Acta Polytechnica


doi:10.14311/APP.2020.27.0022
Acta Polytechnica 27(0):22–31, 2020 © Czech Technical University in Prague, 2020

available online at http://ojs.cvut.cz/ojs/index.php/app

ROLE OF FLUID ON THE CONTACT DEFORMATION RESPONSE
OF BIOLOGICAL TISSUE

Michael V. Swaina,b

a The University of Sydney, Faculty of Dentistry, Biomaterials Unit, AMME, Sydney NSW 2004, Australia
b Don State Technical University, Biomechanics and biomaterials, Rostov-on Don, Russia
correspondence: michael.swain@sydney.edu.au

Abstract. This paper will focus on the role of fluids on the indentation deformation response of tooth
and eye tissues. All natural biological materials contain fluid and function in a fluidic environment,
which plays a critical role in responding to loading events as well as tissue nutrition. The location of this
fluid varies and is considered as both bound and mobile with much of it located in cell compartments
that are also able to respond directly to loading. The extent of the fluid content varies from less
than 10 % in the case of the highly mineralised enamel to more than 80 % in the case of soft eye
tissues. The role of the fluid and its response during loading is also complicated by the hierarchical
structure of biological tissues, be they mineralised or not. The mechanisms by which the presence
of fluid in these materials influences the mechanical response is still poorly understood and has not
been systematically investigated. The present paper presents data generated over many years on
both the above biological tissues and attempts to present indications as to the mechanism(s) by
which the presence of fluid contributes to the deformation. The situation associated with contact
loading with the presence of mobile fluid in the tissues results in a more complex situation than the
classic elastic-plastic contact situation, but the latter still forms the basis for much of the analysis of
instrumented indentation force-displacement load-unloading curves using various shapes of indenters,
especially for mineralised structures. In the case of soft tissues the absence of agreed protocols for
interpretation of force-displacement-time responses is restricting clinical/biological applications.

Keywords: Biological tissues, fluid, indentation.

1. Introduction
Indentation tests provide a simple basis to interro-
gate the local mechanical behaviour of materials. The
developments possible with the advent of computer
based instruments over the past 50 years have enabled
high precision force-displacement data to be gener-
ated with nm and nN precision [1–4]. While these
instruments were primarily designed for classic elastic-
plastic materials, evermore widespread application to
biological tissues has occurred especially over the past
few decades [5]. In many instances minimal differ-
ences in test/instrument parameter requirements are
necessary for conducting tests for instance in the case
of tooth enamel. However, the situation for softer
biological materials such as eye and soft organs gen-
erally is that the instrument requirements are very
different from the original design applications of in-
strumented indentation machines. These instruments
were initially developed to measure the properties of
thin elastic/plastic/brittle films on classic engineering
materials, which generally required high displacement
resolution (<nm) with reasonable forces (10mN). The
situation for soft biological systems however is for
very low loads (<1mN) and substantial displacements
(up to 100 µm). Currently there are virtually no
specific nano-indentation instruments developed for
soft biological tissues and as such this community

has had to adopt atomic force based systems for this
purpose [5]. The limitations of both approaches often
generates different outcomes when testing the same
tissues, this arises because of the size of the required
indenter, generally spherical tipped, for AFM versus
nano-indenter systems [5]. The situation regarding
software packages to assist with the interpretation of
the resultant indentation force-displacement curves
has become well advanced in the case of elastic/plastic
and thin coating systems but this is not the case for
biological soft tissues and associated materials [6–8].
For the elastic/plastic community well defined ISO
standards have been developed that enables the role of
tip geometry and non-linear response to be addressed
[6]. This unfortunately is not the situation for biolog-
ical tissues. However, as Oyen has recently suggested,
there is a consensus beginning to emerge as to viable
approaches for interpreting the deformation response
of soft tissues and structures [9]. In the case of in-
terpretation of force-displacement behaviour, using
a standard Berkovich diamond pyramid for elastic-
plastic materials, the ISO standard has been shown
to be sufficiently robust as it utilises the basic Oliver
and Pharr approach developed more than 25 years
ago [6]. The outcomes from the incorporated software
in the various instruments are the associated hardness
and contact modulus. With specific assumptions this
can be extended to the case of elastic/plastic thin

