Nonlinear mixed effects models parameters are commonly estimated using maximum likelihood. The properties of these estimators depend on the assumption that residual errors are independent and normally distributed with mean zero and correctly defined variance. Violations of this assumption can cause bias in parameter estimates, invalidate the likelihood ratio test and preclude simulation of real-life like data. The choice of error model is mostly done on a case-by-case basis from a limited set of commonly used models. In this work, two strategies are proposed to extend and unify residual error modeling: a dynamic transform-both-sides approach combined with a power error model (dTBS) capable of handling skewed and/or heteroscedastic residuals, and a t-distributed residual error model allowing for symmetric heavy tails. Ten published pharmacokinetic and pharmacodynamic models as well as stochastic simulation and estimation were used to evaluate the two approaches. dTBS always led to significant improvements in objective function value, with most examples displaying some degree of right-skewness and variances proportional to predictions raised to powers between 0 and 1. The t-distribution led to significant improvement for 5 out of 10 models with degrees of freedom between 3 and 9. Six models were most improved by the t-distribution while four models benefited more from dTBS. Changes in other model parameter estimates were observed. In conclusion, the use of dTBS and/or t-distribution models provides a flexible and easy-to-use framework capable of characterizing all commonly encountered residual error distributions.The online version of this article (doi:10.1007/s10928-015-9460-y) contains supplementary material, which is available to authorized users. Population modeling is increasingly used to analyze data arising from clinical trials. Nonlinear mixed effects models (NLMEM) enable simultaneous analysis of data gathered from all study patients with the aim of determining an underlying structural model driving the observations as well as characterizing inter-individual variability (IIV), which explains why different individuals can show different responses to a given drug. In most cases, some information is available beforehand about the structural model based on the knowledge on the underlying system. For example, models of different systems which have been developed in multiple disease areas , 2 can bMisspecifications of the residual error model impact both the estimation of and the simulation from NLMEM. Let us considerer first the impact of a misspecification of the scedasticity. Maximum likelihood (ML) estimation utilizes the expected variance of the modeled outcome in order to compute the likelihood to maximize. Estimation of model parameters will thus depend on the residual variance model, and parameter estimates may be biased if the wrong variance model is chosen . InferenIt is thus important to address potential misspecifications of the residual error model. Even though elaborate models have been developed and advocated , residuaWe propose that two approaches shall be considered in order to extend supported scedasticity relationships and enable objective selection of the distribution shape. The first approach, referred to as the dynamic TBS (dTBS), is based on the classical TBS approach but allows both the shape and the scedasticity parameters to be estimated. The second approach replaces the assumption of normality of the residuals by the assumption of a different parametric distribution. In this paper we investigated the assumption that the residuals arise from a Student’s t-distribution with estimated degree of freedom, which allows for heavier tails than the normal distribution if needed. The aim of the present work was to investigate the dTBS and t-distribution approaches using both real data examples and simulations in order to provide a comprehensive framework for characterization of the residual error model in NLMEM.Y, which depends on model parameters θ and independent variables x, is defined in Eq. Y according to this model is defined in Eq. ζ = 1) slope–intercept model, namely the additive error model  given the model, f is a function describing the structural model, x are independent variables, θ are model parameters, ζ is a power parameter and εslope and εintercept are assumed independent with mean 0 and variance Let us first describe a general framework for the modeling of PK–PD data. A generic model for a given set of observed data stimated  to allowVar(Y) is appropriate and the residuals are normally distributed.LLY is minus two times the log-likelihood of the observed data Y, Var(Y) is the variance of Y given the model and f is the expectation of Y given the model.The set of parameters which fit a set of data best are estimated by minimizing minus two times the log-likelihood, also referred to as objective function value (OFV), which is computed assuming a normal distribution of the residual error terms Eq. . Minimizλ accounting for skewness. A value of λ greater than 1 indicates left skewness, while a value of λ lower than 1 indicates right skewness. Special cases are a value of 1, which indicates no skewness, i.e., normally distributed residuals on the untransformed scale, and a value of 0, which corresponds to a log-normal distribution. The Box–Cox transformation can also handle negative observations by adding a constant to all observations before transformations to ensure their positivity. Whereas the traditional TBS approach assumes that the transformed variable has a constant or homoscedastic variance, we propose to combine the TBS approach with a more flexible power residual variance model. The resulting dTBS model and its corresponding variance are defined in Eqs. h is the Box–Cox transformation function, X is a random variable, λ is the shape parameter of the Box–Cox transformation, ζ is a power parameter and ε are assumed independent with mean 0 and variance σ2.If the distribution of the residuals appears skewed on the untransformed scale, ML estimation can still be performed using the TBS approach. Observations and predictions are transformed so that residuals, obtained as the differences between the transformed observations and the transformed predictions, can be assumed normally distributed. The Box–Cox transformation Eq.  is a comY can be approximated from the variance of the transformed data h as stated in Eq. Structural model parameters estimated using the dTBS model will have exactly the same interpretation as if no transformation had been used, which is a major advantage of this approach. However, parameters related to the residual error model do not translate directly to the original untransformed scale. According to Taylor series expansion, the variance of the untransformed data Dynamic estimation of the new error model parameters λ and ζ needed to be addressed. Whereas no modification of the ML algorithm as implemented in NONMEM  is requiModifying the minimization criterion to reflect the likelihood of the data on the untransformed scale instead of the transformed scale enables quantitative comparison between transformations and thus dynamic estimation of λ –18. The Implementation of the dynamic estimation of λ was readily available in NONMEM VI  and was ν. The t-distribution approaches the normal distribution when ν tends towards infinity, and shows heavier and heavier tails as ν decreases. The likelihood of the data when assuming t-distributed residuals is displayed in Eq. ν was set to 3 to guarantee full definition of the distribution and the upper bound was set to 200 which was considered the ν for which the t-distribution comes back to a normal distribution. An example control file using the t-distribution can be found in Online Resource 4.LY is the likelihood of the data Y, Γ is the gamma function, ν is the degree of freedom, f is the model prediction, Var(Y) is the variance of Y given the model and X is a random variable.Instead of using transformations to obtain normally distributed residuals, one can change the distributional assumption itself. In this work we investigated the use of a Student’s t-distribution, which is a symmetric distribution defined by its degree of freedom The dTBS and t-distribution approaches were tested separately on 10 real data examples –31, whicIn the dTBS approach, the Box–Cox and power parameters were estimated simultaneously using both the FOCEI and SAEM methods. Estimation of the Box–Cox parameter alone  and estimation of the power parameter alone  were also investigated using the FOCEI method. For the t-distribution approach, the scedasticity model was kept identical to the original model and the degree of freedom was estimated simultaneously to all other model parameters using the Laplacian method with user-defined likelihood.2 distribution. The degree of freedom of this distribution was set to the difference in the total number of estimated model parameters between these two models. The new strategies were judged to significantly improve model fit if the absolute value of ΔOFV was greater than 3.84 for the t-distribution (1 degree of freedom) and greater than 5.99 for dTBS (2 degrees of freedom). Parameter estimates and if available their SEs obtained from the asymptotic covariance matrix were contrasted. Improvements in fit were also investigated based on plots of observations versus individual predictions, individual plots and visual predictive checks. The distribution and scedasticity of conditional weighted residuals (CWRES), normalized prediction errors (NPDE) and individual weighted residuals (IWRES) were analyzed. CWRES and NPDE are not provided by NONMEM when using user-supplied likelihood and were obtained by evaluation of the model and (transformed) data at the final parameter estimates. Further investigations regarding influential individuals and predictive properties were also undertaken. Changes in individual OFVs (OFVi) were investigated as influence diagnostics in order to detect whether most or a subset of individuals benefited from a given residual error model structure. Cross-validation techniques using 10 splits of the data  were used to assess the predictive performance of the dTBS approach.The impact of the new error models was assessed based on diagnostic tools commonly used in NLMEM. The likelihood ratio test (LRT) was used to assess whether the proposed approaches significantly improved model fit. The LRT was based on the difference in OFV (ΔOFV) between the new and the original error model, which was assumed to follow a χStochastic simulations and estimations (SSEs) were performed in order to investigate the estimation properties of the new error parameters in terms of bias, precision and type I error rate. The simulation model was a one-compartment disposition, first order absorption and elimination model displaying either an additive, a proportional or an additive on log scale error model. Population values used for simulation were a clearance (CL) of 10 l/h, a volume of distribution (V) of 100 l and an absorption constant (KA) of 1/h. The standard deviation (SD) of the IIV was set to 30 % for all three parameters. The RUV was set to 0.2 for the additive and additive on log models and to 20 % for the proportional model. The dataset comprised 400 observations from 50 patients from whom 8 PK samples were taken 0.25, 0.5, 1, 2, 5, 8, 12 and 24 h after administration of a single oral dose of 1000 mg. dTBS scenarios were run using both the FOCEI and SAEM estimation methods while t-distribution scenarios were run using the Laplace estimation method. All scenarios were investigated based on 500 SSE samples.All fits were performed using NONMEM 7.2 and 7.3  aided byλ estimates confirmed the direction of the skewness found using FOCEI but indicated a higher degree of skewness . Approximated power on the untransformed scale stayed similar between the two estimation methods. Estimating both dTBS parameters simultaneously was significantly better than estimating only one of them for all models except phenobarbital. ΔOFV were significant for 6 out of 10 models when only the Box–Cox parameter or the power parameter were estimated. Only two examples (cladribine and cyclophosphamide/metabolite) displayed