Estimating fractal dimension of microalgal flocs through confocal laser scanning microscopy and computer modelling Patricio López Expósito*, Angeles Blanco, Carlos Negro Chemical Engineering Department, Complutense University of Madrid. Avda. Complutense s/n, Madrid 28040, Spain. Tel.+34 913944247, fax +34 913944243.
[email protected].
Estimating fractal dimension of microalgal flocs through confocal laser scanning microscopy and computer modelling Abstract Flocculation followed by settling is gaining momentum as a means to concentrate microalgal biomass due to the low investment and operation costs of the process. Microalgal flocculation can be further optimised by knowing the relationship between the hydrodynamic conditions applied in the process and the geometric properties of the flocs, namely characteristic size and fractal dimension, Df, given that settling rate is highly dependent on these two parameters. Current methods to characterize the geometry of flocs rely on estimating the 2D fractal dimension from microscopic images, which may result in inaccuracies caused by the overlapping or superimposition of aggregate structures prompted when the image of a 3D object is projected a on the plane, and due to the fact that the estimation performed is dependent on the orientation of the particle during image acquisition. The present paper describes a new procedure to estimate Df of Chlorella sorokiniana aggregates by correlating the 2D fractal dimension of the real aggregates microscopic images with the 2D fractal dimensions of computer generated flocs of prescribed 3D geometry. This procedure avoids the inaccuracies entailed with floc imaging and those due to the random orientation of the floc during image acquisition.
Glossary AS: aluminium sulphate CCA: cluster-cluster aggregation CLSM: Confocal laser scanning microscopy D2: 2D fractal dimension Df: fractal dimension FD: fractal dimension G: velocity gradient MFD: maximum Feret diameter MFDD: maximum Feret diameter distribution PFD: projected fractal dimension PAC: polyaluminium chloride Re: Reynolds number
1. Introduction The cost associated to harvesting remains one of the critical factors that hinder the mass production of microalgae as industrial feedstock. Flocculation followed by settling is gaining momentum as a means to concentrate microalgal biomass due to its low investment and operation costs (Wan et al. 2015). In order to increase the profit margins expected from microalgal biomass production at industrial level, it is desirable to optimise the harvesting process to the greatest possible extent. Such optimization can be achieved by selecting a flocculant that offers a good compromise between effectiveness and price, and once the flocculant is selected, by optimising the flocculation and settling processes themselves. While the literature offers numerous references describing the flocculation of various microalgal strains employing flocculation agents of different chemical nature (Vandamme et al. 2013), the optimization of flocculation coupled with settling has not enjoyed the same degree of attention. Among the different aspects likely of being optimized, of especial relevance are mixing and settling velocity (Ahmad et al. 2011). Settling velocity is dependent on particle size and morphology, the latter through the fractal dimension (Df). For a
fixed settler and operating conditions, settling velocity will be higher at larger floc size. For a given floc size, settling velocity generally decreases with increasing Df values. The relation between these two parameters is however complex, for the aggregate translational hydrodynamic radius is a function of its geometry (Harshe et al. 2010). Understanding the relationship between mixing conditions and floc geometry may help to find an optimum compromise between stirring requirements and settling velocity in flocculation coupled with settling processes. The present work contributes to the above idea by proposing a method to estimate the 3D geometry of microalgal aggregates produced through flocculation. The geometric characterisation of particle aggregates is generally carried out through the estimation of the 2D fractal dimension (D2) of their microscopic images, either taken with