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http://dx.doi.org/10.14311/APP.2020.27.0022
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vol. 27/2020 Role of fluid on the contact deformation response of biological tissue

films on various elastic/plastic substrates [10]. More
detailed outcomes for elastic/plastic materials such
as the determination of the stress-strain, yield stress
and work hardening have been empirically known for
more than 60 years based upon the work of Tabor [11].
The use of spherical tipped indenters to quantify the
nano-indentation response of elastic/plastic materials
was pioneered by Field more than 25 years ago [12, 13].
Details such as the role of work hardening and sur-
face property gradients and their role on pile-up and
sinking-in of the impression have limited the uptake
of this approach although a recent study by Leitner
et al [14] shows great progress in being able to match
small pillar compression tests with nano-indentation
test outcomes. As will be shown below in the case
of teeth, the elastic/plastic analysis with pointed or
spherical tipped indenters has provided considerable
detail of the properties of enamel, dentine and as
well as their diseased states (caries and molar incisor
hyper-mineralisation) and in particular to their spa-
tial variation [15–20]. This information has been able
to show a raft of outcomes relevant to the effect of
clinical procedures, basic hierarchical size dependence
and a basis to interpret creep [21–23]. However as will
be shown below more critical recent ultrastructural
analysis of teeth, especially for enamel, has led to the
questioning of some of these outcomes [24]. In the
case of soft tissues, with a focus on eye tissue, there
are serious issues regarding what is the basis for the
deformation observed. Eye tissue, like many soft gel
systems, contain a very high percentage of fluid, up
to 80 %, some of which can be considered bound and
some mobile as elegantly illustrated by Oyen [9, 25].
However even with the bound fluid some of this may
exist in cellular structures, which limit its general
movement but does not prevent local displacement
as the outer cell membranes are deformed. While gel
like materials may be considered isotropic, biological
tissues display hierarchical structure, which will re-
sult in likely scaling effects and in addition they have
structural anisotropy [26]. These latter features have
evolved with organism development and are genuinely
optimised for function with variations associated with
species etc. The very high fluid content, the high
degree of extensibility of such biological tissues plus
their ability to fully recover limit the adequacy of
current (elastic/plastic/viscoelastic) approaches to in-
terpret the outcomes. There have been two major
approaches for interpreting the outcomes (for soft tis-
sues) of force-displacement response generated during
testing of these structures; visco-elastic [27] and more
recently poro-elastic [9]. The former considers the
material as primarily a viscous body, which can be
considered as equivalent to various spring and dashpot
combinations or Prony series that are fitted to match
the experimental outcomes [28]. Whereas the poro-
elastic approach considers the material to be bi- or
multi-phasic with one phase being porous and contin-
uous but behaving elastically while the other is fluid

that must flow through the porous elastic structure
as a consequence of a stress or pressure gradient [29].
The latter field was first introduced to soil mechanics
by Darcy [30] and developed further by Biot [31]. Ap-
plication of poro-elastic behaviour of biological tissues
was given a major boost by the work of Mow and
colleagues who investigated the deformation response
of cartilage tissue, especially of joints, using contact
deformation [32, 33]. Other investigations by Cowin
et al explored the role of hierarchy on poro-elastic
behaviour of bone under simple compression tests [34].
A relatively simple methodology to extract the various
elastic components (4 for an isotropic material) and
permeability of the body was developed by Galli and
Oyen but involved an optimisation parameter fitting
of a specific model that becomes slightly more com-
plex when realistic loading rates are used to generate
loading, then upon achieving max load, creep data
[35, 36]. More recent strategies to determine the poro-
elastic response of gels have been developed by Lai
and Hu [37] who have proposed the use of DMA sys-
tems involving frequency sweeps along with testing at
different contact dimensions. This approach enables
determination of whether visco-elastic or poro-elastic
behaviour is the controlling mechanism as visco-elastic
systems should be specimen or indenter size invariant
while the fluid flow associated with poro-elastic be-
haviour is contact size dependent as deformation with
the latter is related to fluid transport. There have also
been novel approaches using fractional visco-elastic
theory, which is somewhat easier to analytical model
and invert than standard visco-elastic and poro-elastic
solutions [38].

2. Anatomical aspects
2.1. Teeth
Figure 1a shows an overview of the anatomy of tooth
tissue [39]. There are three major structural com-
ponents, the outer external layer of enamel that is
directly exposed to the oral cavity environment and is
non-vital, the dentine which surrounds the pulp space
which is vital and contains extensive innervation and
fluid transport and in addition there is the cementum
layer that connects the dentine in the root region of
the tooth to the periodontal ligament that binds the
tooth into the jaw. The focus here will be only on the
enamel and dentine. The composition of the enamel
layer shows hierarchical behaviour that is illustrated
in Fig 1b and is predominately mineralized 85vol%, 10
vol% fluid and 4 to 5vol% residual proteins [40]. The
smallest feature are the hydroxyapatite nanowires, ap-
proximately 25 by 50 nm in dimension that are also
continuous from DEJ to the surface and are bundled
into rods (approx. 5 µm diameter) that form the
second level of the hierarchy. These rods also are
bundled into aligned groups called Hunter-Schreger
bands that are some 50 to 100 µms in width that are
readily observed on a polished surfaces of enamel that
form the 3rd level of hierarchy [41, 42].

