controversy. Wartime was marked by the US Atomic Energy Commission’s (AEC) attempts to downplay the consequences of exposure to radiation and by the classified status of research on the topic. The studies that the AEC sponsored were often designed to prove that it was relatively harmless for humans to work at facilities such as Oak Ridge, a major national nuclear facility for the Manhattan Project, irrespective of the costs paid by humans used as experimental subjects Olwell . As LindIn the aftermath of the bombings of Hiroshima and Nagasaki there was a radical change in the conceptualization of radiation safety as it shifted from being an issue of secondary concern to radiologists and radiological physicists to a major task and the subject of a new discipline. The broad public concern about the effects of radiation, as well as the rapid development and adoption of new medical technologies (such as the radioisotope teletherapy units) and the emergence of the nuclear industry posed numerous challenges in the field of radiation protection.In early spring 1953 experts in radiation protection representing their countries—the US, Canada, and England—met at Arden House in Harriman, on the outskirts of New York. The meeting resulted in agreement on some final recommendations for new radiation protection standards. This was the third in a series of conferences that became known as the Tripartite Conferences on Radiation Protection. The first had taken place in September 1949 at Chalk River, Ontario, the site of the Anglo-Canadian wartime nuclear research project, the second the following summer at Harwell, the UK’s new atomic research facility. The tripartite initiative resulted from informal contacts between scientists researching ionizing radiation. At stake in Harriman was the harmonization of protection practices and close technical cooperation among the three countries. This meeting symbolized the governments’ recognition of the dangers ionizing radiation posed to human health and served as an acknowledgment that work in the burgeoning nuclear industries and in military laboratories could not continue without revised radiation protection standards and an agreed system of international regulation Taylor .In this period safety standards issued by national and international regulatory institutions were heavily based on the study of bomb survivors, limiting their ability to account for low levels of radiation exposure Lindee . The mas6global experiment, Rentetzi shows that the IAEA’s agenda included not only technical assistance to member states but presupposed research and thus a reconceptualization of scientific experimentation. What started as an intercomparison of radiation doses among a few European institutions in the early 1960s ended up being an immense open-ended experimental procedure that involved participating laboratories from across the world. Through a step-by-step analysis of the development of IAEA’s dosimetry, Rentetzi argues that radiation protection has never been simply a technical issue, but instead it also required multinational diplomacy and the institutional system of the UN in order to be standardized across the globe.The special issue begins with two essays that question the role of major UN organizations in framing radiation protection on a global level. Linda Richards shows how the WHO’s approach of conceptualizing radiation protection as an institutional responsibility and a human right to health failed due to the preeminence of American risk models of radiation regulation that have dominated the discussion. Her paper reveals the untold story of how Brock Chisholm, the WHO’s first Director General, became the leading advocate of a new concept of radiation protection as a human right to health, encompassing physical, mental, and social well-being. Despite his activities, the actors who set the agenda and actually defined radiation protection were the scientists working for the US Atomic Energy Commission. As the US was the major funder of the WHO, it was able to discipline the experts of the international organization. Based on extensive archival research, Richards also touches on the conflicts between the newly established IAEA and the WHO over radiation standards and predominance in the field. Maria Rentetzi questions the politics of radiation dosimetry by focusing on the beginnings of the IAEA’s radiation dose intercomparison program that took shape during the early 1960s. In collaboration with the WHO, the agency tried to standardize dosimetry on a global level. Introducing the concept of a The next two essays address the development of nuclear safety and health physics in different national contexts, highlighting the ways that knowledge and practices move across national and international institutions. Focusing on Spain, Ana Romero de Pablos explores how the circulation of nuclear artifacts deeply transforms knowledge about their use, scientific practices, and industrial management—while also reshaping notions of radiation safety and creating an entanglement of the political and diplomatic with the technical and scientific realm. In 1964, a Westinghouse nuclear power reactor arrived in Spain, bringing along regulations and experimental practices related to radiation safety and protection that were new to the local community of scientists and engineers. Romero de Pablos’s paper gives us a glimpse of how international organizations such as the IAEA affect local nuclear practices, how political and economic considerations are decisive over technological solutions, and how Spain’s first nuclear power plant prompted a stream of legal, economic, and scientific transformations in relation to nuclear safety. This study is greatly benefited by unique and rare material from the archives of Tecnatom, the engineering company that coordinated the construction of the plant. John DiMoia highlights the power of knowledge and practice transfer in the field of radiation protection in a radically different context, that of postwar South Korea. Challenging the American-dominated institutional history of Korea, DiMoia argues that Koreans crafted a version of health physics at the intersection of medicine and agriculture, and in a way that suited both their colonial past and their cooperation with new American counterparts. His provocative essay suggests that by exploring the Korean version of radiation protection, we can see the rise of a cluster of related interests, including