Electronic health data are routinely used for population drug studies. Due to the ethical dilemma in carrying out experimental drug studies on pregnant women, the effects of medication usage during pregnancy on fetal and maternal outcomes are largely evaluated using this data collection medium. One major limitation in this type of study is the delayed inclusion of pregnancies in the cohort. For example, in the province of Quebec, Canada, a major pregnancy cohort only captured pregnancies after 20 weeks gestation. The purpose of this study was to demonstrate three methods that can be used to assess the extent of selection bias due to the delayed inclusion of pregnancies. We use causal directed acyclic graphs to explain the source of this selection bias. In an example involving a cohort of pregnant asthmatic women reconstructed from the linkage of administrative health databases from the province of Quebec, we use numerical derivations, a simulation study and a sensitivity analysis to investigate the potential for bias and loss of power due to the delayed inclusion. We find that this selection bias can be partially mitigated by controlling for variables related to (spontaneous or therapeutic) abortion and the outcome of interest. The three proposed methods allow for the pre and post hoc ascertainment of the bias. While delayed pregnancy inclusion selection bias (which includes “live birth bias”) can produce substantial bias in pregnancy drug studies, all three methods are effective at producing estimates of the size of the bias. DAGsdirected acyclic graphsRAMQRégie de l'assurance maladie du Québec1Due to ethical constraints, the evaluation of drug safety during pregnancy is generally restricted to observational studies, where patients are followed through time without intervention.Electronic health data, extracted from health system or medical insurance administrative (claims) databases, are highly desirable due to their availability and coverage of large portions of the target population within countries’ administrative divisions.We describe an example from the province of Quebec, Canada that aims to evaluate the safety of similarly indicated asthma medications on pregnancy outcomes. The usage of electronic health data in this example relies on an extraction of provincial medical insurance data where the cohort is defined in terms of “deliveries,” that is, all pregnancies that surpass a 20 week threshold.2While many of the principles evaluated in this article apply in a large range of settings, we focus on the safety of asthma medication taken by pregnant asthmatic women in a cohort of pregnancies. Current guidelines suggest that pregnant women suffering from asthma continue their standard treatment throughout pregnancy due to the dangers of uncontrolled asthma provoked by stopping therapy.≤45 years with at least one asthma diagnosis in the 2 years prior to delivery and a random sample of other pregnant women. For inclusion, these women also had to be covered by the Québec public drug insurance plan in the year prior to and during pregnancy. Eltonsy et al2‐agonists vs (2) a higher dose of inhaled corticosteroids and no add‐on therapy. The exposure was measured over the first trimester  due to their hypothesis that this corresponds with a teratogenic window, as discussed in the original manuscript.The Québec Asthma and Pregnancy DatabaseThe investigations in this manuscript did not involve individual patient data and the study is therefore exempt from institutional ethics review.3The identification and selection of subjects into an analysis can produce bias in the effect estimation due to selection on a collider variable.parent) affects another (the child) in the direction of the arrow. The dotted lines indicate correlations between two variables due to latent and temporally prior variables. A path between two variables is an unbroken route that proceeds along or against the direction of the arrows. A path is considered open unless (1) conditioning on a variable blocks the path (denoted by a square around the variable) or (2) the path goes through an unadjusted collider: a variable that is affected by two parent variables. Adjusting for a collider opens the previously blocked path. If there is an open path between the outcome and exposure other than the path of interest, estimation of the causal effect will be biased.The arrows (or directed edges) between variables indicate that one variable (the A1) and major congenital malformations (Y) which can occur at any time during gestation. We consider the setting where the early medication exposure (A1) may result in an increased risk of abortion before 20 weeks.D represents the classification as a delivery by the RAMQ. It is possible that there exist unmeasured variables U that affect (spontaneous or therapeutic) abortion before 20 weeks and the outcome , such as smoking and socio‐economic factors.U may be time‐varying or multidimensional, we group it into a single variable. Stratification by D, which is a collider of the variables A1 and U, creates a correlation between these two latter variables, opening up a path between A1 and the outcome Y. This causes confounding of the early exposure (A1) and outcome association. The magnitude of the bias will depend on the strength of the effect of the unmeasured variable U on abortion and outcome. This bias should be considered in any pregnancy cohort where failed or terminated pregnancies are not included. The effect of average exposure over the entire duration of the pregnancy may also be confounded.In the DAG in Figure U cannot be controlled for in the analysis, one option is to change the question of interest to investigate the effect of exposure to medication past 20 weeks (A2) on the birth outcome, while adjusting for A1 in order to close all backdoor paths. However, this is hardly satisfactory when early exposure is believed to be responsible for a specific birth outcome, such as for congenital malformations.A2 would require that many women changed their treatment categories over the two time points (otherwise the effect of later exposure would be entirely confounded with that of A1). Other options are to explore the extent of the bias using numerical derivations, simulation studies, and sensitivity analyses as we do in the next section.If index event bias has been known to at times invert the association between the exposure of interest and the outcome; for example, smoking has been shown to be protective of subsequent myocardial infarction in cohorts of patients who had a first myocardial infarction, while a harmful effect of smoking is biologically plausible.A structurally equivalent type of bias has been shown to arise in cohorts defined by an index event such as disease occurrence when assessing the association between exposure to medication and an outcome such as mortality.4A1 is an asthma medication in the first trimester of pregnancy and the outcome Y is major congenital malformations.While there are many sources of bias in epidemiologic studies, the particularities of the data determine whether the bias has an important impact on the scientific conclusions. Consider the example concerning selection on births past 20 weeks. A simplified DAG is presented in Figure U in the following development, though additional complexities may be added with modifications to the code. An example of such a variable (U) is antidepressant medication taken during pregnancy. This variable was not assessed and therefore not adjusted for in the Eltonsy study, making it a potential source of some selection bias. There is observational study evidence of impacts of antidepressant medications on spontaneous abortion with odds ratios between 1.1 and 1.7We also only consider a univariate 4.1bA represents the effect size  of exposure on outcome, while bU represents the effect of the unmeasured variable U on outcome. The parameters tA and tU represent the effects of A and U, respectively, on the probability of the pregnancy surviving the 20th week. We suppose that the baseline risks of abortion and gestational malformations are about 18% and 8%,U. Letting the true effect size be bA=1 (no effect) and 1.3, respectively, and setting bU=3 (strong effect of U on outcome), the bias in the marginal effect that conditions on deliveries compared to the true marginal effect is given in 3D graphics in Figure ×100. Even for large associations tA and tU, the bias in our example remains fairly small, dropping to −10% only when being exposed and having U=1 both lead to a 4‐fold increase in the odds of delivery over the baseline and when the true odds ratio for the effect of interest is 1.3. These results suggest that the biased analyses would be estimating odds ratios of 0.9 if there is no effect or roughly 1.2 if the true effect corresponds to an odds ratio of 1.3. While the bias is proportionally small, with sufficient data this could result in different scientific conclusions. Attenuating the association bU results in a reduction in bias . One weakness of this approach is the analyst must assign specifications for the distributions of Y and D and that the results may vary depending on this specification. In our example, we assumed that the probabilities of these binary variables are generated on the logit‐linear scale, conditional on the prior variables.A strength of this approach is that one can visually investigate the trends in bias while modifying the values of two parameters at a time. It is also possible to increase the complexity of the assumed DAG, for instance, by considering the two distinct types of pregnancy loss or having multiple In the Web Appendix 4.2U. Using the same data generating assumptions as in the numerical example and setting a range of values for the parameters tA, tU, bA, and bU, we can alternatively perform a Monte Carlo simulation study to estimate the expected bias and power to detect an effect of A on Y. We generated 1000 datasets each one representing N=10000 pregnancies subject to selection on delivery with the same baseline odds of abortion and gestational malformations . For each dataset, we calculated the odds ratio for the effect of interest using (1) only deliveries and (2) a random subset of pregnancies of the same number (which emulates a setting without selection due to abortion with the same sample size). We look at both bias and power to detect an effect over a wide range of associations in Table D=1 compared to random selection. We see the largest effects on power when the study is just barely well‐powered or under‐powered. For example, when tA=2 and tU=bU=3 and the true effect was 1.2, the selection on a collider reduced the power from 68% to 42%. In the most extreme case (tA=tU=bU=3) with the smallest effect size, power was four times greater without collider bias.The 3D graphic allowed us to observe how the selection bias varies continuously with the importance of the unmeasured variable ries and  a randomWhile the bias in this example is relatively small, it is highly dependent on the baseline risks of outcome and selection. When increasing both baseline risks to 50%, the maximum bias increased to 25%.One strength of this approach is that, unlike for the numerical example, one can vary multiple parameters in the same table; we varied four parameters in Table https://www.r-project.org/) code used in this simulation study.In the Web Appendix 4.32‐agonists and inhaled corticosteroids was assessed during the first trimester of pregnancy. In women with moderate asthma, the contrast of interest was the relative effect of low‐dose inhaled corticosteroids plus long‐acting β2‐agonists vs medium‐dose inhaled corticosteroids therapy on the risk of major congenital malformation. This analysis did not adjust for variables that may cause both pregnancy loss before 20 weeks and the outcome as this type of selection bias was not noted at the time.Sensitivity analysis can be used to evaluate the potential impact of selection bias on the scientific conclusion of a given study. Banack and KaufmanbA in Figure D confounded by the unobserved U. If U is a single binary variable, such as antidepressant use, and assuming that all confounders of the exposure‐outcome are measured and are not caused by nor cause U, sensitivity analysis can be performed using the bias formula presented in VanderWeele.C be all confounders of the association between A and Y, the correction factor for the estimated risk ratio can be given as follows:γ=PY=1|A,D=1,C=c,U=1/PY=1|A,D=1,C=c,U=0 and σA=a=PU=1|A=a,D=1,C. In the example, the sensitivity parameter γ can be interpreted as the conditional risk ratio for antidepressant users vs nonusers, and σA=a can be interpreted as the conditional probability of antidepressant use under exposure a.Corresponding with parameter γ is constant for all