Abstract
Digital volume correlation (DVC), the three-dimensional (3D) extension of digital image correlation (DIC), measures internal 3D material displacement fields by correlating intensity patterns within interrogation windows. In recent years DVC algorithms have gained increased attention in experimental mechanics, material science, and biomechanics. In particular, the application of DVC algorithms to quantify cell-induced material deformations has generated a demand for user-friendly, and computationally efficient DVC approaches capable of detecting large, non-linear deformation fields. We address these challenges by presenting a fast iterative digital volume correlation method (FIDVC), which can be run on a personal computer with computation times on the order of 1–2 min. The FIDVC algorithm employs a unique deformation-warping scheme capable of capturing any general non-linear finite deformation. The validation of the FIDVC algorithm shows that our technique provides a unique, fast and effective experimental approach for measuring non-linear 3D deformations with high spatial resolution.
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References
Maskarinec SA, Franck C, Tirrell DA, Ravichandran G (2009) Quantifying cellular traction forces in three dimensions. Proc Natl Acad Sci U S A 106(52):22108–22113. doi:10.1073/pnas.0904565106
Bay BK, Smith TS, Fyhrie DP, Saad M (1999) Digital volume correlation: three-dimensional strain mapping using X-ray tomography. Exp Mech 39(3):217–226. doi:10.1007/BF02323555
Smith TS, Bay BK, Rashid MM (2002) Digital volume correlation including rotational degrees of freedom during minimization. Exp Mech 42(3):272–278. doi:10.1007/BF02410982
Franck C, Hong S, Maskarinec SA, Tirrell DA, Ravichandran G (2007) Three-dimensional full-field measurements of large deformations in soft materials using confocal microscopy and digital volume correlation. Exp Mech 47(3):427–438. doi:10.1007/s11340-007-9037-9
Gates M, Lambros J, Heath MT (2011) Towards high performance digital volume correlation. Exp Mech 51(4):491–507. doi:10.1007/s11340-010-9445-0
Sutton MA, Wolters WJ, Peters WH, Ranson WF, McNeill SR (1983) Determination of displacements using an improved digital correlation method. Image Vis Comput 1(3):133–139. doi:10.1016/0262-8856(83)90064-1
Sutton MA, Mingqi C, Peters WH, Chao YJ, McNeill SR (1986) Application of an optimized digital correlation method to planar deformation analysis. Image Vis Comput 4(3):143–150. doi:10.1016/0262-8856(86)90057-0
Bruck HA, McNeill SR, Sutton MA, Peters WH (1989) Digital image correlation using Newton-Raphson method of partial differential correction. Exp Mech 29(3):261–267. doi:10.1007/BF02321405
Leclerc H, Périé J-N, Roux S, Hild F (2010) Voxel-scale digital volume correlation. Exp Mech 51(4):479–490. doi:10.1007/s11340-010-9407-6
Pan B, Wu D, Wang Z (2012) Internal displacement and strain measurement using digital volume correlation: a least-squares framework. Meas Sci Technol 23(4):045002. doi:10.1088/0957-0233/23/4/045002
Dembo M, Wang YL (1999) Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys J 76(4):2307–2316. doi:10.1016/S0006-3495(99)77386-8
Lo CM, Wang HB, Dembo M, Wang YL (2000) Cell movement is guided by the rigidity of the substrate. Biophys J 79(1):144–152. doi:10.1016/S0006-3495(00)76279-5
Sabass B, Gardel ML, Waterman CM, Schwarz US (2008) High resolution traction force microscopy based on experimental and computational advances. Biophys J 94(1):207–220. doi:10.1529/biophysj.107.113670
Franck C, Maskarinec SA, Tirrell DA, Ravichandran G (2011) Three-dimensional traction force microscopy: a new tool for quantifying cell-matrix interactions. PLoS One 6(3):e17833. doi:10.1371/journal.pone.0017833
Notbohm J, Kim J-H, Asthagiri AR, Ravichandran G (2012) Three-dimensional analysis of the effect of epidermal growth factor on cell-cell adhesion in epithelial cell clusters. Biophys J 102(6):1323–1330. doi:10.1016/j.bpj.2012.02.016
Soria J (1996) An investigation of the near wake of a circular cylinder using a video-based digital cross-correlation particle image velocimetry technique. Exp Thermal Fluid Sci 12(2):221–233. doi:10.1016/0894-1777(95)00086-0
Scarano F, Riethmuller ML (2000) Advances in iterative multigrid PIV image processing. Exp Fluids 29(7):S051–S060. doi:10.1007/s003480070007
Schrijer FFJ, Scarano F (2006) On the stabilization and spatial resolution of iterative PIV interrogation. In: 13th International Symposium Applied Laser Techniques to Fluid Mechanics Lisbon, Portuguesa
Benoit A, Guérard S, Gillet B, Guillot G, Hild F, Mitton D, Périé J, Roux S (2009) 3D analysis from micro-MRI during in situ compression on cancellous bone. J Biomech 42(14):2381–2386. doi:10.1016/j.jbiomech.2009.06.034
Sutton MA, Orteu JJ, Schreier H (2009) Image correlation for shape, motion and deformation measurements. Springer, New York
Verhulp E, van Rietbergen B, Huiskes R (2003) A three-dimensional digital image correlation technique for strain measurements in microstructures. J Biomech 37(9):1313–1320. doi:10.1016/j.jbiomech.2003.12.036
