Bacillus subtilis sporulation, thereby demonstrating the ability of PSICIC to discern protein localization features at sub-pixel scales. We also used PSICIC to examine the accuracy of cell division in Esherichia coli and found a new role for the Min system in regulating division-site placement throughout the cell length, but only prior to the initiation of cell constriction. These results extend our understanding of the regulation of both asymmetry and accuracy in bacterial division while demonstrating the general applicability of PSICIC as a computational approach for quantitative, high-throughput analysis of cellular images.Live-cell imaging by light microscopy has demonstrated that all cells are spatially and temporally organized. Quantitative, computational image analysis is an important part of cellular imaging, providing both enriched information about individual cell properties and the ability to analyze large datasets. However, such studies are often limited by the small size and variable shape of objects of interest. Here, we address two outstanding problems in bacterial cell division by developing a generally applicable, standardized, and modular software suite termed Projected System of Internal Coordinates from Interpolated Contours (PSICIC) that solves common problems in image quantitation. PSICIC implements interpolated-contour analysis for accurate and precise determination of cell borders and automatically generates internal coordinate systems that are superimposable regardless of cell geometry. We have used PSICIC to establish that the cell-fate determinant, SpoIIE, is asymmetrically localized during  Bacillus subtilis asymmetric-division regulator is itself asymmetrically localized, thereby demonstrating our ability to extract information previously thought inaccessible by light microscopy. We also demonstrated our newfound ability to study characteristics of large populations by studying the accuracy of the symmetric division of Escherichia coli. We discovered a new role for the Min system, which inhibits polar division, in regulating division throughout the cell length. These results deepen our understanding of two important problems in bacterial cell biology while demonstrating the utility of our approach to studying subcellular structure in a wide range of biological systems.Recent studies have shown that all cells, including bacteria, are highly spatially organized. However, many questions about bacterial organization remain unanswered, often due to difficulties associated with visualizing and analyzing structures within such small and variably shaped cells. We have overcome these limitations by developing a generally applicable computational method for quantitatively analyzing cellular images at subpixel resolution. Our method uses interpolation to find cell borders accurately and precisely. Using these contours as a starting point, we automated the construction of a general-purpose internal coordinate system for each cell to facilitate comparisons between differently shaped cells. We applied this new method to two unsolved problems in bacterial cell biology. We first showed that a  Biological light microscopy has been pushed to remarkable limits of resolution, speed, throughput, and ease by advances in protein-labeling methods, sample preparation, and microscopy hardware. This imaging has revealed that the subcellular environments of cells from all kingdoms are exquisitely organized both spatially and temporally. Quantitative analysis of such images to measure cell morphologies and track subcellular components in space and time extends the power of cellular imaging by enabling both the extraction of subtle, non-obvious information and the automatic characterization of large datasets. The obvious power of quantitative analysis has prompted many groups to implement ad-hoc, often labor-intensive methods for analyzing specific aspects of their images of interest Bacillus subtilis sporulation, and the accuracy of cell-division-site placement in Escherichia coli cytokinesis.Cellular imaging studies from the past decade have clearly demonstrated that bacterial cells, like their eukaryotic counterparts, are spatially and temporally organized B. subtilis sporulation involves an asymmetric cell division event that gives rise to a larger mother cell and a smaller forespore F transcription factor in the forespore F activation by SpoIIE is understood, the basis for the preferential activity of SpoIIE in the forespore compartment remains unclear. A recent study used genetic arguments to suggest that SpoIIE is preferentially localized to the forespore face of the sporulation division septum E. coli, unlike B. subtilis sporulation, is a symmetric process that results in two similarly-sized daughters E. coli divides with extreme accuracy, and that the Min system contributes to this accuracy by doing more than simply blocking polar divisions. We also find that in both wild-type cells and cells lacking a functional Min system, the division site is accurately chosen before the cell begins to constrict and the accuracy of division-site placement is not significantly improved after a division pinch appears.Cell division in In addition to contributing to the understanding of sporulation and division, our analyses of SpoIIE localization and division-site accuracy are intended to highlight multiple aspects of the power of PSICIC in analyzing data from different species, extracting single-cell and population statistics, and utilizing both morphological and protein localization information.To achieve robust and accurate quantitation, PSICIC sequentially applies two approaches to address two different imaging problems: interpolation to more precisely identify cell borders, and establishment of internal coordinate systems to enable direct comparisons among cells. When analyzing a digital image, the first task is to identify the regions of interest. In biological applications, this often amounts to defining the cell borders. In phase microscopy, cells appear as dark objects on a light background . TherefoTo overcome the problem of jagged borders caused by thresholding, our method uses interpolated contours to define the outline of a cell . GeneratAt this stage in the analysis, having identified the regions of interest in the image, objects can optionally be filtered out by any number of criteria to remove false positives (such as dirt on the slide) or other undesirable objects (such as cells clumped together). This filtering can be done on the basis of size, shape, or more sophisticated metrics such as the smoothness or curvature of the cell outline.In order to measure the location of objects within the cell, and to be able to compare these measurements between cells that may vary in shape and size, we use the interpolated contours that define the cell outlines to create an internal coordinate system for each cell. This allows measurement of the location, size, and shape of subcellular features, such as the localization of fluorescently-labeled proteins, relative to the geometry of each specific cell. The cells that we study are generally rod-shaped or variants on a rod shape, which suggests the length of the cell as a natural axis from which to begin measurements. PSICIC therefore establishes a projected internal coordinate system by finding a midline connecting the poles of the cell as the long axis, and non-intersecting lines through this midline that locally define the other axis . The firIn order to validate the measurements generated by PSICIC, we tested both its precision and accuracy. Precision was tested computationally by performing measurements on simulated images of known dimensions. Accuracy was tested using micrographs of beads whose dimensions had been independently verified by electron microscopy.in silico experiment, the digital representation of various cells was manipulated to reflect the process of digital imaging: cells were rotated to several different angles to simulate different orientations with respect to a fixed pixel grid, and then blurred to simulate light scattering using a point-spread function similar to that of the imaging apparatus used for the subsequent experiments in this study. Each resulting object was then pixilated by overlaying it with a grid with spacing equivalent to the pixel size used for subsequent data acquisition and assigning each pixel the value of the sum of the intensities of the points within the corresponding grid square , the SpoIIE-GFP peak was shifted towards the forespore daughter cell, while 6 cells (13%) had a SpoIIE-GFP peak shifted towards the mother cell, and two cells (4%) had SpoIIE and FM4-64 peaks that colocalized to within the limits of PSICIC's measurement capabilities . The meaE. coli, which is highly symmetric in wild-type cells E. coli cells have evolved at least two distinct mechanisms that improve the accuracy of division-site placement: the Min system, which prevents division near the cell poles, and nucleoid occlusion, which prevents division from occurring over the nucleoid The automated nature of PSICIC lends itself to the analysis of large numbers of cells to measure distributions of morphological characteristics as well as noise and accuracy of subcellular processes. One such process whose accuracy is actively regulated is division-site placement in E. coli divides and the role of the Min system in achieving this accuracy, we used PSICIC to analyze the pinch position of over 3,000 wild-type and minC mutant cells (in silico approach described above to examine simulated cells with exactly symmetric pinch positions of different depths (To determine the accuracy with which nt cells . We fount depths . We founminC mutants had significantly reduced division-site-placement accuracy (11.5% S.D.). Interestingly, however, when we limited the analysis to cells that divided within the central half of the cell, minC mutants still exhibited significantly (P = 1.3e-53) worse division-site-placement accuracy (8.2% S.D.) compared to wild type (2.9% S.D.)  . These rminC cells, the accuracy of cell division does not significantly correlate with pinch depth (minC mutants were similar and remained relatively unchanged over a wide range of pinch depths (data not shown). This result is consistent with the conclusion that the Min system does not function during the division process and supports a model wherein the division site is fixed before constriction begins. These findings thus suggest that the Min system acts throughout the cell length to regulate division-site accuracy prior to the initiation of cell constriction but does not participate in the division process itself.By examining cells with different extents of division-plane constriction (pinch depth), we were also able to analyze the nature of the division process itself. We found that in both wild-type and ch depth . This reE. coli, exhibit asymmetrical shapes, supporting the usefulness of an internal coordinate system which takes this asymmetry into account for studies of cell shape and localization Advances in fluorescent protein labeling, sample preparation, and image acquisition have pushed light microscopy to its physical limits. Techniques such as deconvolution, photo-activated localization microscopy (PALM), and stochastic optical reconstruction microscopy (STORM) have increased spatial resolution further still B. subtilis sporulation. This result is validated by a recent study demonstrating that during the engulfment phase of sporulation, SpoIIE localization depends on the forespore-specific SpoIIQ protein In this study we exploited the ability of PSICIC to analyze single cells with great precision and obtained new insights into both symmetric and asymmetric bacterial division. We established that the cell-fate determinant SpoIIE is preferentially targeted to the forespore side of the division plane during the asymmetric division of E. coli. Despite the fact that E. coli division has been intensely studied before, the resolution and scale of our PSICIC analysis yielded new insights. Specifically, we found that division accuracy is tightly regulated by the Min system throughout the cell length prior to the initiation of cell constriction, but that once division starts, it proceeds through a constant and highly stereotyped process that is apparently immune to the influence of Min. While our data are strikingly similar to electron microscopy-based measurements of E. coli cell-division accuracy E. coli division B. subtilis cells that proposed that Min does not regulate midcell division-site placement E. coli and that the Min systems of E. coli and B. subtilis differ. Alternatively, the traditional analyses used by the prior studies did not address pixilation effects, implying that the data is inherently binned. For example, if one uses 100 nm pixels, all divisions within 100 nm are reported as perfectly accurate, thereby generating an overestimate of division accuracy and obscuring subtle differences between populations.In addition to addressing single-cell properties such as SpoIIE asymmetry, we also applied PSICIC to population properties such as the accuracy of the symmetric division of http://www.molbio1.princeton.edu/labs/gitai/), and encourage others to modify, expand, and adapt the software capabilities to suit their own applications.The modular nature of PSICIC allows for wide expandability and utility. Once the data has been analyzed and the digital cell constructed, measurements of any sort can be performed, such as morphometrics or fluorescence intensity in either one or two dimensions. The high-throughput capacity allows for screens based on shape or localization phenotypes. Given a series of time-lapse images, individual cells can also be tracked over time in order to observe dynamic changes in shape or localization. In this study we exploited the flexibility of PSICIC to analyze multiple properties of two different bacterial species imaged on two different apparatuses. Though PSICIC was created with bacterial cells in mind, it can easily be applied to both unicellular and multicellular eukaryotic systems and could be readily modified to create a pseudo-radial, rather than pseudo-Cartesian, internal coordinate system for analyzing round cells that lack a clear major axis. Computational analysis of fluorescent microscopy offers many exciting possibilities that will only increase as modern imaging techniques are used and expanded by the research community. We have thus made available the source code, software, and documentation for PSICIC . The number of points, n, can be chosen arbitrarily, but should be chosen to over-sample the original data; if n is too small, data will be missed, but if n is too large, the computation time increases significantly. For the studies reported in this work, n = 200 was found to sufficiently oversample to capture the variation within the data set (data not shown). Each point on the left curve is then connected to the corresponding point on the right curve, resulting in a set of n non-intersecting lines, called the width lines. The midpoints of the width lines are connected to create the midline of the cell. The final step in this process is to optimize the choice of the poles of the cell by moving the poles stepwise along the original contour and repeating the entire process to determine the length of the midline generated. If the new midline is longer than the last, the search continues in that direction; otherwise, the search terminates. This search is performed four times, both clockwise and counterclockwise, starting at both poles, and the longest of the four midlines generated is used. The longest midline together with the set of width lines then forms the coordinate system.In order to define an internal coordinate system for a cell, the cell poles must first be identified. The pair of points on the outline of the cell that are farthest away from each other are used as the first approximation of the poles, an estimate that is refined later. Having defined the poles, the cell outline is partitioned into two curves, one running clockwise from one pole to the other pole, the other counterclockwise. These will be referred to as the left and right halves of the curve (though the nomenclature is arbitrary). The left and right curves are then subdivided into The data can be filtered by any number of criteria. Establishing a minimum area and/or perimeter for objects helps to filter dirt from the images; establishing a maximum area is often necessary to prevent large regions of uneven coloration on the slides from being identified as cells. To filter out cells that are adjacent to one another and cannot therefore be individually identified, filtering based on width was found to be the most effective method (data not shown). The original images overlaid with the cell borders identified by PSICIC were manually verified to check for false positives.Simulated images of 16 symmetrically dividing cells were created in Keynote (Apple). The original images varied in length from 474 pixels to 716 pixels, and pinch depth varied from fully divided to barely pinched (thickness at the pinch 98% that of the rest of the cell). Each of the images was blurred using the MATLAB function imfilter, using a disk filter generated by the fspecial function with a radius of 20 pixels, in order to simulate the point spread function of the microscope. Each of the blurred cells was then rotated to 16 different orientations, to account for any effect of angle on PSICIC measurements. The 256 blurred and rotated cells were each then binned by a factor of 5, 10, 15, 20, and 25 to generate 1280 cells with different extents of pixilation. The cell lengths and pinch positions were then analyzed using PSICIC, and the measurement in pixels was multiplied by the magnification factor of that image for comparison with the known length of the original unprocessed cell image. The position of the pinch was also measured as a percentage of the measured cell length and compared to the known pinch position of exactly 50% of cell length.Molecular Probes FluoSpheres carboxylate-modified microspheres, 1.0 µm, yellow-green fluorescent beads were imaged on 1% agarose pads in water using a QImaging Rolera-XR camera on a Nikon 90i microscope with a Nikon Plan Apo 1.4/100× Oil Ph3 phase objective, using the NIS Elements software package. The images were then analyzed using PSICIC without midline optimization, and the diameter of the beads calculated by multiplying the measured length in pixels with the known pixel size of the microscope objective (0.13 µm/pixel). The measured length was compared to the length measured by transmission electron microscopy that was reported on the certificate of analysis for the specific lot of beads analyzed (lot number 45102), given as 1.1±0.035 µm.spoIIE-gfp kan Cultures of PY79 and Jdb872 (SB201) ix are the points along the midline, px is the initially located peak, lx and rx are the 90%-maximal-intensity boundaries to either side of the peak, and f(x) is the value of the intensity profile at the point x along the midline.Images were analyzed by PSICIC. For each fluorescent channel a one-dimensional intensity profile along the midline of the cell was generated by taking the sum of the interpolated intensities at 20 evenly-spaced points along each width line. The location of peaks in the intensity data was calculated by first finding local maxima in the intensity profile. In order to account for asymmetry in the shapes of these peaks, the points where the intensity crossed a threshold of 90% the peak value on either side of the local maxima were found, and the first moment of the intensity between those points was taken. Specifically, the point marked as the peak is given byThe distance between peaks of SpoIIE-GFP and FM4-64 intensity was calculated for adjacent peaks located within one quarter-cell length of the end of a cell . Peaks not significantly higher than the background fluorescence level, peaks distant from the end of a cell, and peaks with no corresponding nearby peak in the other fluorescent channel were ignored. The sign of the distance between peaks was given as positive if the SpoIIE-GFP peak was closer to the nearby cell end, and negative if the FM4-64 peak was closer to the nearby cell end.E. coli strains BW25113 minC::KanThe resulting images were analyzed using PSICIC. To find the pinch position of a cell, the second set of differences between thickness measurements was taken as an approximation of the second derivative for non-continuous data, and smoothed using a two-point moving average to reduce noise. The maximum of the smoothed data was then located, and the local minimum of the thickness nearest that maximum was taken as the pinch position. A pinch was discarded if the depth of the pinch was outside the range reliably identifiable by PSICIC . Outliers in both data sets were manually examined to ensure validity.t-test for a distribution with unknown mean and variance was used To determine whether the SpoIIE-GFP displacement data was statistically significantly different from a symmetrical distribution, a two sided minC E. coli were significantly different, the Ansari-Bradley test, a non-paramentric test which does not require data to come from a normal distribution, was used. This test requires both distributions to have the same median, a requirement satisfied by our data sets which both have median 0.5 To determine if the variances of the distributions of wild-type and Δhttp://ww.ncbi.nlm.nih.gov/Genbank) accession numbers for the genes and proteins discussed in this paper are E. coli MinC (AAC74260), E. coli MinD (AAC74259), E. coli MinE (AAC74258), E. coli FtsZ (AAC73206), B. subtilis SpoIIE (CAB11840), and B. subtilis SpoIIQ (CAB15672).The GenBank (