levels of C and A and that σA=a is constant over levels of C. Then, the risk ratio estimate and confidence interval can be corrected by multiplying by the correction factor. For rare outcomes, this procedure can also be used to perform a sensitivity analysis for the estimated odds ratios. In Eltonsy et alσA=1=0.25 and σA=0=0.1. In order to raise the lower bound of the confidence interval to 1.0 (and thus conclude a significant effect), the outcome risk ratio γ for exposure to anti‐depressants would have to be at least 9. In this case, CFCRR=5/3 and the maximum sensitivity bound for the estimate would be 1.8 with 95% confidence interval: 1.0‐3.2. Given that such a high value for γ would indicate an unrealistically large increase in risk of induced and spontaneous abortions, it is implausible that selection bias has masked a difference in safety between the two asthma therapy options contrasted. However, due to the low power  of the original results, this still does not provide substantial evidence that an effect does not exist.Investigators might demonstrate the sensitivity of the estimate to the most extreme plausible values for these three sensitivity parameters. For simple usage of this bias formula, it must be assumed that U may also affect the exposure, though these are far less simple than the ones above.U may be considered at a time. This is a limitation because while one variable (such as anti‐depressant use) may not produce enough bias to create a misleading effect estimate, multiple variables  combined may have a greater impact.Alternative bias formulas exist for settings in which 5In this article, we demonstrated that selection bias in electronic medical data may arise when defining the cohort on a postexposure variable such as limiting inclusion to pregnancies that pass a certain time threshold. This includes the bias that arises from selecting only on live births, since this outcome occurs after the exposure to medication during pregnancy. Recent work demonstrated the potential for bias in the estimation of exposure effects when selecting on live births in settings where exposure contributes to the abortion of fetuses.In standard observational studies, investigators will typically only consider adjusting for suspected confounders between the exposure and outcome. Recognizing selection bias should motivate investigators to attempt to measure and adjust for a wider set of covariates, potentially mitigating this additional source of bias. If the additional variables are unavailable, we demonstrated how it is possible to investigate the potential for bias in a given situation. We also showed how one might alternatively assess the sensitivity of the estimated effect to different strengths of selection bias.In addition to the single source of postexposure selection that we investigated in this study, fetal death beyond 20 weeks may pose an additional source of selection bias if these pregnancies are not included in the analysis. If the outcome of interest is undefined for nondeliveries or fetal deaths, then standard methods to estimate population average causal effects no longer apply. Under additional assumptions and external information, one may alternatively estimate the survivor average causal effect,Not all sources of bias in epidemiological studies threaten the overall validity of the conclusions; it is important to investigate the potential size of bias in relation to effect estimates. A greater understanding of the mechanics of statistical association can also guide attempts to reduce estimation bias. These pursuits will lead to more reliable studies and more nuanced conclusions of causal effects.This paper considers methodological approaches to data analysis and bias. MES and LB have no conflicts of interest to report. No data were collected for this study. All data were simulated or obtained in aggregate from existing publications. Click here for additional data file.


LD spectrum are available in the literature though have not been implemented. This review summarises the literature and shows how it can be implemented. The implementation proceeds by first determining volume loss that occurs when a spherical liposome is subjected to flow. Calcein fluorescence can be used for this purpose since at high concentrations (> 60 mM) it has low intensity fluorescence with maxima at 525 and 563 nm whereas at low concentrations (<1 mM) the fluorescence intensity is enhanced and the band shifts to 536 nm. The scattering calculation process yields the average axis ratios of the distorted liposome ellipsoids and extent of orientation of the liposomes in flow. The scattering calculations require methods to estimate liposome integrity, volume loss, and orientation when subjected to shear stresses under flow.The interpretation of data from absorbance spectroscopy experiments of liposomes in flow systems is often complicated by the fact that there is currently no easy way to account for scattering artefacts. This has proved particularly problematic for linear dichroism (LD) spectroscopy, which may be used to determine binding modes of small molecules, peptides and proteins to liposomes if we can extract the absorbance signal from the combined absorbance/scattering experiment. Equations for a modified Rayleigh-Gans-Debye (RGD) approximation to the turbidity (scattering)  LD experiments that involve both polarised light and non-spherical particles. This article integrates a review of the literature covering the theoretical frameworks for scattering analysis, and outlines and implements how it can be applied in practice to extract absorbance spectra from liposome LD measurements. A roadmap for the approach adopted is first to use calcein leakage experiments to measure the volume loss when the spherical liposome is distorted in flow. Then, it is possible to use the volume loss and the scattering signal outside an absorbance region to estimate shape of the flow-distorted liposome from which we can calculate the orientation parameter for the LD experiment. An estimate of the surface area (or lipid density) change is also determined.Liposomes are spherical lipid bilayers Fig.  that encz denote the sample orientation direction (the direction of flow)  is considered and expressed in terms of the polarisation of the transition moment and the orientation parameter, S,. For liposomes where the analytes of interest are usually oriented normal to the bilayer  works quite well as an integral probe added to the lipids at the start of the liposome preparation. It is sometime also desireable to fill liposomes with a different solution than is outside the liposome. Unless liposomes are particularly leaky (see below), this can be achieved by adding the desired molecule to the resuspension buffer and running the extruded liposome solution down a sepharose column 4B column  and collecting the second coloured band to be eluted off the column in a mobile phase of EDTA (0.1 mM), TES (10 mM), and NaCl (100 mM).Diphenylhexatriene (DPH)  whereas at low concentrations (< 1 mM) the intensity is significant. This means that vesicles filled with calcein will have only very low fluorescence, but, if the calcein leaks out, the fluorescence switches on and its wavelength maximum and intensity can be used to measure how much has leaked. Vesicles can be prepared containing 50 mM calcein by adding calcein to the resuspension buffer. After extrusion to the required size, external calcein can be removed by size-exclusion chromatography to exclude free dye.ALD is the true absorbance LD and τLD is the so-called turbidity LD which is the signal resulting from photons that do not reach the detector because they are scattered . Unfortunately the refractive index-matching approach does not solve the scattering interference problem at lower wavelengths where sucrose absorbs. Using microvolume Couette flow cells   to give the maximum possible fluorescence signal.At concentrations, above 50 mM, the fluorescence is very weak and the solutions are very dark. In the context of liposome leakage, the wavelength dependence of calcein fluorescence has the advantage over the usually used intensity measurements of directly enabling a quick estimate of liposome integrity. As the chromatography step of producing calcein filled liposomes in a calcein-free solution produced samples with different total amounts of calcein, referencing the calibration to the total calcein present in an experiment is essential. This can be done by rupturing remaining vesicles at the end of a leakage experiment  using detergent  in the transmission path after the sample enables only calcein fluorescence to be detected Fig. , whereasIt is apparent that most of the stationary liposome samples of Fig. S = 0.030 for bacteriorhodopsin and soy-PC liposomes .Although Eq.  has beeng = 4. However, our liposomes are comparable in size to the wavelength of the light we use to study them and empirically, we find g < 4. As outlined below, Gans and Debye modified Rayleigh scattering giving the Rayleigh-Gans-Debye (RGD) approximation , Y' is perpendicular to the plane defined by X and the propagation vector of the scattered light . In endeavouring to understand LD, it is necessary to relate the laboratory fixed axis system, { s, Fig. , and Z' τLD to the isotropic scattering (the scattering depolarisation ratio). Mikati et al., f is a function describing the orientation of the particle, (IZ − IY) is the difference in intensities of light scattered from Z polarised and Y polarised incident light, where Z is the orientation (flow) direction and Y is perpendicular both to Z and the direction of propagation of light. The angles ϕ and θ are defined in Fig. θ and sinβ.The scattering approach of Mikati et al. uses theti et al. did not ti et al. can be iti et al. is7\docuf (and thus S) may be calculated to a reasonable approximation for flow LD using the Peterlin-Stuart probability distribution dsis the probability that a particle will be found in the solid angle ds around the orientation axis s. Although strictly f is a function of time, the implicit assumption in both Mikati and Meeten et al.  satisfying the normalisationn et al.  is that S can be determined from fromn is the refractive index of the medium, ω is frequency, ε0 and c0 are the permittivity and speed of light in vacuum. ThusThe other part of Eq.  which hiSi  and the electric field of the incident radiation expressed in terms of the {X, Y', Z'} axis system.k is the modulus of the wave vector of the light , ω is the angular frequency of the light, r is the distance of the scattered wave from the scattering centre, E is the electric field vector of the scattered light, and E0 is the electric field vector of the incident light. For small (compared with the wavelength of light) isotropic particles, within the RGD approximation only the amplitudes S1 and S2 are non-zero and equate to the polarizations perpendicular and parallel to the scattering plane respectively Following the literature  interfere because of their different origins in space. R therefore represents a phase factor to correct for these interference effects, relating the phases of all the scattered waves to a common origin.In the literature, Eq.  is commoY'Z' coordinate system for incident light polarised along either Z or Y. The vectors are For the LD experiment, we need to determine the scattered light vector in the Y, Z}coordinate system to {Y', Z'}. From Eqs. (N particles it follows thatThe transformation matrix takes the {rom Eqs. –16) for forY, Z}α by only determining the ratio of τLD and τA. When α is required in RGD calculations, the simple uniform value ((m − 1)/(2π))dV is often used for isotropic particles with a relative refractive index, m, close to 1. Liposomes usually do have a similar refractive index to that of the surrounding medium; however, in any work involving hollow particles (as in liposomes), where the refractive index of the particle centre is not identical to that of its outer shell, the polarisability is not constant and α needs to reflect this. Application of theory from Yoshikawa et al. , depend on the particle shape, size, axis ratio and orientation. The RGD form factor with a wavelength relationship of k4 is attractively simple. However, it was found not to work for tubulin microtubules  for liposomes of size 170–300 nm, and found Mie theory together with a constant term described the behaviour better. The expressions used in  and the vector that lies on the bisector of – X and the scattering vector, s For solid ovoids:Alternatively, for rod-like particles:KO and the corresponding arguments in Eq. .s in Eq.  denote tI0/r2. Previous workers have failed to explain exactly how this parameter can be determined and by taking ratios of e.g. LD and absorbance avoided the issue. Determination of I0 for a