Enamel Birefringence Interpretator (EBI, v 0.1): a freeware to interpret enamel birefringence

   The mathematical approach used to interpret enamel birefringence (Sousa et al., J Microsc, 2006) can now be applied with the software Enamel Birefringence Interpretator (EBI v.0.1), developed by Gonzaga Y. and Sousa F.B., available for free download here:

https://drive.google.com/drive/folders/1T6jK8vd5dxB1wrFn3B1AEvClFLNCVCot

  Once downloaded, double click opens the following window:

  There are two columns, each one with four empty boxes. Mineral volume fraction (based on a  mineral density of 2.99 gcm-3) and the value of observed birefringence (BRobs) in water are the minimum data required to obtain an interpretation. This later means that data on water and organic volume fraction will be obtained. The data of the study of Angmar et al (1963), published in a recent post in this blog, will be used as an example. Taking data of the point located at 100 microns from the enable surface of tooth a, it is possible to convert mineral volume fraction to the value based on a mineral density of 2.99 gcm-3 using Eq. (1) published in the same post. The result is a mineral volume fraction of 0.9234 (92.34%). The corresponding BRobs value in water is (-) 0.002 (insert as -20; see that the box is multiplied by 1E-4) and in air is (-)0.001875 (insert as -18.75). Ten click "Calculate". The following result will appear.

  The results show the non-mineral volume fraction (V2) and the organic (beta), water (alfa), firmly bound water (alfa 1) and loosely bound water (alfa 2) volume fractions. It is now easier to implement the interpretation of enamel birefringence. The reader is now able, for example, to quantify the water and organic volumes of artificial enamel caries from Theuns et al (Caries Res, 1993) and to compare result with predicted values according to Sousa et al (J Microsc, 2009). The differences between experimental and predicted values of water volume can be compared with data published in Fig. 4 of Sousa et al. (Caries Res, 2013). 

  NOTE: mineral volume should be based on a mineral density of 2.99 gcm-3 (see Elliott JC. Structure, crystal chemistry and density of enamel apatites; in Chadwick D, Cardew G (eds): Dental Enamel. Ciba Foundation Symposium 205. Wiley, Chichester, 1997, pp 54–72).

Degree of water transport in enamel inversely related to the water volume to organic volume ratio: an evidence

    As normal enamel dehydrates in air at room temperature, a plateau in the water volume remaining into enamel pores (firmly bound water) is reached after a certain time. This water volume represents the equilibrium moisture content. Water is the main vehicle in enamel for the transport of materials, which occurs by diffusion. It was recenly highlighted that as enamel dehydrates, the ratio of water volume to organic volume decreases in the pores (Medeiros et al., J Micros, 2013; DOI: 10.1111/jmi.12037). This reduced ratio represents an increased viscosity, according to the Einstein equation for diffusion, slowing down diffusion. Medeiros et al. (2013) hipothesized that transport of materials is slower in dried than in wet enamel because of the expected higher viscosity in the former. As enamel dehydrates, the organic volume remains the same while the water volume decreases.
   There is preliminary published evidence supporting this hipothesys. Houwink B.(The limited usefulness of Thulet's solution in imbibition experiments in dental enamel. British Dental Journal, v.126: 447-450, 1969) reported (in vitro study with ground sections using polarizing microscopy; see Table Ib on page 448) that normal human enamel dried at room temperature for 1.5 h recovered the original water content after 2 h of imbibition in water; while enamel dried for 2.5 days took 2.5 days of water imbibition to recover the original water content. This suggests that the time required to reach maximum infiltration  of a given material in normal enamel is inversely proportional to the water volume to organic volume ratio remaining in the pores. This has important implications for pathogenesis, diagnosis, remineralization and infiltration of enamel caries. For caries pathogenesis, the faster inward diffusion rate of water in wet enamel is expected to play a role in the depth of artificial and in situ caries lesions. For diagnosis, opacity of enamel should be determined after equilibium moisture content is established only, for consistency between studies. For resin infiltration, it is expected to be slower in dried than in wet enamel. Sousa et al. (Caries Res, 47: 183-192, 2013; Doi: 10.1159/000345378) reported how permeability can be measured at histological points of enamel caries lesion and its relationship to the expected amount of infiltrant that can fill the pores.

