Theoretical models predict that spatial self-organization can have important, unexpected implications by affecting the functioning of ecosystems in terms of resilience and productivity. Whether and how these emergent effects depend on specific formulations of the underlying mechanisms are questions that are often ignored. Here, we compare two alternative models of regular spatial pattern formation in mussel beds that have different mechanistic descriptions of the facilitative interactions between mussels. The first mechanism involves a reduced mussel loss rate at high density owing to mutual protection between the mussels, which is the basis of prior studies on the pattern formation in mussels. The second mechanism assumes, based on novel experimental evidence, that mussels feed more efficiently on top of mussel-generated hummocks. Model simulations point out that the second mechanism produces very similar types of spatial patterns in mussel beds. Yet the mechanisms predict a strikingly contrasting effect of these spatial patterns on ecosystem functioning, in terms of productivity and resilience. In the first model, where high mussel densities reduce mussel loss rates, patterns are predicted to strongly increase productivity and decrease the recovery time of the bed following a disturbance. When pattern formation is generated by increased feeding efficiency on hummocks, only minor emergent effects of pattern formation on ecosystem functioning are predicted. Our results provide a warning against predictions of the implications and emergent properties of spatial self-organization, when the mechanisms that underlie self-organization are incompletely understood and not based on the experimental study. ExampleAlthough many studies put forward mechanistic explanations for observed patterns based on proposed interactions between organisms and environmental variables, empirical support is often limited, and alternative mechanisms are only rarely considered. However, alternative mechanisms that equally explain the observed spatial pattern are often easily derived ,14. The Mytilus edulis), called mussel beds, are commonly found in intertidal soft-bottom substrates, and vary in size from ten to one hundred thousand square metres [et al. [Here, we propose and compare two models with alternative mechanistic explanations of self-organized spatial patterns in young mussel beds on intertidal flats. Large aggregations of the blue mussel 2) and took the samples to the laboratory for analysis. Relative elevation was determined using a Trimble laser level (www.trimble.com). Dry biomass per square metre and individual weight of five mussels were determined after drying at 80°C for 28 h.We tested the hypothesis that on top of elevated hummocks, mussel biomass or density is higher as mussels have improved access to algal food, against the alternative hypothesis that biomass or density is highest at the up-flow side of each mussel patch, as they experienced a minimal level of competition from mussels upstream. For this, we conducted a field study on a striped mussel bed near Schiermonnikoog, The Netherlands . We sampled mussels at the front, middle and rear position of a mussel hummock (samples covered about 0.0314 m(b)a,b; one-way ANOVA, biomass: F2,30 = 8.4258, p < 0.001; density: F2,30 = 10.153, p < 0.001). This suggests that mussel survival or growth is higher at the top of a hummock, compared with the sides. Moreover, regression analysis of the relation between mussel density and sediment elevation reveals that sediment elevation is positively related to mussel density . These results point at the possible importance of sediment accumulation and subsequent hummock formation for mussel growth. Our results suggest that sediment accumulation is a possible alternative mechanism for local facilitation, as mussels improve their own growth and that of local conspecifics by accumulating sediment underneath them.The results showed that mussel density and biomass are significantly higher in the middle compared with the front or rear positions  and (ii) denote the two alternative positive feedbacks as mentioned above.Here, we develop and compare two spatially explicit models that formalize alternative mechanisms for the local facilitation process. The first mechanism involves a positive effect of mussel density on mussel survival rates, as clumping and attachment to other mussels with byssus threads reduces chances of predation and wave dislodgement. This mechanism is the central hypothesis of a prior paper on self-organized pattern formation in mussel beds ,7. The sFigure 2(a)A in the lower water layer overlying a particular location  on the mussel bed can be expressed asAup is the concentration of algae in the surface layer; f is the rate of mass transfer between the benthic boundary layer and the rest of the water column. The second term represents the uptake of algae by the mussels, assuming a linear relation between mussel uptake and algal concentration, where the coefficient ∂A/∂X multiplied by the advection constant V.We start by constructing a general continuous-time spatial model for spatial pattern formation in mussel beds. On intertidal flats, the filtration of algae by mussels occurs mostly in the lower water layer ,29. Algae describes the conversion constant of ingested algae to mussel biomass. The second term is used to represent all losses in biomass owing to wave dislodgment and mortality (e.g. predation). Furthermore, the movement of mussels is described by the classical diffusion approximation, where diffusion is a linear function of the Laplacian operator ∇2M with diffusion coefficient DM.Mussel growth and mortality in soft-sediment mussel beds are mostly determined by the availability of algal food and by wave dislodgment and predation. We therefore describe the rate of change of mussel biomass per square metre with the expression:(b)et al. [A large number of papers in the literature show that by generating clumps, mussels can reduce their losses to predation and wave dislodgement. Following this observation, van de Koppel et al.  proposedkM is the value of mussel biomass at which mortality is half-maximal, and dM is the maximal per capita mussel mortality rate. The concept and algorithm details and descriptions of the coefficients can be found in [Here, found in  and elec(c)S is defined as the sediment deposited by the mussels on top of the pre-existing tidal flat surface,  k1 describes the deposition of sediment in the form of pseudofaeces per unit mussels, while dS describes the proportional rate of erosion of sediment. Sediment is assumed to disperse in a diffusive manner, proportional to a diffusion constant DS, because of the effects of water flow and hydraulic diffusivity, where the dispersive scale of sediment is greater or equal to that of the mussels.Below, we construct an alternative model that includes the feedback between sediment accumulation induced by the mussels and improved uptake of algae by these mussels, reflecting the results of our field survey. First, we need to describe the rate of accumulation of sediment as a function of local sedimentation and erosion processes. We assume that sedimentation is mostly the result of the filtration activities of mussels, while erosion is proportional to the amount of sediment present:c (c > 0). Thus, the uptake feedback is modelled as a monotonously increasing function of sediment elevation; the higher the elevation, the higher the uptake rate and the more algae are consumed by the mussels. The explicit dependence of sediment accumulation is chosen as c and g are constant. Parameter c defines the maximum uptake rate (per hour), kS is the saturation constant of sediment accumulation (in centimetres per square metre) and g sets the proportion of G(S) that is attained when the sediment level is zero, and thus equal to the background sediment level (dimensionless). Hence, when S → 0; g gets closer to 1, the uptake coefficient G(S) levels off to a maximum. A small g imposes a stronger positive-feedback effect of the sediment on the uptake rate. This scenario closely follows our assumption that the positive effect of sediment accumulation acts through the hummock development. With this mechanism, we assume a constant mussel loss rate x direction driving the advection. We adopted periodic boundary conditions in the flow direction to mimic predepletion of the water by the bed surrounding the simulated domain. Reflecting boundaries were adopted in the other direction. Starting conditions consisted of a homogeneous equilibrium with a slight random perturbation.To investigate the effect of the alternative feedback mechanisms on spatial pattern formation, we performed a two-dimensional numerical simulation of the models derived above. The spatial patterns result from Euler integration of the finite-difference equations with discretization of the diffusion and advection operators . The modAup), which is the parameter that clearly distinguishes different intertidal habitats. We therefore analysed the changes in the models' predictions with respect to this parameter using spatial bifurcation analysis [An important focus is the question of whether the models' predictions differ with regard to the effects that patterns have on the functioning of the mussel bed, in terms of (i) bed-wide production of biomass and (ii) resilience to disturbances. To answer the first question, we studied the difference in predicted mussel biomass at equilibrium, comparing the average biomass in the patterned and the homogeneous state. This difference, however, is sensitive to changes in, for instance, the algal input concentration  is defined as the period taken for mussel biomass to reach 0.97 Meq from a 0.9 Meq (or 0.5 Meq) perturbation from the previous equilibrium, where Meq refers to equilibrium biomass. We implement the simulation based on the spatial scale of two wavelengths, and adopt bidirectional advection for the algal differential equation, where advection direction switches sign every 6 h. Bidirectional advection includes both the ebb tide and flood tide processes, which leads to the development of stationary patterns that allow for measurement of the return time to equilibrium. Both the unidirectional and bidirectional set-up generate qualitatively similar results, but equilibrium biomass in the unidirectional set-up is intrinsically fluctuating because of the movement of the banded solution.The second question concerns the effects that the alternative mechanism has on resilience, in terms of the time required to return to equilibrium. A recent study  has showet al. . Here, t4.