# Use of Digital Image Correlation Method to Measure Bio-Tissue Deformation

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## Abstract

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_{x}is proportional to the displacement of crosshead, but the strain ε

_{y}indicates the viscoelastic behavior of tested bio-tissue. In addition, the tested bio-tissue’s linear birefringence extracted by a Mueller matrix polarimetry is for comparison and is in good agreement. As noted above, the integration of the optical parameter measurement system and the digital image correlation method is proposed in this paper to analyze the relationship between the strain changes and optical parameters of biological tissue, and thus the relative optic-stress coefficient can be significantly characterized if Young’s modulus of biological tissue is known.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Deformation and Displacement

#### 2.2. Digital Image Correlation Method

#### 2.3. Strain Field Calculation

#### 2.4. Image Distortion Correction

#### 2.5. Stokes Vector and Mueller Matrix Polarimetry

## 3. Experimental Procedure

#### 3.1. Image Measurement System

#### 3.2. Test Specimen

#### 3.3. Experimental Process

## 4. Results and Discussion

#### 4.1. Rigid Body Translation Experiment

#### 4.2. Chicken Breast Bio-Tissue Tensile Testing

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Freddi, A.; Olmi, G.; Cristofolini, L. Experimental Stress Analysis for Materials and Structures: Stress Analysis Models for Developing Design Methodologies; Springer: Cham, Switzerland, 2015; pp. 172–175. [Google Scholar]
- Post, D.; Han, B. Handbook on Experimental Mechanics; Springer: Boston, MA, USA, 2008; Moiré Interferometry; pp. 627–654. [Google Scholar]
- Sutton, M.A.; Orteu, J.J.; Schreier, H.W. Image Correlation for Shape, Motion and Deformation Measurements; Springer Science + Business Media: New York, NY, USA, 2009; pp. 7–10. [Google Scholar]
- Sutton, M.A.; Wolters, W.J.; Peters, W.H.; Ranson, W.F.; McNeill, S.R. Determination of displacements using an improved digital correlation method. Image Vis. Comput.
**1983**, 1, 133–139. [Google Scholar] [CrossRef] - Sutton, M.A.; Cheng, M.; Peters, W.H.; Chao, Y.J.; McNeill, S.R. Application of an optimized digital correlation method to planar deformation analysis. Image Vis. Comput.
**1986**, 4, 143–150. [Google Scholar] [CrossRef] - Sutton, M.A.; McNeill, S.R.; Jang, J.; Babai, M. Effects of Subpixel Image Restoration On Digital Correlation Error Estimates. Opt. Eng.
**1988**, 27, 271070. [Google Scholar] [CrossRef] - Tong, W. An Evaluation of Digital Image Correlation Criteria for Strain Mapping Applications. Strain
**2005**, 41, 167–175. [Google Scholar] [CrossRef] - Pan, B.; Asundi, A.; Xie, H.; Gao, J. Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements. Opt. Laser. Eng.
**2009**, 47, 865–874. [Google Scholar] [CrossRef] - Pan, B.; Yu, L.; Wu, D.; Tang, L. Systematic errors in two-dimensional digital image correlation due to lens distortion. Opt. Laser. Eng.
**2013**, 51, 140–147. [Google Scholar] [CrossRef] - Gao, Z.; Desai, J.P. Estimating zero-strain states of very soft tissue under gravity loading using digital image correlation. Med. Image Anal.
**2010**, 14, 126–137. [Google Scholar] [CrossRef] [Green Version] - Luyckx, T.; Verstraete, M.; Roo, K.D.; Waele, W.D.; Bellemans, J.; Victor, J. Digital image correlation as a tool for three-dimensional strain analysis in human tendon tissue. J. Exp. Orthop.
**2014**, 1, 7. [Google Scholar] [CrossRef] [Green Version] - Laura, C.S.; Darryl, G.T. The use of 2D ultrasound elastography for measuring tendon motion and strain. J. Biomech.
**2014**, 47, 750–754. [Google Scholar] [CrossRef] [Green Version] - Luyckx, T.; Verstraete, M.; De Roo, K.; Dewaele, W.; Victor, J.; Bellemans, J. The effect of single radius TKA implantation and joint line proximalisation on the strain pattern in the sMCL of the knee. Orthop. Proc.
**2013**, 95, 401. [Google Scholar] - Spencer, M.; Siegmund, T.; Mongeau, L. Determination of superior surface strains and stresses, and vocal fold contact pressure in a synthetic larynx model using digital image correlation. J. Acoust. Soc. Am.