a worse model fit than with the original model when estimating a single power parameter, which was related to the fact that they were originally modelled with combined error models. Estimates of λ obtained using a fixed additive error model on the transformed scale differed from those obtained using dTBS. However, the direction of the estimated skewness stayed identical except for moxonidine PK and prazosin, whose estimated λ values indicated left-skewness using dTBS but right-skewness using the Box–Cox alone. The estimated power ζ also differed depending on whether it was estimated alone or together with λ. For most models, these changes however translated into similar scedasticity, as evidenced by small differences between approximated powers on the untransformed scale when using the dTBS, Box–Cox and power error models (Online Resource 5). These results confirmed that only the combined approach could correct simultaneously for skewness and scedasticity and thus the Box–Cox or power error models alone were not further investigated in this work.Estimating the Box–Cox and power parameters simultaneously led to significant ΔOFV in comparison to the original model for all investigated datasets. ΔOFV were large, ranging from −243 for the moxonidine PK example to −7 for the phenobarbital example Fig. . The estEstimates of non-residual error model parameters and related precision using the dTBS approach differed from those obtained using the original models in a number of cases. Table Changes in plots of observations versus individual predictions, individual plots and visual predictive checks were typically minor (data not shown). Residual distributions of CWRES, NPDE and IWRES showed some improvement for examples with high ΔOFV such as moxonidine PK, ethambutol and prazosin Fig.  but littν values spanned the entire range of possible ν values (from ν = 3 to 200) with point estimates between 3 and 9 for significantly improved models  often led to minimization problems and a failure of the covariance step, and this regardless of which distribution was used. In the cladribine, ethambutol and paclitaxel examples, ν stayed around any given initial guesses but changes in OFV were nevertheless observed when fixing ν to different values. Models for which estimation of ν was not possible will not be discussed here.Using a t-distribution with estimated degrees of freedom led to significant improvement in ΔOFV for five out of the seven models for which the estimation of the degree of freedom was successful. The cyclophosphamide/metabolite and phenobarbital examples did not benefit from t-distributed residuals Fig. ; Table 2As with the dTBS approach, physiologically plausible changes in estimates of non-residual error model parameters using the t-distribution approach were observed Table . Individλ estimates were unbiased with the additive on log error model error model but showed downward bias of 0.13 and 0.26 for the additive and proportional error models. Using SAEM instead of FOCEI removed the bias on λ for the proportional error model. Estimates of δ (ζ was reparameterized in the simulation exercise) were unbiased even in the presence of bias in λ. The SEs of dTBS parameters were small (below 0.25) for the proportional and additive on log models. Precision on λ was poor (SE = 0.73) for the additive model. Type I error was controlled at the investigated dataset size for the additive and additive on log error models when using FOCEI and for the proportional error model when using SAEM. Other model parameter estimates and related precision were similar whether dTBS parameters were estimated or fixed to their true values.Simulated additive, proportional and additive on log error models could be re-estimated using dTBS Table . λ estimAdditive, proportional and additive on log scale error models simulated under the normality assumption could be re-estimated using the t-distribution. The estimates of the degrees of freedom tended towards the given upper bound of 200. Type I error was close to 0 % for all simulated error models.Implementation of both the dTBS and the t-distribution approaches in NONMEM was successful apart from stability issues related to the use of the Laplacian method with some of the investigated models. The additional error parameters could be estimated using ML and OFV could be compared to select the most appropriate model. The new error models improved model fit for the investigated real data examples.Significant OFV drops were observed for all models when allowing for skewness in the residual error. OFV was expected to be sensitive to changes in the residual error, and power to detect such changes is expected to be high as all observations contribute to the determination of the residual error model.λ indicated some degree of skewness in the distribution of the residuals for all models. Absence of skewness could not be excluded for the phenobarbital and cladribine examples, for which asymptotic 95 % confidence intervals on λ included the reference value of 1. The estimated shape parameter indicated right-skewed residuals  on the untransformed scale for 7 out of 10 models. This is in line with the type of data used here, where the presence of left-censoring as a result of the impossibility to observe negative endpoint values often leads to right-skewness of the residuals. Two PK examples with rich sampling showed left-skewness (moxonidine PK and prazosin) possibly as a consequence of absorption model misspecifications. Box–Cox estimates for variables which were simultaneously modeled (ACTH/cortisol and cyclophosphamide/metabolite) stayed similar, which was not unexpected since both profiles and assays were homogenous in the studied cases.Point estimates of λ differed greatly depending on whether the power parameter ζ was estimated or fixed to 0 as in the traditional TBS approach. This could be explained by the fact that in the latter case, λ determines not only the skewness but also the scedasticity, which is then equal to the power of (1 − λ). It appeared that estimating λ alone was correcting for scedasticity more than for skewness, which makes sense as scedasticity is expected to have a much higher impact on model fit than skewness. This was best illustrated in the paclitaxel example, originally modelled with a Box–Cox transformation of 0.2 corresponding to a scedasticity of 0.8 on the untransformed scale . Using dTBS, both the right-skewness and the lower than proportional scedasticity were confirmed but were free to take on slightly lower values . It follows that to correct for both skewness and scedasticity, one should use the full dTBS approach and not the Box–Cox transformation alone. Regarding the value of λ itself, skewness is most likely multifactorial and depends on a mixture of endpoint type , study design (inclusion/exclusion criteria), assay characteristics, and model misspecification. Identification and categorization of causes leading to the presence of skewed residuals by data and/or model types is not straightforward and as such it will be difficult to anticipate the likely value of λ in a given setting.The shape parameter The approximated power on the untransformed scale was estimated to be proportional (four models), close to additive (two models) or somewhere in between (three models). The ACTH/cortisol model showed the highest scedasticity, with an error approximately proportional to the square of the ACTH predictions, which may be explained by the dichotomous nature of this endpoint, with a cluster of values very close to 5 and the other above 15. There was no clear trend between original and dTBS scedasticity, with some models keeping their original scedasticity  and others differing. Phenobarbital was however the only model for which the additive error model was found to fit the data better than the original proportional model. This had been concluded previously  and is tAs already observed for individual parameter distributions , better Visualizing the impact of changes in other model parameter estimates in order to diagnose the RUV model did not prove more supportive than residual diagnostics, which was not unexpected since the impact of changes in the RUV model should be minor compared to changes in the structural model. However, estimating dTBS error parameters could lead to changes at all levels of NLMEM: estimates of fixed and random effects as well as related precision. Part of the difficulty in interpretation is due to the interaction between the different levels of variability in NLMEM.Limitations of commonly used goodness-of-fit diagnostics drew focus on the OFV as the main criterion to indicate improvement of the residual error model. To complement this criterion, additional investigations using influence diagnostics and predictive properties were conducted in this work. Changes in individual OFV were used to investigate the influence of individuals on dTBS parameters (Online Resource 6). The dTBS approach always benefitted the majority of individuals in a given dataset, with an average proportion of individuals improved of 64 % (range [51–100 %]) over the 10 models. The size of the overall OFV drop was related to the number of individuals who benefited from dTBS, the highest ΔOFVs being observed in examples for which dTBS was highly beneficial for many individuals. The proportion of individuals responsible for the significant part of the ΔOFV was 14 % on average. This may appear low, but it is important to note that the very nature of distributions such as the Box–Cox predisposes it to individual influence, as only a limited part of the distribution really deviates from a normal distribution. The superiority of the dTBS model when taking all individuals into account was confirmed by better predictive properties as assessed through cross-validation. The OFV sum over cross-validation datasets was lower with dTBS than with the original models for all examples except cladribine and pefloxacin, and dTBS parameter estimates were consistent between training datasets (data not shown). The two examples that showed worse predictive properties and inconsistent estimates  also displayed high SEs on dTBS parameters, which would discourage the use of the dTBS error model. To summarize, this indicated that accounting for deviations, even if they are small and localized, is beneficial on the group level, and it is known that a limited number of outliers can overwhelm ML estimation . The invν below 10. As with the dTBS approach, reasons to observe heavy tails in the distribution of the data are most likely multifactorial, and the anticipation of the value of ν in a given setting is difficult.The 10 investigated real data examples benefitted from various degrees of heavy tails. Examples with highest ΔOFV often had an estimated degree of freedom of 3, and all models showing a significant improvement had a Residual diagnostics faced the same limitations as with dTBS, namely the lack of specificity and the sensitivity to ε-shrinkage. Changes in residual plots were not always visible but in general more pronounced than with dTBS. This could be expected as the t-distribution allows more extreme residuals (and this more frequently) than the Box–Cox transformation. Changes in goodness-of-fit plots based on individual predictions were also not always straightforward to detect, but in some cases such as moxonidine PK an overall better agreement was seen at the cost of few outlying data points.Individual influence was also investigated for the t-distribution, even if it was not unexpected when using such distributions. The conveyed picture was similar to that observed with the dTBS approach. The average proportion of individuals improved when the t-distribution lead to a significant ΔOFV was 71 % (range [51–86 %]) over five models, with a proportion of individuals responsible for the significant part of the ΔOFV of 29 % on average. Predictive properties using cross-validation were not investigated for the t-distribution due to the instability of the investigated models with the Laplacian method.The incorporation of IIV in RUV, either as a continuous distribution  or a mixλ despite low SE led to a doubling of the type I error with the FOCEI method when an interaction