It is an open question whether turbulent mixing across density surfaces is sufficiently large to play a dominant role in closing the deep branch of the ocean meridional overturning circulation. The diapycnal and isopycnal mixing experiment in the Southern Ocean found the turbulent diffusivity inferred from the vertical spreading of a tracer to be an order of magnitude larger than that inferred from the microstructure profiles at the mean tracer depth of 1,500 m in the Drake Passage. Using a high-resolution ocean model, it is shown that the fast vertical spreading of tracer occurs when it comes in contact with mixing hotspots over rough topography. The sparsity of such hotspots is made up for by enhanced tracer residence time in their vicinity due to diffusion toward weak bottom flows. The increased tracer residence time may explain the large vertical fluxes of heat and salt required to close the abyssal circulation. Turbulent mixing next to rough topographic features is believed to be key in the closure of the abyssal ocean circulation. Here, using Southern Ocean data, the authors show that mixing hotspots trap fluid and mix it for long periods, explaining the global impact of relatively few mixing hotspots. Turbulent mixing in the ocean interior plays a leading role in supporting the ocean meridional overturning circulation (MOC) and its associated transports of heat, carbon and biological nutrients. In particular, mixing across density surfaces  is the main process that allows bottom waters to rise across the stable ocean stratification up to a depth of about 2,000 m. Shallower waters are brought to the surface by the westerly winds blowing over the Southern Ocean without any need of diapycnal mixingκ, which measures the rate at which the turbulence spreads a tracer across density surfaces over time. Munk2 s−1, a value three orders of magnitudes larger than the molecular diffusivity for heat, is required to allow the observed 6 m3 s−1) flow across the deep ocean density surfaces. Values of κ an order of magnitude larger or smaller would imply an MOC much larger or smaller than observed.Diapycnal mixing in the deep ocean is primarily the result of breaking internal waves or benthic boundary layer processes occurring at scales from millimetres to tens of metres. The mixing generated by all these turbulent processes is typically quantified in terms of a turbulent diapycnal diffusivity, κ in the abyssal ocean is the remarkable range of scales involved, from the millimetre scales of mixing to the thousands of kilometres of the MOC. Simultaneous direct measurements over such a large range of scales is beyond present technologies. Oceanographers have therefore resorted to several different approaches over the last five decades to paint a full picture. Direct measurements with turbulent probes deployed along vertical casts, recently reviewed by Waterhouse et al.2 s−1 in most of the ocean interior, except within a few hundred metres of rough topographic features, where the values are one to two orders of magnitude larger. Tracer release experiments have confirmed that mixing rates are weak in the upper kilometre of the ocean and increase to 2 s−1 around rough ocean topography4562 s−1 below 2,000 m89A major challenge in directly estimating the average The diapycnal and isopycnal mixing experiment in the Southern Ocean (DIMES) was conceived with the explicit goal of investigating the role of topography in setting the distribution of diapycnal and isopycnal mixing in the Antarctic Circumpolar Current (ACC), a key region for the global MOC. The experiment consisted of a release in 2009 of an anthropogenic tracer in the ACC, upstream of Drake Passage, on a neutral density surface at a depth of roughly 1,500 m at the location shown by a star in 2 s−1 with small vertical variations upstream of the Drake Passage, where topography is relatively smooth and turbulence is weak2 s−1, while the microstructure-based diffusivity is an order of magnitude smaller at the mean depth of the tracer, albeit being up to two orders of magnitudes larger close to topography1213141516The microstructure and tracer-based methods both found κ of 2 s−1.In this paper, we employ a high-resolution numerical model of the ACC flow in the Drake Passage to reconcile the tracer and microstructure estimates of mixing. More specifically, we inject a numerical tracer in the model to investigate how often it is advected by the mean currents and mesoscale eddies over topographic features where diapycnal mixing is very large. The vertical profile of diffusivity acting on the numerical tracer is prescribed based on DIMES microstructure data. We find that the numerical tracer spreads rapidly across density surfaces, because it is advected over the seamounts and ridges that stick up above the abyssal plains at the tracer depth and spends enough time there to experience an overall 2 s−1 across a density surface whose mean depth is close to 1,500 m. In the conclusion, we will argue that a similar picture may apply to the rest of the deep ocean as well, where the long residence time of tracers near mixing hotspots results in large fluxes across density surfaces.This study, using a combination of microstructure and tracer observations together with numerical simulations, suggests that in the Drake Passage region, topographically induced diapycnal mixing, together with lateral stirring by mean flows and mesoscale eddies, is sufficiently strong to mix tracers at a rate of κ, and the rate of turbulent kinetic energy dissipation, Starting with OsbornN2=−gγz/ρ0 is the buoyancy frequency, g is the gravitational acceleration, ρ0 is a reference density, and γz is the vertical gradient of neutral density, that is, the vertical gradient of in-situ density minus the dynamically irrelevant gradient due to compressibility of seawaterκ by up to a factor of about three20where http://dimes.ucsd.edu/en/ for details of cruises).As part of the DIMES experiment, a number of vertical profiles of N2 (κ (hab) coordinate. The hab coordinate is used to capture the bottom enhancement of κ due to turbulence induced by interactions of bottom flows with topography. The majority of profiles ended within 50±25 m of the bottom. To isolate the surface mixed layer and region of strong T/S interleaving, data shallower than 1,000 m were not included in this analysis. A 500 m running mean was applied to the resulting average profiles to reduce high frequency fluctuations. The standard error was computed using a bootstrap method treating each profile as an independent sample. Detailed cruise information as well as a more detailed description of the methodology are provided in St. Laurent et al.et al.22Mean vertical profiles of buoyancy frequency N2 ,   by imposing the mean diffusivity profile in hab. Thus, seamounts and ridges will result in large κ values further up in the water column than in deep valleys and trenches. Assuming that the profile of κ is only a function of hab may seem naive, but it is supported by the measurements. Panel (b) in N2 and κ as a function of hab averaged on casts over topography deeper and shallower than 2,500 m, respectively. Both N2 are larger over shallower topography, but their ratio κ is very similar, if plotted as a function of hab. Thus the mean of all profiles seems to be representative of the entire domain of our focus.Our goal is to test whether the mixing profiles measured with the microstructure profilers are consistent with the overall mixing sampled by a tracer released in the same region. To this end, we constructed a three-dimensional (3D) κ map that is only a function of hab, we ignored regional variations in the profile of κ. For example, it appears that κ is larger where bottom velocities are largerκ profile only function of hab, as shown next, suggests that regional variations are not of leading order importance for our study.By imposing a 3D 3SF5) was released in February of 2009 along the neutral density surface of 27.9 kg m−3 at the location marked as a yellow star in The microstructure profiles present a largely under-sampled view of a highly heterogeneous mixing field in the Drake Passage region. To obtain a measure of the spatiotemporal averaged mixing in the same region, an anthropogenic tracer was released in the South Pacific Ocean as a part of DIMES. The passive chemical trifluoromethyl sulphur pentafluoride , is shown in −5 m2 s−1. The value of κ(hab) at the depth of the centre of mass of the tracer as a function of time is shown as a red-dashed line in the top panel of −3 m2 s−1, while the tracer above hab=1,000 m experienced an averaged diapycnal diffusivity more than an order of magnitude smaller ∼4 × 10−5 m2 s−1. The overall diapycnal diffusivity Encouraged by this comparison, we now use the model output to understand the seeming discrepancy between the microstructure-based hab. The probability that tracer is found at a certain hab is given by the function,The importance of strong mixing close to the topography is better quantified by studying the distribution of tracer as a function of depth above the bottom H is the ocean depth, the integral in the numerator is restricted to tracer deeper than hab, while the integral in the denominator is taken over the total volume of the simulation and it remains constant until the tracer leaves the integration domain. The probability function P(hab), plotted in κ as a function of hab. While most of the tracer sits far above the bottom, where κ(hab) values are O(10−5) m2 s−1, the small fraction of tracer within a kilometre of the ocean bottom experiences κ(hab) values one to two orders of magnitude larger. The overall P(hab) × κ(hab) integrated over all hab. Determining whether the integral of this product is dominated by contributions within the bottom kilometre or above is tantamount to asking whether the tracer comes in sufficient contact with pronounced rough topography to experience a net large average diapycnal diffusivity or not. This is the key question posed in this work.where κ(hab) × P(hab) is shown as a black line in P(hab) × κ(hab). This confirms that even though the amount of tracer decays strongly towards the ocean floor (κ towards the bottom (P(hab) near the bottom compared with those an equal distance above the peak are largely due to trapping of tracer near the bottom, as will be discussed belowThe product an floor , the expe bottom  makes upbottom  efficient stirring of the tracer over the whole domain by mesoscale eddies bringing the tracer in contact with rough topographic features, and (ii) long residence time of the tracer around these features, which leads to high tracer concentrations in regions of strong mixing. While the first point has been made previously in the literature, the second point does not seem to have been fully appreciated.Our conclusion that the enhancement of mixing close to the ocean bottom dominates the spreading of the tracer resonates with an argument first proposed by Armi29302 s−1, while concurrent measurements based on microstructure profiles of dissipation of turbulent kinetic energy found much smaller values of 2 s−1 at the same depth. A numerical model was used to follow the evolution of the tracer as it was advected by the strong jets and geostrophic eddies that characterize the horizontal circulation in the Southern Ocean. The tracer experienced both the very high mixing above shallow topographic features and the much weaker mixing over deeper bathymetry. Thus the diapycnal diffusivity experienced by the tracer was the average of strong mixing over shallow hotspots and weak mixing elsewhere.We used microstructure profiles collected as part of the DIMES experiment to illustrate that diapycnal mixing in the Drake Passage is