(a)Comparison of the predictions of the models reveals that very similar spatial patterns develop, irrespective of the type of facilitative interactions between mussels . In bothAup. Both the decreased losses model and the sediment accumulation model have a homogeneous, non-zero state for all Aup values above a minimum Bifurcation analysis revealed a clear effect of algal supply on the characteristics of the patterned mussel beds, where the presence of patterning strongly depended on the value of algal input terature . This imanalysis . Howevera, green lines versus black lines) for all parameter values where stable patterns are predicted. In the sediment accumulation model, this difference is much smaller, or even reversed, depending on the algal input concentration. This points at an important difference between the decreased losses model and sediment accumulation model, in that increased production, which is considered an important emergent effect of spatial self-organization on ecosystem functioning in the decreased losses model [The bifurcation analyses reveal a striking difference between the decreased losses model and the sediment accumulation model in terms of the implications of spatial self-organization for ecosystem functioning. In the decreased losses model, average mussel biomass is much higher in the patterned equilibrium compared with the homogeneous equilibrium a). Qualitatively similar differences between simulations were found in the model with the sediment accumulation feedback model (b).Comparison of the models shows a remarkable difference between the reduced losses model and both sediment accumulation models with respect to the ecological resilience to a 10 and 50 per cent reduction in biomass . We compared simulation trajectories, where the patterns were left intact with simulations where mussel biomass was nearly homogenized, and studied the time the system needed to return to the patterned equilibrium. The recovery time of these two simulations we in turn compared with the recovery time in the homogeneous system. First of all, in all models, mussel biomass recovered much faster after a perturbation if the patterns were left intact than if the biomass was redistributed near-homogeneously. This difference increases as the critical threshold proached a. Qualitck model b.FigureAup approached the critical thresholds We found a remarkable quantitative difference in the recovery time between the reduced losses model and the sediment accumulation model. With both models, recovery times were found to increase in the homogeneous state when ing down . Criticaing down ,39. Stri(c)S, but of the accumulation relative to the average surroundings, using a feedback function Ω. Although different in detail, this model again predicts similar patterns, but very different effects of the patterns on ecosystem functioning relative to the reduced losses model . Hence, despite the simplicity of the models we used, they clearly point to the sensitivity of the predicted emergent properties to the underlying mechanism.Our model still includes a very simplified description of the effect of enhanced sediment accumulation on the uptake and growth of the mussels. Specifically, we relate uptake to absolute sediment accumulation, while relative sediment elevation of the mounts with respect to the surrounding sediment could be an alternative explanatory variable, especially when the entire sediment bed increases in elevation. For this reason, we have also analysed a second model in which growth stimulation is not a function of the absolute sediment accumulation 5.The process of spatial self-organization is the central explanation for the occurrence of regular or otherwise coherent spatial patterns in ecosystems lacking underlying abiotic heterogeneity . HoweverOur results show that very similar spatial patterning emerges under both mechanisms. Hence, observation of the characteristics of the spatial pattern will not disqualify either of the proposed mechanisms. However, the models predict a strikingly different effect of spatial self-organization on ecosystem functioning, especially in terms of established mussel biomass in equilibrium. The bifurcation analysis reveals that in the decreased losses model, spatial self-organization causes a large increase of mussel biomass relative to that predicted for homogeneous beds, over an extensive range of parameter values. This prediction can be explained by the local facilitation process within mussels, in which the mussels attach themselves to each other with byssal threads, thereby reducing predation or wave dislodgement. Conversely, the analysis of the sediment accumulation model reveals only a minor or even negative effect of pattern formation on bed-wide production, especially when algal concentration in the upper layer is high. Only when algal concentration is insufficient to support mussels in a homogeneous bed, but is high enough to support a patterned bed , no such reduction was observed in the patterned state; spatial patterning seemed to nullify the phenomenon of critical slowing down. This effect, however, was completely absent in the sediment accumulation model. Hence, the effects of patterning on resilience seem to depend strongly on the mechanisms that underlie the patterning, similar to what is predicted for bed-wide production.A very conspicuous feature of patterned mussel beds is the co-occurring patterning in the geomorphic landscape, caused by the excretion of mud particles by the mussels, which generate mounds that are elevated on average 30 cm above the ambient sediment. The results of our field experiment clearly point out that on these mounts, a higher density of mussel biomass persists. We hypothesize that the higher density is most probably explained by improved growth conditions, caused by increased water flow rate over raised mounts. Alternative explanations such as increased recruitment on top of the hummocks or active or passive movement can probably be excluded. First, most mussel beds develop from a near-even spread of larvae on unpatterned sediment. Second, passive movement would probably remove the mussels from the mounts as mounts catch more wave action. Finally, active movement could contribute to the accumulation of mussels on the hummocks, but prior observations  revealedCritical slowing down (e.g. a longer return time to equilibrium following disturbance) is one of the most prominent early-warning indicators for the proximity of catastrophic tipping point in ecological systems . A recenIn the past decade, large bodies of theoretical studies have appeared in the literature explaining spatial patterns observed in a wide variety of ecosystems. Often, these studies were based on a single explanatory mechanism, based on the intuition of the modeller rather than on a firm empirical basis, and assuming that process could be derived from pattern. Our study emphasizes that for mussels, alternative mechanisms can equally well explain the same spatial pattern, and that models, at most, give insight into possible mechanisms, rather than accurate understanding of mechanisms of pattern formation. Moreover, alternative model formulations can provide contrasting predictions of the emergent properties of spatial patterning for ecosystem functioning, and of the response of ecosystems to changing conditions. Hence, for a full understanding of the importance of spatial patterns in driving ecosystem characteristic and dynamics, alternative mechanisms should be investigated, and their assumptions validated in field studies.The distinction between observation of patterns and inference of their underlying mechanisms, as put forward in this paper, has implications that go beyond the system studied here. For instance, since chaos was discovered by May in the 1970s from a simple population model ,46, math


Muricea muricata specimens were successfully acquired by X-ray computed tomography with spatial resolution ranging from 4.5 to 25 micrometers. The success mainly depended on specimen immobilization. More than i.e. only followed the main branch or “turned” into a secondary branch, many others bifurcated or fused. A majority of bifurcations were observed at branching points. However, some canals appeared and/or ended anywhere along a branch. At the tip of a branch, all canals fused into a unique chamber. Three-dimensional high-resolution tomographic imaging gives a non-destructive insight to the coral ultrastructure and helps understanding the organization of the canal network. Advanced image-processing techniques greatly reduce human observer's effort and provide methods to both visualize and quantify the structures of interest.The long-term goal of our study is to understand the internal organization of the octocoral stem canals, as well as their physiological and functional role in the growth of the colonies, and finally to assess the influence of climatic changes on this species. Here we focus on imaging tools, namely acquisition and processing of three-dimensional high-resolution images, with emphasis on automated extraction of canal pathways. Our aim was to evaluate the feasibility of the whole process, to point out and solve – if possible – technical problems related to the specimen conditioning, to determine the best acquisition parameters and to develop necessary image-processing algorithms. The pathways extracted are expected to facilitate the structural analysis of the colonies, namely to help observing the distribution, formation and number of canals along the colony. Five volumetric images of  Cnidaria: Octocorallia: Holaxonia) are marine animals whose polyps grow forming complex tree-like networks. They are basically formed by a holdfast strongly attached to a hard substrate and a main stem, from which branches furcate in a diverse array of patterns Branching patterns are omnipresent in nature, from geological structures such as river drainage networks and glaciers to organic systems such as leaf vessels, and the mammalian blood-vessels and bronchi, among many others There is a remarkable analogy between octocoral networks and the branching organization of plants. Noted for the first time by Leonardo Da Vinci, the number of vessels in a tree trunk is directly related to the number of leaves in the tree crown what is formally known today as the pipe-model theory According to Despite the expected great importance of stem canals for the colonial arrangement, regeneration and growth of a coral group comprising over three thousand species distributed worldwide, it is also unclear how are their anatomy, organization, skeletal composition and, most important, their configurations at the branching points. All we know at the moment is that it is a complex network spreading throughout the whole colony, that the number of canals decreases towards the branch tips and that the canal wall is densely packed with calcite spindle-like sclerites Coral reef scientist are facing new environmental challenges, which require the development of new experimental techniques. Constant accumulation of atmospheric The micro-CT imaging is gaining attention because of its high resolution and non-destructive characteristics. In this context, “non-destructive” refers to the fact that the specimen can be reused after image acquisition, as opposed to such techniques as cutting it into tiny slices, in order to observe its micro-structure. Previously, standard CT images were used to evaluate the form and growth of sponges and corals Scleractinia) and velvet finger (Montipora digitata) Acropora, Goniopora and Porites. Strucutural properties measured in segmented images and physical properties deduced from numerical simulation were also used to compare Acropora and PoritesTo assess the usefulness of corals as scaffold material, the average internal diameter of ducts was manually measured in two species: stony coral  the technical problems related to the conditioning of specimens, to determine the best acquisition parameters and to provide a support for the development of necessary image-processing algorithms. The pathways extracted are expected to facilitate the structural analysis of the colonies, namely to help observing the distribution, formation, and number of canals along the colony, and finally to assess the influence of climatic changes on this species.It is technically unfeasible to acquire one single image representing a whole colony with a sufficient spatial resolution. Furthermore, even if it was feasible, the resulting image size would not be manageable on a standard personal computer. Therefore, the best trade-off was searched between the image resolution