The accumulation of soluble and insoluble amyloid-β (Aβ) in the brain indicates failure of elimination of Aβ from the brain with age and Alzheimer's disease (AD). There is a variety of mechanisms for elimination of Aβ from the brain. They include the action of microglia and enzymes together with receptor-mediated absorption of Aβ into the blood and periarterial lymphatic drainage of Aβ. Although the brain possesses no conventional lymphatics, experimental studies have shown that fluid and solutes, such as Aβ, are eliminated from the brain along 100 nm wide basement membranes in the walls of cerebral capillaries and arteries. This lymphatic drainage pathway is reflected in the deposition of Aβ in the walls of human arteries with age and AD as cerebral amyloid angiopathy (CAA). Initially, Aβ diffuses through the extracellular spaces of gray matter in the brain and then enters basement membranes in capillaries and arteries to flow out of the brain. Although diffusion through the extracellular spaces of the brain has been well characterized, the exact mechanism whereby perivascular elimination of Aβ occurs has not been resolved. Here we use a computational model to describe the process of periarterial drainage in the context of diffusion in the brain, demonstrating that periarterial drainage along basement membranes is very rapid compared with diffusion. Our results are a validation of experimental data and are significant in the context of failure of periarterial drainage as a mechanism underlying the pathogenesis of AD as well as complications associated with its immunotherapy. Alzheimer's disease (AD) is characterized pathologically by the accumulation of soluble and insoluble amyloid-β (Aβ) in the extracellular spaces of the brain and tau-related neurofibrillary tangles within neurons , begin their journey out of the brain by entering interstitial fluid ISF and passing through the narrow ECS in the brain before entering the perivascular drainage pathways within basement membranes (100–150 nm thick) in the walls of capillaries and arteries  devised by Nicholson and Phillips, demonstrating that molecules execute random walks through the extracellular space  using a time-dependent solver over 32 min. This period was divided into 2 min for the injection of molecules and 30 min observation time. The geometries used are a two-dimensional (2D) coronal and a 2D sagittal section from the Allen Brain Atlas  was used to carry out a mesh convergence study on the coronal slice to ensure that the choice of mesh resolution does not alter the results. The mesh convergence study was based on the “Adaptive mesh refinement” option in the COMSOL solver. This option adapts the mesh size according to an error indicator ε, which in this case was chosen as the root mean square of the derivative of dextran concentration d Figure . The conmax, chosen to be 1. Then Δx represents the side length of the smallest triangular mesh element and u represents the flow velocity. With Δx = 2.36·10−6m, u = 8.33·10−6ms−1, and choosing C = 0.5 we obtain Δt = 0.14s.The optimal time step for the simulations was determined using the Courant-Friedrichs-Lewy (CFL) condition, where the Courant numberc is the concentration of the substance within the ECS in moll−1 or M, u is the convective velocity vector in m s−1, k is the uptake rate in s−1 and D* is the effective diffusion coefficient in m2 s−1 –(5) form the governing equations of the system.All simulation parameters are summarized in Table D* becomes a matrixAs discussed above the mouse brain is simplified by homogenizing all gray and white matter . Accordingly, we have homogenized the tortuosity λ values reported in Syková and Nicholson . BecauseD* for dextran (3 kDa) was obtained directly from Nicholson and Tao  into the blood  therefore becomesAs in Carare et al.  0.5 µl oAdditionally, one has to take into account the convective flow generated by the injection of tracer into the brain. We have conducted test simulations on the coronal slice using various convective flow velocities. These tests show that velocities of up 4.0 × 10-6 m s-1  have a negligible effect on the tracer distribution. As we regard higher velocities than that too high given the time frame of the injection we have omitted this initial convective flow for the remaining simulations.kb, which can be modeled in COMSOL using a “Reactions” node to account for production and consumption of chemical species. If we call the concentration of dextran in the ECS c and the concentration of dextran in the basement membranes cb, then kb acts as a take-up coefficient and the term −kbc is part of Equation (3), while the equations for the transport of species in the basement membrane receive a source term sb = kbc. Note that although we use different names for the concentrations of tracer in the ECS and the basement membrane these concentrations both describe dextran, but in different compartments. Note that in this representation we are modeling the two phenomena—parenchymal diffusion and perivascular convective flow—as two separate “layers” on the geometry. This means that every point in space is at the same parenchymal and perivascular.Molecules “switch” from being in the ECS to being in the perivascular drainage pathways in the basement membranes of cerebral arteries at rate As we assume that convective flow in the basement membrane is the dominant transport process we eliminate diffusion by setting the diffusion coefficient The boundary conditions are the same as for the ECS part of the simulation with the exception of the needle tip, which is changed to “No Flux” (Equation 4).ub. As the lymphatic drainage pathways follow the basement membranes inside the walls of all arteries in the brain modeling these pathways explicitly and in detail is beyond the scope of this paper. Instead we can utilize measurements taken by Carare et al.  =  in the coronal slice and ub =  =  in the sagittal slice.As the “production” of dextran in the basement membrane is directly coupled to the “loss” of dextran from the ECS the only parameter that remains to be determined is the perivascular drainage velocity e et al.  about the et al. : (a) DexThis representation of the perivascular drainage pathways and their geometries is notably extremely simplified. However, a realistic representation could only be achieved through modeling of the whole vascular tree in the brain. For the aim of this paper, which is the comparison of the macroscopic phenomenon of dextran reaching 2.5 mm in 5 min to the effect of diffusion, our representation was deemed sufficient. Foley et al.  have alsL is an appropriate length scale, U is velocity, and D is the diffusion coefficient. Here we choose the height of the mouse brain as the length scale. The Peclet number can be used to determine the balance between diffusion and advection that is required to obtain the expected results.All simulation cases are listed in Table The goal of this paper is to show that diffusion alone is not enough to explain perivascular drainage. First, in cases A and B diffusion and bulk flow are considered as the only driving forces of solute drainage in the brain. The parameters for case C1 were determined from the results of the experiments in Carare et al. , while tThe simulation cases were set up to demonstrate that even if the reported values for diffusion and perivascular drainage have been under- or overestimated, respectively, diffusion alone remains unable to explain the experimental results from Carare et al. . If in ad is the distance betweeen two points with the coordinates  and .To compare diffusion and perivascular drainage the maximum distance a tracer has traveled from the injection site is measured by calculating the largest distance between the injection site and a point whose tracer concentration is at least 0.1 % of the injection concentration. This dextran detection criterion has been established in pilot studies prior to Carare et al. . The disThe maximum distance for each of the simulation cases at both 5 and 30 min after the end of the injection is given in Table Cases A1–3 consider only diffusion as the driving force of solute transport. In none of the simulation cases does dextran reach as far as is expected from the results in Carare et al. . If the In cases B1–3 the effect of bulk flow is considered. Upon comparing these cases to A1 no signifcant effect of bulk flow along the white matter on solute transport is observed.The effect of perivascular drainage is examined in cases C1–4. Only in case C1 does dextran appear to reach the distance of 2.5 mm within 5 min after the injection of dextran. However, the contours are disconnected. To aid the explanation of this in the discussion, Supplementary Figure In order to further analyse the distances dextran traveled in the different simulation cases it is useful to study the maximum distance dextran has traveled over time Figure . Each ofThe sagittal slice produces very similar results compared to the results reported for the coronal slice. Table Supplementary Figure To aid the analysis of the results Figure The results of this study demonstrate that diffusion alone cannot account for the pattern of drainage of fluid and solutes from the brain parenchyma. Our results show that complex convective transport pathways exist in the brain for the clearance of solutes produced during brain metabolism. The drainage pathway, therefore, is partly dependent upon diffusion through the ECS between cell processes in the brain parenchyma and partly reliant upon a more rapid system of convective flow along basement membranes within walls of cerebral capillaries and arteries.x-direction and therefore encounters the boundary of the brain at 2.46 mm.The results of Supplementary Figure For case group B the results presented in Supplementary Figures In case group C both cases C1 and C2 manage to reach the distance mark of 2.5 mm within 5 min. In case C1, however, there are two separate disconnected sections of dextran concentration above the detection limit. To explain this phenomenon Supplementary Figure The simulations on the sagittal slice of the mouse brain have in general revealed very similar results as compared to the coronal slice .The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Traditionally, the merit of a rearrangement scenario between two gene orders has been measured based on a parsimony criteria alone; two scenarios with the same number of rearrangements are considered equally good. In this paper, we acknowledge that each rearrangement has a certain likelihood of occurring based on biological constraints, e.g. physical proximity of the DNA segments implicated or repetitive sequences.Maximum Independent Set problem on circle graphs.We propose optimization problems with the objective of maximizing overall likelihood, by weighting the rearrangements. We study a binary weight function suitable to the representation of sets of genome positions that are most likely to have swapped adjacencies. We give a polynomial-time algorithm for the problem of finding a minimum weight double cut and join scenario among all minimum length scenarios. In the process we solve an optimization problem on colored noncrossing partitions, which is a generalization of the Maximum Independent Set problem on circle graphs. Several variants of the problem are also mentioned.We introduce a model for weighting genome rearrangements and show that under simple yet reasonable conditions, a fundamental distance can be computed in polynomial time. This is achieved