very heterogeneous, being one to two orders of magnitude larger within a kilometre of topographic features than over deep bathymetry. This heterogeneity was used to explain why measurements of diapycnal diffusivity inferred from the vertical dispersion of a passive tracer at ∼1,400 m was of 2 s−1 to 2 s−1. In particular, the long residence time around isolated pronounced topographic features including the Shackleton fracture zone, the Phoenix ridge, and the west Scotia Sea ridge system contributed most of the mixing across density surfaces that are typically 2,000 m above the bottom.Our work offers strong evidence that diapycnal mixing of tracers at mid-depths in the Drake Passage is enhanced because stirring by geostrophic eddies and mean flows brings tracers in contact with shallow seamounts and ridges, where diapycnal diffusivities are one to two orders of magnitude larger than background values. The model further suggests that the large residence time of tracers around topographic features, because of slow mean flows and topographically locked recirculating eddies, is crucial in explaining the large diapycnal diffusivity experienced by the tracer. There is an extensive literature suggesting that the large diapycnal diffusivities inferred from tracer distributions in the deep ocean must be the result of strong mixing at localized hotspots, like rough topographyLarger estimates of mixing from tracer estimates than from microstructure profiles have been reported in other experiments. In the tracer release experiment in the Brazil BasinThe suggestion that boundary-enhanced mixing affects the distribution of tracers over large areas in the ocean interior is not new. Armi2et al.2 s−1 if they are to contribute a leading order transport of κ were not very different from background values of 2 s−1 at mid-depths. However, an accurate estimate of the mixing experienced by a tracer requires accurate knowledge of the residence time spent by the tracer close to the hotspots of strong mixing, which in turn depend on the frequency with which geostrophic eddies and mean flows bring the tracer close to topography and on the topographic steering of currents which tend to trap tracers close to topography. We speculate that a similar picture may apply to the whole Southern Ocean and possibly to all oceans. It should be a priority in future work to estimate the residence time of tracer close to rough topographic features, where mixing is strong, to finally answer the question of whether deep mixing is a leading order process below 2,000 m, where most seamounts and ridges are found27Our study provides evidence that large mixing and long residence times of waters over rough topographic features extend their influence on tracer distributions over the rest of the stratified ocean. This may have important implications for our understanding of the overall role of diapycnal mixing in the ocean beyond the Drake Passage. Garabato κ weighted by the tracer concentration, arguing that this κ by some power of c, like c2, is equally reasonable. Taking a different line of reasoning, it could also be argued that κ ought to represent the mean diapycnal diffusivity that drives the observed dissipation of tracer variance, χ,In the main text, we defined κ by cz2,This is tantamount to weighting the average In et al.The tracer and hydrographic data used in the analysis are available through the online version of Watson How to cite this article: Mashayek, A. et al. Topographic enhancement of vertical turbulent mixing in the Southern Ocean. Nat. Commun.8, 14197 doi: 10.1038/ncomms14197 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


Why does a tumor start where it does within an organ? Location is traditionally viewed as a random event, yet the statistics of the location of tumors argues against this being a random occurrence. There are numerous examples including that of breast cancer. More than half of invasive breast cancer tumors start in the upper outer quadrant of the breast near the armpit, even though it is estimated that only 35 to 40% of breast tissue is in this quadrant. This suggests that there is an unknown microenvironmental factor that significantly increases the risk of cancer in a spatial manner and that is not solely due to genes or toxins. We hypothesize that tumors are more prone to form in healthy tissue at microvascular ‘hot spots’ where there is a high local concentration of microvessels providing an increased blood flow that ensures an ample supply of oxygen, nutrients, and receptors for growth factors that promote the generation of new blood vessels.2, we find good agreement of the fractional probability of at least one hot spot in different regions of the breast with the observed invasive tumor occurrence. However, there is no reason to believe that the microvascular distribution obeys a Poisson distribution.To show the plausibility of our hypothesis, we calculated the fractional probability that there is at least one microvascular hot spot in each region of the breast assuming a Poisson distribution of microvessels in two-dimensional cross sections of breast tissue. We modulated the microvessel density in various regions of the breast according to the total hemoglobin concentration measured by near infrared diffuse optical spectroscopy in different regions of the breast. Defining a hot spot to be a circle of radius 200 μm with at least 5 microvessels, and using a previously measured mean microvessel density of 1 microvessel/mmThe spatial location of a tumor in an organ is not entirely random, indicating an unknown risk factor. Much work needs to be done to understand why a tumor occurs where it does.The online version of this article (10.1186/s41236-017-0006-7) contains supplementary material, which is available to authorized users. While the location of a tumor in an organ is often viewed as random, the statistics of the anatomical distribution of tumors indicates that tumor location is not random in the sense that the probability that a tumor will occur in a given region is not proportional to the volume of that region of the organ. For example, more than half of invasive breast tumors occur in the upper outer quadrant of the breast near the armpit In this paper, we propose that the microvessel density could be a predisposing factor. Our hypothesis is that tumors are prone to develop where there is a high concentration of blood flow that can supply ample oxygen and nutrients to the tumor. We will refer to such regions with a high concentration of microscopic blood vessels as ‘microvascular hot spots’. We will use the breast as an example to discuss our proposition that local variations in the microvascular density could account for the increased tumor incidence in the upper outer quadrant.  of the breast near the armpit . Since Our hypothesis is that incipient tumors preferentially tend to form at ‘microvascular hot spots’ that correspond to small regions of tissue with a high concentration of microvessels. We hypothesize that perhaps small incipient tumors are more likely to flourish and be vascularized if they are located at “microvascular hot spots” where there is a particularly high density of microvessels. We are referring to hot spots present in disease-free/cancer-free tissue that has not been remodeled by proliferating neoplastic tissue . In order for the probability to not be proportional to the size of the region, the salt must be sprinkled unevenly. The table represents the breast. The four unequal regions represent the four quadrants of the breast. The grains of salt represent the microvessels in a cross section of tissue. The center of the circle represents the tumor location.However, as a simple example of such a calculation, we will imagine two-dimensional (2D) cross sections of tissue that have been stained to reveal microvessels as discrete points. Our goal is to calculate the probability R that contains at least n microvessels. Then N = A/(πR2) is the number of non-overlapping circles (regardless of whether they are a hot spot) that can blanket an area A. (Note that N may not be an integer.) Let P be the probability that a circle is a hot spot. Then (1 – P) is the probability that a circle is not a hot spot. (1 – P)N is the probability that there are no hot spots in N circles. Q = 1 - (1 – P)N is the probability that there is at least one hot spot in N circles. Thus, Q ≈ NP ∝ AP if NP < < 1. A plot of Q versus NP is shown in Fig. Mathematically, suppose we define a hot spot as a circle of radius pm that there are m microvessels in a circle of radius R in the ith region of the breast is given by the Poisson distribution: m〉i = ρ(i)πR2 is the average number of microvessels in a circle of radius R and ρ(i) is the areal density of microvessels in the ith region of the breast. We divide the breast into five regions: the upper outer quadrant (UOQ), the upper inner quadrant (UIQ), the lower outer quadrant (LOQ), the lower inner quadrant (LIQ), and the areolar region (AR). Then the probability qn that there are at least n microvessels in a circle of radius R is given byAs a simple example, suppose a two dimensional cross-section of breast tissue has microvessels distributed according to a Poisson distribution. Then the probability R0 with at least n0 microvessels, then the probability P that a circle is a hot spot is Q(i) that there is at least one hot spot in the ith region is given byTo relate this to the notation above, if we define a hot spot as a circle of radius N(i) = A(i)/πR02 is the number of circles that fit in the area A(i) of the ith region. (Note that N(i) may not be an integer.) AT is the total area of a cross section of the breast. Once we obtain Q(i), we normalize it by the sum over Q(i) to obtain the fractional probabilities Qf(i) that there is at least one hot spot in the ith region: where f(i) for the ith region, we do the following. Let h(i) be the total mean hemoglobin concentration measured in the ith region. We estimated the hemoglobin mass mh(i) in the ith region using mh(i) = h(i) Vbb(i) where Vb is the volume of the tissue in the entire breast, and b(i) is the fraction of tissue in the ith region of the breast. The total breast volume Vb will cancel out later so its value does not matter. The total hemoglobin mass Mh in the breast is Fh of hemoglobin in the ith region is Fh(i) = mh(i)/MT. We take the ratio the hemoglobin mass fraction to the breast tissue fraction to get f(i), the microvessel density modulation factor: f(i) = Fh(i)/b(i). The microvessel density ρ(i) in the ith region is given by ρ(i) = f(i)ρ0 where ρ0 is the measured areal density of microvessels. Measurements of the 2D density ρ0 of microvessels in breast tissue have found values of 1 microvessel/mm2  mean hemoglobin concentration in the various breast regions for postmenopausal women  are another way to determine the fraction of tissue in different quadrants. Patients undergoing a breast MRI lie prone with their breasts hanging in a pendulous fashion. However, in MRI images, it is sometimes difficult to know exactly where to delineate the boundary between the different quadrants since patients may be slightly tilted, e.g., because they lean more on one elbow than the other.We modulated the density of microvessels in each region of the breast using infrared measurements of the total mean hemoglobin concentration in the various breast regions for postmenopausal women  could be used to identify microvascular hot spots and hence, patients and regions with a higher risk of cancer. This technique uses diffuse scattering of near-infrared light to assess the local concentrations of metabolites such as oxygenated and deoxygenated hemoglobin with a spatial resolution of approximately 1 cm