Hu Z, Xie H, Lu J, Hua T, Zhu J (2010) Study of the performance of different subpixel image correlation methods in 3D digital image correlation. Appl Opt 49(21):4044–4051. doi:10.1364/AO.49.004044
Huang J, Pan X, Li S, Peng X, Xiong C, Fang J (2011) A digital volume correlation technique for 3-D deformation measurements of soft gels. Int J Appl. Mech 3(2):335–354. doi:10.1142/S1758825111001019
Huang J, Pan X, Peng X, Yuan Y, Xiong C, Fang J, Yuan F (2012) Digital image correlation with self-adaptive gaussian windows. Exp Mech 53:505–512. doi:10.1007/s11340-012-9639-8
Nogueira J, Lecuona A, Rodríguez PA (2001) Local field correction PIV, implemented by means of simple algorithms, and multigrid versions. Meas Sci Technol 12(11):1911–1921. doi:10.1088/0957-0233/12/11/321
Nogueira J, Lecuona A, Rodríguez PA (1999) Local field correction PIV: on the increase of accuracy of digital PIV systems. Exp Fluids 27:107–116. doi:10.1007/s003480050335
Nogueira J, Lecuona A, Rodríguez PA, Alfaro JA, Acosta A (2005) Limits on the resolution of correlation PIV iterative methods. Practical implementation and design of weighting functions. Exp Fluids 39(2):314–321. doi:10.1007/s00348-005-1017-1
Huang HT, Fiedler HE, Wang JJ (1993) Limitation and improvement of PIV. Exp Fluids 15-15(4–5):263–273. doi:10.1007/BF00223404
Jambunathan K, Ju XY, Dobbins DN, Ashforth-Frost S (1995) An improved cross correlation technique for particle image velocimetry. Meas Sci Technol 6:507–514
Wereley ST, Meinhart CD (2001) Second-order accurate particle image velocimetry. Exp Fluids 31:258–268
Scarano F (2002) Iterative image deformation methods in PIV. Meas Sci Technol 13:R1–R19. doi:10.1088/0957-0233/13/1/201
Astarita T (2006) Analysis of interpolation schemes for image deformation methods in PIV: effect of noise on the accuracy and spatial resolution. Exp Fluids 40(6):977–987. doi:10.1007/s00348-006-0139-4
Ruijters D, ter Haar Romeny BM, Suetens P (2008) Efficient GPU-based texture interpolation using uniform B-splines. J Graph Tools 13(4):61–69
Schrijer FFJ, Scarano F (2008) Effect of predictorcorrector filtering on the stability and spatial resolution of iterative PIV interrogation. Exp Fluids 45(5):927–941. doi:10.1007/s00348-008-0511-7
Westerweel J, Scarano F (2005) Universal outlier detection for PIV data. Exp Fluids 39(6):1096–1100. doi:10.1007/s00348-005-0016-6
Hur SS, Zhao Y, Li Y-S, Botvinick E, Chien S (2009) Live cells exert 3-dimensional traction forces on their substrata. Cell Mol Bioeng 2(3):425–436. doi:10.1007/s12195-009-0082-6
Liu L, Morgan EF (2007) Accuracy and precision of digital volume correlation in quantifying displacements and strains in trabecular bone. J Biomech 40(15):3516–3520. doi:10.1016/j.jbiomech.2007.04.019
Rannou J, et al (2010) Three dimensional experimental and numerical multiscale analysis of a fatigue crack. Comput Methods Appl Mech Eng 199(21–22):1307–1325. doi:10.1016/j.cma.2009.09.013
Carroll JD, Abuzaid W, Lambros J, Sehitoglu H (2013) High resolution digital image correlation measurements of strain accumulation in fatigue crack growth. Int J Fatigue 57:140–150. doi:10.1016/j.ijfatigue.2012.06.010
Roeder BA (2005) Local, three-dimensional strain measurements within largely deformed extracellular matrix constructs. J Biomech Eng 126(6):699. doi:10.1115/1.1824127
Farid H, Simoncelli EP (2004) Differentiation of discrete multidimensional signals. IEEE Trans Image Process 13(4):496–508. doi:10.1109/TIP.2004.823819
Thornley D (2006) Anisotropic multidimensional Savitzky-Golay kernels for smoothing, differentiation and reconstruction. Department of Computing Technical Report, vol 8
Zhang B, Zerubia J, Olivo-Marin J (2007) Gaussian approximations of fluorescence microscope point-spread function models. Appl Opt 46(10):1819. doi:10.1364/AO.46.001819
Richardson WH (1972) Bayesian-based iterative method of image restoration. J Opt Soc Am 62(1):55. doi:10.1364/JOSA.62.000055
Scarano F (2003) Theory of non-isotropic spatial resolution in PIV. Exp Fluids 35(3):268–277. doi:10.1007/s00348-003-0655-4
Prewitt JMS (1970) Object enhancement and extraction. In: Lipkin BS, Rosenfeld A (eds) Pict. process. psychopictorics. Academic Press Inc., New York
Gonzalez RC, Woods RE (2008) Digital image processing, 3rd edn. Prentice Hall, Upper Saddle River
Bower AF (2010) Applied mechanics of solids. CRC Press, Boca Raton
Acknowledgments
This work is in part supported by NIH R21 Al101469-01 and an NSF Graduate Research Fellowship to E.B.K. The authors wish to thank Dr. Allan Bower for his helpful discussions regarding the algorithm’s convergence, Dr. Gabriel Taubin for his valuable input on numerical gradient techniques, and Ronnie Bar-Kochba for help with the GPU implementation of the code.
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Eyal Bar-Kochba and Jennet Toyjanova contributed equally to this work.
Erik Andrews is a posthumous author.
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Bar-Kochba, E., Toyjanova, J., Andrews, E. et al. A Fast Iterative Digital Volume Correlation Algorithm for Large Deformations. Exp Mech 55, 261–274 (2015). https://doi.org/10.1007/s11340-014-9874-2
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DOI: https://doi.org/10.1007/s11340-014-9874-2