The emergence of large, fine-grained mobility datasets offers significant opportunities for the development and application of new methodologies for transportation analysis. In this paper, the link between routing behaviour and traffic patterns in urban areas is examined, introducing a method to derive estimates of traffic patterns from a large collection of fine-grained routing data. Using this dataset, the interconnectivity between road network junctions is extracted in the form of a Markov chain. This representation encodes the probability of the successive usage of adjacent road junctions, encoding routes as flows between decision points rather than flows along road segments. This network of functional interactions is then integrated within a modified Markov chain Monte Carlo (MCMC) framework, adapted for the estimation of urban traffic patterns. As part of this approach, the data-derived links between major junctions influence the movement of directed random walks executed across the network to model origin-destination journeys. The simulation process yields estimates of traffic distribution across the road network. The paper presents an implementation of the modified MCMC approach for London, United Kingdom, building an MCMC model based on a dataset of nearly 700000 minicab routes. Validation of the approach clarifies how each element of the MCMC framework contributes to junction prediction performance, and finds promising results in relation to the estimation of junction choice and minicab traffic distribution. The paper concludes by summarising the potential for the development and extension of this approach to the wider urban modelling domain. The recent emergence of new, large mobility datasets represents a significant opportunity for transportation researchers and engineers alike. While transportation research has always built heavily on data, never before have transportation datasets been available at the spatial and temporal scale and granularity that they are today. As these datasets move towards tracking individual travellers in near real time, the need for the development of new methodologies for understanding and managing transportation systems becomes even more pressing.One area where new datasets offer significant promise is in the analysis of routing behaviour. The reduced cost and subsequent proliferation of GPS-equipped  devices has enabled the passive collection of large datasets describing the fine-scale routing behaviours of hundreds or thousands travellers, such as those using private vehicles , 2, minibetween locations. Large-scale routing datasets allow us to examine links between different parts of the road network, understanding how locations are interconnected and dependent on each other. Using this perspective, traffic along a route can be viewed as consisting of multiple constituent flows, each dependent on a set of past and future locations. This insight offers a number of opportunities for the understanding and estimation of traffic patterns under normal and disrupted conditions.Traffic patterns are conventionally analysed through the movement of vehicular traffic along a single stretch of road. The arrival of large-scale routing datasets, however, potentially enables a dissection of traffic patterns, allowing us to understand how traffic is moving In this paper, a method is introduced for the estimation of urban traffic patterns from location-to-location interconnectivity. Links between locations are constructed from large-scale routing data, which links together locations based on sequential usage. This interconnectivity of locations on the road network reflects the basis of how traffic flow is generated. The approach introduced in this paper makes use of these relationships, introducing a novel probabilistic model of mobility that simulates urban traffic patterns based on the structure of locational connectivity.state space, a representation of the states of a system. The likelihood of transition between states is assessed through the previously observed relationship between current and next possible states. The potential for a shift between two states is characterised with a transition probability, extracted from prior observations. The inclusion of multiple states leads to the construction of a Markov chain, a network link representation of inter-state connectivity. Once the chain is defined, the execution of repeated random walks across the Markov chain allow the generation of system-level distributions of system state changes. The distribution generated reflects the nature of the transition probabilities between states within the Markov chain. The MCMC approach has been used across a number of fields, including computational biology, social science and economics.At the heart of this approach is a Markov chain Monte Carlo (MCMC) model, modified for the purpose of traffic pattern prediction. Conventional MCMC is a domain-neutral statistical approach to the modelling and prediction of system behaviour. Predictions are constructed through modelling of probabilistic transitions between across The use of MCMC approaches within transportation and geographic research goes back some time, being used in a variety of applications. The approach has been used in developing trip matrix distributions , analysiThis paper introduces a new methodology for the application of MCMC in estimating traffic patterns within urban areas. The work derives transition probabilities for movement between important locations on the urban road network from large granular routing datasets, extracting the inherent interconnectivity between these locations. Across this Markov chain, multiple routes are then generated through the execution of random walks, leading to the production of traffic pattern estimations. In order to achieve the application of MCMC in this context, a number of amendments to the conventional approaches are incorporated. The aim of this paper will be to test whether the novel approach to MCMC is a useful framework for modelling route choice, and whether, in sum, modelled routes are reflective of wider traffic flow.The paper is laid out as follows. In the next section the modified MCMC approach for predicting urban traffic patterns is introduced, outlining the specification of the Markov chain and amendments to conventional MCMC methods to allow its application in traffic pattern prediction. The third section moves onto the application of the approach, detailing the routing datasets involved and approaches taken in its implementation in London, United Kingdom. Following this, the resulting from traffic modelling is validated against observed movement choice and traffic flow data. In the final section, in addition to summarising the findings, the potential future applications of this approach will be discussed.The generic Markov chain Monte Carlo (MCMC) approach describes the relationship between current and future system states. Within the context of estimating urban traffic patterns, aside from specifying the nature of these states and their connectivity, its application towards how traffic estimates are generated requires a number of important further considerations. To achieve this, a number conceptual advances to the conventional MCMC approach are outlined—first, addressing the nature of state space, then addressing how random walks proceed across this space. The implementation of the model outlined here, utilising a large dataset of observed route choices, is described in the next section. Elements of the model framework design outlined in this section will be validated later in this paper.The state space describes all of the states in which a system, modelled using MCMC, may exist. These states reflect the most important points within the represented systems, from which system transitions may occur. Therefore, in adapting this approach for generating estimates of traffic distributions, the state space should reflect the points in urban space that most strongly influence the traffic redistribution.In considering urban space, the clearest candidates are major road junctions. These are locations at which senses are heightened and route choices must be considered , and offThe calculation of transition probabilities between major junctions is derived from large-scale route choice data. Iterating through each route individually, the major junctions traversed during the route are recorded. Across the entire route dataset, the sum of traversals between each ordered pair of junctions is derived. Transition probabilities are finally calculated according to observed transitions involving other available alternatives, under given prior conditions.Conventional MCMC models predict transitions between current and future states, minimising the influence of prior context. Within route choice decision-making, however, this bipartite transition may not adequately reflect the momentum inherent in goal-directed travel. Earlier research indicates that there is a human preference for travel along direct and continuous routes , suggestimmediately prior state (e.g. the previous junction) with the current state in the specification of future state transition probabilities. The implementation of a prior state will capture the sense of directional continuity natural to traffic movement. While further prior states could be included at this stage, these would potentially over fit the model, reducing flexibility outside of predefined paths. The consideration of only current and the immediately prior state retains the indication of momentum while remaining flexible.The incorporation of momentum is achieved by including the nature of j, in determining the connectivity between states j and all possible future states kn, the prior state, i, is implemented too. The probability of transitioning between the current state, j, and any of the future possible states kn is adjusted from P(i|j) to P(k|(j|i). In i and current state j, is k2.A schematic demonstrating the incorporation of the prior state within the Markov chain is outlined in i and the current state j, the next state is determined according to a vector of transition probabilities Tp. A state is chosen and the walk progresses iteratively through the state-space until an exit condition is met. In this case, the random walk begins at a junction near to the origin and ends on reaching the junction nearest to the destination.This configuration is used as the basis of the construction of random walks across the Markov chain. Given the prior state Within the current configuration of the model, there is a risk that the random walk does not efficiently reach the trip destination. To account for this, the next amendment to the MCMC approach involves the introduction of a weighting towards the direction of the trip destination, used during the generation of random walks. Further to the practical requirements, this amendment also effectively describes elements of the human navigation process, specifically the documented intention to travel broadly in the direction of the trip destination , 15, 16.Tp) are multiplied by a vector of deviation probabilities, Td. This second vector describes the probability of selecting any given junction based on its deviation from the straight-line angle to the destination point. The exact derivation of these values for this case is detailed later. The probability, therefore, of selecting k now becomes:k is a potential future junction, n represents all potential future states, Pp represents the transition probability to that junction, and Pd represents the probability of converging towards that junction with respect to the direction of the destination.In introducing the destination weighting, the vector of transition probabilities . Given the limited points at which traversal can be made, it is assumed that available crossing points form an initial subgoal via which the routes are directed.Within the amended MCMC model, a subgoal routine is integrated whereby an initial target destination is set as the crossing point of a geographic feature intersecting origin and destination. The walk will initially navigate to the