confocal microscopy or with online microscopy (Chakraborti et al. 2000, Schmid et al. 2003). Although providing some information on the shape of the aggregates, both approaches present drawbacks that limit their use as predictor of settling velocity. First, there is no general correspondence between D2 and Df (Orhan et al. 2016). On the other hand, both confocal microscopy and online microscopy yield a 2D projection of a 3D object, which implies a loss of information of the object´s geometry. Therefore, in the image, some 3D structures of the aggregate will be overlapped, i.e. not visible, while others will appear superimposed on the projection plane, creating thus a distorted profile of the object. Given that D2 is obtained from the relation of scale and perimeter of the floc projected, its estimation based on the floc profile will lead to inaccurate results. Finally, the D2 of flocs is dependent on the orientation of the particle at the moment of taking its image or projection (Wentzel et al. 2003), thus the fractal dimension based on processing online microscopy images of the aggregates suspension may yield inaccurate results. Confocal laser scanning microscopy (CLSM) avoids the randomness associated to floc orientation to a great extent given that the flocs tend to settle on the orientation offering the maximal area to the ground of the cuvette or glass where they are deposited. Nevertheless, when flocs analysed are large, confocal laser fails to penetrate all planes in the sample and is therefore unable to resolve the complete 3D geometry of the aggregate. The present work aims to overcome the limitations cited above by devising a new method to estimate the 3D fractal dimension of microalgal flocs that combines confocal microscopy images of real flocs and computer generated models of cell aggregates. Our process involves measuring the maximum Feret diameter (MFD) and D2 fractal dimension of microalgal aggregates on their CLSM images and generating several populations of virtual flocs with different input Df having their sizes coerced to the MFDs measured on the real flocs. The average Df of the real flocs is then estimated to be equal to the input Df of the virtual population of aggregates having the average D2 closest to that measured on CLSM images.
Fractal dimension estimation method Online microscopy Confocal microscopy Confocal microscopy and computer modelling
Composite profile error YES YES NO
YES NO
Direct estimation of Df NO NO
Image acquisition time FAST SLOW
NO
YES
SLOW
Orientation error
Table 1. Comparison of the different optical methods to estimate the fractal dimension of microalgal flocs.
2. Materials and methods 2.1. Microalgal cultures Microalgal culture samples were taken from a 5.5 L photobiorreactor (PBR) operated with a strain of Chlorella sorokiniana (CCAP No. 211/8K) grown in tris-acetate-phosphate medium (TAP medium) (Gorman and Levine 1965). The PBR was maintained at a temperature between 23 to 25 ºC and was aerated with 0.2 µm filtered air at 2 L min1 . pH was maintained at 7.5 through an on-demand automatic CO2 supply (0.2 L min-1). Light was provided by means of four fluorescent cool white light bulbs in a 12 hours cycle. The culture was maintained at 0.2 g L-1 dry biomass concentration. 2.2. Flocculation
Medium molecular weight chitosan (Sigma-Aldrich 448877, CAS Number 9012-76-4) was employed as flocculation agent. The flocculant solution was prepared by dissolving the chitosan in a solution of glacial acetic acid 1% vol. The solution was mechanically stirred at 400 rpm for 1 hour and left to settle for 24 hours. Flocculation essays were carried out in 600 mL beakers with 200 mL of microalgal culture. Stirring was achieved by means of a four-blade 45 pitch impeller of diameter 4.95 cm (Np = 1.27). Three different stirring speeds were considered, namely 200, 350 and 500 rpm, which corresponded to Reynolds numbers 8.2 x 103, 1.4 x 104 and 2.0 x 104 and velocity gradients (G) 263, 611 and 1043 s-1 respectively. In each case a dose of 5 ppm of chitosan solution was added to the stirred microalgal sample. After two minutes of stirring, 0.5 mL of a commercial dispersant (Nopco ESA 120) was added to the flocculating system to prevent aggregation after sampling.
