Four-dimensionalmotilitytracking ofbiological cellsby digital holographicmicroscopyXiao YuJisoo HongChanggeng LiuMichaelCrossDonald T. HaynieMyung K. KimFour-dimensional motility tracking of biological cellsby digital holographic microscopyXiao Yu,a,* Jisoo Hong,aChanggeng Liu,aMichael Cross,bDonald T. Haynie,band Myung K. KimaaUniversity of South Florida, Department of Physics, Digital Holography and Microscopy Laboratory, Tampa, Florida 33620bUniversity of South Florida, Department of Physics, Nanomedicine and Nanobiotechnology Laboratory, Tampa, Florida 33620Abstract. Three-dimensional profiling and tracking by digital holography microscopy (DHM) provide label-freeand quantitative analysis of the characteristics and dynamic processes of objects, since DHM can record real-time data for microscale objects and produce a single hologram containing all the information about their three-dimensional structures. Here, we have utilized DHM to visualize suspended microspheres and microfibers inthreedimensions, andrecordthefour-dimensional trajectories of free-swimmingcells intheabsenceofmechanical focusadjustment. Thedisplacement of microfibersduetointeractionswithcellsinthreespatialdimensions has been measured as a function of time at subsecond and micrometer levels in a direct and straight-forwardmanner. It hasthusbeenshownthat DHMisahighlyefficient andversatilemeansforquantitativetracking and analysis of cell motility. 2014 Society of Photo-Optical Instrumentation Engineers (SPIE) [DOI: 10.1117/1.JBO.19.4.045001]Keywords: digital holography; microscopy; three-dimensional profiling; four-dimensional tracking; microspheres; microfibers; cells.Paper 140025R received Jan. 15, 2014; revised manuscript received Mar. 2, 2014; accepted for publication Mar. 10, 2014; publishedonline Apr. 3, 2014.1 IntroductionMotility is a major characteristic of living cells, and it includesthe form of movement of cells as well as movement within cells.Understanding the origin of cellular or intracellular motility pro-vides information about the functional status of cells. Awide vari-ety of cells, such as fibroblasts, amoeba, etc., move by means ofcrawling over substrate, and cell substrate interactions play a cru-cial role in the migratory behavior of these adhesive cells. A cellmust exert apropulsiveforcetoovercomefrictionandmovealongasurface, andaccuratemeasurementsofthemagnitudeanddirectionof tractionforcesareneededtounderstandcellmotility. Theseforcesareknowntobeabletodeformflexiblesubstrates. Knowledgeofsubstrateelasticity, suchasstiffness,and optical measurement of substrate distortion can then be com-bined to obtain estimates of the traction forces of cells.Digital holography microscopy (DHM) is an emerging tech-nology of a new paradigm in general imaging and biomedicalapplications.1,2Various techniques of DHM, including the quan-titativephasemicroscopybydigital holography(DH-QPM),havebeenproventobepotent toolsfor cellular microscopy.DH-QPM allows measurement of optical thickness with nano-meter-scale accuracy by single shot, wide-field acquisition, andit yieldsphaseprofileswithout someofthecomplicationsofother phase imaging methods. The phase image is immediatelyand directly available on calculating the two-dimensional com-plex array of the holographic image, and the phase profile con-veys quantitative information about the physical thickness andindex of refraction of cells. DH-QPM has been applied to quan-titatively image and analyze living cells in a collagen matrix.3,4Phase profiles of the shape change of cardiomyocytes have beenevaluated to yield quantitative parameters characterizing the celldynamics.5WehaverecentlyutilizedDH-QPMtostudythewrinkling of a silicone rubber film by motile fibroblasts.6Thewrinkle formation has been visualized, quantitative measures ofsurfacedeformationhavebeenextracted, andcellulartractionforce has been estimated in a direct and straightforward manner.A nonwrinkling substrate, collagen-coated