particular emitter although complex is possible, however, hard to do accurately in part because of the difficulty in a classical LD experimental setup of determining a value for r. An alternative is to parametrise I0/r2 via the fitting of a scattering curve to a spectrum with known liposome deformation and orientation.A key parameter for calculating the scattering is the instrument parameter I0/r2also accounts for the reduction in value of the form factors due to the liposomes not being made of solid lipid if we parametrise with approximately the same size particles since the general form factor equation is:B and thickness p . Thus, to account for hollow particles, the factor B is scaled by the reduction in lipid volume.Parametrising S directly following McLachlan et al.  and 1.05 × 10−12 for the experimental 7% surface area increase for soybean PC  demonstrates that the 360 nm region is polarised along the long axis of the molecule. Thus, since our lipids do not absorb at 360 nm, DPH acts as a marker to detect the orientation of lipids via LD, with the negative signal seen at 360 nm indicating DPH is indeed inserted parallel to the membrane normal  fits were also attempted for the same liposome data, however, although similar fits could be obtained at higher vesicle concentrations, rod-fitting did not work well at low concentrations and was therefore rejected in favour of purely ovoid scattering.S, to calculate the turbidity linear dichroism of liposomes. The combination enables the absorption linear dichroism even in the presence of significant scattering to be determined. Values for the degree of deformation and volume loss in the LD experiment is a by-product of the spectral correction process. Thus we only need to do the calcein fluorescence assay for the calibrating liposome sample. In this work, we selected a stable set of liposome deformation data to act as a standard from which to calculate instrument parameters τLD for any lipid system collected in that instrument configuration. Thus, for the first time, we showed that literature theory can be applied to extract the true absorbance LD spectra of light scattering samples, rather than only ratios.In this work, we have reviewed literature scattering theory for flow LD spectroscopy and illustrated an implementation of the Rayleigh-Gans-Debye scattering theory. We have relied on the expansion of RGD theory undertaken by van de Hulst , Meeten Although the focus in this review has been almost exclusively on flow LD spectroscopy, any optical spectroscopy technique which is less complicated can be addressed with the same approach. The differential intensity term would in general be replaced by an isotropic incident intensity term and we would not need to worry about flow-induced particle volume changes during the experiment.k4 dependence. However, it has been previously shown that this power relationship does not fit experiment for liposomes. Instead the relationship that is demonstrated is far closer to that of classical Mie theory, with a k2 dependence. Since our particles are approaching the limits of the size restriction outlined by RGD theory, and just barely under the minimum for Mie theory, it is not unreasonable to see elements of both in effect. The main differences in the approximations for each approach are the particle shape factors, since Mie is primarily restricted to spherical particles whereas RGD allows for asymmetrical particles, and a constant term. The parametrisation approach taken here allows us to take into account unknown constants ) into the I0/r2 term. Therefore, what we have illustrated is a quasi RGD-Mie theory instead of strictly classical RGD.According to Rayleigh theory, the relationship that a particle has with the wavelength of the incident light has a λmax can be used to determine calcein concentration below ~ 45 mM with fluorescence depending approximately linearly on concentration between 45 and 10 mM. Leakage depends upon the type of lipid and the duration of flow, with the shorter chain DMPC exhibiting the highest degree of leakage even when stationary, questioning the usefulness of the extensive DMPC liposome work in the literature for kinetics and comparison studies.A calcein fluorescence intensity assay to measure volume loss from liposomes when stationary and when deformed under shear flow was also illustrated. Calcein fluorescence not only enhances significantly with dilution as is well established but also shifts from 525/563 nm to 536 nm. 1/


Salt weathering is one of the major causes of the damage both in cultural heritage as well as in civil engineering constructions. A special case develops when there is a continuous wicking of a salt solution into a material in combination with evaporation of the moisture at its surface. In this study we are interested in the case where the absorption rate is much higher than the evaporation and as a result a salt concentration will build up at the drying surface resulting in crystallization. To this end we propose a simplified model to describe this mechanism. In order to check the model the NaCl concentration profiles were measured non-destructively by Nuclear Magnetic Resonance during a combined wicking and evaporation experiment with limestone. A good correlation was found between the model and the measured NaCl concentration profiles. Salt weathering is one of the major causes of the destruction of our cultural heritage. Ions such as chlorides, sulphates and nitrates are well known to be the cause; the damage is by the crystallization of these soluble salts within the pores. These salts can only be transported within liquid. Therefore the liquid transport processes are dominant in determining where the accumulation will take place and therefore where salt crystallization and possible damage can occur. Often there is a continuous wicking of a salt solution. This can be encountered if the construction is in contact with groundwater or as often seen in marine environments when it is in contact with seawater. In these circumstances ions will be advected along with the capillary moisture flow into the material .When there is continuous wicking of a solution into a material in combination with evaporation of the moisture at the surface of the material an equilibrium will develop between wicking of the salt solution and the evaporation flux at the drying surface. Based on the sharp front model Hall  has showOne of the very first studies about combined wicking and evaporation action was carried out by Lewin . AlthougIn this study the focus was on the NaCl transport in a porous material, i.e., limestone, along with the moisture flow and in particular on the build-up of the concentration near the drying surface. To this end we will first discuss a simplified model to describe the concentration build up. The model was checked by performing non-destructive measurement of the concentration build up using Nuclear Magnetic Resonance (NMR). This setup will be briefly discussed in the next sections, as well as the influence of the one-dimensional resolution of the NMR on the measured concentration profiles. Finally the results of the measurements will be presented and discussed.c is the ion concentration, D* the macroscopic diffusivity of the ions within the porous material and u the macroscopic velocity of the liquid in the porous material, i.e., the Darcy speed.In Fig. *, i.e.;* > 1 is a correction factor for the increase in path length due to the tortuous nature of pores.The macroscopic diffusivity of the ions within a porous material is related to the microscopic diffusivity of the ions through the pores by the tortuosity TPe > 1, advection will be dominant and there will be a concentration gradient and as a result the salts will accumulate near the surface. Whereas in the case of Pe < 1, diffusion is dominant and we expect a homogenous distribution of salt. This Pe-number was also found to be very useful for giving an indication of the effect of poulticing [Pe > 1, where ions will be advected towards the surface and there will be a concentration build up near the interface giving rise to crystallization.Therefore the first part of the right hand side of Eq. ulticing . In thisu, will be constant throughout the sample. The liquid speed will be completely determined by the drying condition at the top, i.e., the liquid flux ql at the surface is given by:β is the mass transfer coefficient which is dependent on many parameters such as the air velocity, porosity and surface roughness, ha the relative humidity of the air and hm the relative humidity of the materials at the interface, which is a function of both the moisture content θ and the salt concentration. As the salt concentration is slowly changing near the drying surface the liquid speed will change slowly in time even if the drying airflow is kept constant. Therefore the salt concentration will have a large influence on the evaporation [As the sample is completely saturated the liquid speed, poration , 15.As long as there is no crystallization at the drying surface the boundary condition for the ion transport is determined by the no flux condition, i.e.;co is the concentration of the liquid being absorbed at the wicking surface If we now assume that in the first-order approximation the liquid flow throughout the sample and the concentration at the inflow are constant, we can solve the partial differential Eq. α(t) is a constant, which is a function of the time reflecting the increase of the concentration at the boundary. If we assume that the liquid velocity is constant, the increase of total ion content will be linear in time due to the regular advection of ions. Therefore by integrating Eq. l (here it is assumed that l > 4D*/u) we can get an expression for α(t), i.e.;At the wicking surface where the salt solution is absorbed the boundary condition is given by a constant flux, i.e.;Hence it can be seen that as long as the liquid speed is constant, the concentration rise at the surface will increase linearly with time.o as -cHence as the ion diffusivity is constant, the peak width is fully determined by the liquid velocity and as the liquid velocity increases the peak width near the surface will decrease.c* is the threshold concentration at which the crystallization starts and γ is a crystallization rate. In this case the crystallization term does not only indicate whether the crystallization will take place either inside near or outside at the surface of the sample.As soon as the ion concentration has reached the threshold level for crystallization, this mechanism will start and in this case the ion transport can be described by adding a sink term to Eq. Nuclear Magnetic Resonance (NMR) was used for the measurement described in this study. This methods allows a non-destructively and quantitative measurement of both the moisture and NaCl-concentration profiles in an experiment . ThThe sample is moved through the NMR with the help of a stepper motor. The moisture is first measured at the center of the NMR, after which the NMR machine is switched over to sodium and its content is then measured in order to determine the NaCl concentration. Subsequently the sample is moved to a new position and the procedure is repeated until a complete moisture and NaCl concentration profile is measured. Measuring the moisture content takes in the order of 40 s, where as it takes about 120 s to measure the Na concentration. With the NMR relaxation parameters used in the NMR experiment no signal is obtained from salt crystals and only free moving ions are measured. The measurement time of a complete profile takes is in the order of 3 h, whereas the total experiment took 50 days; hence variations of the profile during a measurement can be discarded.The NMR measurements are performed with a given one dimensional NMR resolution, reflecting the length scale over which the measurements are averaged, i.e., every measurement point is the average over a certain length, analogue to cutting the sample up into slices of a certain thickness. At the same time, the step motor allows to measure a point every 0.5 mm as the resolution of the step motor is much higher. As a result of the one dimensional NMR resolution, profiles will be smoothened. An example is shown in Fig. The material used in these experiments is a biomicritic limestone from Sardinia. This limestone is very widespread in the Mediterranean basin and has been much used in buildings and monuments because it can be easily carved. These materials are characterized by a high porosity of 34% and poor mechanical properties so it weathers easily –20. The D* = 0.48 10−9 m2 s−1. As the bulk diffusion coefficient of NaCl in water is on average in the order of 1.5 10−9 m2 s−1 in the range from 1 to 6 m [T* = 3, which is in the order of values as reported