## Abstract

## Objective

The aim of this research was to determine the association between sorptivity of water and the state of mineralization in carious enamel of different stages of severity.

## Methods

As a preliminary work, water droplets of 1.5 μL were placed on the surfaces of hydroxyapatite (HA) discs of different densities. The water droplet profile was dynamically recorded every second over a period of 10 s using a contact angle meter to determine the relationship between sorptivity and density. To measure and calculate sorptivity on enamel surfaces, varnish was painted on the labial surface of 96 extracted caries-free human teeth, leaving two 1.4 ± 0.1 mm diameter circular exposed test sites. The specimens were randomly divided into 6 groups (n = 16) and subjected to 0(G0), 7(G7), 14(G14), 21(G21), 28(G28) and 35(G35) days of pH cycling, respectively. A 0.7 μL water droplet was placed on each exposed site and Optical Coherence Tomography was used to measure its height every 10 seconds for 2 min. Sorptivity was computed by considering sorption equations and Washburn’s analysis of capillary kinetics and correction for evaporation was also performed. Micro-Computed Tomography scans of the specimens were obtained and delta Z (ΔZ) is the parameter used to measure mineral loss. ΔZ at 10 μm (ΔZ _{10} ) and 50 μm (ΔZ _{50} ) from the surface were calculated. One-way ANOVA and Post-hoc Tukey tests were used to compare sorptivity between groups and bivariate correlations were used to analyze the association between sorptivity and ΔZ.

## Results

Sorptivity was found to be inversely and linearly correlated with HA density with R ^{2} value of 0.95. With enamel, there is a general trend of increase in mean sorptivity from G0 to G35, except for a decrease in G21. The same trends were observed for both ΔZ _{10} and ΔZ _{50} . The decrease in sorptivity in G21 coincided with the presence of a surface hypermineralized layer in G21 samples. Post-hoc Tukey showed significant differences in mean sorptivity between G0 and G14, G0 and G21 as well as G14 and G21. Post-hoc Dunnett’s T3 showed significant differences for ΔZ _{10} between G0 and G14 as well as G14 and G21. Significant correlation between mean sorptivity and ΔZ _{10} was detected with Pearson correlation coefficient of 0.461. For ΔZ _{50} , post-hoc Tukey showed significant differences between G0 and G14 but no significant difference was detected between G14 and G21. No correlations were detected between mean sorptivity and ΔZ _{50} .

## Significance

Sorptivity was found to be inversely and linearly correlated with HA density with R ^{2} value of 0.95. With enamel, there is a general trend of increase in mean sorptivity from G0 to G35, except for a decrease in G21. The same trends were observed for both ΔZ _{10} and ΔZ _{50} . The decrease in sorptivity in G21 coincided with the presence of a surface hypermineralized layer in G21 samples.

## 1

## Introduction

The formation of dental caries typically starts with demineralization of the surface of enamel and progresses in depth, causing enamel to appear white and opaque, especially with air drying of the surface [ , ]. This white appearance of early, non-cavitated enamel caries is due to the change in refractive index resulting from mineral loss of enamel. Non-cavitated enamel caries lesion could present, both in vitro and in vivo, with two types of mineral distribution cross-sectionally [ ], i.e. one that has a surface layer which is porous but still mineral-rich, covering a subsurface lesion which is low in mineral (10−70 vol%) [ ]; and another one where the mineral content is lowest at the surface and gradually increasing with the depth of the lesion [ , ]. The latter is sometimes termed as ‘active’ or ‘surface-softened’ lesions whilst the former are considered ‘arrested’ [ ]. Clinically, lesions with these two mineral distributions are not distinguishable.

It has been established that non-cavitated caries is reversible if remineralization is provided early to arrest its progress [ , ]. There is currently a plethora of remineralization agents with various delivery systems, and the protocols that typically accompany these materials range from in office treatment, take-home products to combination therapies [ ]. One of the known effects of these remineralization therapies is the formation of a protective surface layer which is highly mineralized while the subsurface region remain hypomineralized [ ]. Even saliva, which is rich in remineralizing ions such as calcium and phosphate, is known to remineralize mainly the enamel surface [ ]. However, recent systematic reviews [ , ] conducted on the management of post-orthodontic non-cavitated caries lesions concluded that there is a lack of compelling clinical evidence to support the success of remineralization with the use of various methods and remineralizing materials. Sonesson et al. [ ] also mentioned that the results from the reviewed studies showed either no significant improvement or that the studies conducted were biased.

One of the reasons these therapies show mixed results could be that caries lesions with different mineral distributions, namely with and without a surface layer, is clinically indistinguishable and hence being included into the same crude category for investigation. However, it has previously been shown that the degree of demineralization and mineral distribution and lesion depth influences the quantity and characteristics of remineralization [ , ]. Lippert et al. studied the response of caries lesions with three different sub-surface mineral distributions to fluoride under demineralizing conditions. They found that baseline lesion severity impacts the extent of the fluoride dose-response [ , ]. Wierichs et al. also reported that re- and demineralization characteristics of enamel depended directly on baseline mineral loss and lesion depth and that samples used in studies should be balanced with respect to these physical factors [ ].