environmental science and the effects of industrialization.and diplomatic, shaping research agendas on radiation protection. Ana Barahona offers an analysis of the development of Mexico’s radiobiology, including radiation protection, as a complex field that required the support of the IAEA and of an extended local network of scientists and institutions. She traces the development of radiation dosimetry and protection programs in the country, which were both strongly supported by the IAEA. In her detailed study, Barahona unravels entangled scientific interactions on local and international levels, shedding light on the inextricable relation between radiobiology research, nuclear industrial establishments, and radiation protection. In the end, what unites all the papers in the special issue is their focus on the role of UN international organizations such as WHO and IAEA in shaping local contexts and imposing regulatory frames during periods in which the international organizations were struggling to create their own niche in the field.The special issue ends with an essay that examines the ways in which the technical collaboration between national and international institutions was deeply political Today the renewed interest in nuclear power plants and the use of advanced nuclear medical technologies pose new challenges to the field of radiation protection. Scientists have only recently realized that radiation protection is not a purely scientific matter, but is also a social and political concern. In February 2016, the IAEA organized an international conference on the “Human and Organizational Aspects of Assuring Nuclear Safety” that focused mainly on nuclear power plants. It was the first time that the agency placed such an emphasis on the human factors affecting the safety culture of the nuclear industry and called for a reconceptualization of the term. In his introductory remarks the then Director General Yukiya Amano urged participants to reflect upon the lessons that had been learned over the last 30 years, that is, since the Chernobyl disaster. In addition, the IAEA’s 2015 Director General’s Report on the Fukushima Daiichi Accident left no doubts that human and organizational factors played a significant role in the management of the nuclear disaster following the earthquake and the subsequent tsunami in Japan. As Amano argued, “[a] major factor that contributed to the accident was the widespread assumption in Japan that its nuclear power plants were so safe that an accident of this magnitude was simply unthinkable”  held its international congress in Glasgow under the overarching theme “Living with Radiation—Engaging with Society.” As the organizers argued, “[t]he management of protection will always involve social decisions and choices.” William Magwood, Director-General of the Nuclear Energy Agency (NEA), a specialized agency within the OECD, wrote in his 2016 report on the Fukushima accident that “we must address the human aspects of safety, such as ensuring effective safety cultures for both operators and regulators and continuing to learn from safety research, including through the NEA’s international joint research projects.” And in the sector of nuclear medicine, the “Bonn Call for Action,” a joint position statement published by the IAEA and the WHO in 2012, argued for a holistic approach to the problem of radiation protection and called for the inclusion of actors from civil society as well. One of the call’s major proposed actions is to improve radiation safety culture in health care.7World Nuclear Industry Status ReportAt the same time, over the last decade the nuclear industry has been largely left behind by the booming demand for clean energy. Especially after the Fukushima accident and due to major concerns over radiation protection among the general public, more reactors were permanently shut down than built. It seems that investors have abandoned nuclear technology—not only because of the new public awareness, but also due to high costs and delays in construction. Obviously, given the lack of new investments, the average age of the world’s reactors is increasing, requiring ever more resources dedicated to maintenance and safety. According to the 2021 World Nuclear Industry Status Report, out of the 438 reactors in operation globally in 2002, only 415 were operating in mid-2020, the lowest number over the last 30 years. Also, out of the 52 new plants under construction at the time of the report, at least 33 were behind schedule, mainly because of the luck of investments. Not a single project came up in the first half of 2020 and global nuclear investment dropped drastically while resources spent on wind and solar energy are increasing. Only China continued to invest in nuclear energy, bypassing France to become second after the U.S. in nuclear energy production. In the foreword of the report, Naoto Kan, Japan’s prime minister at the time of the Fukushima disaster, proclaimed that, “I now believe that the time has come for Japan and the world to end its reliance on nuclear power” (Yet, late in 2021, the European Commission surprised the world by publishing a draft proposal that classifies nuclear energy as climate-friendly, a taxonomy that aims to revive the nuclear industry. And the EU is not alone in promoting nuclear energy as sustainable. In addressing the 2020 United Nations General Assembly, IAEA’s Director General Rafael Mariano Grossi confirmed that “nuclear power is part of the solution to the climate crisis.”Uranium 20209Critical voices, however, remind us that the nuclear industry is not and cannot be sustainable given that nuclear power plants are uniquely threatened by climate change—just think of the Fukushima accident – or more recently, by war (Brown & Solomon However, technological and scientific standards alone have not been sufficient in protecting humans and the environment from radiation. This special issue hopes to keep up the momentum created by the above agencies and institutions and, in addition, offer a historical and critical perspective on why human and social risks have been underrated. We bring together scholars working on the history of the nuclear sciences and the role of international organizations in shaping policies, promoting specific lines of research and technologies, and producing standards—while arguing that humanities and social sciences have much to contribute to the current debate on radiation protection.