The use of digital image correlation in the biomechanical

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International Biomechanics

ISSN: (Print) 2333-5432 (Online) Journal homepage: http://www.tandfonline.com/loi/tbbe20

The use of digital image correlation in the biomechanical area: a review Marco Palanca, Gianluca Tozzi & Luca Cristofolini To cite this article: Marco Palanca, Gianluca Tozzi & Luca Cristofolini (2016) The use of digital image correlation in the biomechanical area: a review, International Biomechanics, 3:1, 1-21, DOI: 10.1080/23335432.2015.1117395 To link to this article: http://dx.doi.org/10.1080/23335432.2015.1117395

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Date: 22 December 2015, At: 00:58

International Biomechanics, 2015 Vol. 3, No. 1, 1–21 http://dx.doi.org/10.1080/23335432.2015.1117395

OPEN ACCESS

The use of digital image correlation in the biomechanical area: a review Marco Palancaa  , Gianluca Tozzib and Luca Cristofolinic 

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a

School of Engineering and Architecture, University of Bologna, Bologna, Italy; bSchool of Engineering, University of Portsmouth, Portsmouth, UK; cSchool of Engineering and Architecture, Department of Industrial Engineering, University of Bologna, Bologna, Italy

ARTICLE HISTORY

ABSTRACT

This paper offers an overview of the potentialities and limitations of digital image correlation (DIC) as a technique for measuring displacements and strain in biomechanical applications. This review is mainly intended for biomechanists who are not yet familiar with DIC. This review includes over 150 papers and covers different dimensional scales, from the microscopic level (tissue level) up to macroscopic one (organ level). As DIC involves a high degree of computation, and of operatordependent decisions, reliability of displacement and strain measurements by means of DIC cannot be taken for granted. Methodological problems and existing solutions are summarized and compared, whilst open issues are addressed. Topics addressed include: preparation methods for the speckle pattern on different tissues; software settings; systematic and random error associated with DIC measurement. Applications to hard and soft tissues at different dimensional scales are described and analyzed in terms of strengths and limitations. The potentialities and limitations of DIC are highlighted, also in comparison with other experimental techniques (strain gauges, other optical techniques, digital volume correlation) and numerical methods (finite element analysis), where synergies and complementarities are discussed. In order to provide an overview accessible to different scientists working in the field of biomechanics, this paper intentionally does not report details of the algorithms and codes used in the different studies.

1. Introduction 1.1.  Why is it important to measure full-field displacements and strains? The measurement of displacement and strain is an important task in experimental biomechanics because it allows the characterization of biological tissues, organs and their interactions with biomedical devices. For instance, the stiffness is computed as the ratio between the load and the displacement; bone remodelling is a well-known stress/ strain-driven process (Wolff’s law); bone fracture is governed by a strain-based failure criterion (Bayraktar et al. 2004). Due to the features of biological specimens, which are mainly inhomogeneous and anisotropic, it is extremely important to obtain full-field measurements, ideally with a contactless technique (Haddadi & Belhabib 2008). On the computational side, finite element (FE) analysis results require experimental data as an input, and must be validated against experimental tests. Pointwise measurements, such as the ones provided by strain gauges, sometimes are not sufficient to fully monitor an experiment. Full-field measurements are very important when local damages, such as a crack initiation or propagation, must be identified. CONTACT  Luca Cristofolini 

Received 29 December 2014 Accepted 3 November 2015 KEYWORDS

Digital image correlation (DIC); in vitro biomechanical tests; displacement and strain measurement; accuracy and precision error; hard tissue; soft tissue

1.2.  Overview of full-field, contactless optical measurement techniques Among the different optical techniques, the ones most frequently used nowadays are the digital ones that allow automation of the acquisition and analysis process. After an initial stage of general diffidence during the 80s followed by the first successful applications on mechanical tests in the 90s, optical measurement techniques become very appealing and are increasingly applied in the ­industrial and research environments. These measurement techniques allow:

• Full-field measurement through visualization of strain gradients and concentrations. This produces a more complete description of the behaviour of biological specimens during in vitro tests; • Contactless measurements that enable the measurement of strain without disturbing the local mechanical response of the material. This requirement is particularly important for deformable materials such as soft tissues (liver, intervertebral discs, etc.); • Relatively simple preparation of the surface compared to other measurement techniques, such

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© 2015 The Author(s)Published by Taylor & Francis. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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as the application of strain gauges or fibre Bragg grating sensors. Such features are mandatory for typical biomechanical tests on non-homogeneous and anisotropic materials, and specimens with a complex geometry. At the same time, an optical measurement technique must be accurate and precise. Some optical measurement techniques, such as holographic interferometry, speckle interferometry (including its digital version, electronic speckle pattern interferometry are highly accurate, but they are too sensitive to small displacements, and therefore unsuitable for deformable materials such as biological tissues (Freddi et al. 2015). Other optical techniques, such as Moiré interferometry, require the preparation of a regular pattern on the specimen surface (Post & Han 2008; Freddi et al. 2015), which can be very difficult for biological specimens having an irregular geometry. In general, all such techniques have recently found very limited application because of their complexity in practical use. A promising optical technique for the biomechanical field is the digital image correlation (DIC) (Sutton et al. 2009), which is able to overcome most such limitations (Freddi et al. 2015).

1.3. Aim The purpose of this paper is to provide an overview on the operating principles of DIC, and of its applications in biomechanical area. This review is conceived for biomechanists who want to improve their knowledge about DIC, and need to critically understand the underlying benefits and limitations related to biomechanical applications.

2.  Introducing DIC 2.1.  History of DIC The increasing diffusion of DIC can be explained by its flexibility, scalability to a wide range of dimensions, the robustness of its operating principle, and its (apparent) ease of use (Tyson et al. 2002; Pan et al. 2009; Sutton et al. 2009; Soons et al. 2012; Amiot et al. 2013; Freddi et al. 2015). DIC was introduced in the early of 80s, with the first system developed at the University of South Carolina (Peters & Ranson 1982; Sutton et al. 1983; Chu et al. 1985; Bruck et al. 1989), and has been subsequently improved (Luo et al. 1992, 1994; Helm et al. 1996). The first applications of DIC in biomechanics date back to the 90s (Bay 1995, Bay, Yerby et al. 1999). During the first decade of the new century, DIC was applied regularly in the biomechanical field, with home-written algorithms (Nicolella et al. 2001; Zhang et al. 2002a, 2002b). Later on, several companies developed proprietary DIC systems (Tables 1–2). Additionally, DIC

libraries are also available as part of software suites, such as MATLAB (MathWorks, Natick, MA, USA) and Mathematica (Wolfram, Champaign, IL, USA). Reviews on the use of DIC for traditional engineering materials can be found (Hild & Roux 2006; Pan et al. 2009).

2.2.  Operating principle DIC is based on sets of images of the surface of the specimen in the undeformed (reference) and deformed states (Figure 1). DIC can be implemented both in a bi-dimensional (2D-DIC, with a single camera) and a tri-dimensional (3D-DIC, using two or more cameras) version. A calibration is necessary to initialize the spatial correlation processes of DIC. The images are divided in smaller sub-images (facets), and a matching algorithm is used to match the facets between the reference and deformed states. The displacement field is then computed. Subsequently, the strain field is obtained by derivation. More details about the operating principle are reported in Appendix 1. The main advantages and disadvantages of DIC (Schmidt et al. 2003; Sutton et al. 2009) are summarized in Table 3.