polyacrylamide (PAA),was also employed to make direct measurement of elastic defor-mations, albeit at discrete locations.7The Youngs modulus ofPAAcanbeadjustedbycontrollingtheconcentrationsofthemonomer and crosslinker. DH-QPM, with its capacity of yield-ing quantitative measures of deformation directly, has beenemployed to measure the Youngs modulus of PAA,8which pro-vided a very effective process for achieving high-precisionquantitative phase microscopy. When cells are cultured on sub-stratesofidentical chemical propertiesbut different rigidities,theyareabletodetect andrespondtosubstratestiffness byshowing various motility patterns and morphologies.9The sub-strate thengenerates deformationdue tothe tractionforcesexertedbycells. WehaveutilizedDH-QPMtostudymotilefibroblasts deforming PAA gel,10where the cell substrate adhe-sionhasbeen visualizedandquantitativemeasuresofsurfacedeformationhavebeenextracted. Thesubstratestiffnessandquantitative measures of substrate deformation have been com-bined to produce estimates of the traction forces and character-izehowtheseforcesvarydependingonthesubstraterigidity.DH-QPM is thus shown to be an effective approach for meas-uringthe tractionforcesofcellsculturedon elastic substrate.Three-dimensional profiling and tracking by digital hologra-phy provide label-free, quantitative analysis on the characteris-tics and dynamic process of objects. Kempkes et al. have utilizeddigital in-line holography (DIH) to image and analyze short andstraight fibersinsuspensioninathree-dimensional volume.11Microfluidic phenomenahavebeenstudiedbyDIH, andasindicators of theflowpattern, thetrajectories andvelocitiesof latex microspheres and red blood cells have been measuredinthree-dimensional volumeandtime.12Athree-dimensionaldistribution of polystyrene spheres has been obtained by*Address all correspondence to: Xiao Yu, E-mail:xyu4@mail.usf.edu 0091-3286/2014/$25.00 2014SPIEJournal of Biomedical Optics 045001-1 April 2014 Vol. 19(4)Journal of Biomedical Optics 19(4), 045001 (April 2014)deconvolutionof three-dimensional reconstructionof aholo-gram.13Red blood cells and HT-1080 fibrosarcoma cells in a col-lagentissuemodel havebeentrackedinthreedimensionsbyevaluating quantitative phase profiles by DH-QPM.4Three-dimensional localizationofweaklyscatteringobjectsinDHMhasbeenpresentedbyRayleigh-Sommerfeldback-propagationmethod.14Helical trajectories of humanspermwithinalargevolume have been tracked and analyzed by DHM, and the sta-tisticsinformationoftheswimpath, pattern, speed, etc., wererevealed.15In this paper, specimens of suspended polymer microspheresand curved microfibers are visualized in three dimensions; andthe corresponding characteristics are investigated quantitatively.Free-swimmingcells, suchaschilomonas, paramecium, etc.,senseandrespondtotheirsurroundingsbyswimmingtowardorawayfromstimuli. ThesemovingmicrobesaretrackedinthreedimensionsandasafunctionoftimebyDHMwithoutneed for mechanical focus adjustment. Moreover, for a sampleconsists of cells and suspended microfibers, the displacement offibersduetointeractionwithswimmingcellsinthreedimen-sions is monitored by DHM. The main results we are reportinghere are: (1) demonstration of DHM technique for three-dimen-sional profiling of a curved fiber structure. There are few pub-lications of 3-D localization of fibers, and the fibers reported areallshortandstraightsegments.11Wearethefirsttoreportonthree-dimensional localizationof arbitrary-shapedfiber struc-tures; (2)introductionofdifferential holographyasamethodtothree-dimensional orfour-dimensional imagethechangingpositionofamicrobeorfiber. Manygroups12,16haveutilizeddifferential holography method to imaging or tracking par-ticles/cells; however, more complicated structures such as arbi-trary-shaped fibers have not been studied in this method yet; and(3) application of the method to mechanical interaction betweena microbe and fiber. In the study of cell-environment