2.3. Confocal Laser Microscopy image acquisition Aggregate microscopic images were taken with a confocal laser microscope Olympus FV1200, using a laser excitation of 405 nm and receiving the emission from 594 nm. No especial sample preparation was used for image acquisition: a drop of the microalgal sample in consideration was placed on a slide by means of a broad-tipped Pasteur pipet to avoid damaging the aggregates. The flocs were left to settle at the bottom of the slide before image acquisition so that they most likely present the maximal surface area projected on the horizontal plane. 2.4. Fractal analysis of the microscopy images Image processing was carried out with the Fiji distribution of ImgeJ 1.151h. Each image stack acquired was projected on the Z plane and the resulting image was made binary for further 2D analysis. The flocs of each image were automatically selected and stored in single files by means of a script. The MFD of each floc was automatically measured. The estimation of D2 was done through the BoneJ plugin Fractal Dimension tool applying 18 different box sizes, from 200 to 6, with a reduction rate of 1.2. 2.5. Generation of fractal-like virtual flocs A cluster-cluster aggregation model was employed to simulate the fractal growth of microalgal flocs. The fractallike nature of particle aggregates can be described by the following scaling power-law: 𝑅𝑔
𝑁 = 𝑘𝑓 ( 𝑎 )𝐷𝑓 , where N is the number of particles forming the aggregate, kf is the fractal pre-factor, Rg is the gyration radius of the floc, a is the mean diameter of the primary particle, and Df is the fractal dimension. In order to ensure constant geometric properties, the above scaling law must be fulfilled all along the process of generation of virtual aggregates. Filippov et al. (2000) proposed an expression to guaranty the fulfilment of the scaling law at all steps in the process of generating an aggregate from the combination of two smaller clusters (CCA aggregation model).
𝑎2 (𝑁1 + 𝑁2 ) 𝑁1 + 𝑁2 𝐷2 𝑁1 + 𝑁2 𝑁1 + 𝑁2 𝛤 = ( ) 𝑓− 𝑅𝑔1 − 𝑅𝑔2 (𝑁1 𝑁2 ) 𝑘𝑓 𝑁2 𝑁1 2
In the above expression, Γ is the distance between the centres of masses of the combining clusters, N1 and N2 are the number of particles in each of the small clusters, kf is the fractal pre-factor, Rg1 and Rg2 are the radii of gyration of each cluster. Skorupski et al. (2014) devised an algorithm to merge virtual clusters based on eq. 2. The key steps in the algorithm is to randomly select two particles among the most external cells in the combining clusters and perform the necessary translations and rotations to achieve the merging through the selected cells without any particle being overlapped. In the present work, we applied the mentioned algorithm with small modifications, namely in the generation of the random 3D direction on which the clusters are combined, and in the fact that we recalculated the masses centre of the aggregate being generated at each growth step. The modified merging method was incorporated into an algorithm to grow a cluster up to a prescribed characteristic size with a given
fractal dimension. Sintering was not considered in the generation of aggregates. A schematic representation of this growth algorithm is given in Fig. 1. The algorithm was implemented using in Python 2.7. We assumed microalgal cells to be spheres having a radius corresponding to the average measured radius of freely suspended Chlorella cells measured on the confocal microscopy image of a sample. The generation of virtual flocs consists in the aggregation of two small similar or equal clusters to form a larger aggregate. The process is repeated until the prescribed number of particles forming the cluster is reached or a prescribed characteristic size is attained. If the size of the floc being cropped surpasses the pre-set length plus the tolerance, the process is restarted. The virtual flocs generated in our programme were stored as Python objects containing the geometrical data of the floc in terms of its primary particles spatial coordinates, the position of its masses centre, the radius of gyration and the location of the primary cell most distantly placed from the centre of masses. Additionally the flocs held information about those cells being at a distance from the masses centre greater or equal to Γ - 2a. Those cells are considered as being outer cells and are therefore likely to intervene in the growth process either by overlapping with cells from the other cluster or by constituting the site of connection between clusters. Establishing a list of outer cells helps reduce the computational time required to generate virtual flocs. The 3D fractal dimension and the MFD were the two geometric parameters considered as input to generate the virtual aggregates. Due to the discrete nature of clusters it is obvious that it is not generally possible to create a virtual floc of an exact prescribed MFD given a fractal dimension. To account for this fact, a tolerance length of 5 µm was allowed in the generation of virtual aggregates. Nine fractal dimensions were input to the algorithm ranging from 1.3 to 2.1 with 0.1 steps. The MFDs input to the algorithm were the ones measured on the flocculated samples at the three stirring conditions. 2.6. Fractal analysis of virtual flocs, virtual settling algorithm As stated above, the 2D fractal dimension of flocs is dependent on the orientation in which it is measured. Given that the flocs imaged through the microscope were settled, the computer generated flocs were also virtually settled before obtaining their projection on the Z-plane. This was achieved by applying two types of rotations. The first rotation was done around the vector resulting from performing the cross product vector between the displacement vector between the masses centre and the furthest cell of the aggregate and the projection of this vector on the Z-plane. This rotation settled the aggregate on the Z-plane. The second rotation was performed around the displacement vector formed between the masses centre and the projection of the furthest cell on the Z plane. In this case, the angle was chosen after applying 360 rotations to the floc in 1 degree steps. The selected angle was that yielding the floc projection on the Z-plane with the maximal surface area in pixels so as to mimic actual settling. The projections of the virtual aggregates were stored as Portable Network Graphics (png) files as binary images. As in the case of the real flocs, the determination of D2 of the virtual flocs projections was carried out through the Fiji BoneJ plugin using the same specifications.
