Langmuir 1997, 13, 35-40
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Three-Dimensional Modeling of an Activated Sludge Floc F. Zartarian,† C. Mustin,‡ G. Villemin,‡ T. Ait-Ettager,§ A. Thill,† J. Y. Bottero,*,† J. L. Mallet,§ and D. Snidaro| Laboratoire des Ge´ osciences de l’Environnement, CEREGE, URA 132 CNRS, Universite´ Aix-Marseille III, BP 80, 13545 Aix-en-Provence cedex 4, France, Centre de Pe´ dologie Biologique, UPR 6831 et Universite´ H. Poincarre´ , 17 rue Notre Dame des Pauvres, BP 5, 54501 Vandoeuvre-le` s-Nancy cedex, France, Laboratoire d’Informatique et d’Analyses d’Images, ENSG-INPL, Rue du Doyen M. Roubault, BP 40, 54501 Vandoeuvre-le` s-Nancy cedex, France, and Cirsee Lyonnaise des Eaux, 38 rue du pre´ sident Wilson, 78230 Le Pecq, France Received June 10, 1996. In Final Form: October 21, 1996X A new interpolation method called discrete smooth interpolation was used to construct a 3-D model of an activated sludge floc from digitized microtome sections. This method comprises several advantages: rapidity, almost completely automated, precision, high quality of representation, and, most importantly, availability of specific tools to manipulate the 3-D model. Some parameters of the floc such as the size, the surface area, and the volume were directly measured on the 3-D reconstructed object. The contour and surface are fractal with fractal dimensions of 1.4 and 2.4, respectively. Local curvatures were also calculated and show great deformations of the surface due to anisotropic growth within the floc. Discrete smooth interpolation constitutes a powerful tool to improve the understanding of the floc structure complexity.
Introduction The activated sludge process is one of the most common techniques in wastewater treatment. This biological process is based on the growth of microbial populations in a flocculated form, at the expense of the biodegradable organic matter present in water. The activity of the biomass depends on a lot of parameters as oxygen, nutriments, geometry of the reactors, etc. The activity is generally ensured by aggregated bacteria which have to be eliminated by settling in order to generate new bacteria flocs. It is well-known that some general parameters such as the aggregation kinetic, floc break-up, and settling are correlated with the floc structure and morphology.1-5 The efficiency of the activated sludge process seems also to be closely related to the physical characteristics of the flocs (settling capacity, substrate transfer and utilization, floc aggregation and breakup, solid-liquid separation, dewatering, etc.).6-8 The bacteria floc structure is far from being well-known and understood. To date only simplified or approximated models were proposed to describe the structure and then applied to further calculations. For example, spherical models were often used to approximate the floc shape; the floc morphology was often characterized using parameters calculated in projection such as longest distance of the aggregate, projected surface area, or projected perimeter.9 This description can provide only a partial view of the †
Universite´ Aix-Marseille III. UPR 6831 et Universite´ H. Poincarre´. § Laboratoire d’Informatique et d’Analyses d’Images. | Cirsee Lyonnaise des Eaux. X Abstract published in Advance ACS Abstracts, January 1, 1997.
reality. The internal structure of aggregates was also approximated. Logan et al.10,11 assumed a uniform distribution of microorganisms within the floc to study the flow of liquids through the aggregate. This hypothesis was finally found to be too simplistic by Li and Ganczarczyk.12 Because of the lack of precise knowledge of the pore geometry of flocs, empirical factors were often introduced for the calculation of diffusivity of oxygen within the floc,13 liquid flow, density, mass transfer, etc. The importance of very thorough investigations of the floc structure has been clearly outlined here. Nevertheless a major difficulty in understanding the structural properties of flocs is that there is still no single technique allowing a satisfactory description of this complex structure. This is mainly due to the difficulties encountered in experimental techniques, especially in sample preparation and handling. Only the recent development of floc embedding procedures and image analysis enabled a more complete approach of this problem. These methods have been investigated by the work of Mitani14 and further by Ganczarczyk et al.15 and Zartarian et al.16 Microscopic examinations of serial sections of flocs fixed in resin can be used for the direct study of the floc morphology and mass structure. The development of these techniques gave access to new possibilities for both experimental and theoretical investigations of the floc structure.6,16 But so far these investigations were limited to the 2-D domain. A new approach consists of investigating the morphology of the flocs by using a discrete smooth interpolation (DSI) technique. Recently, Gerard et al.17,18 used a DSI pro-
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(1) Jullien, R.; Bottet, R. Aggregates and fractal aggregates; World Scientific Publisher: Singapore. (2) Gregory, J. Colloids Surf. 1988, 31, 231-253. (3) Bottero, J. Y.; Tchoubar, D.; Axelos, M. A. V.; Quienne, P.; Fiessinger, F. Langmuir 1990, 6, 596-602. (4) Klimpel, R. C.; Hogg, R. Colloids Surf. 1991, 55, 279-288. (5) Lartiges, B. S.; Bottero, J. Y.; Derrendinger, L. S.; Tekely, P.; Humbert, B.; Suty, H. Langmuir, in press. (6) Li, D. H.; Ganczarczyk, J. J. Environ. Sci. Technol. 1989, 23 (11), 1385-1389. (7) Li, D. H.; Ganczarczyk, J. J. Water Environ. Res. 1992, 64 (3), 236-240. (8) Eriksson, L.; Ha¨rdin, A. M. Water Sci. Technol. 1984, 16, 55-68.