3.  Surface pattern preparation on biological specimens For an optimal use of DIC, the surface of interest must have a random pattern, which deforms together with the specimen surface. If the specimen presents a natural random pattern, due to an intrinsic texture or inhomogeneity, this can be directly exploited by the DIC system. In all other cases, a random pattern must be generated. To ensure accuracy and precision of the computed displacements and strains, the speckle pattern should meet some requirements (Lecompte et al. 2006; Yaofeng & Pang 2007; Pan et al. 2008; Sutton et al. 2009; Barranger et al. 2010; Crammond et al. 2013):

•  Random distribution, in order to make each area of the surface of the specimen univocally identifiable; •  High contrast, to allow the image correlation algorithm works effectively; • Black/white ratio of 50:50, to avoid regions that cannot be properly recognized; • Roughness should be kept at minimum, in order to avoid alteration of the surface geometry. • Probably the most important issue in biomechanical applications is the size of the speckle dots (in relation to the specimen size), in order to optimally exploit the resolution of the camera (Lionello & Cristofolini 2014). In fact, the larger the measurement window, the larger the corresponding area

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International Biomechanics 

covered by each pixel (for a given sensor resolution) and therefore the dots of the speckle pattern. In order to obtain the best speckle pattern for the specific application, the dimension of the speckle should be different for each application. The ideal size of the speckle dots corresponds to 3–5 pixels (Sutton et al. 2009). The magnification factor, M, is defined as the ratio between the number of pixels on the long side of the camera sensor and the long side of the measurement window (M indicates how many pixels correspond to the unit length of the physical specimen). Thus, the ideal size of the speckle dots corresponds to 3–5 pixels divided by M. For example, using a camera-sensor of 5 Megapixels (2448 × 2050 pixels) on a field of view of 2  mm  ×  2  mm (e.g. few trabeculae), yields an optimal dimension of the speckle pattern of about 0.003 mm. The same camera-sensor applied to a larger area of interest of 2 m × 2 m (e.g. a whole human body) would require larger speckle dots, about 3.25 mm. Recently, a tool (a script in MATLAB) was developed to evaluate the quality and suitability of a given speckle pattern for a given DIC application (Estrada & Franck 2015). The techniques to prepare a speckle pattern most commonly used are (Tables 1–2):

• High-contrast paint sprayed with an airbrush airgun (Figure 2(a)): this technique is suitable for both small and large deformations (Barranger et al. 2010; Lionello & Cristofolini 2014), as the speckle dot itself is strained during the deformation. • A dispersion of toner/graphite powder (Figure 2(b)) randomly placed on the specimen: this is a remarkable technique in case of small deformations, particularly for soft tissues, due to an optimal adhesion on moist surfaces. Conversely, in case of large deformations it can produce an underestimation of the strain, as the powder particles displace but do not strain when the underlying specimen is deformed (Barranger et al. 2010). The black-on-white speckle pattern is most frequently used: first a uniform white background is created, on which black speckles are added. This preparation provides the optimal contrast. If the surface of the specimen itself is already of a light colour (i.e. bone), preparation of the white background could be avoided. The use of water-based paints minimizes the alteration on biological specimens (Freddi et al. 2015). In sporadic cases (Genovese, Lee et al. 2013, Lionello et al. 2014; Luyckx et al. 2014), especially for soft tissues, the white-on-black speckle pattern can be used (Figure

 3

2(c)). The difference lies in the colour of the background (black or dark blue), and of the speckles (white). The dark background is obtained through immersion of the specimen in some colouring agent (typically methylene blue staining). This prevents delamination and crumbling of the background layer even at large deformations, which may occur with a paint layer. The white speckle pattern is then produced with an airgun. It has been shown that application of methylene blue on ligaments increases their stiffness by 0.8%. Deposition of the white pattern further increased the stiffness to 1.7% (Lionello et al. 2014). A different preparation of the specimen was used, where ethidium bromide nuclear staining was used to incorporate a high-contrast pattern (Ning et al. 2010). This allows a permanent incorporation of the pattern into the microstructure of the specimen.

4.  Correlation algorithm parameters In order to obtain the best results from this versatile measurement technique, a number of parameters must be adapted to the specific application (Figure 3):

• Facet size (dimension of the sub-image used in the computation); • Grid spacing (step between consecutive facets); • Strain computation window (typically larger than the single facet) used to derive the strain field over a larger area, in order to attenuate the noise • Validity quote (Minimum percentage of computation points that must be available for strain to be calculated over a given computation window); •  Filtering (sometimes applied at the different stages of the correlation to reduce noise). The values assigned to such parameters determine the accuracy, precision and spatial resolution (Palanca, Brugo et al. 2015; see below). There is no universally optimal set of parameters, due to the numerous possible uses of DIC, particularly in biomechanics. A choice must be made in relation to the specific application (i.e. tissue, anatomy and dimensions of the specimens). Only in few papers the DIC parameters are detailed (Tables 1–2).

4.1.  Facet size The digital images are divided into sub-images, called facets, of M × N pixels (typically squared). Each facet is represented by a grey-level distribution, which is, in most cases, interpolated by a bi-cubic spline to obtain an approximation of grey-scale between adjacent pixels. Each facet is summarized by the information about the pattern, and its location in space. The correlation algorithm identifies the best-matching region at different load steps. The influence

Cartilage – animal Bovine carpometacarpal joint cartilage Bovine articular cartilage Porcine articular cartilage Porcine intervertebral disc (FSU L4-L5)

Cartilage – human Human cartilage from patellae

Porcine left ventricular wall

Mice carotid arterial Mice carotid arterial Mice carotid arteries Mice suprarenal aorta with abdominal aneurysm Mice suprarenal aorta Porcine aortic arch N.A

N.A

N.A

N.A

0.683 N.A 59.56 23

N.A

N.A

51.2 mm × 10.2 mm

4

888 μm × 703 μm

N.A

N.A

N.A

N.A

N.A

N.A

N.A

N.A

2.2

290 μm × 770 μm

20

Cardiovascular – animal Bovine aorta 25 mm × 18 mm

Powder

Airbrush

N.A

Natural pattern

N.A

Airbrush

Airbrush

Airbrush

Airbrush

Ethidium bromide nuclear Airbrush

Powder

Airbrush

Natural pattern

147

Type of random pattern N.A

Pixel size (μm) N.A

Field of view

Cardiovascular – human Human aortic N.A. tissue Human heart 100 mm × 100 mm

Specimen

Compression test

Unconfined compression Tensile test

Unconfined compression

Tensile test

Indentation test

Pressure test

Pressure test

Pressure test on lesions

Pressure and tensile test Pressure test

Pressure test

Tensile test

Myocardial movements

Inflation test

Type of mechanical test

Young’s modulus; Poisson ratio Displacement distribution Strain distribution

Young’s modulus; Poisson ratio

Normal strain

Displacement and strain distribution

Strain distribution

Strain distribution

Strain distribution

Displacement and strain distribution Strain distribution

Full-field displacement; strain distribution Lagrangian strain

Displacement and strain distribution Displacement and strain distribution

Reported quantities

Table 1. Papers presenting applications of DIC to biomechanical investigations of the soft tissues.

