A series of experiments involving the particle image velocimetry technique are carried out to analyse the quantitative effectiveness of the synthesized vortical structures towards actual flow separation control. The streamwise vortices are synthesized from the synthetic jet actuator and introduced into the attached and separating boundary layer developed on the flat plate surface. Two types of actuators with different geometrical set-ups are used to analyse the evolution of vortical structures in the near wall region and their impact towards achieving separation delay in the boundary layer. First, a single circular jet is synthesized by varying actuator operating parameters and issued into the boundary layer to evaluate the dynamics of the interaction between the vortical structures and the near wall low momentum fluid in the separated region. Second, an array of jets has been issued into the artificially separated region to assess the effectiveness of various vortical structures towards achieving the reattachment of the separated flow in the streamwise direction. On an aircraft wing, the flow separation occurs when the boundary-layer travels far enough against an adverse pressure gradient. The velocity of the particles nearest to the surface falls almost to zero. The boundary-layer flow becomes detached from the surface and instead takes the forms of eddies and vortices and results in enlarged drag, particularly pressure drag. This paper explains the novelty of the synthetic jet actuator (SJA) towards achieving the reattachment of boundary-layer separation and, hence, flow separation control on aircraft wings.By employing the SJA, the jet is synthesized from the ambient fluid by a forced periodic excitation of the diaphragm to produce a train of consecutive streamwise vortices that interact with the boundary layer to exchange momentum with the relatively less energetic near wall fluid. The vortical structures are produced over a broader range of length and timescale, and their exclusive attributes make them attractive fluidic actuators for a number of flow control applications. Smith et al.  and Mall5 to 7.25 × 105. For inactive actuators, the aerofoil stalled for α > 5°, and when the actuators were active, fully attached flow was achieved for up to α > 17.5°. As a result of flow reattachment, or delay of separation, a substantial 100 % increase in lift was achieved and up to 45 % decrease in pressure drag was observed. For α > 17.5°, the lift was increased, however, the enhancement in lift was also accompanied by an increase in drag. Tensi et al.  normal to the plate surface, a laser light sheet is produced through the glass-bottomed floor of the test section, whilst positioning the camera, such that its optical axis is facing the side wall of the flume and the laser sheet. The suitable laser light sheet with desired thickness and width is formed using a combination of cylindrical and spherical lens and was directed to the required area on the test plate using a 50 mm-thick laser mirror mounted at 45° on a support. For safety purpose, the ends of the laser head and sides of the glass flume were enclosed and fully covered using black paper to avoid any unwanted laser leakage.Along the streamwise plane  is the excitation frequency and can be non-dimensionalised in Strouhal number asAccording to the slug model Glezer , the strThe Reynolds number is related with the stroke length and can be expressed as follows:For incompressible isothermal flow, the boundary-layer thickness is non-dimensionalised by the orifice diameterL’ and ‘ReL’, the jet velocity-to-freestream velocity ratio (VR) is considered and is given byIn addition to the key parameters that is ‘The smallest frequency used in the experiments is 1 Hz which is at least two times greater than Tollmien–Schlichting wave, so the effect of SJA does not influence the stability of the boundary layer. However, the stability is confirmed by calculating the indifference Reynolds number to be ≈383 which is not exceeding the minimum value of 520.2 interrogation area.The velocity profiles are drawn at three different locations deemed critical for final measurements. With the no slip condition at the wall, a good match with Blasius profile is met to confirm the zero-pressure gradient nature of the boundary layer Fig. . The proThe eventual impact of the passing vortex in the boundary layer can be apprehended by the way of quantitatively evaluating the transient effect on the undisturbed boundary-layer profile. Hence, the transient variation of the centerline phase-averaged velocity profiles for tilted vortices has been undertaken. The velocity contours are shown in Fig. t/T = 0.25, where ‘t’ is the time from start of actuation cycle, the deficit is quite significant caused by the downstream branch of the vortex and the deficit region is far away from the wall, as the vortex has had travelled far away from the wall surface by virtue of larger stroke length. The abrupt decrement from y/δ = 0.5 to 0.78 is due to the upper side of the downstream branch having opposite sense of rotation relative to the local velocity. Similarly, the lower part of the downstream branch exhibits the same sense as the local velocity hence suggesting a far steeper velocity gradient from y/δ = 0.78 to 1.05. Such a gradient subsequently results in the velocity over shoot in the region outside the boundary layer.For four phase points evenly distributed over the actuation cycle, the profile is shown in Fig. t/T = 0.50, the upstream branch approaches the measurement area and it displays clockwise vorticity having similar sense in the upper part as the local velocity and the opposite sense in the lower part. From y/δ = 0.4 to 0.65, the abrupt velocity increment is due to the upper part of the upstream branch. However, the lower part of the upstream branch decelerates the local velocity from y/δ = 0.65 to 0.85. Further deep towards the outermost part of the boundary layer, the velocity increment is due to the upwash of the fluid. At t/T = 1, the vortex of the previous cycle has passed the measurement plane, as the newer structure approaches. There appears a velocity increment near the wall region and then a decent decrement at about y/δ = 0.2 caused by the passing trailing secondary and tertiary vortices. Second, the velocity gradient near the wall region is larger in the case of tilted vortices than the stretched and hairpins, where the velocity gradient is generated by the upwash of the fluid resulted from the counter rotating legs. On the other hand in TVR’s, when the primary vortex has had moved away from the wall, the near wall velocity gradient could still be seen which is far significant and is generated by the trailing counter rotating tertiary vortices inducing a low momentum fluid downwash towards the wall. The tertiary vortices are, in fact, the trailing streamwise vortices with the opposite sense of rotation to secondary vortices thus result in downwash of the fluid. The appearance of secondary and tertiary vortices is more evident in the dye visualization technique , the largest velocity deficit appears closer to the central plane in the outer boundary-layer region which is the direct consequence of the low momentum fluid lift up due to the interaction of the vortex head and the counter rotating legs with the local fluid. A stretched vortex clearly produces a stronger inflexion and larger deficit than the hairpins. Away from the centerline, such as y/δ = 0.4 caused by the secondary trailing vortex and second at y/δ = 0.9 due to the primary vortex. There appears a gradual reduction in the maximum gradient achieved corresponding to the movement away from the region of maximum downwash induced by the trailing tertiary vortex pair. Similarly, there is a spanwise velocity increment that coincides with the gradual movement from the inboard side of the trailing secondary vortex pair responsible to induce a flow away from the wall. Moreover, towards the boundary-layer edge, a localized region of velocity deceleration is noticed that is produced by the interaction of the primary tilted vortex that tends to protrude out of the boundary layer.The tilted vortices influence the boundary layer up to the very edge and beyond, as the deficit area widens up quite significantly. In the near wall region, the gradient seems rather enhanced especially on the closer locations to the central plane. The maximum gradient occurs at the central plane that corresponds to the fluid downwash induced by the tertiary vortices that remain closer to the wall. The gradient is steepest and is shifted to the central plane, where the maximum momentum redistribution and fluid mixing occur eventually. The change in velocity profiles is significant around the central plane. First, for central plane, there is an abrupt variation at ReL, and L are kept similar to those mentioned