crossing point, and then, once that sub-goal is complete, onwards towards their destination. Crossing point selections are made probabilistically, based on the origin and destination of the walk, drawn from prior observations within the dataset. This probabilistic process is defined prior to the execution of the random walk across the Markov chain.The MCMC approach is implemented for the metropolitan region of London, United Kingdom. In this section, the datasets and specifications used in constructing the Markov chain and random walk elements of the MCMC model are defined. This implementation represents only one possible configuration of the MCMC model outlined in the last section. This configuration will be tested during model validation in the next section.The primary requirement for the specification of the Markov chain is a routing dataset describing the interconnections between junctions on the road network. For the London case study this is achieved through a large dataset of minicab GPS traces. Trace data was provided by Addison Lee Limited—the largest private hire minicab company in London—for three months between December 2010 and February 2011. In addition to the GPS data, trip logs were provided enabling identification of the origin and destination of the 690045 trips, undertaken by 2950 drivers, encompassed within the dataset. The Addison Lee business model means origin-destination trips are charged on a fixed rate, meaning minicab drivers are incentivised to minimise their journey times. The routes taken during the course of these journeys will be used to define the Markov chain.While minicab routes provide only a limited representation of the entire distribution of traffic within London, it is important to note that the main requirement of the dataset is in the specification of the interconnectivity between junction locations. A benefit of the scale of the dataset is that trips are observed across the whole of London. However, a sizeable majority—84%—of the journeys take place solely in inner and central London regions, with 95% of trips having either an origin or destination within inner or central London. While this still leaves over 110000 trips available for the definition of junction connectivity in outer London areas, these definitions will be based on fewer observations and so potentially more open to bias. Further discussion of these limitations will be outlined in later discussions.In constructing the Markov chain, the dataset is divided into a calibration and validation partitions according to an 80:20 split of randomly sorted routes. The calibration dataset—containing 552036 journeys—will be used for the specification of the Markov chain (described in detail later), with the validation dataset—consisting of 138009 routes—reserved for establishing the accuracy of the final MCMC estimates.State space is defined as the set of major junctions on the London road network. These definitions are drawn from the Ordnance Survey Integrated Transport Network (ITN) dataset, the most comprehensive GIS representation of the UK road network. The extraction of major junctions from this dataset requires two definitions.The first specification involves the definition of what a major junction encompasses. For London, these definitions follow the road network hierarchy specified by Transport for London and the UK Department of Transport. In this case, only junctions that intersect those roads defined by one of the top two classifications—‘Motorway’ and ‘A-Road’—will be defined as major junctions . ‘Motorways’ and ‘A Roads’ carry large volumes of urban traffic and, as such, intersections between these roads can be expected to be salient locations, significant in route decision-making.The second specification involves the geographic location of these features. A location is required for the angular deviation elements of the model outlined earlier. However, within the ITN dataset, major junctions are often made up of multiple road segments, offering no single location at which the junction exists. To reach a solution, first, all intersecting points between major roads are clustered together where found within a 250-metre radius of each other. The 250-metre buffer ensures that all points at even very large junctions are covered, while differentiating between closely distributed smaller junctions. Once these clusters are established, the centroid of all these points is calculated, defining the single location for that junction. This process yields 816 junction points across the entire London road network.Assessing observed route flow through this subset of junctions, the strong central London concentration of trips is demonstrated. In the central London areas of Knightsbridge, the South Bank, Soho and the City of London, an average of 4079 trips pass through each junction; outside of these regions the average falls to 365 trips. A maximum trip count of 15980 is observed at the Hyde Park Corner junction between Knightsbridge and Westminster. The increase in trips passing central London is matched, however, with an increase in the spatial density of junctions in these areas.The specification of interconnectivity between junctions is drawn from the routing patterns described within the minicab route dataset. Routes are analysed with respect to their movement across the junction network, and inter-junction connectivity calculated in terms movements via triplets—prior, current and future—of junctions. These connections are derived from the calibration dataset of 552036 routes, described earlier.i to junction j to k, the observation augments the probability of movement to all kn given prior and current junctions i and j. In other words, in a given situation where movement from junctions i to j to k is observed, the probability of this event occurring in future is increased, and the probability of transitions from i to j to all other kn are reduced.In specifying these probabilities, each path is inspected. Where the individual is observed traversing the network from junction The strength of connectivity between junctions is differentiated by time of day, with transition probabilities calculated separately for journeys taking place during the daytime (7am to 7pm) or evening (7pm to 7am) hours. This distinction aims to capture temporal deviations in movement patterns borne through congestion avoidance at certain times of the day.Once all inter-junction connections are constructed, a final phase of chain pruning is undertaken. During this phase all connections with a probability of lower than 0.025 are removed from the structure. This is to reduce the potential influence of erroneous connections persisting within the datasets, and increase the overall speed of route computation.The probability of selecting a junction that deviates from the direction of the destination is again derived from the route dataset. Assessing once more the connectivity between junctions during each journey, the angular deviation that the selection of a given junction represents, relative to the direction of the destination, is calculated.Running this process for all junction-to-junction selections across the entire dataset, one is able to derive the frequency distribution for junction selection by degree of deviation. A discrete probability distribution is simply derived from this data for each 0.9° shift, generating 200 categories for all absolute deviations up to 180°. This specification does not therefore account for U-turning or backtracking, assuming a continuous direction of travel towards the destination. The derived distribution, shown in The final set of estimations is extracted with respect to the traversal of crossing points over waterways in London. London has two main waterways with limited points of traversal—the River Thames  and Lea Valley (running north to south in east London). Referring once again to the route dataset, only trips that traverse either of the two rivers are extracted. This subset of cross-river journeys is then aggregated by origin and destination locations, defined at postal region granularity, for extraction of region-to-region bridge choice probability. By breaking down trips origin and destination locations, a link is made between geography of the route and the probability of selecting each possible river crossing.Examining each journey between an origin-destination pair, the popularity of each bridge, in linking the two regions, is ascertained, and a probability of selecting any specific crossing point derived. These estimates are again calculated separately for both day (7am to 7pm) and evening (7pm to 7am) hours. So, for example, if moving from region W1 to SE16, there exists a 0.35 probability of taking Westminster Bridge, a 0.25 chance of taking London Bridge and a 0.183 chance of selecting Blackfriars Bridge.Extract the journey origin and destination point locations on the road network.Identify a start junction from where to begin the journey. Specified as the nearest junction to the origin location falling within a maximum 45° deviation from the straight-line angle between origin and destination locations. The deviation constraint ensures initial choices are directed towards the eventual target.Identify a final junction. Identified as the nearest junction to the destination coordinate.Establish whether start and final junctions are on separate riverbanks. If so, identify a crossing point through probabilistic selection (outlined above). Set the crossing point as an initial subgoal junction on route.Identify the second junction from potential connections from the start junction. Given that a prior junction has yet to be specified, this junction is selected according to its deviation from the straight-line distance between origin and destination junctions. The inverse of the angular deviation from straight line to the destination junction is calculated for each potential junction. The junction with the highest score is set as the next junction, with the start junction then specified as the previous junction.Pp). Calculate angular deviation towards each junction away from straight line towards the destination, and identify corresponding probability of selection (Pd). Using both Pp and Pd, calculate overall likelihood of selection of each option, according to Start iterative junction selection process. At each junction, identify probabilities of successive junctions based on current and prior junction selections , lane-weighted time (87.97%) and turn-weighted distance (91.64%) paths—reflecting that over short distances only a limited number of paths are generally available. Given these findings, a shortest distance path assumption is employed in identifying paths between selected junctions.Road segment routes between junction pairs are generated using a modified version of the A-star network search algorithm. The A-star search approach incorporates a Euclidean distance heuristic into a network search to primarily improve the efficiency of shortest path generation. Rather than searching the entire road network for the optimal route between origin and destination, the minimisation of straight-line distance away from the target location effectively reduces the search space, speeding up path calculation. A small modification is introduced into the method whereby the junction location is specified as the target coordinate, and all roads within a 100-metre radius of that point (indicative of the bounds of the effective view shed around the junction) are specified as potential destination roads. The path search terminates on arrival at a destination road.The model was written in Java, implementing the JUNG network modelling library and the GeoTools library for spatial association calculations. All junction connection probabilities were pre-processed and queried during route modelling from a locally held MySQL database. Route modelling was executed on a standalone desktop Apple iMac, with a 3.4 GHz Intel Core i7 processor and 16GB RAM.The validation stage will examine two dimensions of the MCMC route modelling approach. First, we must assess the ability of the model to predict observed