by solving a generalization of the  A huge body of work exists on modeling the evolution of whole chromosomes . The maiAlmost all versions of the problem are NP-Hard if content modifying operations such at duplication, loss, and insertion are allowed , 3. FortOne of the most important problems in comparative genomics is the inference of ancestral gene orders, i.e., paleogenetics. Given a realistic model of evolution, one can infer ancestral adjacencies of high confidence from present-day genomes –8. HowevThe apparent difficulty of the ancestral inference problem—because of the potentially astronomical number of parsimonious sorting scenarios—highlights the importance of methods that infer scenarios that conform to some extra biological constraints. Yet, aside from methods that weight inversions based on their length –16, to opositional constraints, i.e., sets of positions in the genome that are likely to swap adjacencies. Two examples of constraints that fit this paradigm are: (1) the physical 3D location of DNA segments in a nucleus and, (2) repetitive sequences that are the cause or consequence of rearrangement mechanisms. We illustrate the utility of our model with 3D constraints in the “In this paper we use a weight function on rearrangements suitable for modeling colored noncrossing partitions, called Minimum Noncrossing Colored Partition. It is a generalization of the Maximum Independent Set problem on circle graphs  is the set of integers from 1 to n.Recall that entclass1pt{minimais a partitionof  such that for any classesif we haveforand, thenAnoncrossing colored partitionis a noncrossing partition where for anyA noncrossing partition n-gon with the property that if you draw a line between all pairs of vertices in the same class, for all classes, then no two lines from different classes intersect. A colored partition has colored vertices, and respects the property that any pair of vertices in the same class of the partition have the same color  Minimum Noncrossing Colored Partition problem, which according to Lemma Minimum Local Parsimonious Scenario on a single component. We describe the algorithm on an instance that has been embedded on a line where the left-most vertex ① represents the smallest element of the set, as shown in Fig. i, j], let NCP be the number of classes in the MNCP on that subproblem. Thus, NCP corresponds to the Minimum Noncrossing Colored Partition of .We present a polynomial-time algorithm for the i, j] we have j. The second case is applicable when element j is the same color as element i; in this case i and j become part of the same class, all the other classes staying the same. The third case tests combinations of subproblems; this case is pertinent when the For any interval  from the set of adjacency edges of A ordered according to a circular embedding of C. The color function col maps each element to its corresponding adjacency edge’s color.First, transform an instance of MLPS on a single component to an instance of MNCP. Given a cycle n] corresponds to a partition of adjacency edges of genome A. We show that there always exists a scenario of DCJs whose prefix separates C into connected components according to the partition. Any two edges of the same component can be chosen for a DCJ [n], an edge partition of size k can be achieved with k is minimum over all feasible partitions and the remaining DCJs of the scenario are likely, the constructed scenario has a minimum number of rare DCJs. Now transform an optimal solution of MNCP into an optimal solution for MLPS. Clearly, any partition of [1, or a DCJ  and the In fact, the two problems are equivalent. We omit the reduction in the other direction since it is out of the scope of this paper.Minimum Noncrossing Colored Partition can be computed in polynomial time for a single component independent of all others. Yet it is possible to mix components in a parsimonious DCJ scenario. As described in Fig. mix components are those that act on one edge from an AA (BB respectively) the set of A p, q) can be mixed in several ways. For all possible DCJs that mix them, we compute the MNCP on the resulting components. The minimum MNCP over all mixings is the cost in rare moves for mixing the two paths. To compute the pairs of paths to be mixed in an optimal solution, we use the inverse of these costs—the number of likely moves—as weights in a bipartite graph.Any pair  with the maximum number of likely DCJs for the mixing of paths p and q. Any even-length path could alternatively be used independently of any other, so there is a vertex v alone (computed using the MNCP on that component). Algorithm 1 computes the minimum number of rare DCJs in a parsimonious scenario. It is easy to modify the algorithm to give the list of DCJs. Take the elements of MNCPonComp computes the Minimum Noncrossing Colored Partition on the given component c. In other words it builds the color function col according to the component c and then calls MNCP where n is the number of adjacency edges on the A side of the component c. The function maxMix computes the maximum number of likely DCJs over all possible DCJs that use one edge from p and one edge from q. The function d(AA) computes the sum of DCJ distances from each component in AA using Formula w.The function alls MNCP, n, col Minimum Noncrossing Colored Partition on the component.To summarize, any path can be mixed at most once in a parsimonious scenario. Potential mixings, as well as potential non-mixings, are encoded into a bipartite graph with edges weighted by the cost of a mix. A maximum weight matching in this graph corresponds to a scenario that minimizes the number of rare moves on the paths. All other connected components of the graph are sorted using the AA and elements of BB. A particular adjacency edge e from a given path f from a path e, f), e being an edge from a path in AA and f being an edge from a path in BB, we will compute the MNCP on the resulting mix. If the number of edges in the paths AA (respectively BB) is n(AA) (respectively n(BB)), then the running time of our algorithm is The running time of our algorithm is dominated by the weighting of the edges on the bipartite graph. Consider all mixings done between elements of maxMix that computes the maximum number of likely DCJs over all possible mixings of two paths. The analysis includes the multiplicative term n(AA)n(BB) reflecting the process of actually trying all possible mixings when labeling the edges of the bipartite graph. We now show how to mix paths more efficiently.In the previous section, edges of the bipartite graph are scored by the function A-edges of a component of the graph G to be those edges connecting two nodes in genome A. Consider paths p is the path with A-edges t1 and t2, and q is the path with A-edges t3 and t4  returns the maximum of MNCPonComp or MNCPonComp or Due to the bijection between mixing scenarios on maxMix removes a linear factor from the overall computation time. Note AA and BB so that Our new version of m is less than c. For each pair of paths, we compute MNCPonComp three times, so the number of steps required to label all the edges of the complete bipartite graph is at mosty, x, |AA|, and |BB| are clearly O(n). Since the largest terms "The number of parsimonious DCJ scenarios between two genomes is exponential in the distance between them. However, many of the scenarios are probably unrealistic in the biological sense. This paper takes a step towards modeling realistic scenarios by posing optimization problems that take into account positional constraints. An example of such a positional constraint is the 3D proximity of genome segments given by Hi-C experiments.An  et al.   from oneMinimum Local Parsimonious Scenario corresponds to finding a maximum likelihood scenario in a situation where likely and unlikely scenarios are both rare, and the difference between the likelihoods of likely and unlikely moves is not very large. In this situation, a most parsimonious scenario made of k unlikely moves is more likely than a non-parsimonious scenario made of From a biological perspective, a solution to Minimum Noncrossing Colored Partition problem—a generalization of the Maximum Independent Set problem on circle graphs—for weighting the edges of a bipartite graph, on which we obtain a maximum matching. While this technique is essential to our algorithm for finding DCJ scenarios, we believe it will also come in handy for an algorithm that finds likely inversion scenarios . A multitude of biologically relevant variations on this problem exist, including variations on the model of genome rearrangement, a variant where edges have multiple colors, and a bi-directional sorting variant where edges are weighted on both genomes according to the chromatin conformation on each. Models that incorporate uncertainty or evolution in the Hi-C data would also be relevant. We hope that this work provokes further study from both the algorithmic and the biological perspectives.We introduce the


Many variable selection techniques have been proposed for the clustering of gene expression data. While these methods tend to filter out irrelevant genes and identify informative genes that contribute to a clustering solution, they are based on criteria that do not consider the potential interactive influence among individual genes. Motivated by ensemble clustering, there is a strong interest in leveraging the structure of gene networks for gene selection, so that the relationship information between genes can be effectively utilized, while the selected genes are expected to preserve all the possible clustering structures in the data.We present a new filter method that uses the gene connectivity in the gene co-expression network as the evaluation criteria for variable selection. The gene connectivity measures the importance of the genes in term of their expression similarity with others in the co-expression network. The hard threshold and soft threshold transformations are employed to construct the gene co-expression networks. Both simulation studies and real data analysis have shown that the network based on soft thresholding is more effective in selecting relevant variables and provides better clustering results compared to the hard thresholding transformation and two other canonical filter methods for variable selection. Furthermore, a new module analysis approach is proposed to reveal the higher order organization of the gene space, where the genes of a module share significant topological similarity and are associated with a consensus partition of the sample space. We demonstrate that the identified modules can lead to biologically meaningful sample partitions that might be missed by other methods.http://nba.uth.tmc.edu/homepage/liu/netVar/.By leveraging the structure of gene co-expression network, first we propose a variable selection method that selects individual genes with top connectivity. Both simulation studies and real data application have demonstrated that our method has better performance in terms of the reliability of the selected genes and sample clustering results. In addition, we propose a module recovery method that can help discover novel sample partitions that might be hidden when performing clustering analyses using all available genes. The source code of our program is available at  Variable selection in high-dimensional clustering analysis has drawn attention recently in a variety of fields, including statistics, machine learning, pattern recognition and bioinformatics. Generally, variable