To the Editor:We have read the comments(2) was only presented to show the general form of the exponential model used. The dependence with the radial distance was only explicit in Eq. (2),(2) which is:There is no doubt that the model we used must be a function of the radial distance. d is the radial out‐of‐field distance. Thus Eq. (2) is the same as the one proposed by Mihailidis.where (3–6)are actually the main reasons that motivated the use of a PSD over more common detector types, such as silicon diodes that overrespond to low photon energies due to the higher interaction probability per unit mass of Silicon compared to water. PSDs like the W1 have been shown to be water equivalent over a large range of energy, including radiological energies,As pointed out,15×15 cm2 field made with both the W1 and the CC04 agreed to within 5% for depths greater than 1.5 cm for 6 MV and 23 MV beams. At shallower depths, the dose gradient varied more rapidly and discrepancies up to 10% were observed. In these cases the poorer spatial resolution of the ion chamber could explain part of the observed differences. Comparison between a parallel plate ion chamber and the W1 agreed to within 0.2 and 0.1 cGy for doses of 0.5 cGy for photon and electron beams, respectively. These discrepancies were within the estimated statistical uncertainties. Having been able to measure small surface doses out of the primary radiation field with a detector calibrated using the manufacturer's recommended procedure is, in our opinion, a testimony of the great versatility of PSD detectors. When comparing doses between 6 MV and 23 MV it is important to recall that our measurements were taken at a depth of 1.5 cm (the average depth of CIED at our institution), which is shallower than other published data. For example, Fig. 18 of TG‐36Furthermore, side‐by‐side comparison between the Exradin W1 and ion chambers  for out‐of‐field measurements were also performed, and a manuscript on that topic is currently in press.Our observations at shallow depths appear to be in line with other surface dose measurements close to the field edges.It is important to stress again that the point of our manuscript is not to propose or recommend the use of lead shielding as a perfect solution to protect CIEDs, but instead to show that such shielding is a simple and inexpensive method of reducing doses to CIED. We agree that results can greatly vary depending on the linac type and the geometry of its head. Linacs from other manufacturers will likely show a different behavior. Nevertheless, the simple model we propose could be fitted to any data and help estimate dose to CIED in regions where treatment planning systems are well known to offer suboptimal dose calculation accuracy. In that regard, Fig. 2There is mounting evidences that the presence of neutrons is strongly correlated with CIED events during radiation therapy,This work is licensed under a Creative Commons Attribution 3.0 Unported License.


There is a limited amount of home advantage research concerned with winter sports. There is also a distinct lackof studies that investigate home advantage in the context of para sport events. This paper addresses this gap in the knowledge by examining home advantage in the Winter Paralympic Games.Using a standardised measure of success, we compared the performances of host nations at home with their own performances away from home between 1976 and 2014. Both country level and individual sport level analysis is conducted for this time period. Comparisons are also drawn with the Winter Olympic Games since 1992, the point from which both the Winter Olympic Games and the Winter Paralympic Games have been hosted by the same nations and in the same years.Clear evidence of a home advantage effect in the Winter Paralympic Games was found at country level. When examining individual sports, only alpine skiing and cross country skiing returned a significant home advantage effect. When comparing home advantage in the Winter Paralympic Games with the Winter Olympic Games for the last seven host nations (1992–2014), we found that home advantage was generally more pronounced  in the case of the former.The causes of home advantage in the Winter Paralympic Games are unclear and should be investigated further. There is a generally well-established body of academic literature that investigates the phenomenon of home advantage in sport. Courneya and Carron reviewed studies that documented the extent of the home advantage and concluded that it exists in major team sports . They weMore recently Jamieson conducted a meta-analysis of studies on home advantage  and suggA subset of home advantage research is concerned with international multi-sport events, although these studies are rarely cited, or analysed as a separate category, in major literature reviews. For the most part, the Summer Olympic Games have been at the heart of previous research efforts –12. A lip < 0.05), suggesting that judges were scoring home competitors disproportionately higher than away competitors [Even though home advantage in para sports has not been investigated thus far, it has been documented to a certain extent in specific winter sports among non-disabled athletes. Bray and Carron found some evidence of home advantage in elite-level alpine skiing including statistical significance on some measures . A subsepetitors . Home adpetitors , 16, 17.To analyse the overall performance of host nations in the Winter Paralympic Games when competing at home and away from home.To examine sport-specific variations in home advantage in the Winter Paralympic Games.To compare the size of the home advantage effect in the Winter Paralympic Games with the Winter Olympic Games.Following the Balmer et al. study , attempthttps://www.paralympic.org/results/historical) and recorded in SPSS (version 24). As illustrated by the data presented in Table The results of each edition of the Winter Paralympic Games between 1976 and 2014 were sourced from the official website of the Paralympic Movement  and 2010 (post-home) was 3.26 and 3.12%, respectively—an average of 3.19%. Therefore, its performance at home in 2006 was 0.83% points better than its average pre/post-home performance (i.e. 4.02 minus 3.19%). In instances where there was no valid pre-home or post-home data , only the available away (pre or post) data point is utilised in the home advantage calculation. The number of countries included in the analysis varied for each sport, since not all sports have been contested in each edition of the Winter Paralympic Games. For example Sweden, the 1976 host, was eliminated from the biathlon analysis because biathlon was introduced in 1988 and hence there was no home data point to compare with away data points.https://www.olympic.org/olympic-results and the time period chosen for this analysis was 1992–2014. The rationale for this restriction was that 1992 was the point from which both the Winter Olympic Games and the Winter Paralympic Games have been hosted by the same nations and in the same years. For this comparative analysis, the data for the sports of alpine skiing, cross country skiing and biathlon are based on six observations each (1992–2014) whereas the scores for ice hockey (1996–2014), curling (2006–2014) and speed skating (1994–1998) are based on five, three and two data points respectively, based on the availability of matched pairs.Selected comparisons at country level and sport-specific level are also drawn with the Winter Olympic Games. The results of the Winter Olympic Games were obtained from In consideration of the limited number of observations available, a Wilcoxon signed rank test was used to determine whether there was a genuine difference in nations’ performance under host and non-host conditions. A Spearman’s rank-order correlation was run to assess the relationship between team quality and home advantage at country level.The overall market share of the nine host nations in the Winter Paralympic Games from 1976 to 2014 is presented in Fig. z = −2.666, p = 0.008), which suggests that there is a genuine home advantage effect.The key point from Fig. Because we are comparing performance typically in a single home edition (two in the case of Norway and Sweden) with pooled data for multiple away editions (between five and ten) over a long time period (nearly four decades), it is possible that the estimates of home advantage in Fig. z = −2.934, p = 0.003). If we accept away performance to be a reliable indicator of team quality, then there is a strong positive correlation between host nations’ average away market share and the size of the home advantage effect .When comparing the market share of host nations at home with their average performance in the immediate pre-home and post-home (away) editions, we found that all previous host nations performed better at home. The difference between the mean home market share (17.79%) and the mean away market share (8.78%) using this approach was 9.01% points, which is slightly less than the mean differential obtained by comparing nations’ home performances with all their away performances (10.01% points). However, our results still suggest that when nations compete on home soil in the Winter Paralympic Games, their performance in terms of market share improves. The Wilcoxon signed rank test confirms that the observed difference between home and away performances was significant  and cross country skiing  returned statistically significant diffTable z = −1.690, p = 0.091).Table p > 0.05).Figure The academic literature on home advantage in sport can be categorised along two broad lines: 1) descriptive research, which focuses on investigating the prevalence and magnitude of home advantage in different sporting contexts; 2) explanatory research that examines the factors that contribute to home advantage. While home advantage is known to exist in professional team sports  and, to  descript explanatp < 0.05). In other words, strong evidence of a home advantage effect was identified. This finding resonates with previous research in the context of the Winter Olympic Games between 1908 and 1998 [Our analysis shows that host nations in the Winter Paralympic Games performed considerably better at home than away from home and that the difference between home and away performances was statistically significant . The prevalence of home advantage in alpine skiing in our study is in line with previous evidence from the Winter Olympic Games [Our analysis also points to sport-specific variations in home advantage in the Winter Paralympic Games. Across the six sports to be held in the Winter Paralympic Games to date, only alpine skiing and cross country skiing exhibited a significant home advantage effect , we found that host nations typically performed better at home in both competitions in this time frame and that home advantage was generally more pronounced  in the case of the Winter Paralympic Games. The reasons underpinning the differences in the magnitude of home advantage between the two competitions at both country level and sport-specific level are worthy of further investigation.This research has extended the evidence base of home advantage in international multi-sport events and, to the best of our knowledge, is the first formal attempt to examine home advantage in the context of a para sport competition. In summary, there is clear evidence of a home advantage effect in the Winter Paralympic Games at country level and its magnitude appears to be greater than in the Winter Olympic Games. In addition to investigating the factors that contribute to these findings, future research should apply similar methods to the Summer Paralympic Games, which incorporates more sports and events.