junction-to-junction movement choices, including how each element of the model contributes to the prediction. Second, we must assess how well the complete segment-based routes correspond to the observed set of routes, indicative of traffic flow. Through these stages, the strengths and weaknesses of the approach can be better established.For validation, junction and route predictions are calculated for the remaining 20% validation partition of the minicab dataset. During this stage, 138009 routes are modelled from observed origin and destination points, observed and predicted junction and route choices are extracted.The ability of the MCMC approach to correctly predict the selection of a junction is a highly important indicator of the model’s predictive power. This stage of validation will provide an opportunity to explore the predictive capability of the approach, yet it furthermore allows an exploration of how each constituent element of the model contributes towards prediction.The accuracy of the junction selection process is judged by assessing how often the model correctly predicts an observed junction selection. For each observed junction choice, information pertinent to that choice  is extracted and input for the simulation of a corresponding choice using the MCMC approach. Insight is gained by assessing how well the model performs, and the circumstances under which performance varies.a) the removal of the prior state assumption (adjusting transition probabilities from P(k|(j|i) to P(i|j)); b) the removal of the destination directionality assumption; c) the removal of both the prior state and directionality assumptions; and d) the removal of all probabilistic connectivity, accounting for destination directionality alone (junction connectivity is still used in deriving the choice set).In the first instance, this accuracy test is performed using both the complete model framework and an array of adjusted model configurations. These adjustments to the structure allow an examination of the influence of each element of the model in improving or reducing predictive power. The model adjustments to be tested include The statistics selected to assess performance describe how well each model performs in the identification and selection the observed chosen junction. In incorporating Precision ) and Recall ) measures a better understanding how often the model over predicts or fails to predict a junction is further established (these will become more useful where assessing variation in junction prediction). The performance measures in predicting junction selection are presented in As can be shown in Poor performance is shown by the most ‘stripped down’ approaches. The removal of previous junction momentum and destination directionality assumptions, as in model C, leads to the poorest performance. This indicates that the sense of momentum achieved by including the previous junction is required, and the connectivity of junctions alone is not enough to predict choice. Poor performance is shown again where only considering the direction of the destination, in model D. A better result is achieved where momentum is considered but destination direction is ignored, as seen in model C. These results indicate that inter-junction connectivity contributes more to model performance than destination directionality, but only when both the previous and current junctions are combined in forming the prediction.In summary, it is clear that probabilistic inter-junction connectivity is a highly important element of the model, but some information around the orientation of the destination is also required. This provides reasonable validation of the proposed framework design. However, doubts remain around the role of incorporating information relating to momentum, through consideration of the previous node. Further tests will explore the performance of the complete model framework in more detail, including where momentum information leads to an improved or reduced model performance.where the model performs well, where it does not, and the reasons behind these. These findings may provide insight for subsequent development and improvement of the approach.The second set of junction selection validation tests examines variation in the performance of the complete modelling framework. Specifically, locational variation in performance will be explored, identifying For this stage, precision and recall scores are calculated for each junction. These scores indicate where the model is performing accurately, relative to incorrect  and missed  selections. These results can be mapped to indicate spatial variation across the city.The first map, shown in not chosen (marked with a lower score). The spread is less strongly spatially correlated, with only a few specific locations—marked A, B and C—showing particularly poor performance. These junctions appear to be ignored in favour of other dominant routes nearby (point C runs close to a dominant thoroughfare running west to east).The map showing variation in recall scores, in Extending the validation of model structure outlined earlier, the third map, shown in The second stage of validation will assess the performance of the complete MCMC approach in predicting the distribution of traffic flow. At this stage, a complete segment-based route is generated for each of the 138009 origin-destination journeys within the validation dataset. The validation will test whether the generated set of routes is adequately reflective of observed patterns of traffic distribution.It is important to note that observed and modelled routes are not compared against each other during the validation. There are a considerable number of unique behavioural and situational factors involved in real-world route choice, factors that are not captured by this modelling framework. Furthermore, in incorporating prior choices within the model framework, minor deviations in junction choice are likely to be compounded by subsequent selections. It is unfair therefore to argue that deviations between observed and modelled routes are indicative of a poor model fit. Instead, the model should reflect the same general arrangement of traffic, for the given set of origins and destinations, as indicated in the validation dataset.The MCMC-derived traffic estimations fall across 119360 road segments, with a mean route count of 158.48 trips along each link. Standard deviation in trips along each route is 601.71, with a maximum trip count of 13750, an upper quartile of 38 and a lower quartile of 1. In comparison, the validation dataset shows greater diversity, represented by over 143834 road segments, with a lower mean count of 114.17. The standard deviation of the observed count is 369.65, reaching a maximum at 7684, with the upper quartile at 38 and lower quartile at 1. The Mean Error (ME) of 43.99, indicating a small over-prediction by the model in general.Examining these errors in absolute terms, the Mean Absolute Error (MAE) arrives at 89.90 with the Root Mean Squared Error (RMSE) considerably higher at 343.27. This difference is indicative of considerable variance in error terms, however, given the similar interquartile range of each dataset, this is likely caused by large variance in traffic on segments with high traffic volumes.y) and the modelled data (x) as falling along the line y = 31.236 + 0.53x. The coefficient of determination (R2) is found to be 0.74. These indicators would suggest a strong overall prediction of variation within the real data by the modelled representation. The strength of this fit can be observed in the plot between modelled and real values, shown with the line of best fit, in Similarities in route distributions are assessed through plotting a simple linear regression between the two real and modelled datasets, and calculation of the goodness-of-fit between the modelled and real distributions. During this process, the best fitting line was identified between the observed route counts  ahead of an alternative—destination direction may be temporarily ignored in order to use a better route. It should be established the locations where destination direction is important, and where is it less so. Similarly, alternative definitions of state space should be given consideration. Road network classifications, although simple to implement, do not necessarily align with all decision-making points or locational salience. Dual network centrality measures or major junctions identified from overall traffic flow offer two potential avenues for exploration.There are a multitude of directions by which this research may be extended towards the wider urban and transportation modelling domain. In the first instance it would be interesting to explore how well the method performs using a different dataset, particularly one that is more reflective of all traffic flow, rather than only minicab journeys. Another extension may lie in using the routes creating through the MCMC approach in the generation of a choice set between given origins and destinations during discrete choice modelling. Third, the encapsulation of the traffic system as a set of interconnected locations potentially also enables an exploration of network coupling and dependence, within the context of modelling disruption. For instance, in London, according to the minicab dataset, if a traveller has passed two junctions northbound from Kennington Road and along Kennington Lane, there is a 0.92 chance they will continue north onto Elephant and Castle roundabout. This simple insight describes the spatial pattern of dependency upon a location, and provides an indicator of the potential impact were network disruption to occur at that point.The conceptualisation of the road network as a set of interconnected junctions furthermore potentially helps highlight points of redundancy on the network. Whereas road-level traffic metrics may mask the degree of interactions between two locations, the Markov chain structure of interconnectivity provides greater detail on local level interactions. This potentially allows transport planners to more accurately identify underused routes through the road network, enabling improvements to junction design or the urban realm.The model presented during this paper has focussed primarily on traffic patterns, yet one clear extension would be its integration with a traffic flow model and trip distribution matrix, enabling the simulation of traffic dynamics. Not only would this enable the simulation of congestion dynamics, but furthermore establish whether the junction interconnectivities derived from the minicab dataset replicate the behaviours of the entire transport network. This simulation framework would additionally allow full scenario testing, such as the closure of a major junction, yielding spatial and temporal estimates of emerging congestion.While the application of this approach has focussed on road transportation, there are opportunities too for its extension to other transportation domains too. The principle of the interconnectivity of locations extends beyond the road network, and new datasets are becoming available to help capture these patterns. For instance, the distribution of smart cards around urban transit systems may capture probabilistic interactions between origins and destinations. The traces of pedestrian routes may help identify the main locations at which route choices are made, likely reflected some deviations from those used to model vehicular route choice.Drawbacks in the approach can be associated with its greatest strength, namely its representation of junction interconnectivity. While strongly interconnected junctions reflect high volume interactions between two points, the high strength of connection was shown to override diversity of routing behaviour associated with those junctions. For instance, the probability of turning off a heavily used route to a more minor route was slightly reduced by the continuity of observed distribution along the main road. While the destination directionality measure compensates against this effect to an extent, arriving at a balance between these factors requires further examination.