S0743-7463(96)00566-5 CCC: $14.00
(9) Li, D. H.; Ganczarczyk, J. J. Res. J. Water Pollut. Control Fed. 1991, 63 (5), 806-814. (10) Logan, B. E.; Hunt, J. R. Limnol. Oceanogr. 1987, 32, 10341040. (11) Logan, B. E.; Alldredge, A. L. Mar. Biol. 1989, 101, 443-448. (12) Li, D. H.; Ganczarczyk, J. J. Biotech. Bioeng. 1990, 35, 57-65. (13) Smith, P. G.; Coakley, P. Water Res. 1984, 18 (1), 117-122. (14) Mitani, T.; Unno, H.; Akehata, T. Water Pollut. Res. 1983, 6, 69. (15) Ganczarczyk, J. J.; Zahid, W. M.; Li, D. H. Water Res. 1992, 26, 1695-1699. (16) Zartarian, F.; Mustin, C.; Bottero, J. Y.; Villemin, G.; Thomas, F.; Aillie`re, L.; Champenois, M.; Grulois, P. Water Sci. Technol. 1995, 30 (11), 243-250. (17) Gerard, H. M.; Bouchet, P.; Jacquemin, P.; Le Melinaire, P.; Mallet, J. L. Acta Stereol. 1992, 11 (1), 187-192. (18) Gerard, H. M. Anat. Rec., in press.
© 1997 American Chemical Society
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Figure 1. (a) Optical micrograph of a microtome section of an activated sludge floc (thickness 0.2 µm, magnification ×100, 2.5 cm ) 20 µm). (b) Digitized contour line of the floc section, 2.5 cm ) 200 µm.
cedure to reconstruct embryo organ images from histological sections. These authors compared the obtained models to those given in the literature in order to evaluate the reliability and the precision of the method. They concluded that this method is very well adapted for this kind of work. The efficiency of DSI in smoothing the shape defects while preserving detail accuracy was verified on all studied embryonic organs. Thus, since the DSI is well suited for the modeling of human embryo organs, this method can be similarly applied to the 3-D reconstruction of an activated sludge floc from microtome sections. Furthermore it can be used for calculations yielding quantitative information about the floc surface properties. The aim of the present work is to extend previous analysis methods to the third spatial dimension and, for the first
time, to image the 3-D morphology of an activated sludge floc by using a DSI technique. Materials and Methods Sludge Samples. The activated sludge samples were taken from the aeration tank at the Nancy (France) metropolitan wastewater treatment plant (300 000 inhabitants equivalents; organic loading 0.2-0.4 kg BOD5 kg-1 (volatile suspended matter) VSS‚day-1 (after primary settling). Sample Preparation. The sludge was concentrated by elimination of one-third of the supernatant after 30 min of settling in a 1000 mL glass cylinder. One milliliter of the liquor obtained was fixed in a blood collecting tube with 1 mL of 2% osmium tetraoxide in a 0.1 M sodium phosphate buffer (pH 7.2) for 1 h. Excess osmium tetraoxide was removed with phosphate buffer.
