## 4 Discussion  
The absorption and emission spectra of dispersions prepared from the decomposition of DMSO in the presence of Ca(CH\({}_{3}\)CO\({}_{2}\))\({}_{2}\) were remarkably similar to the one obtained for dispersions prepared by dissolving CaS\({}_{(\bullet)}\) mineral in DMSO or from the reaction of Na\({}_{2}\)S and Ca(CH\({}_{3}\)CO\({}_{2}\))\({}_{2}\) in DMSO. These dispersions absorb light from the UV to the visible. The observed emission was consistent with the fluorescence spectra of CaS nanostructures obtained from the microwave-mediated decomposition of other organic sulfides [28]. There are several models to describe cell proliferation discussed in the literature. The application of these models to specific cases depends on the complexity of the cell culture and its environment. One of the simplest mathematical models is a power law of the form:  
\[\mathbf{N}(t)=\mathbf{N}(t=\mathbf{0})*t^{\mathbf{\alpha}} \tag{2}\]  
where \(N(t)\) and \(N(t=0)\) represent the number of cells at any time \(t\) and the initial number of cells after inoculation has been completed, respectively. In Equation (2), \(t\) is time and \(\alpha\) is constants. Modeling the experimental data with a power law of the form described by Equation (2) resulted in the values of \(\alpha\) summarized in Table 3. The values of \(\alpha\) for the growth of carcinoma and normal fibroblasts used as a control in the experiments described in Sections 3.3 and 3.4 were between 0.2 and 0.5 in the region of maximum growth, and between 0.4 and 0.49 in the entire time scale of our measurements. These values were lower than the typical third power law found in tumors, likely the result of two-dimensional growth, but fell within the power measured in several systems [37]. Significantly, the values of \(\alpha\) found in the proliferation of carcinoma and normal fibroblasts reflect an increase in cell density with time. The value of \(\alpha\) for those carcinoma cells exposed to a single dose of CaS, on the other hand, was negative and reflects a decrease in carcinoma cell density. This marked difference in the proliferation of carcinoma cells and normal fibroblasts led us to propose that CaS is cancer-specific. The development of cancer-specific chemotherapies has been the subject of basic and applied research for years. Major limitations in the application of nanotechnologies as \begin{table}
\begin{tabular}{c c c c} \hline \hline
**System** & **Interaction Energy** & **CaS—Functional Group** & **Ca-S Bond Length (Å)** \\  & (k/mol) & Minimum Distance (Å) & **Ca-S Bond Length (Å)** \\  & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._ \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **In[**\(N\) (\(t=0\))**\(\pm\)\(\mathbf{\sigma_{N}}\) & \(\mathbf{\alpha}\)\(\pm\)\(\mathbf{\sigma_{\kappa}}\) \\ \hline \multirow{2}{*}{Carcinoma treated} & 4.8 \(\pm\) 0.6 & \(-\)0.06 \(\pm\) 0.08 \\  & (4.6 \(\pm\) 0.3) & (\(-\)0.09 \(\pm\) 0.1) \\ \hline \multirow{2}{*}{Carcinoma untreated} & 2.694 \(\pm\) 0.002 & 0.4808 \(\pm\) 0.000 \\  & (2.8 \(\pm\) 0.1) & (0.45 \(\pm\) 0.03) \\ \hline \multirow{2}{*}{Fibroblast treated} & 3.4 \(\pm\) 0.2 & 0.22 \(\pm\) 0.07 \\  & (2.6 \(\pm\) 0.8) & (0.4 \(\pm\) 0.2) \\ \hline \multirow{2}{*}{Fibroblast untreated} & 2.4 \(\pm\) 0.4 & 0.6 \(\pm\) 0.1 \\  & (2.4 \(\pm\) 0.3) & (0.49 \(\pm\) 0.09) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Values of \(\alpha\) obtained from a linear regression analysis to a log–log plot according to a power function model for cell growth as a function of time in the region of maximum growth. Values of \(\alpha\) that correspond to the total time scale studied are indicated in parenthesis. targeted cell cancer and metastatic therapy include toxicology [38; 39; 40], lack of biodegradability [41; 42; 43; 44], and size to facilitate access to the--normal and newly developed due to angiogenesis--small vasculature system in humans and elimination by the body [45; 46; 47; 48; 49].