Dehydration of normal enamel: new paper (Medeiros et al., J Microsc 2013)

          What is the parameter to define air dried enamel at room temperature? It is reasonable to say that it is when water content is stabilized over time at a certain temperature and relative humidity of the air.  This subject is addressed in a recent paper (Medeiros et al., Journal of Microscopy, 250, 2013, DOI: 10.1111/jmi.12037; http://onlinelibrary.wiley.com/doi/10.1111/jmi.12037/abstract) that explores enamel birefringence to obtain quantitative volumetric data of water loss at normal enamel histological points during air drying. The paper analyzes ground sections of normal enamel and reports an inward water diffusion, driven by osmotic pressure of a protein gradient, following prisms paths, similar to what was reported by Atkinson (British Dental Journal, 83: 205-214, 1947).  The main findings are:

- during air drying at 25 C and relative humidity of 50%, normal enamel looses water from the outer to the inner layers, following prisms paths;
- loosely bound water is lost until a plateau is reached, i.e. when an equilibrium moisture content is established;
- the equilibrium moisture content at the histological points along the enamel thickness is reached following an apparent diffusion rate (median) of 3.47 x10 -8 cm2s-1;
- outer enamel reaches equilibrium moisture content earlier than inner enamel;
- equilibrium moisture content is achieved after 40 h and 90 h for depths of 1 mm and 2 mm in enamel, respectively;  
- due to the lower water volume in dried enamel, and a corresponding lower ratio of water to organic matter, a lower diffusion rate for materials is expected in dried enamel compared to wet enamel;
- the inward water diffusion (related to the osmotic pressure exerted by an increasing protein gradient from the outer to the inner layers) has implications in the transport of materials in enamel (including acid, bleaching agents, etc), and in the optical and mechanical properties;
- the observation of such phenomenon in ground sections is explained by the fact that prisms are partially surrounded by the prisms sheaths (the main pathways for transport of materials in enamel), which do not connect each other in cross section, and that intraprismatic pores house the least mobile water of enamel due to a higher capillary force compared to that in the prisms sheaths (which are larger pores);
- the paper describes a method using the combination of a lambda filter plus a quarter wave filter (yielding a retardance of 680 nm) to detect the sequence of qualitative changes in enamel birefringence during air drying of ground sections;
- it is now open the possibility of studying the role of this inward water diffusion in the transport of materials in normal enamel.

Theuns et al. (Caries Res, 1993): data on mineral volume and birefringence of artificial enamel caries

   Theuns et al (Relationships between birefringence and mineral content in artificial caries lesion of enamel. Caries Research, 27:9-14, 1993) published data on the mineral volume and birefringence in water of artificial enamel caries that can be used to derive water and organic volumes. Data on the surface layer are of particular importance because they can be used to quantify the amount of organic volume in the outer layer of enamel caries close the acidic gel used to create the artificial caries lesion. If organic matter is incorporated into enamel during cariogenic challenge with gels in vitro, permeability and optical properties might be altered significantly compared to situations where no organic content is available for incorporation. The quantity of organic matter can be compared with that commonly found in normal enamel (~2%). Using equations for interpretation of enamel birefringence from Sousa et al. (J Microsc, 2006), anyone can test this.
  Numerical data, extracted from graphs in the article using image analysis software, follow below (Vmin = mineral volume based on a mineral density of 2.99 gm-3; BRwater =birefringence in water with sign, positive or negative; total of 72 lines):

Vmin        BRwater (x 10-4)

33.56 24.07
49.126 9.63
49.832 32.18
49.832 47.4
52.659 -0.37
54.072 21.11
54.425 22.96
55.132 22.59
55.309 24.255
58.321 26.105
58.675 26.475
59.028 24.07
59.028 -0.37
59.028 27.955
62.384 30.74
63.268 10.74
64.681 9.075
64.858 1.11
65.388 29.63
65.388 20.925
65.388 -0.37
65.741 17.5
66.801 20.925
67.154 22.035
68.224 12.18
68.224 12.775
68.224 5.735
68.224 3.7
68.224 -7.965
68.997 9.26
69.814 37.585
71.05 12.775
71.05 -0.185
71.227 44.44
71.227 23.145
71.58 16.29
72.994 3.515
72.994 5.735
72.994 -7.965
73.347 4.44
74.054 10.185
74.054 17.215
74.76 -4.255
74.937 17.77
75.997 13.33
76.88 12.22
76.88 -0.555
77.235 24.995
77.596 -5.005
77.596 -7.595
78.126 -10.925
78.126 6.29
78.656 -8.705
78.709 8.695
79.539 -16.66
79.893 -10.37
79.893 -0.37
80.599 -5.56
80.599 -19.63
80.776 -19.815
82.366 -17.225
82.719 -12.045
82.896 7.77
83.779 -0.555
83.779 -23.33
84.133 -10.74
84.133 -12.775
84.133 -3.7
84.663 -3.885
84.663 -10.555
86.429 -20.925
86.429 -2.59
 

   As an example, line 2 results in an organic volume of 31.547 % and a total water volume of 19.327 %. Summed with mineral volume of 49.126% yields 100%, for numerical validation.