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Michael V. Swain Acta Polytechnica

a) b)

c)

Figure 1. a) Over-view of the structure of teeth [39]. b) Hierarchical structure of enamel [42], and c) Atom probe
tomography of enamel crystallites [43].

There are also gradients in microstructural uni-
formity and composition as well as minor amounts
of incorporated remnant proteins that increase from
the surface to the dentine-enamel junction (DEJ). A
more in-depth compositional analysis of enamel using
atomic probe tomography also shows that the chemi-
cal composition of crystallites varies and that there are
localised organic components present at some triple
points as well as Mg rich amorphous lenses present
in these locations [42]. A typical illustration of the
chemical composition of these structures is shown in
Fig 1c. Dentine is a no less complex structure than
enamel as is illustrated in Fig 2. The hierarchy is more
complex but consists of near unidirectional tubules
aligned perpendicular to the dentine enamel junction
that extend to the pulp. The density and size of the
tubules increase towards the pulp from 0.5 to 1 µm
diameter. Surrounding these tubules is a mineral rich
peri-tubular cuff approximately of 0.5 to 1 µm thick,
which also contains finer microtubules approx. 100
nm diameter normal to the axis of the main tubules
and that extend through the mineralised cuff into
the inter-tubular dentine. The latter region contains
mineralised type IV collagen as well as fluid and rem-

nant growth factors. The volume fraction of fluid
is approximately 30vol%, while that of collagen IV
is 20vol % and mineralized tissue at 50vol%. Fluid
is able to move within the dentine when loaded and
this can trigger pain sensation from the enervation
arrangement at the pulp and within the dentine [43].

Caries is the most prevalent affliction of humans and
is associated with the development of acidic conditions
from the fermentation of carbohydrates by various
pathogens in the mouth [44]. The formation of these
acids in protected locations associated with difficulty
of adequate oral hygiene results in acid induced dem-
ineralisation of tooth structure. Two common areas
where these conditions occur and demineralisation
results are about the fissures of molar teeth and the
proximal space between teeth [45]. Both areas are
difficult for clinical detection often resulting in sub-
stantial extent of demineralisation including into the
underlying dentine. The form of the demineralisation
is very subtle, with this occurring at both the bound-
aries between rods and within individual crystallites
in the rods of enamel [46]. While in dentine dissolu-
tion of the minor tubules precedes that of the major
tubules. Loss of mineral also occurs within the inter-

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vol. 27/2020 Role of fluid on the contact deformation response of biological tissue

Figure 2. Overview of the structure of dentine showing the complex tubule features as well as microtubules through
the peri-tubular mineralised cuff.

tubular space. In the case of enamel there is often
greater mineral loss beneath the surface with a harder
surface layer present while in the case of dentine there
is usually an almost linear gradient in mineral den-
sity from the surface with a hyper-mineralized region
just in front of the active area of dissolution that is
associated with the pulp/odontobast defence system,
which deposits mineral occluding the tubules to pre-
vent the migration of pathogens into the pulp space
[47]. Typical examples of demineralisation for enamel
and dentine are shown in Fig 3. A plot of the mineral
density of a proximal lesion in enamel is shown in
Fig 4, which indicates that up to 50% loss of mineral
occurs, yet the overall enamel structure remains intact.
Note the small locations of mineral loss from within
the cores of the tubules as well as at some triple point
regions of crystallites. In the case of dentine (Fig 3c)
the loss of mineral results in a higher fluid content
and partially degraded collagen that is much more
permeable than sound dentine [48].

2.2. Eyes
Here we shall only focus on the external surface of
the eye namely the cornea, limbus and sclera regions
which are shown in Figure 5 [51]. The composition of
eye tissue is predominantly fluid with collagen fibres
and proteoglycans holding the collagen in specific ar-
rangements to provide the optical clarity of the cornea
and with partially permeable membranes restraining
the fluid. The sclera and limbus regions are less well
organised than the cornea and with slightly different
volume fractions of liquid present. A high resolution
cross-sectional view of cornea reveals the nature of
the collagen fibre bundles that are aligned parallel to
the surface resulting in an orthotropic structure with
radial variations in the density and organisation of
the fibers and the associated mechanical properties
[50]. There are a range of degenerate diseases of the
eye that influence the organisation of the collagen
arrangement, which have a consequential outcome on
the ability of the lens to focus images on the retina.