A complicating factor in this practice is the potential bias in the estimates defining safe drug exposure. Moreover, it prevents the assessment of variability. The objective of the current investigation was therefore (a) to demonstrate the feasibility of applying nonlinear mixed effects modelling for the evaluation of toxicokinetics and (b) to assess the bias and accuracy in summary measures of systemic exposure for each method. Here, simulation scenarios were evaluated, which mimic toxicology protocols in rodents. To ensure differences in pharmacokinetic properties are accounted for, hypothetical drugs with varying disposition properties were considered. Data analysis was performed using non-compartmental methods and nonlinear mixed effects modelling. Exposure levels were expressed as area under the concentration versus time curve (AUC), peak concentrations (Cmax) and time above a predefined threshold (TAT). Results were then compared with the reference values to assess the bias and precision of parameter estimates. Higher accuracy and precision were observed for model-based estimates , irrespective of group or treatment duration, as compared with non-compartmental analysis. Despite the focus of guidelines on establishing safety thresholds for the evaluation of new molecules in humans, current methods neglect uncertainty, lack of precision and bias in parameter estimates. The use of nonlinear mixed effects modelling for the analysis of toxicokinetics provides insight into variability and should be considered for predicting safe exposure in humans.Current toxicity protocols relate measures of systemic exposure  contains supplementary material, which is available to authorized users. The purpose of toxicokinetic studies in the evaluation of safety pharmacology and toxicity is the prediction of the risk that exposure to a new chemical or biological entity represents to humans , 2. Undequalitative indicator of acceptable risk. Even though support for the existence of thresholds has been argued on biological grounds . Irr. Irr6].  grounds –9, the Nmax), which serve as basis for the maximum allowed exposure in dose escalation studies in humans [The definition of the NOAEL varies from source to source . Its caln humans . The afon humans , 12. TheWhilst the scope and intent of such guidance are well described since 1994, when it was introduced by the ICH, there has been much less attention to requirements for the analysis and interpretation of the data. In fact, precise details on the design of toxicokinetic studies or the statistical methods for calculating or estimating the endpoints or variables of interest, are not specified –15. Instmax) can then be either derived from the composite profile or by averaging individual estimates from serial profiles in satellite animals when frequent sampling schemes are feasible. Given that the parameters of interest are expressed as point estimates, within- and between-subject variability as well as uncertainty in estimation are not accounted for. In addition, pharmacokinetic data generated from different experiments are not evaluated in an integrated manner, whereby drug disposition  can be described mechanistically or at least compartmentally in terms of both first and zero order processes. This is further complicated by another major limitation in the way exposure is described by naïve pooling approaches, i.e., the impossibility to accurately derive parameters such as cumulative exposure, which may be physiologically a more relevant parameter for late onset or cumulative effects  [As a consequence, safety thresholds are primarily derived from inferences about the putative pharmacokinetic profiles in the actual treatment group. Furthermore, these thresholds rely on the accuracy of composite profiles obtained from limited sampling in individual animals. Composite profiles consist of pooled concentration data, which is averaged per time point under the assumption that inter-individual differences are simply residual variability, rather than intrinsic differences in pharmacokinetic processes . Pharmaccosides) , 21. TimBy contrast, population pharmacokinetic-pharmacodynamic methodologies have the potential to overcome most of the aforementioned problems. Whilst the application of modelling in the evaluation of efficacy is widespread and well-established across different therapeutic areas –24, currThe aim of this investigation was therefore to assess the relative performance of model-based approaches as compared to empirical methods currently used to analyse toxicokinetic data. We show that, modelling is an iterative process which allows further insight into relevant biological processes as well as into data gaps, providing the basis for experimental protocol optimisation. We illustrate the concepts by exploring a variety of scenarios in which hypothetical drugs with different disposition properties are evaluated.max) of individual non-steroidal anti-inflammatory drugs and relative risk (RR) of upper gastrointestinal bleeding/perforation [Using historical reference data from a range of non-steroidal anti-inflammatory compounds for which pharmacokinetic parameter estimates were known in rodents, a model-based approach was used to simulate the outcomes of a 3-month study protocol, in which toxicokinetic data for three hypothetical drugs were evaluated. The selection of non-steroidal anti-inflammatory compounds as paradigm for this analysis is due to the mechanisms underlying both short and long term adverse events as well as the evidence for a correlation between drug levels and incidence of such events in humans. In fact, a relationship has been identified between the degree of inhibition of cyclooxygenase at the maximum plasma concentration  elimination as well as a two-compartment pharmacokinetics. Parameter values for each scenario are shown in Table Experimental procedures were defined according to current guidelines for the assessment of toxicity. A summary of the sampling schemes and experimental conditions is shown in Table max), the time above a threshold drug concentration (TAT), the predicted 6-month cumulative AUC and the predicted 6-month Cmax. These exposure measures can be seen alongside the formula used for their calculation in Table n = 200 replicates) were performed assuming repeat dosing for up to 6 months (3 months beyond the treatment duration presented the investigated studies) in order to evaluate the implications of longer periods of drug exposure.Five different measures of exposure were derived from the simulated concentration profiles obtained from the models used for simulation. They included the 24-h area under the concentration versus time curve (AUC), the maximum concentration , as implemented in NONMEM. Model building steps were limited to the same structural models used for the initial simulations under the assumption that pharmacokinetic properties of the drugs are known at the time toxicology experiments are performed. Model convergence was determined by successful minimisation and estimation of the covariance step. Data below the lower quantification limit (BQL) were omitted to mimic experimental conditions in which imputation methods are not applied. Estimates for all five measures of exposure were calculated by using same procedures applied for the reference values obtained during the initial simulation step  was repeated 200 times. Bias and precision were assessed by the relative error, scaled relative mean error (SRME) and the coefficient of variation (CV) respectively :\documenAll simulations and fitting procedures described above were performed in NONMEM 7.1 . Data maThe use of simulated data for the evaluation of hypothetical scenarios provided clear insight of the impact of current practices on the accuracy and precision of safety thresholds, and in particular of the NOAEL. Irrespective of the use of serial or sparse sampling schemes for the characterisation of the concentration versus time profiles, model convergence rates were usually high, with successful completion of the covariance step. An overview of the convergence rates is presented in Table max and TAT. All other experimental conditions, including an overview of the scaled relative mean error (SRME) and the coefficient of variation (CV) are presented in tabular format as supplemental material (Table S1).To facilitate the comparison of the magnitude of bias and precision, results from modelling are shown together with the parameter values obtained from non-compartmental analysis where applicable. Due to the large number of experimental conditions to be summarised, here we present a brief description of the relative errors obtained in the 3-month protocol, for AUC, Cmax and TAT. The relative errors were clearly smaller when measures of exposure were derived by modelling, as compared to the results obtained by non-compartmental analysis. In fact, the accuracy and precision of model-based estimates for all three measures of exposure were similar across the different dosing groups and treatment durations. Non-compartmental estimates of exposure showed significantly higher bias and less precision in all scenarios. The performance for model-based exposure estimates derived from the 3-month protocol is summarised in Fig. In Fig. max was consistently over-estimated by the non-compartmental method. We also demonstrate that the use of arithmetic and geometric means for NCA had minor impact in these relatively small groups.Our results also reveal the impact of composite versus serial sampling on bias and precision. For both model-based and non-compartmental methods, the coefficient of variation increased with composite designs , as compared to serial sampling designs . However, the increase in precision for non-compartmental method was larger than for model-based estimates. It should also be noted that CLastly, it was found that that nonlinearity in pharmacokinetics also has an important effect on bias and precision when sparse samples and limited number of dose levels are evaluated experimentally. Model-based estimates in the 1 CMT + MM scenario showed increased bias compared to the 1 CMT and 2 CMT scenarios.In this investigation we have attempted to identify important limitations in the use of non-compartmental methods for the analysis of toxicokinetic data. Irrespective of the limited number of scenarios, our findings illustrate the feasibility of using hierarchical models for the evaluation of toxicokinetic data using a well-established parameterisation for drug disposition processes. Furthermore, given that model performance in the analysis of toxicokinetic data has been previously evaluated , we haveIt is important to highlight that the use of compartmental models, instead of physiologically-based pharmacokinetic models in this exercise was required to avoid issues such as parameter identifiability , which wAs shown in Table max, which is consistently over-estimated. This is due to the definition of peak concentrations in non-compartmental analysis where CM is necessarily greater than or equal to max represents the time point which maximises the true concentration–time profile. When the sampling scheme contains other observations in the region of Tmax there is potential for neighbouring sampling times to produce higher than predicted concentrations due to natural variability. This is a fundamental limitation in the methodology in that more samples around Tmax which intuitively should increase confidence, actually leads to more bias. In other words, with non-compartmental analysis precisely estimating Tmax comes at the unavoidable cost of biased estimation of Cmax. Model-based analysis has an additional advantage in this respect. Without model misspecification issues, maximum likelihood estimates are  unbiased and have the property that increased sampling uniformly increases precision. The implications of model specification issues are discussed further in the limitations section. Given that the residual variability in the scenarios was not large , the bias seen here may increase with larger residual noise, which may occur in real life. The issue of bias can be further mitigated by the appropriate use of predictive checks. An example of the procedures can be found in the supplemental material for naproxen [max.On the other hand, the presence of bias in some of the experimental conditions presented here has clear implications for the so-called safety margin and toxicological cover to be used as proxy for risk during clinical development, especially for Cnaproxen , where pIn contrast to non-compartmental methods, our investigation was based on an integrated analysis of the data, i.e. by combining the results from all experimental cohorts. This is undoubtedly the primary driver of the increased accuracy and precision in model-based estimates –40. In fIt is important to realise that the typical point estimates of parameters derived from empirical methods to describe drug exposure give an undue measure of certainty, allowing for the propagation of uncertainty from estimation to uncertainty in safety thresholds, such as NOAEL. Whilst there exist methods for estimating uncertainty in a composite or destructive sampling approach –46, theiAs demonstrated here, model-based methods allow simulations to be performed in conjunction with estimation procedures, enabling the assessment of uncertainty associated with a variety of causes such as uninformative study design, large variability and/or unknown covariates. This entails an increase in the quality of the decision-making process and ultimately in the interpretation of the estimated safety thresholds .Given the success of modelling and simulation in drug development –50, one max), the impact is likely to be small as long as the model fit to the data is good. This is because these measures are highly dependent on the observations. Therefore, accurate prediction of the observed profiles during model evaluation is likely to result in accurate prediction of these exposure variables. Model misspecification however, may lead to significant bias when exposure predictions are made outside the experimental context  [In the present investigation, the impact of model misspecification in the analysis of general toxicity data was not investigated. For exposure measures which have a corresponding estimate based on non-compartmental methods (e.g. AUC and Cegimens) , 54. Thiegimens) . FinallyIn summary, evaluation of safety is paramount for the progression of new molecules into humans. Historically, toxicology experiments have evolved based the assumption that experimental findings suffice to demonstrate the absence or presence of risk. This assumption disregards growing evidence of the advantages of data integration for the characterisation of drug properties. Whilst the challenges R&D faces to translate toxicity findings from animals to humans may remain, the use of an integrated approach to the analysis and interpretation of toxicokinetic data represents further adherence to the 3Rs principle, enabling significant reduction in number of animals required for the evaluation of toxicokinetics.Supplementary material 1 (DOCX 373 kb)Supplementary material 2 (PDF 97 kb)Below is the link to the electronic supplementary material.