earlier.For the second set of experiments, the design of flat plate is altered by attaching an inclined plate to the trailing edge. It is inclined upward at an angle of 5° to generate the artificial separation on the inclined surface, as shown in Fig. X/C (‘C’ is the streamwise inclined plate length), where the upcoming streamlines seem to deflect sideways. After the separation (known as the baseline), the streamlines are pointing downwards indicating the reverse flow. For controlled cases, the footprints induced by the synthetic jet are shown in Fig. f = 2. The separation line has been pushed back considerably even for the lowest ‘VR’ (case a). Note that at this ‘VR’ value, the hairpins just start to form as identified in parameter map , as the hairpins are becoming stronger and more capable to withstand the near wall shear. Therefore, they interact strongly with the local low momentum fluid in the near wall region. The high velocity streaks are becoming more prominent, as the separation line is pushed further back. Finally, the vortices are turned to tilted vortex rings, as the ‘VR’ is increased . Because of their tendency of protruding out of the boundary layer, the primary vortices do not affect the separation delay significantly. For tilted vortices case, the separation delay is caused by the trailing induced vortices that remain essentially within the boundary layer.St = 1.8, the footprints induced are shown in Fig. f = 4. At smaller VR (case a), the hairpins produce a pair of high-speed streaks similar to the stretched vortices. At slightly larger VR, there is only one single high-speed streak (case b) and the separation line is pushed back to about 45 % of C. As the velocity ratio increases, the flow pattern seems to deviate in lateral direction. For tilted vortices , the high-speed streaks are strengthening and are transformed to a single streak stretching out from each orifice. At high VR (case f), there appears a decrease in separation effect, as the tilted vortices are pushed out of the boundary layer and the downstream course of the trailing vortices is far too steep. It appears that further increase in ‘VR’ and ‘L’ does not help to achieve any additional streamwise delay rather the flow is becoming more swirling. Hence, it could be deduced that relatively higher ‘VR’ and ‘L’ would not be considered as the desirable parameters to operate the SJA for maximum flow separation control. The quantitative flow separation delay in the form of contours is given in Fig. f’ and dimensionless stroke length ‘L’ yields diagonal curves. The maximum delay is achieved at frequency 4 Hz and the stroke length is from 4 to 6. The novelty of SJA concerns with the fact that it consumes minimum input energy to yield the best control effect. Therefore, it must be operated at lowest possible stroke length to ensure minimum possible input energy.For A series of particle image velocimetry (PIV) experiments have been conducted to evaluate the dynamics of vortical structures to confine the synthetic jet actuator operating parameters, where the best separation delay effect is achieved. The stretched vortices appear to influence the boundary layer in the similar manner as the hairpins in that the occurrence of the maximum velocity gradient in the near wall region is consistent with the fluid downwash towards the wall produced by the interaction of the counter rotating vortex legs. The stretched vortices are more likely to produce a rather fuller profile with a larger velocity deficit area across the boundary-layer thickness. Subsequently, this would appear to be capable of higher momentum redistribution of fluid from the outer part of the boundary layer towards the wall.However, considering the quantitative evaluation, it appears that the tilted vortex rings seem to push the base line backwards to the maximum extent. It appears that secondary and tertiary vortices produced in the wake of the primary tilted vortex are the most effective structures towards flow separation delay. The tertiary vortices interact with the near wall fluid in the same way, as the primary hairpins in that they tend to force the fluid downwash towards the wall on the centre line. The effect seems more acute compared with the hairpins, as they interact with the fluid readily energized by the interaction of secondary vortices. Second, the fluid downwash on the single centre line is far more enhanced than the hairpins and stretch vortex rings (SVR) which tend to produce two streaks outboard of the vortex legs. In the artificially produced separation region, the single high-speed streaks seem to delay the separation to a maximum when compared with two streaks. The tilted vortices produced at low-velocity ratio are more effective than those produced at larger velocity ratio. At higher velocity ratio, the swirling flow around the separation line is achieved that inhibits the further delay of the baseline.


Typical survival studies follow individuals to an event and measure explanatory variables for that event, sometimes repeatedly over the course of follow up. The Cox regression model has been used widely in the analyses of time to diagnosis or death from disease. The associations between the survival outcome and time dependent measures may be biased unless they are modeled appropriately.In this paper we explore the Time Dependent Cox Regression Model (TDCM), which quantifies the effect of repeated measures of covariates in the analysis of time to event data. This model is commonly used in biomedical research but sometimes does not explicitly adjust for the times at which time dependent explanatory variables are measured. This approach can yield different estimates of association compared to a model that adjusts for these times. In order to address the question of how different these estimates are from a statistical perspective, we compare the TDCM to Pooled Logistic Regression (PLR) and Cross Sectional Pooling (CSP), considering models that adjust and do not adjust for time in PLR and CSP.In a series of simulations we found that time adjusted CSP provided identical results to the TDCM while the PLR showed larger parameter estimates compared to the time adjusted CSP and the TDCM in scenarios with high event rates. We also observed upwardly biased estimates in the unadjusted CSP and unadjusted PLR methods. The time adjusted PLR had a positive bias in the time dependent Age effect with reduced bias when the event rate is low. The PLR methods showed a negative bias in the Sex effect, a subject level covariate, when compared to the other methods. The Cox models yielded reliable estimates for the Sex effect in all scenarios considered.We conclude that survival analyses that explicitly account in the statistical model for the times at which time dependent covariates are measured provide more reliable estimates compared to unadjusted analyses. We present results from the Framingham Heart Study in which lipid measurements and myocardial infarction data events were collected over a period of 26 years.The online version of this article (doi:10.1186/s12874-016-0248-6) contains supplementary material, which is available to authorized users. A time dependent explanatory variable is one whose value for a subject may change over the period of time that the subject is observed , 2. The There is extensive literature and a wide range of statistical packages for modeling time dependent covariate data. Some previous work includes Fisher and Lin ; CupplesModels that can accommodate time-dependent covariates are commonly used in biomedical research but sometimes do not explicitly adjust for time in the model. Not adjusting for time can yield different estimates of association compared to a model that adjusts for time. In order to address the question of how different these estimates are, we compare three methods that model the association between a longitudinal process and a time-to-event outcome. We consider the TDCM in which the longitudinal measures are used as time dependent covariates in a Cox model . We compThe Framingham Heart Study (FHS) has been collecting data prospectively since 1948 to examine the relationship of potential risk factors to the development of cardiovascular disease . Since rOur main objectives are to: (i) compare the TDCM to Pooled Logistic Regression (time adjusted and unadjusted models) and Cross Sectional Pooling (time adjusted and unadjusted models) in simulation studies; and (ii) illustrate the methods and compare their results by applying them to FHS data. We begin by presenting an overview of these methods for modeling time dependent covariates in the context of longitudinal and survival data. We then evaluate the methods using simulation studies and conclude with a discussion of the results from the simulation and the Framingham Heart Study.In modeling longitudinal and survival data the main focus may