## Abstract

Water quality and socioeconomics influence caries in populations. This study broadens previous studies on how caries is associated with fluoride and calcium in drinking water and with family income by quantifying the combined effect of the three independent variables. The effects of calcium and fluoride can be described as independent effects of the two ions or, alternatively, in the form of saturation with respect to fluorite (CaF2). A general linear model describes this relationship with high significance and the model confirms the important protective effect of calcium and fluoride, independently against caries. From the model, the relative importance of fluoride and calcium to protect against caries is quantified. The relationship between caries and family income is also highly significant. It is illustrated how the linear 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 al. 1941; Featherstone 1999, 2000; McDonagh et al. 2000; Ekstrand et al. 2003; Fejerskov et al. 2015; US Dept. of Health and Human Services 2015). The natural concentration of fluoride in drinking water varies a great deal depending on the water source. Often, surface water has a low concentration of fluoride. Groundwater fluoride concentrations depend on the geology of the aquifers. Sandy aquifers have a low fluoride concentration. Water sources with such low fluoride concentrations, for example 0.1 mg F/L, are supplemented with fluoride up to 1 mg F/L in, for example, USA, Australia, and several other countries.

It has also been shown that calcium in drinking water reduces development of dental caries measured as the number of Decayed, Filled, and Missing tooth Surfaces (DMF-S) (Bruvo et al. 2008). The study by Bruvo et al. (2008) comprised 52,057 15-year-old school children in 249 Danish municipalities in 2004. It was shown that ln(DMF-S) is linearly related to the concentrations of calcium and fluoride in drinking water. The two ions act independently of each other. Figure 1 gives a survey of the distribution of caries measured as DMF-S in the municipalities in Denmark in 2004 together with the distributions of the calcium and fluoride in drinking water. This figure clearly shows the high prevalence of caries in areas with low concentrations of fluoride and calcium in the drinking water. These areas have sandy aquifers.

Figure 1

Distribution of DMF-S, fluoride and calcium in Denmark (2004) among 15-year-old children.

Figure 1

Distribution of DMF-S, fluoride and calcium in Denmark (2004) among 15-year-old children.

It is also very well documented that socioeconomic factors have important effects on caries prevalence, for example family income, parents' education, gender and resources allocated in the municipalities to dental visits/dental care (Petersen 1992; Christensen et al. 2010; Kirkeskov et al. 2010; Peres et al. 2000; Fejerskov et al. 2015). Kirkeskov et al. (2010) investigated the effect of fluoride, income and gender on caries among 5-year-old and 12-year-old school children in 2004 in Denmark. In addition to the protective effect of fluoride, the study showed a significant increase in DMF-S at reduced incomes.

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. (2008). The average DMF-S for all Danish municipalities in 2004 for 15-year-old children was 2.9 surfaces.

Danish water supply relies 100% on groundwater. Chemical data were retrieved from 3,364 water works for the period 1995–2004. The calcium concentrations varied from 31–171 mg/L with an average of 83.5 mg/L and the fluoride concentrations varied from 0.06–1.6 mg/L with an average concentration of 0.33 mg/L. The low calcium and fluoride concentrations are associated with sandy groundwater aquifers in Western Denmark and the high calcium concentrations are related to chalk aquifers. In the chalk aquifers, both high and low fluoride concentrations were observed, probably related to the presence or absence of the mineral fluorite, CaF2, in the chalk deposits.

The average family income per year from 249 municipalities in 2002 was obtained from Statistics Denmark (2017). The family income is the sum of salaries, not including social income (support for housing, children, etc.). It varied by a factor of 3.1 from TDKK 127–397 per year (thousands of Danish crowns, which in TEURO is 18.5–53 per year, or TUS$18.6–58.4 per year). It appears that the inequality in income in Denmark is relatively low. The average family income per year was TDKK 232 (TEURO 31.1, TUS$ 34.1).

As explained in the work by Bruvo et al. (2008), a general linear model with the logarithm of DMF-S as the dependent variable was used, applying the R software (R Development Core Team 2011).