selection algorithms can be categorized as either wrappers or filters. In the context of clustering, the wrapper approach searches for variables best suited to a specific clustering algorithm aiming to improve the clustering performance,2. The wDNA microarray datasets are examples of high-dimensional data characterized by low sample sizes and high dimensionality of variables. Clustering microarray data can be very useful for biological and medical studies. For example, based on the gene expression profiles, interesting cluster distinctions can be found among groups of samples, which may correspond to particular phenotypes, such as different types of cancer. In addiIn this study, we propose a novel network-based method to achieve variable selection for microarray clustering analysis. Network analysis plays an increasingly important role in the exploration of information communication and has been used to study the information on the relationship between genes or proteins,16. Hereij between the expression profiles of genes i and j, we use the absolute value of the Pearson correlation sij = abs), where xi and xj represent the gene expression profiles for genes i and j, respectively. Therefore the similarity matrix can be denoted by S = [sij], where the values of sij lie between 0 and 1. However, since microarray gene expression data are typically quite noisy, directly employing the similarity matrix for gene co-expression network analysis may not be appropriate. We find it useful to employ the following transformations that map a similarity matrix into an adjacency matrix. The first transformation is the signum function which implements hard thresholding. Specifically,To define a measure of similarity sij is an element of the adjacency matrix and sij is an element of the similarity matrix. In hard thresholding, the value of the parameter τ determines the number of genes and edges included in the resulting unweighted network. Typically, an arbitrary value of τ is chosen to exclude spurious edges, but this may lead to a loss of information. To address this issue in hard thresholding, a “soft” power transformation function has been proposed[Here aproposed:β, where β > =1. Soft thresholding results in a completely connected network with each edge being assigned a weight.with a single parameter ki of gene i is define byWith the n × n symmetric adjacency matrix, the connectivity (node degree) i simply equals to the number of genes that it is directly connected to in the unweighted network. For the soft thresholding transformation, the connectivity of gene i equals the sum of weights between gene i and all other genes in the weighted network. To select the relevant genes for microarray clustering analysis, we first rank the genes according to their connectivity. For the hard thresholding transformation, the genes with connectivity of 0 are removed from the original network. Therefore, the gene connectivity ranking is only applicable on the set of genes included in the resulting unweighted network, which is of a reduced size depending on the value of the threshold τ. In the weighted network, the ranking can be obtained for all the genes. Finally, the genes with low ranks are filtered out, while the genes with top ranks are considered to have high degree of connectivity and are selected for clustering analysis.For the hard thresholding transformation, the connectivity of gene Jij based on the gene connectivity in the transformed network.Our module identification method is based on the node similarity measure of their relative interconnectedness coupled with the hierarchical clustering method. Instead of using the gene correlation coefficients directly as the similarity measure, we calculate the Jaccard similarity coefficient hij  =   ∑ uaiuauj, which equals the number of genes to which both i and j are connected in the case of hard thresholding, and the total interconnectedness of genes i and j in the soft thresholding transformation. And ki  =   ∑ uaiu is the node connectivity as defined in equation (3). Therefore, the similarity measure will be affected by the selection of the transformation parameters. In our implementation, we adjust the hard thresholding parameter τ or the power function parameter β to explore their effects on the results of module identification. Once the topological similarity measure matrix is obtained, we re-order it by hierarchical clustering of each row and column to put similar genes in an adjacency zone[Where ncy zone. Since tThe performance of our method for variable selection is evaluated by the F-score, where F = 2*Precision*Recall/. The precision is the proportion of selected variables that are truly relevant, and the recall is the proportion of truly relevant variables that are selected by our method, also known as the true positive rate. The F-score ranges between 0 and 1, and can be interpreted as a weighted average of the precision and recall.1) is compared to the true clustering (p2) to assess the performance. The CER is defined asBased on the selected genes, we cluster samples using the K-means algorithm with 50 iterations. The sample clustering performance is evaluated by the classification error rate (CER). The derived sample clustering  and each sample Xi is a d - dimensional vector that follows N and is independent of other samples. Thus, the clustering structure is determined by the specification of μi’s that are defined asWe used a simulation setting similar to that in Witten and Tibshirani. A simuld  =  diag  where fc σ1, …, σd are set such that the population variance of each variable is one. In the simulation, the first 20 genes together can be considered as a module since their expression profiles are highly correlated and this module differentiates samples in class C1 from the others. Whereas the next 20 genes form another module that differentiates samples in class C2 from others. Therefore, these two sets of genes exhibit different sample partitions.Where μ is a positive constant and set to 1 in the experiment. This configuration of μ sets the first 40 genes as informative genes and the other genes as noise. We take ∑ We describe herein the performance of our method with two network inference methods on a simulated dataset. In the hard thresholding transformation, we considered the effects of two parameters on the performance of variable selection: the hard threshold τ that determines the number of genes and edges included in the unweighted co-expression network, and the percentage of genes to be selected based on their connectivity in the resulted network, determined by equation (3). With a greater value of τ, the resulting network will have a smaller number of genes and edges, but the connection strength (correlation coefficient) between paired genes will be higher. We reported the average F-scores and CER values based on 100 simulated datasets for two different dimensionalities  and a high CER (0.29), as shown in Figure 5 and a hβ. It not only takes into account the information of all the genes, but also reduces the effect of noise induced correlation by the power function, assuming that the noise correlation occurs more likely at smaller values than the correlation associated with true gene relationships.As shown in above analysis, the network variable selection based on hard-thresholding transformation was influenced by both the network size and the gene connectivity filtering. It may be challenging to optimize both of these two factors in real data analysis. To resolve this problem, we used a soft thresholding transformation for gene selection that is only dependent on the power function parameter β to construct a series of gene co-expression networks. Results in Figure β=1). We further found the performance was not a monotonic function of β. Among the four power functions with different parameters β, the optimal value of F-score and CER were achieved when β was set to 3, which may result in the optimized state for emphasizing the correlation associated with true gene relationships by diminishing the noisy effects in this simulation setting. We observed similar results when d=1000 . The genes selected from each method were used for clustering samples with the K-means algorithm. Our proposed network algorithm consistently outperformed the other two methods, particularly at a low dimensionality (20–100), where all of these methods reached their best performance , we varied the threshold τ to retain the top 1% of correlation coefficients for calculating the Jaccard similarity coefficients between genes. This cutoff is roughly consistent with our simulation setting where there are 40 informative genes and 40*40 informative gene pairs among 500*500 total number of gene pairs (0.64%). We also tested the performance on the top 5% of correlations. Figure We also performed soft thresholding transformation and obtained similar results Figure d and e, Along with simulations, we applied our method to two real experimental datasets: Leukemia and ColoThe leukemia dataset consists of 72 patients with two subtypes of acute leukemia: acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). The latter is composed of two subclasses, B-cell and T-cell types. Therefore there could be two possible biologically meaningful clustering solutions including one with two-clusters of samples (AML and ALL) and the other with three clusters .=3), reflecting possibly different variable compositions between the simulated dataset and the leukemia data. As shown in Figure Following Dudoit and Fridlyand, three pWe also analyzed the colon cancer data by Alon et al., which cVariable selection for clustering is never a trivial problem. This is particularly true in high dimensional data analysis, where few dozens of informative variables are often dispersed over a noisy background with thousands of noninformative variables. Traditional approaches to filtering out the irrelevant features are based on certain criteria that do not account for potential interactive influence from other individual variables. Motivated by ensemble clustering, we propose a new filter score, the gene connectivity in the co-expression network, which takes into account all of the information gained from other nodes in the network in terms of expression similarity; therefore, the selected genes are expected sustain a consensus sample partition that populates through the partition pool induced by individual genes.To obtain the connectivity of each gene, we have applied two network inference methods based on a hard thresholding and a soft thresholding adjacency function. In the first method, we use a hard threshold parameter τ to infer the gene network, followed by filtering the nodes based on their connectivity rank. Therefore, the resulted feature gene set is affected by the resulting network size and the stringency of the connectivity rank. The marginal gene connectivity obtained from hard thresholding transformation is estimated solely based on the given gene and its neighbourhood in the network with reduced size. Therefore, to retain more information of the entire network, we employ the soft thresholding transformation to build a complete network including all genes, where each gene is connected to all the other genes in the network with weighted connection strength. Our simulation results showed that soft thresholding is more effective and provides better clustering results compared to the hard thresholding method in terms of clustering error rate and variable selection. We realize although the connectivity