As a result, the model allows to analyze how both the velocity field of marine currents and the two components of turbulent diffusivity affect the spatial distributions of phytoplankton abundances in the Modified Atlantic Water, the upper layer of the water column of the Mediterranean Sea. Specifically, the spatio-temporal dynamics of four phytoplankton populations, responsible for about 80% of the total chlorophyll a, are reproduced. Results for phytoplankton abundances obtained by the model are converted in chlorophyll a concentrations and compared with field data collected in twelve marine sites along the Cape Passero (Sicily)- Misurata (Libya) transect. Statistical checks indicate a good agreement between theoretical and experimental distributions of chlorophyll concentration. The study can be extended to predict the spatio-temporal behaviour of the primary production, and to prevent the consequent decline of some fish species in the Mediterranean Sea.Field data on chlorophyll distribution are investigated in a two-dimensional spatial domain of the Mediterranean Sea by using for phytoplankton abundances an advection-diffusion-reaction model, which includes real values for physical and biological variables. The study exploits indeed hydrological and nutrients data acquired  In particular, field observations focused on the spatial distribution of chlorophyll concentration, which is the main marker of the phytoplankton populations9. These represent the base of the marine food web, and are used to estimate the biomass primary production in all aquatic ecosystems10.During the last decades, the study of the spatio-temporal behaviour of phytoplankton abundance assumed a role of fundamental importance to predict the effects induced by physical and hydrological changes on the fish abundances in marine ecosystems19. On the other side, some authors introduced two- and three-dimensional models21, in which the habitat of planktonic groups is considered homogenous for the nutrient and the environmental parameters are fixed constant in the whole ecosystem. In particular, these assumptions are connected with the lack of experimental data, whose availability is crucial for the estimation of some environmental variables18, such as the light intensity, the velocity field of marine currents, the horizontal and vertical turbulent diffusivities. Moreover, unlike some one-dimensional models18, the numerical results for phytoplankton abundances are not converted in chlorophyll concentration, and therefore the comparison between theoretical results and experimental data can not be performed. For these reasons, the theoretical chlorophyll concentration obtained by the phytoplankton abundances has been never reproduced in the vertical water plane of the marine ecosystems. In general, the analyses are usually carried out on the horizontal water plane by using the remote sensing data23, while it would be more useful to reproduce the field data collected in the vertical water plane, where the biodiversity of marine species can be investigated.Theoretical models for population dynamics allowed to reproduce the spatio-temporal distributions of phytoplankton groups in a one-dimensional spatial domain by considering the effects of heterogeneity of the limiting factors along the water columnchlorophyll a (chl a) and divinil chlorophyll a (Dvchl a) concentration in the Strait of Sicily.Here we introduce a more realistic two-dimensional model, which takes into account the physical and biochemical processes responsible for a strong spatial heterogeneity, typical of the Mediterranean Sea. This allows to reproduce the experimental spatial distributions of 25. The bathymetry dataset used in Fig. http://www.ngdc.noaa.gov/)26.The sampling was carried out on a grid of 72 hydrographic profiles covering the Gulf of Syrte and the Strait of Sicily. In particular, our analysis focuses on the north-south transect 12 sites) crossing the eastern sill of the Strait of Sicily between Cape Passero and Misurata  and Atlantic Libyan Current (ALC), cause different environmental conditions for the phytoplankton growth between the Sicilian coast and Libyan coast. Moreover, the strong winds support the upwelling of nutrients close to the Sicilian coast. This favours the growth of phytoplankton populations also during the summer season when, on the contrary, it should be expected a decrease of the primary production of biomass due to the reduced water mixing. For these features, the whole area represents an important region for the spawning and growth of sardines and anchoviesIn this work, a two-dimensional advection-reaction-diffusion model is used to reproduce, on a vertical “water plane”, the spatio-temporal dynamics of four picophytoplankton populations. Specifically we consider the vertical “water plane” defined by the transect direction (x-axis) and the water surface-seabed direction (z-axis). The differential equations for the phytoplankton dynamics take into account the following contributions: (i) biomass production (birth and death); (ii) passive movement connected with turbulence and local transport; (iii) active movement of microorganisms along the water column.29, i.e. light intensity and nutrient concentration. Specifically, the decrease of the light intensity as a function of depth, associated with an opposite gradient for nutrients, allows each phytoplankton population to have a positive net growth rate within its production layer18. Accordingly, the magnitude and the position of the chlorophyll peaks within the two-dimensional spatial domain are strictly connected with the spatial distribution of the limiting factors30, which however depend on the hydrological conditions of the transect investigated.The biomass primary production is described by a reaction term, which takes into account the nonlinear interactions between the growth of phytoplankton abundance and the two limiting factors22. However, the role of hydrological and physical variables has never been studied in a vertical water plane, where vertical chlorophyll profiles, and eventual deep chlorophyll maxima (DCMs), can be observed and analyzed. Moreover, our study presents three further novelties compared to previous investigations based on advection-diffusion-reaction models: (i) the two horizontal components of the velocity field are those measured in the transect during the oceanographic survey (15–30 July 2008); (ii) the vertical turbulent diffusivity is estimated on the basis of the Pacanowski and Philander model32, by using the experimental data collected in situ; (iii) the horizontal turbulent diffusivity is fixed according to the theoretical results presented in previous works33.Regarding this point, it is worth to recall that the effects of mixing and local transport (passive movement) on the phytoplankton dynamics are taken into account by inserting in our equations diffusion and advection terms, respectively. Both terms are also included in the differential equation for the nutrient dynamics in order to well reproduce the two-dimensional distribution of phosphate concentration along the transect. By this way, in our analysis we consider both the direct effects of the hydrological and physical variables on the spatio-temporal behaviour of all phytoplankton groups, and those indirectly induced by the non-linear interactions between phytoplankton and the nutrient dynamics. These effects on the phytoplankton dynamics have been investigated previously in horizontal water planes11.Finally, the active movement of each planktonic group is considered by using a taxis term, which depends on the behaviour of the net growth rate along the water column in accordance with previous studieschlorophyll a concentration in the two-dimensional spatial domain of the Cape Passero-Misurata transect. Here, the hydrological parameters guarantee oligotrophic conditions during the summer season, with phosphates being the nutrient component which plays the role of limiting factor for the phytoplankton growth34.On this theoretical basis, we devise an advection-diffusion-reaction model which allows to reproduce the map of 39, i.e. Synechococcus, Prochlorococcus (HL-ecotype), Prochlorococcus (LL-ecotype) and the whole picoeukaryotes domain, which are the main groups in the Strait of Sicily (see Supplementary Information). Then we present a two-dimensional advection-reaction-diffusion model, obtaining the spatio-temporal dynamics for the phytoplankton abundances of these populations.In the following, first we consider four picophytoplankton populationscells/m3, into chl a and Dvchl a concentrations, expressed in μg/dm3, by using the experimental cellular content measured by Vaulet and Courties, and the conversion curves obtained by Brunet et al.40.As a second step, we convert the phytoplankton abundances, expressed in χ2 test. Then, the results of these statistical tests are compared with those obtained by the “full” version of the model, in which all biological parameters are fixed (see Supplementary Information). Finally, a qualitative comparison between numerical results and experimental data is also performed for the average phosphate concentration and the average chlorophyll concentration in the Modified Atlantic Water (MAW).As a third step, the vertical chlorophyll distributions extracted from the theoretical map are compared with the corresponding experimental profiles collected during MedSudMed-08 oceanographic survey (15–30 July 2008), by performing statistical checks based on the x, along the transect, so that Eqs  approach, where space and time discretizations are considered separately. This method was useful to combine various discretizations for the diffusion, advection and taxis terms together with the non-linear reaction term. Indeed, we solved the differential equations of the model by performing a centered-in-space differencing for the diffusion terms, and a third-order upwind-biased differencing for the advection and taxis terms. The increment of the spatial variables is set at 5.0 km for the et al.45, while the phosphate concentrations are fixed equal to those measured along the