and field-of-view (FOV). We conjecture that, if the whole extent of the colony is covered by a collection of smaller overlapping images, appropriate image-processing techniques can align the partial images and subsequently retrieve useful global characteristics of the colony, provided that the spatial location of each image is known with sufficient precision and that the specimen is appropriately immobilized during the acquisition.Muricea muricata were taken in Colombian territorial waters of the Caribbean Sea .The method can be subdivided into three distinct steps: initialization, pathway tracking and post-processing. The core of the approach proposed is an algorithm designed to extract the pathway of a canal, from a starting point located in this canal, until a stopping criterion is reached. As dozens of canals can be present in a single image volume, the initialization step was devised to automate the localization of the starting points in each canal. The architecture of the canal network proved rather complex, so that the initialization needs to be performed at least in each ramification of the colony. However, with such a strategy, some pathways may be extracted twice or more. Furthermore, for various reasons, the stopping criteria may fail. The role of the post-processing step is therefore two-fold: to detect and cut the line segments, the behavior of which is erratic compared to other nearby pathways, on the one hand, and to detect and fuse the lines that follow the same canal, on the other hand. All the image-processing algorithms and the graphical user interface have been implemented using the CreaTools software development platform  images Our algorithm  also iteThe orientation estimates based on the inertia matrix proved unreliable, owing to the highly irregular shape and densities at the boundaries of the canals. For the same reason we rejected the alternative orientation estimates and “tubularness” criteria from the literature, based on derivatives, namely on gradient flow or on the eigen-analysis of the Hessian matrix, which are even more sensitive to such irregularities. Instead, we drew our inspiration from the HD filter that was originally devised to improve the visualization of small vessels in MRA In the seminal filter, ed  and  . The choght cone  with angOnce the local orientation t point  , accordiThe tracking stops when the cylinders reach the image boundary or the difference between The initial orientation of the pathway is set orthogonal to the cross-section used to find the starting points. The initialization of the cylinder dimensions is based on  overlap . This caAs mentioned in the previous section, the pathway tracking requires a starting point within each canal. In medical imaging, an interactive selection of a starting point is often performed. This solution can also be adopted in our application. However, due to the large number of canals to be extracted, some automation is desirable. We developed a pragmatic solution, where all the processing is nearly automatic, but some interactive help can be provided in case of failure. The process begins by selecting one axial cross-section in each branch of the octocoral, located halfway between the ends of the branch –5. The sThe goal of the post-processing is to “clean” the set of the pathways extracted: cut their erratic parts, if any, and combine the pathways located within the same canal into a single pathway. It is very unlikely to find an isolated canal without other almost parallel canals nearby. Therefore, when a part of a pathway extracted is too far from the neighboring pathways, this part is probably erratic and should be cut. Our algorithm determines the average distance between each pathway extracted and its nearest neighbor. Then it identifies the pathways, for which this distance is significantly larger than the mean distance observed in the whole set. Within each of thus detected outlying pathways the actually erratic parts are determined by analyzing the gray-levels of the pathway points. Points that significantly deviate from the mean gray-level are removed. Two pathways are located within the same canal if they are not separated by a canal wall. This is detected by analyzing the gray-level profiles between the points of the neighboring pathways. The locations of such point pairs are averaged. These steps  are detaTo evaluate the methods proposed, the pathways automatically extracted were compared to reference pathways. As ground truth was not available, the reference pathways were interactively drawn by a trained observer. In order to assess the accuracy of the pathway extraction algorithm itself, while avoiding possible errors induced by incorrect locations of automatic seed points, the algorithm was initialized with manually selected points. Separately, we evaluated the accuracy of the automatic detection of seed points within canals, in the cases where this option was exploitable. Four datasets  were used in the evaluation. The dataset BASE, as well as the long straight isolated branch in S3 (on the left in http://www.mevislab.de/), has been used to manually mark the pathway points along all the perceptible canals. A careful tracing of the pathways was very time-consuming and required several iterations to cope with unexpected canal bifurcations and endings.A custom-made tool, based on MeVisLab  near the center of each canal perceptible in each initial cross-section. The automatic seed points were compared with these reference points in two steps.First, the automatic points were labeled as correct  and acceptable acquisition time (below one hour). Additionally, from medical imaging experience, CT is well suited to visualize calcified structures When dealing with 3D images, the external structure of objects can be assessed using relatively standard software tools such as thresholding, mathematical morphology and surface rendering a branch .The measure of overlap between the extracted pathways and the reference ones depends on the criterion defining the true positive, false positive and false negative points. With a criterion based on a maximum distance The parameter settings were empirically fixed during the development, based on limited training data. These settings may potentially be suboptimal and their sensitivity was not rigorously assessed. Nevertheless, we believe that the algorithms are relatively robust to the parameter settings, since they achieved consistent scores in images having a wide range of characteristics , as stated in the previous section.i.e. only followed the main branch or “turned” into a secondary branch, many others bifurcated or fused. Particularly noteworthy, branching points consistently showed canal bifurcations allowing the original canal to continue towards the tip but maintaining a connection with the new branch. This bifurcation process was also consistent with an increase in the canal dimension as a preamble to division. These observations answer our former question on the relationship of the canal network and branching. This also opens the possibility that canal bifurcation at branching points can be modeled with respect to the ratio between mother and daughter branches likewise many other aspects of gorgonian form and growth Pseudoplexaura porosaOur previous understanding of the stem canal network in octocorals was rather simplistic, in short: the number of canals decreases linearly towards the branch tips Muricea muricata the number of canals just before fusion varied from 10 to 12, whereas in another gorgonian species, Eunicea mammosa, the minimum number of canals found in a number of dissected colonies was sixteen, a multiple of eight Telestidaee.g., Telesto and Carijoa) form hollow tubes emerging from stolons, which have an apical polyp with subordinate lateral polyps After examining the structure of the gorgonian stem canal network with high-resolution X-ray computed tomography imaging the growth of the network, as well as of the colony, appears as a more complex process than previously thought. It was unknown if sites in the colony producing new canals could be either at the colony base, at the branch tips or both. Now it is clear that a significant number of canals originate at branching points, which is a process that should reiterate when the first polyp started to multiply and form the primary branch. Here we observed that stem canals fused at the branch tips, forming a unique chamber of complex architecture. In the analyzed apical regions of in vivo assays. For instance, mesocosm ocean acidification and calcification experiments, which are in great need of methods providing fine resolution images of growth and calcification e.g., Muricea muricata, which is made of calcite sclerites. With a micro-CT approach similar to the one developed here, one might examine a large extent of canals and other calcifying structures as a measure of dissolution, for instance, following the same specimen multiple times along the experiment. This would open an entirely new era of non-destructive possibilities for growth and calcification experimentation in corals.This study answered some questions on the nature and organization of the pseudovascular tree-like network of a colonial animal, but raised new ones. The imaging method tested here opens a number of applications and possibilities to study important biological and environmental questions for coral biology. The non-destructive approach is likely to make the method suitable for diverse ms e.g., . CurrentIn summary, our work not only contributes to better understand the internal organization of octocoral tree-like networks but provides a non-destructive computerized method to examine the skeletal ultrastructure of octocorals, which has many applications. Using the methods developed here we can reconstruct the pathway of each stem canal, with minimum user interaction. Given the small size (micrometers) of the structures to analyze, high resolution X-ray computed tomography images were needed. To the best of our knowledge the images acquired within this study belong to the first attempts to assess the internal structure of canals in octocorals by means of micro-CT, which demonstrated to be feasible without the need of histological or other destructive methods. Using our method applied onto these images, a 3D representation of the canal network was generated for the first time. Results that otherwise would have needed a great deal of serial histological sectioning, which damages the specimens and involves fixation artifacts.Figure S1Delineation of the canal region. (A) Cross-sectional image. (B) Region (TIFF)Click here for additional data file.Figure S2Quasi-periodic pattern of the canal region. (A) Unrolled canal region (TIFF)Click here for additional data file.Figure S3Low-pass filtering in the frequency domain. (A) Fourier transform of the original signal. (B) Original and filtered signal.(TIFF)Click here for additional data file.Figure S4Detecting points located in different canals. (A) Cross-sectional image with a pair of points located in different canals. (B) Image intensity profile between these points. The dashed line corresponds to the threshold equal to (TIFF)Click here for additional data file.Figure S5Definition of true positive, false positive and false negative points. True positive (TP), false positive (FP) and false negative (FN) points are labeled based on distances between the corresponding points in the extracted pathway (TIFF)Click here for additional data file.File S1Appendix. Automated determination of the seed points. Post-processing. Pathway evaluation measures.(PDF)Click here for additional data file.


