This retraction stems from infiltration instability induced surface generation, which leads to an increase in reactive surface area when a porous medium dissolves in an imposing flow field. There is very good agreement between observations made with in situ, X-ray tomography and model predictions. Both show that the value of reactive surface area reflects a balance between flow-dependent surface generation and destruction, i.e. the “dry” geometric surface area of a porous material, measured without a flow field, is not necessarily the upper limit of its reactive surface area when in contact with reactive flow. This understanding also contributes to reconciling the discrepancies between field and laboratory derived solid-fluid reaction kinetics.The dissolution of porous materials in a flow field controls the fluid pathways through rocks and soils and shapes the morphology of landscapes. Identifying the dissolution front, the interface between the reactive and the unreactive volumes in a dissolving medium, is a prerequisite for describing dissolution-induced structure emergence and transformation. Despite its fundamental importance, the report on the dynamics of a dissolution front in an evolving natural microstructure is scarce. Here we show an unexpected, spontaneous migration of the dissolution front  In a reacting porous medium, a reaction front is an isosurface over which the chemical affinity of a reaction reduces to zero in the velocity direction. This isosurface separates the reacting surface from the remaining geometric surface and is the ideal boundary of the region of interest (ROI), for measuring the kinetics of water-rock interactions. At any given instant, the inherent heterogeneities of natural porous materials that are not encompassed by this isosurface do not contribute to the chemical reaction. Therefore, the ability to track an evolving reaction front can greatly simplify the analysis of many geochemical processes by allowing unambiguous identification of the temporal ROI.et al., Submitted, 2017)2. This feedback leads to morphological instability of the migrating dissolution front, referred to as reactive infiltration instability (RII)4. RII is fundamental to many geological self-organisation phenomena5. However, the behaviour of a dissolution front in the presence of the RII in natural microstructures remains elusive10, presumably because of the technical challenge of observing it experimentally14 and effectively incorporating parameters to describe the inherent heterogeneities of porous media into numerical simulations21. A comprehensive overview of the subject can be found in Szymczak et al.19 and references therein. A formulation of the problem from the perspective of a feedback loop consisting of flow field, reactivity field and solid-fluid conversion is presented in .The dissolution front is the reaction front of a solid dissolution reaction. In a dissolving medium with a pressure driven flow field, there is a positive feedback between the mineral dissolution rate and the local permeability , pH0 and pHeq, represent the initial and equilibrium states of the rock dissolving fluid (pH used as a master variable), rdiss represents the mineral dissolution rate (mol·m−2·s−1), which typically depends on pH and the mineral saturation index (SI); v represents the fluid velocity and s, the streamline as the integral path. A represents the specific surface area . In the numerator, surface area is defined as the spatial change of material density  and two concepts of surface area are used in this study. Geometric surface area (GSA) is the surface area within a sample or a simulation domain and is independent of the imposed flow field. Reactive surface area (RSA) is the portion of GSA on which the dissolution reaction occurs, i.e. chemical conversion is not zero. We use the word area when a quantity is referred to, i.e. GSA and RSA refer to the measurable amounts of geometric and reactive surfaces, respectively. Equation s needed for the RS to equal the LS varies greatly along different flow paths, owing to the heterogeneous spatial distribution of flow velocity and the geometric surface23. In a chalk sample with a steady state flow field, variation in the physical properties (represented by the RS) of as much as 6 orders of magnitude has been observed . The dissolution front, as an isosurface, consists of all the points on each and every s that satisfies Equation A) or longer residence time (s/v) yields shorter s.Given a flow field, the position of the dissolution front along any streamline can be determined using a plug flow approximation:4. For example, local permeability differences, often stemming from the local variations of material density, can be amplified by RII24. The solid-pore interfaces in porous media are defined by sharp spatial change of material density25. The pore surfaces are also the sites of fluid-solid interaction. Therefore, RII can increase the internal surface of a porous medium. In a simulation of a 7 × 7 × 14 μm3 volume of real chalk  and a constant volumetric flowrate (5 μm3/min). The GSA started decreasing after 450 s because of solid depletion. The same figure also shows that the non-monotonic microstructure evolution cannot be seen from the overall mass balance. The solid residual, indicated by 1 – Φ , decreased monotonically while the centre of mass (CoM) in the axial direction changed with time. First it moved toward the fluid outlet (positive displacement) because of preferential upstream dissolution but then later, it moved backward because solid near the fluid entrance did not react, bypassed by the channelled fluid.Infiltration instability amplifies the transport heterogeneities in a porous medium by channelling the more reactive fluid toward the more permeable flow pathsalk Fig. , the GSA0 s Fig. . The simt = 0  and t = 400 s. During this period, the region of the warmer colours  to monitor the dynamics of the microstructural evolution discussed above. A cylindrical chalk sample (ø × L = 0.9 × 2 mm) was used as a fast reacting model rock. The percolation fluid (ultrapure deionised water equilibrated with 8 bar CO2 at 50 °C) and slow flow rate (0.016 ml/min) were chosen such that the dissolution front would be contained within the field of view (FOV) accessible with μCT. The density of the porous material was reflected by the local, X-ray, linear absorption coefficient of the sample26. The sample’s internal geometric surface was indicated by the spatial variations in porosity25. Both quantities were measured from the intensity units of the reconstructed greyscale images.We used t = 28.5 h (red). Figure 27. Comparison of the images from t = 0 and 28.5 h indicates that the amplification of the pre-existing heterogeneities contributed considerably to the increase in surface area – a phenomenon characteristic of infiltration instability2. Fig. 3). Also shown is the displacement of the centre of mass in the axial direction determined from X-ray absorption (columns). The dynamics of these quantities agrees very well with the numerical simulation , the intensity at each time step was subtracted from that of the following step so the difference reflected a spatial distribution of the solid removal rate. Figure in situ measurement, we have adopted a definition of surface area that does not rely on the displacement of solid-fluid interface. The complexity of a porous medium is typically characterized by a two point correlation function25. This correlation describes the probability of any two random points in a porous medium belonging to the same phase as a function of their distance. When calculating the specific surface area A of the medium, one calculates the first derivative of this probability density function as the distance approaches zero. The physical significance of this method is that the geometric surface in a porous material is defined as the amplitude and frequency of the spatial variations of material density. This is a definition applicable to both greyscale and binarised tomographic datasets. With this definition, surface area can increase in a greyscale dataset if the porosity difference between any neighbouring voxels is enhanced. This manner of surface increase is not possible in a binarised dataset because the contrast of porosity is fixed at 1 and the voxels are assigned to either solid or pore. Therefore, a mechanism that relies on the expansion of idealized , binary pore geometry to explain reactant retraction has to invoke the displacement of solid-fluid interface and cannot explain the surface area generation stemming from any locally enhanced structural difference.The unexpected retraction of the dissolution front is different from the receding of reactant observable in an expanding pore as part of a flow field, although both