interactionby DHM, the 3-D trajectory of a free-swimming copepod andthe complex flow around it has been performed and polystyrenespheres were seeded as the marker of the flow.17On the otherhand, we are the first to monitor the interaction between a cellandfiber, whichincludes more complicatedstructures. Theeffectiveness of this method is quantified in terms of the maxi-mum number and speed of the moving cells that can be tracked,aswellasthedirectionofthemotion(lateralandaxial). Theresults from this work can be further used to implement an opti-cal trap that can automatically track and capture cells with speci-fied characteristics,suchasspeed, size, orshape.2 ApparatusThe DHM setup used in this work is illustrated in Fig. 1. It con-sists of a MachZehnder interferometer illuminated with a HeNelaser.1,2Theobject armcontainsasamplestageandamicro-scopeobjectivethat projectsamagnifiedimageoftheobjectontoa charge-coupleddevice (CCD) camera. The referencearmsimilarlycontainsMO2, sothat theholographicinterfer-encepatterncontainsfringesduetointerferencebetweenthediffracted object field and the off-axis reference field. Thenumerical apertureof themicroscopeobjectives is 0.25andthe magnification is 10. The specification of CCD is1024 768pixels, andthepixel sizeis4.65 4.65 m2. Thecaptured holographic image is numerically converted intoFourier domain to obtain the angular spectrum1,2and a spatialfilteristhenappliedtoretainthereal imagepeakalone. Thefiltered angular spectrum is propagated to appropriate distance,and by an inverse Fourier transform, reconstructed as an array ofcomplex numbers containing the amplitude and phase images ofthe sample. A background image without objects on the samplestage is first recorded by DHM. In the experiment, aberrationsand background distortions of the optical field are minimized bysubtractingthe backgroundimage.1,2,18,193 Experiments and Results3.1 Three-DimensionalLocalization of SuspendedMicrospheresIn combination with microscopy, DHM is able to produce singlehologram containing all the information about the three-dimen-sional structure of micro-scale objects. In a first experiment, theapplicabilityof DHMandautofocusingalgorithmis investi-gatedbyperformingthree-dimensional profilingof polymermicrospheres (Type 7510A, Duke Scientific Corporation,Palo Alto, California, mean diameter 9.6 m). Figure 2(a)presents the hologram of microspheres in suspension capturedby DHM. Angular spectrummethod1,2is applied and thereconstructed amplitude image is shown in Fig. 2(b) where sev-eral in-focus andout-of-focus microspheres are seenat thisreconstructionplane. Thefieldof viewis 90 90 m2with464 464pixels. The microsphere focuses the incominglight and forms a bright spot along the optical path.Therefore, thepatternof themicrosphereappears tohaveamaximumintensityat thecenter near thein-focusplaneandthe surrounding is dark. Then, an autofocusing algorithmFig. 1DHM setup. Ms: mirrors; BSs: beam splitters; MOs: microscope objectives; S: sample object.Journal of Biomedical Optics 045001-2 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopybased on peak searching can be applied to identify the in-focusposition ofeachparticle.The hologram is numerically reconstructed in longitudinaldirectionZfrom100mto 100m, in 2msteps. Theautofocusingalgorithmis thenappliedbysearchingonthereconstructedimagesfor theplanesthat containtheobjectswith the peak and sharpest details to establish the all-in-focus profile.20At each pixel, the intensity variation in longi-tudinal direction is investigated to find out the peak intensity.The peak intensity value becomes a pixel of an in-focus profileand its location in longitudinal direction is recorded as a cor-responding depth map value. The combination of all-in-focusintensity profiles Fig. 2(c) and the corresponding depthmaps Fig. 2(d) enables to produce the three-dimensionalvisualization of microspheres and a threshold on the intensityallowsfor distinguishingobjectsfromother elements, illus-tratedinFig. 