3. Results and discussion 3.1. Microalgal flocs image acquisition and geometric characterisation A first image acquisition set of the raw C. sorokiniana culture without flocculation was carried out. The analysis of the images yielded an average cell diameter of 3.0 µm (SD = 1.5 µm). This average diameter was later used as the primary particle diameter in the simulation of aggregate growth Confocal images of induced flocs obtained at 200, 350 and 500 rpm respectively are shown in Fig. 2. In each flocculation condition, 120 aggregates were considered for further analysis. The MFD and Df of each aggregate
were analysed on each individual floc. Fig. 3 shows a univariate plot depicting the floc MFDs measured on the confocal microscopy images for each experimental condition.
Figure 2. Laser confocal microscopy images of C. sorokiniana flocs induced at 200, 350 and 500 rpm.
Each colour in the graph represents one of the three experimental conditions tested. It can be observed that at the mildest stirring conditions, the majority of flocs, 80 %, lay in the size interval between 90 and 240 µm. When produced at 350 rpm, 80 % of the flocs have MFDs in the size interval between 64 and 158 µm. 80 % of the flocs induced at 500 rpm presented sizes in the interval 42 to 129 µm. The sizes of the 120 flocs measured for each experimental condition were latter used to set the lengths of the computer generated aggregates.
Figure 3. MFD of flocs obtained at different mixing conditions.
D2 of the aggregates for each mixing condition are shown in Fig. 4a as the slope of the lines MFD / Df vs. MFD. The MFD of the flocs induced at lowest speed (transition Reynolds number) are scattered over a much wider interval of lengths than those produced at higher velocities (turbulent Reynolds) and reach values close to 500 µm. The average D2 measured for the 200, 350 and 500 rpm induced flocs were 1.49, 1.40 and 1.31 respectively (SD 0.07, 0.09 and 0.11). These results seem to be consistent with the PFDs observed in other studies employing similar flocculation set-ups in the aggregation of cyanobacteria. Yuheng et al. (2011) observed aggregates of D2 in the interval 1.2 to 1.5 when flocculating Microcystis aeruginosa with dual coagulation and flocculation systems based on AS and PAC at initial G of 500 s-1. Dong et al. (2014) measured D2 values in the Fig. 4a. MFD/ D2 as a function of MFD interval 1.8 to 2.56 in M. aeruginosa flocs induced through a for the three mixing conditions. chitosan-based flocculant at low variable velocity gradients (105.5 -1 and 8.1 s ). Given the small SD observed in D2 for all flocculation conditions, it can be asserted that the flocs are close to monofractality. Fig. 4b depicts D2 as a function of MFD for the three flocculation conditions. In the graph it is possible to observe that D2 increases at larger MFDs in all mixing conditions, being this trend more pronounced in
the flocs induced at lowest speed. The decrease in floc size and D2 with increasing shear rate has been observed elsewhere in the literature, e.g. Chakraborti et al. (2000) and Wyatt et al. (2013).
Fig. 4b. D2 of flocs produced at 200, 350 and 200 rpm vs. MFD.