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Figure 2. Graphic displays of the top of the partial reconstructed floc. Vertical axis (z) was multiplied by 3. (a) Intermediate strata between two successive contour lines are revealed by the alternation of colors. Triangulated mesh has been displayed on three surfaces. (b) Intermediate surfaces were associated to generate only one surface which was submitted to the smoothing procedure. The flocs were then dehydrated in successive acetone baths (5 min at 10, 20, 40, and 60%, 15 min at 80%, 2 × 15 min at 95%, and 3 × 20 min at 100% acetone) and embedded in an epoxy resin (Kit Embed 812, Euromedex) in three stages. First, onethird of the acetone was replaced by the same volume of resin; then, two-thirds of the resulting mixed liquor was replaced by resin. The sample was placed under vacuum for 4 h after each step. Finally all the supernatant was replaced by the resin. The flocs remained in pure resin for 12 h under atmospheric pressure. The well-impregnated flocs were sampled by a pipet with a wide opening and transferred into a mold filled with resin. Polymerization was carried out for 12 h at 60 °C. Microtome Sectioning. An ultramicrotome (Reichert OM U2) was used to slice the resin-fixed flocs into very thin sections (0.2 µm thick). One selected floc was entirely cut. All sections were kept and fixed on glass slides by flame. The sections were stained with toluidine blue (0.1%) and covered with coverglass fixed with Eukitt (Polylabo 82601). About 2500 serial sections were realized to cut this floc. Microscopy and Image Analysis. The images of the floc sections as seen under a light microscope (Nachet NS 400, or Leica Dialux 20 magnification ×100, used in dark field) were digitized with an image analysis system and the contour lines of the floc were then outlined by the system and converted into x, y coordinates (Figure 1). To assure an exact superimposition of the successive contour lines, the edges of the resin bloc sections were also digitized and used as a landmark. Only one section every 3 µm was selected. This allowed a satisfactory compromise
between the resolution desired and a reasonable number of sections to analyze (almost 270 sections). 3-D Reconstruction. The software GOCAD (version 9.1.a) developed at the Nancy School of Geology (France), was used on a Hewlett-Packard 715 workstation under the UNIX operating system. This software was written using the C programming language and the user interface uses X-Windows. Under the DSI environment,19,20 the partial information required to get a triangulated surface is (1) the exact location of some points, (2) the approximate location of some other points, and (3) some vectorial constraints on the shape of the surface (i.e., the normal at the surface at some points). The digitized profiles were transferred to the UNIX workstation. The problem is how to create an open surface (a surface with upper and lower borders in our case) that best fits the spatial distribution of points of two adjacents contours? For many steps of the floc reconstruction, the data set is underdefined or too ambiguous to generate a “well-formed” or “logical” surface that we have in mind. In these cases, it is necessary to force the Delaunay triangulation algorithm that uses GOCAD for the surface construction. To find the best surface between two complicated curves, the projection plane for triangulation has been made more precise by increasing the data density (more nodes), by creating specific links between nodes, or by using knowledge given by intermediate slides. (19) Mallet J. L. Discrete Smooth Interpolation. Assoc. Computer Machinery, Transaction Graphics. 1989, 8 (2), 121-144. (20) Mallet, J. L. Computer Aided Design J. 1992, 24 (4), 178-191.
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Figure 3. View of the final 3-D reconstructed floc (1.8 cm ) 100 µm). The information gap between the successive contour lines was filled in by means of the triangulation algorithm, forming a web of triangular patches by selecting sets of three points on adjacent contours. After the reconstruction, the smoothing procedure was applied to the constructed surface. The DSI algorithm carries out a spatial redistribution of the apexes of the triangles, correcting the mathematical data. The final surface was then displayed as a fully shaded 3-D image of the reconstructed structure. Using Computer Aided Design (CAD) tools, the reconstructed floc could then be manipulated: rotated, magnified, measured, isolated external or internal contours could be partially or totally shown, animation and new sections could be generated.
Results and Discussion The triangulation algorithm was highly effective in automatically generating a 3-D representation from different section profiles, except for the association of complex contours (especially multiple branching or transition from convex contour to horseshoe contour). In this case, an interactive environment and batch programs have been developed allowing the user to indicate the correct association between the different contour lines. In our work, this interactive procedure was very intensively used: Due to the numerous contour lines to interpolate in each section, a large number complex junctions were encountered. Only 70 sections (one every 7 µm) were finally interpolated, but each time the creation of an intermediate level (every 3.5 µm) was necessary to resolve the junction problems. In this work, the intermediate digitized sections, not selected for the interpolation, were very useful to help the user to interpret the structure and to indicate the correct association. The same user did all the operations to assure unchanging vision of the configuration of the structure and interpretation of the way to interpolate. The floc was reconstructed by strata (Figure 2a) along the z axis. All partial surfaces were then associated to create only one surface which then underwent the smoothing procedure of the DSI environment (Figure 2b). Figure 3 presents different views of the final reconstructed 3-D floc. The stereoscopic impression of the solid
model is produced by the utilization of colors and the effects of shade and light. This representation greatly improves the perception of complex shapes. Figure 4 reveals the exceptionally high quality of this way of representation. The use of CAD tools developed under the DSI environment was of particular interest to manipulate the 3-D model. One of them was to perform quantitative studies such as direct measurements of the size, the surface area and the volume of the floc. With 687, 521, and 454 µm along the x, y, and z axes, respectively, the 3-Dreconstructed floc displayed relatively large dimensions. At the chosen resolution, the measured surface area is 1.93 mm2 and the occupied volume is 0.031 mm3. The ratio surface/volume ratio has a value of 62 mm-1. As a comparison, a sphere with the same volume has an 8 times lower surface/volume ratio. Using CAD capabilities, new planar sections (independent of the experimental ones) could be obtained and displayed easily. The perimeter (P) vs area (A) relation was studied on these new sections obtained along the x, y, and z axes of the reconstructed model. The results (Figure 5) indicate that the perimeter P follows a power law of the area A according to the fractal law described by Feder21
P ∼ ADp/2
(1)
where Dp is the fractal dimension of the section perimeter. This indicates the fractal nature of the contour of the floc. The fractal dimension Dp calculated for different orientations of the sections is ∼1.3 ( 0.08. Similar results were obtained by Li and Ganczarczyk6 on microtome sections of embedded flocs. The fractal dimensions they obtained for the sectional perimeter were in the range of 1.131.22. With the fractal dimension of the contour Dp known, the surface fractal dimension Ds (which characterizes the (21) Feder, J. In Fractals. Physics of Solids and Liquids; Plenum Press: New York and London, 1988; p 280.