## RESULTS AND DISCUSSION

### Effect of drinking water calcium and fluoride concentrations on dental caries

Very high significances (p < 4.5 × 10−4–2.7 × 10−15) were obtained for all three independent variables: calcium concentration (CCa, mg/L), fluoride concentration (CF, mg/L) and average family income per year in the municipality (IC, TDKK) using the following linear model (R2 = 0.42):

(1)
From Equation (1), one can derive a ‘substitution ratio’ between calcium and fluoride: for a fixed DMF-S and a fixed family income IC, what increase in fluoride concentration would balance a certain decrease in calcium concentration and vice versa. The result is:
(2)
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).

Figure 2

Effect of calcium and fluoride on caries measured as DMF-S. Calculated values for a fixed average yearly income, IC, of TDKK 232 (TEURO 31).

Figure 2

Effect of calcium and fluoride on caries measured as DMF-S. Calculated values for a fixed average yearly income, IC, 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 (CaF2), the saturation index, DSCaF2 = SICaF2 = log({Ca++}{F}2/Ks), where {Ca++} and {F} are the activities of calcium and fluoride and Ks is the solubility product for CaF2. The saturation index was calculated using the PHREEQC software (Parkhurst & Appelo 1999) estimating the calcium activity from the total calcium concentration, and the ionic water composition, taking into account all major complexes formed with calcium in drinking water giving the pH, the concentration of bicarbonate and all other ionic species. For fluoride, complexation is not important. The fluorite saturation index values were negative, showing that the water was undersaturated with respect to fluorite.

The degree of saturation together with the average family income per year (IC, TDKK) was also highly significant (p < 1.8 × 10−4–2 × 16−16) using a linear model (R2 = 0.46):
(3)

Like Equation (1), Equation (3) emphasizes that it is the combined effect of calcium and fluoride that matters.

The significance of the fluorite saturation index may point to a possible mechanism. During tooth-brushing, fluorite probably precipitates in the biofilm layer on tooth surfaces. This precipitate acts as a reservoir of calcium and fluoride that supplies these ions to the tooth surface and thus protects against caries. If the fluorite saturation index is low, the fluorite reservoir is more rapidly dissolved in drinking water and human saliva and the caries protective effect of the fluorite reservoir disappears faster. This hypothesis is supported by the work of Whitford et al. (2002) who showed that plaque fluoride concentrations are dependent on plaque calcium concentrations.