in literature for many coarse porous building materials and stones [Before the combined wicking/drying experiments was initiated the diffusion of a 3 m NaCl (mole/kg) solution in a sample was measured. The NaCl concentration profiles during diffusion were measured for 72 h. The measured ion concentration profiles after applying the Boltzmann–Matano transformation  are give1 to 6 m  we find d stones , 25.Fig.The results of the combined wick action and evaporation experiment are given in Fig. u/D* as determined from the individual fits of the profiles. Since D* is almost constant, within a first-order approximation this figure reflects the change in the liquid flow speed throughout our experiment. As can be seen during the first 5–10 days, as the concentration rises rapidly at the surface to 4 m, the liquid speed is dropping fast. As the sample has a fixed length of 0.1 m we see that the Pe-number is initially in the order of 20 and is decreasing to 3.5 towards the end of the experiment. This reflects the rapid change at the boundary as the NaCl concentration increases which will have a large influence on the sorption isotherm and therefore on the evaporation. After 10 days the liquid speed remains constant to the first-order. This is reflected in the almost linear increase of the concentration at the surface as indicated by the simplified model.From the fitted profiles we can determine the NaCl concentration at the drying surface. The results for all measured concentration profiles are given in Fig. As can furthermore be seen from fitted profile as provided in Fig. As can be seen as soon as the 6 m is reached and crystallization starts, the measured NaCl profiles does not significantly change. This indicates that crystallization must take place at the top of the sample. Indeed after the experiment was performed, a thick layer of salt was found on the top of the sample and no mechanical damage to the stone was observed, showing that the crystallization rate is high enough to compensate for the ion influx.The aim of this paper was to investigate the ion transport during combined wicking and evaporation; a situation which is often encountered in situ. It has been demonstrated by NMR that the NaCl concentration profiles can be measured non-destructively and quantitatively. The measured NaCl concentration profiles can be described by a simplified model, which only takes into account the liquid flow speed and the diffusivity of the ions in the material. This model reveals that although this combined wicking and evaporation is a slow process the concentration will continue to increase for many years, giving rise to salt crystallization and eventual damage. This combined process is dependent on the evaporation at the surface and therefore will strongly depend on the external condition during the yearly cycle in situ (see e.g. ).


Propagation of elastic waves along a direction has special interests in practical applications. These concerns generate the design of an elastic wave metamaterial with electrically switchable properties, which is studied in this work. The structure contains a T-shaped waveguide in a plate with the 3D printing technology; and the active control system is used to tune the propagation direction of the flexural wave. The piezoelectric patches which are connected by the negative capacitance circuits are applied to behave as the active control system. The finite element simulation is performed to give the theoretical prediction of the switchable waveguide and the tunable equivalent parameters are achieved by the electrical circuits. The active control experiments are finally carried out to support the numerical design. This is mainly because that these periodic systems have superior properties, such as the wave band gaps12, negative refraction16, acoustic cloaks19, etc. These behaviors can be used to tune the wave propagation. Acoustic couplers20, sensors21 and waveguides22 are several typical applications of phononic crystals and elastic wave metamaterials.During the past decades, phononic crystals and elastic wave metamaterials which have the periodic characteristics have received lots of attentionet al.23 presented the switchable acoustic demultiplexers based on the fluid-fluid phononic crystals. Zhang et al.24 used the supercell plane wave method to investigate defect modes by introducing the bend-shaped linear defects. Wang et al.26 discussed wave guides with the reconfigurable and coupled-resonator properties. Yao et al.27 presented the flexural waves in the phononic crystal plate with linear defects to show the guide behaviors.Another important characteristic of phononic crystals and elastic wave metamaterials is the defect state. It’s well known that if there are some defects in these periodic structures, the elastic wave will be localized near the defect (for the point defect) or propagate along the defects (for the line defects). So the propagation direction and some other properties of elastic waves can be controlled by designing different waveguides. For instance, Rostami-Dogolsara 32. In order to derive the broadband control of elastic waves in a flexible plate, Tateo et al.33 presented an experimental investigation about a periodic array of shunted piezoelectric patches with the negative capacitance. Casadei et al.34 discussed about the experimental demonstration of a tunable acoustic waveguide which was implemented on a phononic plate. By connecting gradient negative capacitance circuits to an array of piezoelectric patches, Chen et al.35 designed a metamaterial-based sensing system with the gradient bending stiffness. They demonstrated that the proposed system can achieve more than two orders of magnitude amplification of flexural wave signals to overcome the detection limit. In this work, we propose an elastic wave metamaterial with a T-shaped switchable waveguide by the active control system. With the electrical tunability, the switchable properties of the elastic wave are realized.In recent years, special attention has been focused on the active control effects on phononic crystals and elastic wave metamaterials, which can show many interesting resultsOn the other hand, compared with the traditional materials, phononic crystals and elastic wave metamaterials have unique band gap characteristics. At present, they have shown broad prospects in waveguides, filters, new vibration and noise reduction materials and other devices. Phononic crystals and elastic wave metamaterials have become the hot research topic in many fields, such as engineering mechanics, physics, mechanical engineering, etc. The research in this field has attracted extensive attention and has broad development prospects.36. So based on the 3D printing technology, special phononic crystals and elastic wave metamaterials would be achieved.Nowadays, the 3D printing technology has gradually replaced the traditional manufacturing technology. It’s mainly due to that the 3D printing technology can make most structural shapes with the precise size at different scales. As the structure becomes more complex by this method, the manufacturing cost will not increase. The 3D printing technology offers the opportunity for the traditional design and control of periodically patterned structures. And even it can realize some special characteristics, e.g. the negative stiffness and Poisson’s ratioIn this section, the active control system is bonded on an elastic wave metamaterial plate which consists of the piezoelectric patches and negative capacitance circuits. Phononic crystals and elastic wave metamaterials have band gaps, in which elastic waves cannot propagate. When the elastic metamaterials have the defect like the point and line cases, the elastic wave will be limited to the point defect or propagate along the line defect. Phononic crystals and elastic wave metamaterials are the artificial structures with the periodic elastic constants and densities. Negative capacitance circuits can change the inherent elastic modules, which results in tuning the band gap structure. Then the elastic waves in specific frequencies can be controlled to propagate along the direction as we design. Then the propagation direction of elastic waves will be changed actively. Based on the finite element method, switchable properties of elastic waves in the metamaterial plate will be presented and the validity of numerical results will be verified by the experiment.z-axis, and the x, y and z directions are described as 1, 2 and 3, respectively. The piezoelectric equation can be expressed as37S1 and T1 denote the strain and stress along the x direction; d31 and E3 is the electric field intensity along the z direction; and D3 is the electric displacement.Assume that the polarization direction is along the 38s is Laplacian operator; Z is the complex impedance of the shunting circuit; As is the electrode area; and hp is the patch thickness.Substituting the expressions of the electric displacement and electric field into Eq. , the relThen the inherent elastic modules of the patch can be derived by Eq.  as3\docuCp, compensation resistance R0, operational amplifier, fixed resistances R1 and sliding rheostat R2 are included. In the experiment, the operational amplifier LM324N is applied and the complex impedance Z can be defined asα = (R2 × C)/(R1 × Cp).As shown in Fig. α to change the inherent elastic modulus of piezoelectric patches and perform as the active control action on the elastic wave.Therefore, we can tune the value of The periodic structure consists of a thin resin plate with 5 mm thickness and the periodic arrangement of surface-bonded hollow cylinders. The external diameter of the hollow cylinder is 34 mm and internal diameter is 26 mm, as well as the height of the hollow cylinder is 30 mm. These cylinders are arranged as the square lattice with the constant 40 mm. As shown in Fig. The structural optimization by the optimization method, such as the genetic algorithm, is not performed. During the preparation of this work, several different kinds of the periodic structures are compared. Such as cuboid columns, solid and hollow cylinders are arranged as the square lattice and we find that the periodical structure with hollow cylinders can show the satisfied result. Then different structural parameters are considered to improve the model. We know that it’s not the periodic structure with the best effect. It should be noted that in this work, the active control can show more importance.α = 0.9 is applied.The propagation properties of the elastic waves in the periodic structure are simulated by the finite element software COMSOL. As shown in Fig. As shown in Fig. In order to compare these results, the negative capacitance circuits are applied on the left side of the horizontal channel. The mean stress of the left and right sides with the same frequency range from 5300 Hz to 5500 Hz are simulated, and the results are shown in Fig. E = 2.5 GPa, the density ρ = 1300 kg/m3 and the Poisson’s ratio ν = 0.41. The material parameters of the P-4 piezoelectric patch are shown in Table To demonstrate the validity of the numerical simulations, we carry out the active control experiments on the waveguide structure, in which the P-4 piezoelectric patches are boned at the line defect. The waveguide structure is fabricated by the 3D printing technology. The Young’s modulus The experimental setup is illustrated in Fig. Figure We know that the experimental testing system cannot present the displacement distribution field like the numerical results. It can test the acceleration signal at a certain point. So we set three receiving points for the acceleration signal on the left or right side to get the information about the wave propagation. When the acceleration signals of the three points on the left are much higher than those on the right, we can assume that the elastic wave changes the direction and propagates along the left of the waveguide. On the other hand, similar behaviors can also be derived if the wave propagates along the right side. These acceleration responses are shown in Figs Previous investigations on the elastic waveguides are mainly concentrated on the propagation of elastic waves only along a single direction. In this work, the switchable waveguide of the elastic wave metamaterials is achieved by the active control action. In order to control the material parameters, the switchable waveguide is connected with the piezoelectric patches which are attached by the negative capacitance circuits. Furthermore, the experimental model is fabricated by the 3D printing technology and bonded by the active control system. The validity of the numerical simulation is supported by the experiment. This study is expected to be helpful to design the elastic wave metamaterials with the active control action.