2(e). Infact, wetakeeverycenterpositionofbrightest points in Fig. 2(c) as X-Y locations of particlesandFig. 2(d) is used to determine the Z-locationof thoseparticles identifiedinFig. 2(c). Figure 2(d) is mostly noisyandZinformationof onlythelocations wheretheparticlesare present is actually used. Figures 2(f)2(h) show theXY, XZ, and YZ views of the three-dimensional profile, respec-tively. Thisstraightforwardautofocusingalgorithmisabletodeterminefocalplanesforall theobjectsinthereconstructedvolumeautomatically. Thecombinationof depthmapZandaxial X-Y position of objects allows for quantitative three-dimensionalprofiling.Fig. 2Three-dimensional profiling of suspended microspheres. Field of view of (a)(d) is 90 90 m2with 464 464 pixels. (a) hologram; (b) amplitude image; (c) all-in-focus intensity profile; (d) depth posi-tion profile; (e) three-dimensional profile (90 90 120 m3) and grey-scale representation of intensity;(f) XYview of three-dimensional profile (90 90m2); and (g) XZview of three-dimensional.Journal of Biomedical Optics 045001-3 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopyThe accuracyof this measurement systemwas estimatedusingamicrosphere(2m)fixedonaglassslide.21Aseriesofhologramsofthefixedparticlewasrecordedat10fps, upto8s. Figure3(a)isonehologramofthefixedparticleandFig. 3(b) shows the temporal changes for the measured Z posi-tions of the particle ina stepof 0. 005m. The standarddeviation of the measured Z positions is estimated to be0.039m,which isthe depth accuracy of the system.3.2 Three-DimensionalProfiling of StationaryMicrofibersNonwoven and randomly oriented microfibers were spun ontoglasscoverslipsfromco-poly(L-gluatmicacid4, L-tyrosine1)(PLEY) dissolved in water and crosslinked as described previ-ously.22The diameter of fibers is 0.25.0 m. Figure 4(a)presents a hologram of microfiber. The angular spectrum methodis applied to obtain the reconstructed amplitude image inFig. 4(b). The microfiber appears curved and elongated, consis-tent with our previous work.22The field of view is 90 90m2with 464 464pixels. The hologram is then reconstructed fromZ 100 to 100m, in 1m steps. Adding these 201 recon-structed images of amplitude yields the axial projection shownin Fig. 4(c). The final image has the same number of pixels aseach reconstructed image. The projected image is converted intobinary by threshold and segmentation, shown in Fig. 4(d). Thebinaryimageisthenaxiallyback-projectedalongthepathofamplitudeover the setofreconstructed images.We apply the same autofocusing algorithm on the resultantimagestorecordthemaximumintensityvalueat eachpixelalong thereconstructiondirectionandthe axialXYanddepthpositionZof wherethemaximumintensityoccurredat thesame time. The obtained all-in-focus intensity profile Fig. 4(e)and the corresponding depth map Fig. 4(f) are then combined togenerate the three-dimensional visualization of microfiber and athreshold on intensity is chosen to highlight the area of regionalinterest. However, therestill exist noisypoint cloudsresultedfrom noise in the three-dimensional profile Fig. 4(g). To addressthis, an average and polynomial curve-fitting algorithm account-ing for errors is adopted. The fitted line of the point clouds (stan-dard deviations in the X and Z directions are 0.21 and 0.06 m)in the three-dimensional coordinate is present in Fig. 4(h).Figures 4(i)4(k) showthe XY, XZ, and YZviews of thethree-dimensional profile, respectively. Zcoordinateprovidesthe depth information of real image of microfiber in thereconstructionvolume. Thelengthofthemicrofiberinthree-dimensional volume is determined from X, Y, and Z coordinatesofrealimage ofmicrofiber, that is126m.3.3 Four-Dimensional Motility Tracking of a MovingChilomonas CellChilomonas are fast-moving cells, which sense and respond totheir surroundings by swimming towards or away from stimuli.A time-lapse hologram movie of the movement of