water column in the sampling sites.As initial conditions, we assumed for each picophytoplankton group a low cell concentration uniformly distributed within the domain studied in agreement with Ryabov tmax = 2 · 104 h) long enough to reach the stationary solution46.In order to obtain the steady spatial distributions, we solved numerically our equations over a time interval chla, which accounts for 20% of the total quantity of chl a and Dvchl a. This contribution is uniformly distributed along the MAW (z-axis), but changes along the Cape Passero–Misurata transect (x-axis) chla((x) by calculating the 20% of fluorescence data acquired in each hydrological station, and interpolating the results obtained for all sampling sites of the transect. On the basis of these assumptions, we obtain the spatio-temporal behaviour of the total chl a and Dvchl a concentration for the whole domain investigated.According to previous studies(Dv)chl a concentrations of the four picophytoplankton groups, the total chl a and Dvchl a concentration and the phosphate concentration in stationary conditions are shown in Fig. chl a and Dvchl a concentration in the remaining part of the Cape Passero–Misurata transect. Indeed, the theoretical results indicate that the most part of chlorophyll concentration is due to the presence of picoeukaryotes and Prochlorococcus LL, which prevail in the Strait of Sicily during the summer season, when the oligotrophic conditions guarantee higher light intensity in deeper layers of the water column. In particular, these two groups dominate the marine ecosystem between the Sicilian coast and the Libyan coast in correspondence of the deep chlorophyll maximum (DCM). More specifically, the chlorophyll peak for picoeukaryotes is localized along the whole transect in the intermediate layers of the MAW, while that for Prochlorococcus LL is only obtained between the Medina Sill and the Libyan coast in deeper layers of the water column. These results are in a good agreement with the experimental findings obtained for each phytoplankton group by other authors38.The theoretical results of the chl a and Dvchl a concentration and the phosphate concentration obtained by the model with the experimental data collected during the MedSudMed-08 oceanographic survey  located close to Cape Passero . Finally, the comparison between the theoretical distributions and the experimental data shows a good agreement for the nutrient concentration in the whole domain, except in the hydrological stations localized close to Medina Sill. Here, in the intermediate layers of the MAW, the phosphate concentration obtained by the reduced model is overestimated respect to the values detected by the field observations. However, this behaviour can be explained by an approximative estimation of the horizontal turbulent diffusivity used within the area confined between the Sicilian coast and the Medina Sill (see the Supplementary Information).We also compare the steady spatial distribution for the total see Fig. . From a see Fig. . These dchlorophyll a concentration with the corresponding theoretical vertical distributions extracted from the contour maps obtained by the reduced model at the steady state. Here we observe a good qualitative agreement between experimental data (green line) and numerical results (red points) in all hydrological stations investigated. We also perform a quantitative analysis, based on the goodness-of-fit test χ2, for the 12 stations of the transect. The results of the χ2 test, shown in Table M6-M9) localized in the central part of the Strait of Sicily, where the geostrophic currents take on the same direction of the transect. The best reduced chi-square  located close to the Sicilian coast.Moreover, the numerical results show that, close to the coastal zones, the DCM is quite shallow because of a high phosphate concentration, while it is quite deep between the stations 18, in this study we do not observe a connection between the magnitude and width of the DCM.The analysis performed for the width of the DCM indicates that the experimental findings are well reproduced by the reduced model only in hydrological stations close to the coastal zones. Conversely, the width of DCM is mostly underestimated respect to the field observations in the hydrological stations localized in the middle of the Strait of Sicily. This result is connected with the difficulty to determine the correct values for the horizontal and vertical turbulent diffusivities. Finally, unlike other analysis performed on advection-diffusion-reaction modelschlorophyll a and phosphate within the Cape Passero -Misurata transect. Here, the theoretical results indicate that the hydrological conditions in the coastal zones generate the rising of the nutrients in the shallower layers of the MAW, causing an enhancement of the average chlorophyll concentration. In particular, an average chlorophyll peak is observed between the Sicilian coast and the Medina Sill (station M3), while another peak is present close to the Libyan coast (station M12). In the first case, the upwelling of the nutrients and the consequent growth of the phytoplankton biomass are due to the combined effect of the Atlantic Ionian Stream (AIS) and a higher water mixing. In the second case, the increase of average chlorophyll concentration is mainly due to the presence of the Atlantic Libyan Current (ALC), which carries nutrients from the Gulf of Syrte. Conversely, the reduced mixing between the Medina Sill and the Libyan coast causes in the MAW very low values of average phosphate concentration and, as a consequence, of chlorophyll concentration. In general, we observe for the average chlorophyll concentration a good agreement between the numerical results and experimental findings along the whole transect, except in the station M2. On the other hand, the average phosphate concentration is well reproduced close to the coastal zones, while some differences are observed in the hydrological stations localized in the middle of the transect.In Fig. chlorophyll a distributions can be ascribed to: (i) the lack of experimental data on the horizontal turbulent diffusivity, necessary to better estimate the effects of high turbulence close to the coastal zones; (ii) the difficulty to determine the correct value for the vertical turbulent diffusivity in the upwelling regions; (iii) the necessity to neglect the zonal component (perpendicular to the transect) of the geostrophic velocity, because of the two-dimensional structure of the model; (iv) the lack of experimental data for the half-saturation coefficients of all picophytoplankton groups involved in our study. Moreover, the contribution of the nano- and micro-phytoplankton fraction to the total chlorophyll concentration could be underestimated close to the Sicilian coast, where the high nutrient concentration could be responsible for the growth of diatoms and Dinophytes.In conclusion, the analysis performed in this section shows that the discrepancies between theoretical and experimental chlorophyll a concentration which fit quite well the field observations.Anyway, the results presented in this section indicate that the two-dimensional model provides, in wide areas of the marine ecosystem, spatial distributions of In this work we presented an innovative study on the spatio-temporal dynamics of phytoplankton in a marine ecosystem located in the Strait of Sicily. Initially, we performed an analysis on the two-dimensional distributions of chlorophyll and phosphate concentration obtained from data sampled, during the summer season, in twelve hydrological stations, located along the Cape Passero–Misurata transect. Here, field observations indicate the presence of a strong spatial heterogeneity in physical and chemical variables such as velocity field, water density, and nutrient concentration. Moreover, we observed that the characteristics of the vertical chlorophyll profile in each sampling site are strictly connected with the horizontal velocities of marine currents, turbulent diffusivities , and nutrient concentration at the boundaries of the ecosystem.In this work we used a two-dimensional advection-reaction-diffusion model, while neglecting the terms of the local transport in the direction perpendicular to the transect, since in the most hydrological stations investigated during the summer period the velocity field is parallel to the transect, and the contribution of the zonal geostrophic velocity on the local transport can be therefore neglected . Conversely, the strong wind at the marine surface induces the upwelling of nutrients close to the Sicilian coast, while favouring the growth of phytoplankton populations also during the summer season. Moreover, an increase of the chlorophyll concentration is also observed close to Libyan coast due to the presence of the Atlantic Libyan Current (ALC), which carries nutrients from the Gulf of Syrte.The spatio-temporal dynamics of the four planktonic populations was obtained by the model equations, taking into account explicitly the effects of environmental variables. More in detail, we considered the different hydrological features of the 12 stations along the transect investigated. In particular, we found that the strong stratification of the Mediterranean Sea in the summer seasonWe note also that in our equations the effects of the mixing, local transport (passive movement), and non-linear interactions between phytoplankton and nutrient dynamics are modeled by the diffusion and advection terms. Moreover, our model exploits values of hydrological and physical variables experimentally measured, including horizontal components of the velocity field and vertical turbulent diffusivity obtained from field observations.49. Indeed previous investigations showed that the anchovy population prevails in the upwelling region50, where the high nutrient concentrations favour the growth of larger size phytoplankton groups, which are at the basis of the food chain of this fish species. On the other hand, sardines, which are able to capture smaller size phytoplankton and zooplankton, dominate geographical areas with reduced