1

1

15

21

10

1

1

1

1

1

1

1

N.A

1

4

Number of specimens

Home written

Home written

Home written

N.A

Home written

Home written

Home written

Home written

Home written

Home written

Vic-3D modified Vic-3D

Home written

DaVis

Aramis 3D

DIC system

F_S: 9 × 9

N.A

F_S: 20/40/60; G_S: from 8 to 120 N.A

N.A

N.A

N.A

N.A

N.A

G_S: 8 × 4

F_S: 43 × 43; G_S: 5 F_S: 15 × 15

N.A

F_S: 121 × 121; G_S: 1

N.A

DIC parameters

Note

Comparison with ESPI

Combined with a fringe projection method

pDIC

pDIC

Singular speckle pattern

In vivo

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Spera et al. (2011)

Zhang et al. (2005)

Wang et al. (2003)

Wang et al. (2002)

Narmoneva (2002)

Genovese, Lee et al. (2013) Genovese and Humphrey (2015) Genovese et al. (2015)

Genovese, Lee et al. (2011) Genovese et al. (2012)

Sutton, Ke et al. (2008) Ning et al. (2010)

Zhang et al. (2002a)

Hokka et al. (2015)

Kim et al. (2011)

References

4    M. Palanca et al.

40 mm × 40 mm

24 mm × 21 mm

100 mm × 75 mm

20 mm × 20 mm

Field of view

50

13.3

12 mm × 38 mm

Human skin

Keratinized tissue – animal Bovine hoof horn 8.5 mm × 6.4 mm

Poppy seeds as marker

N.A

Airbrush

Airbrush

N.A

Poppy seeds as marker

N.A

N.A

Powder

Airbrush

N.A

N.A

Airbrush

Airbrush

Powder

Airbrush

Powder

Type of random pattern

6.7

3.4

30

30

Pixel size (μm)

Keratinized tissue – human Human skin 100 mm × 70 mm

Tendon and ligament – animal Mice Achilles N.A tendon Porcine uterosaN.A cral and cardinal ligaments Porcine uterosaN.A cral and cardinal ligaments

Tendon and ligament – human Human vocal 8.5 mm × 6.8 mm ligaments Human tendon N.A

Bovine posterior sclera

Eye – animal Bovine cornea

Human posterior sclera; optic nerve

Eye – human Eye - human Human posterior sclera

Specimen

Tensile test

In-plane point loading Tensile test

Bi-axial test

Tensile test

Tensile test

Tensile test

Tensile test

Inflation test

Inflation test

Inflation test

Inflation test

Type of mechanical test

Full-field displacement; strain distribution

Displacement distribution Displacement distribution

Displacement and strain distribution

Axial displacement and strain Axial displacement and strain

Normal and shear in-plane strain

Axial strain

Displacement distribution Displacement distribution

Displacement distribution; circumferential and meridian strain Displacement and strain distribution

Reported quantities

1

32

1

22

18

8

6

1

10

9

1

57

Number of specimens

Home written

Vic-3D

Vic-3D

ProAnalyst

ProAnalyst

Home written

Vic-3D

Vic-2D

Vic-3D

Vic-3D

Home written

Vic-3D

DIC system

N.A

N.A

N.A

N.A

N.A

N.A

N.A

N.A

N.A

F_S: 35 × 35

F_S: 9 × 9; C_W: 21 × 21

N.A

DIC parameters

Note

High-speed camera

In vivo

Use of ultrasound images

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(Continued)

Zhang and Arola (2004)

Ottenio et al. (2015)

Evans and Holt (2009)

Becker and De Vita (2015)

Tan et al. (2015)

Okotie et al. (2012)

Luyckx et al. (2014)

Kelleher et al. (2010)

Myers et al. (2010)

Boyce et al. (2008)

Pyne et al. (2014)

Coudrillier et al. (2012)

References

International Biomechanics   5

4 N.A

5.6 mm × 4.2 mm

N.A

Scales from Cyprinus carpio Mice skin

N.A

N.A

Lamb gallbladder

Human lower limb muscles

N.A

Silicon gel

N.A

11

N.A

N.A

N.A

Painted

Airbrush

N.A

Natural pattern

Airbrush

Airbrush

Indentation test

Airflow test;

Indentation test

Compression test

Unconfined compression test Pressure test

Tensile test

Deformation distribution

Displacement and strain distribution Displacement and strain distribution

Displacement distribution

Deformation distribution Strain in longitudinal direction Displacement distribution Full-strain distribution

Displacement and strain distribution

Axial and lateral strain

Strain distribution

Displacement distribution; in-plane normal strain, inplane shear strain Strain distribution

Reported quantities Axial and lateral strain

1

N.A.

N.A

4

1

N.A

10

1

15

10

6

10

2

Number of specimens N.A.

Vic-3D

Vic-3D

Aramis 3D

Home written

Home written

Vic-3D

Home written

Aramis 3D

Vic-3D

Vic-2D

N.A

Home written

Home written

DIC system Home written

N.A

F_S: 23 × 23

N.A.

F_S: 21 × 21; C_W: 41 × 41 px N.A

N.A

N.A

N.A

F_S: 21 × 21; G_S: 5

N.A

N.A

N.A

F_S: 21 × 21; G_S: 10; C_W: 50 × 50

DIC parameters N.A

Use of high speed camera; 3D with a single camera

Use of ultrasound images

pDIC

Microscopy DIC

Note

Moerman et al. (2009)

Spencer et al. (2008)

Cox et al. (2008)

Affagard et al. (2014)

Genovese et al. (2014)

Libertiaux et al. (2011)

Gao and Desai (2010)

Ahn and Kim (2010)

Brunon et al. (2011)

Myers et al. (2008)

Marino Cugno Garrano et al. (2012) Karimi et al. (2015)

Soons et al. (2012)

References Kelly et al. (2006)

Notes: References are listed in chronological order within each subsection. N.A = information not available. F_S = facet size. G_S = grid spacing. C_W = computation window. Istra-4D by Dantec Dynamics (Skovlunde, Denmark), Aramis 3D by GOM (Braunschweig, Germany), Vic-2D and Vic-3D by Vision Solution (Irvine, California, USA), StrainMaster and DaVis by LaVision (Goettingen, Germany). ProAnalyst by Xcited (Woburn, Maine, USA). Rapid Correlation by XStream Software (Ottawa, Ontario, Canada).

N.A

Synthetic vocal fold

N.A

N.A

Porcine brain

Artificial soft tissue Heart valve tissue

N.A

N.A

Porcine livers N.A

Airbrush

3.3

Internal organs – animal Porcine liver 100 mm × 80 mm Natural pattern

Inflation test

Airbrush

Indentation test

Tensile test

Tensile test

Tensile test

Bending test

Type of mechanical test Compression test

Airbrush

N.A.

N.A

Airbrush

Airbrush

Type of random pattern Natural pattern

Internal organs – human Human cervical N.A tissue Human liver 25 mm × 25 mm

6.8

14 mm × 17 mm

Beaks of granivorous birds

Pixel size (μm) N.A

Field of view N.A

Specimen Chondrocyte-seeded agarose hydrogels

Table 1. (Continued)

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6    M. Palanca et al.

1.30; 0.65 7.7

17 N.A

2.6 mm2 × 2 mm2; 1.3 mm2 × 1 mm2

23.2 mm2 × 15.4 mm2

8 mm2 × 8.7 mm2

N.A

Bovine cortical bone

Human teeth

Whole organ – human

Single trabecular of bovine femora

Cortical bone from bovine femoral shaft Bovine fibro lamellar bone

3 mm2 × 4 mm2 3

N.A.

0.137; 0.339

180 μm2 × 141 μm2; 445 μm2 × 350 μm2

Cortical bone of bovine tibias

N.A.

0.137; 0.339

180 μm2 × 141 μm2; 445 μm2 × 350 μm2

Cortical bone of bovine tibias

Ovine early bone callus

0.137; 0.339

2.6

3.6 mm2 × 2.7 mm2

180 μm2 × 141 μm2; 445 μm2 × 350 μm2

N.A.

N.A.

N.A

N.A. 8.9

N.A

N.A

N.A.

N.A

N.A

Field of view

Cortical bone of bovine tibias

Tissue level – animal

Human cortical bone from femur

Interface human bone cement Human trabecular bone from femur

Tissue level – human Trabecular bone from human femoral head Slices of human thoracic spinal motion segments Trabecular bone of human cadaveric knee

Specimen

Pixel size (μm)

Powder

Ink jet printing

Airbrush

Airbrush

Powder

Natural pattern

Natural pattern

Natural pattern

Natural pattern

Natural pattern

Airbrush

N.A.