between predictions and residuals was present. This was corrected when using the SAEM method, hinting towards limitations of the FOCEI method in the presence of scedasticity and high nonlinearity. Bias of −10 % on λ in the additive model did not lead to an increase in type I error, probably due to the high SE observed for this parameter. Part of this bias could be linked to the censoring of negative concentrations (around 1 % of simulated concentrations per dataset), which may have induced some right-skewness in the simulated data. The high uncertainty on λ could be linked to the relatively low variance used for this model, as SE on λ decreased to levels similar to those observed for the proportional and additive on log models when residual variance was increased (data not shown). Estimates and precision of parameters not related to the residual error were consistent across all error models in the simulated settings.The design investigated here presented rich sampling at the individual level but a moderate number of total observations as compared to the real data examples. The downward bias of −25 % in ν = 3 allows 14.5 % of the residuals to have an absolute value greater than 1.96, compared to 2.8 % with a dTBS distribution with λ = 2 and 5 % for the normal distribution, given a SD of 1 for all. Models with more extreme outliers may thus benefit from a t-distribution more than they do from dTBS even if these outliers are not symmetric, as was seen in the moxonidine PK and prazosin examples. Overall, both approaches have the advantage of being capable of handling potential outliers while avoiding subjective predefined exclusion criteria or case-by-case handling of outlying data points. It can also be noted that both approaches, in particular the t-distribution, address kurtosis and can thus correct both for peaked and/or heavy-tailed distributions. When using these approaches, one naturally needs to ensure the absence of trends in the estimated skewness or outlying data points to avoid any masking of potential model misspecification by the residual error model, particularly during model building. However, once a model is deemed as good as it can be, handling often inevitable remaining model misspecification through the use of one of the proposed approaches is more indicated than simply ignoring it. The two approaches could also be combined, allowing for both heavy tails and skewness. This would also permit to treat dTBS and the t-distribution as nested models and thus to select the most beneficial one based on truly comparable ΔOFV. This was done using the prazosin example (model code provided in Online Resource 7). In this example, no skewness was detected when estimating ν, λ and ζ simultaneously, confirming that the t-distribution was more beneficial. However, as for any component of a model, any added complexity always needs to be balanced with potential gains, which may be more limited for the residual error than for other components of the model.Interestingly, dTBS and t-distribution ΔOFV were often similar and real data examples truly benefitting from the two approaches were the same. This could at first seem counterintuitive as the two error models have conflicting assumptions regarding the presence of skewness. However, the dTBS and t-distribution approaches are similar in that they both allow some individual predictions to be further away from the observations. The difference lies in the balance (t-distribution) or the mismatch (dTBS) between the numbers of positive and negative high residuals, thus the presence or absence of skewness. One can easily imagine that if uni- or bilateral outlier observations are present, an approach that allows some type of outliers will be beneficial even if the symmetry is misspecified. Another difference between the two approaches lies in the number of outlying residuals they allow, and more generally where the mass of the residuals is expected to be. For example, a t-distribution with When to use the proposed approaches is naturally a relevant question. The choice between these approaches can be guided by the presence or absence of skewness in the residual distribution. If a final model is obtained through traditional model building, it is recommended to apply dTBS and/or t-distributions as a mean to improve the robustness of conclusions drawn from the model. However, these approaches could also be introduced earlier in the model building, when choices between error models are usually made and when diagnostics indicate deviations from standard residual error assumptions. If they appear beneficial, they should be retained. If possible, RUV parameters should not be fixed during model building to maintain flexibility with regards to changes in other, more important parts of the model.The dTBS and Student’s t-distribution approaches are two approaches capable of addressing non-normal residuals. The dTBS approach is able to adjust both skewness and scedasticity while the t-distribution allows for symmetric heavy tails in the residual distribution. Both approaches can be combined in a general and flexible framework which addresses the trial-and-error strategy usually employed for residual error model building. While getting the statistical model right is not a primary aim, it is believed that scrutiny towards residual error assumptions will enhance the quality of model-based analysis and any subsequent simulations.Supplementary material 1 (DOCX 37 kb)Supplementary material 2 (DOCX 16 kb)Supplementary material 3 (DOCX 15 kb)Supplementary material 4 (DOCX 17 kb)Supplementary material 5 (DOCX 24 kb)Supplementary material 6 (DOCX 238 kb)Supplementary material 7 (DOCX 17 kb)


Calculation results revealed that the stress–strain relation and failure characteristics of the three models vary between each other. The combination model without interface or with a strong interface presented continuous failure, while weak interface exhibited ‘cut off’ effect. Thus, conceptual models of bi-material model and bi-body model were established. Then numerical experiments of tri-axial compression were carried out for the two models. The relationships between stress evolution, failure zone and deformation rate fluctuations as well as the displacement of interface were detailed analyzed. Results show that two breakaway points of deformation rate actually demonstrate the starting and penetration of the main rupture, respectively. It is distinguishable due to the large fluctuation. The bi-material model shows general continuous failure while bi-body model shows ‘V’ type shear zone in weak body and failure in strong body near the interface due to the interface effect. With the increasing of confining pressure, the ‘cut off’ effect of weak interface is not obvious. These conclusions lay the theoretical foundation for further development of constitutive model for soft rock–coal combination body.Considering the structure effect of tunnel stability in western mining of China, three typical kinds of numerical model were respectively built as follows based on the strain softening constitutive model and linear elastic–perfectly plastic model for soft rock and interface: R–M, R–C Western mines in China are mainly located in Jurassic and Cretaceous weakly cemented soft rock strata. Due to the special diagenetic environment, the soft rocks present special characteristics of weak cementation, easy weathering and easy disturbance which cause the extremely unstable mechanical behavior. Therefore, roadways are usually excavated in relatively stable coal seam resulting in the special structure feature of weakly cemented soft rock–coal in surrounding rock. The roof, coal seam and floor constitute a composite bearing system. Dynamic disasters such as roof shock and weak impact induced by tunnel excavation and mining disturbance are actually a result of the unstable deformation of the whole mechanical system caused by the interaction of geological bodies with different mechanical properties  the composite structure contains contact interface with low bonding strength denoted as R–Cw–M.Let R, M and C represent soft rock, coal and contact interface, respectively. For different bonding state, the following models can be established: (1) the composite structure dose not contain contact interface denoted as R–M model; (2) the composite structure contains contact interface with high bonding strength denoted as R–CE and ν are respectively the elastic modulus and Poisson’s ratio of the hardest geologic body, Δnmin is the minimum element size of the contact area in normal direction. Obviously, the smaller the minimum element size, the higher the calculation stiffness of contact interface. The two different models are shown in Fig. Damage behaviors of the three models were compared based on different modeling approaches and interface parameters. The contact parameters for strong bonding and weak bonding were set as shown in Table s–M model and R–M model, the evolution law of stress and strain is very similar, and the peak stress is at the fundamental superposition. The stiffness of R–Cs–M at pre-peak stage is slightly lower than the R–M model, while the stress drop at the post-peak stage is slightly higher. However, the peak strength of R–Cw–M model was lower than that of above two models, and the shift is apparent, resulting in a greater strain. This shows that the strain softening behavior of the model is more serious.Figure s–M model. Due to the strong bonding, the model also exhibits continuous failure, but the length of the shear band is short, and the damage range of the rock is smaller compared to R–M model. In R–Cw–M model, two symmetrical shear zones starting from contact interface extend to the middle of coal body. However, they are unable to across the interface and extend to the rock due to the weak bonding strength. From the above results, it presents continuous failure behavior in R–M model and R–Cs–M model which can be defined as bi-material model, while damage is concentrated in weak media in R–Cw–M model which is regarded as bi-body model.Figure The three-dimensional cylinder with a diameter of 50 mm and height of 100 mm was established. The model was meshed uniformly into 20 elements in the radial direction and 40 elements in the axial direction, respectively. A confining pressure of 2 MPa was applied on the lateral circumference. Only axial motion was allowed on the loading face and other directions were constrained. The physico-mechanics parameters and the post-peak attenuation of soft rock and coal is set the same with section 3.1. The interface parameters were set as shown in Table −7 m/s. The servo control method is used in order to avoid the inertia effect caused by loading rate. The loading velocity of both models is continuously adjusted according to the value range of the maximal unbalanced force. This process would lead to stress fluctuation around its initial stage and the peak point. In order to monitor the failure characteristics, a group of watching points were set as follows: 16 points were evenly arranged at the interface to monitor the axial displacement  in R–Cs–M model appeared three times from the initial stress fluctuation to the residual stage, where the first and second jump are negative corresponding to the pre-peak stage and post-peak strain-softening stage, respectively. These sudden jumps are due to the failure of the coal at the two loading points, where rock mass is in the elastic stage, and release elastic strain energy to the coal body. The third fluctuation jump is positive and greater than the former two, and the corresponding loading step is at the end of the strain softening stage. This appears in the later stage of strain softening where the main rupture in coal body is extended to the rock, and deformation velocities of rock mass also shows negative fluctuation due to the main rupture of the integral model.The deformation velocities of the monitoring points present obvious fluctuation from pre-peak fluctuating stage to the post-peak residual stage, indicating that the models close to the interface zones are damaged violently. The abnormal jumps of deformation velocity exactly illustrate the approach of the main rupture. The velocity jump of