Our results enable decision makers to assess the following milestones: (1) a minimum of 33% reduction of CO2 emissions by 2055 in order to stay below 550 ppm by 2100 (this milestone goes up to 46% in the case of delayed policies); and (2) carbon neutrality and the effective implementation of innovative geoengineering technologies (10% negative emissions) before 2060 in order to return to 350 ppm in 2100, under the assumption of getting out of the baseline scenario without delay. Finally, we emphasize the need to use adaptive path-based approach instead of single point target for climate policy design.The planetary boundary framework constitutes an opportunity for decision makers to define climate policy through the lens of adaptive governance. Here, we use the DICE model to analyze the set of adaptive climate policies that comply with the two planetary boundaries related to climate change: (1) staying below a CO Experts12 concentrations fell to 450 ppm (±100 ppm), indicating a danger zone when concentrations of CO2 rise within the range of 350–550 ppm”Nine planetary boundaries have recently been defined12 emissions2 emissions) and the lag of global warming  according to different constraints and criteria. In what follows, we use the basic processes of the DICE model to model the dynamics of 6 state variables with a time step of 5 years (see TAT(t)) and in the ocean (TLO(t)), a carbon stock in the atmosphere MAT(t), a carbon stock in the ocean MUP(t), the world capital stock K(t), and the CO2 emission control rate μ(t). Policy options rely on two controls: the fraction, of the gross world product (GWP) that is reinvested in the world capital stock, I(t), as well as the relative increase, αμ(t), (every 5 years) of the CO2 emission reduction rate, μ(t), defined as follows:Among IAMs, the DICE model3031μ(t) in  and αμ(t) in . The set of all the states for which there is a control strategy such that the earth state can be maintained at all times in the planning horizon T inside the planetary boundary is called the “viability set” or the “viability kernel” Viab. The viability kernel Viab is composed of all initial states of systems for which there is at least a sequence of action policies u(t) which influences the evolution of x(t) at time t and allows the system to stay in this same viability kernel into the future. In discrete time, it can be formally defined as the set of initial states for which there exists a trajectory that does not leave K until the finite horizon T:One objective of the viability theory is to determine the present states in It is important to note that in a sequential decision process, the mathematical term “initial states” refers to “present state”, i.e. “now”. That is, the “present state” is the initial state of any decision process into the future. Within the viability kernel, the system can be maintained in a desirable state indefinitely for so long as it is not disturbed - it is, by definition, the set of all the viable states. The computation of a viability kernel also yields the set of controls that maintain the system, the so-called the viable controls.Viab and the viable controls is quite challenging. For our calculations, we have used Saint-Pierre’s algorithm2 concentrations), the other dimensions being not constrained. However, given the computational challenges associated with finding all viable states and controls, we have to limit the range of our analysis. We chose a range delimited by the minimum and maximum values for each of the six state variables of the baseline and temperature-limited scenarios. From the range of analysis, it is then necessary to define a range for the actual viability computations by finding all states reachable from the analysis range. 6 states of the world and 11 × 11 policy options for each time step yielding 3.10 × 1037 (11 × 1118) policy options between 2010 and 2100 (18 time steps of 5 years).Some reflection should make it clear that calculating As outlined above, our analysis focused on two key thresholds, 350 and 550 ppm by 2100. Here we present the results of the analysis in terms of key attributes of the structure of the control variable and the most important state variables to track in order to remain viable. We will first address the 550 ppm goal followed by the more restrictive 350 ppm target.μ(t) and the carbon stocks MAT(t) and MUP(t) in the atmosphere and in the upper part of the oceans. Therefore, it is necessary to closely monitor these stocks in order to derive adaptive climate policies with the objective of not crossing the planetary boundary. Note that the economic variable  is the fourth most important variable (CO2 emissions are connected to the economy). The more we advance in time, the more the Sobol index for the atmospheric carbon stock increases . This is the result of the fact that unlike the emission control rate, it is easier to control the carbon stock earlier than later. Moreover, the fact that the second order Sobol index μ clearly depends on the amount of carbon MAT(t) in the atmosphere.We analyzed all combinations of the world states from 2010 and 2100 in order to characterize the adaptive policies, for each world state, that enable the planetary system to stay below 550 ppm until 2100. Our computations generated all viable states as a function of time. In order to represent this very large data set for 8 variables, we focus the analysis on the most influential variables for the viability of the system using Sobol indices see –c and SI2 concentration in the atmosphere close to 550 ppm in 2060, see the lower boundary of the viability set in 2 emissions will enable a lower effort in the future. In 2 concentration is below 550 ppm around this time, it is then easier to maintain this concentration until 2100 because the peak atmospheric carbon concentration has been limited and the main emission reduction effort has already been done.The set of viable states that complies with the planetary boundary of 550 ppm in 2010 is represented in time see : we needstem see . However2 concentration, emission reduction rate and in terms of relative difference Qd(t) of GWP according to the gross world product of the baseline scenario GWPBS(t), defined as follows:Although we have followed the baseline scenario for decades, governments are still struggling with a global agreement. It is thus natural to ask what the effect of delayed policies is. We use 2010 data as initial conditions in our analysis for assessing all possible pathways from the 2010 data (2010 scenario) and from two delayed policies scenarios  for the 2010 scenario (respectively for the 2025 and 2035 scenario). If effective policies are delayed, the peak will be very close to 550 ppm despite greater efforts. The mean increase of emission reduction rate is equal to 71% for the 2035 scenario (respectively 61% for the 2010 scenario) for a minimum CO2 concentration in 2100 around 455 ppm (respectively around 375 ppm for the 2010 scenario); therefore, efforts are greater for a worse result. In addition, the milestone “33% in 2055” becomes “46% in 2055” because of the lag in CO2 peak illustrating the importance of thinking of climate targets in terms of trajectories and not in terms of single points, the latter being meaningless in the case of lagged systems such as in the case of climate dynamics. Moreover, there is a risk that additional efforts will not be possible in practice because it is always more difficult to reach major agreements in order to provide significant interventions despite the emergency of the situation . It is therefore essential to begin immediately, as delay will be costly in terms of achieving climate stabilization goals35All scenarios consider carbon neutrality by 2090 unlike 2060 for the temperature-limited scenario and 2235 for the “‘baseline”’ scenario see . For the2 emissions (66% of the pathways exhibit a complete reduction of CO2 emission to zero in 2055 for the 2010 scenario), involving a relative decrease of GWP in the first years before an increase of this relative difference of GWP from 2060. It follows that the economy will grow faster than in the baseline scenario in the long term due to the benefits from avoiding climate change. As is almost always the case with the management of common-pool resources, during the transient period away from the inefficient trajectory (overuse) to the efficient trajectory, there is an immediate negative impact of use reduction (in our case an emission reduction yielding a lower CO2 concentration). Eventually, use reduction generates net benefits which, in our case, occur by 2100  than the GWP in the baseline scenario because calculated trajectories rely on early total reduction of CO2 concentrations in the atmosphere below 350 ppm. The maximum peak of CO2 is as important as the emission control rate13μ(t) to be higher than 1, i.e. we allow 10% negative emissions. This maximum limit for negative emissions is still being debated in the scientific community and estimates vary from 10 to 30 GtCO2/year2/year in 2100. The cost of negative emissions is a topic that is also still being debated  = 1.1) before 2075. After this date, it is not possible to bounce back to 350 ppm by 2100. Between 2045 and 2065, the relative difference of net output is negative in all cases since economic efforts are critical for complying with this planetary boundary by 2100. The date from which negative emissions are effectively introduced significantly influences the results. For instance, if we focus on the trajectories that consider negative emissions only from 2075, carbon neutrality has to be reached by 2050  not delay efficient policies for navigating away from the baseline scenario; and (2) develop and implement geoengineering technologies enabling not only carbon neutrality, but 10% negative emissions before 2060. Reaching this objective of 10% of negative emissions requires the development of new strategies based on innovative geoengineering technologies that can be effective in the short term46482 concentration by sequestering current CO2 from the atmosphere2 emission reduction2 emissions2 emissions is immediately required for facing climate challenge, and ocean acidification53Although the sensitivity of our results to key assumptions on the implementation of geoengineering technologies (and to effective abatement and damage costs) should make us cautious about translating our quantitative results into decision-making process, this sensitivity can be used to help determine where we should invest in learning and gathering information. However, beyond our quantitative conclusions, our approach may contribute not only towards mapping out all possible options and all possible future trajectories but also towards investigating a wider set of views for designing climate policies for supporting both COHow to cite this article: Mathias, J.-D. et al. On our rapidly shrinking capacity to comply with the planetary boundaries on climate change. Sci. Rep.7, 42061; doi: 10.1038/srep42061 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


