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 (a2exp) and firmly bound water (a1exp) 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:
a2exp= a2theo - 0.5759 – 0.7396*Db (1)
a2theo (the theoretical loosely bound water volume fraction) is:
1) The loosely (a2exp) and firmly bound water (a1exp) 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:
a2exp= a2theo - 0.5759 – 0.7396*Db (1)
a2theo (the theoretical loosely bound water volume fraction) is:
a2theo = 0.6987 – 1.2487*(V1/100)
+ 0.544*(V1/100)2 (2).
a2exp + a1exp = a (3)
a2exp + a1exp = a (3)
∆β is
the experimental organic volume minus the predicted organic volume:
btheo = 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:
btheo = 0.08724;
Db = 0.122465-0.08724= 0.03522 [3.522 for inserting into Eq. (1)]
a2theo = 0.0479 [4.79 for inserting into Eq. (1)];
a2exp = 0.01609 (experimental loosely bound water);
a1exp = 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
56% of a2exp (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 a2exp (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.
btheo = 0.08724;
Db = 0.122465-0.08724= 0.03522 [3.522 for inserting into Eq. (1)]
a2theo = 0.0479 [4.79 for inserting into Eq. (1)];
a2exp = 0.01609 (experimental loosely bound water);
a1exp = 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 a2exp (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 a2exp (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.
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