monitoring points (a4 and a5) in R–Cw–M model were basically the same at the initial elastic loading stage while deviated in the late stage. The first fluctuation of monitoring point a4 appears before the stress fluctuation point at pre-peak stage and the negative fluctuation is not obvious, while a5 presents obvious negative jump. At the strain softening stage, a large positive jump appears in point a4, while the monitoring points a5, a6 and a7 produce a large negative fluctuation. This indicates that the zones near the contact surface are suffered severe damage. From the above results, the failure evolution processes in the two models are completely different although the stress evolutions show the same changing law. The jumps of deformation velocities can be regarded as the precursor information of failure and a sign of the main rupture perforation.The deformation velocity of monitoring points  in coal body.From the failure process, it presents general shear failure along a penetrating band from coal to rock in R–Cw–M model.However, these shear bands are unable to pass through the interface. Besides, stress state of the rock near the interface is changed and the strength is weakened. Thus, it presents local shear failure in X-shaped of coal body and general transverse shear failure along the zone nearby the interface in R–CThe displacement variations in the loading direction at the contact interface can well reflect the failure characteristic of coal–rock body which includes the failure information. Displacement evolutions of the interface can be obtained through 3D surface interpolation in MATLAB according to the axis displacement results of watching points showed in the Fig. s–M model. At the elastic stage, that is, before the step 7900, the displacement is distributed uniformly from the middle to the edge of the interface. When loading to the step 8200, the displacements from the middle to the edge are gradually reduced caused by the local shear band in the middle of the interface. However, the interface deformation remains symmetric. At the peak point (step 8400), the displacements become highly asymmetric due to the inhomogeneous failure. At load step 9000, the model is yielded asymmetric deformation and the axial deformation of certain elements appears negative fluctuation. Thereafter, the axial deformation of the interface presents asymmetric distribution. Owing to the further development and perforation of the failure bands, the differences of axial displacements are gradually increased. For instance, the maximum displacement differences at step 100000 and 120000 are 0.04 and 0.1 mm, respectively. Thus, the asymmetric distribution of the axial displacement and the negative fluctuation of the watching points also contain the failure information.Figure w–M model. When the model is loaded on the elastic stage, the axial displacements are distributed basically uniformly, and the maximum displacement difference is only 0.006 mm. The homogeneous degree of the displacement is reduced at step 16000. When loading to step 16200, the displacements are gradually increased from edge to inner with symmetric distribution. At the peak point (step 16600), the displacement differences on the interface are increased. The displacement of each monitoring point presents obviously asymmetric distribution owing to the shear bands.Figure Figure w–M model is higher than that of R–Cs–M model. Moreover, the axial deformation of the watching points b1, b2, b7, b8 and b9 which close to the end face remain small during the loading process due to the restriction effect at the end face.From the above analysis, this location is just the loading point where presents obvious shear band in coal body, so it can be used as the precursory information of the model rupture. The fluctuation of displacement in R–Cs–M model. There are two asymmetry shear zones under uni-axial compression, one is the main shear band, and the other is not obvious. The Shear zone is developed from the right-bottom side of the coal body and extended to the left-bottom of the rock mass. With the confining pressure increasing to 2 MPa, the distribution of shear bands are still differentiated clearly and the overall failure behavior is enhanced. Only one shear zone appears in the model when the confining pressure is increased to 4 MPa, and its width is further enlarged. The decreasing of penetrating area indicates that the strength of the combined model is improved. When the confining pressure is increased to 6 MPa, the shear bands present good continuous pattern, and the model shows overall shear failure and typical unstable characteristics of bi-material model. The shear bands become blur when the confining pressure is raised to 8 MPa, and a large area of plastic zone appeared in the combined model. The model presents local shear and whole plastic failure. From the failure evolution, the strength of combined model was enhanced due to the increasing of confining pressure, especially for the coal body. If the confining pressure is lower than 4 MPa, the model also presents overall failure characteristics, but the shear strain is not continuous in the vicinity of the interface. When the confining pressure exceeds 4 MPa, the “cut off” effect of the interface is weakened due to the high pressure, and failure is mainly depending on the strength of geologic bodies.Figure w–M model under different confining pressures. The failure pattern of combined model presents the same inverted “V” type with the increasing of confining pressures, but its width is increased. Besides, the shear plastic zone in the rock near the interface is gradually increasing. The shear zone is gradually extended to the middle part of interface under the lower confining pressure and connected together when the confining pressure is increased to 8 MPa. The combined model presents shear failure of coal body and the plastic failure of rock near the interface. The “cut off” effect of interface is not obviously weakened under high confining pressure which is different from the R–Cs–M model. The sub layer in the composite model does not present the overall failure characteristic.Figure For the combined model without consideration of interface effect or with strong bonding, it presents continuous failure along an shear band which is started form the weak geologic body and extended to the strong body. This model can be defined as bi-material model. The “cut off” effect of interface is weakened with the increasing of confining pressure.For the combined model with weak bonding, it presents partial failure in weak body along shear band with inverted “V” type, and this model can be defined as bi-body model. Displacements of the monitoring points on the interface appear obvious uneven distribution due to the localized deformation. The “cut off” effect of interface is not obvious under high confining pressure.The failure evolution of the composite model shows a good correspondence with the deformation rate of the rock mass near the interface, and failure information can be captured accordingly. The first jump point of the deformation rate demonstrates the initiation of the main rupture, and can be regarded as the precursor information of the failure. The second jump point represents the perforation of the main rupture. The amplitude of the sudden jump is violent in whole failure wave process, so it can be recognized.The failure characteristic of surrounding rock in underground engineering and roof and floor in mines should be analyzed based on the bearing capacity system of the combined surrounding rock and roof-coal-floor. Among them, the failure of each medium is not only depends on the self-strength, but also on the contact interface bonding of other surrounding media and stress state.According to the composite fabric feature of weakly cemented soft rock–coal, a calculating model for two-element combined model is established. Then the failure behavior and stress evolution considering different interface effects were detailed analyzed based on numerical simulation, the main findings are as follows:


We present a novel device that allows the user to measure the Young Modulus of a material at the opening of a 5 mm diameter needle. The device relies on a miniaturized cantilever spring mounted at the end of the needle and interrogated via Fabry-Pérot optical fiber interferometry. The probe is repetitively brought in and out of contact with the sample at the end of the needle by means of a steel cable that is controlled via a piezoelectric actuator located at the proximal end. We demonstrate the ability of our device to detect and quantify layers of varying stiffness during needle insertion in a gelatin phantom and to successfully locate tissue boundaries in bovine liver tissue embedded in gelatin. For example, in the classification of skin conditions (such as scars or burn wounds) and the following control of disease progression or healing, physicians in most cases prefer visual assessment and subjective scaling above quantitative mechanical information  nanoindentation  would clearly be multiple. By integrating an indenter at the tip of a needle one could not only quantify between layers of different stiffness, but also navigate to the target location and perform a minimally invasive measurement based on the tissue mechanical properties. An example of an r et al. . The indin situ. Thanks to the remote actuation of the sensor by a piezoelectric translator the size of the needle is limited to the dimensions of the indentation probe at the tip. The performance of our indenter is tested on an engineered layered sample as well as on biological tissue.Here, we demonstrate a ferrule-top indenter on the distal end of a rigid needle and we show its ability to quantify local mechanical properties of tissue The indenter relies on the working principle of bulkier ferrule-top instruments, which is here briefly discussed  similar to those that are commonly used to actuate the tip of surgical steerable needles , which is used to select a position for needle insertion. To reduce vibrations, the setup is built on a passive anti-vibration stage.d is the length of the cavity, λ is the central wavelength of the laser, φ0 is a constant phase shift that only depends on the geometry of the probe, and W0 and V are the midpoint interference signal ((Wmax + Wmin)/2) and the fringe visibility ((Wmax−Wmin)/(Wmax + Wmin)), respectively. One can recognize that a displacement of the mirror can be immediately identified from the output signal of the photodiode. In our setup, this principle is employed to assess the position of both the cantilever and the sensor . In order to linearize the amplitude response over the complete deflection range we modulated the wavelength of the laser around the central wavelength (λc) according to van Hoorn et al.  around This time dependent response contains a DC component, encoding for the movement of the reflective surface, and a component that oscillates at frequency Wdc) and the high frequency component (which we will denote with Wω) are now described by the first and second term of the Taylor expansion, respectively. It can be readily observed from Eq. Wdc and Wω are separated by a 90 deg phase shift. This particular relation allows one to linearize the output signal and apply phase unwrapping to obtain a continuous linear response for the displacement of the mirror (Dm): The low frequency component . In the first specimen a stiffness gradient was created by compiling layers (10 mm in height) with decreasing mass gelatin to water ratio, hence creating a sample with layers of decreasing stiffness from bottom to top. Starting from a layer of 15 % mass gelatin at the bottom, each following layer contained 2.5 % less mass gelatin, ultimately creating a specimen with 6 layers of decreasing stiffness: 15 %, 12.5 %, 10 %, 7.5 %, 5 % and 2.5 % mass gelatin. For each layer, the gelatin was dissolved in demineralised water at 60 ° C, poured in the container and kept at 4 ° C for 30 minutes to allow the layer to stiffen. After the final layer was poured, the sample was stored 4 ° C overnight and measured the next day.3) fixated in a gelatin solution. To create a base layer (20 mm in height), gelatin was