The theory is then applied to experimental data from electroreceptors of paddlefish, which have two distinct types of internal noisy oscillators, one forcing the other. The theory provides an analytical description of their afferent spiking statistics during spontaneous firing, and replicates a pronounced dependence of ISI serial correlation coefficients on the relative frequency of the driving oscillations, and furthermore allows extraction of certain parameters of the intrinsic oscillators embedded in these electroreceptors.Stochastic signals with pronounced oscillatory components are frequently encountered in neural systems. Input currents to a neuron in the form of stochastic oscillations could be of exogenous origin, e.g. sensory input or synaptic input from a network rhythm. They shape spike firing statistics in a characteristic way, which we explore theoretically in this report. We consider a perfect integrate-and-fire neuron that is stimulated by a constant base current (to drive regular spontaneous firing), along with Gaussian narrow-band noise (a simple example of stochastic oscillations), and a broadband noise. We derive expressions for the  We explore how a neuron responds to a special type of input signal which is oscillatory but noisy (narrow-band noise). These fluctuations could be due to sensory input, due to oscillatory activity of a surrounding network, or due to a natural stimulus. We study theoretically the effects of noisy oscillations on an idealized model neuron, which would otherwise produce as output a series of action potentials at regular intervals. Because our model is comparably simple, we can describe the effects on ISI statistics analytically with formulas that we test against computer simulations of the model. Moreover, we can compare our theoretical predictions to experimental data from electroreceptors of paddlefish - a biological example for spiking neurons that are naturally stimulated by stochastic oscillatory input. In particular, our theory provides a simple explanation of the seemingly complicated patterns of correlations between interspike intervals, that are observed for the electro-afferents in paddlefish; the theory shows also good agreement with respect to other independent spike train statistics. Our findings further the understanding of how nervous activity is shaped by oscillatory noisy signals, which can emerge in the neural networks of the brain, in the sensory periphery, and in the environment. Oscillatory activity is common in neural systems. Mechanical oscillations form an important class of sensory stimuli, for instance, in hearing, but may also be generated autonomously by mechanosensory hair cells stochastic oscillations, and are characterized by a preferred frequency band of spectral power. An individual neuron's activity may be affected by stochastic oscillations via synaptic input to it, or from its own endogenous fluctuations. Although stochastic oscillations are frequently found in neural systems, there is generally poor understanding of how an input current of this kind affects the firing pattern of a neuron, its ability to transmit information about time-dependent stimuli, and its interaction with other cells in a neural network. This is in marked contrast to the often studied (non-stationary) problem of how a deterministic periodic driving affects neural activity  driving, different analytical approaches and results exist see e.g. . Expliciin vivo paddlefish preparations in which external environmental noise due to water motion was minimized.Extensive experimental results pertinent to this problem of how stochastic oscillations shape the spontaneous spiking of a sensory neuron exist for the peripheral electroreceptors in paddlefish, which embed two distinct types of stochastic oscillators, one running at approx. 25 Hz, residing in a population of epithelial cells, which drives another in the peripheral terminals of afferents, running at approximately twice higher frequency. It was shown that the forcing from stochastic epithelial oscillations leads to rather complicated firing statistics of afferent firing, with multiple peaks in spike train power spectra, and extended-range correlations in the ISI sequence, continuing for tens of ISIs not reset after spiking. Important parameters of the model are: (i) the frequency ratio In this paper, we present novel analytical results for the firing statistics of a perfect integrate-and-fire (PIF) neuron model, which is driven by noisy oscillations For this simple model, we calculate approximations for the ISI density and the ISI serial correlations and compare them to numerical simulations of the model. When discussing our explicit results, we focus on changes of the ISI statistics upon varying the ratio We then compare our formulas for the ISI statistics to experimental data from electroreceptor afferents of paddlefish, obtained previously In this work, we aim at (i) the statistics of individual interspike intervals (ISI) by means of their probability density function (pdf), its coefficient of variation (CV), and its skewness, and (ii) the correlations between ISIs as quantified by the serial correlation coefficient (SCC). We study these statistics for the perfect integrate-and-fire (PIF) model and compare the theoretical results to experimental data.ethods, we also show some of the statistics as functions of our small parameter Despite the apparent simplicity of the PIF model, the fire-and-reset condition severely complicates the analysis. For the calculation of the ISI density and ISI correlations, one has to solve a first-passage-time problem in the form of a Fokker-Planck equation in a four-dimensional state-space spanned by the voltage and all the noise variables. The fire-and-reset condition imposes a complicated boundary condition on a half-space Our results are valid for arbitrary time scales of harmonic noise and OU noise; the general formulas are provided in the For the ISI density with weak total noise, a short-correlated Ornstein-Uhlenbeck process tain see :(6)with is another important statistic, which characterizes the variability of ISIs. For a sufficiently high quality factor We can draw a few conclusions from oise cf. . Remarkaoise cf.  sectionanth-order interval distribution (see Methods). For a high quality factor of the harmonic noise and a small correlation time of the OU broadband noise, the formula for the SCC can be considerably simplified to readThe serial correlation coefficient (SCC) reduce the amplitude of the serial correlations at all lags. In contrast, an increase in the variance of the harmonic noise amplifies the serial correlations. Secondly, spike intervals are correlated mainly due to the correlations in the driving stochastic oscillations, and hence the SCC shows an overall decay with the “lag constant” The dependence of the serial correlation coefficient All of these predictions are confirmed in the comparisons to numerical simulations in  . They loAnother validation of our analytical result at very high coherence of the harmonic noise is illustrated in The overall length of the ISI correlations can be characterized by the correlation lag, defined asin vivo electroreceptors of paddlefish. A single peripheral electroreceptor (ER) in paddlefish embeds two distinct oscillators. One resides in a population of epithelial cells , and can be recorded near an epithelium. This EO is coupled synaptically to another oscillator associated with the terminal of a given primary sensory afferent neuron  The theory developed in the previous sections was applied to experimental data obtained from in vivo preparation of paddlefish, an extracellular single unit recording offers information about the firing of an ER afferent. However, parameters of the epithelial oscillator, such as its effective quality factor and its variance, are hidden (Discussion). Previous computational studies have shown that a model of two unidirectionally coupled oscillators reproduces well the spontaneous and response dynamics of paddlefish ERs In the ethods). External noise was minimized, and a criterion for stationarity of long data segments was imposed. The data were in the form of sequences of spike times We analyzed spontaneous spiking activity from a sample of From a given spike sequence, we estimated the SCCs, the probability density of ISIs, and the power spectral density of the spike train. mean ISI . They alean ISI  showed aTo apply our theory to experimental data, we extracted from the serial correlations of an afferent spike train the four parameters needed for the PIF model: the quality factor To calculate the probability densities of ISIs and the PSDs, we needed to accept a value for the correlation time of OU broadband noise, Finally, The quality of fit is further illustrated in The application of the fitting procedure to our sample of ERs provided the following sample-averaged values for the parameters of the PIF model:Next, we analyzed how the statistical properties of afferent ISIs depend on the parameters of epithelial oscillations. In contrast to analytical or numerical analyses, which allow studying the dependence of a given statistical measure versus a single control parameter, other parameters being fixed, here instead each experimental data point on the scatter plots of tal data , having k-th afferent. The mean trend from theory formed a straight line with positive slope, correctly predicting that the correlation lag increases for more coherent epithelial oscillations. More than expected of the experimental data points (47/56 = 84%) fell within the predicted ±1 SD (68%) bands.To quantitatively compare experimental data to expectations from theory, we calculated The ISI variability metric y ratio  , with thFinally, This report analyzed a scenario in which the membrane potential and spiking of a neuron is forced by weak noisy oscillatory input, in a narrow but non-vanishing frequency band. Our goal was to study the effects of narrow-band noise input on the output spiking statistics of a neuron. Our analysis centered around a perfect integrate-and-fire model of a single neuron, stimulated by a mixture of stochastic oscillations and broadband noise. We obtained novel explicit expressions for the probability density and serial correlation coefficients of the model's interspike intervals (ISIs). By a perturbation calculation of the Fokker-Planck equation, we derived a structurally simple form for the serial correlation coefficient. This novel derivation helps to solve the inverse problem: using the spike statistics of a neuron to estimate parameters of the underlying stochastic processes that drive its firing. No other body of theory has rigorously addressed the implications of narrow-band stochastic input for neural firing statistics, despite much acclaim of the widespread roles of oscillators in nervous systems.Our new analytical formulas compare extremely well with results from our numerical simulations of the spiking neuron model, provided that the variance of the total input noise is weak, such that the coefficient of variation of spiking output remains low, less than approximately 0.3.We compared the PIF theory to spike time data from a well-defined experimental system, the electroreceptor afferents of paddlefish, which receive stochastic synaptic driving in a narrow frequency band from ongoing oscillations arising in their sensory epithelia. For a given afferent's sequence of ISIs, a fitting procedure was used to extract four parameters needed for the PIF model, and the model's output was computed. The only appreciable discrepancy