chilomonaswasrecordedat 30fps(Video1). Thefieldof viewis 9090m2with 464 464pixels. An excerpt of 14 frames istakenandthedifferencebetweenconsecutivehologrampairsis calculated pixel by pixel h1 h2; h3 h4; : : : hn1 hn toeliminate background structure and retain only the object infor-mation, where hnis the nth hologram of selected frames. Theresulting seven different holograms (from a total of 14) are thensummed h2 h1 h4 h3: : : h13 h14 into a single holo-gramFig.5(a),whichcontainsalltheinformationonmovingcells.16Reconstruction by the angular spectrummethod isapplied on the resultant hologram and Fig. 5(b) is the amplitudeimagereconstructedat the specificplane Z 0.The three-dimensional trajectory of the moving chilomonaswas built up by firstly reconstructing the two-dimensionalresultant hologram from Z 80 to 120m, in 2msteps. The same algorithm of numerical autofocusing is then uti-lized, keeping the maximum intensity value at each pixel in thereconstructed image along Z direction to obtain the all-in-focusintensityprojectionFig. 5(c), andcombiningwiththedepthposition where in-focus intensity occurred Fig. 5(d) to determinethe focal planes for the entire trajectory in the reconstructed vol-ume. A threshold of intensity is applied to eliminate the unnec-essary background, and the center position and the meanintensityof everypoints cloudrepresentingeverytrajectoryof chilomonas are determined. The combination of depth posi-tionsZandXYdisplacement of cellsallowsfor quantitativethree-dimensional motilitytracking. Thecell is estimatedtomove a total path length of 93 m at the velocity of198ms. Figure 5(e) demonstrates the applicability ofDHMfor automatically four-dimensional tracking of livingcells with temporal and spatial resolution at the subsecondandmicrolevel. Figures5(f)5(h)showtheXY, XZ, andYZviews of the three-dimensional trajectory, respectively. It isworth mentioning that cells can change their shape whentheyaremoving, soonehastodefinethepositionsof cellsFig. 3Depth accuracy estimation of a fix particle (2 m). (a) Hologramof the fix particle; (b) Temporal plotof in-focus Zpositions of the particle.Journal of Biomedical Optics 045001-4 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopyto perform the cell tracking. Center of mass can be a reason-able definition of the position of cells, and morphology changesand center of mass methods have been discussed in the litera-tures,suchas (Ref. 23) wherethe cellsreported had asize ofhundreds of micron. On the other hand, in our case, the chilo-monas cell is relatively small and has a more rigid shape, chang-ingof shapeisnotan issuehere.3.4 Three-DimensionalDisplacement of Microfiberby Swimming ParameciumA hologram movie of paramecium moving through a microfib-ersmeshwasrecordedat17fps(Video2).Acellisseentoswim through fibers and cause obvious displacement of fibers.Two hologramframes showing cell approaching to fibersFig. 6(a) andswimmingawayafter pullingfibersFig. 6(b)are extracted. The field of view is 200 200m2with768 768pixels. The different hologramFig. 6(c) clearlyshowsthedisplacementofthefiberduetothemovementofcell andthetrajectoryof cell. Thereconstructedamplitudeimages from angular spectrum method at Z 0 andZ 8mareshowninFigs. 6(d) and6(e), respectively.Different partsofthefiberappeartobeinfocusat differentreconstructed planes. Autofocusing algorithm at thereconstruction volume from Z 60m to 70m is appliedandtheall-in-focusintensityanddepthpositioninformationareobtainedinFigs.6(f)and6(g).Tobest visualize the displacement of the fiber inthree-dimensional volume, we analyze the two tracks of the displace-ment of the fiber independently. For brevity, most of thefollowingdescriptionsrefertothefirst track. Numerical seg-mentation and thresholds are applied to Fig. 6(f) and theFig. 