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, then – providing constant DMF-S – the concentrations of calcium or fluoride should be increased by: • ΔCCa = 37 mg/L • ΔCF = 0.24 mg/L These are the concentrations of calcium or fluoride that should be added to the water if one goes from the municipality with average income to the municipality with the lowest income and one wants to maintain caries neutrality (‘zero solution’). The addition of fluoride required is a little lower than the average fluoride concentration in Danish water supplies (0.33 mg/L) and the addition of calcium is a little less than half the average calcium concentration in Danish water supplies (83.5 mg/L). The effect on caries of a DKK 100,000 yearly income reduction is therefore almost the same as the effect of removing most of the protective fluoride from average Danish drinking water. These numbers illustrate that family income has an important influence on caries prevalence. This is most likely due to high income families having greater resources for childcare and caries protective measures. The DMF-S data used in this study are from 2004 where the average DMF-S for 15-year-old children was 2.9. In 2010, the average caries prevalence in Denmark for this group had decreased by 28% to 2.1 (SCOR 2010, Central Dentistry Register, The Danish Health Authority). One may speculate whether this decrease in caries can be explained by our linear model due to an increase in family income. In order to investigate this hypothesis, we obtained from Statistics Denmark the average family income from 2010 and the inflation rate from 2004 to 2010. From this information, we obtained an increase in family income in fixed prices of 13%, and by inserting the inflation-corrected average yearly family income for 2010 in Equation (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. 2015). ### Model uncertainties Although the effects of calcium, fluoride and family income on caries are highly significant in Equation (1) and Equation (3), there are many model uncertainties as reflected in the R2 values of 0.41 and 0.46 and in the differences between observed and model calculated DMF-S, Figure 3. Figure 3 Observed DMF-S versus model calculated DMF-S in the Danish municipalities (2004) for 15-year-old children. Figure 3 Observed DMF-S versus model calculated DMF-S in the Danish municipalities (2004) for 15-year-old children. Below, four types of model uncertainties are listed. First, one has to realize that the dependent variable (DMF-S) and the independent variables (calcium, fluoride and income) are average values for each municipality and there may be considerable variability within the municipalities. Secondly, caries determined by DMF-S has an inherent variability because it is a subjective determination by the dentist and there may be a trend in clinical practice versus time. Thus, younger generations of dentists may evaluate a decayed surface differently than older generations. Given that older generations have seen the disease some 40 years ago when nearly 90% of all children in Denmark were affected by dental caries, their threshold for giving a diagnosis may naturally be lower than that for younger generations. Thirdly, all the 15-year-old school children have not lived in the same place all their lives so the exposition to calcium and fluoride may have changed through their childhood. However, Denmark is a country with less geographical mobility than for instance the USA. Most Danes remain in the same municipality for decades, especially after having had children. Fourth, not surprisingly, it is a very rough approximation to use family income to reflect socioeconomic factors such as educational level, dental care, etc. In Denmark, dental care in schools among municipalities has been very equal for many years due to state regulations. Therefore, household income does not affect dental care in schools. Instead, variations in household income may reflect variations in educational level and thereby the understanding of caries caused by a combination of reduced oral hygiene and exposition for sugar. It has to be emphasized that our data on caries prevalence are valid only for 15-year-old children in 2004. The caries prevalence varies with age, however, we hypothesize that the effects of calcium, fluoride and family income shown in this study still apply in principle, although not with the same coefficients in the linear Equations (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: (4) By applying the variable EFC, Equation (1) can be reformulated and simplified in terms of EFC as follows: (5) This relationship is shown in Figure 4 for the average Danish family income in 2002 and the lowest and the highest income that year. Figure 4 Caries among 15-year-old children measured as DMF-S versus the equivalent fluoride concentration. Shown for average, lowest and highest Danish average family income per year (2002) (IC, TDKK: 232, 139, 398). Figure 4 Caries among 15-year-old children measured as DMF-S versus the equivalent fluoride concentration. Shown for average, lowest and highest Danish average family income per year (2002) (IC, TDKK: 232, 139, 398). Equation (5) as well as Equation (3) underline the