are associated with an increase in the surface area as pore structure develops. The surface increase in this study is directly related to infiltration instability and to the enhancement of local porosity/permeability contrast resulting from this instability. In both the simulation and the in situ measurement, the enhanced local porosity contrast was the predominant reason for the increase of RSA. In the greyscale simulation, the solid-fluid interface was not tracked explicitly and no idealized/simplified geometry had been assumed for surface area calculation. Only after a predominant flow channel appeared was the mechanism of pore expansion applicable to the highly irregular shape of the channel. However, when this expansion began, the overall surface area had already started to decrease because of solid depletion. The expansion of pore dimension thus cannot explain the momentary increase of surface in our simulation. Similarly, in the in situ measurement, the surface area was defined by the intensity contrast of neighbouring voxels. Because of the very fine grains of chalk, the in situ μCT generally do not fully resolve the features and most of the voxels contain a mixture of void space and mineral and is therefore represented by a greyvalue. As is shown clearly in Fig. in situ μCT clearly showed an increase of surface area in the greyscale images (according to the adopted definition), no evidence showed that this increase was related to the expansion of any fully resolved, pre-existing pores. Instead, the enhancement of porosity contrast in the simulation and of the intensity contrast in the in situ measurement were both in concord with the inherent tendency of infiltration instability to amplify local structural differences.Meanwhile, in both our simulation and Another factor that differentiates our results from previous reports is that our investigation – both simulation and experiment – covered the whole flow domain in a physically realistic microstructure, rather than focusing on a single pore. If the reactant retraction is derived, theoretically, from a single pore geometry with a special analytical form , it can be challenging to prove that similar phenomena can be expected for any other, most likely highly irregular, geometry in natural porous media. The focus on a single pore has also excluded the consideration of the competition and merging of pores developing in parallel. For example, one would not be surprised by seeing a retraction of reactant from a pore that is failing the competition to channelize reactive fluid. This retraction, however, is contributing to the advancement of the reaction front in other pores that can only be observed if the complete flow field is monitored.in situ imaging.Nevertheless, it is a great question to ask whether, within a fully resolved rock sample, the development of pores can always be perceived as an expansion of binary pore geometry on a sufficiently small scale. If so, the enhancement of density contrast near the reaction front as a result of infiltration instability loses its physical significance because material density is inherently an continuous  property. An unambiguous answer to this question will rely on a fully resolved wormholing process, i.e. seeing through the development of pores without unclassified, grey voxels. This level of imaging capacity is currently beyond our reach. However, one could speculate a potential paradox in the binary preconception. If a rock sample is not perfusable, i.e. pores are not interconnected in the direction of the pressure gradient, one cannot observe competing wormhole development because the transport of reactants and products in the “dead” pores rely exclusively on diffusion and therefore, the positive coupling between advection and mineral dissolution does not form. If a sample is perfusable, wormholing becomes a pre-templated process where the many, pre-existing flow paths expand. In either case, no new, perfusable pore is created in the flow direction, contradicting our observation with the It is also of interest to put the results into the context of the conventional conceptual framework of the instability problem – that is, to define dissolution regimes  based on visual “patterns” that relies on the relative size of the system dimension and the reactant penetration depth. No front retraction can be observed during face dissolution in the absence of infiltration instability. The prerequisites for face dissolution are that (1) the penetration length of the reactant is small compare to the field of view (FOV) and that (2) the migrating front is, to a large extent, stable. In face dissolution, the negative feedback, often stemming from both diffusion and the limited availability of solid, is strong and deteriorates the growth of perturbation. The dissolution front propagates as a plug flow and do not amplify heterogeneities on its pathway. In contrast, for uniform/homogeneous dissolution, the front retraction may or may not exist. This uncertainty is related to the fact that this dissolution regime (“uniform”) merely tells that the penetration length of the reactant is greater than the FOV. It does not contain the information whether instability exists within the FOV. The reaction “front” is a very special reaction rate isosurface, where the Gibbs free energy increases to 0 in the flow direction. In general, there is an infinite number of rate isosurfaces in the flow field, where the specified rate does not have to equal zero. Any of these isosurfaces is subject to similar stability analysis as is the reaction front. In a uniformly dissolving medium, if all rate isosurfaces are stable, then one would not observe any enhancement of heterogeneity leading to surface generation. The front retraction does not exist because of the absence of instability. On the other hand, if any of the rate isosurface is not stable, then instability exists and a retraction of the front is possible. It is worth emphasizing that whether instability exists or not does not rely on whether the FOV can capture the entire reactive subvolume, or whether the reaction front develops within the limited size of a system.On a related note, the qualitatively similar observations across the few orders of magnitude are subject to a similar argument. There are two similarities between the experimental observation and the numerical simulation. First, a transient increase in surface area, leading to the receding of reaction front, was identified in both cases. Second, the subvolume of the system that showed an increase in surface area moved in the flow direction, both experimentally and in the numerical simulation. These similar behaviours are not specific to any length scale and are grounded on two common factors. First, the increase of surface area relies on a balance between surface generation and destruction. New surface is constantly generated given that there is a positive feedback between fluid flow and dissolution reaction. This positive feedback is scale invariant and relies only on the simultaneous presence of advection and reactants. Surface destruction is a natural consequence of solid depletion, which is subject to mass balancing and is not scale specific either. Second, the observation of the reactive subvolume migration in the flow direction relies on the control of the reactant penetration depth. This control was achieved by choosing the flow rate in the experiment so that the ratio between the reactant penetrated subvolume and the whole domain was similar to the same ratio in the numerical simulation, i.e. the flow rate in the simulation needed to be much smaller than that in the experiment so only a portion of the domain was reactive at any given moment. The same strategy of penetration control can be used on any length scale, given that the predominant mass transfer mechanisms are known. These two common factors resulted in the similar behaviours on the two length scales.e.g., the Gibbs free energy dependence of reaction rate)28. We have shown that the surface area of a porous material can be different with and without flowing fluid2. Perhaps more surprising is that, given the same rock sample, the RSA can be greater with a flow field, even when the sample is chemically homogeneous and when there is no precipitation of secondary phases. This contradicts the long held assumption that the geometric surface area measured ex situ is the upper limit for the reactive surface area, as the latter is subject to fluid accessibility. This difference may also have contributed to the repeated reporting of discrepancies between laboratory and field kinetic measurements29. In reality, in many geologic systems, flow is divergent, i.e., velocity decreases with distance from the fluid source. In such cases, from the cumulative