be on the longitudinal component, the survival component, or both, depending on the objectives of a study. When the focus is on one aspect, the other component is then secondary; so its parameters may be viewed as nuisance parameters . Our goaTi*, δi, , i = 1, 2, …, n] observations where Ti is the time-to-event for the ith subject. The vector Yi(t) = t is a set of longitudinal measures, and mi ≤ p is the number of time intervals for the ith subject. In addition, each subject has possibly right censored failure Ti = min and the event indicator δi . The parameter δi indicates whether the observed failure time is a true failure time Ti*, or a censoring time Ci.In this section, we consider methods for modeling the association between longitudinal measures and time-to-event data in a survival model. We consider the underlying model to include longitudinal response data and time-to-event data for a sample of size n, consisting of [Y) at the beginning of each time interval and all intervals are of the same length . In this context, the regression coefficients represent the association between Y and an event that occurs during the subsequent interval. We require this study design in order to compare the PLR model, which does not explicitly consider time, with those approaches that do incorporate time into the model. For CSP and TDCM, time intervals of equal length are not needed as an assumption of the model. In all the models that we considered, the assumption is that the time dependent covariates remain constant between examination times.The study design that we consider in our paper has fixed time points where each person has observations at which covariates are measured. Such a study design is common for longitudinal studies. In particular, individuals are measured for a time-varying covariate (A time dependent explanatory variable is one that may change over the period of time that the subject is observed . The most can be written as:The hazard for the TDCM at time h0(t) represents the baseline hazard function, Xi is a vector of time invariant explanatory covariates with regression parameters. Yik(t) is a general covariate form in which mi = p is the number of longitudinal measures for each subject i. We define t1 < t2 < t3 < … < tD as a set of ordered observed event times with D unique failure times and Yi(ti) as the covariates associated with the individual whose failure time is ti for i = 1, …, D failure times. The parameter βk measures the association between the observed longitudinal measures and the hazard of failure time h(t). The risk set R(ti) at failure time ti is the set of all individuals who are still under study at a time just prior to ti. In most applications, βk = 0 for intervals other than the current one (ti). The partial likelihood based on the hazard function specified in (1) can be written as:Where i to fail from the risk set, given the risk set at failure time ti and given that one failure occurs. The inference is similar to the Cox model. The only difference is that the values of Yi(ti) now change for each risk set. The α and β estimates can be obtained by maximizing the likelihood in (2). In TDCM the covariates are measured repeatedly and an assumption of this model is that the hazard depends on the covariate through its current value.In the partial likelihood above, each term is the conditional probability of choosing individual The use of standard logistic regression techniques to estimate hazard rates was detailed by Efron . His appIn PLR, logistic regression is used to link predictors to the event outcome. The outcome is an event indicator, which records whether an event occurs in the interval or not and does not account for when the event occurs within the interval. A response occurring near the beginning of a follow-up period is treated the same in analysis as one occurring at the end of that period. This model relates the probability of an event occurring in an interval to a logistic function of the risk factors .3\documeβo is the intercept for the logistic model. The Yi(tk) represent the observed longitudinal measures for the interval; the parameter θk denotes the effect of time tk. The time point tk is an element of the vector representing when the longitudinal measures were recorded. Thus, this model adjusts for the interval in which the observations were made. In our application of this model, we assumed a linear trend on the time effects θk. One drawback of PLR is that the model does not utilize information for the point in time during the interval at which an event occurs or the exact time in an interval that an individual is lost to follow-up. Thus, the contribution of the risk factor to disease is dependent on the length of follow-up period [The parameter p period . While tp period . This prp period .We should also note that the PLR model provides estimates of conditional odds ratios for having the event in an interval rather than of the hazard ratio. Efron  discusseThe CSP uses Cox regression within interval to utilize information on the length of time to event within each interval as well as whether or not the event occurs. The model relates the instantaneous risk of an event to the longitudinal measures though a hazard function.hj0(t) represents the baseline hazard function for the jth interval, γ is the association parameter; t is the time-to-event in the interval. In the time adjusted CSP a stratified Cox model is implemented with time intervals (j) when longitudinal measurements were taken. In the unadjusted model, the hazard is assumed to be the same across all time intervals and analysis is performed without stratification. In stratified Cox with time intervals, the regression coefficients are assumed to be the same in each interval; however, the baseline hazard function may vary.Where We conducted a series of simulations to evaluate the performance of the CSP, TDCM and PLR methods for modeling longitudinal and survival data. We structured the simulated data to resemble observed data from the Framingham Heart Study as the covariates were measured at specific time intervals (each ~4 years) and held fixed until the next measurement time point. For the simulations we used 5 year intervals. In Table We simulated independent multivariate datasets consisting of longitudinal measures and time-to-event outcomes. The following algorithm was implemented to generate the longitudinal data using steps 1–5 and the survival data using steps 6 and 7:normal  and Sex ~ Bernoulli (0.54)Baseline Age ~ Generate baseline covariates similar to FHS.φβ(tij)) for each subject  and for each time point  using the linear model: φβ(tij) = Ui1 + Ui2 * tij + τ * AgeG) of the random effects, covariance matrix and residual errors were obtained by fitting a random effects model to the FHS data.Parameter estimates for the mean and variance-covariance matrix  from a bivariate normal distribution with mean and variance-covariance (G) obtained (2a). The random effects  represent the intercept and slope.Generate random effects  from a multivariate normal distribution with mean φβ(tij) and variance (V): Generate the observed longitudinal measures  are measured at regular 5 year intervals. The models are designed to capture the covariate measurements at specific longitudinal time points similar to the Framingham Heart Study.4.Choose parameter estimate values for Age, Sex and the link parameter which measures the strength of the association between the longitudinal measures and the time-to-event.5.T) for each time period in which the longitudinal measures were taken, from the inverse of the cumulative hazard distribution. Survival times generated with the Cox proportional hazard model using the Exponential and Weibull distributions. When the shape is equal to 1, the Weibull distribution equals the exponential distribution. By varying the shape parameter and the scale parameter, the required event rates  can be attained for the survival data.Generate the time-to-event  = λ(t)exp{α1Age + α2Sex + γYij}.Survival times are generated for each interval to depend on the longitudinal measures at the beginning of the interval and a set of covariates (Age at each exam and Sex). The survival time for each participant was computed by considering the cumulative survival time across intervals until an event occurred. Subjects without an event at the last interval are censored after the 5-year period of the interval.Yij) were generated from a multivariate normal distribution with means and variances specified above in the simulation scheme. Survival time was generated for each interval using the value of age from the start of the interval. The survival time for each participant was computed by considering the cumulative survival time across intervals until an event occurred. Each replicated data set was simulated to contain 1000 subjects with up to 6 observation intervals. We