between model and experiment was observed in the skewness of ISI distributions in which the model showed consistently smaller values and in the low frequency regime of spike train power spectra, in which the model showed excess noise power. This low frequency regime is presumably shaped by spike-frequency adaptation, which we did not incorporate in our model to keep it analytically tractable.The fitting parameters varied considerably for different units, reflecting natural variability of the electroreceptors. These natural ranges of values permitted us to check whether different functional relationships were correctly predicted by the theory. For example, in both theory and experiment, the temporal extent of the SCCs  extracellular field potentials prevalent in mammalian cortex Specifically, our results show how the structure of a neuron's serial ISI correlations depends characteristically on the frequency ratio of weak stochastic oscillatory input, and the intrinsic periodicity of a neuron receiving the input, with extreme SCC behavior occurring at integer multiples. We have delineated other parameters which strongly affect SCCs including the quality factor of stochastic oscillatory drive (i.e. its bandwidth and coherence), the neuron's mean firing rate, and the overall level of spike timing noise (its CV). Our results bear general importance for the effects of weak stochastic oscillations on the spiking statistics of neurons in other systems, and are relevant to the study of neuronal firing in many brain regions. We have defined a basis in theory for using serial correlations to detect and characterize weak interactions of physiological oscillators, which may apply to other organ systems as well i-th ISI. Calculations are simplified without loss of generality by restricting the stationary ensemble of spike trains to those realizations having a spike at time n-th order interval, defined as the sum of n-th spike time:nth-order intervals, for all n-th-order intervalWe used conventional metrics, summarized here for clarity, to characterize the statistics of a stationary spike train given by the set of spike times ISI probability densitymean of the nth-order interval is variance is coefficient of variation (CV), defined as the ratio between ISI standard deviation and mean is given byskewness defined byserial correlation coefficient (SCC)nth-order variances by the formula The In this paper we gave parameters of the model simulation in terms of n-th-order interval is given by The mean ISI in the PIF model is independent of the properties of a noise with zero mean nth-order intervals can be interpreted as a first-passage time (FPT). In fact, in the PIF model the statistics of the sum of n-th spike time and the FPT with respect to the boundary nth spike depends only on the total distance To obtain higher moments as well as the probability density of through the boundary with negative velocity. Mathematically, this entails the boundary conditionThe FPT problem can be solved by using the Fokker-Planck equation for the probability density see e.g. . This equpon firing. How can one obtain this probability density? To this end, let us for the moment reconsider the original setup, where the trajectories are reset if The initial condition is determined by the fact that at time nth-order interval density The time-dependent solution of the Fokker-Planck nth-order interval density can be derived from the characteristic functionΦ:The For stochastic oscillations with a high quality factor nth-order variance, we consider the Laplace transform of the nth-order interval densityTo compute the nth-order varianceApplying the transformation (50) to the FPE (37) leads to an equation for  of  cf. :(57)Againth-order variance given above, the SCC can be computed using Knowing the Here we briefly discuss the range of validity for our approximations. In general, we expect our theory to be valid whenever The plots illustrate that the theory works well for Polyodon spathula) were recorded in in vivo preparations with procedures detailed in Data from pwelch of MATLAB's Signal Processing Toolbox).Analyses of spike time sequences from paddlefish electroreceptor afferents were performed using MATLAB's Signal Processing and Statistics Toolboxes. A spike train, The following procedure was used to extract 4 parameters of the PIF model  and (21).nlinfit with the formula (12), where The experimental SCCs were fitted using MATLAB function Finally, the intensity of OU noise,


Malunion of proximal humeral fractures can lead to a severely impaired shoulder function. Loss of motion is often the main issue in patients and can be secondary to osseous, soft-tissue as well as neurological damage to the shoulder. Malunion of the articular surface of the humeral head can lead to pain, chronic degenerative changes secondary to joint incongruity and mechanical block to the range of movement. A 46-year-old otherwise healthy male chef presented with malunion and collapse of his previous plate fixation for a four-part proximal humerus fracture. We describe the first documented case of the use of a focal resurfacing system for dealing with such an osseous mechanical block in the presence of an otherwise preserved articular surface in a high-demand patient. HemiCAP can be successfully used in proximal humeral fracture malunion where there is a localized cartilage defect, allowing restoration of joint congruity while preserving the bone stock. Malunion of proximal humeral fractures, especially the three- and four-part types, can lead to severe functional impairment due to deformity, articular incongruity, avascular necrosis, posttraumatic arthritis as well as associated soft tissue and neurological injury. In the absence of avascular necrosis and with a relatively preserved articular surface, a reconstruction procedure rather than a head sacrificing procedure may be preferable if anatomic restoration is possible. This is challenging, however, with a high complication rate and variable outcome results.The HemiCAP system  allows a more focal resurfacing of an articular surface and is indicated in the management of humeral head osteoarthritis, avascular necrosis as well as management of local chondral defects and other isolated defects such as Hill-Sachs lesions restoring articular congruity and preserving bone stock. The system provides instruments to map and prepare the focal damaged area to allow implantation of a cobalt–chrome and titanium implant  that preThe HemiCAP system has been used successfully in the correction of Hill-Sachs lesion for recurrent anterior shoulder instability. However,An active 46-year-old right hand-dominant nonsmoking healthy male chef presented with a four-part proximal humeral fracture following a motorcycling accident . In viewWe felt that the bony spur was the main cause of his limited function. Given his high-demand requirement and otherwise normal-appearing articular surface that was not significantly malrotated, we elected to perform a joint-preserving procedure. Excision of the prominent bony region was considered over a restorative osteotomy; the former, however, would leave an exposed area of bone that could go on to cause pain, with the risk of recurrence of the mechanical block due to bony outgrowth. We, therefore, opted to focally resurface the area using the HemiCAP system.Under general anesthesia with an interscalene block and the patient in the beach chair position, a standard anterior deltopectoral approach was used through the old incision. The previous fixation plate and screws were successfully removed first and the malunion of the fracture and the presence of an intact rotator cuff were confirmed. The subdeltoid and subacromial adhesions were then released and the subscapularis and the associated capsule were incised at the lesser tuberosity and lifted off to expose the humeral head. Adequate release of the soft tissues with retraction allowed the bony spur to be easily visualised and brought into the operating field by extension and external rotation. This was removed using a fine saw .A guidewire was then placed central to the defect and perpendicular to the articular surface with a drill guide used to demarcate the area of concern and allowing measurement of the appropriate articular component diameter (25 mm) required to resurface the defect. A cannulated drill was then used in order to prepare the head to receive the headless titanium post. A trial Cap was then used to confirm that the post was at a correct depth so that the final prosthetic surface would be at the same level as the articular surface. The instrumentation provides a contact probe that maps the surface curvature in two planes, obtaining offsets at four indexing points. A sizing card was then used to select the appropriate articular component. An appropriate surface reamer based on the offset measurements was then used to prepare the exposed articular surface. A trial was then used to confirm the fit, ensuring that this was congruent with the edge of the surrounding humeral surface. The appropriate articular component was then placed in its post , restoriPostoperative radiographs demonstrated adequate restoration of the humeral head articular surface at the area where the bony spur was removed. The patient was discharged on the first postoperative day and had no complications.The patient was placed in a sling for comfort and early passive and active assisted range of movement was encouraged from the first postoperative day to minimize stiffness. Shoulder rehabilitation progressed from passive range of motion, active assisted to active shoulder movements, with a focus on improving proprioception, stability and power of both the scapula-thoracic and the gleno-humeral joints.At the 6-month follow-up, an examination revealed 140° forward flexion, 120° abduction and 35° external rotation, and the patient was pain-free. The 12-month follow-up revealed 150° forward flexion, 120° abduction and 35° external rotation, and the patient was pain-free. He had gone back to work full time and had adequate function of his arm. Repeat radiographic assessment showed no loosening or displacement of the prosthesis, no new bony outgrowth and no changes to the opposing glenoid articular surface . His posMalunion of the proximal humeral fractures can result from conservative management of the injury, inadequate reduction at fixation or postoperative loss of an adequate reduction. It can lead to severe functional impairment, and its management is difficult and depends on the resulting deformity, the condition of the articular surface, soft tissues as well as patient characteristics. SurgicalIn our high-demand patient, the problem was relatively localized and a more limited procedure to either a corrective osteotomy or a standard resurfacing was preferable. We felt that an isolated excision osteotomy of the bony spur would not have been ideal, in that it would be difficult to restore a smooth continuous humeral head surface and would give the possibility of recurrence due to bony outgrowth.et al.[et al.,[The role of routine preoperative computerized tomography (CT) scanning has been discussed and is controversial. Bernstein et al. conclude.[et al., who recoWe therefore suggest another indication of the HemiCAP focal resurfacing (or similar) system that can provide a good solution in certain cases of proximal humeral fracture malunion, where there is a localized surface problem with an otherwise relatively preserved articular surface, allowing restoration of a smooth continuous surface while preserving bone stock.