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Figure 4. Detail of the floc surface complexity.
In this case it is possible to use the numerous tools available. As an example, another CAD tool allows the calculation of the local curvature at each point of the triangulated surface. The local curvature C is defined on one point of the surface by eq 3
C ) 1/R
(3)
where R is the local radius of curvature of the surface.25 At each point, two principal curvatures, one minimum (C1) and one maximum (C2) can always be found. The total local curvature K is then given by eq 4
K ) C1C2
Figure 5. Log perimeter/log area plots along x, y, z.
roughness of the surface) can then be easily obtained using the codimension rule21,22
Ds ) Dp + 1
(2)
In our case, the surface fractal dimension from eq 2 is Ds ) 2.31. This value is in good agreement with the recent result of Ganczarczyk23 who found an average value of 2.25. Our results can also be compared to surface fractal dimensions of biofilms24 found to be in a 2.1-2.8 range. These results show that the preparation technique used in this work does not greatly modify the structure of the flocs. We can think that a strong modification due to the multiple stages of the preparation would lead to values which would be different of those obtained in the literature. (22) Mandelbrot, B. R. In The fractal geometry of nature; W. H. Freeman and Co.: New York, 1974; p 468. (23) Ganczarczyk, J. J. Newsl. IAWQ 1995, 8 (1), 4-7. (24) Zahid, W.; Ganczarczyk, J. Water Res. 1994, 28 (10), 22292231.
(4)
K corresponds to a local criterion of anisotropy of the surface. CAD tools enable the 3-D display of properties associated to the surface. In Figure 6 the color of each node of the surface is associated its corresponding K value, thus providing easy visualization of the property (here the roughness of the surface) and greatly facilitating the understanding of the surface complexity. For instance (Figure 6), green areas correspond to isotrope and smooth zones while blue ones indicate an important local curvature which could be interpreted as a particular growth area on the floc (corresponding to the development of particular bacterial population, to a preferential site of particle attachment, etc.). The DSI technique is a great improvement in investigating the external surface characteristics of activated sludge flocs using simple and fast operating tools. It is of particular interest because surface roughness is involved in hydrodynamic performance of the liquid layer surrounding the aggregate such as mass transfer processes. It must be emphasized here that only the surface can be characterized with this method. So far this modeling technique unfortunately does not provide any information about the internal structure of the floc. (25) Vicsek, T. In Fractal growth phenomena; World Scientific: Singapore and River Edge, NJ, 1989; p 355.
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Figure 6. 3-D visualization of the total local curvature. Each node of the surface has been painted following a scale of color corresponding to the value of K calculated on this node.
This study presents, for the first time, a direct visualization of the activated sludge floc morphology and the possibility of easy and rapid characterization of the external surface properties of the aggregate. Although limited results are presented here because of the limited range of samples we studied, it is an important first step. Conclusion A new interpolation method (the DSI) was applied here for the 3-D modeling of an activated sludge floc reconstructed from digitized microtome section images. The use of specific tools developed under the DSI environment allows not only the visualization of the model but also its easy manipulation as a real mathematical object. Then it offers new possibilities of mathematical characterization of the surface properties. Undoubtedly, this method will greatly improve the fundamental approach of floc morphogenesis. In the future, other reconstruction options
could be developed, either on new flocs generated under various conditions to obtain a larger spectrum of the studied characteristics correlated to sludge properties or on other kinds of microscopic aggregates. The use of a confocal microscope which provides optical images of floc sections (which can directly be digitized) without using a microtome, will dramatically reduce sample preparation time. New developments expected in computer modeling will speed up the reconstruction procedure by a more automated solver for linking problems. At the present time, this is one of the major options of the research program. Acknowledgment. This work benefited from a financial support of CIRSEE (Lyonnaise des Eaux) and Eureka EEC Programme STEP 2000 Sludge. LA960566U