Although some reports indicate that protein synthesis dependent process may be induced by updating information, the role of protein synthesis and degradation in changing the content of pre-existing memory is yet unclear. In this study, we utilized an object rearrangement task, in which partial information related to a pre-existing memory is changed, promoting memory modification. Inhibitors of both protein synthesis and protein degradation impaired adequate incorporation of the altered information, each in a distinctive way. These results indicate that protein synthesis and degradation play key roles in memory modification. Memory formation in real life usually involves partial change of pre-existing memory. Though numerous studies have highlighted the molecular mechanism of memory formation, it is largely unknown how previously formed memory is altered or updated in the process.A candidate mechanism of memory updating could involve dynamic regulation of memory stability after memory reactivation. Conventionally, it was thought that memory is consolidated by a protein synthesis-dependent process only once per item and persists thereafter in a stable state. However, accumulating evidence suggests that memory reactivation induces a reconsolidating process that depends on the protein synthesis -4. WhileHowever, the previous studies only focused on the strength of the memory for demonstrating the requirement of protein synthesis and degradation in the incorporation of changed information. Another major memory updating process in real-life is partially modifying the content of the initial memory rather than simply strengthening or weakening the memory. In the present study, we aimed to reveal the role of protein synthesis and degradation in the incorporation of partially modified information into the pre-existing memory, by using an object rearrangement task.To assess the incorporation of changed information into the preexisting memory, we chose an object-location memory task . This taTo evaluate the preference for switched/unswitched objects, we measured the duration of exploration time for each object and calculated the percentage of the two switched/unswitched objects exploration time from the total exploration time. The preference to the switched objects was higher on day 2, indicating that the subjects have well recognized the original position or configuration of each object Figure . This reAlthough there was a slight difference in the preference for each of the four objects at the first day, it was statistically non-significant Figure . The twoAs our aim was to focus on the associative memory between the objects and their location, we targeted hippocampus which seems to be more specifically involved in object-location memory ,14. HippOn day 3, the anisomycin-injected group showed higher preference to the switched object compared to the vehicle-injected control group Figure , suggestIn this study, we have provided a novel scheme of object-in-place memory task to assess whether the mice have correctly changed the contents of pre-existing object-location associative memory, making it possible to investigate the process of modifying memory. In previous studies focusing on the modification of pre-formed memory, the memory task commonly involved strengthening the memory by repeated training over days or weakening it by an experimental extinction protocol. Our modified object rearrangement task has an advantage that the memory is not simply altered in its strength, but that the partial contents of the pre-formed memory are rapidly reorganized to incorporate changed information. Based on this advantage, this task is likely to be valuable for studies on dynamic memory modification process. Using this task, we have found that protein synthesis and degradation are required for incorporating partially modified information into the pre-existing memory.de novo protein synthesis.Considering the effect of anisomycin on the memory modification, the original memory might be expected to be destabilized by anisomycin after reactivation on day 2 as it would undergo a protein synthesis dependent reconsolidation process, possibly resulting in the chance level preference for each object on day 3. However, anisomycin-injected mice acted on day 3 as if the second object configuration is novel, resulting in higher preference for the switched objects. One possible explanation for this is that not every component of the related memory becomes labile in this stage to be sensitive to protein synthesis inhibitor. For example, the memories for unswitched objects might have been less affected by anisomycin being maintained relatively intact, while the memories for switched objects may have been more affected, being reactivated and destabilized. This may result in higher explorative preference for the switched objects, as the location for switched objects becomes more novel than the location for the unswitched objects. It is also possible that the consolidation-like process for incorporating additional information (i.e. switched location) is more sensitive to protein synthesis inhibitor than the reconsolidation process. In any case, our result indicates that incorporation of changed information into the pre-existing memory requires The interpretation of the effect of proteasome inhibition is more complicated. If the process to incorporate the changed information is a simple additional learning of the novel information, the effect of a certain drug might be expected to be either impairment of modification leaving the memory unchanged or no effect leading to successful incorporation of the new information. In this study, however, the inhibition of protein degradation appeared to affect even the memory for unchanged information. Therefore, memory reactivation on day 2 is likely to have induced complex processes involving modification to the previous memory, in which the protein degradation plays a major role.Previous reports suggest that destabilization of the reactivated memory precedes the protein synthesis-dependent process. However, the retrieval process of four-object rearrangement task differs from that of contextual fear conditioning as it incorporates additional information rather than simply recovers the memory state. Although the memory reactivation-induced protein degradation seems to be critical to form successfully modified memory, the full process may also, in parts, include consolidation-like process to encode the novel memory components. This process may be induced independently of destabilization of the previous memory. In this case, protein degradation inhibition would impair destabilization of the reactivated memory and possibly the following restabilization process, without affecting the independent consolidation-like process. The imbalance between these two essential components induced by protein degradation inhibition might have lead to higher preference for the unswitched objects on day 3. In addition, the protein degradation might have a unique role in either restabilization of the previous memory or in a consolidation-like process to incorporate additional information. We cannot exclude the possibility that protein degradation is involved in the consolidation process in the four-object task used in the present study, although it does not seems to be the case, at least acutely, in contextual fear memory .We have locally treated the inhibitors in hippocampus based on references that indicate hippocampus as a region specifically involved in object location memory rather than the object identity memory. The results using PKMzeta inhibitor demonstrates that hippocampus is at least one of the memory storage sites for object location memory while it is not a critical storage site for object identity memory . TherefoAlthough more studies are required to fully understand the mechanism, the present study suggests that protein synthesis and degradation play important roles in modifying the memory in object-location memory paradigm. This evidence supports the hypothesis that memory dynamically changes after retrieval through protein turnover. In addition, we expect that the scheme used here or other modes of the object rearrangement task can be utilized for the investigation into the memory modification mechanism in the future.The authors declare that they have no competing interests.JHC: experiment design and implementation, manuscript writing.JEK: behavior experiments and sample preparationBKK: experiment design and advice, manuscript writing.All authors read and approved the final manuscript.


A major stumbling block for researchers developing experimental models of mechanotransduction is the control of experimental variables, in particular the transmission of the mechanical forces at the cellular level. A previous evaluation of state of the art commercial perfusion chambers showed that flow regimes, applied to impart a defined mechanical stimulus to cells, are poorly controlled and that data from studies in which different chambers are utilized can not be compared, even if the target stress regimes are comparable.This study provides a novel chamber design to provide both physiologically-based flow regimes, improvements in control of experimental variables, as well as ease of use compared to commercial chambers. This novel design achieves controlled stresses through five gasket designs and both single- and dual-flow regimes.The imparted shear stress within the gasket geometry is well controlled. Fifty percent of the entire area of the 10 × 21 mm universal gasket , is exposed to target stresses. In the 8 mm diameter circular area at the center of the chamber (where outcome measures are made), over 92% of the area is exposed to the target stress (± 2.5%). In addition, other gasket geometries provide specific gradients of stress that vary with distance from the chamber inlet. Bench-top testing of the novel chamber prototype shows improvements, in the ease of use as well as in performance, compared to the other commercial chambers. The design of the chamber eliminates flow deviations due to leakage and bubbles and allows actual flow profiles to better conform with those predicted in computational models.in vivo situations. Overall, the improved perfusion flow chamber provides the needed resolution, standardization and in vitro model analogous to in vivo conditions to make the step towards greater use in research and the opportunity to enter the diagnostic and therapeutic market.The novel flow chamber design provides predictable and well defined mechanical forces at the surface of a cell monolayer, showing improvement over previously tested commercial chambers. The predictability of the imparted stress improves both experiment repeatability as well as the accuracy of inter-study comparisons. Carefully controlling the stresses on cells is critical in effectively mimicking  Elucidation of cellular mechanisms of mechanotransduction is a critical step in uncovering physiologic mechanisms of tissue generation and repair. The biochemical and biophysical environment of virtually every cell in the body is affected by transduction of mechanical forces and chemical signals. Numerous research studies have used flow chambers to study the transduction of mechanical forces to cells, including those of the vascular endothelium , bone 22-7, renaThe current state of the art comprises the parallel-plate flow chamber, where fluid perfuses across the specimen between critically spaced plates that make up the top and bottom of the chamber ,3,14,15.Furthermore, it is not clear to how well perfusion chambers emulate aspects of physiologic flow regimes including spatiotemporal control of stress magnitudes and gradients. The common parallel-plate design found in many chambers incorporates a one-sided shear stress imparted to the cell monolayer. In typical experimental use, cells are seeded on a coverslip that is placed on the chamber floor; fluid moves over the apical surface of the cells, subjecting them to shear stress via fluid drag. Physiologically, cells may experience a more complex or multidimensional stress. For example, in