We examined the correlation of wear effects with dielectric properties of carbon nanofibers -reinforced high-density polyethylene (HDPE) composites. Wear testing for the nanocomposites over up to 120 h was carried out, and then, dielectric permittivity and dielectric loss factor of the polymer composites with the increased wear time were studied. Scanning electron microscope and optical microscope observations were made to analyze the microstructure features of the nanocomposites. The results reveal that there exist approximate linear relationships of permittivity with wear coefficient for the nanocomposites. Composites containing silanized CNFs with the sufficiently thick coating exhibited high wear resistance. The change in permittivity was more sensitive to the increased wear coefficient for the nanocomposites with lower wear resistance. This work provides potential for further research on the application of dielectric signals to detect the effects of wear process on lifetime of polymeric materials. Making polymers into nanocomposites with the addition of appropriate nanofillers has been shown to be an effective way to obtain a multitude of enhanced properties and even extend to multi-functionalities not normally considered possible for polymeric materials. A variety of properties, such as physical, thermal, mechanical and others, as well as combinations of them, have been investigated for numerous nanocomposites in order to meet the burgeoning demands of industry. For example, carbon nanofillers, such as carbon nanotubes (CNTs) and carbon nanofibers (CNFs), not only improve electrical conductivity and dielectric properties, but also show enhanced tribological performance for polymers -8. In ad® nanofibers, which have been widely used, is >98%, and thus, the use of CNFs will not require time/energy-consuming purification processes. In addition, CNFs have graphene-layered structures, which provide vast numbers of active edges on the surface for functionalization purposes. The enormous amount of edges on CNFs enable these nanofillers to be functionalized easily compared to CNTs, which have stable and smooth tube structures, requiring much more dramatic methods of functionalization, typically using strong acids [Among various nanoscale fillers, owing to high aspect ratios and potential for multi-functionality, CNTs and CNFs are commonly used as the reinforced materials for polymer composites -17. For ng acids . Therefothicker coating layers on the nanofibers that function as bridges, or transition zones, to enhance entanglements between the nanofibers and non-polar polymers, e.g. polyethylene [Numerous attempts of using functionalized CNFs as the reinforcement in nanocomposites have been investigated to accomplish the purpose of improving interaction and adhesion between the nanofillers and polymers -24. For ethylene -17. In oethylene . Dynamicethylene -30.However, there is dearth of information on how mechanical behavior such as wear/friction processes  affects structures and properties of nanocomposites used in biosystems. Therefore, there are many concerns that need to be addressed on the application of nanomodified polymers to joint replacements. One of the most critical issues is related to the effects of the wear process on the stability of nanocomposites, both physically and chemically. Even though in the resulting nanocomposites, silanization provides non-polar coatings on the nanofiber surface and polyethylene is also a non-polar polymer, it is not known whether the continuous wear process can create polar groups in the nanocomposites and what relationship would be between the wear rate/wear period and the potential polar group created by the wear process. Such polar groups inside the polymer matrix may directly influence the chemical stability of the polymer and thus affect the practical lifetime of the joint replacements. Moreover, if the wear process creates polar groups in the polymer matrix, such groups can also be maintained in the debris, which has been proved to have a relationship with bone loss.It is well known that dielectric response is a reflection of dipole movements in insulative materials under an electric field. There are many applications of dielectric measurements to polymeric materials, since dielectric response is very sensitive to polar groups in the polymers ,32. For In this study, we have investigated the dielectric property changes with wear time and the degree of wear for HDPE nanocomposites containing our previously silane-treated CNFs (thin and thick coatings). The silane coatings not only enhanced the interaction of HDPE matrix and the CNF reinforcement, but also provided a non-polar hydrocarbon layer to cover the nanofiber surface. We hypothesized that the wear process can create polar groups by cutting some polymer chains and causing separation of nanofibers with the polymer matrix, as well as causing damage to the nanofiber structure. Thus, it may be deduced that with the longer wear time, dielectric response can be stronger since more wear can result in more polar groups on the surface and near the surface . In addition, we postulate that the coating thickness can not only affect wear resistance of the resulting composites, but also impact the dielectric properties of the composites. In order to compare with a nanocomposite containing pre-existing polar groups, oxidized nanofibers (ox-CNFs) were used for this purpose. Subsequently, we prepared four types of nanocomposites including three types of composites with different thickness of silane coatings on the CNF surface. In order to gain both sufficient sensitivity of dielectric responses and relatively preferable wear resistance, a 3% wt concentration of carbon fibers was chosen. The experimental results remarkably revealed that approximate linear relationships of permittivity with wear coefficient for the nanocomposites. The change in permittivity was more sensitive to the increased wear coefficient for the nanocomposites with lower wear resistance.-3. The pretreated ox-CNFs as the filler were obtained from Applied Sciences Inc., which are approximately 60 to 150 nm in diameter and 30 to 100 microns in length. Octadecyltrimethoxysilane (ODMS)  was manufactured by Sigma–Aldrich. Acetone was obtained from J.T. Baker. Ethanol was purchased from Decon Laboratories Inc.The high-density polyethylene used as a matrix in this research was supplied by Equistar (LB010000) with density of 0.953 g cmThe ox-CNFs were modified under subsequent treatment in boiling ODMS–ethanol solution. Then, the condensation reaction of ox-CNFs and silane coupling agent can occur due to the reactive hydroxyl groups on the surface of organosilane after hydrolysis, forming a silane layer to cover ox-CNF surface. By changing the ratio of ODMS to ox-CNF added and the percentage of ethanol and water in this reaction, we can control the degree of hydrolysis and the thickness of silane coating. In the previous work, three calculated coating thicknesses were applied using TGA data, which is about 1.2 nm for silanized CNF-A, 2.8 nm for silanized CNF-B and 46 nm for silanized CNF-C .The concentration of 3 wt% CNFs for both ox-CNFs (Nanocomposite-ox) and silanized CNFs  were mixed with HDPE by a Haake Torque Rheometer for uniform dispersion. Mixing was set at 170°C with a rotator speed of 30 rpm. The order of adding the materials was as follows: half amount of HDPE, CNFs, and then another half amount of HDPE. The speed was then raised to 70 rpm for 15 min.The polymeric nanocomposites were hot-pressing at 178°C for 10 min via a hydraulic presser. Then, they were allowed to cool down to room temperature naturally after turning off the heat. All samples were cut for wear testing and dielectric testing with the same size of 20 mm × 20 mm and similar average thickness around 2.5 mm.The detailed study of friction and wear properties of the developed composite was performed in a custom-built rig for the samples with a vertical 1020 carbon steel disk, which is rich in iron and carbon. . The components of the equipment are shown in Figure Specific wear coefficient was calculated using the following equation:w is the wear coefficient, △m is the weight loss, ρ is the density of composites, F is the normal force and d is the linear sliding distance. An Adventurer Pro analytic scale was used to determine mass loss, with a detectable range of 0.1 mg.where -3 to 107 Hz. Debris produced by friction was removed by nitrogen gas rather than a solvent to avoid any effects related to them, and then dielectric analysis testing was conducted. The change in dielectric properties was measured before and after each wear testing . The frequency ranges were chosen from 101 to 106 Hz for both dielectric constant and loss factor.The frequency dependence of permittivity and dielectric loss under a constant temperature was determined by using an Alpha-N High Resolution Dielectric Analyzer equipped with Au parallel plate sensors, with frequencies from 10The microstructure features on the fracture interface of both ox-CNF and silanized CNF nanocomposite specimens were observed by field-emission scanning electron microscopy (FESEM type Quanta 200F) in order to characterize the interaction and adhesion between fibers and matrix. FESEM images for fractured surfaces were prepared by freezing in liquid nitrogen for 10 min prior to fracturing. The surfaces of all samples were sputter-coated with gold for electrical conductivity. Additionally, the morphology of the composites was observed using optical microscope (Olympus BX51TRF) equipped with a camera (Olympus U-CMAD 3).Figure Dispersion of the various CNFs (oxidized and silanized) in the HDPE matrix was observed through field-emission SEM (FESEM). The FESEM images in Figure The effect of the silane-coating thickness on CNFs on the wear coefficient of the resulting nanocomposites versus wear time was studied. The wear coefficient comparison of composites was calculated by Eq. 1. It can be seen from Figure 6 Hz at different wear times for the four nanocomposites is presented in Figure The variation in permittivity with the frequency over a range from 10 to 103 Hz over the increasing wear time were obtained. It displayed the effect of the wear procedure on the dielectric constant of both ox-CNF/HDPE and silanized CNF/HDPE systems. The tendency of all samples was increasing with wear. For ox-CNF-reinforced composites, the hydroxyl groups on the fiber surface were the main contribution of the increased dielectric constant. For silane-treated CNF composites, although the changes were not as obvious as ox-CNF/HDPE because of the silane coating acting as a protective covering that leads to less polar groups in the molecular structure, the trends were still increasing. We supposed that the wear process can create polar groups by cutting some polymer chains and causing separation of nanofibers with the polymer matrix, as well as causing damage to the nanofiber structure. Thus, it may be deduced that with the longer wear time, dielectric response can be stronger since more wear can result in more polar groups on the surface and near the surface. Additionally, the broken chains or polar groups (after the wear process) can be affected by the external electrical field acting on the composite samples. The contribution to the dielectric results may have been due to the active groups produced on the worn surface so causing the variation of polarization. It may come from the slight changes of molecular structure in the composites and/or the active groups were produced on the worn surface so causing the variation of polarization. The relationship between coating thickness on the CNF surface and the permittivity of the resulting nanocomposites, as well as their change rates , which are shown in Figure 3 Hz, Figure 6 Hz, Figure Based on the above testing results, the values of dielectric loss of the four composites were compared by choosing two frequency levels (10Since there has never been any reported study indicating the effects of a mechanical process, such as wear, on dielectric properties of polymeric materials, this original study is purely an exploratory work. The results reveal that there exist relationships between wear effects and dielectric properties for polymeric nanocomposites. Composites containing silanized CNFs with sufficiently thick coatings exhibited high wear resistance. The permittivity of the nanocomposites decreased obviously for the nanocomposites with appropriate silane treatment for the nanofillers throughout the 120-h wear process. For all the nanocomposites prepared in this study, both ox-CNF/HDPE and silanized CNF/HDPE nanocomposites, dielectric constants were sensitive to the wear effects. It was revealed that approximate linear relationships of permittivity with wear coefficient existed for the nanocomposites. Also, the change in permittivity was more sensitive to the increased wear coefficient for the nanocomposites with lower wear resistance. Additionally, the silane-coating thickness played a significant role on the resistance of dielectric loss for the nanocomposites.This work provides potential for the in-depth research on the application of dielectric signals to detect the effects of wear process on lifetime of polymeric materials for the application to joint replacement systems. It may also be extended to the more general case of detecting damage to structural composites in many applications.


