# Assessment of Heavy Metal Distributions in Sand Beaches in the Maltese Islands
## 2 Materials and Methods
### Health Risk Assessment
CR is calculated through the product of the parameters Average Daily Dose (ADD) and slope factor (SF), where the slope factor is a value representing an incremental rate of cancer development in humans derived from a lifetime exposure to toxins. SF values used for computations performed are based on USEPA IRIS (2011) standards and EPA (1994) standards, and are outlined in Table 3[21; 27]. Equations used to calculate the slope factor for dermal contact are as follows:  
\[\text{RFD}_{\text{dermal}}=\text{RFD}_{\text{ingestion}}\times\text{ABS}_{ \text{GI}} \tag{5}\]  
\[\text{SF}_{\text{ingestion}}=\text{SF}_{\text{dermal}}\times\text{ABS}_{ \text{GI}} \tag{6}\]  
where RFD is the reference dose by ingestion or dermal contact of the metal; \(\text{ABS}_{\text{GI}}\) is the gastrointestinal absorbance factor; and SF is the slope factor defined for ingestion or dermal contact with the metal [28]. The Cancer Risk Index (RI) is calculated through the summation of CR individual values calculated for each heavy metal in the sand samples analysed [30]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Symbol** & **Unit** & **Adult Value** & **Children Value** \\ \hline Ingestion Rate & \(\text{IR}_{\text{inggest}}\) & mg/day & 30 & 80 \\ Exposure Frequency & \(\text{EF}_{\text{default}}\) & days/year & 350 & 350 \\  & \(\text{EF}_{\text{modified}}\) & 41 & 41 \\ Exposure Duration & \(\text{ED}_{\text{default}}\) & years & 30 & 6 \\ Average Body Weight & BW & kg & 80 & 18.6 \\ Non-Carcinogens & \(\text{AT}=\text{ED}\times 365\) & days & 10,950 & 2190 \\ Averaging Time & \(\text{AT}_{\text{default}}=\text{70 years}\times 365\) & days & 25,550 & 25,550 \\   Averaging Time & \(\text{AT}_{\text{children-modified}}\) = 6 years \(\times\) 365 & days & Not modified & 2190 \\ Unity Conversion & \(\text{CF}\) & kg/mg & \(1\times 10^{-6}\) & \(1\times 10^{-6}\) \\ Factor & \(\text{SA}\) & \(\text{cm}^{2}\) & 19,960 & 6820 \\   Exposed Skin Area & \(\text{AF}\) & mg/cm\({}^{2}\) & 0.352 & 4.48 \\   Average Adherence & \(\text{AF}\) & mg/cm\({}^{2}\) & 0.352 & 4.48 \\  & \(\text{ABS}\) & / & 0.001 & 0.001 \\ Fraction & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter values used to compute average daily dose by heavy metal ingestion and dermal contact [20; 21; 22; 23; 24; 25]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Metal** & \begin{tabular}{c} **RFD 1 by** \\ **Ingestion** \\ **(mg/kg/day)** \\ \end{tabular} & \begin{tabular}{c} **RFD 1 by** \\ **Dermal Contact** \\ **(mg/kg/day)** \\ \end{tabular} & \begin{tabular}{c} **Slope Factor by** \\ **Ingestion** \\ **(mg/kg/day)** \\ \end{tabular} & \
\begin{tabular}{c} **Slope Factor by** \\ **Dermal Contact** \\ **(mg/kg/day)** \\ \end{tabular} \\ \hline Fe & 0.700 & Not found & Not found & Not found \\ Mn & 0.140 & Not found & Not found & Not found \\ Zn & 0.300 & 0.060 & Not found & Not found \\ Pb & \(3.5\times 10^{-3}\) & \(5.25\times 10^{-4}\) & \(8.5\times 10^{-3}\) & \(5.675\times 10^{-3}\) * \\ Cu & 0.040 & 0.012 & Not found & Not found \\ Sr & 0.6 & Not found & \(8.9\times 10^{-10}\) &
\begin{tabular}{c} \(\text{Cannot be}\) \\ computed \\ \end{tabular} \\ \hline \hline \end{tabular} \({}^{\dagger}\) RFD is the reference dose for each heavy metal. * Computed through Equations (5) and (6).  
\end{table} 
Table 3: RFD and SF values for heavy metals [20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30].