surface perspective  in Grenoble, France. We collected 1999 projections from a single dry scan at 29.5 keV, with an exposure of 500 ms and 360° rotation. The reconstruction had a voxel dimension of 100 nm30. For this study, the reconstructions were intensity aligned, compensated for ring artefacts, denoised with iterative nonlocal means denoising and sharpened by deconvolution. An estimate of voxel level porosity was acquired by interpolating from an intensity based Gaussian mixture model31.A model environment for the numerical simulation was created using X-ray holotomography reconstructions3 in the form of calcite, from fossilized coccolith and skeletal debris, with ~4% silica content. The average porosity is high, ~45%, permeability ranges between 3 and 5 mD and the BET surface was 7.31 m2/g32. We loaded our miniature version of a Hassler core holder  with an Aalborg chalk sample machined into a cylinder of 900 µm diameter and ~2 mm length. To guide the flow of solvent, the chalk cylinder was mounted inside heat shrink tubing , placed between two stainless steel needles that served as fluid in- and outlets and sealed with epoxy resin prior to loading. The sample was confined in ultrapure water at 10 bar at the beginning of the experiment. The shell side containing the confining fluid was then sealed. A syringe pump  was used to drive the ultrapure water (equilibrated with 8 bar CO2 at 50 °C) through the sample at 0.016 ml/min.Percolation experiments were made with outcrop Maastrichtian chalk collected near Aalborg, Denmark . The material contains primarily CaCO33. Over the course of 88 hours, 45 consecutive tomography datasets were collected, with beam energy of 28 keV. Each set consisted of 1200 projections exposed for 1050 ms over 180° rotation. The time resolution was ~110 min. The effective voxel size in the reconstructions was 2.66 µm after down sampling the 3056 × 3056 pixel projection data by a factor of two in both directions. Prior to reconstruction, the interface of the aluminium wall of the core holder to the confining water was tracked and matched with a reference sinogram to compensate for drift and distortion caused by a changing drag force from the tubing during sample rotation. Ring artefacts were suppressed by Fourier-wavelet destriping of the sinograms before reconstructing with the GridRec algorithm34. After reconstruction, we applied iterative non-local means denoising (through 4 cycles) to every time step of the 4D dataset, using a constant noise level estimate and we aligned the dataset spatially, with digital volume correlation using Pearson’s correlation coefficient as the quality metric. Details of the signal processing can be found in Bruns et al.34.The dissolution process was monitored by continuous imaging using X-ray microtomography (μCT) at the P05 beamline of PETRA III at the Deutsches Elektronen-Synchrotron (DESY). The beamline is operated by the Helmholtz-Zentrum Geesthacht35. When a flow field is imposed, the model allows the spatial distribution of voxel porosity to be related to the reactor properties . The simulation domain contains 70 × 70 × 140 = 686,000 voxels, corresponding to a 7 × 7 × 14 μm3 volume of chalk sample. Within each 100 nm voxel, we assumed a linear dependence of the permeability and tortuosity on the voxel level porosity. This assumption means that the pressure drop in the PFR, modelled by Darcy’s law, uses a phenomenological coefficient in the form of a parabolic function of local porosity given by the geometric mean of the connected reactors. The flow field was then solved by the stabilized biconjugate gradient method under the assumption of incompressible flow and continuity.For numerical simulations, we built a reactor network model that treats each voxel as a mixed flow reactor (MFR) and its connection in its octagonal neighbourhood (i.e. 6 nearest neighbours) as an ensemble of plug flow reactors (PFR)37. A 50% subvolume of each voxel was treated as an MFR. An expression of surface area within each PFR is retrieved from the norm of the porosity gradient vector multiplied by the 2nd power of the voxel dimension. The geometric surface area of each voxel is then evaluated by summation over all neighbouring voxels. For example, if an empty voxel (porosity = 1) is surrounded by six solid voxels (porosity = 0), then its geometric surface area is l2 × 6 × |1 − 0|/2, where l is the voxel dimension (100 nm) and the divisor 2 appears because each interface is share by two neighbouring voxels. Half of this geometric surface area is assigned to the MFR (1.5l2) while the other half is assigned to the PFRs (each gets 0.25l2). The reactive surface area is then calculated according to the chemical conversion in each MFR and PFR. In this example, if Ca2+ is released in the MFR and in two of the six PFRs, the reactive surface area of the voxel is 1.5l2 + 0.25l2 × 2, i.e. 20,000 nm2. The geometric surfaces in the other four PFRs are ignored.The reactor model relates the reactant concentration with the mixing state in the reactor. Previous studies illustrated that the local conversion can be determined by the voxel level Damköhler number38 and (2) measuring the evolution of aqueous calcium concentration in a closed free-drift system with dissolving chalk powder. We then solved the Fredholm equation of the 2nd type, an integral differential equation, to delineate the evolution of surface area from that of dissolution rate. The derivation can be found in . This rate profile was then mapped to the LS of Equation −7 m/s and the macroscopic Damköhler number (Da) for the simulation is ~10. The physical significance of this Da is that the ratio between the volume of the system (the simulation domain) to the reactive subvolume of the system  is 10:1 at any instant. pH and the saturation index in each voxel .The dependence of chalk dissolution rate on aqueous calcium concentration was obtained by 1) calculating the far-from-equilibrium rate using the rate law proposed by Plummer and Busenberg calculatAll data needed to evaluate the conclusions in the paper are presented. Additional data related to this paper may be requested from the authors by emailing yiyang@nano.ku.dk.Movie 1Movie 2Movie 3


Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure‐outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of interest is to assess the shape of this relationship. We present two novel IV methods for investigating the shape of the exposure‐outcome relationship: a fractional polynomial method and a piecewise linear method. We divide the population into strata using the exposure distribution, and estimate a causal effect, referred to as a localized average causal effect (LACE), in each stratum of population. The fractional polynomial method performs metaregression on these LACE estimates. The piecewise linear method estimates a continuous piecewise linear function, the gradient of which is the LACE estimate in each stratum. Both methods were demonstrated in a simulation study to estimate the true exposure‐outcome relationship well, particularly when the relationship was a fractional polynomial  or was piecewise linear (for the piecewise linear method). The methods were used to investigate the shape of relationship of body mass index with systolic blood pressure and diastolic blood pressure. For example, the observed association between body mass index (BMI) and all‐cause mortality in a Western context is J‐shaped (or U‐shaped), as risk of mortality is increased for individuals at both ends of the BMI distribution  log function. These powers are used throughout this paper. Fractional polynomials of degree 1 are defined asp∈P. Similarly, fractional polynomials of degree 2 are defined asp1,p2∈P. In both cases, x0 is interpreted as log(x). As fractional polynomials of degree larger than 2 are rarely required in practice, these were not considered in this paper , and the standard error of the LACE estimate is computed as seβ^X|G  for the exposure‐outcome curve can be computed arithmetically under a normal assumption either using the estimated standard errors from the metaregression or by bootstrapping the second and third steps from above .