dissolved at a 12 % mass to water ratio at 60 °C, poured in a container and stored overnight at 4 °C. Subsequently, the liver sample was placed on top of the first gelatin layer and a second solution of gelatin (12%) was poured over the sample until it was fully submerged. The gelatin solution was cooled down to 40 °C prior to pouring to prevent thermal damage of the tissue. After the container was filled with gelatin (± 20 mm above the sample), it was again stored overnight at 4 °C to ensure proper stiffening.The second specimen consisted of a square piece of bovine liver  was maximum 30 μm. The indentation depth (di) inside the sample, however, depends not solely on df but also on the displacement cantilever (dc). The indentation depth was continuously recorded during the measurement and is given by: Four needle insertions were placed in the layered specimen and six in the animal liver specimen. Stiffness data were recorded at seven depth: one at the surface and six at increasing depth, each position separated by 10 mm. At each point in depth 5 indentation curves were recorded at 3 different locations, for a total of 15 indentations per depth position. All the measurements were performed in air in order to best preserve the gelatin structure. For each depth level, the probe at the end of the needle was carefully lowered with the motorized linear stage until contact was found between the indenting tip of the ferrule-top probe and the sample, identified by backwards bending of the cantilever of a few tens of nanometers. Starting from this position, the indentation movement was generated by applying a ramp-shaped voltage profile to the piezoelectric translator. This movement was in turn translated through the needle shaft and resulted in an indentation stroke of the sensor. Prior to each measurement, the system was adjusted such that the stroke of the sensor (k) is known, the load (P) applied during the indentation is: If the spring constant of the cantilever  of the sphere can be determined from the final and maximum indentation depths  , A = πa2 is the area of the contact circle and ν is the Poisson ratio of the indented material. In our case ν = 0.5, as both gelatin and liver tissue were assumed to be incompressible (Humphrey Now, from a geometrical point of view, the radius of the circle of contact can be calculated from: Humphrey .The response of the ferrule-top probe to a ramp-like movement of the piezoelectric transducer as observed in one of our indentation stroke is reported in Fig. In Fig. Figure In the following section we discuss some of the limitations of our indenter in its current form.The design of the cantilever for this experiment was optimized to measure the stiffness of materials with Young Modulus between 1 kPa and 100 kPa. To cover the wide range of biological tissue stiffness, which varies over at least three orders of magnitude (McKee et al. A further obvious limitation of our needle indenter here is its large diameter. Work is under way to reduce the dimensions of all its components to embed the device in a 3 mm diameter needle.Another possible drawback is the risk that, during perforation, some debris of the sample enters the Fabry-Pérot cavity between the fiber and the cantilever. Although we have not observed any nuisance when indenting inside the liver specimen, one could circumvent this problem altogether by designing a membrane based sensor.Finally, for further research on biological samples, sterilization of the device may become necessary. We designed the device such that the sensitive part, which will not survive a repetitive sterilization procedure, can be disposed without discarding the main working elements of the indenter.We have successfully developed a cantilever based, all-optical indenter at the tip of a rigid needle. The indentation measurement is enabled by a sensor that probes the mechanical properties of the underlying specimen by indentation using a microsphere. The sensor is remotely actuated by a strain gauge controlled piezoelectric translator driving a microscopic cable and spring system. The movement of the sensor as well as the movement of the cantilever is interrogated by Fabry-Pérot interferometry. We have performed stiffness measurements at fixed depth positions during needle insertion in gelatin phantoms and animal liver specimens. The measurements showed that we are able to quantify a stiffness gradient in depth and that we can successfully identify stiffer layers in a uniform sample. Measurements in a gelatin embedded animal liver confirmed that we can localize the liver based on mechanical contrast. Moreover, as the needle protrudes further inside the liver tissue, a quantitative analysis of the liver can be made based on the mechanical properties alone. Despite some limitations, our needle may, on the long term, ultimately evolve into a minimally invasive tool for the analysis of the mechanical properties of tissues, with potential applications in needle navigation or tissue diagnostics.


The application of GRID (Gamma Ray Induced Doppler broadening) spectroscopy to the localization of foreign atoms in single crystals is demonstrated on erbium in YAP. By the investigation of the Doppler broadened secondary γ line for two crystalline directions, the Er was determined to be localized on the Y site. Conditions for the nuclear parameters of the impurity atoms used for the application of GRID spectroscopy are discussed. GRID (Gamma Ray Induced Doppler broadening) spectroscopy is based on the analysis of a Doppler broadened secondary γ line which is emitted from a nucleus highly excited due to neutron capture and recoiled after emission of a primary γ quantum. The Doppler broadened γ line contains information about the lifetime of the excited nuclear states as well as the stopping cross section of the recoiling nucleus in the solid [1.2]. The method has been mainly used in polycrystalline samples to determine the lifetime of nuclear levels and to investigate the interaction of low energy ions with atoms of solids ,4.If the recoiling nucleus is embedded in a single crystal its slowing down is non-isotropic. It depends on the surrounding of the recoiling atom and on the crystalline direction. Molecular dynamics (MD) simulations and experiments on single crystals have shown that the energy distribution of the Doppler broadened γ line depends on the orientation of the crystal in relation to the direction of observation –8. Conse3) is shown.In the present paper some conditions necessary for the application of GRID spectroscopy are discussed. As an example, a first test of GRID spectroscopy for lattice site localization of Er in yttrium-aluminium-perovskite  along the [001] and [201] directions. Pretests showed that the 1649 keV transition exhibits a Doppler broadening and that the 1913 keV level has a half-lifetime shorter than 70 fs. The parent 167Er has naturally an isotopic abundance percentage of Iiso = 20 % and a neutron capture cross section of σ = 700 b. However, due to the low probability of the chosen γ transition (5×10–3 per neutron capture), we had to take a host lattice where a high Erbium concentration can be incorporated. Therefore, we took the laser material yttrium aluminium perovskite  or to impurity atoms incorporated by ion implantation. for these thin layers, the layer density D is a more common quantity, and the measured γ intensity is proportional toThe n = 5×1022 cm–3 the effective cross section of the γ emission should be higher than 0.02 b when GAMS4 is used and can be reduced to 5×10–5 b for GAMS5 in future. In case of nuclei having transitions with higher effective cross sections σeff, its concentration n in the crystal could be reduced until the minimum intensity for the used spectrometer is reached.Taking into account that the maximum density of an element in crystals is about γ line.Nuclei suitable for the GRID spectroscopy should show γ cascades with a minimum intensity as given above. Additionally, the lifetime of the intermediate level should be in such an order that the recoiling nucleus interacts with the surrounding crystal and influences the structure of the Doppler broadened For getting a more precise idea about the influence of the lifetime on the Doppler line-profile, we carried out various MD simulations on different crystal lattices and elements. The results of these simulations shows that for the majority of lattice impurity combinations, the influence of the impurity location on the Doppler broadening is most pronounced, if the mean range of the recoiling nucleus is in the order of 2 Å to 3 Å. This mean range corresponds to the atomic bonding length and consequently to the distance to the next neighboring atoms where the recoiling nucleus is scattered.For mean ranges shorter than 2 Å, the majority of the recoiling nuclei decay before interacting with the next neighboring atoms and the lattice symmetry of the host crystal does not affect the Doppler line.For mean ranges larger than 3 Å, the stopping of the recoiling nucleus by the next but one neighboring atoms becomes more and more important. The interaction with these atoms causes a further slowing down and reduces the width of the Doppler broadened line. Characteristic structures due to the initial location of the recoiling atom are more and more wiped out .Seff,However, for a pre-selection of suitable nuclei, we looked for a simple approximation which takes into account only the nuclear parameters of the recoiling nucleus. We found that the product of the initial velocity of the recoiling atom and the half-lifetime of the intermediate level can be used, subsequently called effective mean range v0 is given by the energy Eγ1 of the primary γ transition, the mass m of the recoiling nucleus, and the light velocity [The initial velocity velocity .seff is independent of the used elements of the crystal and it can be calculated easily. For instance, seff is sufficiently close to the simulated mean range to be used as a criterion for the pre-selection.Compared to the mean ranges obtained from the MD simulations seff larger than 3 Å, the difference between the mean range from MD simulation and seff increases depending on the used crystal and the nucleus. A simple estimation is no longer possible.For 167Er from the GRID experiment are included [Taking into account the restrictions concerning the intensity of the γ cascade  and the included .In Seff of the nuclei before emitting the γ lines of 168Er fits to that required for the GRID experiment and, despite of its low probability, the effective intensity of the 1649 keV transition is one of the strongest which could be found.σeff = 4 b is found in the nuclear data sheets. This restricts the application of GRID to foreign atoms in solids to 2.5×1020 cm–3 at GAMS4 and to 6×1017 xm–3 At GAMS5. Especially for heavy nuclei, many γ cascades and lifetimes are not sufficiently known yet. This gives the chance, that the list of suitable nuclei for application of GRID on impurity atoms in crystals will be extended.Up to now, no suitable γ transition stronger than 20 cm–3. With the GAMS5 spectrometer, which is promised to be available in the near future, a minimum density of 6×1017 cm–3 will be possible.MD simulations and first experiments on Er in YAP confirm that GRID experiments can be used to localize foreign atoms in crystals. Due to the nuclear parameters and the experimental conditions, the method can be applied only to a very low number of impurity atoms. With the present high resolution γ spectrometers GAMS4 at ILL, the concentration of the impurities should be higher than 2.5×10