obtained from a soft thresholding network preserves more information of the entire network compared to the hard thresholding transformation, the gene connectivity calculation is still based on the gene and its edges to all the genes in the network, and it does not consider the edges among its neighbors. There are other network related metrics, such as the betweenness centrality of a node that requires knowledge of the entire network topology and indicates how important the node is within the context of the entire network. These network metrics will be evaluated in our future studies. In this work, considering the fact that gene connectivity is easy to calculate and the derived gene hubs represent a large number of other genes in the network well, we use gene connectivity as our evaluation criteria for variable selection.The parameter setting in variable selection methods renders a crucial influence on the performance of the feature genes selected. However, tuning parameter selection in the unsupervised setting is always a challenging problem. In realFurthermore, we developed a module identification method by measuring the node interconnectedness in the co-expression network. Our module identification is based on using a node similarity measure in conjunction with a clustering method. In this study, we chose to use the Jaccard similarity coefficient based on the gene connectivity instead of using the gene correlation coefficients directly. Jaccard similarity takes advantage of the co-expression network information assuming that two nodes having a higher degree of overlapping neighbors are more likely to be in the same functional class than nodes having a lower topological overlap. This is particularly useful when high background noise divert the real network information. We performed a comparison of module structures based on two similarity measures: the Pearson correlation coefficient and the Jaccard similarity coefficient. As shown in Additional fileThe focus in our module analysis is on the high order organization of gene space, rather than their specific corresponding sample partitions. It is particularly useful for discovering unanticipated sample partition structures in data. Unlike the previous methods, our metThe authors declare that they have no competing interest.ZW carried out the simulation studies and real data application and drafted the manuscript. FAS participated in the data analysis and results discussion. QP participated in the design of the study and helped to draft the manuscript. YL conceived and coordinated the study and helped to draft the manuscript. All authors read and approved the final manuscript.Figure S2. Module structure in the gene co-expression network from the simulated dataset of d=1000. (a) and (b): in hard threshold transformation, with top 1% and 5% correlations were included in the network, respectively. (c) and (d): in soft transformation, power function with β=3 and β=7. Figure S3. Comparison of module structure recovery using different similarity measures. The rows and columns of genes have been reordered according to the hierarchical clustering of similarity matrix. (a). Pearson correlation coefficients of 500 genes, no transformation. (b) Jaccard similarity coefficients of 500 genes, no transformation. (c) Pearson correlation coefficients with power transformation with β=3. (d). Jaccard similarity coefficients derived from power transformation with β=3. Figure S4. Comparison of lists of genes selected from different methods. Network refers to our network-based variable selection method. (a) Leukemia dataset and (b) Colon cancer dataset. Figure S5. Clustering performance based on new partition structures identified by our module analysis. The CER curve with various power functions in co-expression network transformation for new partition structures of the Leukemia dataset (a) and Colon dataset (b).Variable selection performance in the simulated dataset (d= 1000). The averaged F-scores  and the CER curves  in hard thresholding and soft thresholding transformation, respectively. The horizontal line in each plot represents the performance based on all genes . Click here for file


This phenomenon which is a result of conductance changes can be employed in sensing applications such as gas sensors.Carbonaceous materials have recently received attention in electronic applications and measurement systems. In this work, we demonstrate the electrical behavior of carbon films fabricated by methane arc discharge decomposition technique. The current-voltage (I-V) characteristics of carbon films are investigated in the presence and absence of gas. The experiment reveals that the current passing through the carbon films increases when the concentration of CO This calls for the need to develop low-cost, sensitive, resettable sensors that can be used to monitor the CO2 concentration in industrial exhaust gases [Continuous emission of carbon dioxide  and the gas cylinder, while the other end was connected to a gas bubbler tube so as to absorb the pollutant gases from the reactor outlet released after the decomposition process. Different values of pure methane gas (200 to 800 ppm) were passed through the chamber using a gas flow meter. A pressure regulator was implemented to make sure the gas flow had the atmospheric pressure. Single-phase AC electrical power was fed to a high-voltage power supply with built-in amplifier to control and manipulate the operating voltage. This voltage was then increased to kilovolt scale using a step-up neon transformer. The neon transformer was used at normal operating frequency (50 Hz) to produce high voltage. This high voltage was applied to the two electrodes to start the methane decomposition process. To monitor the applied high voltage, a high-voltage probe Tektronix  was coupled to a four-channel oscilloscope  to record the signal measurements. Details of the operating parameters of the arc discharge methane decomposition process are provided in Table Once the arc discharge is initiated, methane decomposition starts causing the resultant carbon atoms to deposit and stack up between the two electrodes creating a conductive bridge. The growth time was measured to be 11.6 s at the voltage of 16.4 kV. The carbon film fabricated in this process is inspected using high-resolution optical microscopy, as shown in Figure A scanning electron microscope (SEM) scans the samples with a focused beam of electrons. As the electrons collide with the atoms in the sample, they produce various signals which can be detected and measured . These sAmong all types of carbon allotropes, only graphene, graphite, and CNTs show electrical conductivity. On the other hand, the carbon films also show conducting behavior. This implies that the grown carbonaceous materials belong to one of the above types of graphitized carbon. With reference to similar images from carbon materials published in the literature -21, it c2, and Hα as shown in Figures 2 appearing at 516.75, and hydrogen Hα appearing at 657.33 nm. These species represent the phenomenon of methane cracking under high-voltage arc discharge conditions as described in recent studies [The optical emission during arc discharge decomposition was captured in the wavelengths ranging from 385 to 750 nm through a spectrophotometer , and the data of the recorded spectra was sketched using MATLAB software. Three evolved peaks of methane species were prominent which belong to CH, C studies . As soon studies .2 radical which also indicates that the concentration of C2 is much higher in the methane plasma than the other evolved species. The second spectrum also indicates the pyrolysis process of gaseous hydrocarbons that causes carbon deposition between electrodes. The evolved species consist of swan band C2 which appears at 516.75 nm and C2 at 590 nm, while the two peaks corresponding to hydrogen Hα and CH are absent.The results of the evolved species in the second phase are different from initial ionization process of pure methane regarding the evolved species. In the second phase, the high peak belongs to CThe appearances of the peaks in the spectra of both phases of pure methane are listed in Table Once the carbon film was produced, a series of low DC voltage measurements were conducted on them in order to reveal their actual current-voltage characteristics. To do this, a DC power supply was employed to apply low voltage to the two electrodes and the carbon film in between. Figure After growing the carbon film, both sides of the chamber must be opened to release the methane gas inside it. After about 20 min, when there is almost no gas present in the chamber, we start to apply the DC voltage and measure the resulting I-V characteristics. The measurements were repeated in the presence of gas with concentrations of 200, 400, and 800 ppm. The current-voltage readings are provided in Figure In the presence of gas, higher values of current were read which proves the higher conductivity when the carbon films are subjected to gas. Also, as the concentration of gas was increased from 200 to 800 ppm, the current passing through the channel increased further. This phenomenon can be explained by the fact that gas molecules are adsorbed on the carbon film surface and will increase channel conductivity.In the next step of the study, in order to provide a platform for analytical investigations, MATLAB software was used to fit a curve of exponential form to the corresponding set of experimental data with maximum accuracy (regressions very close to 1). The resulting formula is in the form of Equation 1.a, b, c, and d in Equation 1 and the corresponding regression values as well as R2, SSE, and RMSE errors are provided in Table Constants A set of experiments were carried out to fabricate carbon films using high-voltage arc discharge methane decomposition method. High-resolution optical microscopy as well as OES and SEM imaging techniques were implemented to verify the fact that the substances obtained are carbonaceous materials. The carbon films were then used as the channel in an electrical circuit to measure their current-voltage characteristics. Among all types of carbon allotropes, only graphene, graphite, and CNTs show electrical conductivity. On the other hand, the carbon films also show conducting behavior. This implies that the grown carbon films belong to one of the above types of graphitized carbon. It was observed that higher currents pass through the channel when it is exposed to higher concentrations of gas. A mathematical model was obtained for the experimental results using MATLAB curve fitting tool. With the aid of this mathematical representation, it will be possible to characterize and predict the electrical behavior of the carbon films. This will provide a reliable mathematical model which can be used in gas sensing applications to minimize the need for conducting experimental studies.The authors declare that they have no competing interests.EA carried out the experimental study as well as data collection and analysis, and drafted the manuscript. AE contributed in performing the experiment and also checked the language coherence and technical accuracy of the manuscript. MTA provided the fundamental knowledge and supervised the process and procedure of the experimental study. He also checked for technical and scientific errors.AN applied some optimizing modifications in the programming of the simulation study and also collaborated in the final proofreading. All authors read and approved the final manuscript.


