Quantifying the volume of a foreign liquid infiltrated into carious enamel. Part II

  The refractive index (RI) of the foreign liquid must be determined. Given two liquids, with RIs 1.40 and 1.47, infiltrated into dried carious enamel and resulting in observed birefringence values of -0.0017 and -0.0020, respectively. The fact that carious enamel was dried before infiltration indicates that the liquid penetrated by capillary forces. The main problem with dry carious enamle is that it is opaque, i.e. it lacks interference colors and birefringence. The solution (reported by Meira et al., Arch Oral Biol, 60:883-893, 2015) follows below:

1) The loosely  (a₂^exp) and firmly bound water (a₁^exp) volumes must be determined. Loosely bound water is replaced by air and represents the main available volume for infiltration. It can be determined using the approximation:


 a₂^exp= a₂^theo - 0.5759 – 0.7396*Db    (1)

a₂^theo (the theoretical loosely bound water volume fraction) is:

a₂^theo = 0.6987 – 1.2487*(V₁/100) + 0.544*(V₁/100)²    (2).

a₂^exp +  a₁^exp = a     (3)

∆β  is the experimental organic volume minus the predicted organic volume:

b^theo = 0.08654 + 0.46808*(V₁/100) -0.584*(V₁/100)²    (4).

Following the case described in the previous post "How to measure water and organic enamel volumes from enamel birefringence?" , V1 = 0.80; V2 = 0.20; alpha = 0.077535; and betaexp = 0.122465. The new values are: 
b^theo = 0.08724;
Db  = 0.122465-0.08724= 0.03522 [3.522 for inserting into Eq. (1)]
a₂^theo = 0.0479 [4.79 for inserting into Eq. (1)];
a₂^exp = 0.01609 (experimental loosely bound water);
a₁^exp = 0.077535 - 0.01609 = 0.06144 (experimental firmly bound water);
Enamel composition = 0.8+0.122465+0.01609+0.06144 = 1.00 (100%)

2) The volume infiltrated by liquid with RI 1.40 requires the corresponding observed birefringence measured under polarizing microscopy. Say that -0.0017 was measured. Experimental birefringence must equalize the theoretical birefringence. This is done using Eq. (1) of the post 

How to measure water and organic enamel volumes from enamel birefringence?. 

Doing calculations iteratively, observed birefringences are equalized when:
56% of a₂^exp (0.00901) is replaced by the liquid with RI 1.40. The remaining 44% (0.0708) is filled with air (the medium already present before infiltration).

3) The volume infiltrated by liquid with RI 1.47, with experimental birefringence of -0.0020, is obtained similarly. The final volumes are: 70.2% of a₂^exp (0.011295) is filled with the liquid with RI 1.47. The remaining 29.8% (0.04795) is filled with air (the medium already present before infiltration).
The volume of various liquids (including resin infiltrants used to infiltrate carious enamel) can be quantified using this method.

Quantifying the volume of a foreign liquid infiltrated into carious enamel. Part I

Quantification of the volume of a foreign liquid into enamel has challenged scientists for almost a century. Darling et al. (Arch Oral Biol, 1961) were the first to present a semi-quantitative approach to quantify the volume infiltrated by quinoline and alcohols of different molecular sizes. There still remained a limitation related to the fact that the measured volumes were relative, not absolute. They could not sum the volume of the foreign liquid and the mineral volume and yield 100% of the enamel volume. Their mineral volume data were not determined experimentally.

  The figure shown below illustrates a natural enamel caries lesion under water and air immersion. Under air, most of the surface layer and body of the lesion get opaque so that no birefringence can be measured. How to measure firmly and loosely bound water volumes? This problem has been recently solved by Meira et al. (Arch Oral Biol, 2015; http://dx.doi.org/10.1016/j.archoralbio.2015.03.001). Poole at al (Nature, 1961) and Darling et la (Arch Oral Biol, 1961) discussed that opacity in the body of the lesion was one of the main reasons why their measurements were from the dark zone. To solve the problem, the volume of water removed by drying (loosely bound water volume) have to measured in opaque enamel. This the volume that can be filled by the foreign liquid. The solution will be discussed later in a future post.

How to measure water and organic enamel volumes from enamel birefringence?

How to measure water and organic enamel volumes from enamel birefringence? An example follows below.