the context of developing tissues (during development or engineering of tissues), cells experience multidimensional stresses -24. In fin vitro. Hence, we created a modular perfusion flow chamber for transmission of fluid shear stress on either or both the apical and basal surfaces of cells. In addition, we developed and tested novel gasket geometries to improve upon current chamber designs and to elicit controlled stress regimes that mimic specific aspects of physiological flow on cells.The purpose of this study was to identify and address weaknesses in current chamber designs by designing and testing a novel flow chamber that provides a more physiologic fluid environment for the study of cells In general, parallel plate flow chambers are designed to provide controlled flow of fluid across a cellular monolayer. Furthermore, flow profiles are generally controlled by the mass flow rate into the chamber and by the geometry of the channel through which the fluid flows. The geometry of the channel is typically defined by the surface of the substrate on which cells are seeded, bounded above by a compliant gasket and to the sides by the walls of the chamber and/or the gasket. We expand on this general design principle to create a chamber, and in effect a fluid geometry (via gasket design), that provides a physiologic and controlled mechanical stimulus to cells. We set two goals for the novel chamber, namely to construct a device that provides either single- or dual-flow regimes across the monolayer and to ensure controlled spatiotemporal distribution of shear stress on the cells through definition of appropriate gasket geometries. In addition, we placed particular attention on design for ease of use, as tests with commercial chambers had previously raised concerns with regard to leakage, bubble production, and lack of reproducibility of experimental conditions .in situ (in a slice of tissue), are interposed between the two gaskets and flow is applied. For example, cells are seeded on a porous membrane  that is interposed between two gaskets. The cell monolayer is interposed between two identical fluid layers, each with an independent inlet and outlet .Computational models are created for each design to predict the fluid environment and imparted shear stress in each gasket. The inlet and outlet geometries do not change within the polycarbonate sections of the chamber. Hence, it is assumed that the entering and exiting flow are identical for each case and only the geometry within the rubber gaskets is modelled. Furthermore, the chamber design can accommodate a variety of gasket thicknesses. For the computational fluid dynamics (CFD) study, all gaskets are created with a thickness of 250 μm for comparison with previous predictions for commercial chambers . In addieviously . For eac2 [nd order upwind-discretization scheme in three dimensions, and the wall shear stress is calculated from the wall strain rate (3).The fluid environment is simulated for each model using a computational solver  that calculates the velocity, pressure, and shear stress distribution. Flow is induced via a pressure gradient for each model to achieve a target wall shear stress at the exposed surface of the cell (at the interface with the flow channel's lower surface) is 1 dyn/cm2 -25,7. Alu is the velocity vector, ρ is the fluid density, p is the pressure, μ is the fluid viscosity, τ is shear stress, and 3. Flow is simulated for steady conditions with a local convergence criterion of 0.0001, where conservation of mass is used to validate each solution. It is important to note that, while simulations are calculated to achieve a target shear stress of 1 dyn/cm2, the results of these simulations can be scaled up for flow regimes in the laminar range .where In order to evaluate the chamber design in a realistic laboratory setting, bench-top testing is performed to determine ease of use and performance. During testing, both strengths and weaknesses are noted in comparison to the previously evaluated commercial chambers . Ease of2 on the chamber bottom (at the cell monolayer location). Here, the shear stress distributions are similar for the three cases  250 μm gasket thickness, (b) 500 μm thickness, and (c) dual-flow 250 μm thickness (each layer). The maximum velocity in each case is highest near the inlet/outlet, with a nearly constant magnitude throughout the rest of the geometry (displayed within the plane) Figure . As the s Figure . As seens Figure . In addis Figure . If an 82. The shear stress reaches a maximum near the entrance to the widening and tapering zones. Between the zones of fluid "expansion" and "contraction" , varying gradients of stress are found within the gasket. Focusing on three different locations within the gasket, initially a sharp gradient in stress is found between the gasket center and walls  is created. Here, the velocity again appears similar to planar jet flow due to the widening geometry. However due to the asymmetry and the no-slip condition, the velocity decreases sharply as it approaches the "centerline" wall Figure . Again, The fourth gasket imposes the most abrupt widening and tapering geometry, where the resulting fluid regime parallels planar jet flow Figure . The maxFinally, Gasket V is a variation of the planar jet geometry of the previous gasket, where the length of the widened area is decreased. As a result, the required velocity decreases from that of Gasket IV in the inlet/outlet channels and near the transition zones to the widened channel area Figure . The subBench-top testing of the novel chamber prototype shows improvements, in the ease of use as well as in performance, compared to other commercial chambers Table . The chain vitro studies; however a recent analysis of chamber performance has shown that several commercial chambers deliver spatially varying and unexpected shear stress distributions [Cell perfusion chambers provide a tool to probe and elucidate changes in cell physiology in response to mechanical and biochemical stimuli and can be implemented for cytotoxicity and pharmacokinetic studies as well. A given chamber's utility hinges upon its capacity to provide a controlled and known mechanical force that can also emulate aspects of the cell's physiologic environment. Numerous chamber designs have been implemented in a variety of ibutions . CurrentThe dual-flow chamber design presented in this study addresses many of the issues associated with previous chambers, and is able to impart a variety of controlled mechanical environments through five gasket designs as well as both single- and dual-flow regimes. Using Gasket I, a constant shear stress is applied over the majority of the chamber area, where 95% of the chamber midplane and 50% of the entire chamber is within 5% of the target stress for both the single and dual-flow setup. Furthermore, if a region of interest is considered where cellular response is likely to be observed, an 8 mm circle at the chamber center, over 92% of the region is within 2.5% of the target stress. This gasket design shows an improvement in both achieving the target stress as well as yielding a predictable location of the desired stimulus. Furthermore, the other gasket designs in this study have specific geometry that allow for precise gradients of shear stress to be applied to a cell monolayer, where the desired gradient can be achieved by observing cellular response at the appropriate distance from the gasket inlet. These stress distributions provide for application of "tunable" mechanical regimes appropriate for modelling a variety of physiological scenarios. In all cases, the imparted shear stress distributions are accurate for both modes of flow  as well as standard gasket thicknesses of 250 μm and 500 μm.2, however as the flow regimes are laminar, the predictions shear stresses are scalable to incorporate a wide range of commonly used stress magnitudes (0.1 – 20 dyn/cm2).As this study provides a design and analysis of a cell perfusion chamber using computational methods, certain limitations can occur. All three-dimensional flow simulations have been checked for accuracy using variations of known analytical solutions, where possible. In addition, results are shown for a target shear stress of 1 dyn/cmin utero , forces associated with cell proliferation, epithelial-mesenchymal transformations, patterning and morphogenesis dominate the mechanical environment of a cell [An understanding of the interplay between cells and their enviroment is critical to elucidating mechanisms of physiological and pathophysiological processes. All life on Earth originated from water and fluids comprise at least part of the environment of every cell in every organism on Earth. Throughout a human's lifespan, every cell in the body is bathed in fluid and is hence subjected to deviatoric shear stresses resulting from fluid flows over apical and/or basal surfaces due to pressure gradients arising from breathing, pumping of the heart, and weight bearing in a gravitational environment. These flows may be superimposed with dilatational tensile and/or compressive stresses that occur when a tissue is deformed during breathing, pumping of the heart, and weight bearing. The relative contribution of dilational and deviatoric stresses varies widely depending on the location of the cell within a given tissue, the location of the tissue within the organism, as well as the time in the lifecycle of the organism. For instance, prior to development of the heart f a cell ,22.The novel prototype presented here lends itself particularly for cell mechanotransduction studies ,27 as wein vivo situations. Overall, the improved perfusion flow chamber provides the needed resolution, standardization and in vitro model analogous to in vivo conditions to make the step towards greater use in research and the opportunity to enter the diagnostic and therapeutic market.The perfusion flow chamber technology described in this manuscript overcomes several major drawbacks that are currently associated with existing perfusion flow chambers on the market. Firstly, the flow regime in the novel chamber mimics physiologic conditions, which facilitates the development and translation of cell experiments to clinically relevant scenarios. The new design allows for both the quantification and measured control of the shear stress on cells, as opposed to existing designs, which have unknown or variable shear stress. Carefully controlling the stresses on cells is critical in effectively mimicking The academic institution of the co-authors previously had a non-exclusive licensing agreement with Warner Instruments to produce and market the technology described in this manuscript. To date (26 November 2007), none of the authors has received reimbursements, fees, funding, or salary from Warner Instruments.MKT developed the modular dual flow chamber concept as well as the concept of defining gasket geometry to affect constant magnitude stress and stress gradients to mimic different physiological situations. EA carried out the computational fluid dynamics simulations and was involved in the design of the novel flow chamber and gasket geometries as well as drafting and revised the manuscript. MKT conceived of and supervised all aspects of the study, as well as drafting and revising the manuscript.


