Digital Holography (DH) in microscopic configuration is a powerful tool for the imaging of micro-objects contained into a three dimensional (3D) volume, by a single-shot image acquisition. Many studies report on the ability of DH to track particle, microorganism and cells in 3D. However, very few investigations are performed with objects that change severely their morphology during the observation period. Here we study DH as a tool for 3D tracking an osteosarcoma cell line for which extensive changes in cell morphology are associated to cell motion. Due to the great unpredictable morphological change, retrieving cell’s position in 3D can become a complicated issue. We investigate and discuss in this paper how the tridimensional position can be affected by the continuous change of the cells. Moreover we propose and test some strategies to afford the problems and compare it with others approaches. Finally, results on the 3D tracking and comments are reported and illustrated.
© 2012 OSA
Precise tracking of cells in 3D environments is of great importance in diverse biologic and bio-technologic contexts. 3D cell migration is indeed crucial in embryo morphogenesis , immunology  and tumor progression . Moreover, characterizing migration in 3D matrices might be beneficial for the development of more effective prostheses or scaffolds. Migration has been widely studied and characterized in two-dimensional setups, by means of optical microscopy [4, 5]. Cells, however, display a very different behavior when seeded in 3D matrices like collagen, fibrin or cell derived matrix. Yet, many authors describe 3D cell migration by considering the projection of cell displacements on the focal plane, which might differ considerably from a 3D analysis, especially when long “out-of-focus” displacements occur. Other methods reported so far to track cells in 3D aim at finding the focus of moving cells thus readjusting the focus position at each time point . Few drawbacks might be associated to this operation. Firstly, it requires continuous real-time mechanical displacements of the imaging lens or a time-consuming scanning along the optical axis with the aim to extract the so-called Extended Focus Image (EFI). Secondly, this method might fail when many objects, at different foci, appears in the same field of view. Through DH, it is possible to reconstruct numerically the complex optical wavefront and thus numerical focusing at various distances [7–10]. Instead, the position of each cell is detected by calculating the center of mass of the cell, usually in the quantitative phase-contrast map. This might be an easy task in the case of cells cultivated on flat surfaces, on which they display a characteristic spread morphology and major changes of this (extension/retraction) occur in the time frame of tens of minutes. In 3D environments, cells possess a spindle like morphology in which highly dynamic membrane processes are continuously projected out cell body in order to scan the pericellular environment eventually forming new adhesions . Such a dynamic morphology might hamper the assessment of cell position as well as the estimation of its dimensions, that typically are about few microns. Here we investigate an discuss this problematic issue of accurate 3D tracking of an osteosarcoma cell line for which extensive changes in cell morphology are associated to cell motion. However it depends on morphological changes. We also propose some novel strategies and approaches to afford the problem. In particular we tested for the first time a novel approach for estimating the depth coordinate along the optical axis and furthermore we defined established and tested a new strategies for finding transverse coordinate. Comparison with others approaches have been performed and results are discussed.
2. Experimental set-up
The 3D tracking of the osteosarcoma cells in a gelified collagen matrix was performed experimentally by a transmission holographic microscope, based on optical fiber Mach-Zender configuration. The light source is a DPSS laser (150 mW at a wavelength of 532 nm) whose beam is coupled to an optical fiber. The fiber splits the incoming laser light into two beams, (object-beam and reference-beam) by using a fiber splitter (FS) as shown in the optical set-up in Fig. 1 .
The object-beam impinges on the sample and then is collected by a 10x microscope objective (MO) that provides a focused image on the “image-plane” (IP). The sample is contained inside a micro-incubator (MI) to control both temperature and CO2. A Charge Coupled Device (CCD) camera (1280x1024 square pixels; pixel size: 6.7 μm), is placed at a proper distance from the “image-plane” produced by the imaging microscope objective (MO) objective. Through a beam-splitter (BS), the CCD plane (i.e. the holographic plane, HP) collects both an out-of-focus image of the sample and the reference-beam. On the CCD plane, an interference-pattern (hologram) is generated by the optical interference between the object-beam and the reference-beam. The interference pattern recorded by the CCD contains information about the amplitude as well as the phase of the transmitted wavefront. Time-lapse sequences have been acquired with a frame interval of 5 minutes, for 15 hours total time in order to capture any movements and/or morphological changes of the cells during the experiment. The numerical processing of the hologram allows to evaluating both intensity and phase distribution in each plane between the hologram plane and the image plane.