This is a report of one case of bilateral acetabular rim fracture in association with femoroacetabular impingement (FAI), which was treated with a hip arthroscopic procedure, performing a partial resection, a labral reinsertion, and a subsequential internal fixation with cannulated screws. Up to date, there are in the literature only two reports of rim fracture and “os acetabuli” in association with FAI. In the case we present, the pincer and cam resection were performed without complications; the technique used was published previously. With this technique the head of the screw lays hidden by the reattached labrum. We removed partially the fractured rim fragment and the internal fixation of the remaining portion was achieved with a screw. In the event of a complete resection of the fragment, it would have ended with a LCE angle of 18° and a high probability of hip instability. We believe that this bilateral case helps establish the efficacy and reproducibility of the technique described by Larson. Recently, Ganz et al. have identified in femoroacetabular impingement (FAI) a predominant cause of labral tear of the hip; this situation may be the result of an abnormal contact between the proximal femur and the acetabular rim . SometimThis is a report of one case of bilateral acetabular rim fracture in association with FAI, which was treated with a hip arthroscopic procedure, performing a partial resection (pincer), a labral reinsertion, and a subsequential internal fixation with cannulated screws.A 20-year-old competitive male soccer player, who presented with a two-year history of recurrent bilateral groin pain and stiffness, was admitted to our institution. Bilateral examination showed pain in hip flexion, adduction, and internal rotation (anterior impingement test); abduction and external rotation were normal. The patient had bilateral hip flexion up to 100° and internal rotation of 0°. Plain radiographs of the pelvis showed a well maintained joint space and a combined type FAI image. The alpha angles were 78° for the right side and 76° for the left side; the lateral centre edge (LCE) angle was 45° on the right and 47° on the left. Both hips showed a large superior rim fracture .A magnetic resonance arthrogram showed FAI and an anterosuperior bilateral labral tear . A bilatThe patient was restricted to foot flat weight bearing and two crutches for 6 weeks and progressed back into soccer at 4 months postoperatively. Physiotherapy was indicated starting the 5th day after surgery. At two-year follow-up, he had no pain during soccer or other athletic activities, the hip impingement signs were negative, and the range of motion of his hips had improved to 120° of flexion and 30° of internal rotation. His modified Harris Hip Score showed a variation from 81.3 to 100 points on the right and from 87.1 to 96.1 points on the left, and his visual analogue pain score decreased from 8 to 1. six months  showed that the rim fracture healed. The LCE angle had decreased from 45° to 32° postoperatively in both hips and the hip joint space was still well maintained  and the acetabulum (pincer), have been described as causes of femoroacetabular impingement. During joint motion and weight bearing in hips with FAI abnormal bony contact may occur, and soft tissue structures (cartilage and labrum) could fail . It is aThe literature indicates that arthroscopic management of FAI has shown improvements in its results when the indication is correctly achieved and the technique is properly performed –12. It hIt is very important to maintain the stability of the hip; on one side, it is determined by an appropriate acetabular coverage of the femoral head, and, on the other side, the joint capsule and soft tissues play an important role as stabilizing structures; there are some published reports which show iatrogenic dislocations and subluxations after excessive arthroscopic rim resections –17. The Up to date, there are in the literature only two reports of rim fracture and “os acetabuli” in association with FAI. The first is a report where Epstein and Safran  in 2009 In the case we present, the pincer and cam resection were performed without complications; the technique used was published by Larson and Giveans . As prevWith this technique, the head of the screw lays hidden by the reattached labrum. Like in Larson's publication, we removed partially the fractured rim fragment and the internal fixation of the remaining portion was achieved with a screw. In the event of a complete resection of the fragment, it would have ended witha LCE angle of 18° and a high probability of hip instability.In an attempt to promote healing and ossification of the fracture rim, drilling of the interface with a k-wire is recommended. We believe that correcting the hip impingement and fixing the acetabular fragment with an internal fixation eliminate the shearing forces due to FAI and create compression due to the screw, allowing the fragment to heal.With regard to the surgery gap between both sides, this was because the need of partial load of the operated hip was required in 8 weeks. We believe that this bilateral case may help establish a therapeutic management, described by Larson and reproduced by these authors, and that will bring a little more scientific experience in this rare pathology.


The objective of this study was to clarify the relationships among anatomical landmarks of the glenohumeral joint at different angles of abduction.Fifteen volunteers  were enrolled in this study. Images of externally and internally rotated positions at 45°, 90°, and 135° of abduction in the plane 30° anterior to the trunk were taken using an open magnetic resonance imaging system. Landmarks including the glenoidal long axis with its center, bicipital groove, center of the head, and humeral shaft axis were determined. Using a line set on the surface of the head in the plane parallel to the humeral axis , the glenoid location and rotational relationships were investigated in each position.The average angles of axial rotation were 48° ± 27° at 45º of abduction, 71° ± 20° at 90° of abduction, and 40° ± 27° at 135° of abduction. The trajectories of the glenoid center primarily extended over the anterior portion of the humeral head at 45° of abduction and over the posterior portion at 90° of abduction, while those at 135° of abduction were localized on a small upper portion of the head.The glenohumeral relationships demonstrated that arm abduction might influence shoulder function through its effects on the portion of the humeral surface in contact with the glenoid during rotation and the resultant changes in the glenohumeral relationships. The shoulder has a wide range of motion , 12, 13.Fifteen volunteers  without symptoms or a history of shoulder disease were enrolled in this study. Their mean age was 29 years (range 21–35 years). All participants provided informed consent. The present study was approved by the IRB of our hospital.The right arm was both maximally externally and internally rotated at abduction angles of 45°, 90°, and 135° in the plane 30° anterior to the trunk. The arm was considered to reach the final position at about 135° of elevation when the humerus was perpendicular to the glenoid and the angle was divided to determine the three elevation angles. The elbow was flexed for relaxation. The amount of pronation or supination of the forearm was not specified. Images of these six positions were obtained using a 0.2-T MRI system   and analyzing the plane of abduction. The latter was shown by the angle of its plane to the glenoid plane . Axial rotation of the glenohumeral joint was visualized on the computer screen as follows Fig. b. The eqVariability and reproducibility were previously reported . Two indThe angles of abduction, horizontal abduction, and axial rotation in each position are shown in Table t test: p < 0.0001, p < 0.0001).Figure The aim of the current study was to reveal the glenohumeral relationships during rotation at different angles of abduction. Healthy shoulders maintain stability within a wide range of motion. Previous studies on the positioning of the shoulder joint mainly focused on whether the joint is centered in its range of motion , 16, 17.Several authors have reported the benefits of using an open MRI system to analyze the 3D kinematics of the shoulder joint , 10, 11.In a previous study investigating the rotational alignment of the joint in maximum elevation, we set a line on the surface of the head using the plane parallel to the humeral axis and involving the center of the head and the bicipital groove . The finDuring rotation at 45° of abduction, the glenoid trajectories extended mainly over the anterior portion of the head. The most proximal part of the shaft axis was present in Zone III of the surface of the head. Thus, the center of the head was located between the glenoid and the shaft on which the rotator cuff and other muscles act during that rotation. In that relationship, the glenoid may play the role of the fulcrum, allowing the upper extremity to easily move in front of the trunk. Although the humerus was positioned in the same relationship to the trunk, the joint has multiple axes with varying angles of the humerus to the glenoid, as shown by the large standard deviation in the angle of horizontal abduction. When the arm is elevated from the dependent position, the insertion of the rotator cuff muscles approaches the glenoid surface. The glenoid trajectory range becomes limited, converging to the top of the head. However, the manner in which this range became limited was not uniform. In fact, during rotation at 90° of abduction, the glenoid trajectories extended over the posterior portion of the head. In this posterior head portion of the head, we could extend the arm toward the backside of the trunk.When the arm was highly elevated at 135° of abduction, the glenoid trajectories were more limited than those during rotation at lower abductions. The shaft was stabilized by the shortened rotator cuff on both sides. Glenohumeral relationships in highly elevated positions would be more suitable for supporting the arm and weight held by the arm than for mobility with the glenoid playing the role of the platform. The humerus could pivot against the glenoid, and the angles of axial rotation would still be maintained with the shaft axis tilting in the same posterior–inferior direction. Rotation using the glenoid as the platform would help to generate or preserve rotational torque. Throwing athletes such as baseball players or javelin throwers, who must accelerate their arm rotation while playing their sport, might use the glenohumeral joint in the above-described relationship.As a clinical relevance, information in the current study would be useful for thinking about glenohumeral instability. Gagey et al.  describeCertain shortcomings of this study must be acknowledged. The study was based on only six static positions in a small number of subjects, and each glenoid trajectory connecting the internal and external positions was not analyzed directly during active rotation. The participants had to maintain the same position for scanning for about 10 min, and the actual end range of rotation might be wider than the values obtained in this study. Dynamic studies using a wider range of motion should be performed to supplement the present data and provide a better understanding of shoulder motion. Additionally, each participant had to lie in the supine position in an open MRI system. A system with upright coils should be used to investigate standing or sitting positions and determine the effect of gravity.Although the current study has some limitations, it shows that the angle of abduction might influence shoulder function through its effects on the portion of the humeral surface in contact with the glenoid and the resultant changes in the glenohumeral relationships during rotation.