4Three-dimensional profiling of stationary microfibers. The field of view of (a)(f) is 90 90 m2with 464 464 pixels. (a) hologram; (b) amplitude image; (c) projection image; (d) binary image, micro-fiber 1 and background 0; (e) all-in-focus intensity profile; (f) depth position profile; (g) three-dimensionalprofile (90 90 35m3) and gray-scale representation of intensity; (h) three-dimensional fit(90 90 35m3); (i) XYview of three-dimensional fit (90 90m2); (j) XZview of three-dimensionalfit (90 35 m2); and (k) YZview of three-dimensional fit (90 35m2).Journal of Biomedical Optics 045001-5 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopyall-in-focus intensity image containing only one track of fiber isgenerated in Fig. 6(h). Combined with the obtained depth posi-tion profile Fig. 6(g) and fitting algorithm accounting for errors,the fitted line of the point clouds (standard deviations in X andZdirections are 1.27 and 0.27m) in three-dimensional coor-dinate is present in Fig. 6(i). Similar results for the second trackof fiber are showninFigs. 6(j) and6(k) andthe standarddeviation of its corresponding point clouds in the X and Z direc-tions are estimated to be 0.80 and 0.26 m. The two tracks of thefiber are then plotted in one three-dimensional coordinate,Fig. 6(l) and Figs. 6(m)6(o) show the XY, XZ, and YZ viewsof the three-dimensional plot, respectively. The length and thedisplacement of the fiber are estimated to be 210.1 and 11.1 m.A movie of three-dimensional displacement of the fiber within0.5 s period is also presented (Video 3). The three-dimensionaldisplacement of an individual microfiber due to interaction withparamecium cell has been measured as a function of time at sub-second andmicrometerlevel.Fig. 5Four-dimensional tracking of a moving chilomonas cell (Video 1, MOV, 188 KB) [URL: http://dx.doi.org/10.1117/1.JBO.19.4.045001.1].Thefieldof viewof (a)(d)is90 90m2with464 464 pixels.(a) difference hologram; (b) amplitude image; (c) all-in-focus intensity profile; (d) depth position profile;(e) three-dimensional profile of the trajectory of the cell (90 90 90 m2) and gray-scale representationof intensity. (f) XYview of three-dimensional trajectory (90 90m2); (g) XZview of three-dimensionaltrajectory (90 200 m2); and (h) YZview of three-dimensional trajectory (90 90 m2).Journal of Biomedical Optics 045001-6 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopyFig. 6Three-dimensional displacement of microfiber by swimming paramecium (Video 2, MOV, 384 KB)[URL: http://dx.doi.org/10.1117/1.JBO.19.4.045001.2]. The field of view of (a)(h) and (j) is 200200 m2with 768 768 pixels. (a) hologram1; (b) hologram2; (c) difference of holograms 1 and 2; (d) ampli-tudereconstructedat Z 0; (e) amplitudereconstructedat Z 8 m; (f)all-in-focusintensityprofile;(g) depth position profile; (h) all-in-focus intensity of the first track of the displacement of fiber; (i) three-dimen-sional fitted line of (h) (200 200 20 m3); (j) All-in-focus intensity of the second track of the displacementof fiber; (k) three-dimensional fitted line of (j) (200 200 20 m3); (l) three-dimensional fitted line of thedisplacement of fiber (200 200 20 m3) (Video 3, MOV, 64 KB) [URL: http://dx.doi.org/10.1117/1.JBO.19.4.045001.3]); (m)XYviewof (l)(200 200 m2); (n)XZviewof (l)(200 20m2); and(o)YZview of (l) (200 20m2). For better visualization, the scales of X-Yand Zcoordinates are not in ratio.Journal of Biomedical Optics 045001-7 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopyTothebest ofourknowledge, thisisthefirst quantitativeprofiling and tracking by DHM of the curvature and displace-ment of individual microfiber by swimming cells in three dimen-sions. Displacement couldvarywithcell type, physiologicalstate of the cells, microfiber preparation, etc. Theprospectsseemexcellent forDHMforparticleflowanalysisandthree-dimensional imaging of randomly oriented microfibers, incaseswherequantitativemeasurement ofcharacteristics(size,length, orientation, speed, anddisplacement, etc.) isof greatinterest.4 ConclusionsDHM has been applied to imagesuspended microspheresandstationary microfibers in three