3. Sample preparation
The MG63 osteosarcoma cell line  was cultured in Dulbecco’s modified Eagle medium (DMEM) supplemented with 10% fetal bovine serum (FBS) (Biowittaker, Walkersville, MD, USA), 2mM L-glutamine, 100 U/ml penicillin, and 0,1 mg/ml streptomycin (Sigma, St. Louis, MO, USA). MG63 were cultivated in reconstituted bovine collagen gel (Sigma Aldrich St. Louis MO, USA) that was prepared following manufacturer’s procedure. Briefly, 1 part of 10X DMEM (Gibco, Life Technologies) and 10mM Hepes  (EuroClone) were mixed with 8 parts of collagen (stock solution: 3 mg/ml). The pH of mixture were adjusted to 7.2 adding 0.1 M NaOH. The resulting collagen solution (2.4 mg/ml), was gently mixed with the cells and allowed to gelify for approximately 40 minutes at 37°C, 5% CO2.
4. Approach for detecting the coordinates of the cells
If we consider a coordinate reference volume where XY is the transverse plane while Z is the optical axis of the imaging systems, then the typical approach adopted in DH for the tracking of living cells [14–16] consists into estimate the location in 3D, i.e. estimating the X,Y,Z coordinates of the particle by following three conceptual steps:
- • Detection of cells, i.e. identification of the cell from the phase-contrast map.
- • Estimation of X,Y coordinates are instead determined by the phase reconstruction computed at distance d = Z, i.e. using the Z value computed in the previous step.
Of course different strategies or algorithms have been proposed and can be found in literature for each of the above steps.
4.1 Cell detection
In our investigation, the cell detection is achieved with a simple thresholding filter applied on the phase-contrast map, reconstructed numerically by the digital hologram at the nominal distance, given in the recording step, as shown in Fig. 2 .
For each detected cell, we use a different color label. Note that a first problem to face with is the fact that detection errors occur when there is a spatial superimposition between two or more cells.
4.2 Estimation of the focal plane
About the estimation of the focal plane, autofocus approaches were developed in DH for phase contrast microscopy on pure phase objects for live-cell imaging [17, 19]. There are several algorithms that have been adopted to estimate the in-focus distance [17, 19–21], based on the cumulated edge detection, to quantify the image sharpness of the amplitude reconstructions. The choice of the better shape measurement for automatic focus detection is challenging, because is strongly related to the quality, i.e. the noise, of digital recording . However, in  it was proposed, as a measure of image contrast, an approximation of the Tamura coefficient, defined by7] demonstrated very good performance, it was investigated only on reconstructed amplitude images of strongly macroscopic scattering objects. Here we investigated for the first time the algorithm proposed in  for analysis of pure phase-objects and by applying it to phase-contrast maps. This coefficient has the intrinsic advantage of finding a single focus-value without ambiguity in the entire reconstruction volume. Finally, the recovery of the in-focus distance is obtained solving the following optimization problem:Eq. (1), in which the image I is a suitable region of interest (ROI), extracted by the amplitude reconstruction, calculated at distance d, that contain the cell under analysis. The effectiveness of the estimation of dfoc is related principally to the signal to noise ratio in the ROI. In our experiment, we investigated the algorithm based on Tamura’s coefficient with very good results, confirming its usefulness also in case of phase objects as the cells. As example, the estimated in-focus distance for the cell B, labeled in the Fig. 1(b), is reported in Fig. 3 . The horizontal axis in Fig. 3 represents the Z-axis. The estimated focus distance is the actual position of the cell in respect to the middle plane of the sample volume, indicated by d = 0. It is clearly confirmed that in this case the algorithm is able to recover without ambiguity the right in-focus distance opening the way for a fully automated procedure, when a ROI has been correctly identified and selected. In fact the curve in Fig. 3 present just one minimum.
4.3 Estimation of the (X,Y) coordinates
For what concerns the third step, the estimation of the (X,Y) coordinates of the cell under investigation can be performed through the phase map reconstruction computed at the estimated distance dfoc, obtained by the solution of Eq. (2). Several approaches can be considered. In  the authors use the maximum phase contrast value as a detection of lateral cell displacements. In this case the problem of the (X,Y) estimation is principally related to the presence of noise, that corrupt all values of the phase map. In  was used the centroid method, that is a robust, accurate, and fast technique, widely accepted, but the underlying assumption of the method is that the image is circularly symmetric. However, it performs better than maximum phase contrast value in the presence of high noise because it is calculated on a binary map obtained from the phase reconstruction. A generalization of the centroid method is the weighted centroid method, i.e. the center of mass, that is used for example in . In another strategy  the movement of the cells from one image to the next was measured using a correlation coefficient between each pair of cells images, under the assumption that the Z variation between two subsequent frames is negligible. It is worth to underline that is not possible to determine which strategy is the best between the aforementioned methods, because the knowledge of the exact location of the cell to be tracked should be known. However, since the computation of the (X,Y) position of a cell is mainly influenced by the level of noise and by morphological changes, we investigate on which technique appears to be the most robust with respect these two aspect. In addition, we propose a strategy for the (X,Y) estimation that takes into account both noise and morphological variations.