A “Christmas holiday effect” showing elevated cardiovascular mortality over the Christmas holidays (December 25 to January 7) was demonstrated previously in study from the United States. To separate the effect of seasonality from any holiday effect, a matching analysis was conducted for New Zealand, where the Christmas holiday period falls within the summer season.CI 0.7–7.7%) leading to ≈4 additional deaths per annum. The average age of those with fatal cardiac deaths was 76.8 years (SD 13.5) during the Christmas holiday period, resulting in 148 to 222 years of life lost per annum.New Zealand mortality data for a 25‐year period (1988–2013) was analyzed based on the same methodology used in the previous study. Locally weighted smoothing was used to calculate an “expected” number of deaths for each day of the year. The expected value was compared with the actual number of deaths. In addition, mean age at death was estimated and used to assess the life‐years lost due to excess mortality. There were 738 409 deaths (197 109 coded as cardiac deaths) during the period. We found evidence of a Christmas holiday effect in our of medical facility's cardiac deaths, with an excess event rate of 4.2% (95% United States, suggesting that cardiac mortality does not take a “summer break.”Cardiac mortality is elevated during the Christmas holiday period relative to surrounding time periods. Our findings are consistent with a previously reported study conducted in the  A “Christmas holiday effect” on mortality has been established in the United States, with spikes in deaths from natural causes at both Christmas and New Year's Day.Various possible explanations exist for a mortality holiday effect, including the emotional stress associated with the holidays, changes in diet and alcohol consumption,Individual‐level daily mortality data for 26 years between 1988 and 2013 were sourced from the New Zealand Ministry of Health. Access to the mortality collection data was permitted via an addendum to the data access agreement between the VIEW/PREDICT projectMortality records are centrally coded by the New Zealand Ministry of Health on the basis of death certificates completed by individual certifying physicians. The centralization of the coding is expected to reduce variability that might otherwise occur if the coding were undertaken at a facility or regional level. The possibility of misclassification remains during coding of the cause of death but is unlikely to be specific to the Christmas period because the coding is not done strictly contemporaneously. A World Health Organization report classified New Zealand as a “low ill‐defined coding” country for the coding of ischemic heart disease deaths, giving confidence that the mortality data are robust and accurate.All unique identifiers for data used in the analysis were encrypted, and the PREDICT study was approved by the Northern Region Ethics Committee Y in 2003 (AKY/03/12/314), with subsequent annual approval by the National Multiregion Ethics Committee since 2007 (MEC07/19/EXP).We followed a previously published analysisThe Christmas holiday period was defined as December 25 to January 7. To minimize the established impact of seasonality on mortality, the 2 weeks before (December 11–24) and after (January 8–21) the Christmas period were used as comparison periods in addition to an “all non‐Christmas” time period. The all non‐Christmas period was defined as all dates not between December 25 and January 7 and so includes the pre‐ and post‐Christmas windows.An excess event percentage was calculated based on the difference in number of events between the actual and expected values for each day of the year, for which the expected value was defined by the LOESS data using the following formula: /expected)×100. To get a summary estimate for the impact of the Christmas holiday period on excess mortality, the mean value for all excess event percentages within the time periods  were calculated.t test was conducted and Cohen's d was calculated. Cohen's d is a measure of the size of the difference between 2 values for continuous data.t test will typically result in a statistically significant P value; however, this P value provides no information about the practical significance of the difference between the results.Mean ages at death and standard deviations were calculated for all mortality, all cardiac mortality, and cardiac mortality outside of a medical facility for the 4 time periods identified. To compare the age distributions of the mortality data, a To observe the impact across the age range, a cumulative distribution plot was created. An estimate of decreased life‐years was calculated on the basis of the difference in mean age at death for the Christmas period and the comparison time period, either the pre‐Christmas or all non‐Christmas period, multiplied by the number of events within the Christmas period. This value was then compared with census data to calculate an effect per million persons for the most recent time period, with the denominator provided by the 2013 New Zealand census populationAs a sensitivity analysis, the Christmas holiday period was moved incrementally forward and backward from the baseline Christmas start date of December 25 to test for any boundaries of the holiday effect. To maintain comparability between results, the 2‐week time period was maintained by moving the end date in an identical manner as the start date. Because the LOESS method partially incorporates any Christmas effect in the smoothing algorithm, a sensitivity analysis was undertaken to estimate the size of this impact. This was done by calculating an expected value for each day of the Christmas period by linear interpolation using the last day of the pre‐Christmas period and the first day of the post‐Christmas period.To detect any broad‐scale change in magnitude in the size of any Christmas effect, the 26 years of data were divided in to 4 approximately equal time periods, and subgroup analysis was undertaken, as described.P=0.013) (Table There were 738 409 deaths (of which 197 109 where coded as cardiac deaths) in New Zealand between 1988 and 2013 , with the effect peaking in the 2 weeks starting December 27, for which a 4.5% (95% CI 1.1–7.9%) excess event rate was detected (Table S1). When the start date for a modified Christmas period was on or before December 23, there was no statistically significant Christmas effect. Likewise, if the start date was moved to or beyond December 29, no holiday effect was detected, placing upper and lower bounds on the timing of the Christmas effect. When the a linear interpolation was used to derive the expected values for the Christmas period, an increase in the effect was observed, suggesting that the LOESS method potentially underestimated the size of the effect by ≈0.8% .When a subgroup analysis of the magnitude of the Christmas holiday effect was undertaken, there was no statistically significant difference in the size of the effect between the earlier and later time periods . There was a nonsignificant trend toward an increasing Christmas holiday effect in the later time periods, suggesting against any attenuation of the size of the Christmas effect (Table S3).We found that 4.2% more persons die from a cardiac‐related cause outside of a hospital during the Christmas period than would be expected based on long‐term seasonal trends. This is consistent with reports from the United States that also indicated an increased mortality rate during the Christmas holiday period in the Northern Hemisphere. Because the seasonality, and associated temperature profile, is opposite to the previously reported results from the Northern Hemisphere, this result supports the conclusions of Phillips and colleaguesPersons who die from a cardiac event, in or out of hospital, during the Christmas period are younger by almost a year than those who die from the same or similar condition during the remainder of the year. The decrease in age at death is reduced but is still present when the comparison periods are restricted to the Christmas period and the 2 weeks prior, for which it was found that those who had a fatal cardiac event during the Christmas period were ≈6 months younger than those who died during the previous 2 weeks.Phillips and colleaguesRespiratory diseases: Given that Christmas falls in the summer season within the Southern Hemisphere, respiratory illness seems to be an unlikely contributor to the increased mortality rate. Respiratory disease rates show a strong correlation with the winter season in New ZealandIncreased particulate pollution: Phillips and colleaguesReporting effect: The Christmas holiday effect has now been described in at least 3 different regions,Month‐boundary effect: The Christmas holiday effect is not correlated with a monthly reporting cycle. It has also has been observed in a number of independent jurisdictions, reducing the likelihood of a month‐boundary effect. Causes for the Christmas holiday effect that are unlikely considering the New Zealand data include:Changes in diet and alcohol consumption: The contribution of this factor cannot be further elaborated because it is a function of the holiday period and not of seasonality. Furthermore, the degree of overlap between the general holiday traditions and timing of events between New Zealand and the United States makes any distinction difficult without high‐quality dietary data. Assessing the impact of major holidays on cardiac mortality in cultures that have cultural attributes, including major holidays, distinct from New Zealand and Australia culture may aid in clarification of any dietary component.Emotional stress associated with holidays: The contribution of this factor cannot be further elaborated because this is a function of the holiday and not of seasonality.Inappropriate delay in seeking medical care: The Christmas holiday period is a common time for travel within New Zealand, with people frequently traveling away from the main centers. This could contribute to delays in seeking treatment because of both a lack of familiarity with nearby medical facilities and geographic isolation from appropriate medical care in emergency situations. The reduced age at death Table  recordedDisplacement of death: This would include both hastening and postponement of death for reasons associated with the holiday period. The ability of persons to modify their date of death on the basis of dates of significance has been both confirmedOther suggested explanations are not clarified by the new results:The 2 explanations that are most supported by the data are displacement of death and inappropriate delay in seeking medical care. The modification of the age at death would appear to suggest that access to medical treatment, which would otherwise preserve life, is not available during this period. With regard to displacement of death, the trend within the data is toward concentration of cardiac mortality during the Christmas period, with lower than expected results  before and