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# Indentation testing on biological and soft materials using the bioindenter

The goal of this wiki article is to explain the method of indentation on biological materials (sometimes referred to as bioindentation), what results the method will give and what phenomena should be considered in order to obtain correct results.

## What is the instrumented indentation technique?

The instrumented indentation technique (IIT) has been available in the last twenty to thirty years for hardness and elastic measurements of local mechanical properties, namely on thin films. The IIT has been intensively used in testing of hard materials, including biological materials such as dentin or bone, in both dry and wet conditions. Since then the biology and bioengineering fields have evolved and now knowledge of local mechanical properties of new types of soft biomaterials and biological materials is required in many applications. The natural step, therefore, was to develop an IIT method also for use in the domain of soft and extremely soft materials and tissues[1,2]. However, indentation of soft materials brought some important challenges, directly related to the nature of the samples and the testing conditions:

• very soft (i.e. very compliant) materials,
• permanent immersion in liquid,
• automatic surface detection procedures on samples with an uneven surface

Spatial characterization requires an additional suitable lateral repositioning system and optical microscope. The commonly applied procedure for indentation of such materials includes the use of a spherical indenter (Figure 1), low forces (µN to mN range) and large penetration depths (tens of µm). The instrument should also exhibit very good thermal stability as many materials show time-dependent (poroelastic, see Figure 2) behavior. A typical indentation measurement on cartilage would use a spherical indenter with 500 µm radius, maximum load of 5 mN, loading time 10 seconds, hold period of 30 seconds and unloading time of 10 seconds.

## What are the main types of soft materials?

The main types of soft biological materials (either of human or animal origin) include cartilage (healthy or diseased), cornea (normal or with treatments), tendons, and liver. Examples of man-made soft materials are hydrogels that are used as cell growth media or as scaffolds, various types of scaffolds (bio-resolvable) and microspheres. The applications of indentation are not limited to biomaterials only but include many types of other materials such as sticky films for mobile telephones (OCA – Optically Clear Adhesive), elastomers without or with functional coatings (Au), and foils from hyaluronic acid.

## Why are we interested in the indentation testing of soft materials?

The greatest advantage of the IIT is its ability to characterize local mechanical properties of biological tissues at the scale of cellular (multi)layers in order to understand their mechanical behavior. This is often done to find potential replacement materials whose properties and behavior need to closely match the replaced tissues. There are many reasons for local testing of the mechanical properties of soft biological tissues and biomaterials. Here is a list of the main ones:

• Many biological tissues are subject to mechanical loading and their mechanical characterization can therefore help in the development of equivalent artificial tissues.
• Changes in mechanical properties are often related to diseased states of other tissues and can therefore provide information about the progress of the disease or effects of the medical treatment.
• Nutrition regimes are known to affect some types of cartilage and lead to changes in their mechanical properties.
• Cells are known to ‘feel’ the stiffness of the underlying and surrounding material and thus differentiate and grow in the preferred direction[3,4]. The characterization of mechanical properties of hydrogels used for cell cultures is therefore of great interest. Due to its local character, IIT can easily probe small areas in cartilage where a lesion was experienced and evaluate the level of regeneration on different types of scaffolds[5,6,1].
• The IIT also finds its use in the growing area of biomimetic research in which the structure and mechanical properties of tissues must be carefully characterized to develop graft materials with properties as close as possible to the real tissues.

## What do we obtain by indentation testing of biological materials and biomaterials?

As for any mechanical measurement, the method of analysis of the results is important. The Bioindenter indentation software is ISO 14577 compliant and automatically calculates indentation parameters, including elastic modulus, hardness, creep, relaxation, and work of indentation. However, in addition to the commonly used method for calculation of hardness and elastic modulus (i.e. based on the Oliver and Pharr approach[7]), the Bioindenter indentation software also offers calculation of elastic modulus based on Hertz’s model, which is more appropriate for biological materials than the ISO 14577 standard.

The Hertz’s calculation (Eq. 1) is done on the loading portion of the indentation curve (the Oliver and Pharr approach is done via the fit of the unloading portion, see Figure 3: Schematic illustration of ISO 14577 calculation of elastic modulus and hardness from the unloading portion of the indentation curve. hp is the permanent indentation depth after the removal of the test force., hr is the tangent depth [intersection of the tangent to the unloading curve with the X axis], S is the slope of the unloading curve). Other types of analyses (permeability calculations, etc.) can easily be performed on data exported in ASCII format from the indentation software.