Human cancer is caused by the accumulation of genetic alterations in cells. Of special importance are changes that occur early during malignant transformation because they may result in oncogene addiction and thus represent promising targets for therapeutic intervention. We have previously described a computational approach, called Retracing the Evolutionary Steps in Cancer (RESIC), to determine the temporal sequence of genetic alterations during tumorigenesis from cross-sectional genomic data of tumors at their fully transformed stage. Since alterations within a set of genes belonging to a particular signaling pathway may have similar or equivalent effects, we applied a pathway-based systems biology approach to the RESIC methodology. This method was used to determine whether alterations of specific pathways develop early or late during malignant transformation. When applied to primary glioblastoma (GBM) copy number data from The Cancer Genome Atlas (TCGA) project, RESIC identified a temporal order of pathway alterations consistent with the order of events in secondary GBMs. We then further subdivided the samples into the four main GBM subtypes and determined the relative contributions of each subtype to the overall results: we found that the overall ordering applied for the proneural subtype but differed for mesenchymal samples. The temporal sequence of events could not be identified for neural and classical subtypes, possibly due to a limited number of samples. Moreover, for samples of the proneural subtype, we detected two distinct temporal sequences of events: (i) RAS pathway activation was followed by TP53 inactivation and finally PI3K2 activation, and (ii) RAS activation preceded only AKT activation. This extension of the RESIC methodology provides an evolutionary mathematical approach to identify the temporal sequence of pathway changes driving tumorigenesis and may be useful in guiding the understanding of signaling rearrangements in cancer development. Cancer is a deadly disease that develops through the accumulation of genetic changes over time. Many biological models do not incorporate this temporal aspect of tumor formation and progression, in part due to the difficulty of determining the sequence of events through biological experimentation for most cancer types. We previously developed a computational algorithm with which we can quickly and cost-effectively determine the order in which mutations arise in the tumor even when large numbers of mutations are considered. In this paper, we extended our method to incorporate biological knowledge of the common pathways by which cancer progresses. We applied these techniques to primary glioblastoma, the most common form of brain cancer. We found that when all samples are taken into account, a temporal sequence of pathway events emerges; however, different subtypes of glioblastoma vary in their temporal sequence of events. This algorithm can also be easily applied to other cancer types as clinical data becomes available, showing the benefit of computational and mathematical tools in cancer research. Using temporal information, cancer biologists will be able to develop more accurate animal models of tumor formation and learn more about how mutations interact in time, thus leading to better treatments for cancer. New high-throughput sequencing and microarray technologies provide researchers with access to increasingly large and complex datasets comprising genome-level alterations in cancer There is a growing literature of mathematical, statistical and computational approaches to determining the temporal sequence of events arising during tumorigenesis. Previously published methods include the linear model Retracing the Evolutionary Steps In Cancer (RESIC) We have previously described a computational approach, called In many cases, specific genetic alterations are not necessary for malignant transformation; instead, particular oncogenic phenotypes must be achieved through the emergence of any of a number of alternative mutations  [26], , [3Mμ, where M is the number of genes involved in the pathway and μ is the per gene mutation rate. In a similar manner, the TCGA copy number alteration data We considered a single alteration event occurring within any of the genes in the network to be sufficient to result in a change in signaling of that pathway. Since only focal copy number alterations were considered, and since in most cases, alterations within a signaling pathway reside on separate arms of different chromosomes, we considered the first mutational hit on each gene to be independent of all other mutations in the pathway. Thus, a particular pathway alteration had a mutation rate equivalent to We restricted the set of genes related to GBM development to those that were defined in the pathway diagram in N cells at risk of accumulating the genetic changes leading to cancer. These cells proliferate according to the Moran process We used the RESIC methodology Depending on the fitness values of the various combinations of potential mutations, each path through the network of mutations may have a different likelihood of occurring. The Markov process described above can then be used to calculate the transition rates between individual mutational states, and thus the likelihood of each path through the network. This model is then used to describe the dynamics of populations of patients, each harboring a population of cells at risk of accumulating mutations. The scaling from this micro-model (on the level of a population of cells within a single patient) to the macro-model  is obtained by multiplying the transition rates between mutational states within one patient by the number of patients in each mutational state. We considered the dynamics of patients in steady state: there is a constant influx into the unmutated state and an equal constant outflux from the fully mutated state, accounting for diagnosis of the disease (influx) and deaths of patients or their cure (outflux). These parameters are selected to ensure that fitness values are within biologically meaningful ranges, ie. that a single mutation does not confer too large a fitness effect to be biologically implausible. According to this model, patients enter the system in an unmutated state and then accumulate the mutations of interest. This starting point could be late during tumorigenesis, if the mutations of interest are late events, or pre-cancerous if the mutations of interest are initiating events; either way, since the predictions of the model are compared to data of patients after diagnosis of their disease, this starting point in the model is also after diagnosis of the disease. Note that small influx values into other mutational states, representing diagnosis with a different set of alterations, does not significantly alter the results.At steady state, the population is distributed across all possible states; this steady state distribution can then be compared to the numbers of clinical samples with the corresponding genotypes, where the total number of patients in a dataset is equal to the sum of patients in all states. Since all samples analyzed are collected from patients after diagnosis of their disease, the earliest time point identifiable using such datasets is the time of diagnosis. As outlined above, this definition does not imply that the first mutation arose exactly at the time of diagnosis: since the event resulting in patients entering the system is diagnosis, and all considered events are observable in the patient samples, many events arise prior to diagnosis. This mapping is used to optimize a subset of parameters in the Markov process model  by minimizing the difference between the prediction and the observed frequencies in the dataset. Other parameters, such as cellular population size, mutation rate and influx rate, are estimated from experimental results Similarly, Beerenwinkel et al. found that the selective advantage of mutations has the largest effect on the evolutionary dynamics of tumorigenesis −7 per gene in the pathway per cell division and the stem cell population size per niche was set as N = 100. This choice of value for N was made for computational speed; we had previously found that an order of magnitude variation in this parameter value results in robust results We applied the RESIC methodology We applied the RESIC methodology to the 145 TCGA patient samples for which CNA and point mutation data was available. We analyzed two sets of data: the dataset including CNA only, and the dataset containing CNA and point mutation date. We analyzed both datasets through our pathway-based approach as well as the gene-based approach using pairwise and three-way analyses. We compared the resulting temporal orderings, considering the order to be consistent between the two data types when the percent flux through the mutational diagram varied by no more than three and the dominant temporal sequence remained dominant. We considered an ordering to be weakened if either fewer alleles of a gene could be analyzed, the percent flux decreased by more than three, or a pair or triplet of events could no longer be analyzed when using CNA data only. We considered an ordering to be inconsistent if the dominant temporal order changed between the two analyses, or if an ordering could be determined when using CNA data only, but not when using CNA and point mutation data.In pair-wise analyses, the temporal order of all alterations can be determined simply by combining the pairs of genetic or pathway alterations in the predicted order. For example, if mutation A arises before mutation B, and mutation C arises before mutation A, the order of events is C→A→B. Figure S1Pairwise comparison of three genes results in an ordering of all three genes. We perform pairwise comparisons between alterations to determine the overall order of events. Here we depict all possible combinations of two pairwise orderings that can result in a single linear order of events. We denote the three events A (in red), B (in blue), and C (in green). Black arrows denote the determined orders and gray arrows denote the set of pairwise orderings that result in a three-event order.(EPS)Click here for additional data file.Text S1RESIC analysis results for all GBM samples. The results from the pairwise, three-way, and pathway-based RESIC analyses are displayed.(TXT)Click here for additional data file.Text S2RESIC analysis results for GBM samples belonging to the proneural subtype. The results from the pairwise, three-way, and pathway-based RESIC analyses are shown.(TXT)Click here for additional data file.Text S3RESIC analysis results for GBM samples belonging to the mesenchymal subtype. The results from the pairwise, three-way, and pathway-based RESIC analyses are displayed.(TXT)Click here for additional data file.Text S4RESIC analysis results for GBM samples belonging to the neural subtype. The results from the pairwise, three-way, and pathway-based RESIC analyses are shown.(TXT)Click here for additional data file.Text S5RESIC analysis results for GBM samples belonging to the classical subtype. The results from the pairwise, three-way, and pathway-based RESIC analyses are shown.(TXT)Click here for additional data file.