water mixing during the most part of the year50.These aspects represent a novelty within the landscape of the modeling of phytoplankton dynamics in a vertical water plane. Moreover, the model provides a tool for a better and deeper understanding of the role played by hydrological conditions on the spatial distribution of phytoplankton abundances, which represent the base of the food web for marine ecosystems. Our theoretical findings indeed could be used to analyze the role of environmental variables, through the modifications induced in the phytoplankton distributions, in the dynamics of zooplankton populations and fish species in the Strait of Sicily58. Specifically, environmental conditions were fixed according to field observations, and biological parameters were set in such a way to guarantee, along the water column, the coexistence of all four populations45.In our analysis, we considered the presence of two limiting factors responsible for the competition among the four picophytoplankton populations modeled. The biological parameters were set to values typical of these planktonic groups, according to previous field observations carried out in the Strait of Sicily9. Indeed, a correct modeling of phytoplankton dynamics should also take into account that the half-saturation constants depend on the nutrient concentration and the light intensity, which change as a function of the position  within the two-dimensional domain. However, a preliminary analysis (results here not reported) based on the full model has been performed, obtaining spatial distributions of phytoplankton abundances in a quite good agreement  with the field data acquired along the Cape Passero - Misurata transect.Moreover, the heterogeneous composition of each picophytoplankton population showed a spatial variability, modeled by varying the values of half-saturation constants along the transect analyzed. About this, our modeling actually pays the lack of an adequate knowledge of the mechanism used by phytoplankton cells to absorb nutrient molecules and energy from the marine waters under the different environmental conditionsx along the transect, instead of the full model where all biological parameters are fixed. In particular, the values of half-saturation constants for each station were initially fixed in such a way that the boundaries of the production layer of each population are localized at depths determined according to the theoretical expression by Ryabov et al.45. The final values of half-saturation constants were obtained by using an iterative procedure, based on χ2 test, which optimizes the theoretical profiles of chlorophyll distributions compared with those obtained by field data (see Supplementary Information). Moreover, in our analysis we imposed an additional constraint: in all hydrological stations the theoretical abundances (cell concentrations) for each phytoplankton population have to be in a good agreement with those experimentally observed by Brunet et al.36. Our theoretical results satisfy also this condition.Anyway, due to the characteristics of the marine ecosystem analyzed (see Supplementary Information), in view of better reproducing the experimental data, we assumed half-saturation constants as space dependent parameters. So we used a reduced model in which the values of half-saturation constants depend on the position 36. Then we extracted from the chlorophyll map the theoretical chlorophyll profiles, comparing them with the experimental profiles collected in the 12 stations during the MedSudMed-08 oceanographic survey (15–30 July 2008). At this stage we applied the above cited optimization procedure, obtaining theoretical profiles in a good agreement with those obtained from field observations, and strongly dependent on the hydrological variables , characterized by different values in the various stations analyzed. Moreover, from a qualitative point of view, we observed that the magnitude, depth and width of the DCMs predicted by the reduced model match quite well those obtained by field observations. We also calculated, in each station, the average chlorophyll concentration along the water column, finding a good agreement between theoretical results and experimental data in the whole transect, except in station M2. Finally, the good agreement between predicted results and experimental data for the average phosphate concentration represented a further validation of the reduced model proposed.In our analysis the theoretical 2D distribution of chlorophyll concentration was obtained by exploiting the conversion curvesχ2 goodness-of-fit test. The results showed that the best reduced chi-square is obtained for the hydrological stations localized between the Medina Sill and the Libyan coast, where the turbulent diffusivities take on low values and the geostrophic currents are parallel to the direction of the transect. Conversely, the worst values of χ2 are obtained between the Sicilian coast and the Medina Sill, where the high vertical turbulent diffusivity triggers the upwelling of nutrient from deeper layers, and the direction of the marine currents is not parallel to the transect.We also compared quantitatively theoretical and experimental chlorophyll profiles, performing the χ2 test for the reduced and full models, by using the Akaike Information Criterion and the Cohen’s effect size measure59. In particular, both statistical checks show that also the full model is able to well reproduce the experimental chlorophyll profiles in the most part of the transect, even if the best χ2 values are obtained by the reduced model. As a final remark we note that, from a conceptual point of view it appears more correct to use the reduced model, which takes into account the spatial variability of the half-saturation constants. These parameters indeed depend strongly on the environmental conditions, such as water turbidity which influences the light intensity along the water column, and nutrient concentration. The reduced model allows to take into account this dependence by including site specific values for half-saturation constants. Finally, the small values of the Cohen’s effect size measure allows to extend to the full model the good agreement between experimental and theoretical distributions of chlorophyll, obtained when the reduced model is used.Afterwards, we also compared the results of the In general, this study indicates that the advection-diffusion-reaction model proposed is able to reproduce correctly the spatial distributions of the chlorophyll concentration, when biological and environmental parameters are set to values typical  of the ecosystem considered (Strait of Sicily). Anyway, it is expected that the theoretical distributions for chlorophyll concentration could be improved by using a 3D model, which should allow to take into account the effects of diffusion and advection along the third dimension (perpendicularly to the transect), here not considered because of the 2D structure of the experimental dataset. In particular, the implementation of the 3D model would allow to obtain a better agreement between the theoretical results and the experimental data in the hydrological stations where the velocity field is not parallel to the transect. Moreover, a better modeling needs a deeper knowledge of biological and environmental parameters such as: (i) horizontal and vertical turbulent diffusivities close to coastal zones; (ii) dependence of the half-saturation constants on the spatial distributions of nutrient concentration and light intensity; (iii) real contribution of the nano- and micro-phytoplankton fraction to the chlorophyll concentration in the coastal zones; (iv) the inflow and outflow of nutrients and chlorophyll coming from the boundaries of the marine ecosystem.21. Finally, we wish to notice how the model and, more in general, the whole approach proposed represent a powerful tool to analyze and predict the effects of global warming on phytoplankton dynamics, in view of preventing the decline of the primary production in marine ecosystems18.In conclusion, the model proposed in this work appears as a valid candidate to predict the chlorophyll spatial distribution in marine ecosystems characterized by heterogeneous environmental conditions. Specifically, our findings indicate that the model is able to reproduce phytoplankton dynamics in aquatic ecosystems with different levels of eutrophication. We note that this model can be extended, including higher trophic levels such as zooplankton populations, in view of reproducing and predicting the spatio-temporal behaviour of fish populationsth–30th July 2008 during the MedSudMed-08 Oceanographic Survey carried out in the Central Mediterranean Sea (CMED) on board the CNR R/V Urania. This area was investigated by using a grid of 72 hydrographic profiles, which covered the Gulf of Syrte and a north-south transect crossing the eastern sill of the Strait of Sicily between Cape Passero and Misurata24 were acquired by using the Chelsea Aqua 3 sensor mounted on the probe. All parameters were processed, generating for each site a text file, in which the experimental values are given with a 1 m step18.For each sampling site, continuous vertical profiles of conductivity, temperature, density and pressure were collected from the surface to the bottom of the water column by means of a CTD-rosette system, consisting of a CTD SBE 911 plus probe (Sea-Bird Inc.), and a General Oceanics rosette with 24 Niskin Bottles61. At the same time, the main surface circulation patterns were evaluated by the Absolute Dynamic Topography during the investigated period.The vertical profiles of the two horizontal components of the current velocity have been acquired by using a Lowered Acoustic Doppler Current Profiler system (LADCP) and computed by applying the Lamont-Doherty Earth Observatory (LDEO) processing softwareM12. Here, we assumed that the velocities were the same as in the nearest station L2718. Indeed, we recall that the vertical profiles of horizontal marine currents and water density were necessary to estimate the spatial distribution of the vertical turbulent diffusivity32 