The case describes the fabrication of a unilaterally fixed anterior fiber‐reinforced composite bridge in a 14‐year‐old girl. Using this technique, it is possible to temporarily replace a missing anterior tooth until a definitive restoration can be inserted. It was decided to place a fiber‐reinforced composite bridge with unilateral anchorage as an intermediate solution. After 1 year the restoration was still in service, but some revision was needed.dens invaginatus at our dental school. A dens invaginatus, also known as dens in dente is the consequence of an invagination of enamel epithelium into the pulp space. The reported prevalence varies widely between 0.3% and 10%.dens invaginatus.A 14‐year‐old girl introduced herself with a Dens invaginatus shows multiple morphological variations in crown and root formation from type 1 with almost no morphological changes to type 3 which can be associated with periapical infection.The absence of the lateral incisor caused a restriction in phonetics and esthetics which was disturbing the patient Figure . After d2The lost upper left lateral incisor was replaced by fiber‐reinforced composite bridge with unilateral anchorage which was fixed to the left central incisor. The main problem of the planned restoration was that the space width was too big to get an adequate result by restoring only the missing tooth. Furthermore, attention had to be paid to the hypomineralization of the remaining front teeth. The main concern was to realize an affordable and esthetically appealing rehabilitation of the front teeth in the upper jaw.® duo  was used as a restorative material. Unbonded composite samples were polymerized on the enamel surface for a more detailed color determination. The patient's occlusion was checked.As a first step, plaster models were made and the front teeth were remodeled with a wax‐up in the laboratory situation. Afterwards, a silicon mold was prepared in order to establish a mock‐up and use it for an intraoral demonstration for the patient. Furthermore, different colors were chosen and tested intraorally. The nanohybrid composite CeramX®  was fixed with x‐flow® A3 (Dentsply Sirona Inc.). The thickness of the composite between teeth and ribbon was kept as thin as possible . Dentin core layering was performed using the D1 and D2 shades of the composite system  as a snow‐white composite was used to mimic the hypomineralization which was seen on the upper front teeth. As a final layer, enamel E2 shade was applied.The composite was used in combination with the Etch & Rinse adhesive XP Bondm Figure . As a nem Figure . Venus® ® Enhance finishing system and PoGo® One Step Diamond Micro‐Polisher (Dentsply Sirona Inc.) were used for polishing  to ensure a long‐lasting result. The use of different dentin and enamel imitating composites to build up the intermediate tooth according to the anatomical layering technique provides a final aspect with natural opalescence, translucency, and opacity. The use of a denture tooth may also be considered instead of direct remodeling the missing tooth. This method is easier, faster and in some cases esthetically more acceptable than the direct fabrication of a tooth. However, in this case the challenge was to imitate the hypomineralizations which would not have been possible with a denture tooth. Furthermore, the shape and the incisal color of denture teeth are difficult to match to the adjacent teeth in some cases.At the follow‐up after 1 year, the restoration was still in place, but some revisions had to be done. This included some esthetical improvements of the margins of the composite restorations which were detectable and showed some staining. On the palatal side, the fiberglass ribbon was partly exposed and needed to be recovered with composite. In addition, some changes in the natural teeth were obvious at the follow‐up. In comparison to the upper right central incisor, the left one sowed some intrusion and distal tipping, which also included the pontic. It might be speculated that this was the consequence of the unilateral force effect on the incisor caused by the pontic. When comparing the Figure 4In conclusion, the fixed anterior fiber‐reinforced composite resin bridge fabrication technique suggests an alternative treatment option for the temporarily replacement of a missing anterior tooth. Using this technique, it is possible to restore esthetics and function. It is more comfortable than a removable appliance, nonirritating, and hygienic. Generally, it does not require any tooth substance loss and can be repaired, modified, or removed from teeth without any iatrogenic damage. Clinical long‐time studies have to show whether it can also serve as a permanent restoration.On behalf of all authors, the corresponding author states that there is no conflict of interest.VP: was treating the patient and was preparing the manuscript. SZ: is corresponding author, was preparing the manuscript, performed follow‐up‐examinations, and made revisions. LM: was supervising VP and proofreading the manuscript.


The dependence on model-fitting to evaluate particle trajectories makes it difficult for single particle tracking (SPT) to resolve the heterogeneous molecular motions typical of cells. We present here a global spatiotemporal sampler for SPT solutions using a Metropolis-Hastings algorithm. The sampler does not find just the most likely solution but also assesses its likelihood and presents alternative solutions. This enables the estimation of the tracking error. Furthermore the algorithm samples the parameters that govern the tracking process and therefore does not require any tweaking by the user. We demonstrate the algorithm on synthetic and single molecule data sets. Metrics for the comparison of SPT are generalised to be applied to a SPT sampler. We illustrate using the example of the diffusion coefficient how the distribution of the tracking solutions can be propagated into a distribution of derived quantities. We also discuss the major challenges that are posed by the realisation of a SPT sampler. Single molecule imaging is increasingly facilitating high-resolution investigations of molecular motion at the plasma membrane of cells e.g. –4). Hidd. Hidd4])To evaluate particle motion in general one must measure the instantaneous values of motion parameters as they fluctuate along the particle trajectory and ultimately requires single frame sensitivity. The most accurate way to achieve this is from the globally optimal spatiotemporal solution to SPT. In this idealised approach each possible choice of particle reconnections and associated motion parameter values is considered and their consequences compared along the entire length of the tracks, therefore automatically exploiting all the information in the data to output the most likely empirical estimate of reconnections and parameters, and places confidence limits on them. Achieving the globally optimal solution has been the goal of SPT for decades but it has proven to be computationally prohibitive because of the colossal size of the configuration space of particle reconnection possibilities at high particle density, low signal-to-noise ratio (SNR) and fast particle movement typical of single molecule images in cells . A wide Here we present the Biggles tracker, an automatic Bayesian Inference-based, Gibbs-sampler, GLobal EStimator of particle tracks and parameters that converges towards the globally optimal spatiotemporal solution in a computationally time practical for real-world tracking. Biggles allows to estimate the uncertainty in the tracking solution and finds probable alternative solutions. It therefore opens the possibility to propagate the tracking error to the estimation of derived biophysical quantities such as diffusion coefficients.Y, which are the spatial and temporal  coordinates of the single particle spots detected in the images (referred to as observations), a hypothesis for the assignment of these observations to tracks, the track partition ω, and some global parametrised model, θ, for the properties of the system. , while the parameter sampler .Biggles finds the probability of any given set of tracks and motion parameters given the data. In a Bayesian framework , this al sampler , which algorithm , which cacceptance probability of the Metropolis-Hastings sampler , ωi−1. The nine move types are the main branches of which one is randomly chosen. Cartoons of the move types are shown in Q(ω*|ωi−1) = 1/9×1/(number of tracks)×1/2×1/. The sampling structure ensures thatQ being a PMF. As already mentioned above, for a valid track we require that it contains observations at a minimum of two time points , and we note that two tracks having the same observations and therefore the same links may not be equal, since a track may have unobserved states before the first or after the last observation. To improve the performance of the algorithm, we also limit the maximum speed of the particle .The  sampler  step ③ iω* is set to ωi−1. Since in such a case accepting and rejecting leads to the same result, ωi = ωi−1, we regard the proposal as identity as opposed to accepted or rejected. It means that Q(ω|ω) > 0 for most ω. We tried to minimise the identity proposals in the move design, e.g. we do not attempt a death move if the partition contains no tracks or we do not attempt to split a track that has only three observations and so on. The occurrence of the identity proposal is not a theoretical novelty. Q(ω|ω) > 0 also occurs if Q is a Gaussian distribution. However since the Gaussian distribution is continuous rather than discrete, it is very unlikely that a proposal sampled from it is equal to the last sample and special considerations of such a case are unnecessary. The distinction only takes effect in the calculation of the acceptance rate, where identity proposals are treated as rejected proposals even though their acceptance probability is equal to one.It is possible that the execution of a move does not lead to a valid track partition. For instance, at the end of the birth move, the created track may contain no observations purely by chance. In such a case P, of the Metropolis-Hastings sampler, P(θ) are the parameter priors and P(ω|θ) is the probability of the track partition, which takes the assignment of observations to tracks into account but not their physical properties. P(ω|θ) is assumed to depend separably on four parameters in θ, according to closed-form distributions. The likelihood P is factorised into the likelihood of the clutter observations P and the product of the likelihoods of the observations assigned to tracks, K is the number of tracks and Yi are the observations assigned to track ki. The likelihood P is evaluated using a state space approach [To evaluate the target distribution, approach . The (unn filter  to estimn filter . The obsAssigning the observations to tracks (done by the partition sampler),Estimating the track’s states from the observations of the track using the Kalman filter (i.e. inferring the model),Calculating the likelihood of the observations