Current methods of determining the proportion of people who benefit from a preventive intervention and the years of life gained can underestimate the former and overestimate the latter. We describe how to overcome these errors, using two examples relating to the prevention of myocardial infarction (MI) and stroke, one using a specified polypill daily from age 50 and another reducing salt intake in the population. Standard life table analysis was used to calculate the person-years of life gained without an MI or stroke, based on estimates of the incidence of these disorders in England and Wales. The proportion of individuals who benefit was taken as everyone who would, without treatment, have an MI or stroke (holistic model), rather than limiting the benefit to the proportion calculated from the relative risk reduction (reductionist model), as is current practice. Under the holistic model, 33 % of people who take the polypill from age 50 benefit, gaining, on average, 8 years of life without an MI or stroke (19 % and 14 years under the reductionist model). Estimates for reducing salt intake by 6 g/day are 33 % and 2.8 years respectively under the holistic model (6 % and 16 years under the reductionist model). In the prevention of disorders such as stroke by reducing exposure to causal factors such as blood pressure, the use of a holistic model corrects the underestimation of the proportion of people who benefit and the overestimation of their years of life gained associated with current methods. In spite of many publications on the effects of interventions to prevent chronic diseases, there is no satisfactory method of accurately estimating and expressing the resulting health benefits. The benefits are often presented as the relative and absolute risk reductions, but these two measures can give contradictory impressions of the size of the benefit. For example, a preventive intervention that reduces the risk of a disease by 70 % confers an absolute risk reduction of only 0.7 % a year if the prevalence of the disease without treatment were 1 %. The absolute risk reduction takes account of the background incidence but estimates vary according to the place, time, and the time interval over which the risk reduction is considered , and for disorders that become more common with increasing age, the estimates will not be a simple multiple of the time interval.The difficulties can be overcome by using standard life table methods to estimate the person-years of life gained without the clinical events health interventions are designed to prevent . But thThe standard method of calculating these two measures of benefit, which is appropriate when the preventive effect benefits only a proportion of people who would, in the absence of intervention, have been affected, is to use the relative risk reduction to separate, into two groups, the number of people who would have had a clinical event that the intervention is designed to prevent: one that experiences all the benefit, and another that experiences no benefit. For example, if, in 1,000 people, ten would have a clinical event in the absence of treatment, and the preventive treatment reduces risk by 50 %, the benefit is taken to be limited to five of the ten, while the other five have no benefit at all. This model (which we refer to as the reductionist model) is sometimes appropriate, for example, with the use of folic acid supplements before and during early pregnancy to prevent a neural tube defect. In this example the only babies who benefit are those in whom the defect was prevented. Not all babies who would have had a neural tube defect in the absence of taking a folic acid supplement benefit; those who have such a defect in spite of taking supplements receive no benefit.The standard method that uses the reductionist model is, however, not appropriate for the prevention of a chronic disease, such as ischaemic heart disease, in which clinical events arise from the disease over time, and the preventive effect is expected to benefit everyone who would, in the absence of intervention, have been affected. In these circumstances the incidence of clinical events arising from the disease is reduced by reducing exposure to the causes of the disease. In expectation, the clinical events will be delayed in everyone who would have had an ischaemic heart disease event when not taking preventive treatment, some for short periods and others by longer. The benefit will not be restricted to those for whom the ischaemic heart disease event was completely prevented; it will also extend to those for whom the event was delayed. In our example above, in which ten people have a clinical event in the absence of treatment, in expectation, all ten would benefit by having their clinical event delayed as well as prevented altogether. This implies a different model, which we propose here and refer to as the holistic model. The total person-years of life gained is the same for both models, say 100; in the holistic model each person who benefits gains 10 years on average (100/10) but in the reductionist model it is 20 (100/5).We here use two examples to illustrate the application of the holistic model in determining health benefits: (1) the prevention of myocardial infarction and stroke through taking a combination of blood pressure lowering drugs and a statin (polypill), and (2) the prevention of these disorders through reducing daily salt intake.proportion; HBp) over their lifetime (up to age 99 or prior death), and among these (2) the average years of life gained without the disorder or disorders that the intervention is designed to prevent . At the end of each year of age a person could be: (1) alive without the specified disorder, or (2) alive or dead with the specified disorder, or (3) dead without the specified disorder. This takes into account so called “competing” causes of death. Over time, individuals can move from 1 to 2 or from 1 to 3, but not from 2 to 3, 2 to 1, nor 3 to 1. Separate sex specific life tables were constructed for people who do not receive the preventive intervention and for those who do.Standard life table methods were used to estimate two specified health benefits, namely (1) the proportion of individuals who adopt a preventive intervention who will directly benefit from the intervention  use of a daily four component polypill consisting of amlodipine 2.5 mg, losartan 25 mg, hydrochlorothiazide 12.5 mg, and simvastatin 20 mg taken from ages 50, 60, 70 or 80 and (2) daily salt intake reductions of 1.5, 3, 4.5 and 6.0 g. We used these two examples because their effects are well documented quantitatively, and because of their potential in preventing cardiovascular disease [Statistical analyses were performed using the R statistical package.p and HBag) using the holistic model, according to the age at which people start to take the polypill. The table also shows the relative and absolute risk reductions. The relative risk reduction is 56 % in people starting treatment at age 50, and the absolute annual risk reduction is 0.37 %. An estimated 33 % of people taking the preventive treatment benefit (HBp), and these gain, on average, 8.0 years of life without a myocardial infarction or stroke (HBag). The remaining 67 % do not benefit, because they die from another disorder before they would have had a myocardial infarction or stroke.Table Table p) and they gain, on average, 2.8 years without a myocardial infarction or stroke (HBag).Table Table p) and, among these, the average years of life gained without the disorder in question  is a simple, informative way of expressing benefits in preventive medicine. Our analysis shows the importance of determining whether a holistic or reductionist model is used to calculate these estimates.Specifying both the percentage of people who benefit from a health intervention  is used to identify people for preventive treatment . Giving Regardless of whether, in a particular context, the reductionist or holistic model is appropriate, the two specified measures of health benefit overcome limitations associated with the use of relative and absolute risk reduction, but the latter are still needed to calculate the two specified measures of health benefit. Our estimate of the benefit is robust for two reasons. First the estimates of relative risk reduction come from the results of large cohort studies and many randomized trials that show considerable consistency between studies. Second, sensitivity analyses showed that estimation of the specified health benefits were robust to small changes in the estimates of relative risk reduction, with an approximate proportional relationship between relative risk reduction and years of life gained without a myocardial infarction or stroke. So, for example, a 5 % change in the relative risk reduction would result in about a 5 % change in years of life gained. Sensitivity analyses also showed that changes in the incidences of the disorders in question affect the percentage of people who benefit from preventive interventions to an approximately proportionate extent, so that, for example, doubling the incidence in our examples increases the proportion of people who benefit from 33 to 50 %, or from 1:2 to 2:2. However, among those who benefit, the gain in life without the specified disorders remains similar.Sometimes the benefit from a health intervention is expressed as the number needed to treat (NNT), which is the inverse of the absolute risk reduction. The NNT defined in this way is valid under the reductionist model, but not under the holistic model. The benefit from a health intervention is also sometimes expressed as the years of life gained divided by the number of people who adopt the preventive intervention. This is misleading, because some people who adopt the intervention cannot possibly benefit, for example, a person who takes a statin and dies in a road traffic accident a month later or someone who simply stops treatment. Instead of estimating the benefit to everyone adopting the intervention, it is more informative to separately estimate the proportion of people who will benefit, and among them estimate the average years of life gained without a clinical event the treatment prevents.If the age-specific incidence rate of serious adverse effects were known, these could be included in the life table analysis together with the incidence of myocardial infarction or stroke. The benefit is then the avoidance of all these outcomes rather than preventing a myocardial infarction or stroke only. In our examples, the issue is minor, because there is strong evidence that salt reduction and the components of the polypill are almost free from serious adverse effects, with the exception of the rare occurrence of statin induced rhabdomyolysis. If this were included as a hazard, neither the percentage of people who benefit nor the years of life gained would differ at the level of precision used here, because of the rarity of the adverse reaction. Current estimates suggest that statin therapy may increase the risk of clinical diabetes by about 9 % . Our metIn this paper we consider years of life gained without an incident myocardial infarction or stroke. The same method of analysis as that described here could be applied to the prevention of death from these disorders, in which case the proportion of people benefitting would be less as not everyone who has a myocardial infarction or stroke will die from these disorders, but the years of life gained would be greater due to the inclusion of years of life after a first clinical event, as well as years gained before such an event. We selected myocardial infarction and stroke since they are “hard” end points for which estimates of incidence are available. Had, for example, angina been included, the benefits would have been greater.The approach we propose, which is based on using standard life-table methods could, to advantage, be readily adopted, relying on estimates of relative and absolute risk reductions and data on cause-specific mortality from national vital statistics. The calculations are straightforward. Life-table methods are often used in economic cost-benefit analyses, but less so in papers that assess only health benefits.In summary, the health benefits of preventive interventions are usefully presented in terms of the proportion of people receiving an intervention who benefit from it and their average years of life gained. These two measures overcome the apparent contradictory impressions arising from reporting estimates of the absolute and relative risk reduction. In the prevention of chronic disease, where the biological actions of an intervention exhibit continuous effects, the two measures of health benefit, calculated using the holistic model, provide a simple and accurate summary of the impact of the intervention for individuals and for populations as a whole.