fit the methods described in section 2 to analyze each of 1000 replicated data sets and used 10,000 replicates to evaluate Type I error. We assessed the performance of these methods using bias, accuracy and coverage. Bias was assessed as the deviation in the estimate from the true simulated parameter. Mean square error (MSE) provided a measure of overall accuracy by incorporating the bias and the variability. Coverage of the confidence interval was the proportion of times the obtained confidence interval contains the true specified value.The parameter estimates used in our simulations for the random effects, covariance matrix and residual errors were obtained by fitting a random effects model to the FHS Data. Baseline age at entry to the study was simulated from a normal distribution with mean 35 and standard deviation 5; sex was assigned according to a draw from a Bernoulli distribution with proportion female = 0.54; these parameters are similar to those of the FHS Data. The observed longitudinal measures  Unadjusted Cross-sectional pooling (CSP_UN); 2) Adjusted Cross-sectional pooling (CSP_AD); (3) Time dependent Cox regression models (TDCM); (4) Unadjusted Pooled logistic regression (PLR_UN); (5) Adjusted Pooled logistic regression (PLR_AD). In Table  AdjustedWe present results from the simulation studies for the methods described in section 2. Type I errors were computed for the longitudinal effect on survival, (γ = 0), using 10,000 replicates and a sample size of 1000 Table . In all α1 = 0.050) and Sex (α2 = − 0.500) parameters were constant in all the models. In Table We varied the event rate  and the association parameter . The Age (α1 = 0.050) and Sex (α2 = − 0.500). The standard errors were smaller in the unadjusted models compared to the time adjusted models. The results showed that the time adjusted PLR had a positive bias in the Age effect with reduced bias when the event rate is low. The PLR methods showed a negative bias in the Sex effect compared to the other methods. The Cox models yielded reliable estimates for the Sex effect in all scenarios considered. The PLR had higher estimates for the Sex effect compared to the other methods. When the event rate was 50 %, the Age effect was similar in both the time adjusted and the unadjusted models, but with extreme event rates (10 % or 90 %) there was significant bias in the unadjusted. These results suggest that the time adjusted Cox models provide more reliable estimates compared to the unadjusted Cox and logistic models. In the supplement we present results for the comparison of the longitudinal effect on survival and the Age effect on survival with a sample size of 100  data were collected over a period of 26 years. Since 1948 three generations of participants have been followed over the years: the Original cohort (recruited in 1948), their Offspring (recruited in 1971) and a Third Generation (recruited in 2002). Among the Offspring participants, triglycerides (TG) were measured at fairly similar time intervals of ~4 year each over a period of 26 years. The time to myocardial infarction was recorded for each participant, although some subjects were censored by the end of the study period in 2005. We log transformed the TG measures in our analysis to reduce skewness. A total of 2262 subjects with complete data were followed from 1979–2005 and data were collected at the start of each exam  and moderate association of the longitudinal measures to survival (γ = 0.500), as shown in Fig. 0 % and mIn this paper we explored time dependent Cox regression methods that link longitudinal and survival data in order to quantify the association between a longitudinal process and a survival outcome, and have shown that statistical performance may be improved in models that explicitly include time as a covariate. We considered models that adjust and do not adjust for time in the Pooled Logistic Regression and the Cross Sectional Pooling methods. We conducted a series of simulations to compare these methods in their ability to estimate the link parameter. The performance was assessed through bias, coverage probabilities and Type I error rates. We analyzed data from FHS in which triglyceride measurements and Myocardial Infarction (MI) data were collected over a period of 26 years (1979–2005). To our knowledge this is the first paper that compares time adjusted and unadjusted models for modeling time dependent covariate data.From the simulations we see that time adjusted, time dependent Cox regression methods performed best at estimating the association parameter compared to the unadjusted Cox and logistic models. Our results indicate that in some instances the PLR provides higher biased estimates and standard errors compared to the Cox models. The PLR and the time dependent Cox regression methods provide similar results when the event is rare, consistent with the results presented by Green and Symons . In the The FHS sample provided results that were consistent with the simulation results for a low event rate and moderate association. Thus, we did not find large differences in the estimates from the different approaches. Had the event rates been high and there were a strong association between the longitudinal measures and the survival time, we would have expected to see greater differences in the estimates from the unadjusted models, with the time-unadjusted PLR and CSP approaches having higher estimates.There is extensive literature on comparison of the logistic regression model and the proportional hazard model. Efron  discusseIn time dependent covariate models attention has to be placed on the type of covariates  being considered. Kalbfleisch & Prentice  distinguOne limitation to our study is that we did not consider measurement errors or missing data issues that may arise from longitudinal covariate data that are potentially missing at failure times. In many longitudinal studies participants may drop out early from the study which may lead to missing data in both the failure times as well as the time dependent covariates. Such issues can be addressed in a mixed effects model in which a random effect can be used to capture the individual specific longitudinal trajectories with missing data. Complete-case methods, which discard incomplete observations in survival regression models, may potentially lead to inefficient or biased estimates. In the presence of missing data, there are a number of likelihood and imputation methods for addressing missing data given the observed data. In our study we did not address these issues as our simulations and examples are based on no missing data at each time point. Models that consider measurement error may be more representative of the underlying process. In our study, using Framingham Heart Data, individuals were censored at time of death. A drawback to this approach is that death without prior myocardial infarction may be considered a competing event to our outcome. The main objective of our study was to present an overview of these methods for modeling time dependent covariates in the context of longitudinal and survival data. Exploring methods that consider death as competing risk or event-free composite endpoints are worthy of further research. A limitation to every simulation study is that the results are dependent on the scenarios examined. In this paper, we evaluated a range of models to provide broader insight, but our conclusions must be limited to the scenarios that we examined. In the simulation models the assumption of proportional hazards was considered in all scenarios. Further work is needed to better understand the circumstances when the PLR may differ from Cox models in non-proportional hazard models.In this study we compare three methods for quantifying the association between a longitudinal process and a survival outcome. We characterize the relation between the longitudinal measures and time-to-event in models that account for the time at which the longitudinal measures are recorded. In general, we recommend the use of a stratified Cox model with time intervals or a TDCM when the time-to-event is available, both of which account for time. When the time of the response is not available, a PLR approach may be applied adjusting for the Time interval at which the time dependent covariate measures were taken. If event rates are high and the association between longitudinal measures and survival are strong, the PLR approach without adjustment for time is not recommended. The Cox model provides greater use of the available data compared to the PLR by including time. Thus, when time is available, we recommend using the TDCM or equivalently the stratified CSP approaches with time intervals. Survival analyses that explicitly account for the times at which time dependent covariates are measured appear to provide more reliable estimates compared to unadjusted analyses.