Natural pattern Natural pattern Natural pattern

Type of random pattern

Crack propagation

Three-point bending

Three-point bending Tensile test

Compression test; nanoindentation test Compression test

Tensile test

Micro-crack in stressed cortical bone Tensile test

Shear test

Compression test

Shear fatigue test

Compression test

Compression test

Compression test

Type of mechanical test

Reported quantities

Displacement distribution

Strain distribution, minimal principal distribution Normal strains and shear strain Axial and transversal strain Displacement and strain distribution

Axial strain

Strain distribution; maximum principal strain Principal strain

Principal strain

Displacement distribution Strain distribution Strain distribution; principal strain Interface displacement Displacement and strain distribution Displacement and strain distribution

Table 2. Papers presenting applications of DIC to biomechanical investigations of hard tissue.

N.A.

10

20

N.A

4; 3

7

N.A

N.A

29

12

25

8

6

6

Number of specimens

Home written

Vic-2D

Home written

Home written

Vic-2D

Home written

Home written

Home written

Home written

DaVis

Rapid Correlation Istra-4D

Home written

Home written

Home written

DIC system

F_S: 15 × 15

N.A

F_S: 30 × 70

F_S: 36 × 36

F_S: 29 × 29

F_S: 24 × 18 G_S: 50; F_S: 14 × 10; G_S: 10 F_S: 60 × 60

F_S: 9 × 9 × ; 19 × 19; 31 × 31; 63 × 63 F_S: 51 × 51

N.A

F_S:40 × 40

DIC parameters

Note

Fatigue and fracture

Use of highspeed camera High speed photography

Use of optical microscope

With radiographs unit With radiographs unit

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(Continued)

Zhang et al. (2007)

Yamaguchi et al. (2011) Benecke et al. (2011) Jungmann et al. (2011)

Thompson et al. (2007)

Hoc et al. (2006)

Nicolella et al. (2006)

Nicolella et al. (2005)

Nicolella et al. (2001)

Tang et al. (2015)

Cyganik et al. (2014)

Mann et al. (2008)

Bay, Yerby et al. (1999) McKinley and Bay (2003)

Bay (1995)

References

International Biomechanics   7

250 N.A

N.A

2

87 mm  × 87 mm

100mm2 × 67 mm2

N.A

Dried mandible

Human femur

Human vertebra

Human femur

35

50 mm2 × 37.5 mm2

Acrylic resin mandibular with and without implant

N.A

N.A

Dental composited

47

N.A

50

25 area of 5 mm2

Composite femur

Osseo integrated transfemoral implant system

N.A

N.A

6

15 mm2 × 12 mm2

Mouse tibia

Synthetic Dental composite

N.A

N.A

Rat femora

N.A

12

16 mm2 × 12 mm2

Mouse tibia

N.A

9.5

2 mm2 × 4 mm2

Chelipeds of lobster

Fresh ovine femur

9.3

19 mm2 × 14 mm2

Whole organ – animal Cemented total hip replacement

100

N.A 2

Field of view N.A

Pixel size (μm) N.A

Specimen Human femurs

Table 2. (Continued)

Airbrush

Powder

N.A

Airbrush

Airbrush

Airbrush

Airbrush

Airbrush

Airbrush

Airbrush

N.A

Manually applied with marker

Airbrush

N.A

Airbrush

Type of random pattern Natural pattern

Three-point bending

Curing process

Bending test

Press/flection test

Curing process

Compression test till failure Compression test

Compression test

Compression test

Tensile test

Fatigue test

Compression test

Accuracy and precision test

Sideways fall

Compression test

Type of mechanical test Sideways fall

Axial and transversal strain Strain (sensitivity/experimental error) Displacement and strain distribution Axial and transversal displacement Strains in horizontal direction and in-plane shear strain

Max and average strain

Strain distribution Principal strain

Full-field displacement, strain distribution Displacement and strain distribution Strain (average)

Principal strain

Reported quantities Horizontal and vertical displacement; strain distribution Major principal strain Principal minimum strain Principal strain

N.A

32

12

N. S

10

3

9

N.A

4

8

1

3

1

1

N.A.

Number of specimens 22

Strain Master

Vic-2D

Vic-3D

Vic-3D

Strain Master

Aramis 3D

Vic-3D

Vic-3D

Aramis 3D

Aramis 3D

Home-written

Vic-3D

Istra-4D

Strain Master

Aramis 3D

DIC system Home written

N.A

F_S: 27 × 27; G_S: 10 px; C_W: 150 px2 F_S: 21 × 21

N.A

N.A

F_S: 19 × 19; overlap: 20%

N.A

F_S: 19 × 19; G_S: 9 N.A

F_S: 23 × 23; G_S: 10 px

N.A

F_S: 32 × 32; G_S: 50% F_S: 15 × 15, 19 × 19, 21 × 21, 25 × 25; G_S: 4,7,11,15; C_W: 3, 5, 7, 9, 11, 13, 15 F_S: 25 × 25; G_S: 1, 5 px

N.A

DIC parameters N.A

Use of highspeed DIC

Use of highspeed camera

Note Use of highspeed camera

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Tiossi et al. (2011)

Chuang et al. (2011)

Thompson et al. (2011)

Dickinson et al. (2011)

Li et al. (2009)

Amin Yavari et al. (2013) Carriero et al. (2014)

Sztefek et al. (2010) (Ghosh et al. 2012)

Sachs et al. (2006)

Zhang and Arola (2004)

Grassi et al. (2014)

Tanasic et al. (2012) Helgason et al. (2014) Palanca, Brugo et al. (2015)

References Op Den Buijs and Dragomir-Daescu (2011)

8    M. Palanca et al.

N.A N.A Vic-3D Vic-3D 6 6

N.A Strain Master 20

Press/flection test Compression test N.A N.A Composite femur Composite femur

N.A N.A

Airbrush Airbrush

Sideways fall 200 Composite femur

115 mm2 × 57 mm2

Airbrush

Three-point bending Airbrush 35 50 mm2 × 37.5 mm2 Acrylic resin mandibular with and without implant

Field of view 36 area of 5 mm2 × 5 mm2 Specimen Composite hemi-pelvis

Notes: With each subsection, references are listed in chronological order. N.A = information not available. F_S = facet size. G_S = grid spacing. C_W = computation window. Istra-4D by Dantec Dynamics (Skovlunde, Denmark), Aramis 3D by GOM (Braunschweig, Germany), Vic-2D and Vic-3D by Vision Solution (Irvine, California, USA), StrainMaster and DaVis by LaVision (Goettingen, Germany). ProAnalyst by Xcited (Woburn, Maine, USA). Rapid Correlation by XStream Software (Ottawa, Ontario, Canada).

Grassi et al. (2013) Vaananen et al. (2013)

Gilchrist et al. (2013)

Tiossi et al. (2012) N.A Strain Master N.A

DIC parameters N.A DIC system Vic-3D Number of specimens N.A

Reported quantities Displacement distribution; principal strain Strains in horizontal direction and in-plane shear strain Displacement distribution; minimum principal strain Principal strain Principal strain Type of mechanical test Compression test Type of random pattern Airbrush Pixel size (μm) N.A.

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Note

References Dickinson et al. (2012)

International Biomechanics 

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of the facet size is remarkable (Lava et al. 2009). The facet size must be defined according to: the specimen size (or the field of view), the size of the speckles, and the strain gradients expected based on the loading conditions and the anatomy (Carriero et al. 2014; Freddi et al. 2015). The facet should be larger than speckle dots, to allow detection of small displacements, in relationship to the granularity of the speckle pattern (Sutton et al. 2009). However, the facet should not be unnecessarily large, to avoid loss of resolution (Lionello & Cristofolini 2014).