An exact classification of different gait phases is essential to enable the control of exoskeleton robots and detect the intentions of users. We propose a gait phase classification method based on neural networks using sensor signals from lower limb exoskeleton robots. In such robots, foot sensors with force sensing registers are commonly used to classify gait phases. We describe classifiers that use the orientation of each lower limb segment and the angular velocities of the joints to output the current gait phase. Experiments to obtain the input signals and desired outputs for the learning and validation process are conducted, and two neural network methods ) are used to develop an optimal classifier. Offline and online evaluations using four criteria are used to compare the performance of the classifiers. The proposed NARX-based method exhibits sufficiently good performance to replace foot sensors as a means of classifying gait phases. Walking involves periodic behavior in both legs, with one moving forward as the other bears the weight of the body, thus moving the whole body from one place to another . Such moGait phase classification is a general method for analyzing walking. Walking is the periodic behavior of one stride, measured from one leg’s heel strike (ground contact) to the same leg’s next heel strike. One stride can be further divided into two phases, the stance in which one leg bears the weight of the body and the swing whereby the leg moves forward to propel the body . Each phThere are many applications of gait phase classification information. Based on how and where the information would be used, there are two main areas of application. First, as mentioned above, gait phase information can be used to evaluate and determine the walking pattern of humans. Traditionally, such information is used as quantitative data alongside other spatio-temporal parameters  to diagnose and prescribe pathological gaits and evaluate walking after rehabilitation ,2. SeconGait phase information is especially important for walking-aid devices. FES devices use this information to enable patients with spinal cord injuries to walk via the direct electronic stimulation of lower limb muscles. Lower limb exoskeleton robots are used to help people with walking disabilities and to enhance the performance of healthy subjects. When the robots walk with the user, the control model changes according to information about whether one or both feet are in contact with the ground. Thus, gait phase information is an essential control input. Similarly, in smart lower limb prosthetics, the damping coefficients in artificial knee joints must be changed to simulate those of the human so as to reduce energy consumption and allow lower-limb amputees to walk stably. Gait phase information is a vital component in this scenario.To be of use in the above cases, gait phase information must be correctly classified. It is generally known that a force plate is the most effective means of correctly distinguishing between the two phases of walking. However, force plates have several non-practical features. For example, they are very expensive sensors. Measurements can only be taken at the place where the force plate is installed, and the gait phase is only detectable when a person stamps on the force plate while walking. For gait classification when using walking-aid devices, another important consideration is real-time classification. Although not essential for diagnosis, controlling walking-aid devices requires gait phase classification information to be acquired in real time. Thus, for walking-aid devices, more practical methods are needed.The problem of gait classification can be generalized to that of determining what sensors should be used to acquire walking data and how the gait phase can then be classified. In this scenario, the most important factor is to select the most reliable and suitable sensors. Recent advances in wearable sensor technologies  have see. They also have some disadvantages when used with walking-aid devices, e.g., their classification success rate is lower than that of a force plate, their location on the body may clash with that of the walking-aid device, and accelerometers and gyroscopes must be strapped tightly to the body to acquire reliable data. In addition, multiple wearable sensors require a wired connection to the main controllers, as wireless connections have a limited bandwidth. This can be a significant burden for the wearers. Consequently, we believe that wearable sensors are not sufficiently mature to be used with exoskeleton robots and powered prostheses, but are well-suited to controlling FES.Wearable sensor-based approaches have a number of advantages, e.g., they are not limited to a specific environment, can record any number of measureable steps, and are typically low costAssistive devices such as exoskeleton robots and powered prostheses typically use embedded sensors to control themselves and detect the user’s intentions. These devices generally have encoders or potentiometers on their joints, IMUs, and foot sensors. Because foot contact is directly used to classify the gait phase, foot sensor-based approaches are commonly employed with exoskeleton robots and powered prostheses. However, it is difficult to make a foot sensor that is reliable and robust to different foot sizes and ground conditions. Furthermore, several exoskeleton robot structures cannot easily be fitted with foot sensors .In this paper, we propose a neural network-based gait phase classification method that takes its input from non-foot sensor signals provided by exoskeleton robots. The purpose of the proposed method is to replace the general gait classification methods that use foot sensors. The orientation and angular velocities of lower limb segments are measured and estimated by the sensors, and the data are fed into neural network-based gait phase classifiers. We use two neural networks to determine the best model for classifying gait phases. Ten able-bodied subjects took part in an experimental study. To acquire training and offline validation data, seven people walked while wearing an exoskeleton robot. The developed classifiers were then evaluated in an online manner while the other three people used the exoskeleton robot. Our results show that the proposed method has the potential to replace foot sensor-based classifiers.In this section, we briefly introduce ROBIN-H1, a lower limb exoskeleton robot. The ROBIN-H1 system is used to acquire the walking data used to develop our gait phase classifier, and to verify the classifiers in an online manner. ROBIN-H1 was developed as a walking rehabilitation service for stroke patients. The specification of ROBIN-H1 is presented in ROBIN-H1 is equipped with several sensors to detect walking intent and control itself . AbsolutThe robot has a sensing mode in which various walking parameters of the human using the robot can be measured. In this mode, none of the active joints force the user’s body, but instead compensate for the weight of the exoskeleton and the friction in each active joint. Thus, the user can walk without feeling the additional weight and friction if he/she does not walk too fast. For compensation, we used two models. Equation (1) describes the motion model of ROBIN-H1: was used : (2)τf=fFoot Sensor-based Gait Classification: As mentioned above, to operate in this mode, gait phase information is required for each leg. We use foot sensor signals to classify the gait phase in the experimental stages. To classify the gait phase, the FSR outputs are first aggregated. If the total is above some threshold, the robot is considered to be in the stance phase. The threshold is determined heuristically from several walking trials. The foot sensor signal-based gait phase classification logic is executed at 10 ms intervals.The main controller of the robot is a personal computer. The controller operating system is Microsoft Windows 7, and the robot control software is written in C++. Communication between the main controller, motor controllers, and sensor boards is conducted via a Controller Area Network (CAN). Measured values are filtered by a second-order Butterworth filter at suitable frequencies. The sensed values and states of the robot are recorded at 66.7 Hz and saved to file. To synchronize with other devices such as force plates, the robot has a synchronization device based on two FSRs.To develop a gait phase classifier and verify its performance offline, we first collected walking data. The walking data were acquired from able-bodied volunteers walking across three force plates while wearing ROBIN-H1. When a person walks while wearing an exoskeleton robot, it is known that the kinematics and kinetics of walking are affected by the weight and limited operation range of the robot . Thus, iSeven healthy people who have not suffered any lower limb related disabilities took part in the data acquisition experiment. The experiment was approved by the Public Institutional Review Board of Korea. Before the experiment, we informed the participants about the nature of the experiment, and obtained written consent from each subject. (1)Each subject wears the ROBIN-H1 device and stands at the start position.(2)A synchronization process is conducted between the robot and the force plates.(3)Upon the start signal, the subject starts to walk by moving their right leg forward.(4)The subject selects a convenient walking speed and step size.(5)The subject takes four or five steps, and finally stands still after moving their left leg.(6)Each subject repeats six trials.The experiments were configured as follows: It is possible to divide the data acquired from the above procedure into three categories. The first category is the robot data measured by the sensors on the robot and estimated by the robot’s algorithms. The remaining categories consist of force plate data from the Kistler 9060AA6 plates and the Zebris plate. Although the Kistler and Zebris force plates have different data acquisition software and formats, both types of force plate record their measurement values every 10 ms. Because the acquired data are different, some method of synchronization is needed. ROBIN-H1 has a synchronization device that uses two FSRs. These FSRs are attached to each type of force plate before the experiments. In the synchronization process, we briefly press down strongly on the FSR and the force plate. ROBIN-H1 and both types of force plate record this signal and its occurrence time.V: k is the total number of frames in the dataset; m is the number of frames in the training set and n is the number of frames in the validation set.We first pre-processed the acquired data to transform them into feasible information for machine learning. In this study, we constructed training and validation datasets, and normalized the raw data in the pre-processing step. The three heterogeneous data points (one from each category) were combined into a single point in a time series data using a synchronizing signal. By synchronizing the start points of the three data streams, a synchronized time series was generated using the “synchronize” function of Matlab 2015a. To remove data recorded while standing still (at the start and end points), we cut the time series into several shorter series, and gathered the data from a single right-leg stride into one dataset. The reference points for cutting the data were obtained from the force plate data. In this manner, we obtained time series data set for 78 strides. This was divided into a training dataset T and a validation dataset The machine learning method employed in this paper is a sort of supervised learning technique in which the training and validation sets are composed of pairs of input data Note that the input vector y in the training and validation datasets was generated by the force plate data. As described previously, the best information for classifying the swing and stance phases is the output from force plates inserted in the ground. If the force plate measured a value of more than 5 kg (in the Fz axis), we considered the state to be a stance and set y = 1; otherwise, we considered the phase to be the swing, and set y = 0: The desired output i.e., ith element of input vector ith element in the whole input vector set, and ith element in the input vector set.After forming the training and validation datasets, we normalized the data. Neural networks can be adversely affected by the elements of the input vectors having a wide range of values. To overcome this problem, it is common to apply some form of normalization to restrict the input vector elements to the range , We developed gait phase classifiers using the training dataset. To classify the gait phases, we used two neural