after Christmas.Although the methods presented closely replicate those used in prior publications, some limitations of this current study could be addressed in future work. Ideally, daily temperature would have been linked to mortality events; however, this was not possible with this data set at this stage. This is a limitation, but a recent report indicated that the majority of mortality attributable to temperature was caused by cold conditions, with excessive heat playing a reduced role.Because of the LOESS method used to estimate the “usual” event rate, it is likely that the effect of the Christmas period is underestimated due to the smoothing procedure incorporating part of the Christmas holiday effect into the estimate of expected events. This can be observed in Figure In conclusion, we observed a clear Christmas holiday effect in the New Zealand population for persons suffering a cardiac death outside of a hospital setting, replicating the effect observed in US data. This result in the Southern Hemisphere, with seasonality opposite that in previous reports, helps reaffirm that there is no apparent correlation between any observed Christmas holiday effect and the impact of temperature or seasonality. We found that the age of death was younger for those who died from a cardiac‐related condition during the Christmas period compared with those who died of a similar condition during the remainder of the year and in the pre‐Christmas period. By virtue of studying data from a Southern Hemisphere location, we have been able to clarify the likely causes contributing to the Christmas holiday effect; however, we are not able to make a definitive statement about the cause of the effect. There is the possibility of a displacement effect, in which mortality is being concentrated during the holiday period rather than directly causing additional mortality; however, the use of a different method of estimating the expected deaths will be required to fully explore this issue.This research has been partially funded by 2 research bodies; an Australian National Health and Medical Research Council grant (NHMRC1084347) and a New Zealand Health Research Council grant (HRC49).None.Table S1. Percentage Difference Between Actual and Expected Mortality Event Counts for a Range of Potential Holiday PeriodsTable S2. Percentage Difference Between Calculated Mean Mortality Count and Expected Cardiac Mortality Out of a Medical Facility Where the Christmas Effect Has Been Linearly InterpolatedTable S3. Daily Mean Values for Actual and Expected Mortality Events Divided by Event Type, Location, and Time PeriodFigure S1. Cumulative frequency distributions of cardiac mortality in New Zealand 1988–2013.Figure S2. Comparison of cumulative distribution function for cardiac mortality in the Christmas (blue line) and pre‐Christmas (red line) periods.Figure S3. Mean number of cardiac mortality events occurring outside of a health facility between 1988 and 2013 (points) and locally weighted smoothing representing the expected values for the non‐Christmas period and a linear interpolation for the Christmas period. Each point represents a mean number of mortality events for a particular calendar day, with the color coding representing the time periods of significance with regard to the impact of the holiday effect.Figure S4. Christmas effect stratified by time period.Click here for additional data file.


The ability to produce a controlled sequence of alternating droplets from two separate sources inside a microfluidic system brings several advantages in microfluidic analysis. The effectiveness of this technique for use in an application depends on the ability of the device to replicate the pattern continuously and accurately. In this work we studied the effect of the dispersed phase channel geometry on generating a repeating pattern of alternating droplets in a cross junction microfluidic device. By measuring the radius of curvature of a droplet at the time of break up, and calculating the Laplace pressure using these values, we analyzed how the angle of taper of the dispersed phase inlet channel has an influence on the pattern repetition and uniformity of formed droplet size and spacing in between. The performance of devices with different angle of taper values were studied experimentally. This comparative study indicated that the ability of a cross junction device to generate alternating droplets with uniform size and spacing is highly dependent on the angle of taper of the inlet channels; and it improves with larger taper angles. One branch of microfluidics is the droplet-based microfluidics that allows controlled manipulation of reagents in microchannels in the form of individual packages –or droplets. This significantly improves the uniformity of conditions such as temperature and residence time among the samples carried in droplets due to chaotic advection3, which is not possible to achieve in non-droplet based (continuous) flow regimes due to laminar flow4. It also provides rapid mixing of samples within droplets. Moreover there is no contamination on channel walls in droplet based devices in contrast to continuous flow devices due to the thin film of continuous phase that is between droplets and channel walls5. Due to these advantages droplet based microfluidics has specifically found applications in biological analysis6, chemical synthesis7, high-throughput screening8 and other micro total analysis systems (µTAS)9.The research field of microfluidics has many attractive aspects like high throughput analysis, use of small quantity of reactants, addressing samples individually, precise control over reaction conditions and possibility of automation and integrationIn order to increase the advancement in the analysis and synthesis, it is important to have controlled droplet generation such that size and formation periods of droplets are known. In this paper, the droplet generation geometry is discussed to form alternating droplet sequence by using two different sources. This pattern generation can be used to track different samples and will increase the multiplexing capacities of the microfluidic devices. Samples from different sources can be placed in a known sequence such that tracking of them is facilitated, without any need of additives such as dyes; and if needed they can be merged controllably so that concentration of merged samples are the same.et al. used double T-junction geometry to generate droplets from two separate sources in an alternating manner10. This was later referred as cross junction device which has two dispersed phase inlets from opposite sides and one continuous phase inlet in the middle. None of these channels were tapered. In this work, they have observed four regimes of formation and they characterized these regimes with the capillary number, Ca, which is the ratio of viscous forces to surface tension forces. They have obtained alternating droplet formation for the range 0.001 < Ca < 0.05. They reported that for low Ca, the two dispersed phase coalescence at the junction and alternative formation does not occur. For higher Ca numbers they observed that either droplets do not form or droplets having diameters smaller than the channel width form which later merge.There are three major types of droplet generation geometries; namely flow-focusing, co-flowing and T-junction. Owing to the simple geometry and greater ability to control the droplet size, the T-junction device is the most commonly used geometry. Zheng et al. developed a device to carry out a chemical synthesis for nanoparticle synthesis by first generating droplets from the two sources and then merging them at a later stage with equal or different concentrations7. In this work they have used a double cross junction geometry where the two dispersed phases enter the main channel from opposite sides as in Zhang et al.10. At the merging point of the dispersed channel inlets, they have used a short triangular structure named as ‘wing’ to reduce flow instabilities and backflow. They claimed that the alternating droplet formation is due to the push-pull mechanism between two dispersed phases. When one dispersed phase enters the channel, the other one is pressurized and pushed back; once a droplet is generated the second dispersed phase takes turn and pushes back the initial one. However their study did not characterize the conditions for which alternating droplet formation takes place. Nisisako et al. utilized the cross-junction geometry to generate core-in-shell droplets of two immiscible organic fluids, each being pumped side by side from two dispersed phase inlets11. Hirama et al. reported a device containing cross junction without taper followed by flow-focusing to encapsulate two particles, each from a different source, inside a single bigger droplet by varying the hydrophobicity inside the microchannel network12. This work did not focus on the mechanism of alternating droplet formation. Surya et al. conducted both experimental and numerical studies to identify regimes of droplet generation which were; merged, stable, transitional and laminar13 and used a cross junction geometry composed of straight channels to generate alternating droplets. Similar to Hung et al.7 they also explained the alternative droplet formation with the push-pull mechanism and they characterized the required Ca number and flow ratios for this mechanism, Another numerical study focusing on the same features of droplet generation but by varying the angle at which side channels merge to the main channel and viscosity ratio of the dispersed and continuous phases was performed by Ngo et al.14. They also used cross junction geometry composed of straight channels, however they changed the merging angle of dispersed phase channels and concluded that a merging angle of 90° is better for alternating droplet generation. Jin et al. studied the regularity of alternating mode to conclude that regularly alternating mode of droplet generation is always accompanied by regular merging of droplets15, but they did not study the relevance of the channel geometry to regular alternation, which further emphasizes the need for such a study that we have conducted.Hung This is the first study that shows how inlet channel geometry can be modified to achieve a stable alternating droplet pattern. In this work we have studied the effect of the taper angle of inlet channels (α) Fig.  on the a7, we proposed that varying cross-sectional area of the dispersed phase inlet will affect the pressure exerted by the dispersed phase at the junction; thereby affecting the control over the sequence of droplet formation. This is the first time tapered channels have been used for the dispersed phase channels in a cross junction device for alternating droplet generation, and prior to this work each study conducted on such a device had straight channels with no variation in the cross-sectional area throughout the length of the channel. The only exception that needs to be mentioned is in the case of Hung et al.7 where they have