along the whole Cape Passero-Misurata transect (see Supplementary Information).The horizontal velocities were collected in all sampling sites of the transect except in the station C without carrying out any preliminary filtration. Nitrite, nitrate, silicate and phosphate concentrations were measured successively in laboratory by using a Brän-Luebbe AutoAnalyzer, and following classical methods with slight modifications62.The seawater samples to perform the dissolved inorganic nutrients measurements were collected during the oceanographic survey at standard depths in all hydrological stations of the transect investigated except in the M2 site. The nutrient samples were stored at −20 °45. In particular, we investigate the spatio-temporal behaviour of four picophytoplankton populations, which interact with each other indirectly through the competition for light intensity and nutrient concentration. By solving the equations of the model, we obtain the steady spatial distribution of cell concentration for the populations analyzed in the Strait of Sicily, i.e. Synechococcus, Prochlorococcus HL, picoeukaryotes, and Prochlorococcus LL, indicated by b1, b2, b3, and b4, respectively. Here, bi denotes the phytoplankton abundance (cells per unit volume) of i-th population in the position  within the two-dimensional domain at time t. Moreover, the spatial distributions of the phosphate concentration R and light intensity I are obtained. In our study, the domain is composed by the sum of seven rectangular subdomains, which reproduce the bathymetric profile of the transect together with the vertical boundaries localized in the two hydrological stations close to the two coasts. Specifically, z represents the depth of the water column from the surface (z = 0) to the bottom (z = zb) of each subdomain, while x indicates the distance from the Sicilian coast, measured from Cape Passero (x = 0) to Misurata (xl = 0) along the transect.The dynamics of the primary production of biomass is studied by using an advection-diffusion-reaction model20: (i) net growth (reaction term); (ii) active/passive movement (taxis/advection term); (iii) movement due to turbulence (diffusion term).The dynamics of the picophytoplankton abundance is modeled by including three processesGi)64, which depends on the balance between the gross production rate per capita and the mortality. In particular, the gross production rates are given by 19, while the mortality due to respiration, death, and grazing is described by the specific loss rates (mi).The reaction term describes how the limiting resources affect the net phytoplankton growth rate /∂z)11. In particular, this function is defined as Gi/∂z > 0, Gi/∂z < 0, and vi = 0 (motionless phytoplankton) if ∂Gi/∂z = 0, where 51.The taxis term provides a realistic description of motility skills of the planktonic groups, and depends on the swimming velocity 45. In particular, the diffusion term reproduces the effects of the turbulence on the two-dimensional distribution of phytoplankton groups through the horizontal (Dh(x)) and the vertical ) turbulent diffusivities, which change as a function of the depth (z) and the length (x), while remaining constant with the time. Hence, as a preliminary step, we obtain the values of vertical turbulent diffusivity from field observations by exploiting the model devised by Pacanowski and Philander31. The horizontal turbulent diffusivity is fixed in accordance with values estimated by other authors65 (see Supplementary Information).The non-active movement of all phytoplankton groups depends on the turbulence (diffusion term) and the local transport (advection term) of biomassvh) of the marine currents along the x-direction. Since in the most part of the transect the velocity field is parallel to the x-direction  are calculated by using the experimental data collected during the oceanographic MedSudMed-08 survey (see Supplementary Information).The advection term allows to describe the effects on the picophytoplankton distributions induced by the horizontal velocity component  is further increased by the recycling process of the dead phytoplankton. Moreover, the effects of the local transport and turbulence, responsible for the mixing of nutrients in the 2D domain, are taken into account by inserting in the differential equation for the phosphate concentration an advection term and two diffusion terms, respectively.The phosphate concentration I is assumed to depend on the site considered along the transect, and to decrease exponentially with the depth z, according to the Lambert-Beer’s law67.Finally, the light intensity εi, mi, 1/Yi, and ai are the nutrient recycling coefficient, the specific loss rate, the nutrient content, and the chl a-normalized average absorption coefficient of the i-th picophytoplankton population, respectively; abg is the background turbidity; Iin(x) is the incident light intensity at the water surface, taking on different values along the transect (x-direction).Thus, the four-population model is defined by the following equations:20, that is we assume that no biomass can enter or leave the area investigated. Therefore, we fix the biomass fluxes to vanish at the boundaries of the domain:Respect to the phytoplankton populations the marine ecosystem is closedFor the nutrient (phospates) we assume: (i) no nutrient flux through the water surface; (ii) nutrient concentration at the other three boundaries fixed equal to the values measured during the oceanographic survey. Therefore, we set the phosphate fluxes at the boundaries of the domain as follows:mentclass2pt{minimSupplementary Information


To quantify polygenic effects, i.e. undetected genetic effects, in large-scale association studies, we propose a generalized estimating equation (GEE) based estimation framework. We develop a marginal model for single-variant association test statistics of complex diseases that generalizes existing approaches such as LD Score regression and that is applicable to population-based designs, to family-based designs or to arbitrary combinations of both. We extend the standard GEE approach so that the parameters of the proposed marginal model can be estimated based on working-correlation/linkage-disequilibrium (LD) matrices from external reference panels. Our method achieves substantial efficiency gains over standard approaches, while it is robust against misspecification of the LD structure, i.e. the LD structure of the reference panel can differ substantially from the true LD structure in the study population. In simulation studies and in applications to population-based and family-based studies, we illustrate the features of the proposed GEE framework. Our results suggest that our approach can be up to 100% more efficient than existing methodology. While genome-wide association studies (GWAS) led to the discovery of many genetic risk loci for complex diseases and traits, the overall magnitude of the combined genetic effects on the disease phenotype of interest that is explained by GWAS findings is much smaller than classical heritability studies suggested , we can stateThe derivation of this approximation can be found in Appendix A of the Biostatistics online). Equation , , 2.5), aIf we utilize the assumption of normally distributed genetic effects for the moment, we can conclude that the equation  is valid of GCTA  by assumBiostatistics online, we show how the original GEE assumption of independent clusters can be relaxed in such a way, i.e. the sandwich-variance estimator can be extended to the scenario of sparsely correlated clusters and how the classical asymptotic results can be reestablished. Now, we describe the GEE objects to estimate the parameters in the mean model for the association test statistics. The following description and the derivations in the Biostatistics online are strongly related to Biostatistics online). We denote the true, unknown parameter by Now, we propose our PolyGEE approach to estimate the parameters ond 1 cM , we can atistics . GEE appatistics . The obsur model  and 2.2 e design  is fixedfunction . We use Biostatistics online), we can reestablish the following results for the asymptotic existence of the estimator Biostatistics online. The two key points in the proofs of Propositions 3 and 5 are the utilization of a central limit theorem for weakly dependent data and the modification of the sandwich-variance estimator to account for the specified dependence structure of the clusters.Under the assumption of sparsely correlated clusters and reasonable technical conditions , schizophrenia (SCZ), major depressive disorder (MDD), attention deficit disorder (ADHD), and autism spectrum disorder (ASD). We analyzed the data from the PGC-Cross-Disorder Group for SCZ  Consortium association study for autism spectrum disorder (ASD)  implies equation ), assumiAt a genome-wide level, we derived a general marginal model for single-variant association test statistics of complex diseases. We proposed the PolyGEE methodology to estimate the amount of polygenic effects and confounding biases from the association test statistics of large-scale association studies using this model. We showed via simulation studies and the application to real data that our approach is substantially more efficient than the existing LD Score regression framework, i.e. the estimates are more precise. The increased efficiency of our approach is achieved by incorporating detailed local LD information from the external reference panels, e.g. 1000 Genomes project, into the estimation step. However, our GEE approach does not require that the reference panel and the study data are exact matches in terms of the LD structure. The approach is robust against deviations of the sample LD structure from the reference panel and can compute asymptotic valid standard errors. Our theoretical derivations and assumptions lead to general valid results for the estimation framework. For further research, this makes it possible to extend the mean model to incorporate more components or estimate the genetic correlation between two traits.Supplementary DataClick here for additional data file.