Studies of the performance of individuals with dyslexia in perceptual tasks suggest that their implicit inference of sound statistics is impaired. Previously, using two-tone frequency discrimination, we found that the effect of previous trials' frequencies on the judgments of individuals with dyslexia decays faster than the effect on controls' judgments, and that the adaptation  of their ERP responses to tones is shorter . Here, w Dyslexia, a specific and significant impairment in the development of reading skills that is not accounted for by mental age, visual acuity problems, or inadequate schooling , affectsRaviv et al., 2012The neural mechanism that may underlie the implicit learning of experimental statistics is adaptation; that is, an automatic, implicit, and stimulus-specific decrease of the response to repeated stimuli. Importantly, the rate of decay of the behavioral effect of previous trials in serial discrimination is similar to the rate of decay of neural adaptation, as measured by magnetoencephalography (MEG) . InspireAs ERP responses cannot be used to localize the cortical source of this group difference, we now recruited the participants from the ERP study  to take  P2 e.g. . All corz = 0.5, p=0.57). In scans, good readers (controls) performed better than dyslexic participants , suggesting that they gained more from the short pre-scan practice  when all participants were considered. For each of these voxels, we calculated the dynamics of adaptation, among control participants and among participants with dyslexia, as follows. We estimated ay model : βTOA=a+To locate regions in which the fitted ical map .z = 2.6, p<0.01, effect size r = 0.42; Mann-Whitney U-tests). In the right primary auditory cortex, the z = 1.5, p=0.15, effect size r = 0.23; Mann-Whitney U-tests). In addition to the whole-brain, data-driven analysis, we conducted an ROI, hypothesis-driven analysis. Given our previous ERP findings that P2 (and to a lesser extent N1) of individuals with dyslexia shows shorter adaptation , we condTaken together, the whole-brain and ROI analyses revealed a significant group difference in the timescales of adaptation in the left superior temporal cortex, left primary auditory cortex, and the right insular cortex. BOLD activity in both auditory regions was previously shown to correlate with the magnitude of N1–P2 responses . The rigWe characterized the cortical distribution of the decay of BOLD adaptation for participants with dyslexia and control participants, thus extending our previous behavioral and ERP study . We founThe broad distribution of dyslexics' faster decay of adaptation is in line with recent observations of a domain general abnormally small adaptation in dyslexia . The resWe should note that the timescale of impaired retention in dyslexia is slower than that of sensory memory (iconic or echoic memory is <<1 s). Still, it is expected to affect the perception of individuals with dyslexia owing to their reduced cross-trial retention. It is therefore expected to impede their performance in a broad range of perceptual tasks, such as entrainment to rapid stimuli e.g., , but onlIn summary, the data collected in this study point to the specific neural structures that underlie the ‘anchoring deficit’ in dyslexia, namely a reduced use of stimulus statistics . These dIn the two-tone frequency discrimination task, subjects were asked to indicate which of two sequentially presented tones had a higher pitch. The tones were 50 ms long, presented at comfortable intensity, and were drawn from a uniform distribution between 800 Hz and 1250 Hz. The frequency difference within each pair was randomly drawn at between 1% and 20%  T1-weighted magnetization-prepared rapid acquisition gradient-echo (MPRAGE) images were acquired using a 3T Magnetom Skyra Siemens scanner and a 32-channel head coil at the ELSC Neuroimaging Unit (ENU). The cortical surface was reconstructed from the high-resolution anatomical images using standard procedures implemented by the BrainVoyager QX software package . The functional T2*-weighted MRI protocols were based on a multislice gradient echo-planar imaging and obtained under the following parameters: TR = 1 s, TE = 30 ms, flip angle = 90°, imaging matrix = 64 × 64, field-of-view=192 mm; 42 slices with 3 mm slice thickness and no gap were oriented in AC-PC plane, covering the whole brain, with functional voxels of 3 × 3 × 3 mm and multiband parallel imaging with an acceleration factor of 3 .Preprocessing of functional scans in BrainVoyager included 3D motion correction, slice scan time correction, and removal of low frequencies up to three cycles per scan . The anatomical and functional images were transformed to the Talairach coordinate system using trilinear interpolation. Each voxel’s time course was z-score normalized and smoothed using a 3D Gaussian filter . A standard (two gamma) hemodynamic response function  was convWhole-brain significance results were corrected for multiple comparison false-positive biases by a Monte-Carlo cluster correction , impleme In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Andrew King as the Senior Editor. The following individual involved in review of your submission has agreed to reveal his identity: John Stein (Reviewer #2).Thank you for submitting your article "Widespread shorter cortical adaptation in dyslexia" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:This study builds on the authors' previous work that demonstrated using behavioral measurements and EEG recordings that dyslexics show a faster decay of implicit memory than controls, which may account for their longer reading times. Here they used fMRI to investigate which cortical areas show these shorter neural adaptation effects. The authors calculate time constants of adaptation and find these to be significantly different in the dyslexic subjects in a region of left non-primary cortex and in the right anterior insula close to frontal operculum. The reviewers agreed that this study has a solid theoretical and empirical foundation in the previous work carried out by the authors and by other groups, and that the results are presented clearly and potentially add important new details to the framework for understanding dyslexia. The success of the authors in demonstrating differences in the time constant between the groups using the sluggish BOLD response is notable. Nevertheless, the reviewers had some difficulty reconciling these data with the previous neurophysiological data.Essential revisions:1) The study does not show widespread significant shorter cortical adaptation as suggested in the title. The regions in which significant group differences are small and include high-level multimodal cortex that is not predicted by the previous work. The N1 and P2 responses are generally regarded as arising from non-primary auditory cortex in the posterior superior plane and the previous neurophysiological data fitted with the idea that there might be a less stable representation of sensory information over time in dyslexia promoted by this group, which is a compelling idea. A specific test of this idea would require a comparison of the time constants in the generator of the N1, conventionally regarded as in planum temporale (there are probably two generators in PT as suggested by the work of Lutkenhoner). The reviewers were unanimous that a region of interest analysis is needed, though this might be focused on this region for which there is a strong prior based on the previous work.2) Examination of the areas in which there is a decrease in tau without correction for multiple comparisons shows a widespread swathe of differences that I find difficult to reconcile with the hypothesised deficit in the sensory trace. For example, there is shorter tau in primary somatosensory cortex and motor cortex. Do the authors think this is consistent with the anchoring deficit model?3) The authors suggest that poorer behavioral performance by the dyslexia group in the scanner could be related to their impairment in learning the task after training compared to the control group. An alternative possibility that needs to be discussed is that these results are due to the added acoustic noise of scanning, since continuous fMRI sampling as opposed to sparse sampling was employed. It is well known that individuals with dyslexia tend to have trouble with noise exclusion, and a tone-discrimination task with relatively sensitive pitch differences will be disproportionately difficulty for dyslexic individuals in the presence of noise. There is a paper by Chait et al., 2007 to that effect (tones in noise) specifically, if a citation is needed, as well as the larger noise-exclusion literature .4) Some attempt should be made to explain why the decay is faster in dyslexics by fitting the results into what is already known about dyslexics' relative insensitivity to amplitude and frequency modulations. For example, lower frequency sensitivity may impair auditory entrainment to a tone; could this underlie the difference in adaptation time constant?5) All the reviewers were struck by the capacity to extract adaptation and adaptation-recovery time course information from fMRI data, but it was agreed that a clearer explanation is warranted of how this can be studied using a method that has a time lag of several seconds.6 The characteristics of the dyslexics should be given in brief for those who haven't read the previous paper. More details are also