3.2. Generation and projection of virtual flocs 3D flocs of sizes within the intervals defined by real flocs MFDs and the set tolerance were successfully generated by means of the algorithm described above. As mentioned, 120 flocs were generated resembling the MFDs measured on the real flocs. Fig. 5 depicts three aggregates of different fractal dimension with a size of 430 ± 5 µm.
Df = 1.7
Df = 1.9
Df = 2.1
Figure 5. Virtual aggregates of MFD approximately 430 µm having FD 1.7, 1.9 and 2.1 respectively. .
Likewise, the algorithm to virtually settle the flocs generated was also capable of estimating the maximal pixel surface area of each floc. Fig. 6 shows the projections of a virtual floc (Df 1.7) at three rotation angles that result in three projected areas, minimal, intermediate and maximal.
Minimal area
Intermediate area
Maximal area
Figure 6. Three projections of the same floc resulting in minimal, intermediate and maximal pixel area.
3.3. Projected fractal dimension of the computer generated flocs respectively. In total, 27 groups of flocs corresponding to 9 input fractal dimensions and three MFD distributions (200, 350 and . 500 rpm) were generated and analysed. Fig. 7 depicts the ratio MFD / D2 as a function of MFD for each virtual aggregate generated following the size distributions of the three experimental conditions considered. The slope of each series of points represents the average D2 in each case.
Fig. 7. MFD / D2 as a function of MFD resembling those of the real ones induced at 200, 350 and 500 rpm.
The average D2 measured for each input Df in the three distributions of MFD is presented in table 2. Fig. 8 shows these values in a graphical form. The measured D2 for a given input Df is dependent on the average size of the flocs used as input for the generation of the virtual flocs. At input Df values below 1.6, smaller flocs (those resembling the size distribution of real flocs produced at higher speed) present D2 values closer to the input Df. For values above input Df 1.6, the measured D2 becomes smaller at increasing input Df values. This dependence between D2 and cluster size was also observed by Jullien et al. (1994). The virtual floc populations whose D2 best match the D2 of real flocs induces at 200, 350 and 500 rpm are those having input Df 1.9, 1.7 and 1.4 respectively. MFDD 200 rpm
MFDD 350 rpm
MFDD 500 rpm
Input Df
D2
SD
D2
SD
D2
SD
1.3
1.24
0.04
1.27
0.04
1.29
0.03
1.4
1.29
0.04
1.31
0.04
1.31
0.03
1.5
1.35
0.04
1.37
0.03
1.37
0.04
1.6
1.39
0.04
1.40
0.04
1.39
0.04
1.7
1.41
0.04
1.40
0.04
1.39
0.04
1.8
1.45
0.04
1.44
0.04
1.42
0.05
1.9
1.48
0.04
1.47
0.04
1.44
0.05
2.0
I.S2
0.03
1.50
0.03
1.47
0.05
2.1
1.53
0.04
1.51
0.04
1.48
0.05
Table 2. Average D2 obtained in the projections of virtual flocs of prescribed Df for each size distribution.
Fig. 8. D2 as a function of the input Df for virtual flocs MFDD corresponding to flocs induced at 200, 350 and 500 rpm.
3.4. Conclusions A method to estimate the fractal dimension of microalgal flocs based on confocal laser scanning microscopy imaging and computer simulation was developed. The method is based on constraining the size distribution and average D2 of virtual floc populations so as to resemble those of real flocs. Three flocculation experiments were carried out with Chlorella sorokiniana cultures applying different stirring conditions. The sizes and projected fractal dimensions obtained through the analysis of confocal microscopic images of aggregates yielded values consistent with the literature. In all cases, Df appears to increase at larger floc sizes. The virtual flocs generated through the growth and settling algorithms devised in the study present fractal character and are in agreement with other studies of fractal growth modelling. Population size distribution of generated flocs seems to have a noticeable influence on the measured D2 for all input Df, this trend being more pronounced for Df values over 1.6 in all input distributions. This influence of size appears to resemble the actual nature of real flocs. The method proposed seems to be a good alternative to estimate D f of microalgal flocs resulting from the flocculation of pelagic microalgae when it is not possible to reliably reconstruct the 3D image of their aggregates. The modelling approach followed in the present study could serve as platform for the development of a method to estimate the fractal dimension of microalgal aggregates solely employing size distribution information of flocculated cultures gathered through dynamic laser scattering or laser reflectance by correlating it with size distribution data of virtual aggregates. This could open the way toward devising flocculation systems in which floc geometry and hence, settling velocity, can be on-line controlled through tuning mixing conditions.