importance of the combined effect of the calcium and fluoride concentrations on caries. It is common practice in many countries, for example USA, Australia and the Middle East, to fluoridate water in order to protect against caries. A typical fluoride level is 0.7–0.9 mg/L and the recommended fluoride level from the US Dept. of Health & Human Services (2015) is 0.7 mg/L. This may be taken as a minimum goal for EFC 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 10odH (German hardness degree) which equals a hardness of 178 mg CaCO3/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 concentration of 33 mg Ca/L. Since the fluoride concentration is 0.51 mg/L, the equivalent fluoride concentration in the drinking water after softening will be EFC = 0.7 mg/L. This corresponds to the above-mentioned minimum EFC. The Broendby raw water (groundwater) currently and naturally has a water hardness of 22odH and the calcium concentration is 120 mg/L. With a fluoride concentration of 0.51 mg/L, the raw water EFC = 1.3 mg/L. The water softening in Broendby will – according to Equation (5) – lead to an increase in DMF-S of 46%. In 2004, the DMF-S in Broendby was 2.47. The 46% increase corresponds to an increase in DMF-S of 1.1 tooth surfaces in 15-year-old children. The calculated increase in caries of 46% is a significant increase. If a ‘zero solution’ is wanted where the caries level is unchanged after softening, 0.6 mg/L fluoride has to be added to a level of 1.1 mg F/L. This fluoride level would not be unusual for the local geological conditions around Broendby and south of Copenhagen. However, due to the general decrease in caries experience in Denmark in recent years, a lower addition of fluoride than 0.6 mg/L would probably suffice. Another action to counteract increases in caries could be to carry out educational and information campaigns where the population is told to maintain high oral hygiene and to prevent too much sugar in the diet, not least for children in kindergartens and schools. Dental caries requires biofilms on tooth surfaces in combination with an intake of sucrose. Dental caries will not develop if one of these variables becomes totally removed. In Broendby, this is a particular challenge because of the high number of ethnic groups where many languages are represented. According to the model in Equations (1) or (5), the predicted average DMF-S in Broendby in 2004 is 2.06. In reality, the DMF-S was 2.47. The underestimation of DMF-S might be due to the lack of an ‘ethnic factor’ in the equation. The incorporation of an ethnic factor could be a task for future model development! Finally, it should be emphasized that the modeling of caries in this paper relates to 15-year-old school children. Later on in life, new caries experiences will inevitably develop and contribute to degradation of teeth, which eventually may lead to expensive teeth restorations. Therefore, a change in water chemistry through softening has a lifelong negative effect on caries. ## PERSPECTIVES FOR WATER DESALINATION Desalination of sea water and brackish water is a technology that is being developed strongly due to water scarcity in many places around the globe, for example in the Middle East, North America, Asia and Australia. The global desalination capacity in 2015 served about 300 million people from 18,426 plants with a total capacity of 86.8 × 106 m3/day (Wikipedia 2017). Desalination removes most of the ions from the water, in particular divalent cations and anions. Water without calcium and fluoride strongly promotes caries. Therefore, it is common practice to add fluoride to a level of 0.7–0.9 mg/L. Calcium may be added in order to prevent corrosion in steel components of the water supply system. For a case study in Perth, Australia, the recommended calcium concentration was 40 mg/L (Rygaard et al. 2011). This together with the usual fluoride concentrations would give an equivalent fluoride concentration, EFC, of about 1 mg/L. The removal of ions from water, partly or almost totally, may have other health effects than increased caries prevalence. Removal of water hardness (calcium and magnesium) may increase diseases for example cardiovascular mortality, but much more information is needed (Cotruvo & Bartram 2003). In one respect, however, low water hardness is beneficial because it reduces atopic dermatitis in infants (Engebretsen et al. 2017). ## 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 (fluoride equivalence). The combined effect of fluoride and calcium is underlined in this study by introducing a new water quality variable, the equivalent fluoride concentration, EFC, which contains the equivalent protection effect of calcium expressed in mg/L fluoride. The combined effect of calcium and fluoride is alternatively expressed in the form of the saturation with respect to calcium fluorite (CaF2). This may indicate that fluorite precipitation and dissolution in biofilm fluids on the tooth surfaces is involved in caries processes. For Danish conditions, we can predict that if the average family income per year decreases by 100 TDKK (13.4 TEURO or 14.7 TUS$) then 0.24 mg F/L or 37 mg Ca/L should be added to the water to maintain unchanged caries experience.