Health camp is generally organized to provide health care services to the people deprived of health care facilities. The aim of this project was to assess the proportions of disease among attendees of health camp and study the drug prescribing pattern in a free health camp.A case study was performed from 1 day health camp to determine the proportions of disease and drug prescribing pattern. Data collection was performed using log book maintained in the health camp and patient’s demographic details, disease diagnosed and drug prescribed was obtained from same log book.A total of 317 patients were included in the study. The majority of the patients were in the range of 41–50 years. On the basis of study on ethnicity, Brahmins and Chettris, were found to be predominant ethnic groups with gastrointestinal disorders as the major disease. The total number of medications prescribed was 510, with non-steroidal anti-inflammatory drugs (NSAIDs) and antipeptic ulcer drugs being commonly prescribed. The average number of drugs per prescription and the percentage of antibiotics prescribed were 1.6 and 21.4 %, respectively. It was observed that 96.8 % of prescription was by generic names. Likewise, 100 % of prescription included drugs from essential drug list.Majority of the patients were of working age group. Headache and fever were found to be the most prevalent cases and NSAIDs were the most commonly prescribed medications. The drug prescribing pattern of the free health camp complied with WHO recommended prescribing indicators. The rational use of drugs requires that “patients receive medications appropriate to their clinical needs, in doses that meet their own individual requirements for an adequate period of time, at the lowest cost to them and their community” . In 2010Health Camp is generally organized to provide health care services to the people who are generally out of reach to the basic health care facilities. Disease prevention as well as treatment of medical issues should be the main objective of any kind of health camps . PrevaleFree health camps are being organized by different organizations in different parts of the country. A study on drug prescribing pattern in a particular community might be helpful to organize a health camp where the participants could benefit the most. Additionally, such studies provide useful guidance to the organizers of health camp because organizing the health camp and evaluating its outcome is crucial and very few results regarding the use of medication in the health camp has been reported.All the patients attending the health camp were included in the study. A total of 317 patients were assessed.The protocol of the study was approved by Research Committee of School of Health and Allied Sciences, Pokhara University and Helsinki ethical guidelines were followed during the entire study. A case study was conducted using the information of the free health camp program organized by School of Health and Allied Sciences, Pokhara University, Kaski, Nepal. The health camp was conducted at Dhorphirdi Village Development Committee of Tanahun district of Nepal with a team of 6 medical doctors, 6 registered pharmacists and 36 pharmacy students , who participated voluntarily in the program.The medications for the health camp were donated by Nepalese Pharmaceutical Industries, wholesalers and some retail pharmacies. Most of the drugs were dispensed from camp itself and only few medications which were not available were requested to purchase from outside. The medication were prescribed by the medical doctors and dispensed by pharmacists. The dispensing of medications was performed in a homemade paper envelope and all the necessary information like name of drug, dose, frequency, time, before or after food was delivered verbally as well as in written form. As a part of counseling, cross questioning was conducted to ensure they received correct information.The data was collected from the log book maintained by the registered pharmacists in the health camp, which was initially prepared to enter all the necessary information like patient’s name, age, gender, ethnicity, disease diagnosed and drugs prescribed. Informed verbal consent was obtained from patients before enrolling them in the studies.The WHO prescribing indicators were used to assess the appropriateness of prescribing pattern .The average number of drugs prescribed per encounter: calculated to measure the degree of polypharmacy. It was calculated by dividing the total number of different drug products prescribed by the number of encounters.Percentage of drugs prescribed by generic name: calculated to measure the tendency of prescribing by generic name. It was calculated by dividing the number of drugs prescribed by generic name by total number of drugs prescribed, multiplied by 100.Percentage of encounters in which an antibiotic was prescribed: calculated to measure the overall use of commonly overused forms of drug therapy. It was calculated by dividing the number of patient encounters in which an antibiotic was prescribed by the total number of encounters, multiplied by 100.Percentage of drugs prescribed from an essential drug list (EDL): calculated to measure the degree to which practices confirm to a national drug policy as indicated in the national drug list of Nepal. Percentage was calculated by dividing number of products prescribed which were in essential drug list by the total number of drugs prescribed, multiplied by 100.The prescribing indicators measured in this study wereData were analyzed using SPSS  and Microsoft Excel 2007. In the statistical analysis, frequencies, percentage and average were determined.A total of 317 patients were assessed in a 1 day free health camp organized by School of Health and Allied Sciences, Pokhara University, Nepal on May 18, 2013.About 23 % of the patients were of age group 41–50 years n = 69), followed by 16 % of the patients in the range of 31–40 years (n = 51). This showed that majority of patients were of working age (30–50 years). The most common problem was headache and fever and this symptomatic problem was followed by gastrointestinal disorders  and Brahmins (12.2 %) constitute higher percentage of the population . Support.6 % and A total of 510 medications were prescribed. Among them, NSAIDs 29.41 %) were most commonly prescribed medication which is followed by antipeptic ulcer drugs (19.41 %) and vitamins and supplements (15.88 %) Table . NSAIDs .41 % werThe average number of drugs per prescription was 1.6 Table , which wMajority of the patients participated in the health camp were of working age group and female participants dominated the male participants in number. Among the studied symptoms and diseases, headache and fever were found to be the most prevalent. NSAIDs were the most commonly prescribed medications. In this study, the drug prescribing pattern complies with WHO recommended prescribing indicators. Since, health camp has a direct impact on disease prevention and treatment, similar studies related to the prescribing pattern are warranted in the future as well in order to assess the success of the health camp.