given the model (i.e. states and the error estimates).t2 is considered clutter. The Kalman filter estimates the particle states from the observations of the track, which are marked by black dots in the state space. The states and their error estimates in turn imply how likely it is to find the observations at their actual positions. The likelihood of the individual observation R and the state estimation error. The full equations are given in the supplied appendix 5 sections 3.2 and 3.3. In t2; the observation that previously was clutter is now part of the track and the other observation is now considered clutter. The Kalman filter provides new state estimates of all observations of the track, which leads in turn to new observation likelihood estimates. For example the likelihood of the observation at t1 is reduced after the update move, while the likelihood of the observation at t3 is increased. An example showing observations and estimated states of a track is giving in An example is depicted in R that contributes to the innovation covariance is sampled as part of the parameter sampling stage of the Gibbs sampler, P are described in the supplementary notes.The 2 × 2 covariance matrix of the observation noise R, the further four parameters in θ control the track partitioning. The birth rate λb is the average number of tracks that begin at time point t in a normalised area A. The clutter rate λc is the average number of spurious observations that are found at time t in a normalised area A. We use the symbol “po is the probability that a particle is observed at time t and the survival probability ps is the probability that a track that is present at time t − 1 is also present at time t. We note this implies the assumption that the track length is exponentially distributed with mean 1/(1 − ps). This is not a limitation for imaging fluorophores, since it reflects the bleaching behaviour of fluorescent molecules. Quantum dots, which are used in bioimaging as well, do have for practical purposes an infinite life time. The posterior distribution P can be sampled directly and is separable, b, λc and the probabilities, po, ps are assumed to follow Gamma and Beta distributions, respectively, where the parameters for the Gamma and Beta distributions are derived from the current partition sample by counting the number of tracks, their lengths and so on, R, is sampled from an inverse Wishart distribution, where the parameters are derived from the track observations and the track model. In summary we haveθ0 are initialised to some values. In principle we need only specify loose “plausible” bounds of θ0. Our current implementation initialises θ0 to uncontroversial typical values. The rates λb and λc have improper uninformative priors on them being positive, ps and po have uniform priors over  and R has an inverse Wishart prior In addition to the three parameters that determine minimum partition, ω0. For the second chain, we use a randomised greedy algorithm to assign as many observations as possible to tracks to create the initial partition. No further links can be added to such a partition, which is therefore referred to as a maximum partition. Usually, Ω has many maximum partitions. The sole purpose of this approach is to get two starting partitions that are far away from each other. To assess the convergence of the two chains we implemented two tests. The first test is based on the similarity of partitions. We consider a track partition as a graph, where the observations are the nodes and the links are the edges. We use the graph edit distance (GED) [b, λc, po and ps. A Biggles chain is ergodic, which is shown in the supplementary information. The initial part of the sampling before the sampling chain has reached the limiting distribution (the target distribution) is called burn-in phase. In order to assess the convergence to the limiting distribution of the Metropolis-Hastings sampler we run two chains. The first chain starts with the partition without any links, i.e. where all observations are assigned to the clutter. This is the ce (GED)  as similce (GED) , 30 statkB large, depending on the number of observations, N. Therefore we record 1 in every n samples, thereby thinning the chain, where n linearly depends on the acceptance rate at the end of the burn-in phase. In the present implementation every 1 in 8 samples would be recorded if the acceptance rate were 25%.By design the Metropolis-Hastings partition sampler will yield correlated samples. That reduces the effective sample size  and incrThe burn-in phase is longer than the target distribution sampling phase. Experience shows that the ratio of the number of target distribution samples to the number of burn-in samples has a median of about 3.5% and a mean of 5.5%. The maximal observed value is 25%.At the point of convergence, the Gibbs sampler starts to sample candidate-sets of tracks and parameters whose distribution matches that of the joint posterior distribution. We may therefore interpret results such as the sample mode and sample variance as maximum empirical estimates and experimental errors respectively. The ability of Biggles to directly return a representative sample of tracking results and parameters, and thus to place confidence limits on these, is powerful and, as far as we are aware, it is novel in this field.realisation of the ground truth (GTR). That means we have three stages of ground truth; the parameters, the tracks states simulated from these parameters and the observations created from the states. We enable a range of behaviours in the simulation; random walk, directed motion, a combination of both and track splitting.To demonstrate Biggles we use synthetic and single molecule microscopy (SMM) data sets. For our simulations, we first generate tracks with a given birth rate x and y is pixel, where one pixel is 160nm×160nm for the SMM data sets that we present. The unit of time is the frame index. The time lag between two frames is 0.05 seconds for the SMM data sets.If not mentioned otherwise, the unit of b, λc, po and ps for two of these data sets in comparison with parameter samples given the GTR, P. The ground truth value for the parameter is indicated by a vertical line. First we see that the distributions derived from the GTR are are well distributed around the ground truth parameter values, albeit with some bias in the survival probability. Moreover, we observe very good agreement between the Biggles posterior distributions and those derived from the GTR , and also recall = TP/(TP + FN) and precision = TP/(TP + FP). All measures have a range between 0 and 1, where 1 is best and 0 is worst. If pmin = 1 then only links that occur in all records are considered positives. The number of FP is lowest and FN is highest. When pmin is reduced, FP will increase and FN will drop. If pmin = 0 then any link that at least occurred in one sample will be considered as positive, which gives a large number of FP, while ideally the number of FN should go to zero. In other words, if a link is in the GTR then we expect it will at least occur in one sample. The two left panels of pmin < 0.6, while it significantly drops for pmin near 0 and 1. For the less crowded data set we find higher JSC (between 0.97 and 0.99 at pmin = 0.5) than for more crowded data sets (between 0.92 and 0.98 at pmin = 0.5). The two right panels of pmin = 0.5 are marked with a dot. We observe that with lower pmin the recall increases, i.e. less GTR links are missed, while with higher pmin the precision increases, i.e. less false predictions are made. For the data sets with lower track density we observe recall and precision higher than 0.99 at pmin = 0.5 and for data sets with higher track density we observe recall and precision values of at least 0.96 at pmin = 0.5. For some low track density data sets we observe almost perfect recall at pmin = 0 and almost perfect precision at pmin = 1. However also for the higher density data sets we get recall and precision of at least 0.99 at the extreme ends of pmin. We did not calculate the receiver operating characteristic (ROC) curve, since we did not calculate the number of TN. However, the plot recall versus precision is a similar visualisation; rather than assessing how many negatives have been falsely classified as positive as in ROC, we assess how many of the classified positives are true positives.We calculate the frequency with which any two observations have been linked and use it as probability estimate, ure from . HoweverWe use the synthetic data of Single molecules show a variety of modes of motion. While we did not fully explore the behaviour of our algorithm under such conditions, we do provide some illustrative tracking examples in D, for the GTR as well as for every recorded sample. The diffusion coefficient was calculated from the mean squared displacement, 〈r2(τ)〉, for time lag τ. The estimate is calculated from the positions of the observations assigned to the tracks. The mean was taken over all tracks, see Supplementary Notes. Each of the two panels show the data of five realisations of a ground truth partition (GTR), i.e. 5 sets of observations generated from the same ground truth states. The diffusion coefficient of each GTR is shown by a vertical line. They are different for each realisation due to the random nature of the generation. Each set of observations was used as input for Biggles and D was estimated for each recorded sample, 4000 samples per run. The D of the samples are shown as histograms in the same colour as the related D of the GTR. We calculated to each data set confidence intervals (CI) and counted how often it contains the D of the GTR. The CI to confidence level X% is calculated as the smallest interval that contains at least X% of the samples. We found an agreement of 52% for a 70% CI and 75% for a 95% CI. This is a very encouraging result. However the procedure somewhat underestimates the errors. This will be subject to future investigations.We demonstrate the sampling of a derived quantity using the example of the diffusion rate , see Figpx to 12px. Simulated particles moved in a random walk (D = 0.02px2/frame and D = 0.32px2/frame). After the generation of the GT particle trace the observation model was applied. A particle was observed at any time with a given probability, po ∈ {0.9, 0.7, 0.5}. The particle observation was sampled from a normal distribution with the GT particle location as mean. We assumed two different localisation errors, 0.1px and 0.4px. The life time of the particle tracks was exponentially distributed. We added uniformly distributed spurious detection which resulted in a density of 0.4±0.1 observations per 100px×100px and frame. The resulting data sets had on average 2003±575 observations.We compared Biggles with uTrack . For thepx and high observation probability both trackers perform very well. Biggles remains stable for a low localisation error, even if the observation probability drops. The uTrack tracker on the other hand drops in performance if the observation rate goes down. For