Thermochemical conversion of biomass offers an efficient and economically process to provide gaseous, liquid and solid fuels and prepare chemicals derived from biomass. Computational fluid dynamic (CFD) modeling applications on biomass thermochemical processes help to optimize the design and operation of thermochemical reactors. Recent progression in numerical techniques and computing efficacy has advanced CFD as a widely used approach to provide efficient design solutions in industry. This paper introduces the fundamentals involved in developing a CFD solution. Mathematical equations governing the fluid flow, heat and mass transfer and chemical reactions in thermochemical systems are described and sub-models for individual processes are presented. It provides a review of various applications of CFD in the biomass thermochemical process field. Thermochemical conversion of biomass offers a possible process to provide gaseous, liquid and solid fuels and prepare chemicals derived from biomass. Many efforts have been done on making thermochemical processes more efficient and economically acceptable. A significant portion of these efforts over the past two decades has focused on the development of numerical models of thermochemical reactors  that can help to design and analyze the thermochemical process. Due to a combination of increased computer efficacy and advanced numerical techniques, the numerical simulation techniques such as CFD became a reality and offer an effective means of quantifying the physical and chemical process in the biomass thermochemical reactors under various operating conditions within a virtual environment. The resulting accurate simulations can help to optimize the system design and operation and understand the dynamic process inside the reactors.The use of biomass as a COCFD modeling techniques are becoming widespread in the biomass thermochemical conversion area. Researchers have been using CFD to simulate and analyze the performance of thermochemical conversion equipment such as fluidized beds, fixed beds, combustion furnaces, firing boilers, rotating cones and rotary kilns. CFD programs predict not only fluid flow behavior, but also heat and mass transfer, chemical reactions , phase changes , and mechanical movement (e.g. rotating cone reactor). Compared to the experimental data, CFD model results are capable of predicting qualitative information and in many cases accurate quantitative information. CFD modeling has established itself as a powerful tool for the development of new ideas and technologies.However, CFD modeling for biomass thermochemical conversion still face significant challenges due to the complexity of the biomass feedstock and the thermochemical process. Biomass is a mixture of hemicellulose, cellulose, lignin and minor amounts of other organics with proportion and chemical structure affected by variety. Inorganic ash is also part of the biomass composition. The complex structure makes biomass compositions pyrolyze or degrade at different rates by different mechanisms and affect each other during thermochemical process, and it makes the biomass particle feedstock has anisotropic properties in physical characterization . How to In this paper, we attempt to summarize the current state of various CFD applications concerning the biomass thermochemical conversion process. The challenges faced by modelers using CFD in the biomass pyrolysis are also discussed.et al.[Computational fluid dynamics is a design and analysis tool that uses computers to simulate fluid flow, heat and mass transfer, chemical reactions, solid and fluid interaction and other related phenomena. Comparing to the physical experiment operation, CFD modeling is cost saving, timely, safe and easy to scale-up. CFD codes turn computers into a virtual laboratory and perform the equivalent “numerical experiments” conveniently providing insight, foresight and return on investment. Various numerical techniques known as direct numerical simulation (DNS), vortex dynamics and discretization methods have been employed in the solution of the CFD model equations. The most widely used numerical techniques are discretization methods mainly including finite difference , finite elements  and finite volumes method (based on control-volume formulation). Finite difference techniques are rarely used in engineering flows due to the difficulties in the handling of complex geometry . Finite et al..Biomass thermochemical conversion refers to the processes of biomass gasification for gaseous fuel or syngas, fast pyrolysis for liquid bio-oil, carbonization for solid carbon or combustion for heat energy. The differences among these thermal processes are determined by the operation conditions of feed properties, oxidizer  amount, temperature, heating rate and residence time. These conditions change the proportions of the gas, liquid and solid products. CFD models of the thermochemical processes include description of fluid flow, heat and mass transfer, and chemical reactions. The process fundamental governing equations are the conservation laws of mass, momentum, energy and species, namely the following CFD enforces these conservation laws over a discretized flow domain in order to compute the systematic changes in mass, momentum and energy as fluid crosses the boundaries of each discrete region .The biomass thermo conversion includes complex chemical and physical processes such as vaporization, devolatilization, volatile secondary reactions, char oxidation, coupled with the transport phenomena. Many studies have been made and many models have been built to describe the process , 5–9.The devolatilization process begins when the biomass temperature reaches a critical level. Many biomass devolatilization models have been developed and several reviews of these models have been made , 6, 8. OThe one-step global mechanisms can be shown as:k =Aexp(−Ea / RT ) , and the devolatilization rate ismp is the biomass particle mass, mp,0 is the initial particle mass, and fv,0 is the initial volatile fraction [The reaction kinetic rate (k) is expressed in single-step Arrhenius fashion as fraction .k1 and k2 are competing rates that may control the devolatilization over different temperature ranges. The two kinetic rates are weighted to yield an expression for the devolatilization asmv(t) is the volatile yield up to time t, mp,0 is the initial particle mass at injection, α1 and α2 are yield factors, ma is ash content in the particle [For two-step Arrhenius reaction schemes, the kinetic devolatilization rate expressions of the form proposed by Kobayashi  are:(7)particle .The major limitation of one-step global schemes is that they are neither able to predict the composition of volatiles nor account for various components of the virgin biomass. One-step multi-reaction schemes have been developed to address these shortcomings and can be shown as:One of the more recent developments in one-step multi-reaction schemes for biomass fuels is the use of the distributed activation energy (DAE) approach.The major shortcoming of the one-step multi-reaction schemes is that they neglect secondary reactions (cracking of tar to light molecular weight volatiles). Multi-step semi-global schemes attempt to address this shortcoming of multi-reaction schemes by considering reaction routes for both primary and secondary reactions. There are many literature positions which introduced the kinetics data of these mechanisms. Another general biomass devolatilization model is developed extending the chemical percolation devolatilization (CPD) model from coal. The CPD model is extended to devolatilization of biomass major components based on the consideration of their chemical structure and its transformation under various mechanisms. The model considers multiple mechanisms, including bridge breaking and rearranging, side-chain cracking and gas release, tar distillation, and cross-linking. The same reaction scheme is applied for biomass as for coals:13C nuclear magnetic resonance (NMR) measurements. The kinetic rate variables kb, kc, and kδ are defined in Arrhenius form. The literature positions [The chemical structure parameters in the original CPD model are defined directly taken from ositions , 12 intrThe devolatilization tar is a mixture of condensable hydrocarbons. The secondary tar crack reactions occur homogeneously in the gas phase or heterogeneously at the surface of the biomass or char particles. Tar is a complex mixture of many kinds of components and the cracking mechanism is very comprehensive. In the present study, tar cracking is considered to follow the overall reaction schemes such as:Many experimental investigation and model studies have been done on the cracking process. The model stoichiometric coefficients and kinetics data can be found in the literatures , 8.The biomass devolatilization and cracking gas species will react with the supplied oxidizer and with each other such as water gas shift reaction. The heat generated by exothermic reactions is important for the release of volatiles and ignition of char. The common homogeneous reactions are:More reaction mechanisms and the kinetic parameters can be found from the literature .2 and H2O are complex processes that involve balancing the rate of mass diffusion of the oxidizing chemical species to the surface of biomass particle with the surface reaction of these species with the char. The overall rate of a char particle is determined by the oxygen diffusion to the particle surface and the rate of surface reaction, which depend on the temperature and composition of the gaseous environment and the size, porosity and temperature of the particle. The commonly simplified reactions models consider the following overall reactions:Char is the solid devolatilization residue. Heterogeneous reactions of char with the gas species such as OThe literature positions that introduced and reviewed the char surface reactions and the kinetic relationship can be found , 7, 13.Although Navier-Stokes equations are viewed as the basis of fluid mechanics describing the conservation laws of mass, momentum, and energy, they have a limited amount of applications in the areas of biomass thermochemical conversion. The additional processes may influence the dynamics of the thermochemical reactor system. The basic governing equations need to be strengthened with special additional physical models or assumptions to fully represent the physical process. The important additional models include turbulence models, porous media and multiphase models, heat transfer with radiation models, and mass transfer and diffusion.Turbulent flows are characterized by fluctuating velocity fields primarily due to the complex geometry and/or high flow rates. Turbulence affects the heat and mass transfer and plays an essential role in some processes such as biomass gasification/pyrolysis in fluidized bed and non-premixed combustion in furnaces. The Navier-Stokes equations can be solved directly for laminar flows, but for turbulent flows the direct numerical simulation (DNS) with full solution of the transport equations at all length and time scales is too computationally expensive since the fluctuations can be of small scale and high frequency. The DNS is only restricted to simple turbulent flows with low to moderate Reynolds numbers. In the cases of high Reynolds number flows in complex geometries, a complete time-dependent solution of the instantaneous Navier-Stokes equations is beyond the nowadays computational capabilities. Hence, turbulence models are required to account for the effects of turbulence rather than simulate it directly in practical engineering applications. Two alternative methods are employed to transform the Navier-Stokes equations so that the small eddies do not have to be directly simulated: Reynolds averaging and filtering. Both methods introduce additional terms in the governing equations