dimensions, track motility of cellsand monitor the displacement of fibers due to interaction withswimming cells in four dimensions. The three-dimensional posi-tions of objects have been determined subsequently from recon-structedhologramsbyautofocusingalgorithmbasedonpeaksearching along the reconstruction direction. The techniqueopens up new perspectives for DHM in biological cells imaging.The approach is sensitive to cellular motility and can be appliedin the field of label-free, noninvasive, dynamic 3-D cells migra-tion analysis without mechanical realignment. It can detect andquantify cellular motility and characteristics over time. DHM isshown to be an effective approach to study motility of biologicalcells with temporal and spatial resolution at the subsecond andmicrometer level. In the future work, we are going to apply thismethod to study how crawling cells move through fiber junglesin four dimensions and quantify how traction forces vary due totheenvironment. Thiswill provideanovel imagingofthree-dimensional profiles of cellular motility and reveals the dynamicprocessin biologicalaspects.AcknowledgmentsThis research was supported in part by the National EyeInstitute of the National Institutes of Health under AwardNo.R21EY021876.References1. M. K. Kim, Principles and techniques of digital holographic micros-copy, SPIE Reviews 1, 150 (2010).2. M.K.Kim,DigitalHolographicMicroscopyPrinciples,Techniques,and Applications, Springer Series in Optical Sciences, NewYork,Vol. 162 (2011).3. F. Dubois et al., Digital holographic microscopy for the three-dimen-sional dynamic analysis of in vitro cancer cell migration,J.Biomed.Opt. 11(5), 054032 (2006).4. P. Langehanenberg et al., Automated three-dimensional tracking of liv-ingcellsbydigital holographicmicroscopy,J. Biomed. Opt. 14(1),014018 (2009).5. N. T. Shaked et al., Whole-cell-analysis of live cardiomyocytes usingwide-fieldinterferometricphasemicroscopy,Biomed. Opt. Express1(2), 706719 (2010).6. X. Yuet al., Measurement of thetractionforceof biological cellsby digital holography, Biomed. Opt. Express 3(1), 153159(2012).7. M. Dembo and Y. L. Wang, Stresses at the cell-to-substrate interfaceduring locomotion of fibroblasts, Biophys. J. 76(4), 23072316(1999).8. X. Yu et al., Measurement of Youngs Modulus of Polyacrylamide Gelby Digital Holography, in Digital Holography and Three-DimensionalImaging, OSATechinal Digest (CD), OSA, Washington, DC, paperDTuC32 (2011).9. R. J. Pelham, Jr. and Y. L. Wang, Cell locomotion and focal adhesionsare regulated by substrate flexibility, Proc. Natl. Acad. Sci. USA94(25), 1366113665 (1997).10. X. Yu et al., Quantitative imaging and measurement of cell-substratesurface deformation by digital holography, J. of Modern Opt. 59(18),15911598 (2012).11. M. Kempkes et al., Three dimensional digital holographic profiling ofmicro-fibers,Opt. Express 17(4), 29382943 (2009).12. J. Garcia-Sucerquia et al., 4D imaging of fluid flow with digital in-lineholographic microscopy,Optik 119(9), 419423 (2008).13. T. Latychevskaia, F. Gehri, and H. Fink, Depth-resolved holographicreconstructions by three-dimensional deconvolution, Opt. Express18(21), 2252722544 (2010).14. L. Wilson and R. Zhang, 3D localization of weak scatterers in digitalholographic microscopy using Rayleigh-Sommerfeld back-propaga-tion,Opt. Express 20(15), 1673516744 (2012).15. T.W. Su, L. Xue, and A. Ozcan, High-throughput lensfree 3D trackingofhumanspermsrevealsrarestatisticsofhelical trajectories,Proc.Natl. Acad. Sci. USA 109(40), 1601816022 (2012).16. W. Xu et al., Tracking particles in four dimensions with in-line holo-graphic microscopy, Opt. Lett. 28(3), 164166 (2003).17. E. Malkiel et al., The three-dimensional flow field generated by a feed-ing calanoid copepod measured using digital holography, J. Exp. Biol.206(Pt 20), 36573666 (2003).18. P. Ferraro et al., Compensation of the inherent wave front curvature indigital holographic coherent microscopy for