The reduced elastic modulus Er is calculated according to Equation 1

$$E_r={\sqrt{{\pi}}\cdot S\over {2 \cdot \beta \cdot \sqrt{{A_p(h_c)}}}}$$

Equation 1

where is the slope of the unloading curve, β is a correction factor, Ap is the contact area in the contact depth hc. The elastic modulus of the sample EIT is then obtained from equation Equation 2

$${1\over{E_r}}={{1-{\nu}_s^2}\over{E_{IT}}}+{{1-{\nu}_i^2}\over{E_i}}$$

Equation 2

where indexes and refer to the sample and the indenter, respectively. Hardness HIT is calculated from the definition as force divided by the contact area using Equation 3

$$H_{IT}={E_{IT}\over{A_p}(h_c)}$$

Equation 3

The Hertz’s fit to the loading portion of the indentation curve is done according to Figure 4 and the calculation of elastic modulus is done using Eq. 4. This equation includes hoffset, which takes into account the initial phase of contact where some soft layers (epithelium) or debris can be present on the surface of the material. Using Equation 4 the Hertz’s fit is then done on the portion of the loading curve which represents the material itself.

$$F={4\over3}E_r{\sqrt{R}}(h-h_{offset})^\frac{3}{2}$$

Equation 4

Further properties, such as indentation creep or relaxation, can also be obtained from the indentation curves, namely during a hold period at a constant force (Figure 5). The simplest formula for creep calculation is given by Eq. 5

$$C_IT={{h_m-h_i}\over{h_i}}$$

Equation 5

where hm is the depth at the end of the hold period and hi is the depth at the beginning of the hold period.

## Creep measurements

For more details on the characterization of poroelasticity, see for example Swain et al, Hu et al, or Kalcioglu et al in [8–10].

## Examples of measurements on biological materials and biomaterials

After several years of use of the Bioindenter for indentation of soft materials the most interesting areas for this type of technique have been identified. These include:

### Cartilage

Osteoarthritis is one of the most common joint diseases and affects about fifty percent of the world’s population. Although some progress has been made in its treatment, considerable knowledge is required for understanding the different mechanisms of disease initiation, the effects of nutrition, advancement of the disease, and its treatment.

Such research is currently underway in many laboratories and one of the hottest topics is also characterization of the mechanical properties of cartilage. Most of these experiments are done on laboratory animals, i.e. rats or mice. The first phase of the research was concentrated on cartography of the stiffness of the cartilage in regions subjected to different loading during daily locomotion (see Figure 6 for the experimental setup and Figure 7 for typical indentation curves). These results of the indentation tests will help in the development and evaluation of osteoarthritis treatments.

## Tissue regeneration

With the development of scaffolds for tissue regeneration and also the increase of 3D printing of scaffolds, research has been conducted in order to understand the process of reconstruction of the new cartilage. A study carried out by Anton Paar TriTec focused on the evolution of cartilage regeneration after introducing scaffolds in lesion (diameter of the lesion was ~2 mm) on a goat’s femur.

The indentation measurements showed that the healthy and regenerating cartilage exhibited large differences both in elastic modulus and in creep behavior. Due to its suitable special resolution, the indentation could easily measure the stiffness (i.e. elastic modulus) of the healthy and the regenerating cartilage (Figure 8 and Figure 9).

## Cornea

The cornea, corneoscleral rim, and sclera represent regions of eye that play an important role in clear vision. Some cornea diseases or injuries can lead to partial or total blindness or chronic ocular surface pain. Treatments of such events can rely on regrowth of stem cells based in the limbal region. Survival and self-renewal of the limbal stem cells also depend on the biomechanical properties of the environment, i.e. cornea, corneoscleral rim, and sclera. It is therefore important to know the elastic modulus and permeability of the corneoscleral rim.

Also, some of the corneal treatments (e.g. crosslinking) can affect the stiffness of the cornea and therefore indicate the effectiveness of the treatment method. A recent study, carried out in collaboration with the University of Freiburg (DE), showed the differences in stiffness of the central cornea, limbus and sclera.

Together with stiffness difference, creep was also measured during the hold period (see Figure 10). Clearly the creep was much larger in the limbus than in the cornea and sclera, indicating higher ability to conduct fluid in the limbus than in the two other regions.

## Hydrogels

A series of indentations was also performed on very soft Petrisoft hydrogels (Matrigen Life Technologies, Brea, USA). These hydrogels are provided as a culture medium with various elastic moduli. All tested samples were provided in a Petri dish and were fully immersed in liquid. Their elastic modulus varied between 2 kPa and 24 kPa (Figure 11). A spherical indenter with 500 µm radius and maximum load of 50 µN was used; the maximum depth with these conditions was 72 µm.