This configuration has significant potential for reducing the laser power required for adaptive optics multiphoton imaging, and for facilitating integration with existing systems.Multiphoton microscopy enables imaging deep into scattering tissues. The efficient generation of non-linear optical effects is related to both the pulse duration  and the size of the focused spot. Aberrations introduced by refractive index inhomogeneity in the sample distort the wavefront and enlarge the focal spot, which reduces the multiphoton signal. Traditional approaches to adaptive optics wavefront correction are not effective in thick or multi-layered scattering media. In this report, we present sensorless adaptive optics (SAO) using low-coherence interferometric detection of the excitation light for depth-resolved aberration correction of two-photon excited fluorescence (TPEF) in biological tissue. We demonstrate coherence-gated SAO TPEF using a transmissive multi-actuator adaptive lens for  The use of MPM for The adaptive optics (AO) techniques that have been developed for astronomical telescopes can also be applied to microscopy and ocular imaging to correct for refractive errors and enable diffraction-limited focusing. Conventional AO systems developed for retinal imaging use a Hartmann-Shack Wavefront Sensor (HS-WFS) to detect the wavefront aberrations and, in a closed feedback loop control, guide the shape of an adaptive element, such as a deformable mirror, to correct the wavefront aberrations351011121314Sensorless Adaptive Optics (SAO) techniques have been developed to overcome the limitations of the HS-WFS. Image-based SAO methods that optimize the shape of the deformable element to correct the wavefront based on indirect measurements have been successfully used in microscopy to perform aberration correction16171892122in vivo retinal imaging, the combination of AO with MPM should be fast (on the order of seconds), and should minimize the high-energy laser exposure on the delicate light-sensitive tissue. We present a novel depth-resolved SAO for MPM that is well suited to retinal imaging applications. We combined MPM imaging with depth-resolved SAO using the same light source, but separate detection systems. The light used for MPM microscopy typically consists of a train of pulses that are on the order of femtoseconds in duration. The femtosecond-pulsed light source can be selected to have adequate bandwidth (tens of nanometers) for low coherence interferometry detection with an axial resolution on the order of micronsFor in vivo mouse retina imaging. The image acquisition was performed with a home-built multiphoton microscope using a novel transmissive multi-actuator adaptive lens (MAL) as the deformable elementWe present results demonstrating the improvement in the MPM signal after OCT-guided SAO aberration correction on a phantom and for A schematic of our experimental imaging system is presented in Two-photon excited fluorescence emission from the sample was de-scanned by the GM and then reflected by the dichroic mirror (DcM) to the photo-multiplier tube (PMT) detector. A short-pass filter, lens, and aperture were placed prior to the PMT to reject residual excitation light and stray reflections.The back-scattered excitation light was de-scanned at the GM, transmitted by the dichroic mirror, and recombined with the reference arm light at the beam splitter. The recombined light was fiber coupled to a spectrometer . The sample and reference light generated an interference pattern on the spectrometer, which was processed into cross-sectional images using a custom GPU-accelerated program2829In vivo imaging of mouse retinal vasculature was also demonstrated using the OCT-guided SAO TPEF. Mice were anesthetized using ketamine (100 mg/kg of body weight) and dexmedetomidine (0.1 mg/kg of body weight), and subcutaneously injected with 100 μL of 100 mg/mL fluorescein. Prior to imaging experiments, the eyes were dilated with 1% Tropicamide, then topical anesthetic  and artificial tear gel  was applied. Lastly, a rigid contact lens was placed on the mouse eye to prevent the cornea from dryingen face OCT images extracted from the volume at a depth corresponding to this focal plane. All imaging experiments were carried out in accordance to the protocols approved by the University Animal Care Committee at Simon Fraser University. The numerical aperture of the imaging beam was calculated to be 0.21. The estimated focal spot size, assuming a Gaussian beam profile for the incident beam, was ~1.5 μm (Gaussian waist). This corresponded to an estimated Rayleigh range for the imaging beam of ~9.5 μm. The laser power incident on the mouse eye was limited to a maximum of ~10 mW for both the OCT-guided SAO optimization and MPM imaging.en face image was generated from the user-selected depth region within the OCT volume by maximum intensity projection (MIP); the sharpness of this 2D en face image, calculated using The SAO optimization algorithm was modified from our previous reports on imaging mice and humans921Ij is the intensity value of the j-th pixel in the OCT en face image, and the summation is performed on the entire OCT en face image.where en face image was extracted, and the coefficient that produced the sharpest image was selected as the optimized value. The optimization of the next Zernike mode continued in a hill-climbing fashion, using the combination of the previously optimized modes as a starting point. Based on the acquisition parameters of the OCT system, the optimization was completed in ~60 s.The wavefront aberrations were represented using a set of orthogonal Zernike polynomials, which allowed us to optimize each Zernike mode independently. The MAL is capable of correcting aberrations up to 4th order Zernike polynomials, however aberration correction was restricted to the second and third order Zernike polynomials  in consideration of the limited stroke of the MAL. We first optimized for defocus (Z = 4), followed by two astigmatisms  and then the two comas . For each Zernike mode, the optimization was performed by first acquiring an OCT volume for 11 different coefficients applied to the MAL. For each coefficient value, an en face image presents the structural appearance of the sample, but is not of particularly high aesthetic quality due to the presence of large speckle and the comparatively low axial resolution. The main purpose of the OCT was to provide depth-resolved aberration correction and cross-sectional aiming of the focal plane in order to improve the MPM; therefore, having exquisite structural images was not important for our applications. However, the OCT image appearance could be improved by using a different light source that has a broader optical bandwidth, for example a titanium sapphire laser. After optimization, the OCT image in The impact of OCT-guided SAO wavefront correction on the quality of the MPM images was first demonstrated on an imaging phantom. Lens paper stained with a fluorescein derivative fluorescent dye (excitable by a two-photon process at the ~800 nm incident wavelength) was covered with a layer of clear epoxy and sealed with a microscope coverslip. An aspheric lens  was used as an objective lens to focus the beam on the phantom. The purpose of the epoxy and coverslip was to introduce distortions for the demonstration of aberration correction with the OCT-guided SAO. The fibers in the lens paper provided a structural back-scattering image for the OCT, with the intention of improving the TPEF signal from the dye, which represented the signal of interest in the phantom. Using the OCT data for optimization, TPEF images from the same location are presented before and after aberration correction in en face OCT images presented are of all the layers to emphasize the shift of the focal position. The optimization performed on the layers in the red box had a ~14% increase in the sharpness metric of the en face OCT and a ~3% brightness increase in the TPEF image. The optimization performed on the layers in the blue box had a ~18% increase in the sharpness metric of the en face OCT and also a ~3% brightness increase in the TPEF image.In order to demonstrate our system’s depth resolved aberration correction capability, images of a two-layer phantom were acquired, with SAO correction performed on each of the layers independently. The two layers of the phantom were separated by ~100 μm as indicated by the blue and red boxes in the OCT B-scans on the left side of in vivo are presented in en face images and TPEF images. Quantitatively, the effect of SAO correction was demonstrated by comparing the signal intensity profile across the dotted lines  taken from the TPEF images.Representative images of the mouse retinal vasculature acquired en face OCT images after the optimization of each Zernike term, in which the ‘hill climbing’ effect of the SAO algorithm is clearly observed.Images with a different field of view acquired from the same imaging session are shown in TPEF images of vasculature at different layers of the mouse inner retina after OCT-guided SAO optimization are shown in in vivo mouse retinal imaging. The aberration correction was performed using coherence-gated OCT images to guide an SAO algorithm. With the presented OCT system configuration, the optimization was performed in ~60 s, following which TPEF image acquisition was performed at ~100 ms per frame. For