The early stages of caries formation result in a complex network of nano-scaled larger-than-normal pores in dental enamel. When demineralized, enamel, which consists of enamel prisms, forms ‘finger-like extensions interspersed with demineralized regions which look like pores on the surface [ ]. Porosity thus increases and mineral density reduces. There is little understanding of the penetration efficiency of mineralizing materials through demineralized enamel, either in the absence or presence of a layer of mineralized surface. A recent study investigated the pore volume of carious enamel by infiltrating them with high penetration coefficient (> 2000 cm/s) liquids. It was found that the mineral volume of enamel caries lesion is poorly correlated with the volume of those liquids in carious enamel pores and that those liquids infiltrated only a small fraction of the pore volume [ ]. Chang et al. studied the relationship between thickness of surface layer and dehydration rate of the lesion and they reported that a small increase in surface layer thickness decreases surface permeability significantly [ ]. If a method can be developed to determine the surface porosity or the presence of a surface layer *in vivo* , then perhaps, remineralization therapies can be made more specific and outcome more reliable.

Sorptivity is one of the measures of the rate of liquid absorption into a porous material. It is defined as the rate at which a liquid is absorbed or desorbed into a medium or surface by means of capillarity [ ]. It is widely used in geo-analysis for characterizing soils and porous construction materials such as brick, stone and concrete [ ]. Sorptivity can be expressed in the equation below [ ],

S=VsA√t,

where <SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='S’>𝑆S

S

is sorptivity, <SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='t’>𝑡t

t

the time interval of infiltration, <SPAN role=presentation tabIndex=0 id=MathJax-Element-4-Frame class=MathJax style="POSITION: relative" data-mathml='A’>𝐴A

A

the contact area over which the absorption of liquid takes place and <SPAN role=presentation tabIndex=0 id=MathJax-Element-5-Frame class=MathJax style="POSITION: relative" data-mathml='Vs’>𝑉𝑠Vs

V s

the cumulative volume absorbed. The SI unit for sorptivity is m⋅s ^{−1/2} or mm⋅s ^{−1/2} .

Another equation that expresses absorption rate by means of capillarity of a bundle of parallel cylindrical tubes is Washburn’s equation [ ], i.e.

L2=γ⋅t⋅r⋅cos(∅)4η,

where <SPAN role=presentation tabIndex=0 id=MathJax-Element-7-Frame class=MathJax style="POSITION: relative" data-mathml='L’>𝐿L

L

is the cumulative distance of penetration in time <SPAN role=presentation tabIndex=0 id=MathJax-Element-8-Frame class=MathJax style="POSITION: relative" data-mathml='t’>𝑡t

t

, whilst <SPAN role=presentation tabIndex=0 id=MathJax-Element-9-Frame class=MathJax style="POSITION: relative" data-mathml='η’>𝜂η

η

is the dynamic viscosity and <SPAN role=presentation tabIndex=0 id=MathJax-Element-10-Frame class=MathJax style="POSITION: relative" data-mathml='γ’>𝛾γ

γ

the surface tension of the penetrating liquid, <SPAN role=presentation tabIndex=0 id=MathJax-Element-11-Frame class=MathJax style="POSITION: relative" data-mathml='∅’>∅∅

∅

the contact angle between the penetrating liquid and the solid substrate and <SPAN role=presentation tabIndex=0 id=MathJax-Element-12-Frame class=MathJax style="POSITION: relative" data-mathml='r’>𝑟r

r

is the radius of the cylindrical tubes. Putting the sorptivity and Washburn equations together, we can see that

S=Lt=12γ⋅r⋅cos(∅)η

Therefore, for a particular liquid with a constant viscosity, surface tension and contact angle, the pore geometry would be expected to be the main factor that influences sorptivity.

Hence, the aim of this study was to investigate the association between sorptivity of water and the porosity (as an inverse function of mineral density) of human enamel. More specifically, the first objective was to establish the association between sorptivity and mineral density using hydropxyapatite (HA) discs of varying but homogenous density. The second objective was then to measure the sorptivity of water in induced caries lesions of different severity which are known to have non-homogenous and multi-laminar porosity characteristics [ ]. And, finally, the third objective was to study how the association between sorptivity and mineral density was affected by such non-homogenous porous characteristics.

## 2

## Materials and methods

## 2.1

## HA discs

As a preliminary study, eleven 4 mm in diameter HA discs of varying density (1.41–1.89 g/cm ^{3} ) and thickness (2.04–2.77 mm) were prepared using HA powder which was compressed with pressures ranging from 31.8 to 286.5 MPa at a speed of 1 mm/min using a Materials Testing Machine (Zwick-Roell 1485, Ulm, Germany). The discs were placed in a desiccator overnight before testing. A water droplet of 1.5 μL was deposited onto the surface of each disc using a micropipette and the water droplet profile was dynamically recorded every second for 10 s, by using a contact-angle meter (Drop Master, KYOMA, Japan). The volume of the water droplet was automatically calculated from the measured profile using the built-in software of the contact-angle meter, and the readings were confirmed using Eq. (4) below.