First of all, we try to minimize the contribution of the noise on the phase maps using a novel denoising method described in . In this way, the techniques mostly depended on the noise, like maximum phase contrast value and the weighted centroid, that use the phase map values, are put in a better condition for the estimation of (X,Y) position. Instead, the other aforementioned techniques, i.e. the centroid method and the correlation coefficient-based strategy, are principally influenced by morphological changes during the cell motility. In fact, during the migration, the cells can change their morphology without really change the 3D position. In this case, since the centroid method is based on the filtered image in the ROI, the morphological modification without real movement can be produce a different centroid, with a significant error in the 3D tracking. For the same reason, in the correlation coefficient-based method, the maximum value of correlation function, that determine the estimated position, may be in the wrong position. Our idea tries to combine the advantages of these methods in respect to both the noise and the morphological variations introducing the concept of Minimum Boundary Filters (MBF). Our method is described by the following steps.
- • Let consider the ROIs containing the cell under analysis in the frames k and k-1.
- • For both ROIs, computes the thresholding filters used in the centroid method, and the weighted centroids.
- • Translates the (k-1)-th filter on the k-th filter by superimposing the corresponding weighted centroids.
- • The MBF is obtained filtering the result of the last superimposition. The centroid of this new image is the estimated position of the cell.
Obviously, our strategy assumes that the Z variation between two subsequent frames is negligible, like in the correction coefficient-based method.
We report in Fig. 4 an example of morphological changes for the three cells under analysis during the migration, and in Fig. 5 the MBF computed at the 22nd frame of the sequence under analysis for the three cells labeled in Fig. 1(b).
The Fig. 5(d) shows that the MBF is very close to the superimposed filters in Fig. 5(a). This means that the cell not had great morphological changes with respect the previous frame. Same situation appears in the Fig. 5(c), 5(f). Instead in Fig. 5(b) is clear that the cell has changed its morphology. Thanks to its MBF, reported in Fig. 4(e), we don’t take this change in the computation of the XY positions. Finally, in order to test our procedure of estimation of 3D positions, and to compare it with other strategies, i.e. centroid, weighted centroid and maximum phase value, we report in Figs. 6 ,7 ,8 the trajectories obtained using the aforementioned methods. For all cases, we use the Tamura coefficient, reported in Eq. (1), for the estimation of in-focus distance.
Observing the Figs. 6,7,8 and the corresponding movies Media 1, Media 2 and Media 3, we can say that the maximum phase value-based method is very unstable compared to the others. Considering the stability as a performance parameter, also we can say that the weighted centroid method and the MBF appear the most efficient. However, as shown in Fig. 7(a), a morphological variation between the current frame and the previous one, produces very different results in the estimation of the positions between the different methods. We assert that MBF seems like a good estimation strategy because it is an algorithm built specifically to take into account the morphological variation between two subsequent frames.
5. Discussion and conclusion
We have investigated some critical issues related to 3D tracking of in vitro cells in case of large morphological changes. We test for the first time Tamura approach to phase objects to determine the Z coordinate, thus showing unambiguous detection on focus positions of each cell. In addition we identified a new strategies to take into account the morphological changes by introducing the concept of Minimum Boundary Filters (MBF). On the basis of differences reported in the present investigation, as resulted by comparing the four different approaches, it is clear that great discrepancies can be obtained. It means that the choice of the right approach is not easy to make a priori but depends on the specific situation. Due to the uncertainties connected with this important issue in 3D tracking, it is important to tailor and find strategies that can be adapted to the specific problem, that in this case are the morphological changes.
This work is supported by the Progetto Operativo Nazionale (PON) project MONitoraggio Innovativo per le Coste e l'Ambiente Marino (MONICA) funded by Italian Ministry of Education, University and Research (MIUR).