network methods, a multilayer perceptron (MLP) and nonlinear autoregressive with external (exogenous) inputs (NARX). MLP networks in which cross-entropy activation functions are used in the output layer are commonly employed for pattern recognition and classification. Walking can be considered as a temporal process, and the current state is dependent on previous states. Thus, walking can be regarded as a dynamical system. The best way to mimic a dynamical system is to use a dynamic recurrent neural network such as NARX. The training algorithm for these networks is generally some variant of back-propagation.Because the gait phase classifiers proposed in this paper are integrated into the ROBIN-H1 control software to control the robot and detect the user’s intentions, high classification accuracy is essential. There are several design factors that must be considered to optimize the performance of a neural network used as a function-mimicking tool ,33. It iIn this study, we applied a growing network model (structure or architecture) strategy to develop the best classifier for ROBIN-H1. The growing network model strategy only deals with the number of nodes in the hidden layer of the MLP and the number of nodes (the number of input time delays) in the input layer of NARX. Among the design factors, the number of hidden layers is not considered in this paper, because the input vector in our problem is only four-dimensional, and increased numbers of hidden layers are commonly necessary when the dimension of the input vector or the number of nodes in the input layer are large . The desThe neural network gait phase classifiers were trained using the Neural Network Toolbox in Matlab 2015a. The “patternnet” function of Matlab 2015a was used to generate MLP-based gait classifiers, and “narxnet” was used to make the NARX-based gait classifiers. To use the “patternnet” function for this classification problem, the output should have two elements: the desired output and the complementary value of the desired output. The weights of the neural network were initialized to random values in the range . In some cases, training algorithms such as scaled conjugate gradient descent or Levenberg–Marquardt cannot find the global minimum because of the initial weights. To solve this local minima problem, we generated 30 networks for each model with different initial weights. The model with the best performance was then chosen to represent the network structure. The training algorithm was back-propagation based on conjugate gradient descent. The maximum number of learning epochs (iterations) was set to 1000. However, to avoid overfitting, the training process was terminated if the error between successive epochs increased by a factor of more than six.To compare the gait phase classifiers, we require some evaluation criterion. Generally, the Classification Success Rate (CSR) is used to validate a classifier. However, additional evaluation criteria are needed to consider certain characteristics of exoskeleton robots, such as the comfort and safety of the user, because the classifiers proposed in this paper are being used to control the robot. To develop an additional evaluation scale, we examined the types of error that appear in gait phase classifiers.(1)The classifier considers a gait phase to have changed before the transition point in the real gait phase The classifier considers the gait phase to have changed after the transition point in the real gait phase The classifier considers the gait phase to have changed, but no transition has occurred in the real gait phase The . Thus, all else being equal, a classifier with no unstable regions is regarded as the best classifier for exoskeleton robots. In this study, in addition to the CSR, we applied the following three evaluation criteria: (1)Max Continuous Error Width: the maximum continuous error between the force plate results and the classification result.(2)Mean and Standard Deviation (Std.) Continuous Error Width: the mean of the continuous error and its standard deviation.(3)Number of unstable regions: the number of cases in which the classification results oscillate.In the case of applying a gait phase classifier to a robot, the extent to which each error type influences the user and the robot will be different. Thus, it is useful to impose a weight on each error type. However, when we calculate the CSR, we simply sum the number of errors and divide the sum by the number of whole frames. Misclassification types 1 and 2 do not affect the robot’s control logic, as long as the continuous error width is not too large (≥15). However, misclassification type 3, in which the classification output oscillates over a short time interval, is not suitable for robot control. For example, when the real gait of the user and the robot is in the stance phase, but the robot recognizes this as the swing phase and operates inappropriately, the user may feel uncomfortable, and could even fall downTo compare the offline performance of the classifiers described in It is clear that the MLP classifiers produced excellent results , with anThere does not appear to be any significant difference in CSR between the MLP-based and NARX-based (97.05%) classifiers . The NARWe implemented the gait phase classifiers on ROBIN-H1, and validated their online performance. It is generally known that the online performance of classifiers is worse than their offline performance. Hence, online validation can be considered as a practical means of identifying the performance of classifiers. For online validation, three subjects who did not attend the data acquisition experiments were asked to wear ROBIN-H1 and complete the same process of the previous experiments. The classifiers developed using Matlab 2015a were implemented in C++ in the robot control software by extracting weight parameters from the generated scripts. In the robot control software, the classification logic was operated periodically at 10 ms intervals. A comparison of the real-time output from the classifier and the force plate measurements for a total of 32 strides is presented in As expected, the MLP-based classifier exhibited worse overall performance than in the offline case. The average CSR (90.75%) produced by the online  MLP netwSimilarly, the NARX-based classifiers performed worse  than in The NARX-based classifiers gave better overall performance than the MLPs. Unlike the offline case, the best online NARX-based classifier had six input time delays.Finally, In this paper, two network-based classifiers have been evaluated in terms of their offline and online performance. It is clear that the overall performance of the classifiers was better in the offline case. The reasons for this are as follows.First, the validation data were obtained from different subjects in each experiment. We doubt whether training data T can represent all walking patterns. When we develop a classifier using machine learning techniques, it is important to obtain representative data. However, even if walking pattern data for every person in the world were simply included in T, it would not be a representative set of walking data; instead, T should include more noise. Therefore, we require an appropriate method to acquire representative data. Additionally, walking while wearing an exoskeleton robot will influence different people in different ways, making it difficult to acquire representative walking patterns. Interestingly, every case of the maximum continuous error width occurred on only certain stride patterns in both the online and offline experiments. Comparing these patterns with the training set patterns may be linked to finding representative walking pattern data.Second, there is a discontinuity in the training dataset T. In the pre-processing procedure described in We believe that the classifiers proposed in this paper are sufficient for use as part of the control logic of exoskeleton robots, despite the fact that their online performance is worse than their offline results. The CSR remains at an acceptable level of above 90%, and the maximum continuous error width is above 35, indicating time differences of about 350 ms between the real and classified phases.This may cause a problem with the robot, but it is unlikely to be critical, because the worst case is rare. The mean of the continuous error width is about 8, corresponding to an 80 ms time difference. This time difference is very short, and would be difficult for a human to recognize.Finally, the best MLP-based classifier exhibited only one unstable region, whereas the best NARX-based classifier had no unstable regions. The performance of the proposed classifiers is better than that of foot sensors using FSRs . As descTo determine the optimal network structures of both neural network-based classifiers, we applied a growing network structure model method . Varying the network structure is a well-known strategy in the neural network literature, so we expected a dramatic difference in classification performance between the optimal structure and others. However, there were no significant differences between similar networks in the offline evaluation. In the online evaluation, there was a 3% difference in CSR for the MLP and a 5% difference in CSR for the NARX between the best and worst structures. Thus, no meaningful tendency was observed. We can carefully infer that this phenomenon is caused by the combination of two factors. First, the problem of gait phase classification using lower leg orientations and angular velocities seems a rather well-defined problem. The input vector and outputs have few dimensions. There are few stochastic and subtle properties in the decision boundaries to transform the input vectors to outputs. Second, we think that the mechanism that prevents overfitting in the Neural Network Tool Box of Matlab 2015a could cause this phenomenon. In the training process, the mechanism checks whether overfitting has occurred in every training epoch. If no overfitting has occurred, the mechanism continues training up to the pre-defined training iteration number limit. Conversely, if overfitting has occurred six times in a row, the mechanism stops training and rolls back the weights of the network to the values prior to the occurrence of overfitting. This automatic process to determine the number of training iterations means that different structures will exhibit similar performance if the network structures are sufficient to simulate the problem. Although the growing network structure model strategy fails to identify much difference in performance between the best and worst structures, it provides an answer as to how the best network structures could be determined.Finally, this paper shows that, in the case of modeling a dynamical system, the NARX network is better than the MLP network and that walking is a dynamical system. However, the time delay inputs and recurrent outputs in the input layer of NARX that make the NARX network good at modeling dynamical systems also cause the network to be easily affected by discontinuities in the training dataset and sensor noise in online operation. This means that it is difficult to make a high-performance NARX network-based classifiers. For this reason, further studies on constructing the training dataset, eradicating noise, and configuring the initial condition of the NARX network are needed.This paper has proposed two neural network-based gait phase classifiers. Because the proposed classifiers will form part of the control logic of an exoskeleton robot, we acquired data from able-bodied people wearing exoskeleton robots to train the two networks. To find the optimal network structure, we trained the networks according to a growing network model strategy. We considered four evaluation criteria and assessed the offline and online performance of the classifiers. The proposed classifiers produced excellent offline results (average CSR: 97%), but their online performance was not so strong. The proposed classifiers outperformed foot sensor signal-based gait phase classification, despite their slightly lower online performance. The best NARX-based classifier did not produce any unstable regions, and exhibited good overall performance. Thus, NARX is an efficient and effective means of modeling the behavior of a dynamic system such as walking.Although the proposed gait classifiers appear to be sufficiently accurate and robust to replace foot sensors in exoskeleton robots, some further improvements could be made. For example, we intend to determine a suitable method of acquiring representative walking pattern data. Secondly, we will apply a more advanced classification method, such as an auto-encoder. Finally, we will validate the proposed classifiers against data from stroke patients.