a localisation error of 0.4px the tracking results are consistently worse. However, for the highest observation probability the performance of both trackers is still good. As before, with lower observation probability the performance of uTrack drops faster than the performance of Biggles. In general Biggles has a better performance than uTrack.The results where compared with the GTR. The number of links in which the trackers differed from the GTR, the GED, was normalised by the number of observations in the input data. Note that the value can be larger than 1, with 2 being an upper boundary. A value of 0 indicates total agreement. For uTrack a single value per data set is shown in μm×16μm (100pixels×100pixels) field of view, in 30s 600 image frames have been acquired and 9761 observations have been detected using an in-house algorithm [To illustrate Biggles we have chosen a typical SMM data set from our lab, which has been imaged for a co-localisation experiment. The data sets was acquired by total internal reflection fluorescence (TIRF) microscopy using organic dyes (enhanced green fluorescent protein) . We imaglgorithm . We recoThe tracking result is plausible. All obvious tracks are found and there are no obviously wrong links with high probability. Biggles considers most of the tracks as uncontroversial. About 10% of the links do not appear in all samples. Most of those links have either a small probability or a high probability. We found 273 links (3.1%) with Biggles expands the concept of the single particle tracker by sampling the posterior distribution of possible tracking solutions and their governing parameters. Therefore, with Biggles we enable the calculation of errors and other descriptive statistics for tracking solutions. The set of all partitions does not come with an canonical distance measure, which is needed for some statistics. There are several possibilities to introduce a distance measure such as: treating the tracking solutions as graphs and employing the GED, or treating tracking solutions as vectors of a high dimensional space where each pair of linkable observations contributes one dimension. We used the GED as part of the convergence assessment.how certain the solution is and how likely alternative solutions are. With Biggles we have now the means to do what we would do in any other measurement process: evaluate the error on our solution.The knowledge of the most likely solution remains of limited use as long as we do not know ps, implies a exponential distribution for the track length. However, tracks of length 0 or 1 are not allowed and all tracks are limited to be no longer than the number of imaged frames. The samples stem in fact from a truncated exponential distribution. Since each observation is either explained as clutter or as observed track the biases in the clutter rate, λc and observation probability, po, are opposing. However overall there is a very good agreement of the sampled parameters with those of the GTR, see Biggles does not need to input parameters that control the tracking process. On the contrary these parameters are a part of the solution. We show a example of parameter distributions in distribution is not known. We treated the GTR links as if they would be certain under the given model, which is not true, since a particle can move in an unlikely manner. However, it should remain the exception that the ground truth is unlikely under the model, since the model shall explain the motion of the particles. In fact, we found very good agreement of the sampled links with the GTR. As expected in the case of higher track density we found more uncertainty in the links. This is not a shortcoming of the algorithm, but its point. In high crowding situations the track assignment is less clear and a higher temporal and spatial resolution would be required to achieve more confidence in a specific tracking solution. With Biggles we quantify our confidence in a specific solution and produce representative samples of alternatives. For the data sets in Rec(pmin) and Pre(pmin) respectively, we do expect to see Rec(pmin) → 1 for pmin → 0 and Pre(pmin) → 1 for pmin → 1. That means, we expect to find any real link in at least in one sample and we expect not to find the same false link in all samples. For the low density in Rec(0) > 0.99 and Pre(1) > 0.99.A direct validation of the Biggles samples is not easy since the ground truth Even though the definition of a track does not include merging or splitting of tracks, splits and merges are represented in Biggles sampling, see Another approach to verify the results of Biggles uses derived quantities. We demonstrated this with the diffusion coefficient. Our results show that on average Biggles accurately reproduces the diffusion constant of the GTR. However for individual data sets the results may deviate from the GTR, significantly in terms of the sample standard deviation.We have demonstrated in There is another possibility to improve performance for large data sets. Our SMM data sets can contain about 500 000 observations. We are developing a chunked version of the algorithm that divides the data into overlapping spatial chunks, tracks the observations in each chunk separately and reconciles the results. This approach will also allow the usage of computing clusters or cloud computing resources.Qm > 0, then the GED between ω and ω′ is at most 6 links, if m is any of the move types merge/split (1 link difference), transfer (6 links), cross-over (4 links), or update (max. 4 links). If the move type m is any of birth/death or extend/reduce then both partitions differ in one track only, with a GED less then T links. All moves at most modify 2 tracks at a time.The sampling process still lacks efficiency. On one hand the track partition samples are correlated which reduces the effective sampling size. The correlation between the track samples lies in the nature of the Metropolis-Hastings proposals. The vast majority of links of the proposal will be identical with the links of the last sample. If Q(ω|ω′) ≫ 0 even if P ≪ P. If for example the update move is applied to a long track, then the update will be attempted at any time point with equal probability. However, often it is the case that there are only very few time points for which the move would produce an acceptable proposal, making the acceptance rate very low. In this regard the proposal mass function is wide in comparison with the target distribution. In the current implementation, Biggles therefore suffers from both a slow exploration speed and a low acceptance rate. Modifications to improve the proposal mass function both increase the complexity of the calculation of the proposal mass ratio and increase the complexity of the proposal creation itself due to the employment of smarter algorithms, extensive internal book keeping and so on.On the other hand, the acceptance rate of the sample recording of data set SMM–9761 is very low as we showed in N. It is therefore not possible to keep a large number of samples in memory. This affects the number of chains that can be kept and their size, but also the number of samples that can be recorded. Especially for multimodal distributions it is important that the chains are long enough to cover the relevant part of Ω. If the chains are too short the assessment of convergence may go wrong. The assessment can go wrong in two ways; the chains have reached the stationary distribution, but are in different parts of it because they are too short to cover the whole support. It is also possible that the chains have not yet reached the stationary distribution, but accidentally it appears as such. The choice of the starting partition is therefore of some importance. Our approach runs two chains with the minimal partition ω0 and a maximal partition ωmax as starting points.The size of a single partition sample is linear in p(l) > 0.99. The interesting subset Ω* ⊂ Ω is much smaller, and often focuses on small spatio-temporal regions. If such regions are disconnected, they could be sampled separately, which further reduces the size of Ω*. Still, the size of Ω* can be substantial. It is very difficult to say how many samples are required to cover it and it depends on the data set.The huge size of Ω seems to imply than any practicable sample size is far too small to explore Ω. However, experience shows that the vast majority of links are uncontroversial with We present in this paper a prototype of a novel approach to single particle tracking (SPT) that samples from the combined probability mass function/probability density function of the track partitions and its governing parameters. This enables not just the estimation of the most likely tracking solution but also provides us with a measure of uncertainty of this solution and likely alternative solutions. Thus Biggles normalises SPT with standard measurements that provide measured value and error estimate. Our approach also has the potential be used to estimate the error on derived quantities as we demonstrated on the diffusion rate. The algorithm can handle different condition without special adjustment, such as random walk, directed motion, change of direction and track branching. We demonstrated that Biggles can analyse data sets with about 10 000 observations. The implementation of Biggles is complex. Smarter algorithms, optimised convergence control and sample recording and professional software engineering will improve the performance of the algorithm. We also indicated other potential improvements. Biggles opens a new direction in SPT.S1 FigThe Q-Q plots of the parameter samples for the GTR and the parameter samples created by Biggles. Shown are a series of ten data sets with low track density(top) and a series of data sets withhigh track density (bottom).(PNG)Click here for additional data file.S2 FigA mixture between directed motion and random walks. Tracks have a chance to change the mode of motion. The grey dots mark the clutter observations.(PNG)Click here for additional data file.S3 FigA mixture between directed motion and random walks. Tracks have a chance to change the mode of motion. The grey dots mark the clutter observations.(PNG)Click here for additional data file.S4 Figd1 = 0.45pix/fr and d2 = 0.9pix/fr. Each track has one mode of mode of motion.A 50-50 mixture between random walks with two different diffusion coefficients, (PNG)Click here for additional data file.S5 FigRandom walks with regions of different densities. Each track has one mode of mode of motion.(PNG)Click here for additional data file.S6 FigShown are the link probabilities.(PNG)Click here for additional data file.S7 Fig(PNG)Click here for additional data file.S8 Figpixel/frame is equivalent to D ≈ 0.26μm2/s at a pixel size of 160nm and a frame rate of 20Hz.A step length of 1(PNG)Click here for additional data file.S1 AppendixDetailed information about the algorithm, discussions of properties of the space of valid track partitions Ω and proof that the partition sampler is ergodic.(PDF)Click here for additional data file.