Image quality in light-sheet fluorescence microscopy is strongly affected by the shape of the illuminating laser beam inside embryos, plants or tissue. While the phase of Gaussian or Bessel beams propagating through thousands of cells can be partly controlled holographically, the propagation of fluorescence light to the detector is difficult to control. With each scatter process a fluorescence photon loses information necessary for the image generation. Using Arabidopsis root tips we demonstrate that ballistic and diffusive fluorescence photons can be separated by analyzing the image spectra in each plane without a priori knowledge. We introduce a theoretical model allowing to extract typical scattering parameters of the biological material. This allows to attenuate image contributions from diffusive photons and to amplify the relevant image contributions from ballistic photons through a depth dependent deconvolution. In consequence, image contrast and resolution are significantly increased and scattering artefacts are minimized especially for Bessel beams with confocal line detection. A fundamental principle in light microscopy is to uncover the composition of matter by sending photons with defined properties onto a piece of matter and detecting the scattered photons. However, things can become very complicated when the investigated object is large and of complex biological structures and multiple light scattering occurs. Photons that have been scattered too often lose their directional information, i.e. photons are no longer ballistic, but become diffusive. This loss of information does not only occur on the illumination side, but also on the detection side. When arriving on the camera, the origin of the photons is often unknownA suitable microscopical method to tackle the problem of light scattering in both the illumination and detection path is light-sheet based microscopy (LSM)2Many technical improvements have been achieved in LSM within the last decade - on the detection side, but especially on the illumination side4566Especially the use of beam shaping elements such as spatial light modulators (SLMs) or digital micromirror devices (DMDs) allows to generate nearly arbitrary illumination beams, which, in the optimal case, can be adapted specifically to the refractive index inhomogeneities of the object, which would otherwise lead to unwanted beam deflections and distortions141617The influence of scattering becomes apparent in an illustrative way when imaging large, scattering structures such as small plants and plant root tips, that consist of regularly shaped cells of variable sizesImage formation in scattering media has been described by wave-optical models212426In this paper we introduce such a procedure and model. Based on the theoretical description of photon diffusion, we present a method that allows to separate efficiently the parts of the image resulting from the minimally scattered  photons and the highly scattered (diffusive) photons. This information can be directly extracted from the image spectra such that no a priori knowledge about the object is required. We demonstrate the principle of separating weakly and strongly scattered fluorescence photons using identical Arabidopsis Thaliana roots, which we image in four different illumination and detection modes. We have developed a concept that quantifies the change of ballistic photons into diffusive photons, which varies with the detection depth and which is implemented in a depth dependent deconvolution of the 3-D images.In this study we investigate the influence of three important components of the imaging chain - the illumination beam, the detection method and the image postprocessing - on the 3D image quality. Further, this chain is studied in four different imaging modes. All variations of these components are performed at exactly the same biological object, an Arabidopsis thaliana root, to enable a meaningful comparison of the imaging modes. The roots are about 120 μm in diameter and scatter strongly both the illumination light and the fluorescent detection light, leading to reduced contrast and resolution, but also to local image artifacts in the back parts of the object.As the first component of the imaging chain, we use a spatial light modulator (SLM) that can switch plane wise the shape of the illumination beam, which is either a Bessel beam or a Gaussian beam optimized to the extent of the object. The beam is scanned laterally in the plane of focus  in the illumination path allows to shape nearly arbitrary illumination beams, which will then be scanned laterally across the object as indicated in The concentric ring system around the thin main lobe of a Bessel beam enables the superior propagation stability and the self-reconstruction capability of the beam. However, it is also the ring system that generates the low image contrast because it excites fluorescence also out of the focal plane. This problem can be well solved by using a confocal line detection scheme, which mainly detects the fluorescence generated by the thin main lobe of the Bessel beam and generates unreached contrast and resolutiondslit = MT · 50 μm) and in confocal line detection mode . x and ky) revealing a broader image spectrum (better transfer of high frequencies) for the conventional Gaussian beam.In total four 3D image stacks each consisting of 260 planes separated by Δy = 0.5 μm were recorded from a single root tip. To allow a fair and precise comparison without bleaching or drift effects, each plane was imaged successively with the above mentioned four different imaging modes. Both the Gaussian  Δz = 300 μm) and the Bessel beam  illumination have been used to image in conventional widefield mode  and the low spatial frequency image components   see . The corQ refers to high contrast in an xz-image slice. The contrast coefficient is plotted in y0  the contrast is improved roughly by 70% for Bessel illumination (compare the bright and dark blue lines) and by 30% for Gaussian illumination (the red line above the green line). The contrast improvement is further enhanced for higher detection depths. For e.g. y0 = 100 μm the contrast coefficient is improved by more than 150% for both illumination modes. For higher detection depth the amount of diffusive photons involved in the image formation increases and image quality drops down. Since diffusive photons are multiply scattered on the way to the detector and thus are displaced in the image plane, they have a higher probability to be blocked by the confocal slit. This effect leads to the enhanced contrast improvement by confocal detection for higher detection depths.For a quantitative comparison of the different imaging modes, the contrast is normalized by the contrast coefficient of the standard imaging mode . The result is plotted in xkz-plane are plotted relative to the spectrum obtained by the standard imaging mode (see the green circle as a reference). The elongation of the confocal image spectra in kx-direction demonstrates that the improved contrast enhancement at high detection depths is caused by the confocal slit, which works in in x-, but not in z-direction. A detailed discussion on the effect of confocal detection with special attention on the difference between Bessel and Gaussian illumination can be found in Since the slit is parallel to the z-axis, only photons displaced in x-direction are blocked thereby increasing optical resolution along x. This effect is shown in The image is formed by ballistic (hardly scattered) and diffusive (multiply scattered) photons. Due to the fact that diffusive photons carry only little high-frequency information about the object, the image quality decreases if the amount of diffusive photons involved in the imaging process increases. Consequently, the image quality is increased if the percentage of ballistic photons is enhanced. This process is called gating3335hill(r) and hdet(r) are the purely optical response functions for light-sheet illumination and detection.  and can be accounted for quantitatively by an object response function hobj, which consists of two parts. One part for diffusive photons, which is nearly of Gaussian shape and broadens with the detection depth y0 and one part describing the ballistic photons by a delta-point function. This is explained in detail in the methods section. The degree of the linearly increasing influence of the object, i.e. the broadening of hobj is expressed by the scattering parameter γ, which is a material constant specific for the object. The corresponding object transfer function Hobj, i.e. the Fourier transform of the response function, describes the signal loss for each spatial frequency kr. It consists of a Gaussian like part for the diffusive photons that narrows with y0 and a constant offset for the ballistic photons that drops off exponentially with y0:A diffusive photon differs from a ballistic photon by its propagation angle θ. Any angular change during the propagation of a fluorescence photon on its way to the detector will result in a wrong position on the camera and to a wrong image contribution. The image is described by Hobj in lateral direction is shown in y0. The experimental data is obtained through angular averaging of the normalized image spectra. c0 of the fluorescent photons leaves the object unscattered, and fractions cj are scattered j times. The parameter μsca describes the probability that a photon is scattered. Each scattering event results in a random change of the propagation direction θ. The probability for a directional change follows a Gaussian distribution p(θ), characterized by the material parameter γ  decrease for higher detection depths. This means that a reduced amount of high frequency information is transferred through the scattering sample. To extract this loss in high frequencies caused by the object, the spectra must be normalized by a reference spectrum at the bottom of the object  to the frequency transfer data, we found μsca = 50 mm−1 and γ = 22.4. The model-fitted curve is plotted in xkz-plane. This is different for confocal detection. Nevertheless, it is possible to extract the scattering parameters by only considering the frequency transfer in kz-direction  instead of more advanced deconvolution algorithms, to make the effect of photon separation better visible. The deconvolution intensifies the influence of ballistic photons on the imaging process at high detection depths, such that it can be classified as a gating technique.With knowledge of the scattering parameters 0-position and 12 different PSFs (see methods section) have been used. The images reveal a strong increase of contrast compared to the unprocessed images displayed in Some overshooting is visible in the left side of The advantages of confocal line detection using a camera with a moving slit (rolling shutter) become clearly visible in A recent study using structured light-sheet illumination reveals a strong image darkening in the central part of the root tips, since the illumination modulation frequency, does not match the PSF broadening. In our study, however, the small central cells can be reasonably resolvedThe gating effect of a confocal slit, i.e. the blocking of diffusive photons, has been analyzed also theoretically. It was shown by 0, the useful image signal decays in the same way. The image background, defined by the diffusive photons, will increase exponentially with the detection depth. The separation between ballistic and diffusive photons, i.e. a strong enhancement in contrast, is possible, as long as the amount of ballistic photons is distinguishable from the noise level.Ideal, diffraction limited imaging is only possible by ballistic photons, which transfer information from the focal plane inside the object to the detector. Since the number of ballistic photons at the detector decreases exponentially with the detection depth y0 is divided by the image spectrum at y0 ≈ 0, which