References and links
2. E. Van Goethem, R. Poincloux, F. Gauffre, I. Maridonneau-Parini, and V. Le Cabec, “Matrix architecture dictates three-dimensional migration modes of human macrophages: differential involvement of proteases and podosome-like structures,” J. Immunol. 184(2), 1049–1061 (2010). [CrossRef] [PubMed]
4. D. Guarnieri, A. De Capua, M. Ventre, A. Borzacchiello, C. Pedone, D. Marasco, M. Ruvo, and P. A. Netti, “Covalently immobilized RGD gradient on PEG hydrogel scaffold influences cell migration parameters,” Acta Biomater. 6(7), 2532–2539 (2010). [CrossRef] [PubMed]
5. M. Ventre, F. Valle, M. Bianchi, F. Biscarini, and P. A. Netti, “Cell fluidics: producing cellular streams on micropatterned synthetic surfaces,” Langmuir 28(1), 714–721 (2012). [CrossRef] [PubMed]
6. Z. N. Demou and L. V. McIntire, “Fully automated three-dimensional tracking of cancer cells in collagen gels: determination of motility phenotypes at the cellular level,” Cancer Res. 62(18), 5301–5307 (2002). [PubMed]
7. P. Memmolo, C. Distante, M. Paturzo, A. Finizio, P. Ferraro, and B. Javidi, “Automatic focusing in digital holography and its application to stretched holograms,” Opt. Lett. 36(10), 1945–1947 (2011). [CrossRef] [PubMed]
9. C. P. McElhinney, B. M. Hennelly, and T. J. Naughton, “Extended focused imaging for digital holograms of macroscopic three-dimensional objects,” Appl. Opt. 47(19), D71–D79 (2008). [CrossRef] [PubMed]
10. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14(13), 5895–5908 (2006). [CrossRef] [PubMed]
12. R. T. Franceschi, W. M. James, and G. Zerlauth, “1 alpha, 25-dihydroxyvitamin D3 specific regulation of growth, morphology, and fibronectin in a human osteosarcoma cell line,” J. Cell. Physiol. 123(3), 401–409 (1985). [CrossRef] [PubMed]
13. K. Schumacher, R. Strehl, U. de Vries, and W. W. Minuth, “Advanced technique for long term culture of epithelia in a continuous luminal-basal medium gradient,” Biomaterials 23(3), 805–815 (2002). [CrossRef] [PubMed]
14. P. Langehanenberg, L. Ivanova, I. Bernhardt, S. Ketelhut, A. Vollmer, D. Dirksen, G. Georgiev, G. von Bally, and B. Kemper, “Automated three-dimensional tracking of living cells by digital holographic microscopy,” J. Biomed. Opt. 14(1), 014018 (2009). [CrossRef] [PubMed]
15. J. Persson, A. Mölder, S. G. Pettersson, and K. Alm, “Cell motility studies using digital holographic microscopy,” in Microscopy: Science, Technology, Applications and Education. Microscopy Series4, 1063–1072 (2010).
16. P. Memmolo, A. Finizio, M. Paturzo, L. Miccio, and P. Ferraro, “Twin-beams digital holography for 3D tracking and quantitative phase-contrast microscopy in microfluidics,” Opt. Express 19(25), 25833–25842 (2011). [CrossRef] [PubMed]
17. F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14(13), 5895–5908 (2006). [CrossRef] [PubMed]
18. A. El Mallahi and F. Dubois, “Dependency and precision of the refocusing criterion based on amplitude analysis in digital holographic microscopy,” Opt. Express 19(7), 6684–6698 (2011). [CrossRef] [PubMed]
19. P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt. 47(19), D176–D182 (2008). [CrossRef] [PubMed]
20. S. Lee, J. Y. Lee, W. Yang, and D. Y. Kim, “Autofocusing and edge detection schemes in cell volume measurements with quantitative phase microscopy,” Opt. Express 17(8), 6476–6486 (2009). [CrossRef] [PubMed]
22. J. F. Restrepo and J. Garcia-Sucerquia, “Automatic three-dimensional tracking of particles with high-numerical-aperture digital lensless holographic microscopy,” Opt. Lett. 37(4), 752–754 (2012). [CrossRef] [PubMed]
23. P. Memmolo, I. Esnaola, A. Finizio, M. Paturzo, P. Ferraro, and A. M. Tulino, “SPADEDH: a sparsity-based denoising method of digital holograms without knowing the noise statistics,” Opt. Express 20(15), 17250–17257 (2012). [CrossRef]