used triangular wings to minimize flow instability and avoid back flow of reagents and they have not varied the angle of the triangular inlet to study its effect on the droplet generation.In the design of the microfluidic device a cross-junction geometry is used; inlet channels are tapered instead of being straight as shown in Fig. To quantify the results of our experiments, we introduced variables n and ψ, where n is the number of consecutive droplets formed by each stream of fluid and efficiency (ψ) is defined as the number of times out of 100 generation attempts that each stream generates exactly ‘n’ droplets. If in any of the attempts, number of droplets does not equal to n or the droplet dimensions vary, it is subtracted from 100 : Surface tension, forces due to shear stress applied by the continuous phase and force due to the increased resistance of fluid flow around the forming droplet. The surface tension force is a result of Laplace pressure which is the pressure difference across an interface and it depends on the radius of curvature of the interface.In order to understand the effect of the taper angle on alternating droplet generation it is necessary to look at the forces that dominate droplet formation at the T-junction. Based on the analysis proposed by Garstecki −3 as shown below:μ), speed (U), cross-sectional area (A), continuous phase flow rate (Qc) and surface tension (γ) are as follows:μ = 0.0562 Ns/m217, A = 1.49 × 10−8 m3/s, Qc = 5.01 × 10−11 m3/s, U = 2.32 × 10−3 m/s, γ = 1.642 × 10−2 N/m18.In order to determine what forces are dominating the break-up, we calculated the capillary number (Ca) for our experiments and found that it is in the order of 1019. When the net pressure exerted by the dispersed phase becomes smaller than the pressure exerted in the upper stream (due to continuous phase); a droplet will form16. The net pressure exerted by the dispersed phase is the difference of the pressure in the dispersed phase inlet channel and the Laplace pressure at the interface. Therefore by evaluating the Laplace pressure, we can determine how pressure distribution is affected at the junction.Based on the Ca number range droplet generation is in the squeezing regime; which means that interfacial forces are more significant than shear forces. This in turn means that droplet generation is governed by pressure distribution over the droplet20TT1 is the total pressure change across the junction due to TS1PS is the steady pressure change at the junctionPTS1 is the Laplace pressure difference between the head and tail interfaces of the growing droplet of TS1∆PT and rT are the tail radii in the axial and radial directions respectivelyRH and rH are the head radii in the axial and radial directions respectively.RIn Fig. TS1 decreases which shows that PTT1 decreases as per equation (TS2 (Laplace pressure difference between the head and tail interfaces of the growing droplet of TS2) decreases as per equation  and this causes an additional resistance for the TS2.Secondly as the TS1 keeps growing at the junction Fig. , the carIn Fig. equation  and as iequation  since thequation  since in16, and the value of this maximum pressure jump is given by19Tc and RHc are the tail and head curvature radii in the axial direction at the break off point respectively .∆PFor these reasons TS2 is unable to enter the junction until droplet forms in the channel Fig. . Betweeni.TS2 decreases as per equation  become crucial to the phenomenon of alternation.Secondly, the alternation of droplets depends on the second stream being able to enter the junction as shown in Fig. The mechanism of alternating droplet generation in case of straight channels will be partially the same as has been explained in case of tapered channels. However for the following reasons, tapered channels are more likely to produce synchronized alternating droplet pairs as compared to devices with straight channels:Tc and RHc are measured   Tc and RAt this point it must be pointed out that in straight channels, even after it forms a droplet, SS1 can still enter the junction when SS2 is generating a droplet Fig. . On the COMSOL Multiphysics ® and the results are shown in Fig. PTT1  by using the conventional soft lithography techniques. PDMS was bonded to a glass slide by using oxygen plasma. Syringe pumps were used to inject fluids into the microchannels. The images were captured using an inverted microscope and a CCD camera.The continuous phase fluid was olive oil and the droplet phase fluids were deionized water with added dyes (fountain pen ink) for distinguishing the two droplet phases. The use of surfactant was avoided to understand the capability of the device without any stabilization to droplet interfaces.c) and flow rate fraction (ϕ) which is defined in equation (d1 and Qd2 are the flow rates of two dispersed phases.The independent variables are defined as the taper angle (α), continuous phase flow rate (Qequation 7\documenc) was kept at 2.0 µl/min and in set 2 it was kept at 3.0 µl/min. Within each experiment set, the dispersed phase flow rate (Qd) was varied but kept equal for the two dispersed phase sources, thus the ratio ϕ was varied.Two sets of experiments were performed Table ; in set The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.Supplementary Video S1Supplementary Video S2Supplementary Video S3


Phenylketonuria (PKU) still poses a therapeutic challenge for patients and medical professionals. The aim of the study was to assess both patients’ and their parents’ acceptance of the disease.The study included 218 PKU patients and 178 parents of PKU children who were enrolled in the study on the basis of questionnaire data.Regarding attitude towards the disease, our study demonstrated that 63 (28.9 %) PKU patients did not accept the disease. Patients who found accepting the disease difficult, more frequently perceived themselves as inferior/different in comparison with their peers. In total, 36 % of patients did not want their friends to be aware of their condition, while only 18 % of parents believed that their children’s peers should not know about their disease. In total, 42 % of parents wanted to talk to other parents of PKU children and only 13 % to a doctor. Only 20 % of patients saw the need to discuss their condition with a doctor. In total, 8 % of children, regardless of age, and 14 % of parents preferred to talk to a psychologist.Our data demonstrated that disease acceptance played an essential role in patients’ social integration. The study also indicated the need to overcome communication barriers between patients and their healthy peers and for patients to find the courage to be open about the disease. The importance of support groups for PKU families and the significance of strict cooperation between patients and their families with PKU treatment teams were also revealed. Phenylketonuria (PKU OMIM:261600), first recognised by Dr Asbjørn Følling in 1934 and considered a prime example of predictive medicine, still poses a therapeutic challenge for both patients and medical professionals. Although the dietary management currently recommended enables PKU patients to achieve full personal and social development, for parents of an affected child, the diagnosis means living in a state of constant anxiety. The anxiety, which results from the necessity of adhering to the rules imposed by the disease, is often present from the first days of the child’s life.The disease forces, initially, parents and subsequently patients to learn the principles of nutritional management which includes a daily meticulous control of food intake and a strict adherence to the prescribed health regimen. This means that from early infancy, the implications of the condition shape the social and psychological aspects of PKU patients’ family life. Therefore, a subjective assessment of the quality of life by PKU patients and their families is undoubtedly one of the crucial factors which influences the effectiveness of their therapy. In the case of children, it is the behaviour of adults and their attitude to the disease that affects the outcome of dietary management and the children’s acceptance of the disease.TheWorld Health Organization and TheInternational Association for Child Psychology and Psychiatry recommended self-assessment as the most appropriate method to measure children’s quality of life. Hence, information on the assessment of PKU patients’ and their families’ quality of life should enable the introduction of measures which would facilitate the effective implementation of dietary management standards and improve the families’ quality of life.In 1993 The aim of the study was to assess both patients’ and their parents’ acceptance of the disease and to analyse these attitudes in different age groups. An attempt was made to determine how disease acceptance affected patients’ self-assessment and interpersonal relationships both within the family and in a peer group.The study included 218 individuals with classic PKU  aged 10–35, managed in 9 specialist metabolic clinics in Poland. The PKU patients were enrolled in the study on the basis of questionnaire results. The following inclusion criteria were applied: PKU diagnosed in early infancy in a newborn screening test (at follow-up tests blood PHE concentration >20 mg/dl), exclusion of atypical forms of PKU , a low phenylalanine diet from early infancy, intellectual development within age norm (children within the public education system).Individuals suffering from mild PKU and other chronic diseases were excluded from the study. Characteristics of the PKU patients are presented in Table The study also included 178 parents of PKU children . Over 70 % of them described their family’s economic conditions as very good or good, 25 % as average and 1 % as poor. More than 70 % of parents had vocational or secondary education, 25 % had higher education and 4 % had primary school education.The study used a questionnaire designed by the research team in cooperation with clinical psychologists assisting PKU patients and their families, and experts from the Polish Society of Phenylketonuria. The questionnaire completed by the study participants has been attached.The study was conducted during regional and national meetings of PKU families with therapists. Participation in the survey was voluntary. Members of PKU families not participating in the meetings were not approached and asked to take part in the study. The questionnaire contained 9 questions on the patients’ and their parents’ attitudes to the disease. The questions concerned the acceptance of the disease, self-perception in the context of the disease, social relations and communication needs in the family and the community. Questions for parents and children were similar in format. A Likert-type response scale was used in the survey.The family’s socio-economic status was only assessed by the parents. Children below the age of 15 completed the questionnaire either unassisted or with the help of a qualified researcher.t test or Mann–Whitney test