Caries affected by calcium and fluoride in drinking water and family income

Water quality and socioeconomics in ﬂ uence caries in populations. This study broadens previous studies on how caries is associated with ﬂ uoride and calcium in drinking water and with family income by quantifying the combined effect of the three independent variables. The effects of calcium and ﬂ uoride can be described as independent effects of the two ions or, alternatively, in the form of saturation with respectto ﬂ uorite(CaF 2 ).Agenerallinearmodeldescribesthisrelationshipwithhighsigni ﬁ canceandthe model con ﬁ rms the important protective effect of calcium and ﬂ uoride, independently against caries. From the model, the relative importance of ﬂ uoride and calcium to protect against caries is quanti ﬁ ed. Therelationshipbetweencariesandfamilyincomeisalsohighlysigni ﬁ cant.Itisillustratedhowthelinear model can be applied in planning and analyzing drinking water softening in relation to caries.


INTRODUCTION
It is very well documented that fluoride in drinking water has an important protective effect against dental caries (Dean et   This study aimed at quantifying the combined effect of calcium, fluoride and family income on dental caries in Denmark by 2004 by using linear models. To the knowledge of the authors, this has not been done before.

METHODS
The data material on DMF-S, calcium and fluoride was the same as described by Bruvo et al. (). The average DMF-S for all Danish municipalities in 2004 for 15-yearold children was 2.9 surfaces.
Danish water supply relies 100% on groundwater.

RESULTS AND DISCUSSION
Effect of drinking water calcium and fluoride concentrations on dental caries Very high significances (p < 4.5 × 10 À4 -2.7 × 10 À15 ) were obtained for all three independent variables: calcium concentration (C Ca , mg/L), fluoride concentration (C F , mg/L) and average family income per year in the municipality (IC, TDKK) using the following linear model (R 2 ¼ 0.42): lnDMFÀS ¼ À0:00435 C Ca À 0:682 C F À 1:62 10 À3 IC þ 1:96 (1) Equation (2) shows that in order to maintain a constant DMF-S after decreasing the calcium concentration by for example 100 mg/L, then 0.64 mg/L of fluoride should be added to the water and vice versa. Consequently, Equation (2) shows the relative 'strength' of calcium and fluoride in drinking water to control caries.
Fluoride has by far the largest caries protection effect per unit weight, but since the fluoride concentrations may be low and the calcium concentrations may be high (groundwater from limestone), calcium can play an important role for caries protection.
The importance of calcium and fluoride to achieve caries levels in the range 1-4.5 is illustrated in Figure 2 for a fixed average yearly income level of TDKK 232 (TEURO 31).
In the western areas of Denmark with sandy aquifers with low fluoride and low calcium concentrations in the drinking water, high DMF-S values of 5 or more are observed. In areas with chalk aquifers where the drinking water contains high calcium concentrations, but variable fluoride concentrations, the DMF-S may vary between 2 and 3. It is obvious that in areas with low fluoride concentrations, for example 0.1-0.3 mg F/L, a high calcium concentration in the drinking water is an important protection factor against caries.
Alternative DMF-S model We also tried to apply a new independent combined variable for calcium and fluoride, the degree of saturation with respect to fluorite (CaF 2 ), the saturation index, DS CaF2 ¼

Effect of family income
The effect of family income as a single factor can be derived from Equation (1). Let us assume a decrease in average family income per year of 100 TDKK (TEURO 13.4, TUS$ 14.7). This will lead to an increase in caries of 18%.
The effect of average family income relative to calcium and fluoride in drinking water can be calculated from Equation (1). Again assuming an income decrease of TDKK 100 per year, thenproviding constant DMF-Sthe concentrations of calcium or fluoride should be increased by:  (1) together with the average calcium and fluoride concentrations, the expected 2010 caries level is 2.6 versus the real caries level of 2.1. Consequently, our model can only predict a DMF-S decrease of 10% where the real reduction is 28%. However, it seems that when dental caries is in acceleration, as in the 1960s and 1970s the momentum in the disease seems to be stronger than the 'movement itself'. The same goes for caries in deceleration as in the 1990s and past the millennium. Here a continuing decrease in caries seems to persist even though no major changes have been made in the dental care system in Denmark. For these mechanisms of this disease we, and others, have no real solid explanation (Fejerskov et al. ).

Model uncertainties
Although the effects of calcium, fluoride and family income on caries are highly significant in Equation (1) (1) and (3). This is a subject for further research.

PERSPECTIVES FOR WATER SOFTENING
Equation (1) can be applied in planning water softening in relation to caries. The purpose of water softening is to reduce water hardness and thereby the potential for precipitation of calcium carbonate on surfaces in water installations, bathrooms and on kitchenware. So calcium removal is the primary objective. Some softening processes, for example membrane processes, also lead to fluoride removal. Consequently, softening will lead to increased caries prevalence, if all other factors are kept constant, and it is the combined effect of calcium and fluoride changes that should be taken into account. Therefore a new water quality variable is introduced based on Equation (2), the caries-related equivalent fluoride concentration, EFC: By applying the variable EFC, Equation (1) can be reformulated and simplified in terms of EFC as follows: lnDMF À S ¼ À0:68 EFC À 1:62 10 À3 IC þ 1:96 This relationship is shown in Figure 4 for the average Danish family income in 2002 and the lowest and the highest income that year.
Equation (5) as well as Equation (3)  when planning water softening. Any calcium present in the drinking water will add to the EFC.
The Greater Copenhagen water company HOFOR plans to soften all their water by the pellet method to a final hardness of 10 o dH (German hardness degree) which equals a hardness of 178 mg CaCO 3 /L.
In the first water works within HOFOR to adopt softening, Broendby, the magnesium hardness is 5.4, therefore, the final calcium hardness will be 4.6 corresponding to a calcium con-

CONCLUSIONS
This work presents linear models for caries experiences (DMF-S) among 15-year-old Danish school children that include water chemistry, the concentrations of calcium and fluoride, and family income. The family income is used as a proxy for socioeconomic factors. The variables calcium, fluoride and income are highly significant and they are also quantitatively important determinants for caries.
It is well known that fluoride in drinking water in concentrations as low as 0.5-1 mg/L effectively reduces caries prevalence. However, our work shows that 100 mg/L of calcium has the same protection effect as 0.64 mg/L fluoride The effect of calcium to protect against caries may have important implications for water softening where the calcium concentration is strongly reduced. From a case study it is calculated that the reduction in calcium from 120 mg Ca/L to 33 mg Ca/L by softening, may increase the average caries experience by 46%.