Continuing professional development (CPD) is one of the principal means by which health professionals  maintain, improve, and broaden the knowledge and skills required for optimal patient care and safety. However, the lack of a widely accepted instrument to assess the impact of CPD activities on clinical practice thwarts researchers' comparisons of the effectiveness of CPD activities. Using an integrated model for the study of healthcare professionals' behaviour, our objective is to develop a theory-based, valid, reliable global instrument to assess the impact of accredited CPD activities on clinical practice.Phase 1: We will analyze the instruments identified in a systematic review of factors influencing health professionals' behaviours using criteria that reflect the literature on measurement development and CPD decision makers' priorities. The outcome of this phase will be an inventory of instruments based on social cognitive theories. Phase 2: Working from this inventory, the most relevant instruments and their related items for assessing the concepts listed in the integrated model will be selected. Through an e-Delphi process, we will verify whether these instruments are acceptable, what aspects need revision, and whether important items are missing and should be added. The outcome of this phase will be a new global instrument integrating the most relevant tools to fit our integrated model of healthcare professionals' behaviour. Phase 3: Two data collections are planned: (1) a test-retest of the new instrument, including item analysis, to assess its reliability and (2) a study using the instrument before and after CPD activities with a randomly selected control group to explore the instrument's mere-measurement effect. Phase 4: We will conduct individual interviews and focus groups with key stakeholders to identify anticipated barriers and enablers for implementing the new instrument in CPD practice. Phase 5: Drawing on the results from the previous phases, we will use consensus-building methods to develop with the decision makers a plan to implement the new instrument.This project proposes to give stakeholders a theory-based global instrument to validly and reliably measure the impacts of CPD activities on clinical practice, thus laying the groundwork for more targeted and effective knowledge-translation interventions in the future. While the first cycle comprises the process of creating knowledge, the second one constitutes the process of applying the knowledge thus created. By translating knowledge and evidence into practice, CPD pertains to the action cycle , [, [e.g., perties) . They wiThe goal of phase 2 is to assess the applicability of and adapt any instruments identified in phase 1. We will create a seven-person Development Committee comprised of researchers, CPD decision makers, and an external expert from each of the CPD and knowledge-translation research communities. Members of this committee will largely be from the research team. Examining each instrument selected in phase 1, the Development Committee will choose the most relevant instruments and their related items for assessing the variables (concepts) listed in our integrated conceptual model. Once this task is complete and all items are integrated into a new global instrument, an e-Delphi process will be used to check its face validity and likely acceptability and utility in CPD settings. Acceptability will be assessed with criteria used in phase 1. The resulting global instrument will also be examined for (a) its appropriateness or relevance to behaviours expected to occur after CPD activities, (b) its grammar and readability, and (c) the appearance of bias in two rounds of planned contacts within the entire research team and its network.i.e., one that includes selected instruments) continues to meet the criteria elaborated above. The Development Committee may revise or discard items and variables as necessary. We will begin by developing a French version of the global instrument.Once the team and its networks have provided their feedback, the Development Committee will review the final list of selected instruments and their respective items grouped around variables (concepts) of the integrated conceptual model and ensure that the new global instrument ; (e) use of any or a combination of instructional methods  and material , which must include at least 25% of interactivity; (f) conduct as a one-time intervention; and (g) duration of between at least one and three hours. Individual activities embedded within large programs offering several activities at one setting, such as a two-day conference, will be eligible.Participants will be recruited from attendees of the CPD activities offered by the CPD decision makers and collaborators to this project. Each year, thousands of educational activities are offered through this network. These institutions and organisations reach the vast majority of the 16,000 practising physicians in the province of Québec. Eligibility criteria for CPD activities will include the following: (a) accreditation by one of the CPD decision makers and collaborators to this project; (b) group-based, live activities carried out with groups of 50 participants or less; (c) a focus on behaviour change for any topic or content as stated in the learning objectives established for the activity; (d) occurrence in any setting (Eligibility criteria for physicians will include the following: (a) attending an eligible live CPD activity, (b) being active in clinical practice for a six-month period following the indexed CPD activity, (c) being accessible for a phone interview three months after the indexed CPD activity, (d) speaking fluent French, and (e) not having participated in this study previously.A research assistant will attend a number of eligible CPD activities chosen at random from one of the CPD decision-makers' and collaborators' networks. At registration in the CPD activity, the assistant will enroll participants and ask them to complete a consent form and a sociodemographic questionnaire. The research assistant will also collect data on the CPD activity to which the participants are exposed.e.g., gender, age, type of medical speciality, and years of experience in current practice). CPD activity-level data collected for the study will include CPD activity attended, the clinical area of the activity, the type of needs assessment conducted, the theoretical foundation, the length, the number and type of instructional methods used  [Participant-level data collected for the study will include the participants' sociodemographic details (uch pad) , the numIn accordance with the integrated conceptual model proposed by Godin and colleagues (2008) to predict behaviour of healthcare professionals, our new global instrument will basically assess participants' information, namely, beliefs about consequences and capabilities, social influences, moral norms, perceptions of role and identity, and their intentions, habits, and past behaviours.Two data collections are planned: (1) a test-retest of the new instrument for assessing its reliability and item analysis and (2) a before-and-after study to test the validity of the instrument.First, a group of 50 participating physicians  who attended an eligible CPD activity will be asked to complete the instrument immediately after the CPD activity and to use the same instrument again after two weeks. The research assistant will offer to mail the instrument to the physicians. This first data collection will provide the data for assessing both intra-subject reliability at two weeks and the internal reliability of the instrument. Reliability of the scales will be assessed with Cronbach's alpha for internal consistency and with an intraclass correlation coefficient for stability. It will thus be possible to modify the instrument based on this first set of results. The final choice of the set of items will be based on their indices of distribution and discrimination and their theoretical importance.i.e., if everyone completes the questionnaire twice, it is not possible to ascertain whether the effect can be attributed to the CPD activity or to the action of completing the questionnaire) [Second, we will use a before-and-after study design. In eligible CPD activities, half of the participants, randomly selected, will be asked to complete the evaluation instrument both before and at the end of the CPD activity, and half of the participants will be asked to complete the evaluation instrument after the CPD activity. Data from the participants who will complete the evaluation instrument before and after the CPD activity will allow us to verify the instrument's capacity to detect differences in constructs of the integrated model. Comparing results from participants who completed the instrument before and after the CPD activity and those who completed it only after the activity will allow us to explore the mere-measurement effect (onnaire) .All participants will be contacted three months later by phone in order to collect self-reported clinical behaviour, as targeted in the specific CPD activity. These data will be used to estimate the instrument's effectiveness in predicting behaviour. In accordance with the results of the systematic review of factors predicting behaviour in healthcare professionals , self-reFor the before-and-after data collection, we will seek the participation of 500 CPD enrollees: 125 family physicians/before and after, 125 family physicians/after only, 125 specialists/before and after, and 125 specialists/after only. Apart from sociodemographic results, the integrated model currently proposes seven essential concepts to predict behaviour in healthcare professionals . Also, aUsing EFA, we will explore the factorial structure within the potential seven constructs describing essential concepts to predict behaviour of healthcare professionals. We will then use CFA to assess construct validity.t-test will be verified. Our a priori hypothesis is that physician's intentions will be positively associated with participation in the CPD activity. Physician's intentions after the CPD activity calculated in this group will be contrasted with results obtained in the control group to explore the mere-measurement effect [a priori hypothesis is that the measurement instrument will correlate in the expected direction with self-reported behaviour as well as with changes in self-reported behaviour.We will also assess the relationships between the constructs based on the proposed integrated model using path analysis. Observation of the expected relationships will be further proof of the validity of the model and its constructs. The difference between family physicians and specialists for each construct will be assessed with a multiple-group analysis. Also, in participants who completed the instrument before and after the CPD activity, the effect of participating in a CPD activity and change in the physician's intentions with a paired student t effect . PredictThe objective of phase 4 is to explore the acceptability of the new global instrument by CPD decision makers and gather suggestions of factors that might influence its implementation. Data collection will consist of individual interviews and focus groups with key stakeholders. We will use the contact network of team members to purposefully select participants from within four groups: (1) Québec's key stakeholder CPD organizations, (2) primary care physicians, (3) specialists, and (4) representatives of Québec's Ministry of Health and Social Services. The aim is to highlight anticipated barriers and enablers for implementing the new instrument in CPD practices.We will collect the participants' sociodemographic characteristics and additional information on their organizations. Interviews and focus groups will be structured according to an interview guide that will facilitate semi-structured discussions regarding the instrument. Examples of questions to be included in the interview guide are as follows: Who do you think might have a favourable/negative attitude to this measurement instrument? Can you think of barriers and enablers for implementing this instrument in CPD practice?All interviews and focus groups will be tape-recorded and transcribed verbatim. Analysis of the transcripts will occur concurrently with data collection in both the focus groups and the individual interviews and will use a constant comparative method. Briefly, units of data will be categorized and new units compared with previously identified ones in order to develop or saturate each category . NVivo ; (b) a summary of the barriers and enablers as perceived by key stakeholders for implementing this instrument in CPD practice; and (c) proposed actions to assess the impact of CPD activities. Details of the results of these research activities will be sent to team members in preparation for a face-to-face meeting. The face-to-face meeting will be structured around a specific goal: building consensus regarding an implementation plan for the new instrument to assess the impact of CPD activities. The meeting will be led by an external facilitator. The agenda will aim at achieving agreement on a final plan for implementing the new instrument.This research activity will involve meeting with Québec's medical CPD consultative coordinating body. The research methods used in this phase will be based on consensus-building methods, which will include convening, clarifying responsibilities, deliberating, deciding, and implementing agreement. Consensus building is defined as the process of seeking unanimous agreement . The resOnce the instrument has been found to be valid and reliable, we will create an English version using translation and back-translation methods .This project will serve not only to develop an appropriate instrument to assess the impact of accredited CPD activities on physicians' performance but also to test the integrated conceptual model for the study of healthcare professionals' behaviours and intentions proposed by Godin and colleagues (2008). We acknowledge that external factors such as workplace characteristics, financial incentives, and patient expectations may influence the results of an accredited CPD activity on physicians' performance. However, the principal target of CPD interventions is not organizational or environmental change but individual change. For that reason, our instrument will be designed to measure the impacts of CPD on behavioural change at the individual level. "Individuals are essential units of health education and health behaviour theory, research, and practice. This does not mean that the individual is the only or necessarily the most important unit of intervention. But all other units, whether they are groups, organizations, worksites, communities, or larger units, are composed of individuals."  A reliabThe authors declare that they have no competing interests.All authors collectively drafted the study protocol and approved the final manuscript. FL is its guarantor.