Effect of Fluoridated Water on Plasma Insulin Levels and Glucose Homeostasis in Rats with Renal Deficiency

Abstract

Glucose intolerance in fluorosis areas and when fluoride is administered for the treatment of osteoporosis has been reported. Controlled fluoridation of drinking water is regarded as a safe and effective measure to control dental caries. However, the effect on glucose homeostasis was not studied so far. The aim of this study was to evaluate the effect of the intake of fluoridated water supply on glucose metabolism in rats with normal and deficient renal function. Male Sprague–Dawley rats were divided into eight groups of four rats. Renal insufficiency was induced in four groups (NX) which received drinking water containing 0, 1, 5, and 15 ppm F (NaF) for 60 days. Four groups with simulated surgery acted as controls. There were no differences in plasma glucose concentration after a glucose tolerance test between controls and NX rats and among rats with different intakes of fluoride. However, plasma insulin level increased as a function of fluoride concentration in drinking water, both in controls and in NX rats. It is concluded that the consumption of fluoridated water from water supply did not affect plasma glucose levels even in cases of animals with renal disease. However, a resistance to insulin action was demonstrated

Appendix

After and intravenous dose of NaF (Do), the distribution of fluoride in the body can be represented as detailed in Fig. 4.

Fig. 4

Distribution of fluoride in plasma, bone, and kidney after an intravenous dose (Do). [F] plasma concentration of fluoride, Vo ₋ rate of fluoride uptake by bone tissue, Vo ₊ rate of fluoride released from bone tissue, Vu ₋ rate of renal fluoride excretion, Vu ₊ rate of renal fluoride re-absorption, U cumulative urinary fluoride excretion

In this situation, the variation of plasma fluoride concentration can be represented by the following differential equation:

$$ \frac{{{\rm d} \left[ F \right]}}{{{\rm d} t}} = V{o_{+} } - V{o_{-} } + V{u_{+} } - V{u_{-} } $$

(1)

where

$$ Vu = V{u_{-} } - V{u_{+} } $$

rearranging Eq. 1

$$ \frac{{{\rm d} \left[ F \right]}}{{{\rm d} t}} = V{o_{+} } - V{o_{-} } - Vu. $$

(2)

After an intravenous dose of NaF, it can be supposed that Vo₋ > Vo₊. This assumption is supported by the high plasma fluoride levels reached after the fluoride injection.

Under this consideration, Vo₊ can be considered negligible; as a consequence, Eq. 2 can be written as follows:

$$ {\frac{{{\rm d} \left[ F \right]}}{{{\rm d} t}} = - V{o_{-} } - Vu.} $$

(3)

The preceding differential equation states that after an intravenous dose of fluoride, the decrease in plasma fluoride concentration is a function of the rate of fluoride uptake by bone tissue and the renal excretion of fluoride.

It can be considered that both rates are linear functions of plasma fluoride concentration.

As a consequence

$$ V{o_{-} } = k{o_{-} } \times \left[ F \right] $$

(4)

$$ Vu = ku \times \left[ F \right]. $$

(5)

From Eqs. 3, 4, and 5, the following is obtained:

$$ \frac{{{\rm d} \left[ F \right]}}{{{\rm d} t}} = - k{o_{-} } \times \left[ F \right] - ku \times \left[ F \right] $$

$$ \frac{{{\rm d} \left[ F \right]}}{{{\rm d} t}} = - \left( {k{o_{-} } + ku} \right)\left[ F \right] $$

$$ ke = k{o_{-} } + ku $$

(6)

$$ \frac{{{\rm d} \left[ F \right]}}{{{\rm d} t}} = - ke \times \left[ F \right] $$

(7)

where ke is the rate constant of elimination of fluoride from plasma compartment.

Integrating both members of Eq. 7 and solving

$$ {\hbox{1n}}\frac{{\left[ F \right]}}{{{F_0}}} = - ke \times t $$

(8)

where [F] and [F _o] are the values of plasma fluoride concentration at a definite time and immediately after the injection of NaF, respectively.

Considering the initial concentration of fluoride as the ratio between the intravenous dose (Do) and the distribution volume of fluoride (V _d), Eq. 8 can be rewritten as follows

$$ 1n\left[ F \right] = {\hbox{1n}}\frac{{{D_0}}}{{{V_{\rm d} }}} = ke \times t. $$

(9)

Equation 9 represents the logarithm of plasma fluoride concentration as a linear function of the time. With two or more values of plasma fluoride concentration after an intravenous dose (Do), V _d and ke can be obtained with the last square method of linear regression.

On the other hand, the cumulative urinary excretion of fluoride can be described by the following differential equation:

$$ \frac{{{\rm d} \left[ U \right]}}{{{\rm d} t}} = ku \times \left[ F \right] $$

(10)

where ku is the rate constant of renal fluoride excretion. This equation states that the excretion of fluoride linearly depends on the plasma fluoride levels

Rearranging Eq. 8

$$ \left[ F \right] = \left[ {{F_0}} \right] \times {e^{ - ke \times t}} $$

and replacing in Eq. 10, the following is obtained:

$$ \frac{{{\rm d} \left[ U \right]}}{{{\rm d} t}} = ku \times \left[ {{F_0}} \right] \times {e^{ - ke \times t}}. $$

(11)

Integrating both terms of equation

$$ \left[ U \right] - \left[ {{U_0}} \right] = \frac{{ku \times \left[ {{F_0}} \right]}}{{ke}} \times \left( {1 - {e^{ - ke \times t}}} \right) $$

(12)

as U ₀ = 0:

$$ \left[ U \right] = \frac{{ku \times {D_0}}}{{{V_{\rm d} } \times ke}} \times \left( {1 - {e^{ - ke \times t}}} \right). $$

(13)

After 24 h of the mini dose of NaF, approximately 100% of fluoride not incorporated in bone tissue has been excreted in urine. The cumulative fluoride excretion after 24 h can be considered the limit of Eq. 13 when time tends to infinite. As a consequence, the limit of Eq. 13 can be written:

$$ \frac{{ku \times {D_0}}}{{{V_{\rm d} } \times ke}} \times \left( {1 - {e^{ - ke \times t}}} \right). $$

Solving

$$ \mathop {{\lim }}\limits_{t \to \infty } \left[ U \right] = \mathop {{\lim }}\limits_{t \to \infty } \frac{{ku \times {D_0}}}{{{V_{\text{d}}} \times ke}} \times \left( {1 - {e^{ - ke \times t}}} \right) = {\left[ U \right]_\infty }$$

(14)

where [U]_∞ is the cumulative fluoride excretion after 24 h of the intravenous dose. The value of ku is obtained with Eq. 14 and the values of [U]_∞, Do, V _d, and ke.

With the values of ke and ku using Eq. 6, ko ₋ is obtained.

Finally, with Eq. 4 and the values of ko₋ and basal plasma fluoride concentration, the value of Vo₋ is obtained.