Acknowledgments The authors wish to acknowledge the financial support of the Community of Madrid through the RETO-PROSOSTCM Programme (S2013/MAE-2907). The would also like to thank the Centre for Cytometry and Fluorescence Microscopy of the Complutense University of Madrid (CCMF- UCM) for their advice and assistance in the image acquisition process.
References Ahmad, A., N. M. Yasin, C. Derek and J. Lim (2011). "Optimization of microalgae coagulation process using chitosan." Chemical Engineering Journal 173(3): 879-882. Chakraborti, R. K., J. F. Atkinson and J. E. Van Benschoten (2000). "Characterization of alum floc by image analysis." Environmental science & technology 34(18): 3969-3976. Dong, C., W. Chen and C. Liu (2014). "Flocculation of algal cells by amphoteric chitosan-based flocculant." Bioresource technology 170: 239-247. Filippov, A., M. Zurita and D. Rosner (2000). "Fractal-like aggregates: relation between morphology and physical properties." Journal of Colloid and Interface Science 229(1): 261-273. Gorman, D. S. and R. Levine (1965). "Cytochrome f and plastocyanin: their sequence in the photosynthetic electron transport chain of Chlamydomonas reinhardi." Proceedings of the National Academy of Sciences 54(6): 1665-1669. Harshe, Y. M., L. Ehrl and M. Lattuada (2010). "Hydrodynamic properties of rigid fractal aggregates of arbitrary morphology." Journal of colloid and interface science 352(1): 87-98. Jullien, R., R. Thouy and F. Ehrburger-Dolle (1994). "Numerical investigation of two-dimensional projections of random fractal aggregates." Physical Review E 50(5): 3878. Orhan, O., E. Haffner-Staton, A. La Rocca and M. Fay (2016). "Characterisation of flame-generated soot and sootin-oil using electron tomography volume reconstructions and comparison with traditional 2D-TEM measurements." Tribology International 104: 272-284. Schmid, M., A. Thill, U. Purkhold, M. Walcher, J. Y. Bottero, P. Ginestet, P. H. Nielsen, S. Wuertz and M. Wagner (2003). "Characterization of activated sludge flocs by confocal laser scanning microscopy and image analysis." Water research 37(9): 2043-2052. Skorupski, K., J. Mroczka, T. Wriedt and N. Riefler (2014). "A fast and accurate implementation of tunable algorithms used for generation of fractal-like aggregate models." Physica A: Statistical Mechanics and its Applications 404: 106-117. Vandamme, D., I. Foubert and K. Muylaert (2013). "Flocculation as a low-cost method for harvesting microalgae for bulk biomass production." Trends in biotechnology 31(4): 233-239. Wan, C., M. A. Alam, X.-Q. Zhao, X.-Y. Zhang, S.-L. Guo, S.-H. Ho, J.-S. Chang and F.-W. Bai (2015). "Current progress and future prospect of microalgal biomass harvest using various flocculation technologies." Bioresource technology 184: 251-257. Wentzel, M., H. Gorzawski, K.-H. Naumann, H. Saathoff and S. Weinbruch (2003). "Transmission electron microscopical and aerosol dynamical characterization of soot aerosols." Journal of aerosol science 34(10): 13471370. Wyatt, N. B., T. J. O'Hern, B. Shelden, L. G. Hughes and L. A. Mondy (2013). "Size and structure of Chlorella zofingiensis/FeCl3 flocs in a shear flow." Biotechnology and bioengineering 110(12): 3156-3163. Yuheng, W., Z. Shengguang, L. Na and Y. Yixin (2011). "Influences of various aluminum coagulants on algae floc structure, strength and flotation effect." Procedia Environmental Sciences 8: 75-80.