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%.

## ACKNOWLEDGEMENTS

Statistics Denmark (dst@dst.dk) has kindly provided the Danish family incomes.

## REFERENCES

REFERENCES
Bruvo
,
M.
,
Ekstrand
,
K.
,
Arvin
,
E.
,
Spliid
,
H.
,
Moe
,
D.
,
Kirkeby
,
S.
&
Bardow
,
A.
2008
Optimal drinking water composition for caries control in populations
.
Journal of Dental Research
87
(
4
),
340
343
.
Christensen
,
L. B.
,
Twetman
,
S.
&
Sundby
,
A.
2010
Oral health in children and adolescents with different socio-cultural and socio-economic backgrounds
.
Acta Odontologica Scandinavica
68
(
1
),
34
42
.
Cotruvo
,
J.
&
Bartram
,
J.
, (eds)
2009
Calcium and Magnesium in Drinking Water. Public Health Significance
.
WHO
,
Geneva
.
Ekstrand
,
K. R.
,
Christiansen
,
M. E.
&
Qvist
,
V.
2003
Influence of different variables on the inter-municipality variation in caries experience in Danish adolescents
.
Caries Research
37
,
130
141
.
Engebretsen
,
K. A.
,
Bager
,
P.
,
Wohlfart
,
J.
,
Skov
,
L.
,
Zachariae
,
C.
,
Nybo Andersen
,
A.-M.
,
Melbye
,
M.
&
Thyssen
,
J. P.
2017
Prevalence of atopic dermatitis in infants by domestic water hardness and season of birth: cohort study
.
Journal of Allergy and Clinical Immunology
39
(
5
),
1568
1574
.
Featherstone
,
J. D. B.
1999
Prevention and reversal of dental caries: role of low level fluoride
.
Community Dentistry and Oral Epidemiology
27
(
1
),
31
40
.
Featherstone
,
J. D. B.
2000
The science and practice of caries prevention
.
Journal of the American Dental Association
131
(
7
),
887
899
.
Fejerskov
,
O.
,
,
B.
&
Kidd
,
E.
, (eds)
2015
Dental Caries: The Disease and its Clinical Management
,
3rd edn
.
Wiley-Blackwell
,
UK
.
Kirkeskov
,
L.
,
Kristiansen
,
E.
,
Bøgild
,
H.
,
von-Platten Hallermund
,
F.
,
Sckerl
,
H.
,
Carlsen
,
A.
,
Larsen
,
M. J.
&
Poulsen
,
S.
2010
The association between fluoride in drinking water and dental caries in Danish children. Linking data from health registers, environmental registers and administrative registers
.
Community Dentistry and Oral Epidemiology
38
(
3
),
206
212
.
McDonagh
,
M. S.
,
Whiting
,
P. F.
,
Wilson
,
P. M.
,
Sutton
,
A. J.
,
Chestnutt
,
I.
&
Cooper
,
J.
2000
Systematic review of water fluoridation
.
BMJ
321
,
855
859
.
Parkhurst
,
D. L.
&
Appelo
,
C. A. J.
1999
Users Guide to PHREEQC (Version) – A Computer Program for Speciation, Batch Reaction, One-Dimensional Transport, and Inverse Geochemical Calculations
.
Water-Resources Investigations Report 99-4259
.
US Geological Survey
. .
Peres
,
K. G. D.
,
Bastos
,
J. R. D.
&
Latorre
,
M. D. D. D.
2000
Relationship between severity of dental caries and social behavioral factors in children
.
Revista De Saude Publica
34
(
4
),
402
408
.
Petersen
,
P. E.
1992
Oral health behavior of 6-year-old Danish children
.
Acta Odontologica Scandinavica
50
(
1
),
57
64
.
R Development Core Team: R
2011
A Language and Environment for Statistical Computing
.
R Foundation for Statistical Computing
,
Vienna
,
Austria
.
http://www.R-project.org. Accessed May 2017
.
Rygaard
,
M.
,
Arvin
,
E.
,
Bath
,
A.
&
Binning
,
P. J.
2011
Designing water supplies: optimizing drinking water composition for maximum economic benefit
.
Water Research
45
,
3712
3722
.
SCOR
2010
Average DMF-S for Permanent Teeth for 15-Year-Old Children During the Period 1992–2016
.
Central Dentistry Register
.
The Danish Health Authority. Islands Brygge 67. 2300 Copenhagen S. Denmark. sst@sst.dk
.
Statistics Denmark
2017
Statistics Data Base
.
Information service and Library
.
http://www.dst.dk/bibliotek. Family income: IG911. Accessed May 2017
.
US Dept. of Health and Human Services
2015
U.S. Public Health Service Recommendation for Fluoride Concentration in Drinking Water for the Prevention of Dental Caries
.
Public Health Reports. Vol. 130
.
Whitford
,
G. M.
,
Wasdin
,
J. L.
,
Schafer
,
T. E.
&
,
S. M.
2002
Plaque fluoride concentrations are dependent on plaque calcium concentrations
.
Caries Research
36
,
256
265
.
Wikipedia
2017
.