the imaging phantom, which was stationary, the time required to perform the optimization was not relevant. However, for in vivo imaging, in particular for retinal imaging in a mouse in vivo, a short optimization time was essential for reducing motion artifacts and limiting laser exposure to the tissues of the eye. Through successful optimization and improved image quality after aberration correction, we demonstrated that the motion observed during regular data acquisition with an anesthetized mouse, which is primarily due to breathing and heart beat artifacts, was not a limiting factor for the imaging performance. After successful optimization, we were able to navigate to and acquire aberration-corrected images of different regions of the retina.We have demonstrated a fast depth-resolved aberration correction method for MPM, and shown its ability to improve the TPEF image brightness and sharpness in static phantoms and for et al. can be explored to increase the converging rate and reduce the effect of non-orthogonality and fitting errors of the Zernike modes produced by the optical deformable elementOur SAO optimization time of ~60 s was limited by the speed of the OCT engine (spectrometer readout line rate), number of A-scans in a volume, and the number of points that were used in the optimization search algorithm for each Zernike mode. The optimization time could be readily reduced to several seconds or less by using a state-of-the-art custom spectrometer adjusted to the optical spectrum of the light source, or by reducing the size of the OCT volume during optimization and/or the number of points in the search algorithm. Furthermore, nonlinear multivariate optimization algorithms such as the one presented by Verstraete The impact of performing the aberration correction using a single photon process, and in particular from the same light source that is used for MPM excitation, is evidenced through the strength of the OCT signal used as the merit function and the corresponding time required for optimization. With the bright OCT images, the optimization can be performed from a single acquisition at each step of a Zernike mode coefficient value. In contrast, due to the low signal strength of the TPEF, multiple images would need to be acquired and averaged in order to generate a single data point, making the time needed to run the optimization algorithm on the order of minutesen face images used for the merit function can be extracted from the specific layer of interest without influence from the other retinal layers.An important benefit of using coherence-gated SAO is that a specific depth layer can be selected for optimization. For the case of the imaging phantom, the aberration correction could be repeated at different depths, as was demonstrated in Alternative approaches to coherence-gated aberration correction have been proposed in the literature. The combination of coherence-gated wavefront sensing with two-photon microscopy was reported using a virtual Shack-Hartmann sensor3638In this report, a transmissive multi-actuator adaptive lens (MAL) was used as the aberration correcting element. The methods presented for improving the TPEF signal based on OCT-guided SAO could also be used with other adaptive elements, such as deformable mirrors. Adaptive elements are commonly placed at planes that are optically conjugated to the pupil; this is accomplished using relay lenses, which increases the physical size of the system and the complexity of integration with existing microscopes. For imaging configurations that use an objective lens, the MAL can be positioned adjacent to the back aperture of the objective, simplifying the integration with existing systemsThe successful demonstration of the MAL for MPM optimization using the OCT-guided SAO is encouraging for small animal retinal imaging. Although the laser power incident on the eye was higher than the ANSI recommended limits, the optical intensity was in line with other works that report no physiological changes at the retinaHow to cite this article: Cua, M. et al. Coherence-Gated Sensorless Adaptive Optics Multiphoton Retinal Imaging. Sci. Rep.6, 32223; doi: 10.1038/srep32223 (2016).


Among many of the electrode designs used in electrocardiography (ECG), concentric ring electrodes (CREs) are one of the most promising due to their enhanced spatial resolution. Their development has undergone a great push due to their use in recent years; however, they are not yet widely used in clinical practice. CRE implementation in textiles will lead to a low cost, flexible, comfortable, and robust electrode capable of detecting high spatial resolution ECG signals. A textile CRE set has been designed and developed using screen-printing technology. This is a mature technology in the textile industry and, therefore, does not require heavy investments. Inks employed as conductive elements have been silver and a conducting polymer  polystyrene sulfonate; PEDOT:PSS). Conducting polymers have biocompatibility advantages, they can be used with flexible substrates, and they are available for several printing technologies. CREs implemented with both inks have been compared by analyzing their electric features and their performance in detecting ECG signals. The results reveal that silver CREs present a higher average thickness and slightly lower skin-electrode impedance than PEDOT:PSS CREs. As for ECG recordings with subjects at rest, both CREs allowed the uptake of bipolar concentric ECG signals (BC-ECG) with signal-to-noise ratios similar to that of conventional ECG recordings. Regarding the saturation and alterations of ECGs captured with textile CREs caused by intentional subject movements, silver CREs presented a more stable response  than those of PEDOT:PSS. Moreover, BC-ECG signals provided higher spatial resolution compared to conventional ECG. This improved spatial resolution was manifested in the identification of P1 and P2 waves of atrial activity in most of the BC-ECG signals. It can be concluded that textile silver CREs are more suitable than those of PEDOT:PSS for obtaining BC-ECG records. These developed textile electrodes bring the use of CREs closer to the clinical environment. The recording of electrophysiological signals in its simplest form—that is, through contact electrodes attached to the skin—is subject to continuous studies both to optimize these records and in the search for new technologies that improve the measurement process. Today the diagnosis, therapy, and monitoring of health are based to a large extent on the measurement of signals from the brain, heart, and muscles. Even so, most of the recording systems of these signals continue to have a traditional approach, using monopolar disk electrodes (mainly Ag or AgCl). In recent years, an effort has been made to look for alternative geometries and new technologies for the manufacture of contact electrodes that allow signals to be obtained that are of better quality and/or have more precise information. In addition, systems with multi-electrodes that allow the recording of several signals simultaneously are being imposed. Finally, the integration of electrodes into clothes is being sought, which would lead to medical control beyond the clinical work environment. The use of textile-based electrodes entails a series of special characteristics such as ultra-thinness, light-weighted, high flexibility, stretchability, and conformity . There aTwo important aspects to consider when designing and using electrodes for measuring bioelectric signals are the materials to be used and where to place them. As for the material, you can find electrodes that are of metal inks, conductive polymer inks or are directly of conductive textile. Each of these materials must provide flexibility to improve contact during movement of the individual. Based on this flexibility, designs can be found with conductive foam , conductAs mentioned, one of the techniques for manufacturing electrodes for capturing bioelectric signals is direct printing on a substrate. In recent years, works have been developing printing techniques based on graphic arts such as screen printing, gravure, or inkjet for the manufacture of these electrodes on flexible substrates and more specifically on textiles ,22. The On the other hand, one of the main limitations of surface bioelectric recording by means of conventional disc electrodes is the poor spatial resolution, mainly originating from the blurring effect due to different conductivities of the body volume conductor ,24. To oDespite the improvements introduced by the implementation of the CRE on flexible substrates, CRE use has not been transferred to the clinical environment. In order to facilitate this, we have worked on the design and validation of a set of two CREs developed on a textile substrate that will improve patient comfort during recording, especially for long-term recordings, and that will enable the detection of bioelectric signals with a similar quality to that of conventional bipolar recordings and with enhanced spatial resolution. In the present work, a set of two concentric ring electrodes screen printed onto a textile substrate has been designed and their features have been compared . Two different types of inks were used: one based on silver and another on a conducting polymer  polystyrene sulfonate, PEDOT:PSS).This study is structured in the following