quantitative phase-contrastimaging, Appl. Opt. 42(11), 19381946 (2003).19. T. Colomb et al., Numerical parametric lens for shifting, magnification,andcompleteaberrationcompensationindigital holographicmicros-copy, J.Opt. Soc. Am. A 23(12), 31773190 (2006).20. J.F.RestrepoandJ.Garcia-Sucerquia, Automaticthree-dimensionaltracking of particles with high-numerical-aperture digital lensless holo-graphic microscopy, Opt. Lett. 37(4), 752754 (2012).21. A. Sato et al., Three-dimensional subpixel estimation in holographicposition measurement of an optically trapped nanoparticle, Appl. Opt.52(1), A216A222 (2013).22. D. T. Haynie, D. B. Khadka, and M. C. Cross, Physical properties ofpolypeptide electrospun nanofiber cellculture scaffoldson a wettablesubstrate,Polymers 4(3), 5351553 (2012).23. P.Memmoloetal., Ontheholographic 3Dtracking of in vitrocellscharacterized by a highly-morphological change, Opt. Express20(27), 2848528493 (2012).Xiao Yu received her BSc degree in physics from Nankai University,Tianjin, China, in 2008, and an MSc degree in applied physics fromthe University of South Florida, Tampa, Florida, in 2010. She is cur-rently working toward a PhDdegree at University of South Florida. Hermainresearchinterestsaredigital holographicmicroscopyanditsapplications in the biological field, biomedical imaging, digitalimage processing, etc.Jisoo Hong received his BS and MS degrees in electrical engineeringfrom Seoul National University, Republic of Korea, in 2002 and 2004,respectively. From 2004 to 2008, he was a senior research engineerwithLGElectronics, Korea. InAugust 2012, hereceivedhisPhDdegree from his alma mater. Presently, he is a postdoctoral researcherin the Department of Physics at the University of South Florida, Tampa,Florida. He is interested in incoherent digital holography and its appli-cation to biomedical imaging and three-dimensional (3-D) photography.Changgeng Liu obtained his BS degree in applied physics in 2007andanMSdegreeinopticsfromBeijingUniversityof Technology,Beijing, China, in2010. HeiscurrentlyseekingaPhDdegreeinapplied physics in at the University of South Florida, Tampa,Florida. Hisresearchinterestsincludedigital holography, adaptiveoptics, biomedical imaging, computational optics, phase retrieval, dig-ital imaging processing, and optical systems design.Michael Cross received his Sc degree in computer science from theUniversity of Texas at San Antonio, Texas, in 2005. He is presentlypursuing a PhD degree in applied physics at the University of SouthFlorida, Tampa, Florida. His research interests are atomic forcemicroscopy,laser-scanningconfocal microscopy,andtheirapplica-tions to biomedical engineering and biomaterials.Journal of Biomedical Optics 045001-8 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopyDonaldT. HayniejoinedUSFphysicsin2009, havingbeenvicepresident of research and development at Artificial CellTechnologies Inc., New Haven, Connecticut. He holds a PhD degreeinbiophysicsfromJohnsHopkinsUniversity, Baltimore, Maryland,and he was an NSF postdoctoral fellow at Oxford University,Wellington Square, Oxford. He heads the Nanomedicine andNanobiotechnologyLaboratory. Current researchinterestsincludepolypeptidematerials, cell interactionswithpolypeptidematerials,and molecular mechanisms of cell adhesion and migration.Myung K. Kim is a professor of physics at the USF, and directs theDigital Holography and Microscopy Laboratory. He received his PhDdegree fromthe University of California, Berkeley, in 1986. His currentresearchinterestsareinthedevelopment of novel techniquesandapplications in digital holography, microscopy, interference imaging,optical tomography, biomedical imaging, and manipulation of particlesand microbes by optical force. He has more than 200 publications and13 patents granted or pending.Journal of Biomedical Optics 045001-9 April 2014 Vol. 19(4)Yu et al.: Four-dimensional motility tracking of biological cells by digital holographic microscopy