needed regarding the Monte Carlo simulations for cluster-level multiple comparison corrections to ensure that others could replicate this approach.7) The discussion of the time course of adaptation with regards to the Perrachione et al.,2016 at the beginning of the Discussion section is confusing. In that paper, stimuli were presented for 8 repetitions in blocks of approximately 10 seconds, but each adapting or non-adapting stimulus was presented for 700 ms and at a rate of one per 1200 ms - so when the authors say "adaptation across a window of ~10 seconds was smaller than controls because it was largely recovered" it is unclear how they reconcile this with the stimulation procedure of the Perrachione study.8) It should also be pointed out that Perrachione et al., 2016 reported a group x time x condition interaction in the adaptation response in their study (see Supplementary table S4) for all conditions, which they interpreted as evidence for increasing adaptation in the control group w/ repeated presentation of the same stimulus, whereas such increasing adaptation was attenuated or absent in the dyslexia group. The correspondence between this result and the present observations seems meaningful and is worth commenting on. Essential revisions:1) The study does not show widespread significant shorter cortical adaptation as suggested in the title. The regions in which significant group differences are small and include high-level multimodal cortex that is not predicted by the previous work. The N1 and P2 responses are generally regarded as arising from non-primary auditory cortex in the posterior superior plane and the previous neurophysiological data fitted with the idea that there might be a less stable representation of sensory information over time in dyslexia promoted by this group, which is a compelling idea. A specific test of this idea would require a comparison of the time constants in the generator of the N1, conventionally regarded as in planum temporale (there are probably two generators in PT as suggested by the work of Luktenhoner). The reviewers were unanimous that a region of interest analysis is needed, though this might be focused on this region for which there is a strong prior based on the previous work.Thank you for this comment.1) We changed the title of the paper to "Shorter cortical adaptation in dyslexia is broadly distributed in the superior temporal lobe and includes the primary auditory cortex".2) The description of our ROI analysis now makes this point explicit. We now clarify that our ROI analysis was guided by the literature that mapped the cortical sources of P2 and N1 . The estimated source is somewhat broad, and includes all auditory areas, primary and secondary (PT and STG). We originally conducted an ROI mask for the primary regions . We now added secondary auditory (PT and Planum Polaris) regions. Only one left primary sub-region showed significant group effect. Our whole brain STG observation is also broadly in line with Mayhew et al., , yet specific coordinates are not provided in their paper.2) Examination of the areas in which there is a decrease in tau without correction for multiple comparisons shows a widespread swathe of differences that I find difficult to reconcile with the hypothesised deficit in the sensory trace. For example, there is shorter tau in primary somatosensory cortex and motor cortex. Do the authors think this is consistent with the anchoring deficit model?Yes. We added a short paragraph to the Discussion section to clarify this point. Behavioral observations  and imaging data  are consistent with a multimodal anchoring deficit that has specific temporal characteristics. This faster decay is "post sensory" (i.e. duration of echoic and iconic memories <1 second) and yet it affects perception. The study shows that poor cross trial retention is manifested in poor retention in primary and higher-level cortical areas.3) The authors suggest that poorer behavioral performance by the dyslexia group in the scanner could be related to their impairment in learning the task after training compared to the control group. An alternative possibility that needs to be discussed is that these results are due to the added acoustic noise of scanning, since continuous fMRI sampling as opposed to sparse sampling was employed. It is well known that individuals with dyslexia tend to have trouble with noise exclusion, and a tone-discrimination task with relatively sensitive pitch differences will be disproportionately difficulty for dyslexic individuals in the presence of noise. There is a paper by Chaitet al., 2007 to that effect (tones in noise) specifically, if a citation is needed, as well as the larger noise-exclusion literature .Thank you for pointing this out. We now clarify that the training period was conducted with noise simulating the noise in the scanner, which explains why performance of both groups was not reduced in the scanner compared to their training performance.4) Some attempt should be made to explain why the decay is faster in dyslexics by fitting the results into what is already known about dyslexics' relative insensitivity to amplitude and frequency modulations. For example, lower frequency sensitivity may impair auditory entrainment to a tone; could this underlie the difference in adaptation time constant?This is an important point. We predict that dyslexics' entrainment to unfamiliar stimuli will not be impaired. However, dyslexics' benefits from exposure are reduced compared with good reading controls. Since repetition lowers the measured thresholds, and since most protocols contain stimulus repetitions, we expect dyslexics to have poorer thresholds in a broad range of perceptual tasks . For entrainment, it was specifically shown that tracking familiar stimuli is better than tracking similar yet unfamiliar stimuli. We now explain this in the Discussion section.5) All the reviewers were struck by the capacity to extract adaptation and adaptation-recovery time course information from fMRI data, but it was agreed that a clearer explanation is warranted of how this can be studied using a method that has a time lag of several seconds.The time lag of the fMRI signal is not detrimental to the estimation of the τ values more than to the standard β estimation. In this study we used a block design; each block was defined by its Trial Onset Asynchrony (TOA), and for each TOA there were 3 blocks. Then, a standard modeling with 4 conditions was applied to extract β values for each TOA condition . Next, a model for estimating the decay time constant (τ) value was applied to each voxel: βTOA=a+bexp-TOA/τ, where τ denotes the timescale of adaptation, a is the asymptote level of the BOLD signal and b is the amplitude of adaptation. We added clarifications in the Materials and methods section regarding the nature and benefits of this block design.6 The characteristics of the dyslexics should be given in brief for those who haven't read the previous paper.Group characteristics were now added to the paper new .More details are also needed regarding the Monte Carlo simulations for cluster-level multiple comparison corrections to ensure that others could replicate this approach.The cluster correction was performed using the cluster-size thresholding plugin of the BrainVoyager QX software . The size of the cluster is determined by the significance level that we decide a-priori, as now better clarified in the text .7) The discussion of the time course of adaptation with regards to the Perrachione et al., 2016 at the beginning of the Discussion section is confusing. In that paper, stimuli were presented for 8 repetitions in blocks of approximately 10 seconds, but each adapting or non-adapting stimulus was presented for 700 ms and at a rate of one per 1200 ms - so when the authors say "adaptation across a window of ~10 seconds was smaller than controls because it was largely recovered" it is unclear how they reconcile this with the stimulation procedure of the Perrachione study.Note that we refer to duration of adaptation as the time adaptation lasts rather than the duration of its induction. The duration of adaptation is characterized by the magnitude of the response within the time window of the repetition Block. Perrachione et al., 2016 tracked responses over 10 second (Block duration), and hence tracked the accumulative impact of adaptation as a function of repetition within this time window. The magnitude and duration of (the induced) adaptation both increase with repetition, but to a lesser extent in dyslexics. We now explain this more clearly in the Discussion section.8) It should also be pointed out that Perrachione et al., 2016 reported a group x time x condition interaction in the adaptation response in their study (see Supplementary table S4) for all conditions, which they interpreted as evidence for increasing adaptation in the control group w/ repeated presentation of the same stimulus, whereas such increasing adaptation was attenuated or absent in the dyslexia group. The correspondence between this result and the present observations seems meaningful and is worth commenting on.Thank you for pointing this out. We added this to the Discussion section – this is exactly our prediction – that controls' adaptation is accumulated across repetitions to a larger extent than dyslexics', due to the faster decay of dyslexics' implicit memory trace within this time window . We now clarify it in the manuscript.