4.2.  Grid spacing This parameter indicates the distance between two consecutive facets. It describes the density of facets in the measurement window: the smaller the grid spacing, the larger the number of facets (at a higher computational cost). The influence of the grid spacing on the precision and accuracy of the computed displacement field is minimal (Lava et al. 2009). Conversely, the overlap provides advantages in terms of precision and accuracy of the computed strain field. The density of measurement points should be selected based on the test details (type of specimen, field of view, pattern and strain gradient). For an expected uniform strain (e.g. long bone in bending) larger grid spacing can be preferable. Conversely, if high strain gradients are expected (e.g. specimens with complex geometry), a smaller grid spacing is necessary (Sutton et al. 2009, Palanca, Brugo et al. 2015).

4.3.  Strain computation window Once the displacements have been computed for each facet, the strain field is computed by derivation. While in principle 2 × 2 facets are sufficient to compute the local strain, larger windows are often used to attenuate the noise in the derived strain field. While larger strain computation windows reduce the noise in the DIC-computed strain distribution, this also may result in an attenuation of existing strain gradients, which can be detrimental when analyzing specimens with an irregular geometry (which often occurs with anatomical specimens). This effect is thus similar to the effect of grid spacing (Sutton et al. 2009, Palanca, Brugo et al. 2015).

4.4.  Validity quote The validity quote represents the tolerance for computing/ignoring the strain in a certain region: if the number of valid neighbouring points is below the threshold, the software does not evaluate the strain. A high level of the validity quote means that strains are computed only where redundant information is available, thus providing a more

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Figure 1. Workflow of DIC displacement and strain measurement: as an example, a 3D-DIC arrangement was used to investigate a human tibia. Table 3. Summary of the main potentialities and limitations of DIC. Advantages

•  Full-field measurement of displacement/strain •  For any size and material of specimens • Determination of strain gradient and stress concentrators •  Both for small and large deformation • Usable in vivo •  Synergies with FE • Not invasive*

Disadvantages

• Less accurate and precise than others measurements techniques • Need of a carefully optimization for the specific application • Not real-time • Need of optical access to the specimen •  Requires surface preparation*

*

In most cases, a surface preparation is required. It is a layer of paint or powder fixed on the surface. Sometimes, the natural pattern is usable to track the deformation of the surface.

Figure 2. Example of specimens with different speckle patterns: (a) black-on-white speckle pattern created with the airbrush airgun technique on a porcine vertebral body; (b) black-on-white speckle pattern created with the powder technique on a bovine cornea (picture courtesy of Dr Brad L. Boyce, (Boyce et al. 2008)); (c) Speckle pattern created with airbrush airgun technique, white-on-black, on a human Achilles tendon (picture adapted from (Luyckx et al. 2014)).

International Biomechanics 

 11

computed by means of an FE solver, where DIC-measured displacements are imposed to the FE nodes (Evans & Holt 2009). The continuum assumption (which is intrinsic to FE modelling), acts as a low-pass filter.

5.  Errors affecting DIC measurements in biomechanics Downloaded by [Alma Mater Studiorum - Università di Bologna], [Luca Cristofolini] at 00:58 22 December 2015

5.1.  Accuracy and precision

Figure 3. Detail of the specimen surface prepared with a random speckle pattern, as seen after acquisition as a digital image (i.e. discretized in pixels). Notes: The DIC software parameters are illustrated: to compute the displacement field, the digitized image is divided in subimages (facets, 20 × 20 pixels in this case); a grid spacing of 15 pixels is used in this case (resulting in a partial overlap of 5 pixels); a larger area (computation window, 3 × 3 facets in this case) is used to compute the strain field.

reliable strain value. If the specimen has a complex geometry (i.e. a vertebra, or a pelvis), a lower threshold might be necessary, resulting in less reliable strain estimates.

4.5. Filtering In general, DIC allows obtaining very precise displacement fields (i.e. affected by very low noise, typically sub-pixel). However, as derivation acts as the opposite of a filter (enhancing the noise in the displacement field computed from noisy digital images), the strain field is generally affected by large random error. Filtering can be applied to the digital images, to the DIC-computed displacement field, and/or to the DIC-computed strain field (Baldoni et al. 2015). There are several filters that mainly differ in the intensity of attenuation, and filtering strategy (whether local or global). However, this also smoothens any gradient or stress/strain concentration, resulting in a loss of information. For a homogeneous deformation (i.e. in the diaphysis of a long bone, or a tendon under tension) a smoothing spline can be successfully used to attenuate the noise by averaging the results over the field of view. Larger averaging areas are associated with more severe loss of information (Lava et al. 2010). Conversely, when the specimen is subject to high strain gradients (i.e. an irregular bone such as a vertebra, or a complex structure such as the sclera) a local filtering, should be preferred (at the cost of noisier results, (Wang et al. 2012)). Alternatively, strain can be

It is important to distinguish between systematic error (bias of the average, resulting in lack of accuracy) and random error (large standard deviation, resulting in lack of precision). In fact, accuracy and precision of the DIC measurements cannot be taken for granted if the measurement system and the numerical processing have not been optimized and validated (Figure 4). The errors affecting displacement and strain are originally induced by the overall quality of the native images. The DICcomputed displacement field is less sensitive to modifications of software parameters; their effect is larger on strains (Nicolella et al. 2001; Palanca, Brugo et al. 2015). Accuracy and precision of the DIC in computing the displacements are in the order of 0.01 pixel (Nicolella et al. 2001; Zhang & Arola 2004; Amiot et al. 2013); with some optimizations errors can be further reduced (Barranger et al. 2010). DIC-computed strains are generally quite accurate (systematic errors of the order of few microstrains are negligible in most biomechanical applications). Conversely, large noise usually affects DIC-computed strains: a precision of some hundreds of microstrain can be achieved only under optimal conditions.

5.2.  Errors due to the pattern The DIC analysis relies on the presence of a suitable pattern on the specimen surface. In order to evaluate the errors related to the morphology of the pattern, digital images of the speckle patterns were virtually translated (Haddadi & Belhabib 2008), numerically deformed (Lecompte et al. 2006), correlated in a zero-strain condition (Carriero et al. 2014). An unsuitable speckle pattern is likely to make the correlation impossible at some facets, reducing the number of measurements points (Haddadi & Belhabib 2008). An optimal ratio exists between the facet size and the mean speckle size to reduce errors affecting DIC-computed displacements (Lecompte et al. 2006, 2007). They also showed that a limited scatter of speckle sizes yields more accurate displacement measurements, and that larger dots result in larger random errors in the displacement field. The differences between black-on-white and white-on-black speckle patterns are negligible in terms of measurement quality (Barranger et al. 2010). A clear relationship exists

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between the measurement error and the uniqueness of the pattern, which depends on the speckle size and shape, and on the facet size (Crammond et al. 2013). The airbrush airgun method provides a better control of the dots dimension compared to the use of powder (Myers et al. 2010). Even if an airbrush airgun can only to a limited extent be adjusted to produce the desired speckle dots (Crammond et al. 2013), the performance of DIC is quite robust and tolerant (Wang et al. 2012).

5.3.  Errors affecting the acquired images Random errors affect the images acquired by the digital camera, such as thermal noise (or dark noise), excess noise due to the CCD sensor and electromagnetic noise of the relative measurement chain (Freddi et al. 2015). Moreover, a source of systematic error in 2D-DIC derives from outof-plane displacements of the specimen during loading. 2D-DIC is often chosen in investigations at the tissue level (Sutton, Yan et al. 2008, Pan et al. 2013). They explained the combined effect of the out-of-plane motion of the tested object surface and of the cameras.