way: The sensing part consists of a set of two concentric ring electrodes, each one made up of an inner disc electrode a and an The CRE dimensions are shown in Manufacturing technology used to implement this type of sensor was based on serigraphic technology of thick film. The screen-printing process consists of forcing inks of different characteristics over a substrate through some screens using squeegees. Openings in the screen define the pattern that will be printed on the substrate by serigraphy. The final thickness of the inks can be adjusted by varying the thickness of the screens. Specifically, textile CREs were produced by screen-printing technology using a four-layer design as shown in The screen for the conductors was a 230 mesh of polyester material  and the screen for the dielectric layer was a 175 mesh polyester material . In order to transfer the stencil to the screen mesh, a UV film Dirasol 132  was used. The final screen thickness was 10 µm for the screen for conductors and 15 µm for the screen for the dielectric. The patterns were transferred to the screen by using a UV light source unit. The materials used were the textile Mediatex TT ACQ 120 µm  for the substrate, C2131014D3 Silver ink 59.75%  and C2100629D1 PEDOT:PSS  as the conductive inks and D2081009D6 polymer dielectric  as the dielectric ink. Flexibility is one of the most important characteristics of these inks in order to use them with textiles. Their main characteristics are shown in A physical characterization was made by measuring the final layer thickness with Profilm3D (Filmetrics) with a 20× Mirau objective.An electrical characterization was carried out by measuring the magnitude of the impedance and the angle of the phase by using electrochemical impedance spectroscopy, which was taken with a potentiostat  in a two-electrode configuration supplying a sinusoidal signal of 1 V without any dc bias. The measurement was made between the two terminals of one of the electrodes (pole-to-pole impedance), both with skin contact.The skin-electrode impedance of each CRE pole was carried out using the EIM-105 Prep-Check  in a three-electrode configuration at 10 Hz.2. The recordings were carried out with the subjects lying on a stretcher. This study was approved by the Polytechnic University of Valencia Ethics Committee and adhered to the Declaration of Helsinki. The volunteers were informed about the nature of the study and briefed on the recording protocol before they signed a consent form.In total, ten recording sessions were performed with 7 male and 3 female healthy subjects aged between 20 and 41 years and with body mass indices between 19.6 and 27.4 kg/mTo reduce contact impedance, the skin area on which the electrodes  were placed was previously gently exfoliated  and was also shaved in the case of subjects with excess hair. Two disposable Ag/AgCl electrodes  were positioned on the left leg and right arm for obtaining standard lead-II ECG signals with the ground electrode being on the right leg. First, the silver CRE, previously cleaned with alcohol, was attached to the chest with an adjustable belt that exerted a certain pressure on the skin. The right electrode was positioned as close as possible to CMV1 (position comparable to V1 near to the right atrium) see . ImmediaECG can be corrupted by background noise and different types of interferences, such as baseline drift and power line and abdominal muscle interference. First, the ECG signals were digitally filtered with a fifth-order Butterworth high pass filter with the cutoff frequency being at 0.3 Hz. ECG fiducial points were then obtained by detecting the R wave of the ECG signal with the algorithm proposed by Pan and Tompkins  and sligTo compare the ECG signals recorded by the silver and PEDOT:PSS CREs during rest, the peak-peak amplitude of the averaged beat . In the present study, signal alteration was considered as any visually appreciable variation of the ECG signal recorded during movement with respect to that obtained at rest. Alterations consisted mainly of baseline changes. By contrast, signal saturation was referred to as amplified signals that reached the maximum or minimum output voltage allowed for conditioning the system, made up by the commercial P511 bioamplifiers connected to the DAQ NI USB 6229  with the saturation voltage being ±5 V. Then, the mean time percentage of all the involved subjects was computed for each movement and each position.A magnified view of the two designs is shown in Regarding the electrical characterization, 1 is the series resistance, R2 is the charge-transfer resistance, Q2 is the constant phase element, and the exponent α determines the character of frequency dependence. R1 represents the resistance between electrodes through the skin, R2 represents the transfer of electrons by redox between the electrodes and the skin and Q2 can vary by the roughness, thickness, and composition of the material. The electrode impedance characteristics were analyzed using a modified Ershler-Randles equivalent circuit called ZARC—shown in the inset of The behavior of the two electrodes in the working frequency range is very similar. The difference in the value of Q2 makes sense since they are two different materials with different thickness and roughness. It must be taken into account that PEDOT:PSS is permeable to cations and a redox process occurs in its presence.The skin-electrode impedance measurements during the recording sessions are shown in Regarding the ECG signals detected during rest, it can be observed in To quantify motion artifact sensitivity of both CREs, ECG signals were acquired during intentional movements and analyzed. An electrode for comfortable high spatial resolution surface ECG recording has been manufactured using a textile substrate and with two types of conductive materials, namely silver and PEDOT:PSS. So far, metals such as Ag or AgCl have been used for the construction of these electrodes, but these materials can cause allergies in some individuals. Therefore, the use of totally biocompatible materials, such as some conducting polymers, is a desired alternative. PEDOT:PSS used in this work is a commercial product to which no compound has been added to improve its conductivity or to avoid further problems. However, in view of the results, it would be interesting to add an organic compound such as dimethyl sulfoxide (DMSO) or ethylene glycol to enhance the conductivity one to three orders of magnitude. It should also be noted that some of the manufactured electrodes using PEDOT:PSS had to be discarded since the material had not been deposited uniformly enough to ensure good conductivity and contact area. In this context, some changes to the manufacturing process are required to enhance its reproducibility in terms of correct and uniform deposition of the material. A possible way to improve the response is to first deposit a layer of silver and then on top of this to deposit a layer of PEDOT:PSS .The developed electrodes have been tested in healthy volunteers in order to assess its capability of detecting cardiac activity in patients at rest as the first step toward transferring CREs to clinical applications. It should be noted that in the present work, compared to previous publications ,34,43, lRegarding spatial resolution, previous work that used smaller CREs implemented on flexible plastic substrates  reportedWith this work, we aimed to make a prototype that brings the use of CREs closer to clinical use. To do this, systems must still be developed that are comfortable for the patient, are easy to use, and that provide information that is easy for the physician to interpret. In future work, we propose to analyze the behavior of this type of electrode in stress tests and ambulatory recording systems.The use of silver on textiles presents better characteristics than PEDOT:PSS. Even so, techniques that improve the transfer of PEDOT:PSS to textiles could be used.Both textile silver and PEDOT:PSS CREs implemented on textile substrates are able to detect surface electrocardiographic activity in standard precordial recording positions, similar to V1 and V2 (CMV1 and CMV2).The amplitudes the BC-ECG signals detected with the textile CREs developed are of hundreds of microvolts, which is slightly lower than those of conventional bipolar ECG signals in precordial positions.BC-ECGs recorded with silver and PEDOT:PSS textile CREs presented similar signal to noise ratios with these values being similar to those of BC-ECGs from CREs implemented on plastic substrates published in the literature.Regarding the saturation and alterations of the BC-ECGs associated with movement of the subject, textile silver CRE showed a more stable response  than PEDOT:PSS.Regardless the use of silver or PEDOT:PSS, BC-ECG signals captured with the developed textile CREs have a better spatial resolution than that of conventional recordings (lead II). Specifically, BC-ECG signals have an improved capability of recording atrial activity on the surface, with P1 and P2 waves being associated with the activity of the left and right atria identified in most BC-ECG signals.To sum up, surface ECG records of high spatial resolution could be obtained with a comfortable and simple system using CREs of the proposed dimensions, implemented using screen printing techniques on textile substrates and with Ag ink as the conductive material.