First, enamel ground sections have to be microradiographed to obtain mineral volume at selected histological sites (~ 15x15 micrometers). Given a mineral volume fraction (V1) of 0.80 (80 %) – pore volume fraction (V2) of 0.20 (20%) - and observed birefringence in water of – 0.0020 (measured under polarizing microcopy), the theoretical observed birefringence is given by (Sousa et al., J Microsc 221: 79-83, 2006):

-0.0065*0.85+[0.80*0,2*(1.62²-n2²)²]/{2*(0.8*1.62+0.20*n₂)*[(1+0.80)*n₂² + 0.20*1.62²]}= -0.002    (1)

Where -0.0065 is the corrected intrinsic birefringence of the mineral phase and 0.85 is the mean crystallite alignment. 1.62 is the refractive index (n1) of hydroxyapatite. The variable n2 is given by (Sousa et al., J Microsc 221: 79-83, 2006; Macena et al., Arch Oral Biol, 2014):

n₂ = [1.33*(a₁/V₂)]+[n_i*(a₂/V₂)]+[1.56*(b/V₂)]  (2)

Where alpha1 and alpha2 are the firmly and loosely bound water volumes (alpha1 + alpha2 = total water volume, alpha), respectively, and ni is the refractive index of the immersion medium (water in this case; 1.33). Beta is the organic volume fraction. Thus

n₂ = [1.33*(a₁/0.20)]+[n_i*(a₂/0.20)]+[1.56*(b/0.20)]   (3)

Which is inserted into Eq.(1). And

V₂ = a + b   (4)

The next step is to consider that there are two unknowns (beta and alpha) and two equations: (1) and (4). Thus, the values can be found. The results are alpha = 7.7535% and beta = 12.2465%. So, V1 + alpha +beta = 100%.

Infiltration of natural enamel caries by capillarity: 2D real-time mapping in relation to prisms paths

Changes in enamel birefringence over time can be used to map infiltration of foreign liquids into carious enamel. The video shown was produced using orientation-indepedent polarizing microscopy with two liquid crystals variable retarders (so called dual polscope; Oldenbourg R. Polarization microscopy with the LC-PolScope. In: Goldman RD, Spector DL. eds. Live Cell Imaging: A Laboratory Manual. Cold Spring Harbor:Cold Spring Harbor Laboratory Press; 2005. 1-42)  using time intervals of 0.5 s. A dry natural enamel carious lesion was infiltrated with an aqueous Thoulet's solution with refractive index 1.40 and penetration coefficient of 3.200 cm/s (at 25 degrees Celsius) for 2.5 min. As the liquid penetrates, some parts present infiltration occurring both perpendicularly and parallel to the prism paths while others present infiltration only parallel to prism paths. This has implications in the penetration lengths, which, in turn, influences the time required for full infiltration to be completed. This technique could also be used to validate the most porous lesion area.

First quantitative data on the carious enamel pore volume infiltrated by a foreign liquid

  Enamel birefringence was explored to derive the first absolute quantitative data on the carious enamel pore volume infiltrated by a foreign liquid. Previous studies reported measurements of the amount of foreign liquid infiltrated in the carious enamel pores (Darling et al., Arch Oral Biol, 5:251-73, 1961), but they were relative measurements and did no take into account the organic and water volumes found in the pore volume. Relative measurements mean that all component volumes were not actually measured experimentally; i.e., they did not describe values of the mineral, water, organic, and infiltrant volumes. For example, tt was not possible to say that the mineral volume was 80%, the water volume was 10%, the organic volume 5% and the infiltrate volume 5%. This was one of the important gaps in current knowledge.  
   Meira et al. (Arch Oral Biol, 2015, http://dx.doi.org/10.1016/j.archoralbio.2015.03.001) reported absolute values of the organic, firmly bound water, air, and infiltrant volumes in natural enamel caries. Two liquid infiltrants with penetration coefficients of 2300 cm/s and 3200 cm/s were tested. From 3% to 30% of the pore volume of the surface layer of carious enamel were infiltrated by the liquids.  Most of the pore volume was occupied by organic matter. This evidence indicates that remineralization is not expected to provide full recovery of the mineral lost in carious enamel, and that resin infiltration is not expected to fill the entire pore volume of carious enamel. Absolute data on the pore volumes might provide new insights on how to improve remineralization and resin infiltration of enamel caries lesions.
   Once the pore volume is known, the important research question is how much of it is available for remineralization/infiltration, and what pore component could be removed to improve remineralization/infiltration.