Lipoma in nasal region in a case of Pai syndrome is very rare. Very few cases of Pai syndrome with columellar lipoma with extension to septum and tip have been reported till date.We report a very rare form of nasal lipoma in a case of Pai syndrome with extension to septum and tip in a 4 year old female child.Pai syndrome with columellar lipoma with septal and tip extension should always be kept in mind when evaluating a swelling in the region of nasal tip, collumella and septum with notch in upper lip and corpus callosal lipoma. Lipoma is the most common mesenchymal origin tumor. They are commonly found in trunk, neck, upper and lower extremities. Head and neck region makeupto 13% of lipomas , nasoalaParents of a 4 year old female child presented her with deformity of the nose and difficulty in breathing from right side of the nose for 1 year. She developed the deformity as a small swelling at the tip of the nose of about 0.5 cm which increased progressively to the size of about 1 cm in 1 year. There was no history of trauma, fever, sudden increase in size or pain associated with the swelling. There was no association of similar swelling in any family member. Child was immunised and had achieved milestones appropriate for her age. Parents of the child wanted removal of the swelling as it was a cause of social embarrassment for the child and she had difficulty in breathing from right nostril. The child had an identical twin who was operated for intususseption at 6 months of age.On examination, there was evidence of a diffuse 1.2x1x1.5 cm swelling at the tip of nose in maximum horizontal, vertical and anteroposterior dimensions. The skin over the swelling was found to be normal and free from the swelling. It was soft in consistency. Swelling extended to the nasal columella. Right ala was found to be slightly flared. It was non tender. The septum appeared normal. There was midline cleft of the upper lip (Fig. Nose was opened with stair step incision in the collumella for open rhinoplasty. This incision was chosen over sublabial or septal incision in view of better operative view in the case of former incision. Fatty tissue was found over the left lower lateral cartilage. Right lower lateral cartilage was found to be deficient. Lipoma extended till the middle of collumella on the right of middle crus and right part of the caudal septum. It was excised in toto and specimen was sent for histopathological examination.Postoperative period was uneventful and patient was discharged on the third postoperative day. Histopathology was suggestive of lipoma Fig. . Early fth to 6th decade of life [Lipoma are found mostly in 5 of life . It is tMany liopomas of the nasal and paranasal sinuses have been reported. Lipoma have been reported in oral cavity, hypopharynx, parotid, Retropharyngeal area and larynx . DiagnosMidline cleft of lip along with nasal polyps and corpus callosal lipoma has been described in Pai syndrome . The synPrenatal diagnosis can be done with the help of sonography and MRI . AgenesiNasal lipoma in pediatric age group in association with Pai syndrome in a twin is very rare. With proper knowledge of differentials and appropriate examination supported by cytology and imaging studies, diagnosis can be made. Surgical approach depends upon the position of the lipoma. Open rhinoplasty was the answer in our case.


Our interaction with objects is facilitated by the availability of visual feedback. Here, we investigate how and when visual feedback affects the way we grasp an object. Based on the main views on grasping (reach-and-grasp and double-pointing views), we designed four experiments to test: (1) whether the availability of visual feedback influences the digits independently, and (2) whether the absence of visual feedback affects the initial part of the movement. Our results show that occluding (part of) the hand’s movement path influences the movement trajectory from the beginning. Thus, people consider the available feedback when planning their movements. The influence of the visual feedback depends on which digit is occluded, but its effect is not restricted to the occluded digit. Our findings indicate that the control mechanisms are more complex than those suggested by current views on grasping. Grasping an object is an effortless action that belongs to our everyday routine. Its apparent ease is at odds with the complexity of the underlying transformations. Numerous visual cues are used to estimate the object’s shape and egocentric position, to establish where on its surface to place one’s digits. This information is used to plan the action, which is then monitored online through visual feedback about the hand and finally through haptic feedback when touching the object , index finger occluded, thumb occluded and both digits occluded. Since the design of each experiment depended on the results of the preceding experiment(s), we here describe the aspects of the methods that were common to all experiments, and we describe the aspects that differed between the experiments when we introduce each experiment before presenting its results.In total, 40 participants volunteered to take part in the study. Some of them participated in more than one experiment and four participants took part in all four experiments. There were 20 participants in total per experiment. All signed an informed consent form prior to taking part in the experiment. Participants were right-handed, based on self-report of hand preference, and had normal or corrected to normal vision. The study was part of a research program that was approved by the ethical committee of the Faculty of Human Movement Science of the VU University, Amsterdam.Participants were seated with their head stabilized by a chin rest. In front of them was a table with small indentations to make it easy to place objects at specific positions. Above the table was a large (70 × 70 cm) horizontal surface that rested on four, 24.5 cm high columns that were far enough apart for the participants to be able to move their arm freely below the surface. A monitor (59.5 × 33.3 cm) that had been dismantled to remove the background and lighting, so that one could see through it when it was set to ‘white’, was embedded in this surface. A computer controlled the transparency of regions of this screen, and thereby the different feedback conditions. Bright lights below the surface, illuminating the area between the table and the semi-transparent surface, compensated for the fact that even when the screen was set to white it only let through a small part of the light. The use of partly transparent images on a screen allowed us to let our participants view the actual hand grasping a real target object while occluding specific parts of the information, rather than having to rely on some form of virtual reality.The starting position of the hand was with the index finger and thumb contacting each other at the top of a 6-cm high cylinder. This cylinder was 15 cm to the right of the center of the participant’s body, 40 cm lower than the participant’s eyes and 30 cm from the participant’s chest. The task was to move from this position, along the fronto-parallel plane, to grasp a sphere (25–60 mm diameter) that was positioned some distance (30–50 cm) to the left of the starting position. The size of the sphere and the distance to the sphere differed between the four experiments. We chose relatively large distances so that the movements would take long enough to make use of visual feedback when possible. The movements of the thumb and index finger of the participants’ right hands were recorded at 250 Hz with an Optotrak 3020 motion tracking system .A session started with a calibration procedure. First, we determined the position of the thumb and index finger pads with respect to three infrared-emitting diodes attached to small triangular surfaces that were fixed to the nail of each finger. This was done by measuring the positions of those diodes in combination with an unattached diode held in the finger pad . This was the signal for the participant to move the hand towards the sphere and lift it. After 3 s, the screen became opaque again indicating the end of the trial. One second later the screen turned transparent again, so that participants could find their way back to the starting position. When the digits were within 2 cm of the starting position, the screen turned opaque and a new trial could start.We investigate how the hand deviated from the path taken with full visual feedback (none condition), meaning that the screen turned fully transparent. We first considered the transport and grip components of the movement and then focused on the deviation of the single digits’ trajectories. In the latter