2.3. Observations
2.3.1. Teeth
Nano-indentation testing of enamel and dentine is very
mature and was a focus of research shortly after the
availability of high resolution indentation and AFM
based systems [52]. The analysis of force-displacement
date followed that of elastic/plastic materials to enable
the hardness and modulus to be estimated. Variations
of H and E as a function of position identified gra-
dients across enamel, dentine and higher resolution
studies showed changes across the DEJ. A slightly
different strategy was adopted by He et al, who as
well as probing the variation of H and E spatially,
used spherical tipped indenters to investigate the con-
tact stress-strain response and observed that with
such indenters non-linear behaviour began at very low
contact stresses (H/5) and was associated with sub-
stantial energy loss and hysteretic behaviour [53, 54].
This also agreed with the odd report that showed the
apparent disappearance of indentations when viewed
sometime after formation. He et al also found for
enamel that both the initial loading behaviour and
creep at max load and upon subsequent near complete
unloading was dependent upon the environment with
far less creep occurring for desiccated samples, see
Fig 6 [55].

This behaviour was rationalised in terms of the role
of the remnant proteins present in enamel because of
their perceived presence surrounding all crystallites
and ability to unfold and refold with the breaking
and reformation of weak hydrogen bonds. An alter-
nate approach to rationalise the creep of enamel was
developed considering the behaviour as a series of
spring and dashpots as well as plastic loss mecha-
nisms [55] and also by considering enamel as a brick
like structure held together by proteins which behave
as a viscous component [58]. These two approaches
are schematically shown in Fig 7. A more recent study
has also shown that the hardness and friction response
of enamel is dependent upon the fluid content with
hardness increasing with desiccation while the friction

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Michael V. Swain Acta Polytechnica

Figure 3. Backscattered SEM images of caries in enamel showing loss of mineral [49] both within the rods a) as well
as at the inter-rods b). c) Optical image of cross-section of tooth with fissure caries showing the extensive subsurface
demineralisation. Note the limited influence on the enamel [46].

Figure 4. a) MicroCT image of mineral density of enamel proximal white spot lesion [47], and (b) TEM observations
of the manner in which mineral is lost at the nanoscale [50].

a) b)

Figure 5. a) Schematic illustration of a cross-section of an eye showing the various regions on the surface of the eye
that are mentioned in the text [56]. b) Histology section of the cornea [57]

decreases with the presence of fluid as shown in Fig 8
[59].
The concept of crystallites of enamel being sur-

rounded by protein and resulting in a hierarchical
structure led to the development of an analysis ra-
tionalising the observed size dependent behaviour of
the properties of enamel [61, 62]. This approach was
built upon the work of Ji and Gao which worked well
for bone [63]. With the advent of more recent Atom
Probe Tomography [43] and HRTEM [24] work indi-
cating the lack of a uniform protein/-peptide layer

between crystallites has raised some questions as to
the role of proteins on the resultant mechanical be-
haviour. An issue that has not been widely canvassed
is the role of fluid transport, this is despite knowing
that enamel typically contains up to 10 vol% fluid
which is mobile. More than 3 decades ago Fox in
a pioneering study found, during the cyclic loading
of teeth at relatively low orally relevant loads, that
considerable hysteresis occurred, which was loading
rate and cation presence dependent [64]. Indentation
tests by Bertassoni et al [65] as well as compression

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vol. 27/2020 Role of fluid on the contact deformation response of biological tissue

Figure 6. Indentation force-displacement a) plus creep response of enamel b) at max load and c) at very low load ??

Figure 7. Schematic illustrations of creep behaviour mechanisms for of enamel a) and b) Viscous fluid squeezed
between rigid apatitie crystals [58] and c) Viscoelastic-plastic body "spring + plastic element + dashpot + 2
Kelvin-Voigt bodies" [55].