In this report, we want to emphasize how a laparoscopic bariatric surgical procedure, in experienced hands, has shown to be a valid alternative for the hemorrhage control and the removal of a gastrointestinal tumor in a life‐threatening situation. They arise from the Interstitial cells of Cajal (ICCs) that are implicated in the regulation of gut peristalsis, with a pacemaker role. GISTs are more often located in the stomach (56%) although they can arise in any portion of the digestive tract.Although the treatment of gastrointestinal stromal tumors with tyrosine kinase inhibitors is one of the best examples of the advances of molecular targeted therapy over the last two decades, surgical resection with clear margins remains the mainstay of cure.Herein, we report the cases of two patients from two different Italian hospitals who have undergone a successful laparoscopic sleeve gastrectomy in emergency following the acute bleeding of a gastric GIST.Laparoscopic sleeve gastrectomy (LSG) is the most commonly carried out bariatric surgical procedure worldwide; by removing approximately 75% of the stomach from the greater curvature side, it acts as a restrictive procedure also capable of changes in the secretion of gastrointestinal hormones involved in the weight loss.In this report, we present two cases in which a gastric GIST is not an incidental finding during a laparoscopic bariatric operation but a laparoscopic bariatric surgical procedure, in experienced hands, has shown to be a valid alternative for the hemorrhage control and the removal of a gastrointestinal tumor in a life‐threatening situation.22). Electrocardiogram (ECG) and serum troponin levels excluded an ischemic cardiac event, but the results for complete blood cell counts and hemocoagulation revealed a hemoglobin value of 9.6 g/dL. Two days before, the patient had undergone an esophagogastroduodenoscopy  was used to aspirate and lavage the stomach as well as confirming the localization of the bleeding lesion in the greater curvature at the gastric fundus. Subsequently, a laparoscopic sleeve gastrectomy (LSG) was carried out. Five trocars have been placed in the upper abdominal quadrants: one 12‐mm trocar above the umbilicus in the midline, three 12‐mm trocars in right subcostal, subxiphoid, and left subcostal, and one 5‐mm trocar in the left anterior axillary line. The gastric resection was performed using a linear stapler (Echelon Flex™ 60 Endopath®) applied alongside a 38‐Fr bougie. The next step has been a methylene blue dye test in order to check the sealing of the staple line that was additionally reinforced by nebulization with cyanoacrylate sealant (Glubran 2®) used also to create an adhesion with the greater omentum as a chemical omentoplasty.E coli urinary tract infection which was successfully treated with antibiotics. The diagnosis of gastric GIST was confirmed on the surgical specimen that showed a polypoid mass with hemorrhagic foci 40 × 35 mm in size; surgical resection margins were negative (R0). The mitotic rate was <1/50 HP; CD34, CD 117/C‐kit, and smooth muscle actin were positive; the Ki67‐MIB1 immunostaining indicated a low proliferative rate (count rate 4%). The tumor was staged as GIST of gastric origin in the very low‐risk category so that a systemic adjuvant chemotherapy was not needed2).The patient's postoperative course was uneventful, except for a left subcostal wound infection which was opened and drained at the bedside and for a 32 and a past medical history of hypertension, hyperthyroidism, and atrial fibrillation (AF) under treatment with direct oral anticoagulants (DOACs). The patient also had a history of previous surgery represented by a laparotomic left hemicolectomy for a benignant colonic stenosis. She was initially managed with intubation and received mechanical ventilation, and once hemodynamic stability was achieved, her conditions worsened due to unexpected upper gastrointestinal bleeding (UGIB). She was given a blood transfusion of 4 units of red blood cells, but her hemoglobin value continued to stay under 9.0 g/dL. The following OGD showed an ulcerated submucosal lesion of 3 cm at the greater curvature of the gastric fundus  in emergency state for the acute onset of a respiratory failure accompanied by high‐frequency atrial fibrillation (AF). She had a body mass index (BMI) of 29.52 kg/mIn the management of this acute situation in order to avoid any further delay of surgical intervention, the patient was prepared for an emergency laparoscopy. Four trocars have been placed in the upper abdominal quadrants: one 12‐mm trocar above the umbilicus in the midline, two 12‐mm trocars in right and left subcostal, and one 5‐mm trocar in the right anterior axillary line. The exploration of the abdomen cavity showed the adhesions attributable to the previous lower abdominal surgery as well as the cirrhotic changes of the parenchymal status of the liver. Once the stomach has been exposed, a nodule appeared on its surface near the greater curvature at the fundus. Subsequently, a laparoscopic sleeve gastrectomy (LSG) was carried out. The gastric resection was performed using a linear stapler (Echelon Flex™ 60 Endopath®) applied alongside a 38‐Fr bougie. The gastric specimen  is the only potentially curative option for GISTs. In the case of gastric location, which is the most common, based on the assumption that GISTs do not have the typical lymphotropism, infiltrating behavior and propensity to metastatize of adenocarcinomas, a less extensive surgery like in the case of wedge resections, is suitable to treat the disease and spare the stomach.In the Case 1, the patient was admitted to the emergency department with hematemesis and melena 48 hours following the endoscopic biopsy of a suspicious mass of the greater curvature at the gastric fundus, 30 mm in size. Conventional endoscopic forceps biopsy of GISTs is difficult and does not obtain enough tissue for a definitive diagnosis; EUS‐FNA (Endoscopic ultrasound‐guided‐fine needle aspiration biopsy) is the most established tissue sampling method.In the Case 1, the exploration of the abdomen cavity showed no evidence of gastric exophytic lesions; an intraoperative endoscopy was useful in order to locate the mass and guide the chose of the proper resection. In the Case 2, the location of the tumor was well defined by the presence of a nodular lesion located on the greater curvature at the anterior wall of the gastric fundus.In both cases, in light of the favorable location of the mass at the greater curvature, in the absence of distant disease, laparoscopic sleeve gastrectomy (LSG) has been chosen in order to treat the bleeding, remove the potential GIST, and spare the stomach calibrating the resection by the use of a 38‐Fr bougie placed against the lesser curvature. In addition, the fact that the procedure was carried out by experienced bariatric surgeons allowed to be more confident in facing emergency surgery with the use of a standardized laparoscopic technique, which reduced also operative time. Although LSG is considered an easier technique if compared with other bariatric procedure since no anastomosis is required, it includes some key technical points like the dissection of the stomach from the spleen, necessitating adequate laparoscopic expertise. Moreover in our cases, the presence of a blood‐filled stomach due to the hemorrhage may have had implications on the sealing of the staple line. In the Case 1, aerosolized cyanoacrylate sealant Glubran 2® has been used as a reinforcement of the staple line to prevent leak and bleeding.2). Wang Y et al reported their experience of laparoscopic sleeve gastrectomy in the treatment of GISTs in morbid obese patients. They found the LSG to be the best choice for obese patients combined with GISTs. It can remove tumors and excess stomach away at the same time.The patients’ postoperative recovery was uneventful for major complications. Pathology reports showed in both cases complete surgical resection (R0); the tumors were diagnosed as gastric GISTs in the very low‐risk/low‐risk category, and adjuvant chemotherapy was not necessary.5Gastrointestinal stromal tumors (GISTs) are the most common mesenchymal tumors of the gastrointestinal tract. Surgical resection with free margins of tumor disease (R0) is their only curative option. In the case of potentially resectable gastric tumors, laparoscopic wedge resections are considered the standard therapy. This report describes the application in two cases of the laparoscopic sleeve gastrectomy for the emergency treatment of a bleeding gastric GIST. It can be concluded that a laparoscopic bariatric surgical procedure, in experienced hands, has shown to be a valid alternative for the hemorrhage control and the removal of a gastrointestinal tumor in a life‐threatening situation.The importance of this surgical speciality has too often been underestimated, while the clinical, social, and economic benefits cannot be ignored.The authors declare that they have no competing interests.Consent for publication: Written informed consent was obtained from the patients for publication of this case report and any accompanying images. A copy of the written consent is available for review by the Editor‐in‐Chief of this journal.NC: researched the data, wrote the manuscript, and contributed to the discussion. AP: wrote the manuscript, contributed to the discussion, and reviewed the manuscript. CN: performed one of the bariatric interventions. AB: contributed to the discussion and reviewed the manuscript. GM: wrote the manuscript, contributed to the discussion, and reviewed and edited the manuscript. All authors read and approved the final manuscript.


This data is generated from the analysis of similarities and differences in gene expression levels and pathways among genes  in Vegf family using whole genome expression data generated from normal retina of eighty strains of mice. The results have been published in  Specifications tableValue of the Data•This data can be useful in the construction of new pathways among Vegf genes.•This data could be used as a reference for the new anti-Vegf drug development.•The methodology in this data can be used for comparison of pathways of other genes.1http://www.genenetwork.org/webqtl/main.py) R values, which is equal to ∑R, for all the closely related genes to a Vegf family gene. Re is the average of the all closely related genes to a probe of Vegf family gene. Rn values are the summary of absolute values for all R values of top correlated genes. Ra is the average of Rn This data is generated from the analysis of similarities and differences in regulation of gene expression levels, most correlated genes to their expression levels, and overlapped genes among the top 500 genes that are most correlated to each of genes  in Vegf family. Data is obtained from the whole genome expression data generated from normal retina of eighty strains of mice, including 75 BXD RI strains, the parental strains (C57BL/6J and DBA/2J), the reciprocal crosses, and the BALB/cByJ mice  or expression quantitative trait loci (eQTL) that regulate its expression level was mapped with the GeneNetwork tool. Interval mapping with 1000 permutation tests was conducted to locate the eQTL. A 2000 Bootstrap test was conducted to estimate the suggestive and significant linkage scores. The genomic region of each eQTL was compared to that of other probes 2.1.1In the GeneNetwork platform, firstly identify the data of retina and data sets of Normal HEI Retina from the mouse species and then by typing the gene names in the “Get Any” column and click the “Search”, the Vegf genes were obtained. After that, click the names of each gene to get into a new link page of the gene clicked. In the new link page of the gene of interest, click the “calculation correlation”, and choose either 50 or 500 and then “pearson” as the analytic method. By clicking the “Compute” command, the top related genes were obtained 2.1.2After the top 50 genes which were closely related to one of the Vegf genes were “selected” and collected by clicking the “Add” command, and the other genes from Vegf family were also obtained and “added” to the collection list, all above genes would appear in the page of “BXD Trait collection”. The correlations between the top 50 genes from one Vegf gene and other genes then were obtained by “selecting” all of them and clicking the “Metrix” command .2.1.3After the top 500 genes for each of the gene in the Vegf family were obtained, uploading them into the Excel work sheet and then comparing the names of each gene in this top 500 genes which were most closely related to one Vegf gene with the 500 genes in another different Vegf gene. The gene symbols that matched exactly with each other would be marked as same between these two 500 sets. These genes have been linked together in the figure of the gene list to show their identity.2.22.2.1The eQTL of each probe of gene in the Vegf family was mapped and examined. Overall, there was no eQTL with a score that reaches to the significant level. A total of 10 eQTL exactly at or closed to a suggestive level were identified  in which