## What to consider during indentations in liquid and on biological material

Several issues can be encountered during the indentation process on soft biological tissues or soft materials. These phenomena have to be taken into account so that they will not negatively affect the measurements and lead to erroneous results.

## The effect of capillary forces

For most indentations when the sample is in liquid, capillary forces can be observed (see Figure 12). During indentation in liquid, the capillary forces are mostly negative but they depend on the state of the surface, which can change with deposits of salt from saline solutions after repeated immersion of the indenter in the saline solution.

Meniscus can also change its radius as the indenter is penetrating deeper in the liquid. Based on many observations, the capillary forces during indentation are usually stable (the indenter is moving relatively slowly) and do not perturb the measurement. However, capillary forces become dominant and can be observed during the fast approach phase preceding the indentation.

## The effect of a surface which is not well-defined

In some cases the indentation curve shows slow force increase at the beginning, indicating contact with very soft material. This is usually observed on biological samples where the surface preparation cannot always be perfectly clean. Fragments of tissue or residue of epithelium can be the reason for this ‘soft’ phase at the beginning of the indentation. Figure 14 and Figure 15 show such indentation schematically. The effect of this superficial layer has been taken into account in Eq. 4 which disregards this ‘soft’ phase and calculates the elastic modulus only from the relevant portion of the indentation curve.

Some soft materials are also indented in dry conditions (in air). On these materials, adhesion phenomena are often observed. The adhesive forces can be recorded during the indentation procedure and the resulting plot can look similar to the one shown in Figure 15.

Pull-on adhesion is recorded as the indenter is approaching the surface while pull-off adhesion (with usually much lower negative forces due to larger contact area) is recorded when the indenter is being retracted from the surface. Measurement of the minimum pull-off force allows for calculation of surface energy according to the JKR model (Eq. 6):

$$F_{JKR}={3\over 2}{\pi}RW_{12}=F_{Ad}$$

Equation 6

where FJKR = FAd is the minimum pull-off force, is the radius of the indenter and W12 is the surface energy for the given material combination.

During indentation on samples with adhesive forces, the contact point is usually set to the minimum pull-on force although some researchers prefer to set it to the point where the increasing force crosses the zero-force line.

## Summary

The indentation of biological materials and biomaterials is a very interesting field which is now gaining importance. Although the measurement methods seem to be well established, there are still some challenges that have to be overcome.

## References

1. M.L. Oyen, Handbook of Nanoindentation: With Biological Applications, 1 edition, Pan Stanford Publishing, 2010.
2. J.D. Kaufman, J. Song, C.M. Klapperich, Nanomechanical analysis of bone tissue engineering scaffolds, J. Biomed. Mater. Res. A. 81A (2007) 611–623. doi:10.1002/jbm.a.30976.
3. D.E. Discher, P. Janmey, Y. Wang, Tissue cells feel and respond to the stiffness of their substrate, Science. 310 (2005) 1139–1143.
4. D.E. Discher, D.J. Mooney, P.W. Zandstra, Growth Factors, Matrices, and Forces Combine and Control Stem Cells, Science. 324 (2009) 1673–1677. doi:10.1126/science.1171643.
5. Y. Hu, J.-O. You, D.T. Auguste, Z. Suo, J.J. Vlassak, Indentation: A simple, nondestructive method for characterizing the mechanical and transport properties of pH-sensitive hydrogels, J. Mater. Res. 27 (2012) 152–160. doi:10.1557/jmr.2011.368.
6. I. Levental, K.R. Levental, E.A. Klein, R. Assoian, R.T. Miller, R.G. Wells, P.A. Janmey, A simple indentation device for measuring micrometer-scale tissue stiffness, J. Phys. Condens. Matter. 22 (2010) 194120. doi:10.1088/0953-8984/22/19/194120.
7. W.C. Oliver, G.M. Pharr, Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology, J. Mater. Res. 19 (2004) 3–20.
8. M.V. Swain, J. Nohava, P. Eberwein, A simple basis for determination of the modulus and hydraulic conductivity of human ocular surface using nano-indentation, Acta Biomater. 50 (2017) 312–321. doi:10.1016/j.actbio.2016.12.007.
9. Y. Hu, X. Zhao, J.J. Vlassak, Z. Suo, Using indentation to characterize the poroelasticity of gels, Appl. Phys. Lett. 96 (2010) 121904.
10. Z.I. Kalcioglu, R. Mahmoodian, Y. Hu, Z. Suo, K.J. Van Vliet, From macro- to microscale poroelastic characterization of polymeric hydrogels via indentation, Soft Matter. 8 (2012) 3393. doi:10.1039/c2sm06825g.