This study consisted in analyzing the asymmetry between bilateral third phalanges (coffin bones) in cold-blood horses based on the angle range of the plantar margin of the bone. The study employed a scanner projecting a hybrid set of images, consisting of sinusoidal stripes preceded by a Gray code sequence. As it turned out, three-dimensional scanning can be used to effectively determine the angle range for a selected portion of the studied bone. This provides broad possibilities for osteometric studies, as it enables the determination of angle distribution in a given fragment. The results obtained indicate a weak correlation between age and bilateral third-phalanx asymmetry in terms of the angle range of the plantar margins and no correlation between body weight and the asymmetry described. Structured-light scanning of objects is increasingly used in medicine and related areas of research in the world –3. Most The present study employed a scanner projecting a hybrid set of images, consisting of sinusoidal stripes preceded by a Gray code sequence . The scaWith regard to problems necessitating the use of bone measurement techniques, an especially interesting one is bilateral skeletal asymmetry. It has been described as common both in humans and in animals –22. Markn = 38) were sold from private farms to the Rawicz horse slaughterhouse for reasons unrelated to any musculoskeletal disorders. Bones for analysis were isolated from limbs of randomly selected horses. According to the Polish law, the postmortem use of tissues does not require an approval from the Ethics Committee [The study material comprised bilateral thoracic limb coffin bones of the Polish cold-blood horse, mainly bred and kept as a draft horse . The aniommittee .At the first stage of the study, a part of the autopodium comprising the hoof was separated by severing the pastern joint. Subsequently, each hoof was marked. Then, it was bagged and immersed in water at 95–99°C for 48 h, after which the coffin bone was isolated from the hoof capsule, cleaned, and air-dried at room temperature for a week. Each coffin bone was marked on the articular surface with the number of the horse and a letter indicating the left or right limb. The isolated, dried, and marked coffin bones were laid on the flat surface of the rotary table comprised in the measurement system . The surThe other part of the measurement system was the 3D scanner installed at the appropriate distance . The scaA very significant factor in the measurements was finding the appropriate amplification and shutter settings, so as to enable the scanning of the largest surface possible. The need for entering certain parameters was due to the various colors of the bones measured. Therefore, values were adjusted experimentally for each object. All data processing and the scanning process itself were performed using the FRAMES software, developed by a team working at the Warsaw University of Technology Division of Virtual Reality.During the measurements, it turned out that the three-dimensional scanning method used is better suited for measuring light bones, whose surfaces do not significantly reflect or absorb light. Therefore, better scans were obtained from well-macerated bones, with fat completely removed . Darker,After the measurement of a bone, the points were projected onto a plane, corresponding to the surface of the rotary table. Thus, a two-dimensional image was produced. At the next stage, the bone image was rotated so as to achieve approximate horizontal symmetry. The image of the right coffin bone was flipped horizontally. Subsequently, the images of the left and right coffin bones from the same animal were superimposed using graphics software. The right coffin bone image was shifted and/or rotated so as to achieve the best overlay of the two images. For each image, we delineated the plantar margin of the bone and determined its middle point, which then constituted the zero point of a coordinate system. The margin line was transformed into polar coordinates. In the ±90° angle range, 9 measurement points were defined, spaced 22.5° apart . At eachWith the equation of the best-fit line known, the angle between this line and the line passing through the current measurement point and the center of gravity was calculated. Thus, angle values for all measurement points for the left and right coffin bones were obtained. Example results are shown in p = 0.15) and 0.14 (p = 0.41), respectively. The above results indicate a weak correlation between age and bilateral third-phalanx asymmetry in terms of the angle range of the plantar margins of coffin bones in the studied cold-blood horse population and no correlation between body weight and the asymmetry described.Pearson's linear correlation coefficient was calculated for correlations between mean angle differences and the horses' age and weight. The coefficients were 0.24 (The results of studies on asymmetry between bilateral bones of the equine autopodium are equivocal. Analyses were performed both on live animals –27 and oAvailable literature lacks reports on asymmetry between bilateral coffin bones in horses. The present study is the first one on the subject. Previous studies only assessed bilateral asymmetry between hooves , 31, 32,The choice of an appropriate equine population was an important aspect of the present study. The animals selected had not undergone any training that could contribute to unequal strain on the limbs, as is the case, for example, in race horses. In the study, no correlation was found between body weight and bilateral coffin bone asymmetry in terms of the angle range of the plantar margin. Remarkably, at the same time, a correlation was shown between bilateral coffin bone asymmetry and age. This observation seems to confirm the hypothesis put forward by Leśniak, stating that asymmetry in the structure of bilateral equine limbs and in the load placed on each side occurs regardless of the type of training , 33. SimOur observations also showed that the initial treatment of bones is a very important stage of the process, as the surface should be as fat-free and nonreflective as possible. The equine autopodia for traditional osteometric measurement may be macerated for a shorter time , 19. HowThree-dimensional scanning is a new technique that may be a valuable complement to traditional measurement methods. The present study was a pilot analysis of bilateral third phalanges of equine thoracic limbs. As it turned out, three-dimensional scanning can be used to effectively determine the angle range for a selected portion of the studied bone. This use of the method is of particular value in osteometry, as it enables the performance of additional measurements that cannot be easily performed using traditional measurement techniques. Therefore, it offers broader possibilities for bone structure analysis and angle distribution assessment and, thus, for detailed analysis of bilateral bone asymmetry, but the initial treatment of bones is a very important stage of the process. The surface should be as fat-free and nonreflective as possible. Our researches indicate a weak correlation between age and bilateral third-phalanx asymmetry in terms of the angle range of the plantar margins of coffin bones in the studied cold-blood horse population and no correlation between body weight and the asymmetry described.The presence of bilateral third-phalanx asymmetry in horses has not yet been fully explained; further studies are needed, involving a more general population and including measurements made possible by the use of three-dimensional scanning.