Most orthodontists believe that fixed retainers are necessary to maintain ideal dental relationships. However, untoward side effects might result from their long-term placement. The aim of this study was to evaluate the clinical and radiographic effect of two commonly used fixed retainers on the health of the periodontium.Thirty patients were randomly divided into two groups to receive either a fiber-reinforced composite retainer or a spiral wire retainer extended on the lingual surfaces of both maxillary and mandibular arches from canine to canine. Periapical radiographs were obtained from the patients at the time of placement of the retainers and after the 6-month period to assess the radiographic conditions of the periodontium. Clinical examination was carried out at the same two time intervals.Even though there were no significant differences between the two groups of study at the beginning of the trial, there were statistically significant differences after the 6-month follow-up regarding the main outcomes of the study. Nearly all indices showed to deteriorate after 6 months in the fiber-reinforced group, while in the spiral wire group, this was not the case. As for the secondary outcomes, radiographic examination did not reveal any statistically significant differences after 6 months or between the two groups.It can be concluded that spiral wire retainers elicit less detrimental periodontal response in the short-term follow-up compared to fiber-reinforced composite retainers as revealed by the primary outcomes of the study.NCT01314729ClinicalTrials.gov: The online version of this article (doi:10.1186/s40510-014-0047-8) contains supplementary material, which is available to authorized users. One of the major challenges for orthodontists is the long-term stability of orthodontic treatment. This has urged orthodontists to seek methods to ensure stable results following the completion of orthodontic treatment. Different investigators have either suggested treatment methods that can enhance the stability of treatment –6 or evaFixed mandibular retainers were first introduced in 1970s  and servFixed retainers, in general, have been criticized for their potential to compromise the periodontal status, due to accumulation of plaque and calculus along the retainer ,25. The Even though the effect of different orthodontic fixed retainers on periodontal status has been studied in previous investigations ,15,24,28This study was approved by the Institutional Review Board for the Health Sciences of Shiraz University of Medical Sciences and was registered under the protocol ID NCT01314729 based on the CONSORT statement  with an The sampling was carried out via the convenience sampling method. The patients who were in the finishing phase of treatment, willing to take part in the study and who met the inclusion and exclusion criteria of this clinical trial were selected as subjects. An informed consent was obtained from all the patients.Healthy subjects with no history or presence of a systemic diseaseBeing in the teenage years (13 to 19 years)The inclusion criteria for the participants were as follows:Presence of any syndromeMissing or extraction of any of the upper and lower anterior teethThe exclusion criteria were as follows:All the patients were treated by one orthodontist with straight wire MBT  0.22 slot technique.Within 1 to 3 weeks before the complete removal of the orthodontic appliances, the participants were referred to a dentist specialized in restorative dentistry. Each patient received either of the two fixed lingual retainers: the fiber-reinforced resin composite  bonded on the lingual surfaces of the six upper and lower anterior teeth or a multi-stranded 0.0175-in. stainless steel wire  bonded with a thin layer of flowable composite resin  to the six upper and lower anterior teeth. In order to randomly allocate either of the interventions to the participants of the study, block permutation design was undertaken with ten blocks including four patients in each block. The file number of all the participants eligible to take part in the study was provided for the biostatistician. Assigning each number to either of the interventions was carried out by the biostatistician. The file number and the name of the participants were also provided for the dentist who was responsible for placing the retainers. Therefore, once each patient was referred for fixed retainer insertion, the dentist allocated them to an intervention based on their numbers.The allocation sequence was concealed from the orthodontist until after the placement of the retainer. All the participants underwent scaling and root planing, in case the presence of plaque or calculus prevented proper placement of the retainers. The decision based on which whether the patient required scaling and root planing was taken by the dentist who placed the retainers after careful examination of maxillary and mandibular anterior regions. The patients were referred for the placement of retainer since the restorative dentist was more experienced in placing the retainers than the orthodontist. For each patient, a wire was formed chairside by the orthodontist and was sent to the dentist to minimize any mistakes in forming the wire due to the lack of experience by the dentist. If the patient was allocated to the spiral wire group, the wire would be used by the dentist; otherwise, fiber-reinforced composite would be placed.Once the retainers were placed, the participants were instructed by the same dentist who placed the retainers to undertake meticulous oral hygiene using both superfloss and interdental brushes along with tooth brushing and to avoid visiting another dentist for any purpose other than caries check-up until the recall appointment.Upon removal of the orthodontic appliances and 6 months after the insertion of the retainers, the participants were checked for their periodontal health along the retainer based on different clinical indices. The assessment and scoring of the indices were carried out by a calibrated dentist.To assess the periodontal health from a radiographic viewpoint, three digital periapical radiographs (two from the upper anterior teeth and one containing the lower anterior teeth) were obtained from each individual upon completion of the treatment and after a 6-month interval. The radiographs were obtained by the same radiologist through the parallel cone technique with a Rinn XCP holder .Plaque index (PI), as described by Loe [d by Loe , was evaThe following clinical variables were measured on each individual as the main outcome measures:0 - Absence of plaque deposits1 - Plaque disclosed after running the periodontal probe along the gingival margin.2 - Visible plaque3 - Abundant plaquePlaque accumulation was categorized using the following scale:2.Calculus index (CI) [0 - Absence of calculus1 - Presence of calculus covering up to one third of the tooth surface2 - Presence of calculus covering up to two third of the tooth surface and/or the presence of separate flecks of subgingival calculus3 - Presence of calculus covering more than two third of the tooth surface and/or presence of a continuous band of subgingival calculusdex (CI) ,32 usingThe results were averaged for the six maxillary and mandibular teeth, and a mean value was recorded for the maxilla and mandible in each participant.3.Gingival index (GI) suggested by Loe [0 - Absence of inflammation1 - Mild inflammation, slight change in color, little change in texture, no bleeding on probing2 - Moderate inflammation, moderate glazing, redness, edema and hypertrophy, bleeding on probing3 - Severe inflammation, marked redness, hypertrophy, tendency for spontaneous bleeding, ulcerationd by Loe  includesAn average was calculated for mandibular and maxillary teeth and the mean value was recorded.4.Bleeding on probing (BOP) was measured 15 s after the insertion of a Florida probe [0 - No bleeding1 - Bleeding on probingda probe  into theda probe . A standda probe ,36 to elGI was only assessed on the lingual surfaces so that the presence of any labial inflammation does not affect the results.Since all the indices were to be evaluated on the lingual surfaces of the teeth, the presence of bleeding following the removal of orthodontic appliances on the labial surfaces of the teeth did not play a role in the scoring results.The secondary outcomes of the study were evaluated by assessing the PDL width which is defined as the maximum width of the PDL space of the teeth measured on parallel periapical radiographs. Radiographs were assessed by two radiologists with more than 10 years of clinical experience. The radiologists were blinded to the study and therefore not aware whether the radiographs were taken at the beginning of the trial or after 6 months. They were asked to score the radiographs relatively, that is, for each patient, the periapical radiograph of the 0 and 6 months of each segment were randomly numbered and shown to each radiologist; they were then asked to mark the number they felt had the largest PDL width. After 1 month, they were asked to repeat the process. Based on the reports of the two radiologists, if the PDL width had remained unchanged or had increased over the 6-month period, a negative value was assigned to that segment; however, had the PDL width decreased in diameter, a positive value was assigned to the periapical radiograph of that segment. This classification was based upon this premise that the teeth must have regained their normal PDL width by the final appointment (6 months after completion of orthodontic treatment) ,38; therIn order to evaluate the primary outcome measures, Wilcoxon test was used to evaluate the changes in each group between the 0- and 6-month period. To assess the difference between the two groups, Mann-Whitney test was used. To assess intra- and inter-examiner reliability in scoring periapical radiographs, Kappa coefficient was used. As for assessing the secondary outcome measures, Fisher's exact test was used.n = 3 in the spiral wire group and n = 2 in the fiber-reinforced group) or because a breakage was diagnosed along the retainer. For stability purposes, these patients had to be immediately referred for the placement of the new retainer. The need for scaling and root planing was assessed and was carried out if required in these patients. Therefore, they had to be withdrawn from further evaluation since the subjects were not to receive any professional cleaning during the 6-month follow-up period. The total sample size therefore was 30 (15 in each group) .The kappa coefficient for the intra-examiner reliability in assessing the PDL width was 0.81 which is excellent . Also, tNone of the indices revealed any significant differences between the two groups of study at the baseline, neither in maxillary nor in the mandibular arch, which