This study deals with addictive acts that exhibit a stable pattern not intervening with the normal routine of daily life. Nevertheless, in the long term such behaviour may result in health damage. Alcohol consumption is an example of such addictive habit. The aim is to describe the process of addiction as a dynamical system in the way this is done in the natural and technological sciences. The dynamics of the addictive behaviour is described by a mathematical model consisting of two coupled difference equations. They determine the change in time of two state variables, craving and self-control. The model equations contain terms that represent external forces such as societal rules, peer influences and cues. The latter are formulated as events that are Poisson distributed in time. With the model it is shown how a person can get addicted when changing lifestyle. Although craving is the dominant variable in the process of addiction, the moment of getting dependent is clearly marked by a switch in a variable that fits the definition of addiction vulnerability in the literature. Furthermore, the way chance affects a therapeutic addiction intervention is analysed by carrying out a Monte Carlo simulation. Essential in the dynamical model is a nonlinear component which determines the configuration of the two stable states of the system: being dependent or not dependent. Under identical external conditions both may be stable (hysteresis). With the dynamical systems approach possible switches between the two states are explored (repeated relapses). C that ranges from 0 to 1. It arises as a result of dopamine activity, which in turn is switched on by other processes in the brain. In  the quantity V is a linear function of C—S—E  there is no effect S(U0) = 0. The variable U only takes positive values, while S may be negative. The way the variables A and C may affect S can be incorporated directly in the model because of the one to one mapping S = S(U). It is understood , which equals 80 alcoholic beverages. The value of b can be derived by assuming that half the maximum consumption A = q/2 will result in half the maximum craving in the equilibrium state C = 1/2, it then follows that b = 2d/q = 0.5. The body must be able to restore self-control resource at a time scale that is smaller than that of craving fluctuations, or else self-control would very frequently be completely depleted even in healthy individuals: we take p = 2d = 0.4. Furthermore, we set the maximum capacity of self-control resource at S+ = 0.5. The last two terms of h/2 = kq/2 = pS+/2, so h = 0.2 and k = 0.25. E within the interval . There are two stable branches. A structure with two coexisting stable equilibria for a range of values of the parameter is also found in [The system of difference eqs  and 3)  3) with found in –22. TherWhen trying to apply the dynamical systems approach to the process of addiction in real life, it becomes clear that chance plays an important role. In particular cues  may leadE acquiring a sufficiently large positive value at the start, say E = 1, which then gradually decreases. In such a setting events may occur that trigger acting out addictive behaviours. These triggering events may be the presence of cues, such as social exposure or a mere opportunity of exerting addictive actions [R is a random nonnegative integer that corresponds to the number of cues encountered in a week. As cues come from many unrelated sources, it is reasonable to assume that R(λ(t)) constitutes a Poisson process with time dependent expected intensity λ. We will further assume that with each cue event the variable A increases with q/7 (one-seventh of the maximum consumption per week). It implies that f(R(λ(t));q) is not allowed to exceed the value q(1—V); otherwise the maximum q for one week would be exceeded. If that were the case, then consumption would be at its maximum, A = q. In the supporting information, E and λ become for the current case time dependent: E and λ, respectively, decrease and increase in time. The system can therefore be written asdλ and dE denote the change of λ and E respectively. b as reflecting ‘cue sensitivity’. To gain insight into the behaviour of these equations, we carry out a Monte Carlo simulation. In E (new customs), and cue intensities λ. A) fluctuates randomly in accordance with the random presence of cues, and covaries strongly with craving C. It is seen that when E decreases (as a function of time), C fluctuates at first considerably, but on average remains moderate. At a point were E is small enough however, C jumps to a very stable high level corresponding to a constant craving, and the system settles in the addicted state. Interestingly, it may be noted that from the level of craving C alone it cannot be concluded whether there is a switch to alcohol dependence at some time t. The addiction vulnerability V appears to be a better indicator for that purpose. A new lifestyle with external influences, bringing about activities that are potentially addictive, does not necessarily lead to a full addiction (V = 1). The stationary end values of E and λ determine the outcome.We consider the situation that an individual becomes a member of a community where customs exist that may lead to addiction: adolescents for example, at the brink of the legal drinking age, or adults who enter a new peer group or start a new living in a different culture. This may be mathematically expressed by the parameter  actions . To inclλ(t));q),where R , C(0)=0,aS(t+1)=In a stationary environment with a fixed rate of Poisson distributed cues persons may exhibit a volatile addiction vulnerability. This may lead to repeated relapses triggered by a locally higher intensity of cues . A time S+ and the cue parameter λ. Furthermore, the environmental effect E has to be taken into consideration. Let us set these parameters at valuesThe design of a recovery treatment should start with the definition of an acceptable future lifestyle of an individual after treatment. This lifestyle must correspond with a low addiction vulnerability and therefore requires acceptable values for the self-control parameter C = 0) and maintains high levels of self-control resource; see The other parameters of Eqs –4) rema rema4) rpS+ for the self-control S must be increased and the effect of cues should be decreased. The restoring force can be increased by either increasing the resilience parameter p, or the maximum self-control resource capacity S+, Here we concentrate on an intervention that accomplishes an increase in resilience, e.g., by way of restructuring cognitions in cognitive behaviour therapy. The cue induced effect can be reduced for instance by avoiding environments with high levels of cues associated with the addictive behaviour. It is assumed that during the treatment the self-control restoring force is doubled as a result of therapy, and that the possible effect of cues is halved:We consider the design of a therapeutic intervention that lasts for 7 weeks and study the chance of a success. During treatment the restoring force With Monte Carlo simulation the effect of the treatment is analysed. Success/failure was measured by the value  of the vulnerability at 100 weeks after the start of the treatment. The success rate of 50 interventions is about 70%.For the study of processes in various disciplines, the dynamical systems approach has turned out to be a valuable tool. We explored its applicability in the analysis of lifestyles with potentially addictive behaviour such as a high alcohol consumption. Various authors have presented dynamical systems models for different aspects of the addiction process, including linear systems of differential equations , 25, disThe model that we present focuses on the nonlinear dynamics of several interacting psychological and behavioural variables that have been deemed important concepts in theories of addiction. The nonlinearity in the systems explains various phenomena in addiction such as the presence of discrete states in which the system persists unless it is critically triggered. For example, many people experience difficulties in moderating themselves in acting out an addictive behaviour. They either stay abstinent, or indulge. The abstinence state, although fixed, can become highly unstable—one episode of giving in may set the one off to turn to the other fixed state, the stable drinking state. Our model was inspired by nonlinear systems theory that typically display this type of behaviour. This idea to relate stable and unstable steady states in dynamical systems was previously proposed in . Their mb. The value of b was derived by assuming that the individual will be acting out at half maximum  at craving equilibrium state C = 1/2. For different individuals the parameter may differ in value, resulting in different acting out  levels at this equilibrium craving state. The model predicts that this relationship depends on vulnerability V through (4), and hence depend on environmental or social pressure. How these parameters relate to personality axes [By adding the effect of cues to the model in the form of a stochastic input, the dynamics of the system shows the uncertainty one also meets in daily life of persons who are at risk of getting addicted. The analysis of such a system requires many runs to assess the probability of possible outcomes given some initial state. We simulated the process when a person enters a new life stage with the risk of addiction. With the Monte Carlo method we also considered the case of an initial state with a person being addicted. It is directly followed by a phase in which self-control is stimulated and cues are brought down in a way comparable with a therapeutic intervention. The outcome of the treatment turned out to depend on chance: the intervention was effective in approximately 70% of the 50 cases. This chance is determined by the specific effectiveness of the intervention due to an increase of the psychological resilience and the decrease of the number of cues. Another factor that determines the intervention’s chance of success is self-control capacity of the individual, which was not addressed in the above simulations because it seems likely that this capacity can only be changed over much larger time scales (years). Individual differences in sensitivity to cue elicited craving have been related to major personality axes like the behavioural activation system (BAS), introversion and neuroticism . How theity axes  remains S1 Program(XLSX)Click here for additional data file.