5.4.  Errors due to the correlation process Suboptimal choice of the software parameters can result in large noise, or, conversely, could hide existing strain gradients (Baldoni et al. 2015). The optimal parameters can be identified through virtually imposed displacement tests (Haddadi & Belhabib 2008). Numerically deformed images were prepared to evaluate the accuracy and precision in the displacement field, and identify the optimal parameters (Lava et al. 2009, 2010, 2011) (Wang et al. 2012). A zero-strain test was applied on a vertebra (Figure 4) to investigate the software parameters to estimate the accuracy and precision (Palanca, Brugo et al. 2015).

5.5.  Recommendations to minimize measurement errors in biomechanical applications It is possible and to some extent mandatory to validate DIC measurements by comparison against independent measurements: (Zhang & Arola 2004; Sutton Ke et al. 2008, Gilchrist et al. 2013) compared the DIC-computed strains against single strain gauges. A more extensive validation may include the use of specimens with known material properties, subjected to well-defined loading conditions (Zhang & Arola 2004; Sutton, Ke et al. 2008, Gilchrist et al. 2013). Moreover, preliminary tests to identify the spatial displacements could help in avoiding out-of-plane artefacts in a 2D-DIC. To optimize the speckle pattern for biological specimens (Lionello & Cristofolini 2014; Lionello et al. 2014;

Figure 4.  Example of errors affecting the DIC-computed strain distribution. A porcine vertebra was examined in a zero-strain condition. Notes: Strains were computed with DIC software with default (i.e. not optimized) settings. Any strain readout different from zero is due to errors (a combination of systematic error and random error).

Palanca, Brugo et al. 2015) proposed a factorial design to adjust the airbrush settings so as to a pattern having the desired average speckle size with minimal scatter. The lens distortion generates a systematic error, which can be partially compensated through dedicated algorithms (Yoneyama 2006), or an appropriate calibration (Patterson et al. 2007; Sebastian & Patterson 2012). Such artefacts can be completely eliminated with telecentric lenses (Pan et al. 2013), or by exploiting the central portion of the lens angle (Palanca, Brugo et al. 2015). An in-house smart solution consists in performing 3D deformation measurements with a single camera using a biprism to avoid distortion of the images (Genovese, Casaletto et al. 2013; Genovese, Lee et al. 2013). The illumination must be stable and uniform to reduce the noise and obtain better native images. Moreover, due to the nature of biological specimens, cold light illumination is preferable (i.e. using LED technology). Noise and its influence can be somehow reduced, but not completely eliminated, with high-performance hardware (i.e. lenses, cameras, frame grabber, etc.). To reduce correlation errors due to unsuitable settings, it is important to have a provisional estimate of the expected strain gradients. In case of homogeneous deformation a large facet size, large grid spacing and large computation window are able to produce accurate and precise measurement with limited computation cost (Sutton et al. 2009). Conversely, stress/strain concentrations should be investigated with a high spatial resolution (i.e. small facets and computation windows), to avoid loss of detail. Filtering can help reduce the noise in the DIC-computed strains. However, filtering should be used with extreme caution to avoid loss of information in high-gradient

International Biomechanics 

regions, such as anatomical specimens with an irregular geometry, or in highly inhomogeneous tissues (Baldoni et al. 2015). A careful optimization of the entire measurement chain can reduce the errors (Figure 5) and provide more accurate and precise outputs (Palanca, Brugo et al. 2015).

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6.  Examples of biomechanical applications Big potentiality of DIC lies in its suitability to investigate different kinds of materials, such as soft and hard biological tissue, independently their mechanical behaviour (brittle/ ductile, isotropic/anisotropic, homogeneous/inhomogeneous), for small or large deformation (Sutton et al. 2009).

6.1.  Applications to soft tissue Before the introduction of DIC, strain in soft tissue structures has been initially measured by means of extensometers (Larrabee 1986; Nagarkatti et al. 2001). This method significantly perturbs the specimen under observation, both in terms of local stiffening and notching. A better alternative is based on optical extensometers (i.e. (Holzapfel 2006; Weisbecker et al. 2012)). The main limitation of optical extensometers is that they track the displacement of only two points in the specimen. Therefore, the strain field between such points is averaged, with no information about the local strain distribution. Furthermore, most optical techniques tend to loose correlation when large displacements are involved, which often occurs with soft tissues. DIC overcomes such problems, opening possibilities to new measurements and new data in the experimental tests (Table 1). For example, DIC opened the way to measurements on micrometric scales (tissue level). DIC enabled improvements in the field of microindentation. Originally, indentation focused only on the force-­ indentation relationship. DIC allows measuring the surface

 13

deformation around the point of load application. This methodology was assessed on a silicon gel (Moerman et al. 2009) and on a porcine liver (Ahn & Kim 2010). Singlecamera-DIC combined with a radial-fringe-projection was used to measure the displacement field in the indentation tests on porcine ventricle (Genovese et al. 2015). As the reliability of DIC with microindentation has been proven in vitro, this technique has the potential to be deployed in vivo for future diagnostic purposes. In vitro application of DIC to measure the strain distribution in various components of the cardiovascular system is extremely important, for potential its impact to improve the understanding of pathologies, and deliver better treatment. However, the state of stress/strain is difficult to measure, because of the inherent pseudoelastic nature, the small dimensions of the specimens, and the difficulty in reproducing the physiological working condition. Initially, bovine aorta specimens were investigated by means of DIC by Zhang et al. (2002a): Poisson’s ratio was determined from the displacements, and the corresponding strains up to 40%, in the axial and circumferential directions. This work was based on simplified boundary conditions: the specimens were loaded in a uniaxial tensile test, far from the physiological conditions. Additional experiments were conducted with silicone rubber sheets, providing a validation of DIC under large strains. Later, other works included an improved resemblance to the physiological condition. Mice carotid arteries were subjected to a pressure test to identify significant variations in constitutive material response (Sutton, Ke et al. 2008). This test was performed using a microscopic 3D-DIC, with a field of about 0.2  mm2. Due to the 3D anatomy, only a restricted region of the surface was investigated. The entire surface of a mice carotid was investigated out using a conic mirror, while a single camera was moved (Genovese et al. 2011; Genovese & Humphrey 2015). The

Figure 5. Plots showing how the systematic error and the random noise were dramatically high if no special care was taken to reduce them, and how effective an optimization following the principles of DOE can be, to improve precision and accuracy (Palanca, Brugo et al. 2015).

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distribution of mechanical properties was obtained from the strain field, exploiting an inverse material characterization. As this method allows measuring displacements and strains on the entire surface, complex pathological conditions such as abdominal aortic aneurysms could be investigated (Genovese et al. 2012). The anisotropy of tissue-engineered heart valves was investigated with indentation tests at a microscopic scale (Cox et al. 2008). A pioneering rudimental DIC system allowed evaluating the strain distribution in the human cornea by measuring the in vitro displacement of only few (6) discrete particles (Shin et al. 1997). In order to understand the non-linear viscoelastic and anisotropic behaviour of the cornea, a 3D-DIC was used (Boyce et al. 2008). Bovine corneas were constrained in a custom pressurization chamber and loaded with physiological and pathological pressure. The potentialities of 3D-DIC were exploited to measure the out-of-plane displacements and to obtain the pressure-displacement response. The response at various pressure rates and the creep at different pressures of the bovine posterior sclera were investigated (Myers et al. 2010). A consolidated protocol to measure the spatial displacement field during an inflation test was used for an in-depth investigation of the behaviour of physiological and pathological human posterior sclera (Coudrillier et al. 2012, 2013). A system where the camera can be rotated by 90 degrees around two orthogonal axes (sequential-DIC) allows improving the out-of-plane resolution of a single camera, without losing sensitivity (Pyne et al. 2014). They used sequential-DIC for mapping the optic nerve head deformation. As sequential-DIC requires some time to acquire the images from different angles, it cannot be used for time-critical experiments such as measuring viscoelastic properties. The advent of DIC enabled the incorporation of loading conditions that better replicate the complex in vivo mechanical environment in the eye structure, compared to the crude simplifications of the past (uniaxial tests (Boyce et al. 2007)). Cartilage tissue specimens (1-mm cubes) were subjected to unconfined compression tests; 2D-DIC was used to measure the equilibrium modulus and the Poisson ratio (Wang et al. 2002, 2003). Similarly, the Poisson ratio was measured at the tissue level in tension for the human patellar cartilage (Narmoneva 2002; Zhang et al. 2005). Intervertebral discs are difficult to study, both for their mechanical behaviour and for their anatomical position. Traditionally (Causa et al. 2002; Panjabi 2007) the force–displacement curve of functional spinal units was extracted from displacement transducers under uni- or multi-axial simulators. The strain distribution in the discs was measured with 3D-DIC at the organ level under simulated physiological loading (Spera et al. 2011).