case, we focused on the differences between the trajectories of each digit in conditions with and without occlusion. The dependent measures analyzed were: (1) differences between the transport trajectory in the none condition and the other three conditions; (2) differences between the changes in grip aperture throughout the trajectory in the none condition and the other three conditions; (3) differences between the single digits’ trajectories in the none condition and the other three conditions; (4) the maximum grip aperture; and (5) the movement duration.To analyze how the action unfolded throughout the movement, the trajectories of the transport and each digit were spatially normalized using the total length of the movement. The trajectories were resampled to 100 points, evenly spaced along the three-dimensional trajectory from movement onset to movement end, using cubic spline interpolation. As a measure for the transport of the hand, we used the 3D trajectory of the midpoint between the tips of the digits, rather than that of the wrist  and the movement duration. MGA was defined as the maximum Euclidian distance between the fingertips in individual trials. Finally, movement duration was calculated as the time from movement onset to the moment participants started lifting the object (movement offset). Movement onset was determined as the moment of the last minimum thumb velocity value just prior to the first continuously increasing value of thumb velocity. Movement offset was determined on the basis of the Multiple Sources of Information method  located at two possible distances from the starting point (40 and 50 cm). Although the formal analysis was carried out on the 40 cm distance only, we confirmed that behavior at the 50-cm distance was not evidently different. Black surfaces were displayed on the screen at positions at which they occlude the digits’ movements from the starting position, while not occluding the object and its contact points Fig. . TherefoOccluding most of the hand’s movement path, leaving the object fully visible, affects the trajectory of the movement very modestly Fig. a. The haOccluding one or both digits did not have a systematic effect on the trajectory in the early part of the movement Fig. a. A possF = 5.81; p = 0.0015]. As shown in Fig. F = 11.71; p < 0.0001]. The movement was slowest when both digits were occluded . Although the formal analysis was carried out on the 40-cm distance only, we confirmed that behavior at the 30-cm distance was not evidently different. In this experiment, the occlusion was extended leftward to also cover the digits’ contact points on the sphere. The left edge of the occluding area was chosen such that when both digits were occluded, both contact points were occluded, but a small part of the leftmost edge of the sphere remained visible so that participants were always aware of the position of the sphere. As in experiment 1, 20 participants  performed a single block of 80 trials combining the four conditions and the two distances.The extension of the occlusion to cover the contact points on the target resulted in stronger effects on both transport and grip. Figure Occluding the digits as well as their contact points influenced the digits’ trajectories similarly, but more clearly than only occluding the digits Fig. b. Both dF = 13.84; p < 0.0001]. The influence of occlusion on MGA was similar to that of experiment 1, but the MGAs themselves were overall larger  = 10.72; p < 0.0001]. Occluding both the digits (and their contact points) slowed down the movement , with one digit deviating further in that direction, giving rise to the change in grip aperture. Very surprisingly, occluding the thumb leads to a reduction of the grip aperture. This cannot be explained in relation to the reach-and-grasp view. In the double-pointing view, this increase can only be explained if one assumes that there is also a tendency to deviate away from the occluding surface. In that case, the reduced grip aperture could be a side-effect of a larger deviation away from the occlusion for the thumb (which is occluded) than for the index finger (which is not occluded).Although the ways in which the manipulations influenced the trajectories seem to be robust, the magnitude of the effects is modest. Could this be because we only used a single object throughout the experiments? When participants cannot see the object properly, and repeatedly grasp the same object, they might rely on prior experience instead of on vision to guide their movement. Haptic feedback is undoubtedly involved in such guidance, because haptic feedback is known to play a role in calibrating movements  that could each be presented at one of three possible distances . There were 10 trials for each condition in which the sphere with the diameter of 37 mm was located at 40 cm , and a strongly reduced number of trials per condition for all other combinations: two per size (except 37 mm) for the distances of 30 and 50 cm, and one per size (except 37 mm) for the distance of 40 cm. The 20 participants  ran a total of 100 trials, which took about 30 min. Different objects were presented at different distances in a randomized order.The effects on the transport trajectories in experiment 3 were similar to those in experiment 2. Any occlusion caused a deviation away from the body  = 8.58; p < 0.0001]. The difference between conditions resembled the one found in the previous experiments, but with overall smaller values for the maximum grip aperture in experiment 3  = 9.99; p = 0.0001], with a similar pattern as was observed in the previous 2 experiments  performed a single 30-min block of 100 trials, with 10 trials per condition for the 37-mm wooden sphere located 40 cm from the starting point. Due to technical problems during the recording phase, one participant’s data had to be removed from the analysis.As in experiment 1, no consistent modulation of the transport of the hand was found in the early phase of the movement, but in the second half of the movement the hand showed an overall tendency to move away from the occlusion Fig. d. At theOccluding only the contact points had a slightly more specific effect on the digit of which the contact point was occluded than occluding the digits during the whole movement Fig. d. OccludF = 11.25; p < 0.0001]. The grip aperture mainly increased in the conditions in which the thumb was occluded  = 0.59; p = 0.63]  occlusion of the object has an effect on the later part of the movement. On the other hand, an extended occlusion of visibility of the whole hand’s or of single digits’ paths affects the movement from the very beginning. Our results seem to suggest a way of controlling grasping more different and complex than those previously described in the literature.Previous studies suggest that visual feedback is likely to have most impact on movements when the hand is about to interact with the object Carlton . This isThe grip aperture was not always increased by the occlusion, except when both digits were occluded from the start. In this case, grip aperture was larger from the beginning of the movement. The influence of occluding the individual digits differed across the experiments in a manner that cannot simply be accounted for on the basis of whether the digits, the contact points, or both were occluded.Analyzing the digits separately highlighted the fact that the modulation of the trajectory by blocking online visual feedback differed for the two digits. Participants do not simply move their digits in a safer way (open their grip more) the more the trajectory is occluded. Moreover, their adjustments are not limited to the digit that is occluded. The results of experiments 1, 2 and 3 clearly show that both digits are affected by occluding either digit. The different behavior adopted for each kind of occlusion might reflect various strategies to optimize the limited information available, rather than only adopting a wider margin of safety.The conclusion that there are multiple components to the choice of the path is consistent with the differences between the experiments. When visual feedback of the trajectory was unobstructed (experiment 4), occluding either the thumb’s or the index finger’s contact points had a more specific effect on the final part of the occluded digit’s movement. In particular, when the contact point of the index finger was occluded, the thumb did not deviate from its original path, in accordance with the view that considers the two digits independently (Smeets and Brenner In conclusion, the present findings highlight the importance of distinguishing between visual feedback of the hand and object, as they influence the movement at different stages and in different ways.