**2008**, 123, 1089–1103. [Google Scholar] [CrossRef] [Green Version] - Rizzuto, E.; Carosio, S.; Del Prete, Z. Characterization of a Digital Image Correlation System for Dynamic Strain Measurements of Small Biological Tissues. Exp. Tech.
**2016**, 40, 743–753. [Google Scholar] [CrossRef] - Chuda-Kowalska, M.; Gajewski, T.; Garbowski, T. Mechanical characterization of orthotropic elastic parameters of a foam by the mixed experimental-numerical analysis. J. Theor. Appl. Mech.
**2015**, 53, 383–394. [Google Scholar] [CrossRef] [Green Version] - Chen, T.Y.F.; Chen, T.C.; Cheng, F.Y.; Tsai, A.T.; Lin, M.T. Digital image correlation of SEM images for surface deformation of CMOS IC. Microelectron. Eng.
**2018**, 201, 16–21. [Google Scholar] [CrossRef] - Cheong, W.F.; Prahl, S.A.; Welch, A.J. A review of the optical properties of biological tissues. IEEE J. Quantum Electron.
**1990**, 26, 2166–2185. [Google Scholar] [CrossRef] [Green Version] - Liao, R.; Zeng, N.; Jiang, X.; Li, D.; Yun, T.; He, Y.; Ma, H. Rotating linear polarization imaging technique for anisotropic tissues. J. Biomed. Opt.
**2010**, 15, 036014. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Wood, M.F.; Ghosh, N.; Wallenburg, M.A.; Li, S.H.; Weisel, R.D.; Wilson, B.C.; Li, R.K.; Vitkin, I.A. Polarization birefrin-gence measurements for characterizing the myocardium, including healthy, infarcted, and stem-cell-regenerated tissues. J. Biomed. Opt.
**2010**, 15, 047009. [Google Scholar] [CrossRef] [Green Version] - Chen, H.W.; Huang, C.L.; Lo, Y.L.; Chang, Y.R. Analysis of optically anisotropic properties of biological tissues under stretching based on differential Mueller matrix formalism. J. Biomed. Opt.
**2017**, 22, 035006. [Google Scholar] [CrossRef] - Chen, D.; Zeng, N.; Liu, C.; Ma, H. Characterization of muscle stretching and damage using polarization-sensitive optical coherence tomography (PS-OCT). In SPIE 8553, Optics in Health Care and Biomedical Optics V; Society of Photo-Optical Instrumentation Engineers: Bellingham, WA, USA, 2012. [Google Scholar] [CrossRef]
- Szczurowski, M.K.; Martynkien, T.; Statkiewicz-Barabach, G.; Urbanczyk, W.; Khan, L.; Webb, D.J. Measurements of stress-optic coefficient in polymer optical fibers. Opt. Lett.
**2010**, 35, 2013–2015. [Google Scholar] [CrossRef] [Green Version] - Bertholds, A.; Dandliker, R. Determination of the individual strain-optic coefficients in single-mode optical fibres. J. Light. Technol.
**1988**, 6, 17–20. [Google Scholar] [CrossRef] - Chen, T.Y.F.; Chou, Y.C.; Wang, Z.Y.; Lin, W.Y.; Lin, M.T. Using Digital Image Correlation on SEM Images of Strain Field after Ion Beam Milling for the Residual Stress Measurement of Thin Films. Materials
**2020**, 13, 1291. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pan, B.; Xie, H.; Guo, Z.; Hua, T. Full-field strain measurement using a two-dimensional Savitzky-Golay digital differentiator in digital image correlation. Opt. Eng.
**2007**, 46, 062001. [Google Scholar] [CrossRef] - Farid, H.; Popescu, A.C. Blind Removal of Lens Distortion. J. Opt. Soc. Am. A
**2001**, 18, 2072–2078. [Google Scholar] [CrossRef] [Green Version] - Dally, J.W.; Riley, W.F. Experimental Stress Analysis, 4th ed.; College House Enterprises LLC: Knoxville, TN, USA, 2005. [Google Scholar]
- Pham, T.T.H.; Lo, Y.L. Extraction of effective parameters of anisotropic optical materials using a decoupled analytical method. J. Biomed. Opt.
**2012**, 17, 025006. [Google Scholar] [CrossRef] [PubMed] - Chenault, D.B.; Chipman, R.A. Measurements of linear diattenuation and linear retardance spectra with a rotating sample spectropolarimeter. Appl. Opt.
**1993**, 32, 3513–3519. [Google Scholar] [CrossRef] [PubMed] - Chenault, D.B.; Chipman, R.A. Infrared birefringence spectra for cadmium-sulfide and cadmium selenide. Appl. Opt.
**1993**, 32, 4223–4227. [Google Scholar] [CrossRef] - Chenault, D.B.; Chipman, R.A.; Lu, S.Y. Electro-optic coefficient spectrum of cadmium telluride. Appl. Opt.
**1994**, 33, 7382–7389. [Google Scholar] [CrossRef] - Sornsin, E.A.; Chipman, R.A. Visible Mueller matrix spectropolarimetry. In SPIE 3121, Polarization: Measurement, Analysis, and Remote Sensing; Society of Photo-Optical Instrumentation Engineers: Bellingham, WA, USA, 1997. [Google Scholar] [CrossRef]