The distribution of strain in the entire human Achilles tendon was examined through DIC (Luyckx et al. 2014), while in the past only the average strain could be assessed by means of extensometers. An image correlation process was applied to dynamic ultrasound images to measure the in vivo strain distribution in mice tendon (Okotie et al. 2012). This technique exploited the “natural” speckle pattern of ultrasound images. The biomechanics of bovine hoof has been investigated in uniaxial tension using DIC, so as to obtain a full-field description of the axial strain distribution (Zhang & Arola 2004). The strain gradients observed indicated an inhomogeneous distribution of the mechanical properties, which would otherwise be difficult to assess. The interplay between the uterine cervix tissue and its macroscopic mechanical properties was investigated with DIC (Myers et al. 2008). Strain distributions in the range from 5 to 30% were measured with DIC, and plotted against stress. Recent works were done on porcine uterosacral and cardinal ligaments in uni-axial (Tan et al. 2015) and bi-axial (Becker & De Vita 2015) loading conditions, deploying a simplified DIC (a limited number of poppy seeds used as markers). They determined the mechanical properties (elastic moduli, ultimate tensile strength and strain) of the two major ligaments that support uterus, cervix and vagina. The bi-axial test, moreover, investigated deeply the orthotropic behaviour of these ligaments, formulating a new three-dimensional constitutive model. The spatial deformation of the vocal folds was measured by means of DIC (Spencer et al. 2008; Kelleher et al. 2010). This study focused on the superior surface of a synthetic model of the vocal folds sprayed with a speckle pattern. To extend this promising technique to clinical laryngoscopic evaluations, a non-toxic speckle pattern would be required. DIC was used in vitro to evaluate the spatial deformation field for an entire vocal ligament. FE models, based on the DIC-derived material properties, were created to evaluate how variations of cross section, inhomogeneity and anisotropy affect the fundamental frequency of vibration (Kelleher et al. 2010). An area where DIC outperforms most other strain measurement techniques is that of in vivo measurements, thanks to its limited invasiveness. In vivo applications of DIC are hindered by a number of factors: difficulty/impossibility to create a dedicated speckle pattern, and limited control on the boundary conditions. The displacement of a non-linear elastic, viscoelastic, anisotropic material, highly variable and sensitive to the environment condition, such as the human skin was measured in vivo using DIC under large deformation, enabling the creation of a library of material properties (Evans & Holt 2009). Fast and

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International Biomechanics 

accurate measurement of the displacements and strain of the heart during cardiac surgery can help assessing the best strategy: DIC (exploiting the natural pattern on the myocardium) was adopted in the surgical theatre during a cardiopulmonary bypass surgery (Hokka et al. 2015). DIC was applied to ultrasound breast images to identify cancerous tissue, based on its deformation and stiffness (Han et al. 2012). DIC with ultrasound images has also been used to measure in vivo deformation in tendons (Okotie et al. 2012) and lower limb muscles (Affagard et al. 2014).

6.2.  Applications to hard tissue Historically, the main way to measure strain in hard tissues was by means of strain gauges (Cristofolini & Viceconti 1997; Cristofolini, Conti et al. 2010; Yang et al. 2011; Cristofolini et al. 2013). However, the reinforcement effect of strain gauges may not be negligible (Little et al. 1990; Ajovalasit & Zuccarello 2005). Strain gauges are sometimes too large when compared to the scale at which strains gradients are evaluated in biological tissues (Cristofolini et al. 1997; Nicolella et al. 2001; Amin Yavari et al. 2013). Furthermore, strain gauges only measure at the discrete points where they are attached. Extensometers have sometimes been used to measure deformation in bone specimens, e.g. (Keaveny et al. 1997). Similarly to soft tissue, extensometers may induce micro-damage in bone, and measure the average strain over the gauge length. Relevance of transmission photoelasticity to bone testing is limited by the fact that model materials such as araldite are homogeneous and isotropic. With reflection photoelasticity real bone can be tested, but large errors arise due to the reinforcement effect (Cristofolini et al. 1994, 2003). An overview of applications of strain gauges, in-fibre Bragg grating sensors, DIC and digital volume correlation (DVC) was recently published (Grassi & Isaksson 2015). DIC shows its benefits also with hard tissue, allowing operating at different dimensional scales (Table 2): from small specimens (tissue level), such as cortical bone (Hoc et al. 2006), teeth (Gao et al. 2006), up to large specimens (organ level), such as whole bones (Tayton et al. 2010). In this case small strains are involved, never exceeding 10,000 microstrain (Bayraktar et al. 2004). The problem of characterizing cortical bone at the tissue level (Haversian system) to assess local phenomena, such as micro-damage or bone remodelling, was solved with DIC (Nicolella et al. 2001; Hoc et al. 2006). Single trabeculae of cancellous bone have been investigated with DIC and a high-speed camera in a three-point-bending test (Jungmann et al. 2011). A whole-organ investigation was carried out on teeth (few millimetres) to optimize the stiffness and load transfer in dental implants (Tiossi et al. 2011). DIC and strain

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gauges were used on mouse tibias under axial compression (Sztefek et al. 2010). It was concluded that the spatial resolution of the strain gauges was inadequate to measure the localized peak strains identified by DIC. Similarly, (Vaananen et al. 2013) showed the effectiveness of DIC in identifying the location and modality of fracture in bones (in this preliminary study composite femurs were used). Strains measured with DIC at selected regions were used to validate an FE model of the same composite femur built from computed tomography (Dickinson et al. 2011). This research was further extended by (Grassi et al. 2013), who performed a much larger number of DIC measurements on similar composite femurs. A similar work was carried out on cadaver femurs: a high-speed cameras were used to measure strain and fracture with 2D-DIC, and validate the corresponding FE models (Op Den Buijs & Dragomir-Daescu 2011). This approach was further extended to 3D-DIC using two high-speed cameras (Grassi et al. 2014; Helgason et al. 2014). Due to their limited resolution (1 Megapixel or lower, depending on the frame rate), high-speed cameras were originally introduced to biomechanical investigations only to qualitatively investigate fracture (Cristofolini et al. 2007; de Bakker et al. 2009; Juszczyk et al. 2011; Schileo et al. 2008; Zani et al. 2015). High-speed cameras with sufficient resolution to be integrated in a DIC system became available only recently. A preliminary application to the human vertebra was recently published, where the methods were fine tuned to minimize errors (Palanca, Brugo et al. 2015).