implements similar periodontal status in all the individuals at the beginning of the trial. However, after 6 months, there were significant differences in gingival index and plaque index between the spiral wire and fiber-reinforced composite groups in both arches. In addition, a significant difference was found to exist in the formation of calculus in the mandibular arch after 6 months of follow-up in both study groups. All the scores showed to deteriorate after 6 months in both study groups. However, the scores recorded in the fiber-reinforced group reported worse periodontal status compared to the spiral wire group. The calculus index and bleeding on probing showed no statistically significant difference after 6 months between the two groups.Fischer exact test compared the results of periapical radiographs but failed to reveal any differences between the two groups. This might be attributed to the number of the samples in the study. It was shown that 64% of the maxillary radiographs in the spiral wire group reported a positive value, while in 60% of the maxillary periapical radiographs in the fiber-reinforced group, the PDL had either widened or remained unchanged in its diameter. The differences, though, were not statistically significant. For mandible, these results were 50% and 60%, respectively.In this prospective clinical trial, the effect of two common types of fixed retainers on the health of the periodontium was evaluated. All the study samples were selected within the same age group, as different periodontal issues such as gingival recession tends to be affected with age .Even though it has been concluded that following orthodontic treatment, inflammatory responses do follow , all theThe results of our study showed a significant difference in the accumulation of plaque between the two study groups after 6 months, with worse scores recorded in the fiber-reinforced group. This might be attributed to the fact that fiber-reinforced composites occupy a wider span on the lingual surface of the teeth compared to spiral wire retainers. Even though there was no significant difference in the calculus index between the two groups after the 6-month follow-up, there was a significant increase in the accumulation of calculus in the mandibular arch after the 6-month follow-up in both study groups. This finding is not in agreement with the results of Artun et al. who concluded there were no differences in plaque or calculus accumulation between retainers made of spiral wire and those made of plain wire ,28. In aWhen each retainer was evaluated separately, there was a significant difference between the baseline and 6-month follow-up in the spiral wire group for both the gingival index and bleeding on probing in the maxillary arch and calculus index in the mandibular arch.In the fiber-reinforced composite group, all the measured indices increased in both arches after the 6-month follow-up. The calculus index, however, showed no statistically significant differences in the maxillary arch. This can be attributed to the wider clinical crowns of maxillary incisors which provide better access for oral health maintenance compared to mandibular incisors.It has been suggested that placing fixed orthodontic retainers on the maxillary arch poses more risks on the periodontal health, since the retainer has to be placed gingival enough to avoid premature occlusal contacts ; howeverIt has been claimed that fiber-reinforced composite retainers provide a smoother outer surface, while there seems to be more retention areas along the spiral wire retainers which can contribute to the formation of more calculus along the retainer wire ,24. In oFiber-reinforced composites were recently introduced into dentistry and soon found their way into orthodontics as fixed retainers. Fibers were added to composites on the premise of providing more rigidity to the composites . This adIt can be suggested that in future studies, a control group with removable retainers be added to the study groups. The number of patients included in each study group can be further increased. If cone beam computed tomography finds its way to orthodontics as a routine pre-treatment diagnostic record, it can be further used as a precise tool for assessing the changes in the periodontal ligament. However, due to the increased radiation risk and excessive cost, its use cannot be justified for the sole purpose of assessing the periodontal width. The follow-up duration can be increased up to 2 years as fixed retainers are usually left in place for periods longer than 6 months.The results of this study showed that when the fiber-reinforced composite retainers and spiral wire retainers were compared, less detrimental side effects were observed after 6 months in the spiral wire retainers. From the radiographic viewpoint, the effect of the retainers on the health of the periodontium was statistically insignificant and inconclusive.


Exploration of macroscopic quantum entanglement is of great interest in both fundamental science and practical application. We investigate a hybrid quantum system that consists of two nitrogen-vacancy centers ensembles (NVE) coupled to a superconducting coplanar waveguide resonator (CPWR). The collective magnetic coupling between the NVE and the CPWR is employed to generate macroscopic entanglement between the NVEs, where the CPWR acts as the quantum bus. We find that, this NVE-CPWR hybrid system behaves as a system of three coupled harmonic oscillators, and the excitation prepared initially in the CPWR can be distributed into these two NVEs. In the nondissipative case, the entanglement of NVEs oscillates periodically and the maximal entanglement always keeps unity if the CPWR is initially prepared in the odd coherent state. Considering the dissipative effect from the CPWR and NVEs, the amount of entanglement between these two NVEs strongly depends on the initial state of the CPWR, and the maximal entanglement can be tuned by adjusting the initial states of the total system. The experimental feasibility and challenge with currently available technology are discussed. Especially, the hybrid quantum model including solid-state spin systems and superconducting coplanar waveguide resonator (CPWR) systems12345678910On the other hand, due to the fragile nature of single-particle suffering severely from decoherence, it is desired to explore various channels to effectively construct highly entangled states in larger quantum systems, which is one of the central ingredients for large-scale quantum computation4344454745495153In this work, we investigate a hybrid quantum system that consists of two separated NVEs coupled to a common CPWR, where each pair of NVE-CPWR interaction actually is a coherent coupling between two harmonic oscillators or bosonic fields with a collectively enhanced strength proportional to The system under consideration is illustrated in L, the capacitance Cc, and the inductance Fc) consists of a narrow center conductor and two nearby lateral ground planes, whose Hamiltonian has the following form  transformation60The Hamiltonian of a NVE containing So the total Hamiltonian of the NVE-CPWR coupling system is given byk-th NVE and CPWR with where k-th NVEs and the CPWR, respectively. This is a reasonable assumption for the region of interest, where the decay rates are not dominant, and the CPWR has a very small probability to be detected with a photon. For simplicity, here we have assumed where In this section we will focus on the Entanglement dynamics of Nitrogen-vacancy centers spin ensembles. According to the Heisenberg motion equations, we can obtain the differential equations of the operators Considering the initial conditions Xi, Yi, and Zi  are where the expression of coefficients Suppose that the CPWR is initially prepared in an arbitrary normalized superposition of the coherent state where we have used the relationships h.c. denotes Hermitian conjugate and where Through the calculation, the concurrence of two NVEs has the formHere we have employed the relations Besides, the average phonon number where Firstly, we consider the simple case that the CPWR is initially prepared in the odd coherent state where The entanglement dynamics of NVEs is plotted in In μs at room temperature13C has been reported that it could reach 0.6 msT2 = 1.8 ms in the isotopically pure diamond sampleWe now survey the relevant experimental parameters. First, a full wave frequency 13C defects in the spin ensemble have been ignored, nevertheless, this problem could be alleviated by isotopically purified 12C diamond through the purification technique676970In the above discussion, the the detrimental influence from the nuclear spin, such as κ. Because of the local environment difference, the frequencies of the electron spins in NVE are not identical, and the mean frequency is denoted as m is fixed during the processing. The initial and the final states for the m-th excitation states are also orthogonal. The evolution equation of it is In the following we provide the reason that we can use the quantum jump model Eq.  to studyj-th NVE and the j-th flux qubits, like the method inIn order to measure the macroscopic entanglement in realistic experimetns, we need to transfer the state from the NVEs to the states of two additional small flux qubits, each of which is attached on a NVE. So the task of entanglement dectection can be performed by the direct measurement on the states of additional flux qubits, and implementation of transferring the state from NVEs to flux qubits could be realized by using the SWAP gate between the In summary, we have presented a study on the dynamics of entanglement between spin ensembles via the collective coupling between the CPWR and NVEs in such a hybrid system composed by a CPWR and two NVEs. This NVE-CPWR hybrid system behaves as a system of coupled harmonic oscillators, and the excitation prepared initially in the CPWR can be transferred and distributed in these two NVEs, where the CPWR plays the role of common databus. The decoherence effects from the CPWR and NVEs on the quantum dynamics of the entanglement between spin ensembles have also been studied. Therefore, the present system provides a platform to generate quantum entanglement between two or more NVEs embedded in the same resonator, which may be another route toward building a distributed QIP architecture and future NVE-based quantum network.Before using the concept of concurrence for bipartite entangled nonorthogonal states73where  NVEs Eq. can be rρ areTherefore the elements of the orthogonal form It is easy to obtain the square roots of eigenvalues of the matrix How to cite this article: Liu, Y. et al. Entanglement dynamics of Nitrogen-vacancy centers spin ensembles coupled to a superconducting resonator. Sci. Rep.6, 21775; doi: 10.1038/srep21775 (2016).