were used with respect to the type of distribution of the variables tested. In the case of multiple group comparison, the Kruskal–Wallis test was used as the nonparametric equivalent of one-way analysis of variance (ANOVA). In all these calculations, the statistical significance level was set at p < 0.05.All calculations were performed using the Microsoft Excel spreadsheet and STATISTICA, StatSoft, Inc., version 8.0 statistical package . Statistical evaluation of quantitative data utilised the classical measures of location such as arithmetic means and medians, and measures of variation such as standard deviation and range. Normality distribution of the variables and variance equality of studied features in groups was established with the use of Shapiro–Wilk test and variance equality test. In order to compare groups in pairs for quantitative data, Regarding attitude towards the disease, our study demonstrated that in the group of 218 PKU patients, 63 (29 %) did not acknowledge their disease. Furthermore, out of the 178 parents surveyed, 49 (28 %) displayed a conspicuous lack of acceptance of their children’s disease . In regard to disease acceptance by children, no differences were found between age groups (p = 0.6817).It was observed that parental lack of acceptance increased when the child was between the ages of 7–19  believed that their children felt inferior to their peers because of the disease. The conviction strengthened as the child grew older  and preferred not to discuss their condition with them (p = 0.0008). Similarly, parents who experienced difficulty in accepting their child’s disease were more inclined to believe that their child felt inferior/different from his/her peers (p = 0.0236) and were more likely to prefer their peers not to know about their child’s condition (p = 0.0001) . On the other hand, 36 % of patients did not want their friends to be aware of their condition, while only 18 % of parents believed that their children’s healthy peers should not know about their disease.The study revealed that 71 % of parents experienced anxiety about their children’s future, which increased with the child’s age, while only 42 % of patients were concerned about their future  (p = 0.0022)  Fig. .Fig. 3DiThe study demonstrated that 96 % of parents believed that they devoted a sufficient amount of time to discussing the disease with their children, while only 63 % of children shared this opinion.When given the choice of discussing their condition with a professional  or a peer suffering from the same disease, more than half of PKU patients (56 %) named peers. On the other hand, 42 % of parents declared that they wanted to talk to other parents of PKU children and only 13 % wanted to talk to a doctor. It is remarkable that although both the parents and children consider the doctor to be the main source of information about the disease, only 20 % of patients saw the need to discuss their condition with a doctor. Only approximately 8 % of children, regardless of age, preferred to talk to a psychologist. It is worth mentioning that in the first 3 years of the child’s life, 40 % of parents preferred to consult a psychologist. The number fell to 20 % in the following three years (children aged 4–6) and further decreased to 10 % when the children reached the age of 7  and their parents accepted the condition, while 25 % of the respondents claimed that they would never accept it. The obtained results are consistent with a study by Lord et al. [ % and thThe study demonstrated that non-acknowledgement of the disease had a negative effect on interpersonal relationships and on self-perception in the context of a peer group. Children who did not accept their condition did not want others to be aware of it and felt inferior/different from their healthy peers. Nonetheless, they simultaneously believed that life would be easier for them if all their friends knew about their disease.Similarly, Di Ciommo et al.  noted thOur study demonstrated that professional assistance should be provided to prepare PKU patients to talk openly about their condition. It is important to teach patients adequate interpersonal communication skills as well as ways to verbalise their needs. Educating parents is equally important since our study revealed that parents who found accepting their child’s condition difficult preferred them not to discuss their disease with healthy peers.The study demonstrated that the degree of disease acceptance affected the patients’ perception of their educational abilities and a future career. We found that lack of such acceptance made PKU patients more inclined to see a negative impact of the condition on their academic achievement and to be more concerned about their future career prospects when compared with patients who accepted the disease. The results of the study confirmed that disease acceptance was a critical factor influencing PKU patients’ quality of life.Similar issues concerning disease acceptance have been demonstrated in patients with other chronic diseases such as cystic fibrosis, diabetes or neurodegenerative diseases. The problem of disease acceptance in adolescents and young adults with cystic fibrosis and diabetes was presented by Casier et al. , accordiAn important element of the conducted study was an attempt to investigate how parents perceived their PKU children in the context of their peer group. Our research demonstrated that parents were more likely to believe that their children felt inferior to their healthy peers. In fact, the number of parents making this claim was twice as high as that of children. Despite such a perception of their children’s situation, the parents were convinced that the children should inform their healthy peers about their condition. The obtained results suggest that parents are not aware of the fact that patients prefer their peers not to know about their medical problems. Parents also do not realise that their children often choose to withdraw from their age group, which can result in a lack of close relationships. Discussing the disease also seems to pose a problem for many patients. As our study indicates, parents are usually unaware of their children’s need to discuss their condition specifically with them. In general, parents believe that they have adequately satisfied this need at every stage of their child’s life.Therefore, it would be advisable for medical professionals to devote particular attention to the scope of communication needs within the family in an attempt to improve the current status.The study also explored the patients’ and their parents’ need to discuss the disease with professionals and individuals affected by the disease. The results demonstrated that both the children and their parents wanted to talk about the condition to people in a similar situation. There was a strong need among the patients to talk to their affected peers, while the parents surveyed expressed a desire to discuss the issue with other families of PKU children. Surprisingly, medical professionals involved in PKU patient management were not selected as preferred discussion partners. Despite the fact that all the respondents regard the doctor to be the main source of information on phenylketonuria, they stated a preference for discussing the condition with a group of people sharing a similar experience. Only 17 % of those surveyed stated that they preferred to talk to a doctor about the disease, which may suggest that the need for medical consultation and information about phenylketonuria has been met in both patients and their parents.Our study confirmed the need for promoting age-related and ‘expert patient’-type interventions, especially to help individuals suffering from chronic conditions –14. OtheOur study also demonstrated that the desire expressed by parents of children under the age of 3 to consult a psychologist was as strong as that for talking to other parents of PKU patients. The study revealed that parents of the youngest children (under 6 years of age) felt the greatest need for psychological support.The aforementioned results confirm the benefit of establishing support groups for parents of PKU children as well as providing them with professional psychological care. It is also worth noting that for parents of children under the age of 9, apart from a doctor, a nutritionist constitutes an important source of information about the disease. In the course of our study, we observed that the parents’ need to talk to a nutritionist increased after the child’s 7th birthday and was, at that time, three times stronger than the need to consult a psychologist. Among the parents of school-age children, the need to consult a nutritionist increased in subsequent years.Our findings support the conclusion reached by other authors that a nutritionist plays a significant role not only in the therapeutic process but also in assisting parents with the daily adherence to the PKU diet –19. Our The analysis of the responses obtained from the adult patients surveyed revealed surprising results. It became evident that, in comparison with the earlier periods of the respondents’ lives, both negative self-assessment (patients’ sense of inferiority/difference) and an unfavourable perception of professional development prospects strengthen. It is clear, however, that despite lower self-esteem adult patients do not see the need for a psychological consultation. It was also noted that those patients have different communication needs regarding their peers and medical professionals. The need to maintain relationships with people in a similar situation is strongest for PKU patients under the age of 19, while for patients over the age of 20 this need diminishes, and those patients express a preference to discuss their problems with medical professionals. The majority of adult patients want to talk to a doctor and a nutritionist, while the need for a psychological consultation remains at an unchanged, low level.The study suggests that adult PKU patients express more critical opinions about themselves and their future personal and professional prospects, and their needs for discussing the disease are different from younger patients’.The study, conducted on a large group of PKU patients and their parents, demonstrated that disease acceptance played an essential role in the patients’ social integration and their perception of a future professional career. It is therefore vitally important to make a concerted effort to facilitate an appropriate attitude towards the disease in the family and to improve parent–child communication. The study also revealed the need to overcome communication barriers between patients and their healthy peers and for patients to find the courage to be open about the disease. The importance of support groups for PKU families and of strict cooperation between patients and their families with PKU treatment teams was also revealed.Further research is needed to fully understand the reasons for lack of disease acceptance in both patients and their parents.