χ22 distribution for the best‐fitting fractional polynomial in each class .These methods are available in the nlmr R package . The data‐generating model for individual i isgi∼ Bin, εXi∼ Exp(1), ui∼ Unif, εYi∼N, and h(xi) is the function relating the exposure to the outcome (the exposure‐outcome relationship). Exposure values were taken to be positive and away from zero so that the outcome takes sensible values for log and negative power functions. The IV explains 2.6% of the variance in the exposure.To assess the performance of these methods in realistic scenarios for Mendelian randomization, we performed a simulation study. We simulated data for 10,000 individuals for an IV 3.1For the fractional polynomial method, all possible fractional polynomials of degrees 1 and 2 were considered as the functional form of the exposure‐outcome relationship.1 and β2; these simulations yielded similar results to those discussed here (results not shown). Fixed‐effects metaregression was used in the simulations, however, random‐effects metaregression yielded similar results (results not shown).Combinations of effect sizes for the β parameters were chosen ranging from 0 to 2. For fractional polynomials of degree 2, we also considered effects in opposing directions for βFor the piecewise linear method and comparisons between methods, linear, quadratic, square‐root, and logarithmic functions were considered as the functional form of the exposure‐outcome relationship, as well as a threshold model:3.2χm2 distribution, where m=1 for comparing fractional polynomials of degree 1 and m=2 for comparing polynomials of degree 2.To evaluate the fractional polynomial method, we first fitted the correct fractional polynomial model  and assessed the bias and coverage of the effect parameter estimates. Subsequently, we fitted all fractional polynomials of the same degree and selected the best‐fitting polynomial based on the likelihood. We assessed the proportion of simulations where the best‐fitting fractional polynomial was the correct fractional polynomial. If the correct fractional polynomial was not the best‐fitting fractional polynomial, we tested whether it was in the group of fractional polynomials that fit the data almost as well as the best‐fitting polynomial; defined as those fractional polynomials where twice the difference in the log‐likelihood  was less than the 90th percentile point of a To evaluate the piecewise linear method, we first compared the outcome estimates at the mean exposure value in each quantile to the values of the true model at the same points. The coverages of the bootstrapped 95% CIs were also evaluated at these points.K quantile groups, and y¯k is the expected value of the outcome evaluated at the mean value of the exposure in each quantile group.For comparing the fit of the fractional polynomial and piecewise linear models, we used the following heuristic function:3.3P‐value less than 0.05. The heuristic function In the initial simulations, the population was split based on the IV‐free exposure into decile groups. Further simulations were performed varying the number of strata using 5, 10, 50, and 100 quantile groups. Tests of nonlinearity were performed to assess the impact of the number of strata on the empirical power of each test. The empirical power of each test was reported as the proportion of simulation replicates with For each simulation and set of parameters, 500 replications were performed. Bootstrap 95% CIs were generated using 500 bootstrap samples. All analyses were performed using R version 3.0.2.3.4N for each individual in the population), and allowing the exposure‐outcome relationship to vary  for each individual in the population). We assessed the impact of allowing each of these parameters to vary separately and both to vary together. In addition, we also allowed variation in both parameters to be correlated by drawing the parameters from a bivariate normal distribution with correlation 0.2. For fractional polynomials of degree 2, only the causal parameter for the second polynomial was allowed to vary across individuals.We performed additional simulations in which the underlying assumptions that the effect of the IV on the exposure and the effect of the exposure on the outcome are fixed and independent were relaxed. In these simulations, we assessed both modeling assumptions by allowing the effect of the IV on the exposure to vary , and using the original genetic variant but having a superadditive  and a subadditive  effect on the exposure in the data‐generating model.44.1Comparisons of fractional polynomials for all powers are provided in Table S1 (degree 1) and Table S2 (degree 2); a summary of results for the most commonly encountered powers is given in Table For fractional polynomials of degree 1, when fitting the correct fractional polynomial model, the causal estimate was generally unbiased (Table β=0), the probability of fitting the “correct” fractional polynomial was not estimated as all fractional polynomials with zero coefficients would describe the data equally well. In reality, the true exposure‐outcome relationship is unlikely to have an exact functional form, so the ability to estimate the shape of the relationship is more important that the precise identification of the function.When fitting all the fractional polynomial models, the correct fractional polynomial model was fitted more often for a fractional polynomial of degree 1, and when the power of the fractional polynomial differed substantially from 0. Although the power to detect the correct functional form was low for the logarithmic and square‐root functions, this is to some extent an artifact of the choice of powers; if a basis with only one concave function (either a logarithmic or a square‐root function) were used, then the correct model would be chosen more often. As the causal parameter in the model increased, the correct model was chosen more frequently. However, in all cases, the correct fractional polynomial was in the set of best‐fitting fractional polynomials in at least 89% of simulations. The fractional polynomial test for nonlinearity rejects the null exactly when the linear model is not in the set of best‐fitting fractional polynomials. With a null causal effect (4.2The piecewise linear method performed well when the true model was piecewise linear (such as a linear or a threshold relationship), with the predicted mean values of the outcome similar to their true values at the mean value of the exposure within each decile of the IV‐free exposure Table . The booUsing the heuristic function 4.3The best‐fitting fractional polynomial method had a similar or slightly better model fit (judged by the heuristic function) when a greater number of strata were used Table . HoweverQ test across the simulations. The power of the Cochran Q test also decreased as the number of strata increased, whereas the power of the other tests either remained the same or increased. The quadratic test slightly outperformed the fractional polynomial test when the true model was a quadratic or a threshold model; the fractional polynomial test was slightly superior when the true model was a logarithm or a square‐root model.The coverage under the null  was not overly inflated for any of the tests. In general, the fractional polynomial and quadratic tests were more powerful than the Cochran 4.4In the simulations where we relaxed the assumptions that the IV–exposure and the exposure‐outcome effects are the same for all individuals, we found that the fractional polynomial models of degree 1 and the piecewise linear method both performed well in terms of bias and coverage (Tables S3 and S4). The only concern was that tests of nonlinearity had slightly inflated Type I error rates when the IV‐exposure and exposure‐outcome effects were varied in a correlated way; Type I error rate inflation was not observed when the effects were varied either separately or independently.In the simulations with a low‐frequency genetic variant having a large effect on the exposure (Tables S5 and S6), there was some bias in estimates. This is likely to be the result of weak instrument bias  was used instead of rs2033529, as this variant was not available in UK Biobank; the linkage disequilibrium information was calculated using the European samples from 1000 Genomes  of variants related to BMI to be used as an IV, we extracted the 97 variants previously associated with BMI at a genome‐wide level of significance by the GIANT consortium  after regression of BMI on the allele score, age, sex, and center . Adjustment for age, sex, and center was also made in the regressions to obtain the LACE estimates in each quantile group. If additional population stratification were expected, we could additionally adjust for genetic principal components to minimize the effect of population stratification in biasing IV estimates.Q tests) to investigate heterogeneity in the IV associations with BMI in different strata.To assess the assumption that the effect of the IV on BMI is constant over the entire distribution of BMI, we also considered BMI as the outcome and calculated the associations of the IV with BMI in each of the strata. We then conducted tests . For comparison, the standard two‐stage least squares linear estimate was 0.527 mmHg per 1 kg/m2 increase in BMI  for SBP and 0.433 mmHg  for DBP.The exposure‐outcome relationships for BMI with SBP and DBP estimated using the fractional