that must be modeled for turbulence closure.The Reynolds-averaged Navier-Stokes (RANS) equations represent transport equations for the mean flow quantities only, with all the scales of turbulence being modeled. The RANS models are developed by dividing the instantaneous properties in the conservation equations into mean and fluctuating components, as shown as:The Favre-averaging (density-weighted averaging) of the flow field variables is used to account for the effects of density fluctuations due to turbulence. The classical Reynolds averaging technique brings unclosed Reynolds stress terms in the time-averaged conservation equations and need be modeled for turbulence closure. The Reynolds-averaged approach is generally adopted for practical engineering calculations.Most common RANS models employ the Boussinesq hypothesis  to model the Reynolds stresses terms. The hypothesis states that an increase in turbulence can be represented by an increase in effective fluid viscosity, and that the Reynolds stresses are proportional to the mean velocity gradients via this viscosity. Models based on this hypothesis include Spalart-Allmaras, standard k-ε, RNG k-ε, Realizable k-ε, k-ω and its variants .The Reynolds stress model (RSM) closes the Reynolds-averaged Navier-Stokes equations by solving transport equations for the Reynolds stresses directly, together with an equation for the dissipation rate. The RSM accounts for the effects of streamline curvature, swirl, rotation, and rapid changes in strain rate in a more rigorous manner than one-equation and two-equation models. The fidelity of RSM predictions is still limited by the closure assumptions employed. The modeling of the pressure-strain and dissipation-rate terms is particularly challenging, and often considered to be responsible for compromising the accuracy of RSM predictions. However, use of the RSM is a must when the flow features of interest are the result of anisotropy in the Reynolds stresses, for examples the cyclone flows or highly swirling flows in combustors.Large eddy simulation (LES) solves “filtered” transport equations by permitting direct simulation of large scale turbulent eddies. Filtering removes eddies that are smaller than the filter size, which is usually taken as the mesh size. The filtering process creates additional unknown terms that must be modeled in order to achieve closure. LES provides an accurate solution to the large scale eddies akin to DNS while the smaller eddies below the filter size are modeled. This is because the large turbulent eddies are highly anisotropic and dependent on both the mean velocity gradients and the flow region geometries, while smaller eddies possess length scales determined by the fluid viscosity and are consequently isotropic at high Reynolds numbers. LES offers an alternative method of reducing the errors caused by RANS and providing a more accurate technique for turbulence simulation. However, application of LES to biomass industrial engineering is still in its infancy for it is computational expensive .The radiative transfer equation (RTE) for an absorbing, emitting, and scattering medium at position aL where L is an appropriate length scale is a good indicator of which model to use. When aL≫l the P-1 and Rosseland models are suitable. The P-1 model should typically be used for optical thicknesses large than 1. The Rosseland model is computationally cheaper and more efficient but should only be used for optical thicknesses larger than 3. The Discrete Ordinates model (DOM) model works across the range of optical thicknesses, but is substantially more computationally expensive than the Rosseland model [A semi-transparent medium is considered and the refractive index is equal to unity. The optical thickness nd model , 14.si  fixed in the global Cartesian system, and the integrals over these directions are replaced by numerical quadratures. The DOM considers the radiative transfer equation (RTE) in the direction si as a field equation, thus the RTE is transformed into a transport equation for radiation intensity in the spatial coordinates:The Discrete Ordinates Model (DOM) solves the radiative transfer equation (RTE) for a finite number of discrete solid angles, each associated with a vector direction The standard form DOM suffers from a number of serious drawbacks, such as false scattering and ray effects. Perhaps the most serious drawback of the method is that it does not ensure conservation of radiative energy. This is a result of the fact that the standard discrete ordinates method uses simple quadrature for angular discretization. Thus, it is a logical step in the evolution of the method to move to a fully finite volume approach, in space as well as in direction. The finite volume method uses an exact integration to evaluate solid angle integrals and the method is fully conservative .qr can be directly substituted into the energy equation to account for heat sources (or sinks) due to radiation [P-1 model is the simplest formulation of the more general P-N radiation model, which is based on the expansion of the radiation intensity I into an orthogonal series of spherical harmonics. The method of spherical harmonics provides a vehicle to obtain an approximate solution of arbitrary high order (i.e. accuracy), by transforming the radiative transfer equation into a set of simultaneous partial differential equations. Using only four terms in the series solution of the respective differential equation, the following relation is obtained for the radiation flux:adiation :(26)−∇qThe Rosseland radiation model can be derived from the P-1 radiation model with some approximations. The radiative heat flux vector in a gray medium is approximated byThe Rosseland radiation model differs from the P-1 model in that the Rosseland model assumes the intensity equal to the black-body intensity at the gas temperature. Thus,This model is also called “diffusion approximation” model, since the radiation problem reduces to a simple conduction problem with strongly temperature dependent conductivity. It is important to keep in mind that the diffusion approximation is not valid near a boundary .dI , along a path, ds , can be written as:The main assumption of the Discrete Transfer Radiation Model (DTRM) is that the radiation leaving the surface element in a certain range of solid angles can be approximated by a single ray. The equation for the change of radiant intensity, a is constant along the ray, then I(s) can be estimated as:Here, the refractive index is assumed to be unity. The DTRM integrates The “ray tracing” technique used in the DTRM can provide a prediction of radiative heat transfer between surfaces without explicit view-factor calculations. The accuracy of the model is limited mainly by the number of rays traced and the computational grid .f. An algorithm based on the minimization of Gibbs free energy is used to compute species mole fractions from f. The mixture fraction f is defined in terms of the atomic mass fraction as:Zj is the mass fraction for element j. The subscript ox and fuel denote the value at the oxidizer stream inlet and the fuel stream inlet respectively.The mixture fraction model is used to present the reaction chemistry in the probability density function (PDF) method for solving turbulent-chemistry interaction. The equilibrium model is applied which assumes that the chemistry is rapid enough for chemical equilibrium to always exist at the molecular level. Basing on the simplifying assumptions, the instantaneous thermo chemical state of the fluid is related to the mixture fraction Under the assumption of equal diffusivities, the species equations can be reduced to a single equation for the mean (time-averaged) mixture fraction f̄. And the mean mixture fraction variance Spm is due solely to transfer of mass into the gas phase from reacting sludge particles [The source term articles .The porous media assumption is generally used in the applications of biomass pyrolysis in fixed bed. The arrangement of biomass particles in the fixed bed forms void spaces. The devolatilization volatiles and gases through the particle voids can be described as flow through a porous media. The particle position may change during the conversion process for the devolatilization, combustion and shrinkage of biomass particles. In this process to mesh all associated geometry with a complex unstructured or body fitted system is out of both computational power and CFD algorithms levels. Therefore, the simplified porous media assumption applies Darcy’s law to present the relationship on pressure drop and volume averaged velocity caused by viscous drag:At high flow velocities, the modification of this law provides the correction for inertial losses in the porous medium by Darcy-Forchemier equation:Fluid flow, and heat and mass transfer are described in the sub-domain by the laws of conservation of mass, momentum and energy in the terms of macroscopic variables provided by the volume-averaged Navier-Stocks equations in a version of Darcy’s law. The system can be regarded as a two-phase flow .The flow in biomass fluidized bed gasifier or boilers and furnaces is a typical kind of gas-solid flow with chemical reactions. Thus hydrodynamics of the gas-solid flow can be performed based on the Eulerian–Lagrangian concept. The discrete phase method can be applied to the particle flow when the particle phase can be considered to be sufficiently dilute that the particle-particle interactions and the effects of the particle volume fraction on the gas phase can be assumed neglected. The coupling of the continuous phase and the discrete phase is important and it is solved by tracking the exchange of mass, momentum and energy.xi direction in Cartesian coordinates by [Fxi is the additional force, FD is the drag force per unit particle mass andThe model computes the particle trajectory using a Lagrangian formulation which includes the inertia, hydrodynamic drag, and the force of gravity. The particle trajectory can be predicted for the nates by :(37)d2xBiomass gasification and pyrolysis are thermally degraded processes in insufficiency or absence of air/oxygen aiming at the production of solid , liquid (tar/bio-oil) and gaseous products. The CFD models used to describe these processes have become an important analysis and design tool to achieve the flow and temperature pattern, the products concentration contour and yields. et al. [Fletcher et al.  developeet al. [Gerun et al.  developeThe largest application of CFD models has been to power station boilers and furnaces. Many studies made in relation to coal combustion have been modified to apply to biomass combustion or co-firing. et al. [Dixon et al.  summarizet al. [Kær et al. –28 carriet al. [The co-firing of coal and biomass has been advocated for a number of years as being advantageous on both an environmental and economic basis. The co-combustion of biomass as a minor component presents an interesting intermediate situation with a high reactivity solid. There are a number of commercially available CFD models, and the suitability of the sub-models available for biomass combustion is a key factor in selecting an appropriate code. et al.  carried NOx formation and unburned carbon in ash. The literatures [NOx formation in detail. Ma et al. [NOx formation model. The potassium release during biomass combustion is still a subject of current investigation. Ma et al. assume that the biomass potassium release during devolatilization rapidly forms KOH. NH3 route have been considered for the NOx formation and NH3 route. The particle tracks and temperature distribution are also studied in this work. Good agreement between the predicted and the measured furnace temperature and concentrations of CO2 and NOx has been achieved. NOx emission modeling. The submodels used in these examples are summarized in the table.In the case of biomass burner studies there is considerable interest in eratures –45 descra et al.  performeNOx emission. The CFD model results are satisfactory and have made good agreements with the experimental data in many cases. However, the simulations still have many approximate models as well as some assumptions. To ensure CFD simulations are more than just theoretical exercises, experimental validation is necessary to facilitate the model accuracy. With the progressing of the computing power and the development of chemical and physical models, the CFD applications in the biomass thermochemical conversion will more widely spread in the future.This paper summarized the CFD applications in biomass thermochemical conversion and system design. There is evident that CFD can be used as a powerful tool to predict biomass thermochemical processes as well as to design thermochemical reactors. CFD has played an active part in system design including analysis the distribution of products, flow, temperature, ash deposit and