Anterior talofibular ligament (ATFL) is considered as the weakest ankle ligament that is most prone to injuries. Ultrasound imaging with its portable, non-invasive and non-ionizing radiation nature is increasingly being used for ATFL diagnosis. However, diagnosis of ATFL injuries requires its segmentation from ultrasound images that is a challenging task due to the existence of homogeneous intensity regions, homogeneous textures and low contrast regions in ultrasound images. To address these issues, this research has developed an efficient ATFL segmentation framework that would contribute to accurate and efficient diagnosis of ATFL injuries for clinical evaluation.The developed framework comprises of five computational steps to segment the ATFL ligament region. Initially, region of interest is selected from the original image, which is followed by the adaptive histogram equalization to enhance the contrast level of the ultrasound image. The enhanced contrast image is further optimized by the particle swarm optimization algorithm. Thereafter, the optimized image is processed by the Chan–Vese method to extract the ATFL region through curve evolution; then the resultant image smoothed by morphological operation. The algorithm is tested on 25 subjects’ datasets and the corresponding performance metrics are evaluated to demonstrate its clinical applicability.The performance of the developed framework is evaluated based on various measurement metrics. It was found that estimated computational performance of the developed framework is 12 times faster than existing Chan–Vese method. Furthermore, the developed framework yielded the average sensitivity of 98.3 %, specificity of 96.6 % and accuracy of 96.8 % as compared to the manual segmentation. In addition, the obtained distance using Hausdorff is 14.2 pixels and similarity index by Jaccard is 91 %, which are indicating the enhanced performance whilst segmented area of ATFL region obtained from five normal , five tear  and five thickened  subjects’ datasets show good performance of developed framework to be used in clinical practices.On the basis of obtained results, the developed framework is computationally more efficient and more accurate with lowest rate of coefficient of variation (less than 5 %) that indicates the highest clinical significance of this research in the assessment of ATFL injuries. Ankle ligaments are the most common human joints affected by sports injuries, accidents, high ankle sprains and inflammation . GeneralResearch –12 has rDue to the challenges associated with 2D ultrasound images of ATFL ligament, direct interpretation and visualization of injuries associated with injured ATFL is not recommended as it may lead to wrong diagnosis. This warrants the requirement of computational methods that are capable of delineating ATFL region from 2D ultrasound images , 24. HowIn order to deal with the challenges associated with 2D ultrasound images, several computational approaches were developed to segment different tissues using region based, edge based, thresholding based, wavelet based, pattern or texture classification based, atlas and deformable based methods and non-parametric probabilistic model with shape driven based methods –28. AlthIn order to achieve the main objectives as stated above, a new segmentation framework for ATFL segmentation from 2D ultrasound images is developed in this research that includes five (5) step processes comprising of region of interest (ROI) initialization, adaptive histogram equalization (AHE) , 31, parThe descriptive illustration with detailed approach is discussed in the next section followed by its capability to segment ATFL region from 2D ultrasound images. In the next sections, performance metrics are measured to demonstrate the performance of the developed framework followed by the results and discussion that shows the impact of the developed framework for clinical evaluation of ATFL injuries.In this study, a video  of the ATFL region is acquired using linear probe (5–13 MHz) of iU22 Philips colour ultrasound machine from 25 subjects  with the age ranges from 18–60 (mean 34) years. Institutional medical ethics approval was obtained prior to the study. Subjects were informed about the study protocol and consent form is obtained from all the subjects. A total of 1250 slices are extracted in the video acquired from 25 subjects, each video contains 75 slices representing ultrasound images of ATFL region. The involved three experts have the experience of 18 years, 9 years and 5 years in ultrasound imaging are asked to visually inspect 75 slices of each dataset and assign a grade  to each slices based on the quality according to the method proposed earlier . In mostAs discussed in introduction section of this paper, this research is mainly focuses on three major challenges such as homogeneous intensity, homogeneous texture and low contrast regions that create the difficulties in ATFL interpretation and extraction from ultrasound images. To overcome these problems, a framework is developed to segment the ATFL region from ultrasound images as illustrated in Fig. As presented in Fig. In this research, ROI is initialized prior to post-processing due to the followings reasons: (1) simplifying the input image, (2) reducing the occurrences of errors during ATFL extraction and, 3) better computational performance. For the selection of ROI, variability of ATFL location in ultrasound images is considered and expert radiologist inspected ATFL region in several slices. In this framework, ROI is selected by selecting a defined region of interest that includes presence of ATFL within this region and an automated cropping of selected region is made. An example of ROI selection where ROI initialized region is indicated by green colour rectangle on input image is shown in Fig.  better cContrast enhancement methods such as histogram equalization are widely used in image processing to improve the interpretation capability of the resultant image. However, traditional histogram equalization does not performing well for variable contrast images . In suchx is an input image, δ is the Kronecker delta function. g indicates an image with grey levels. The parameter fw indicates the rectangular kernel with m rows and n columns, and w represents the width of the window. In this research, size of the kernel is considered as equal to the size of input image to cover all the objects. The ROI initialized image shown in Fig. Mathematically, AHE can be described in Eqs. xi(t) and velocity vi(t) are determined and update based on the Eqs. w represents the inertia weight that provides the storage to resultant velocities, c1 and c2 are acceleration constants that are used to speed-up the image particles, u represents a random number range from 0 to 1. The t indicates the time unit. The xi(t) and vi(t) represents the current position and velocity of a particle i at time t. The term yi(t) indicates the personal best position and i.PSO algorithm optimizes a problem iteratively to find out the candidate solution by moving particles around in search space. Each particle has a specific position and velocity. The corresponding position PSO is a problem-independent algorithm, which means that little specific knowledge relevant to given problem is required. What we have known is just the fitness evaluation for each solution. This advantage makes PSO more robust than many other search algorithms. The main benefits of the PSO algorithm as compared to existing genetic algorithm and other heuristic algorithms in image segmentation are as follows: (1) The PSO algorithm is easy to implement and only few parameters have to be adjusted, (2) unlike the genetic algorithm, the PSO algorithm has no evolution operators such as crossover and mutation, which can be the main cause of computational complexity in some cases, (3) in PSO, only global best particle gives out information to the other image particles rather than whole population that makes it more robust, (4) unlike other heuristic algorithms, PSO has the flexibility to control the balance between global and local exploration of the search space.Basically, the PSO algorithm is a multilevel thresholding approach that optimizes the energy level of the input image and helps in efficient curve evolution to extract the desired ATFL ligament region. In image segmentation, the use of PSO method is quite simple and effective, which improves the real-time performance of the image segmentation to a large extent. This research performs the segmentation on ATFL ligament ultrasound images based on the PSO algorithm to optimise the energy level of the image as illustrated in Fig. c1, c2 are constants and φ is an undefined curve. EFTrepresents the external energy function of curve C. H(φ) is heaviside function and δ(φ) is the Dirac one dimensional function. L is the image gradient and μ is a fixed parameter range less than 1. The image Im indicates the input image and the Im depicts the particular image coordinate. Here ∇ stands for the gradient operator. In Eq. ECV depicted the Chan–Vese function.In this research, curve evolution is performed by the Chan–Vese method. The Chan–Vese method is the association of the Mumford–Shah mathematical model, level set method and curve evolution for energy minimization, accurate initialization and curve evolution during segmentation progression, respectively. The entire processing of the Chan–Vese method is described in Eq. Basically, the Chan–Vese method is the extended version of the traditional active contour method , which uThe Chan–Vese method does not depend on the edge function for the termination of shrinking or expanding curve for a preferred object boundary. The Chan–Vese method detects object boundaries much clearer; in case of undefined boundary gradients and noisy image. Thus, the Chan–Vese method is applied on the optimized images (e.g. PSO outcomes) to provide more accurate segmentation results as described in the developed framework. For example, boundary extraction of ATFL is performed by the Chan–Vese method  with 800C is the close operator. A and B are the object sets of a binary image. E and D indicates the erosion and dilation, respectively. The close operation used two inputs such as, an image that need to be smoothed and a structuring element. However, this research used the disk structuring element to preserve the arbitrary shape of the object, which specifies a radius of 10 pixels so that the largest gap gets filled. For instance, during curve evolution the obtained segmented outcomes are not so accurate due to the asymmetrical boundaries and uncertain shape that leads to interpretation problem of the damaged tissues of ATFL as shown in left image of Fig. Morphological operations are used to restore and reconstruct the damaged parts of the extracted image. Out of numerous morphological operations, this research applied the close operation to produce smoother results see Fig. , which iFigure The developed framework was implemented on MATLAB , 54 runnThe reliability of above ground truths generation by different experts is estimated by the intra-observer variability among the experts. In order to measure the reliability of expert’s segmentation, measurement of true positive rate (TPR) among different experts is performed using Eq. In order to analyse the performance of the developed framework, computational time, sensitivity, specificity, accuracy, Hausdorff index, Jaccard index and segmented area metrics are explained in detail in the following sections :Computational time is the amount of time for which a central processing unit (CPU) was used for processing instructions of a computer program that can be measured in seconds .Sensitivity is the proportion of true positives that are correctly identified by a diagnostic test. It shows how good the test is at detecting a disease .7\documeSpecificity is the proportion of the true negatives correctly identified by a diagnostic test. It suggests how good the test is at identifying normal condition .8\documeAccuracy is the proportion of true results, either true positive or true negative, in a population. It measures the degree of accuracy of a diagnostic test on a condition .9\documeH presents the Hausdorff index. a and b are the points defined in sets A and B. ‖a − b‖ is indicating the underlying distance in tests.Hausdorff distance is a validation metrics used in medical image segmentation for shape matching. Hausdorff index determined the degree of similarity between two superimposed sets, which is defined in Eq. J depicts the Jaccard index, A indicates the region segmented by the developed framework and B is the region segmented by the experts.Jaccard index is a similarity measure that lies 0 to 1 as presented in Eq. The extracted desired and meaningful region from an input image is referred to as segmented area, which is determined by the calculation of number of pixels from the extracted region . In thisFor the visual interpretation of segmentation processing of the developed framework and the corresponding outcomes with four sample images is illustrated in Table In this section, performance of the developed framework is evaluated based on the estimation of computation time incurred using the Chan–Vese method and the developed framework at different number of iterations . The computational cost at different iterations is measured, which is illustrated in Table From Table For the computational time, the developed framework yields marked improvement over the Chan–Vese method as the computational time taken by the developed framework (28.9 s) is approximately 12 times lower than the Chan–Vese method (340.6 s) for 800 iterations that results in optimal solution and performs faster than the existing Chan–Vese method.The developed framework is tested for its performance whereby the obtained segmented ATFL results are compared with manually segmented ATFL from 2D ultrasound images by experts. Manual segmentation of ATFL from 2D ultrasound images were perform by three experts radiologist and the reliability of manual segmentation (considered as ground truth) is measured for all three experts. For the reliability, intra-observer variability among the experts is calculated as true positive rate of segmented area as discussed in material and method section of this paper. Therefore, the Table As shown in Table Table In this research, performance of the developed framework is not only be measured against ground truth segmentation, but also using performance metrics such as Hausdorff and Jaccard indexes that represents distance and similarity rate, which is compared with manually segmented ATFL results  datasets from each group of subjects are selected randomly. We have taken five normal subjects , five tear subjects  and five thickened subjects  datasets. First, the developed framework is applied to segment ATFL region from all the datasets and from the resulting segmented ATFL region, pixel area measurement is performed for all datasets  Tool, it would be able to assist the physician to diagnose ATFL disorders faster than the existing manual inspection methods by the clinicians.