polynomial and piecewise linear methods are presented in Figure P‐value of 0.0026 . The best‐fitting fractional polynomial of degree 1 for the relationship between BMI and SBP had power −0.5, and there was no evidence to suggest that a fractional polynomial of degree 2 fitted the data better . The estimate of the exposure‐outcome relationship from the piecewise linear method visually suggested a threshold–type relationship, with a steep slope up to a BMI value of about 32 kg/m2, and a slightly negative slope from 32 kg/m2 onwards. The relationship between BMI and SBP was similar in individuals with no history of hypertension .There was strong evidence that the association between BMI and SBP was nonlinear, with the quadratic test yielding a P‐value = 0.0005, fractional polynomial test P‐value = 0.0114, Cochran Q test P‐value = 0.0049), and there was strong evidence that the best‐fitting fractional polynomial of degree 2 (with p1 and p2 = 3) fitted the data better than the best‐fitting fractional polynomial of degree 1 . There was no evidence of a different relationship between BMI and DBP for underweight individuals, with the exposure‐outcome curve increasing almost linearly up to a BMI of around 40 kg/m2. But for hyperobese individuals (BMI > 40 kg/m2), DBP seemed to decrease sharply. This was particularly evident in the fractional polynomial method, which used a greater number of strata and hence had more resolution to consider the shape of the exposure‐outcome relationship at the extremes of the BMI distribution. One potential reason for this finding is that hyperobese individuals with high DBP are less likely to be enrolled in UK Biobank, perhaps due to differential survival probability. Another reason could be the difficulties in estimating blood pressure in hyperobese individuals .The association between BMI and DBP was also nonlinear .There was no evidence that the associations of the IV with BMI varied between the different strata , with causal estimates being close to unbiased and coverage rates generally maintaining nominal levels . Additionally, tests of nonlinearity were provided and their performance was assessed. The quadratic and fractional polynomial tests had the best performance in terms of Type I error rate and power.6.1The recommendation as to which method to use depends on the aim of the investigation. The fractional polynomial method will always provide a smooth estimate of the exposure‐outcome relationship, and as such has more consistent performance when a large number of strata are chosen . Fractional polynomials of degree 1 had better performance than those of degree 2 in terms of bias and coverage of effect estimates. However, fractional polynomials of degree 1 are less flexible and would not be able to model complex exposure‐outcome relationships. Additionally, they tend to smooth over discrepancies in the data. For example, if the LACE estimate for individuals in the lowest quantile group for BMI was substantially different to the other LACE estimates, then both this difference and any uncertainty in the LACE estimate would be smoothed over somewhat in the fractional polynomial estimate. Preference between the methods therefore comes down to a question of prior belief: if one truly believes the true exposure‐outcome relationship to be smooth, and that estimates in the surrounding quantiles should be used to model the LACE in the target quantile, then the fractional polynomial method should be preferred. However, if one does not want to smooth over estimates, then the piecewise linear method should be preferred; however, the estimate of the exposure‐outcome relationship will be more jagged and variable.The number of strata and divisions between strata should ideally be specified before the analysis according to practical considerations  and the sample size available. If the number of strata is too large, then each stratum will have a small sample size. The LACE estimate in a small stratum will be imprecise and may be susceptible to weak instrument bias  even if there is unmeasured confounding. If the function is heterogeneous, then the situation is more complicated Small, . For exa6.3As has been noted in other contexts, estimates of nonlinear relationships are sensitive to measurement error in the exposure  on blood pressure  in individuals with no history of hypertension using the fractional polynomial and piecewise linear methods on data from UK Biobank. The red point represents the reference point of BMI of 25 kg/m2. Grey lines represent 95 fractional polynomial method used 100 strata, whereas the piecewise linear method used 10 strata.Click here for additional data file.


Cerebral blood flow is regulated over a range of systemic blood pressures through the cerebral autoregulation (CA) control mechanism. The COx measure based on near infrared spectroscopy (NIRS) has been proposed as a suitable technique for the analysis of CA as it is non-invasive and provides a simpler acquisition methodology than other methods. The COx method relies on data binning and thresholding to determine the change between intact and impaired autoregulation zones. In the work reported here we have developed a novel method of differentiating the intact and impaired CA blood pressure regimes using clustering methods on unbinned data. K-means and Gaussian mixture model algorithms were used to analyse a porcine data set. The determination of the lower limit of autoregulation (LLA) was compared to a traditional binned data approach. Good agreement was found between the methods. The work highlights the potential application of using data clustering tools in the monitoring of CA function. Cerebral blood flow (CBF) is regulated over a range of systemic blood pressures by the cerebral autoregulation (CA) control mechanism which acts through complex myogenic, neurogenic, and metabolic mechanisms . This raA number of measures have been developed to determine the patient’s autoregulation status as it is important for the clinician to know whether the patient is operating in an intact or impaired zone and, if the latter, to take appropriate action as required. The correlation between cerebral perfusion pressure (CPP) and transcranial Doppler (TCD)-measured cerebral blood flow (CBF) may be quantified using linear regression to assess autoregulation in patients with neurological conditions. The mean velocity index, Mx, quantifies the degree of correlation between blood pressure (BP) [usually taken as mean arterial pressure (MAP)] and cerebral flow, with positive values associated with an uncontrolled pressure-driven flow regime and hence compromised cerebral haemodynamic function . However2 signal and a blood pressure signal  are acquired over time (top plot). An analysis window of period, T, runs across the signals and the rSO2 and BP data within the window are plotted against each other (middle left plot). The window must be of sufficient length to capture the characteristic periodicity of the physiological slow waves present in the blood pressure signal . NIRS cerebral signals  and between interventions.2 level of approximately 30 mmHg by increasing the minute volume. Hyperventilation was confirmed from the arterial blood gas measurement. After 5 min of stable hyperventilation, arterial and venous blood gases were measured. Minute ventilation was then decreased back to pre-hyperventilation level and end-tidal CO2 was monitored to assess when the animal returned to baseline.The animal was hyperventilated to an end-tidal CO2 level of approximately 55 mmHg by decreasing the minute ventilation. Hypoventilation was confirmed from arterial blood gas measurement. After 5 min of stable hypoventilation, arterial and venous blood gases were measured. Minute ventilation was then increased back to pre-hypoventilation level and end-tidal CO2 monitored to assess when the animal returned to baseline.The animal was then hypoventilated to an end-tidal CO2 was increased to 1.0. The ventilator was then changed to CPAP mode (or inspiratory hold) and the airway pressure was increased to 25 cm H2O for 40 s. Ventilation was again started at baseline settings for 5 min. After this the ventilator was changed to CPAP (or inspiratory hold) and the airway pressure increased to 35 cm H2O for 40 s. Ventilation was then started and the animal allowed to recover to baseline physiological values .The animal was ventilated with baseline ventilator settings, and FiO2 was increased to 1.0. The FiO2 was changed rapidly to 0.08 to create acute hypoxia. When the animal reached the lowest level of SpO2, maintained for 2 min, blood samples were obtained from arterial and venous catheters, the FiO2 was rapidly increased to 1.0. When SpO2 returned to a 100 % plateau for 2 min blood samples were collected from arterial and venous catheters. This hypoxia procedure was then repeated before all settings were returned to baseline and the animal allowed to recover for 10 min.The animal was ventilated with baseline settings, and FiO2 of 1.0. Blood was removed through the central venous catheter until 60 % of the animal’s blood volume (blood volume in ml = 65*weight in kg) was removed in steps of 20 %.The animal was ventilated with baseline settings and FiOThe animal was resuscitated with a combination of half of the shed blood and a balanced electrolyte solution in the same stepwise fashion until the mean arterial blood pressure returned to pre-haemorrhage levels.The behaviour of mean arterial pressure (MAP) during the study for one of the pigs is shown in Fig. 2) in a series of 10 s steps. The calculated metric values were binned in 5 mmHg blood pressure increments and the LLA point detected as the first point below a threshold of 0.5 using an automated algorithm which scans from left to right and setting a flag when two valid median binned points have been seen above the threshold. The next bin below the threshold is then marked as the LLA. Bins with fewer than five data points are marked as invalid.  