Time-delays are common in many physical and biological systems and they give rise to complex dynamic phenomena. The elementary processes involved in template biopolymerization, such as mRNA and protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters and the time delays in these networks. We present here the development of mathematical, time-delay models for protein translation, based on PDE models, which in turn are derived through systematic approximations of first-principles mechanistic models. Theoretical analysis suggests that the key features that determine the time-delays and the agreement between the time-delay and the mechanistic models are ribosome density and distribution, i.e., the number of ribosomes on the mRNA chain relative to their maximum and their distribution along the mRNA chain. Based on analytical considerations and on computational studies, we show that the steady-state and dynamic responses of the time-delay models are in excellent agreement with the detailed mechanistic models, under physiological conditions that correspond to uniform ribosome distribution and for ribosome density up to 70%. The methodology presented here can be used for the development of reduced time-delay models of mRNA synthesis and large genetic networks. The good agreement between the time-delay and the mechanistic models will allow us to use the reduced model and advanced computational methods from nonlinear dynamics in order to perform studies that are not practical using the large-scale mechanistic models. Genetic networks display exceedingly complex and rich behavior which is modulated by multiple mechanisms, including many diverse types of interactions between DNA, mRNA and protein molecules. Mathematical models of gene networks must necessarily consider the essential mechanistic details of the processes involved in order to make reliable predictions. However, even though the description of the process becomes more accurate as more mechanistic details are incorporated into the mathematical model, the added mathematical complexity will make it difficult to parameterize and extract information from such models given the limited amount of experimental data. Protein synthesis is precisely one of the phases in the network machinery where certain mechanistic details are important and should thus be taken into account. Here, we develop a methodology to reduce a mathematical model for protein synthesis by performing approximations on a mechanistic model, retaining the essential details of the process. Our methodology opens up the possibility of utilizing powerful mathematical tools, such as bifurcation analysis, for understanding the complex dynamics displayed by genetic networks and design strategies for metabolic engineering and synthetic biology. Time-delay models are common in mathematical biology, as is demonstrated by the use of mathematical models incorporating time-delays in a wide range of applications. These include population dynamics, the chemostat, neural networks, blood cell maturation, transcriptional regulator dynamics, virus dynamics and genetic networks Complex dynamical behavior can arise as a consequence of time-delays in a system. Biological systems with significant time delays may exhibit limit cycle oscillations and chaos Gene regulatory circuits possess incredibly diverse functions. They function as molecular switches, molecular clocks or as sensors which are able to discriminate noise in the input We focus on the mathematical modeling of protein synthesis (translation), which is central to cellular processes and gene networks. Translation is divided conceptually into three stages: initiation, elongation and termination . First, Mathematical models of protein synthesis have used many diverse approaches and incorporate different levels of mechanistic detail. In Stochastic effects in genetic circuits and protein translation have also been considered E. coliA detailed consideration of ribosome dynamics in protein translation usually leads to models with large numbers of differential equations, complicating the mathematical analysis. For this reason, when modeling genetic circuits mathematically, it is common practice to use heuristic arguments and consider protein synthesis as proportional to the amount of mRNA present, on occasion including a time delay We present here a systematic mathematical framework for the development of a delay differential equation model of template polymerization, such as mRNA and protein synthesis. Our focus has been primarily on protein translation, which represents the main source of delay in bacteria where transcription and translation occur simultaneously. The framework is based on systematically approximating a mechanistic mathematical model of ordinary differential equations (ODEs), first derived in The delay model derived here offers many advantages. First, the systematic framework guarantees that all relevant aspects of the mechanistic model are preserved in the approximation, and it allows a systematic investigation of the validity of the approximations. Second, our reduction of the mechanistic model provides a powerful conceptual picture in which the essential aspects of protein translation are preserved and the numerous mechanistic parameters are condensed into the essential parameters of the process. Third, the time-delay model circumvents the impracticality of the large number of ODEs of the mechanistic model and the framework developed here is amenable to well known computational tools for bifurcation analysis of delay differential equations E. coliThe mechanistic model for protein translation of Heinrich and Rapoport The model described in this section is a version of a TASEP model with deterministic dynamics in terms of ODEs, where a mean field assumption was made. In contrast with typical TASEP models, which consider either constant initiation rates or periodic boundary conditions, the present model considers a finite pool of ribosomes and their initiation rate is a function of the free ribosomes.The model of Treating variables as continuous functions of time, the system dynamics is described by the following system of ODEsThe initiation rate, The elongation and termination fluxes, E. coli, typical ranges for the kinetic parameters and other relevant quantities in the model are given in The reactions in the model are assumed to be irreversible and the reversible association of ribosomes from its subunits is not explicitly modeled. Dilution of concentrations due to cell growth is not included in the model. In general, the reaction rate constants The protein production rate is equal to the rate of ribosomes terminating at the last codon and it is described by the following equationSome additional fundamental quantities in the mechanistic model are the concentration of bound ribosomesWe first introduce new dimensionless variables and parameters for the system, using characteristic values for the total ribosome concentration, umber, , . We defiThe dimensionless mRNA, ribosome and protein concentrations:The dimensionless time variable:The dimensionless, time-dependent, rate constants of initiation, elongation and termination:The mechanistic model, Eqs. 1, may now be written in non-dimensional form:E. coli the ribosomal density averaged over all mRNA species is around 0.3 S. cerevisiaeExperimental data suggests that for most mRNAs in many organisms, the rate limiting step of the translation process is initiation In general, the number of total ribosomes can vary due to changes in the synthesis of their components. In addition, changes in the components of the initiation, elongation and termination processes lead also to changes in the values of the corresponding rate constants. The primary cause responsible for the changes in these rate constants are changes in the availability of amino acids. If we assume that the time average values, ly small :(15)(i) a mean field ribosome distribution to effectively approximate steric hindrance effects ((ii) a hydrodynamic approximation to obtain a PDE model as a reduction of the mechanistic one stic one .The reformulation of the mechanistic model via the hydrodynamic approximation is based on the following principles:The discrete description of the codons, labelled as The number of ribosomes per codon, which was represented by the variable velocity function, as it quantifies the rate of progression of ribosomes along the template. Its use is equivalent to assuming that ribosomes move along the mRNAs continuously in space instead of advancing discretely one codon at a time.The elongation rate constants, The dimensionless PDE model which approximates the mechanistic model of Eqs. 10 is described by the following equationsHydrodynamic approximations have been used in the past in the context of models of TASEP and have yielded non-linear diffusion PDEs for such processes In the special case when the elongation rates constants are time-independent and vary only from codon to codon The following system properties can then be formulated in terms of the PDE model variables:The concentration of bound ribosomes (Eq. 12a)The ribosome density (Eq. 12b)The initiation rate is given by (Eq. 11a)The non-dimensional rate of protein production is (Eq. 4)We used the PDE formulation of the problem to derive a time-delay model of protein synthesis . The delThe time delay appears in our model through two mechanisms, the initiation time delayThe integral equation is complemented by the description of protein production:We use the simple transformation Our systematic reformulation of the problem into a delay differential equation offers two main advantages. First is the lumping of Second, modeling the problem with a single delay equation facilitates the use of numerous analytical and computational tools for the analysis of equations of this type, such as bifurcation analysis i) the transcription and translation rate constants are uniform along the DNA and mRNA templates, respectively, and (ii) there may only be one RNA polymerase per DNA and one ribosome per mRNA. In contrast, we considered the case of non-uniform elongation rate constants and multiple ribosomes on the mRNA template.Our model reduction is similar in spirit to the work in Heinrich and Rapoport rictions .While the model by Heinrich and Rapoport offers the same advantages discussed above, our delay model is based on a systematic derivation from Eqs. 1 which ensures that all essential aspects are captured, and it permits the explicit estimation of the regimes of agreement with the full mechanistic model. In addition, our formulation offers an improvement over previous time-delay models. It accounts for average ribosome sequestration on mRNA chains and allows a good approximation of the ribosome distribution and dynamics. In our model the ribosome distribution may be obtained explicitly and so position dependent effects, such as codon usage and energetic