Figure 8. Observations of a) friction coefficient of enamel wet vs dry, and b) Hardness of enamel with dehydration
time [59].

tests [66] of dentine also displayed creep at maximum
load. The former authors showed that the presence
of proteoglycans also influenced the extent of creep
and subsequent recovery. These authors, like the ear-
lier studies of enamel [54], suggested that the creep

response of dentine was influenced by the presence of
proteins. It is also known that both enamel and den-
tine are permeable with minor amounts of fluid from
the pulp exiting into the oral cavity. The permeability
of dentine, with its high density of open tubules, is

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Michael V. Swain Acta Polytechnica

Figure 9. Force-displacement curves during the indentation of various regions of the external surface of the eye [60].
These force-displacement curves are also strongly loading rate dependent.

greater than enamel and both tissues show increased
permeability when caries is present. In fracture tests
on dentine [43] it was found that the presence of fluid
played a major role in the fracture toughness and was
observed to be drawn into the tubules in the tensile
stress region about the crack tip but was expelled
from tubules after the passage of the crack tip, that
is in the wake of the crack tip. In another study it
was found that in flexure tests of dentine beams the
flexural behaviour including the strength and nominal
E modulus was strain rate dependent for fluid filled
but not for dehydrated samples [67]. Caries has a ma-
jor influence on the deformation behaviour of enamel
and dentine. The extent of mineral loss in teeth is
best illustrated using micro Computed Tomography
(mCT) as shown in Fig 4 for a proximal lesion in
enamel. As shown in studies by Huang et al this loss
of mineral has a major influence on nano-indentation
derived hardness and elastic modulus properties [68].
The interpretation of the force-displacement curves for
the latter outcomes was based upon the assumption
of elastic-plastic behaviour whereas the behaviour of
highly porous materials, which are generally fluid filled.
The latter is far more complex involving both fluid
displacement and crushing or densifying the porous
structure directly beneath the indenter tip as shown
by studies of porous bioceramics [69] and fitted the
failure criterion proposed by Gurson et al [70]. To date
the motion of fluid transport within such a porous
structure has not been addressed. In the case of cari-
ous dentine it was observed that there was a significant
difference in the behaviour of saturated versus dehy-
drated specimens [71]. These authors also noted that
the force-displacement response of fluid filledhighly
demineralised dentine showed a substantial recovery
during unloading, presumably associated with fluid
flow returning to the consolidated material beneath
the area of contact.

2.3.2. Eye results
Indentation tests on eye tissues have become popular
over the past decade, especially with the ability to use

AFM systems with small spherical tipped indenters
(R< 20 µm) [72]. Nano-indentation tests have also
been conducted but have required systems with low
force but large displacement using relatively large in-
denter spherical tips (R ~500 µm) [60, 73]. The AFM
approach has typically involved rapid load/unload
tests and relied upon Hertzian contact analysis for
the determination of the elastic modulus. Whereas
the nano-indentation tests usually involve a slower
loading rate and incorporate a hold period at max
load generating substantial creep response, see Fig 9.
Interpretation of NI results for eyes based upon an
inverse FEA visco-elastic analysis has been conducted
by Abyaneh et al [73]. An alternate highly simpli-
fied poro-elastic approach developed by the author
and colleagues [60] considers localised deformation of
these highly fluid filled tissues as being determined by
the collagen elastic response and movement of fluid
caused by indentation induced transient pressure gra-
dients. At longer hold times at max load the resultant
displacement is determined by the elastic properties
of the structure whereas the short term behaviour is
dependent upon the loading rate and hydraulic con-
ductivity. The aim of the latter approach was an
attempt to develop an output, namely an effective
E and effective hydraulic conductivity K, that was
comparable to the hardness and contact modulus that
has so successfully been used for elastic/plastic mate-
rials. These effective E and K values are recognised as
approximations because as outlined above eye tissues
are highly anisotropic with orthotropic mechanical
properties because of the aligned collagen fibres par-
allel to the surface, they have gradients in collagen
density and are likely to have orthotropic hydraulic
conductivity parameters.

3. Conclusions
The presence of fluid plays a significant role in the
deformation response of biological tissues. In this
overview only two types of tissue are considered,
namely highly mineralised tooth tissue and highly
fluid containing eye tissue. In both instances there is

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vol. 27/2020 Role of fluid on the contact deformation response of biological tissue

clear evidence of the influence of fluid but the mech-
anisms are not well understood. There is a clear
necessity for further critical investigations to under-
stand the mechanisms responsible in these and other
biological tissues. Of even greater need is for collec-
tive agreement as to an approach to interpret the
force-displacement-time curves generated during the
indentation of such complex tissues.

Acknowledgements
The author wishes to thank his many colleagues who
have been part of this journey investigating the inden-
tation responses of teeth and eyes. Also Australian Re-
search Council (ARC DP160104602 and LP180101352)
plus the Government of the Russian Federation (grant No.
14.Z50.31.0046).

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	Acta Polytechnica 27(0):22–31, 2020
	1 Introduction
	2 Anatomical aspects
	2.1 Teeth
	2.2 Eyes
	2.3 Observations
	2.3.1 Teeth
	2.3.2 Eye results


	3 Conclusions
	Acknowledgements
	References