Note that in practice the threshold should be set somewhere between 0 and 1. This is because the expectation is for a value of unity for correlating regions (impaired CA) and a randomly spread out values of COx, with a mean of zero, for non-correlating regions (intact CA). In this work we use a threshold of 0.5. This is at the higher end of the values generally found in the literature which are 0.3 [The COx autoregulation correlation metric was computed as described in Sect.  are 0.3 , 15, 0.4 are 0.3  and 0.5  are 0.3 , 17. We The k-means and Gaussian mixture model methods were applied to the unbinned COx data for each animal. The algorithms used in the work here are described as follows.Choose k initial points as centroids .Calculate the distance from each point to each cluster centroid.Individually assign each point to the centroid that decreases the sum of the within-cluster, sum-of-squares point-to-cluster-centroid distances.Calculate the new centroids from the updated clusters.Repeat 3–4 until convergence or max number of iterations reached.The algorithm was run ten times to reduce the risk of being caught in local minima. The square of the Euclidean distance  is employed as the distance metric and the COx and MAP were not rescaled prior to clustering.A number (N) of Gaussian distributions are fit to the data using an expectation maximization algorithm. This results in N Gaussian distributions for which the posterior probability of membership for each point can be calculated. A point is then said to be a member of the cluster for which it has the highest posterior probability. The whole algorithm is repeated in a similar manner to the k-means method in order to mitigate the effect of falling into local minima during the optimisation process.Note that once the two clusters are found, the LLA is initially determined to be the minimum MAP value in the right hand cluster . An additional step to remove outliers from clusters was also applied before the final LLA determination. This required that all points in the right hand cluster that are further than two standard deviations away from the mean MAP for that cluster are discarded. This limits the LLA to the mean MAP of the cluster minus two standard deviations which we found has the effect of mitigating against obvious noise on the cluster plots.Figure Figure Table Note that a separate data run was performed with the hypo and hyperventilation (which are known to have an effect on autoregulation) portions of the signal removed, however this did not significantly change the COx plots and so all the data was left in the results reported here for completeness.In practice, the accurate identification of the intact and impaired regions, and hence the LLA point is non-trivial due to the variability of the data both on an inter- and intra-patient basis. Noise may affect the signal in a clinical environment which may be device specific  or physiological in nature . The traditional COx measure using binned data makes the task more difficult due to the associated granularity imposed on the data prior to assessment of the LLA point. It is interesting to note that 14 of the 15 studies referenced in this paper use the ICM+  software , 15–18 wOne disadvantage of the study was that the results could not be compared directly to an independent reference signal as historical data was used where no reference signal existed for blood flow or intracranial pressure . However, the cluster-calculated LLA’s could be compared with a standard binned algorithm for determining the LLA from a COx measure. Although this may appear less than ideal, it is worth noting that many of the reference signals that are used in other studies suffer from their own issues. For example TCD, which is required to calculate the Mx measure, requires manual intervention and can be very noisy . In the Further tuning is possible for each method, such as changing the COx threshold for the original binned algorithm or modifying the distance metric for the k-means. However, this was not carried out here as it would effectively be an exercise in over-tuning the methods on a small number of subjects. We argued in Sect. Note that we have focused on the determination of the LLA in this work as the blood pressures associated with the study did not transit the ULAs in any of the animal data. However, in practice in order to find both the LLA and ULA it is trivial to modify this approach to fit three clusters. Additionally, silhouettes  could beThe inspection of the cluster plots of Fig. We have proposed data clustering methods as a novel strategy for determining and delineating the regions of interest in CA data. Both k-means and Gaussian mixture models were employed to successfully partition COx data into the lower impaired region and intact region, with the boundary at the LLA. These new methods may be considered an alternative possible path towards a NIRS-based continuous autoregulation monitoring algorithm for use in noisy environments such as those encountered in clinical practice. Future work will focus on improving the methods by examining larger data sets where the COx results can be compared to reference Mx data obtained from cerebral blood flow measurements.


In this study, we retrospectively investigated case reports with and without midazolam administration via oral, intranasal and rectal before cystometry procedure. We aimed to compare the data to evaluate the effects of sedation before cystometry on the pediatric patients and parents’ satisfaction.A total of 124 ASA I-II pediatric cases aged 5–14 years were retrospectively investigated from the hospital records. One of the three administration routes was chosen; oral midazolam at a dose of 0.5 mg/kg and nasal or rectal midazolam at a dose of 0.3 mg/kg (maximum 15 mg). Heart rate, blood pressure, oxygen saturation, the Wisconsin Hospital of Children Sedation Scale (CHWSS) score and the Groningen Distress Rating Scale (GDRS) score were recorded. Cystometry measurement values, diagnoses of the cases and procedure durations were recorded from the urodynamic laboratory records.80 female, 44 male cases were evaluated. The CHWSS score at the 10th and 20th minutes after the drug administeration was higher in the oral group than the others (p = 0.001). The duration between the administration of the drug and the start of the procedure was shorter in the nasal group (p = 0.01). Parents satisfaction for sedation was 77 % when comparison of the cystometry with and without sedation. Comparison of the cystometry results with or without sedation no significant difference was found between all parameters (p > 0.01).We believe that sedation with midazolam administered through all three routes is a safe, effective and convenient option during cystometry, especially in the young age group. Cystometry is an invasive investigation method used for the diagnosis and follow-up of urination disorders in children. Anxiety at a high rate of 61–71 % is known to develop during cystometry, originating from the unpleasant experiences of bladder and rectal catheterization  were excluded from the study.Sedation is not administered routinely for cystometry at the urodynamics outpatients of our hospital. The experienced urodynamics nurse assess all patients for sedative necessity. The cases that were to be sedated were fasted for minimum of 6 h before the procedure using the routine protocol of our Anesthesia Clinic. One of the three administration routes was chosen by the anesthetist preference: oral midazolam at a dose of 0.5 mg/kg and nasal or rectal midazolam at a dose of 0.3 mg/kg (maximum 15 