is mainly defined by the imaging optics. In principle, the normalized spectrum can be obtained experimentally without the fit functions derived in our model. However, the fit functions provide an additional control and deliver the material parameters μsca and γ.To extract the frequency transfer through the object each image spectrum at yy0. Both the experimentally and theoretically obtained Hobj reveal a quite good coincidence in shape and thereby demonstrate the ongoing transfer of ballistic photons to diffusive photons with increasing y0. Deviations between the measurement data and fit curves can be first a consequence of the inhomogeneous scattering properties of the root tip and second, the characteristic structure size and thus the object spectrum changes with detection depth, such that the effect of the object spectrum cannot be completely eliminated by scaling with a reference spectrum. For example, cells in the middle of the root  have a size of 5 to 7 μm and are smaller than the cells in the two outer cell layers of the root (Epidermis and Protoxylem), which measure 10 to 20 μm. Since the reference spectrum was obtained from an outer cell layer, frequencies from 0.05 to 0.1 μm−1 are more pronounced than in a layer at 50 μm detection depth  and thus are even more suitable for the presented method. Nevertheless, by imaging membrane labeled root tips, we demonstrate that the method is not limited to such samples.Deconvolution with a single response function generates images with either too little or too much contrast (effect of overshooting) depending on the choice of the PSF. However, by adapting the object PSF to the corresponding detection depth, resolution and contrast in the image can be optimized over the complete 3D volume. For illustration of this effect, see Our results prove that scattering of fluorescent light can be well approximated by a PSF even for inhomogeneous samples like Arabidopsis roots. In comparison to other deconvolution techniques, which utilize point like structures in the object to extract the PSFsy0 is of interest. A further reduction of computational efforts is possible, if each of the twelve 3D deconvolution is performed on a section, which is six times thinner than the whole stack. In the end, the computational effort will increase only by a factor of two relative to a standard 3D deconvolution with a single PSF.A perfect depth-dependent deconvolution would require a complete 3D deconvolution for all N xz-planes. A solution with less computational effort is described in the methods part, where twelve 3D deconvolutions for the whole stack have been performed. However, it is not necessary to compute twelve 3D deconvolutions for the whole stack, since only a limited number of planes around the specific plane at Furthermore, all image processing operations can be outsourced directly to camera systems exploiting fast and flexible power of GPUs or FPGAs.By the strong increase in contrast it becomes apparent that Bessel illumination with confocal detection benefits most from the deconvolution and leads to a nearly artefact-free image. The already mentioned artefacts caused by Gaussian illumination are even more obvious after deconvolution. Only without deconvolution, one may argue whether the high contrast achieved by Gaussian illumination or the elimination of artefacts by Bessel illumination leads to the best image quality. In general, this question has to be answered individually for each application. After deconvolution the best image quality is clearly achieved by Bessel illumination.μsca, whereas the decrease in Gaussian widths allowed to extract γ. We tested the universality of our approach by using the two different illumination and detection modes, to extract the same material parameters of the same root tip. Because of the gating effect by confocal detection the influence of the various scattering orders on image formation is changed. Thus the weighting by the photon fractions in the superposition of It was shown in Alternative methods like collimated transmission measurements and goniometryμsca and γ agree with each other reasonably. Further details and illustrating movies can be found in the The results are summarized in the following table  and indiIt will be interesting in biology to analyze both scattering parameters over a longer time, e.g. during root tip development and during responses to external stimuli, since they provide biophysical, structural and possibly mechanical information about the state of the cellular compound. This information is usually not visible with standard fluorescence imaging. It will be an interesting future task to extract this information spatially resolved over areas of different cellular morphology within the root tip.A severe and unsolved problem is the multiple scattering of fluorescent light on the way to the detector, thereby blurring the images. This effect is the stronger, the larger the object and the longer the way of the photons through the scattering object. We have presented an effective and elegant solution to this problem, leading to a significant improvement in image quality. We separated the image contributions of the diffusive and the ballistic photons by postprocessing. Our approach, which does not require a priori information, neither slows down the acquisition speed of light sheet microscopy, nor are any iterative image acquisitions required, as this is the case with adaptive optical approaches. Our algorithm is applicable to most new and existing 3D data sets suffering from image blur due to scattering of fluorescence light. It should be beneficial to every light-sheet microscopist and could in principle be applied to other microscopy techniques.p(r) can be described by a convolution (symbol *) of a 3D object distribution f(r), e.g. the fluorescence emission distribution, with the system PSF hsys(r):The formation of a 3D image hsys(r) of the imaging system is assumed to be shift invariant and contains the information on resolution and contrast. In LSM an effective systems-PSF hsys(r) can be defined, which is given byThe impulse response hill(r) and hdet(r) are the effective illumination PSF and the detection PSF respectively9hSB(r) scanned with velocity T being the exposure time of the camera and dslit the slit width, if confocal detection is applied. For better readability the transversal magnification of the detection optics is set to |M| = 1. Thus the illumination PSF effective for one pixel line during T readswhere hSB(r) (see further explanations in the dslit → ∞ and dslit → ∞ and hill(r) → hSB(r). In this case the system PSF is hill(r)is much broader than hdet(r), the multiplication hill(y) in y-direction is broadened compared to hSB(r). This is the case for a Bessel beam with lateral profile The influence of the rectangular slit function y0 can be seen. This loss of image quality with y0 corresponds to a low pass filtering, which can be modeled by a convolution with an additional object response function hobj describing the influence of the object on the detection process. Consequently, hdet(r) is replaced by hdet(r) * hobj and the effective system PSF can be written asIf LSM is used to capture a 3D image stack of strongly scattering objects a significant decrease in image quality with increasing detection depth hsys is now a function of y0 indicates that the image process is no longer a 3D shift invariant problem and hsys should be used for one specific detection depth y0. Thus, the final 2D-image obtained from position y0 is given byThe fact that hobj on the image process is highly anisotropic and depends on hsheet(r). A good light-sheet has only a small extent in detection direction y. Due to the multiplication in hobj is limited to the light-sheet thickness. The same is true in scanning direction x, if confocal detection is applied  → hSB(r)). This results in a gating effect.hobj, one has to consider the exponential decrease of the number of ballistic photons and the increase in diffusive photons that travel over the distance y0 through the object towards the detector. The larger the detection depth y0, the larger is the average of the scattering order j, which indicates the number of scattering events a fluorescence photon involved in the imaging process has survived. In this way, cj(y0) denotes the percentage of j times scattered photons at depth y0, such that cj=0(y0) is the fraction of ballistic photons contributing to the image. Since every scattering order carries a different amount of information, the image process for each order j is described by a specific object response hjobj,. Then the overall object response hobj is given by the weighted superpositionTo understand the depth dependence of cj depends on the scattering coefficient μsca, which describes the probability for a photon to be scattered while propagating a certain distance through the object. By neglecting absorption, one finds (see As indicated by inds see j = 0), cj(y0) results in the Lambert-Beer law, exp(−μscay0). The term For ballistic photons , which depends on the scattering order and can be approximated byThe second term in A is an unimportant normalization factor. A detailed derivation for y0 to the focal plane. It is important to note that for ballistic photons hj=0obj, becomes a δ-function. This is in agreement with the fact that these photons are not affected by the object. hjobj, also depends on the material specific unit γ, which describes the angular width of the scattering phase function θ being the scattering angle  = 1) and γ → ∞ for forward scatterers (PDFθ(θ) = δ(θ)).where ngle see ). The reHobj hobj was assumed to be a sum of Gaussian functions  In Fourier domain one finds the depth dependent fluorescence photon object transfer function ions see , the Fou0, the influence of the object on the detection process can be eliminated by a deconvolution with Hobj as long as the intensity of the ballistic photons does not drop below the noise level.et al.Q is defined by the ration of high and low frequency contents in the image. Therefor xz-slices of the image p are Fourier transformed in x- and z-direction. In Fourier space the image is divided in an image containing the high spatial frequencies  given in μsca and γ. This method extracts these parameters out of a 3D image stack. Since the most compact form of hobj is found in Fourier domain, the image stack is first Fourier transformed in x- and z-direction. To eliminate variations of the object spectra the data is smoothed in y-direction. Normalizing the smoothed spectra to a reference spectra at y0 = 0 eliminates the influence of the object spectra on the image process. In this manner the normalized and averaged image spectrumWith the model for b being the smoothing interval. The integration along the polar angle φ  and the detection PSF hdet(r) as well as the parameters μsca and γ describing the influence of the object on the detection are known, the system PSF hsys can be calculated by y0. This leads to a huge computation time. Since hsys is not changing rapidly with y0, a more hardware friendly method is possible. Therefore the 3D image is deconvolved several times by a conventional Wiener filter. For each deconvolution the Wiener filter is optimized for another y0 and each deconvolved image pdecon,Wiener is optimized for one specific y0. The depth dependent deconvolved image pdecon(r) is calculated byIf the effective illumination w defined as the shifted Hann window:with the window function yobj is the object dimension in y-direction. The Wiener filter is given byHere A is a compromise between high frequency enhancement and noise suppression. Models for hill(r) and hdet(r) are obtained by the angular spectrum wave propagation method.where How to cite this article: Meinert, T. et al. Separation of ballistic and diffusive fluorescence photons in confocal Light-Sheet Microscopy of Arabidopsis roots. Sci. Rep.6, 30378; doi: 10.1038/srep30378 (2016).