considerations We first performed a computational study in order to identify the ranges of the parameter values for which the time-delay model is in good agreement with the mechanistic model. We compared the dynamic responses to step changes and to periodic forcing of the initiation rate constant. These studies provide the necessary conditions for the successful application of time delay to the modeling and analysis of genetic networks which display complex dynamic behavior E. coli  has a low local density and (ii) is nearly uniform along the chain  in a dynamic situation and (ii) at steady state. We compared the dynamics through simulations of the two models at high flux  a uniform distribution of the ribosomes along the mRNA molecule and (ii) a ribosome density below 0.5. It has been shown that these conditions can be achieved under initiation limiting conditions E. coli and yeast.Theoretical and computational analysis suggests that the time-delay model is an excellent approximation of the mechanistic model under conditions that correspond to In our continuing studies we have used the time-delay model to perform bifurcation analysis of genetic networks having feedback mechanisms operating at the transcriptional level. Such analysis would not be practical using the full mechanistic model and tests the limits of performance of the reduced time-delay model under complex dynamic behavior. In genetic networks, interactions and feedback mechanisms operate through protein concentrations. In turn, the mRNAs in the circuit compete for free ribosomes, essential to produce protein for the interaction circuits. Hence, the important quantities to consider are precisely the protein concentration as well as the amount of free and bound ribosomes. In this context, the good agreement obtained for the ribosome density and protein concentration, (i) the modeling of the variable elongation rate constant, (ii) the modeling of sequence specific degradation of mRNA and (iii) the modeling of mRNA secondary structure effects. It has been shown that these three elements are important for the steady-state and dynamic properties of genetic networks, therefore, a rigorous description of these processes in time-delay models is challenging but very important.In the study of protein translation, we have identified three main areas of future developments: Mathematical models of stochastic systems may be reduced to models with time delays by lumping some of the intermediate processes The method used here may be useful for developing reduced, time-delay models of mRNA transcription, since the underlying biophysical and biochemical phenomena are very similar. Both processes involve molecular machines scanning a template in order to build a polymer chain lacZ message of E. coli, Some differences do exist between the processes of transcription and translation. One has to do with the existence of stall stages at certain sequence positions, where RNA-polymerases may stop for as long as several seconds and generate queueing of several polymerases behind the stalled one In summary, given the complexity and the importance of transcription and translation in biological processes, it is necessary to develop methodologies to systematically reduce detailed mechanistic models of these processes. To reach this objective, the formulation of time-delayed models of coupled template polymerization processes is one of the exciting future developments in the modeling of genetic networks.Text S1Estimation of the Non-Dimensional Initiation Rate Constant(0.03 MB PDF)Click here for additional data file.Text S2Derivation of the PDE Model(0.07 MB PDF)Click here for additional data file.Text S3Integral equation formulation(0.07 MB PDF)Click here for additional data file.Text S4Equivalence with a Previously Proposed Delay Model(0.03 MB PDF)Click here for additional data file.Text S5The Steady State Solution and its Stability(0.04 MB PDF)Click here for additional data file.


Choropleth maps are commonly used in cancer reports and community discussions about cancer rates. Cancer registries increasingly use geographic information system techniques. The Centers for Disease Control and Prevention's Division of Cancer Prevention and Control convened a Map Work Group to help guide application of geographic information system mapping techniques and to promote choropleth mapping of data from central cancer registries supported by the National Program of Cancer Registries, especially for comprehensive cancer control planning and evaluation purposes. In this 2-part series, we answer frequently asked questions about choropleth map design to display cancer incidence data. We recommend that future initiatives consider more advanced mapping, spatial analysis, and spatial statistics techniques and include usability testing with representatives of state and local programs and other cancer prevention partners. In part 1 of this 2-part series, we answered frequently asked questions about the purpose of choropleth maps, geographic units of analysis, cancer sites, age-adjusted rates, rate ratios, and reliability. In Part 2, we address suppression rules to protect the privacy and confidentiality of cancer patients; questions related to mapping cancer stages, rates, and percentages; classes for map display; comparing maps over time; map color schemes, labels, projections, and output media; and limitations in interpretation . However, in rates, the denominator is the study population at risk for developing the disease. In contrast, with percentages, the denominator consists of the total cases across all categories of cases .The spatial patterns observed on rate maps may not be the same as the patterns observed on maps of percentages. For example, suppose that a county has a relatively large number of women at risk for breast cancer, the total number of cancer cases is small, but a large proportion of those cases are advanced stage. The rate map would display the county as having a low advanced-stage breast cancer incidence rate, whereas a map of percentages would display the same county as having a high proportion of advanced-stage breast cancer cases.The choice of categories for grouping rates for mapping can affect the visual appearance of the map and thereby interpretation of mapped results. Selecting the interval may depend on the purpose of the map, the underlying data distribution, and the intended audience for the map -8. Map lFour examples of classification methods  are the Quantiles: The rates for the areas of interest  are first rank-ordered, and then an equal number of observations are placed in each class. The number of classes determines the specific type of quantile map . Quantile maps can be helpful in identifying the spatial patterns of the relative rankings of rates within the geographic units of interest .Equal intervals: The range of the entire dataset  is divided by the desired number of data classes. The upper and lower values for the classes are assigned so that each class has the same width interval  without regard to the number of geographic units  included in each class. Equal interval maps can be used to help identify spatial patterns of absolute values of rates and locations of extreme outliers.Natural breaks : An iterative algorithm is applied to define classes where the variance is minimized within all classes and maximized among classes.Standard deviations: Data are assigned to classes on the basis of where they fall relative to the mean and standard deviations of the data distribution. This classification method may be used to help identify and contrast geographic units  that are above and below the mean.Brewer ,8 reportIf the goal is to compare changes between maps over 2 or more time periods, each rate map in the time series should be prepared by using the same set of intervals to categorize rates ,9. To idHowever, if the goal is to identify areas with the highest and lowest rates on each map in the time series, then intervals that distinguish high and low rates should be defined separately for each map, on the basis of rate data to be displayed in each map.VisCheck is a Web-based tool that people with normal color vision can use to get a sense of how color-blind people see colors  can result in maps that are difficult for color-blind people to read . VisChece colors .ColorBrewer , a Web-based tool that helps identify and create good color schemes for maps and other graphics, indicates which recommended color schemes work well for people with red-green color blindness  can be used to identify specific areas of interest. The number and size of text labels may need to be reduced so that users can identify spatial patterns. As an alternative to detailed text labels, geographic clues  can be used to help orient community members or decision makers. One advantage of Web-based maps is the ability to hide text labels until the user passes a mouse cursor over an area ,16.datum (a reference point for measuring the origin and orientation of latitude and longitude lines); latitudes and longitudes (angles measured from the center of the sphere to reference points on the sphere's surface); and a prime meridian (a reference point for other longitudes).Geographical coordinate systems enable locations to be identified on a 3-dimensional spherical surface . Basic bThe actual surface of the earth is more complex than a sphere. Spheroids (defined by rotation of an ellipse with a longer and shorter axis) provide more accurate representation . DiffereEvery map projection distorts distance, area, shape, direction, or some combination of those factors. Choosing the most appropriate projection depends on the study question. Also, agencies or organizations may prefer a specific projection standard.equal-area because area is not distorted  may be used for publication in a scientific journal. Although the starting point for each of these maps is the same information, changing the map from 1 medium to another may require significant changes in the map design.ColorBrewer Web site includes guidance on the usability of different color schemes for a variety of uses   colors would be optimal, but if the goal is publication of a hard copy, high-quality color map, CMYK (cyan-magenta-yellow-black) colors may be a better choice. Map colors may have a different appearance when displayed on a computer monitor, a projector, or a color printer. The d users) .Similarly, to successfully print a black-and-white copy from a color map, the classes for rates may need to be limited to 4 or 5 categories so that shades of gray can be distinguished. Alternatively, patterns such as hatch marks or other fill symbols and labels may need to be added to help map readers distinguish categories.When choropleth maps are presented, comprehensive cancer control decision makers should be reminded of the following constraints on interpretation:Administrative-political boundaries reflect administrative-political needs and may have little relationship to the true spatial distribution of cancer incidence.modifiable areal unit problem  may have rates that are extremely high or low because of small-number problems .edge effects (Caution also is needed regarding interpretation of the spatial patterns close to the edges of the study area . For exa effects .Application of methods that include information about rates in counties in contiguous states can help inform analysis of the spatial patterns along state boundaries. For example, in 2006, Gregorio et al  reportedSome of the questions commonly raised about using GIS and mapping techniques to present cancer incidence data are covered in this article. However, the process of preparing responses to these questions was not straightforward, and our discussions raised additional issues for future consideration. More advanced mapping, spatial analysis, and spatial statistics techniques also have both strengths and limitations -25. Reco