mg) (9). The calculated dose was sprayed to the patient’s mouth through the syringe without dilution and the patient was instructed not to spit. The drug was administered with the apparatus named Intranasal Mucosal Atomization Device  with a spray mechanism that is fully inserted into the nostril and prevents leakage of the drug during nasal administration. For the rectal route, the 4–5 cm section of a feeding tube was cut and inserted on an injector tip. A lubricant gel was administered for ease of application. Midazolam was given through all three routes without being mixed with any other substance as it could change the concentration and effectiveness.All patients had their parents with them during the procedure and the experienced urodynamics nurse administered a lubricating gel during urethral and rectal catheterization. We formed four groups with the same number of patients as oral, nasal, rectal and the control group not administered sedation and chose the patients for each group according to the order of the presentation date to the clinic. All patients were routinely monitorized at our clinic and heart rate, blood pressure, oxygen saturation, the Wisconsin Hospital of Children Sedation Scale (CHWSS) score Table  Thevara and the The anesthesia forms, cystometry measurement values and diagnoses of the cases included in the evaluation were recorded from the hospital records. The duration from the administration of the drug until the procedure and the duration from the beginning of the procedure to the end were calculated from the urodynamic laboratory records. The families of the patients were called by phone and asked standard questionnaire at post procedure period whether they were satisfied by the sedation during the cystometry procedure by authors . The parents were also asked to compare the procedure with previous experiences, if any.Statistical analysis was performed by using IBM SPSS Statistics for Windows 22  software. Shapiro–wilk test was used to test normality assumption of numerical variables. Frequency, percentage for categorical data and mean ± SD or median (min–max) for numerical data were calculated as descriptive statistics. Chi square or Fisher’s exact test were used to compare categorical variables. Oneway ANOVA and posthoc Duncan test were used for normally distributed variables, Kruskal–Wallis test and posthoc Dunn test were used if the distribution is not normal for comparisions of groups. Wilcoxon test was used to compare the values before and after sedation. A p value of less than .01 was considered statistically significant.The demographic data, duration between drug administration and the procedure, procedure duration, parental satisfaction and CHWSS values of the pediatric patients who received or did not receive sedation with midazolam through three different routes during cystometry at the Pediatric Urology Urodynamic Outpatients Department of our hospital were recorded with a retrospective analysis as shown in Table There are no significant difference between mean age of the groups. The CHWSS score evaluated at the 10th and 20th minutes after the drug was administered was higher in the oral group than the others (p < 0.01). The duration between the administration of the drug and the start of the procedure was shorter in the nasal group (p < 0.01). All these results were statistically significant.Urodynamic diagnoses in the groups with and without sedation are presented at Table The hemodynamic data revealed higher blood pressure values, especially at catheterization and the later stages, in the control group. Following midazolam administration, two patients in the rectal group complained of double vision at the 20th minute while one patient in the rectal group and one in the oral group had hypotension  during the bladder filling stage but no statistically significant difference was found between the groups. None of the patients were found to have developed desaturation. None of the patients spitted during oral administration. Nasal burning was reported in 77 % of the patients during intranasal administration. The cystometry procedure is allowed when the CHWSS score is 5 or less in all group.No statistically significant difference was present between the four groups in terms of GDRS scores at the room entry and cystometry stages. The values are presented at Table Thirteen of the patients who received sedation had undergone a cystometry procedure without sedation about a year ago. The cystometry values of these patients before and after sedation are compared in Table Urodynamic studies are the basic diagnostic method in children with a lower urinary tract symptom and the procedures may need to be repeated to monitor the effectiveness of the treatment. The bladder and rectal catheterization performed during this procedure cause fear and anxiety in pediatric patients. Children may show extreme anxiety during this procedure, especially if they have previous painful experiences. It is therefore sometimes not possible to perform an urodynamic study in these patients. Prevention of stress is required to eliminate the effects of previous painful experiences in children. Methods such as having the parents present, the use of lidocaine gel during catheterization, distraction techniques, warm infusion fluids and hypnosis have been recommended because they decrease the pain and anxiety that occur due to the catheterization during the procedure Gray . HoweverBenzodiazepines provide sedation, anxiolysis and amnesia but do not have an analgesic effect. Midazolam is a benzodiazepine with a rapid effect of short duration and enables quick recovery. It provides great flexibility in terms of drug administration options, especially in pediatric cases, since it can be administered via various routes such as oral, intranasal, sublingual, rectal, intramuscular and intravenous. Oral administration is highly preferred for sedation in children because it does not cause pain and stress. However, its bad taste sometimes makes oral use of the agent difficult. Only the ampoule form is available in our country and sometimes the required dose cannot be given this way due to spitting or vomiting of the patient. The nasal administration of midazolam provides fast and effective sedation due to the rich vascular supply and large mucosal surface but usually causes irritation and burning. It is advantageous as it enables achieving the desired sedation level with a lower dose and earlier and also completing the intervention quicker. The rectal route enables the intended dose to be fully received by the patient and eliminates risks such spitting by the patient and nasal stinging, making it a reliable alternative route. A disadvantage of this method is the possible shame or discomfort of the child during the procedure. A sufficient sedative and anxiolytic effect was seen in all groups in a study where the effectiveness of midazolam administered through four different routes  as premedication was investigated  than the others in our study. The reason for the unwillingness in the control group that did not request sedation and the lack of a difference in the GDRS values could be the high mean age of the patients in this group and therefore the easier acceptance of the cystometry procedure. Sweeney et al. found the mean age in the group that did not require sedation to be significantly higher (8.1 ± 5.1 years) and concluded that children aged 3–7 years should be assessed in terms of sedation in their retrospective study on the need for sedation during urodynamic investigations in children (Sweeney et al. The agent used for sedation in children should enable performing the procedure by decreasing stress and should also not affect the measurements. Bozkurt et al. reported that a single dose of intranasal midazolam did not affect the urodynamic results and provided adequate comfort for the procedure in their study investigating the effect of intranasal midazolam on lower urinary system function in children undergoing an urodynamic study (Bozkurt et al. The limitations of our study retrospective course, small sample size, selection bias.The child needs to be calm and cooperating during the invasive procedure of cystometry. Effective sedation was found with all three administration routes but we feel that the quicker onset of the sedation and lower dose used with the nasal route compared to the oral group are advantages despite the nasal stinging. An advantage of sedation was that cystometry was performed in a shorter time in the sedated patients compared to the control group. We believe that sedation with midazolam administered through all three routes is a safe, effective and convenient option during cystometry, especially in the young age group. Most of the parents are pleased with sedation application.