7.  Synergies with FE in biomechanics Another important feature of DIC is its ability to integrate with FE models, in different ways (Babuska & Oden 2004; Jones & Wilcox 2008, Cristofolini, Schileo et al. 2010): (1)  Experimental identification of model parameters: the high complexity involved in FE models (often including patient-specific detail, inhomogeneous material properties, non-linear interfaces, etc.) requires experimental measurements to identify the input parameters. (2)  Experimental validation of model predictions: as reliability of numerical predictions cannot be taken for granted, quantitative comparison with experimental data is necessary. DIC (if properly optimized) has a similar accuracy, but more noise than strain gauges. However, DIC can provide full-field information. For instance, DIC was used to validate FE models of the proximal femur for the prediction of strains and fracture, both qualitatively (Helgason et al. 2014) and quantitatively (regression between DIC-measured and

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FE-computed stiffness and strain (Dickinson et al. 2011; Op Den Buijs & Dragomir-Daescu 2011; Grassi et al. 2013)). (3) Use of numerical models to improve the experiment: the synergy between a local approach (implemented in most DIC software) and a global approach (FE) can be exploited to reduce the errors in DIC-computed strain field. In fact, usually low-pass filters are used to reduce the noise in the strain maps obtained by derivation of the displacements (Baldoni et al. 2015). This can result in loss of information due to the smoothening of existing gradients. Alternatively, strain can be computed by means of an FE solver, where DIC-measured displacements are imposed to the FE nodes (Evans & Holt 2009). The continuum assumption (which is intrinsic to FE modelling), acts as a low-pass filter. (4)  Use of numerical models for inverse material characterization, based on experimental measurements: integration of numerical and experimental methods allows non-destructive assessment of mechanical properties that are otherwise difficult to measure experimentally. For instance, to investigate the mechanical response of the skin, in vivo strain under point loading was measured by DIC; such measurements were fed into an FE model to estimate the hyperelastic parameters (Evans & Holt 2009). Similarly, specimen-specific FE models of the sclera were fed with DIC-measured quantities (Coudrillier et al. 2013).

8.  Other image correlation tools DIC allows calculating the displacement and/or strain only on the surface of the specimens. An important step forward in the characterization of biological structures consists in measuring displacement and strain fields on entire volumes (Roberts et al. 2014; Freddi et al. 2015). The concept of DVC was introduced by (Bay, Smith et al. 1999, Smith et al. 2002) as a natural extension of DIC to a three-dimensional domain. With the rapid improvement of micro-focus computed tomography (micro-CT), DVC has gained increasing attention as a powerful tool to examine full-field deformations in trabecular bone (Liu & Morgan 2007; Dall’Ara et al. 2014; Gillard et al. 2014; Palanca, Tozzi et al. 2015), cortical bone (Dall’Ara et al. 2014; Palanca, Tozzi et al. 2015), whole bones (Hussein et al. 2012, 2013), cellular scaffolds (Madi et al. 2013) and bone-cement interface (Tozzi et al. 2014).

9. Conclusions This review has shown the potential usefulness of DIC as a full-field, contactless and versatile technique. In fact successful biomechanical applications of DIC can be found at different dimensional scales (from the microscopic tissue level, to macroscopic organ-level specimens), on a wide range of biological specimens (both soft and hard tissue) and for a variety of tests, including fracture. DIC can measure displacements with very high accuracy and precision. However, to obtain accurate and precise measurement of strain, great care is needed to optimize the surface preparation, and the hardware and software settings. Thanks to the versatility of DIC, it can be foreseen that more and more application will be developed in biomechanics in the forthcoming years, both in vitro and in vivo.

Acknowledgements The authors wish to thank Dr Thomas Luyckx and Dr Brad L. Boyce for providing the pictures reproduced in Figure 2.

Disclosure statement No potential conflict of interest was reported by the authors.

ORCID Marco Palanca   http://orcid.org/0000-0002-1231-2728 Luca Cristofolini   http://orcid.org/0000-0002-7473-6868

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Appendix 1. DIC uses digital images to track the displacement of portions of the speckled surface (Figure 1). In the case of 2D-DIC, images of specimen surface in the undeformed (or reference) and deformed states are acquired by one high-spatial-resolution digital image acquisition device (such as a regular digital camera, a high-speed camera, an optical microscope). The digital images (typically in grey scale) are divided into sub-images (facets). In order to obtain an approximation of grey scale between pixels instead of discrete and independent values, the grey-scale distributions are interpolated, usually with a bicubic spline. Images of the deformed states are compared to the reference one in order to match facets and track the displacement. The degree of matching between facets is evaluated by a normalized cross-correlation function such as (A1): N M ∑ ∑

𝜌CC = �

i=1 j=1 N M ∑ ∑ i=1 j=1

F(xi , yj )G(xi� , yj� )

F 2 (xi , yj )

N M ∑ ∑ i=1 j=1

(A1) G2 (xi� , yj� )

or a normalized sum-of-squared-differences such as (A2):

 21

2

𝜌SSD

⎤ ⎡ ⎥ ⎢ � � M N ��⎢ G(xi , yj ) F(xi , yj ) ⎥ − � = ⎥ (A2) ⎢� N M N M i=1 j=1 ⎢ ∑ ∑ ∑ 2 ∑ 2 � � ⎥ F (xi , yj ) G (xi , yj ) ⎥ ⎢ ⎦ ⎣ i=1 j=1 i=1 j=1

where F(x, y) and G(x′, y′) represent the grey-scale value for the pixel at the coordinate (x, y) of the reference image and the coordinate (x′, y′) of the deformed image, respectively. N and M are the dimensions of the facet, usually square. After matching the facets, the full-field displacement is automatically computed by tracking the change in position of points on digitized images. In fact, the coordinates in the reference image (x, y) and in the deformed one (x′, y′) describe the deformation between the two states (A3): x� = x + u + y� = y + v +

𝜕u Δx 𝜕x 𝜕v Δx 𝜕x

+ +

𝜕u Δy 𝜕y 𝜕v Δy 𝜕y

(A3)

where u and v represent the displacements for the facet centres in the x and y directions, respectively. Δx and Δy are the distances in the x and y directions, from the centres of the facet to the point in coordinates (x, y). The gradient terms in A3 indicate that the initial facet of (M  ×  N) pixels will be strained to optimally match the correspondent facet in the deformed status (Peters & Ranson 1982; Bruck et al. 1989; Wang et al. 2002). The strain tensor (A4) is obtained by derivation on displacement gradients (Sutton et al. 2009): +

1 2

+ (

1 2

exx =

𝜕u 𝜕x

eyy =

𝜕v 𝜕y

exy =

1 2

𝜕u 𝜕y

[( )2 𝜕u 𝜕x

[( )2

+

𝜕u 𝜕y

𝜕v 𝜕x

) +

( )2 ] +

𝜕v 𝜕x

( )2 ] + 𝜕v 𝜕y [( )( ) 1 2

𝜕u 𝜕x

𝜕u 𝜕y

( )( )] +

𝜕v 𝜕x

𝜕v 𝜕y

(A4)

( )( ) In order to find the six deformation parameters (u, v, 𝜕u , 𝜕u , 𝜕x 𝜕y ( )( ) 𝜕v 𝜕v , 𝜕y and match the facet, an approximate-solution meth𝜕x od is adopted. Usually, the Newton–Raphson algorithm is used because of its computational economy (Kelley 1999). Other algorithms are also adopted, such as the Levenberg–Marquardt. When the method converges, the displacement field is obtained but discontinuities might appear due to the local grey-scale value. A smoothing algorithm is needed to provide a continuous displacement field and perform a strain analysis. Among the available smoothing algorithms (Wahba 1975; Woltring 1985), some are better suited than others, depending on the features of the noise to be attenuated (Baldoni et al. 2015). 3D-DIC can be considered as an extension of 2D-DIC, as the operating principles are similar, but extended on a third dimension (Luo et al. 1992) by using two or more cameras in stereoscopic vision.