**Figure 2.**Schematic diagram of image distortion [27].

**Figure 3.**Rotating quarter waveplate method for measuring Stokes parameters [20].

**Figure 4.**Experimental setup used to select subset sizes, correct image distortion, and perform rigid body translation.

**Figure 6.**Image for the selection of subset sizes, image distortion correction, and rigid body translation.

**Figure 9.**Comparison of average abs. errors under different criteria for (

**a**) 5 cm, (

**b**) 10 cm, (

**c**) 15 cm, (

**d**) 20 cm.

**Figure 10.**Comparison of standard deviations under different criteria for (

**a**) 5 cm, (

**b**) 10 cm, (

**c**) 15 cm, (

**d**) 20 cm.

**Figure 12.**Displacement measurement results of bio-tissue rigid body plane (

**a**) measurement displacement result (

**b**) average absolute error (

**c**) percentage error.

**Figure 13.**Analysis area of biological tissue. Point 1 is the central area where the laser light passes through; Points 2 and 3 are two random ones in the area.

**Figure 14.**Results of biological tissue tensile testing (

**a**) axial displacement, (

**b**) transverse displacement, (

**c**) axial strain, (

**d**) transverse strain.

**Figure 15.**Optical measurement results of the biological tissue tensile experiment for (

**a**) the first slice, (

**b**) the second slice, (

**c**) the third slice, and (

**d**) the fourth slice.

**Figure 16.**Axial and transverse strain subtracted linear fitting of biological tissue tensile experiment for (

**a**) the first slice, (

**b**) the second slice, (

**c**) the third slice, and (

**d**) the fourth slice.

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**MDPI and ACS Style**

Chen, T.Y.-F.; Dang, N.M.; Wang, Z.-Y.; Chang, L.-W.; Ku, W.-Y.; Lo, Y.-L.; Lin, M.-T.
Use of Digital Image Correlation Method to Measure Bio-Tissue Deformation. *Coatings* **2021**, *11*, 924.
https://doi.org/10.3390/coatings11080924

**AMA Style**

Chen TY-F, Dang NM, Wang Z-Y, Chang L-W, Ku W-Y, Lo Y-L, Lin M-T.
Use of Digital Image Correlation Method to Measure Bio-Tissue Deformation. *Coatings*. 2021; 11(8):924.
https://doi.org/10.3390/coatings11080924

**Chicago/Turabian Style**

Chen, Terry Yuan-Fang, Nhat Minh Dang, Zhao-Ying Wang, Liang-Wei Chang, Wei-Yu Ku, Yu-Lung Lo, and Ming-Tzer Lin.
2021. "Use of Digital Image Correlation Method to Measure Bio-Tissue Deformation" *Coatings* 11, no. 8: 924.
https://doi.org/10.3390/coatings11080924