Aim of this study was to analyze the efficacy and precision of the completely customized lingual appliance (CCLA) regarding the single tooth torque correction. The study also examined external apical root resorptions as possible side effects of torque correction and the changings of the periodontal situation.A case series of three patients were included. The patients showed a single tooth torque problem with a gingival recession and were treated with the CCLA. Plaster casts before and after treatment and plaster casts of the set up were scanned and superimposed. Deviations between the two plaster casts were analyzed at different points of interest. Changes of the gingival recession were compared before and after treatment. Relative root resorptions were measured by the orthopantomograms. Treatment times were assessed by the records of the patients. Results were presented descriptively.The mean change of the most apical part of the root reached by the orthodontic treatment was 1.8 ± 0.3 mm. The largest deviation between set up and final model was measured on the occlusal surface of the tooth 36 with 0.8 mm. Most measurement points showed a deviation of 0.5 mm or less. The depths of the gingival recession showed a significant reduction of 4.7 mm. The widths of the gingival recession were reduced by 1.1 mm. The average relative root resorption of the corrected teeth was 2.7 ± 1.5%. The average treatment time was 13.8 ± 4.5 months.This is the first study showing that the CCLA with its high precision is very effective in correcting single tooth torque problems. Orthodontic torque correction resulted in a significant reduction of gingival recessions and caused only negligible root resorptions. In orthodontic treatment with the completely customized lingual appliance (CCLA) the appliance is manufactured for each patient with individual designed brackets and archwires Fig. .Fig. 1A It was demonstrated that the tooth positions after orthodontic treatment with a CCLA are very close to the planned tooth positions of this set up , 2. A prAfter orthodontic treatment a common method to prevent a relapse in the frontal area is to bond a fixed retainer. This is bonded on the lingual tooth surfaces especially in the lower arch from canine to canine. However, the retainers might have negative effect when they are partially debonded and unnoticed by the patient for a longer time. The teeth rotate around the retention wire either to the buccal or lingual site. There are some studies reporting about undesirable tooth movements due to a broken retainer , 9. ThesThe orthodontic correction of this torque problem can be a chance to save the tooth and improve the gingival recession. There are some studies reporting about the orthodontic correction of this problem with a vestibular appliance. Different techniques are described in these case reports. Some authors use the technique with segmented archwires, some prefer the technique with continuous archwires , 12. TheAim of this study was to analyze the efficacy and precision of the CCLA regarding the single tooth torque correction by comparing the plaster casts before and after orthodontic treatment and the set-up models.The analysis was performed using an optical 3D scanner, digital superposition and measurements of possible gingival recessions on the plaster casts. We also examined external apical root resorptions by orthopantomogram measurements as possible side effects of torque correction and the changings of the periodontal situation.n = 2; males n = 1), being treated at the Department of Orthodontics of the University of Mainz and private praxis Prof. Dr. Dr. h.c. Wiechmann and partners in Bad Essen (both Germany), were included by the following criteria:Three patients . Treatments of all patients were performed with a general archwire sequence of 0.014″ SE-NiTi, 0.016″ X 0.022″ SE-NiTi, 0.016″ X 0.024″ Stainless Steel and 0.018″ X 0.018″ ß-Ti.A 3D Scanner  was used for the digitalization of the plaster casts. Plaster casts of the situation before treatment, from the set up and from the situation after treatment were fixed on special plates, which are necessary to hold the plaster casts during scan process. These fixators are able to rotate, which allows the three dimensional scanning of the models.The scanner is composed of a projector and a camera and works with the method of a stripe projection. The projector produces light stripes from different positions, which are registered by the camera. This is necessary to calculate the three dimensional data. All measurements are composed to a complete set of data by a process called “matching” and saved as a Standard Tessellation Language (STL) – file. The. STL-file is a key file for different systems of the Computer Aided Design (CAD)-system.The program EasySLIM  converted the. STL-files to .pmh-files. In the next step artifacts and unnecessary areas were eliminated by the 3D–Viewer .The digital superposition was done with the program Comparison . The teeth, which were not included into the appliance and not moved by the orthodontic treatment, functioned as stable structures for the superposition. Everything except of these tooth surfaces was cut before proceeding with the superposition.The deviations between two scanned plaster casts were shown by colored pictures and metric values of the deviations were calculated by the software. For the optical representation a color scale has been set up. Negative deviations were colored in yellow and red, positive deviations in blue and purple. Area with no or very low deviation were marked green. White areas of the superposition show sections, where the difference between the two scanned models are undetectable for the software Fig. . The VerGingival recessions were measured with a caliper gauge on the plaster casts before and after orthodontic treatment. Measurements of the width of the recession were performed at the biggest distance of the recession from the gingival limit mesial to distal. Measurements for the depth were performed from the enamel/cementum border of the crown to the gingival apical limit of recession. All measurements were performed three times.External apical root resorptions (EARR) were defined as any reduction regarding the radiographic root length of the orthodontically moved mandibular incisor. Quantitative measurements of the crown and rot length were taken. Any image distortion between the pre- and post-treatment radiographs was calculated using the crown length measurement . It was Treatment time were taken out of patients records and clinical pictures were analyzed descriptively.Results are presented as single values for each patient or as mean values with standard deviations. Differences between the groups are described descriptively.Superposition of the plaster cast before treatment and after treatment showed a mean change of the root of 1.8 mm ± 0.3 mm  into the alveolar bone at the most apical point of the recession .The treatment time of the patients were analyzed due to the patients` records. Average treatment time was 13.8 ± 4.5 months .In the last step we analyzed the clinical situation of the patients by the intraoral pictures. All three patients showed a massive improvement of the periodontal situation after the orthodontic treatment. Torque correction of the affected teeth led to an improvement of the periodontal recession. Two of three patients still had a problem with the hygiene of the gingiva and an inflammation of the gingiva was still observed in these cases Fig. .Fig. 6InThe precision of the CCLA has been analyzed in previous studies –3. PaulsPauls et al., 2010 [The exactness of the 3D scanner is a key factor for the precision of the digitalization of the plaster casts. The orthoX 3D scanner used in the present study provides a precision of less than 20 μm at a scanning time of 45 s. This is the requirement for the quality of the digitalization.The method to measure the EARR in the orthopantomogram was established by Linge and Linge in 1983  and succIn the present study the torque movement of the apex after orthodontic treatment with the CCLA was about 2 mm into the direction of the alveolar bone. The gingival recession improved in all cases with a mean reduction of nearly 5 mm. So far there are only case reports in the present literature describing the periodontal changes after orthodontic single tooth correction. Our results accord with these case reports, which also reported a significant improvement of the periodontal situation due to orthodontic treatment , 12. AllTanaka et al. presented a case report in 2010 and could show a five-year-follow-up of a combined treatment of periodontal surgery and orthodontic treatment for gingival recession in the lower front . The perIn our study all cases were under orthodontic retention with a fixed retainer behind the frontal teeth of the mandible. Two of the retainers were partially debonded what the patients did not notice. It is still unclear in the literature where the unexpected tooth movements under partially debonded retainers come from. Either the retainer was bonded with an active component or masticatory forces can be the origin of stress in the retainer wire .Shaughnessy et al.  pointed To avoid stress between the bonding points of a fixed retainer a novel technique are CAD/CAM-produced lingual retainer. These retainers seem to provide a very accurate fitting to the lingual tooth surface and might prevent unexpected tooth movements caused by residual stress between the bonding points . Future We observed a very low external apical root resorption on the teeth after torque correction. Hohmann et al., 2007 , observeThis is the first study showing that the CCLA with its high precision is very effective in correcting single tooth torque problems. Orthodontic torque correction resulted in a significant reduction of gingival recessions and caused only negligible root resorptions.