Vt=πh63r2+h2,

where <SPAN role=presentation tabIndex=0 id=MathJax-Element-15-Frame class=MathJax style="POSITION: relative" data-mathml='V(t)’>V(t)V(t)

V ( t )

is the volume of the water droplet at time *t* , h is the height of the water droplet and r is the radius of the base of the water droplet. The cumulative volume of water absorbed at time t is thus

Vst=V0-Vt.

<SPAN role=presentation tabIndex=0 id=MathJax-Element-17-Frame class=MathJax style="POSITION: relative" data-mathml='Vs’>𝑉𝑠Vs

V s

was plotted against the square root of time (√t) for each disc and a linear regression line was derived. Based upon Eq. (1) , the slope of the regression line is sorptivity multiplied by the contact area of the water droplet, i.e. *SA* . As the radius (r) of the contact area over which the absorption took place is assumed to be constant, and so is the contact area *A* , the slope of the regression line effectively represents sorptivity. *SA* of each of the HA discs was then plotted against its mineral density (g/cm ^{3} ) to determine the relationship between sorptivity and mineral density of HA.

## 2.2

## Human enamel

## 2.2.1

## Sample preparation

Ninety-six extracted human incisors, canines and premolars with visually caries free smooth surfaces were collected and stored in methylated spirit after receiving the ethical approval from the Medical Ethics Committee of University of Malaya. At the time of the experiment, the roots of the teeth together with calculus, plaque and stains were removed and individually mounted on a resin base, leaving the labial/buccal surface of the teeth exposed. The labial/buccal surfaces of these teeth were then scanned with a swept-source Optical Coherence Tomography (OCT) Imaging System (OCS1300SS, Thorlabs Ltd., UK) to screen for sub-clinical demineralization so as to locate areas with completely sound surfaces. Two layers of acid-resistant nail varnish (Revlon, US) were painted on all the exposed surfaces. After drying, some of the varnish over the identified sound surfaces were removed with a probe and a round template, exposing two circular areas of 1.4 ± 0.1 mm in diameter, and approximately 2−4 mm apart ( Fig. 1 ). The specimens were then randomized into 6 groups with 32 test sites per group. Specimens in the 6 groups were subjected to the modified Featherstone pH cycling model [ , , ] for a duration of 0, 7, 14, 21, 28 and 35 days and labelled as G0, G7, G14, G21, G28 and G35, respectively.

As prescribed by the pH-cycling model, the specimens were placed in glass jars (2 per jar) with 40 mL of demineralization solution containing 2.0 mmol/L Ca, 2.0 mmol/L PO ^{4} , and 0.075 mol/L acetate (pH 4.4) for 6 h in the incubator at 37 °C followed by a rinse with Reverse Osmosis (R.O.) water. The specimens were then placed in glass containers (2 per container) with 20 mL of mineralizing solution containing 1.5 mmol/L Ca, 0.9 mmol/L PO ^{4} , 0.15 mol/L KCl, and 20 mmol/L cacodylate buffer and incubated at 37 °C for 17.5 h. At the end of the pH-cycling process, the specimens were then stored in R.O. water and placed in the incubator (37 °C) until the day of testing.

## 2.2.2

## Measurement of water droplet volume using Optical Coherence Tomography

Since OCT could also dynamically capture the profile of the water droplet, for convenience, it was also used for determining its volume in this part of the study. It is anticipated that OCT will be used for this purpose clinically should the measurement of sorptivity prove to be useful for caries diagnosis. The specimens were removed from the incubator and mounted onto a platform used with a swept-source OCT Imaging System (OCS1300SS, Thorlabs Ltd., UK). The surfaces of the samples were blot-dried with a paper towel and air dried for 30 s immediately before scanning was done. The beam was positioned at the middle of the circular test sites and configured to an axial resolution of 9 μm in air. A 10-μL pipette (Eppendorf Research Plus pipette) was used to deliver 0.7 ± 0.1 μL of R.O. water on the test site. Time lapsed B-scans of the test site were acquired at 10-s intervals for a period of 2 min. Measurements of the height of the water droplet, *h* , and radius of the test site, *r* , ( Fig. 2 ) were done with the digital ruler of the Thorlabs OCT capturing software (Swept Source OCT Imaging System, v2.3.1, Thorlabs). The procedure was repeated 3 times on each test site and a mean height at each time point was recorded. The volume of the water droplet at each time point, <SPAN role=presentation tabIndex=0 id=MathJax-Element-18-Frame class=MathJax style="POSITION: relative" data-mathml='V(t)’>V(t)V(t)

V ( t )

, and the volume of water absorbed, <SPAN role=presentation tabIndex=0 id=MathJax-Element-19-Frame class=MathJax style="POSITION: relative" data-mathml='Vs(t)’>𝑉𝑠(𝑡)Vs(t)

V s ( t )

, were computed similarly to those of the HA disc experiment using Eqs. (4) and (5) .