# Multi-Output Regression with Generative Adversarial Networks (MOR-GANs)
## 4 Silver Nanoparticle Data  
We now explore the application of WGAN to real-world data regression. Reference [32] explores the effects on cells from the lungs of four types of silver nanoparticles (AgNPs): silver nanospheres (AgNS) of diameter 20 nm and 50 nm; short silver nanowires (s-AgNWs) of length 1.5 \(\upmu\)m and diameter 72 nm; and long silver nanowires (l-AgNWs) of length 10 \(\upmu\)m and diameter 72 nm. Silver nanoparticles are increasingly used in consumer products and reports state that up to 14% of products containing AgNPs will release these nanoparticles into ambient air [33; 34] where they can be inhaled into the lungs of workers and consumers. The work in [32] explores the influence of the nanoparticles on airway smooth muscle (ASM) cells, which are an important component of the airways in the lungs, being responsible for narrowing the airways in conditions such as asthma. Bronchi and tracheas from transplant donor lungs were dissected to obtain the cells. These cells were serum-starved overnight and then incubated with 20 nm or 50 nm AgNSs, or s-AgNWs (5 \(\upmu\)g mL\({}^{-1}\) or 25 \(\upmu\)g mL\({}^{-1}\)) or Ag\({}^{+}\) ions (0.25 \(\upmu\)g mL\({}^{-1}\) or 25 \(\upmu\)g mL\({}^{-1}\)) for 24 or 72 h. Change in cell viability assessed by a reduction assay and change in cell proliferation assessed by the rate of DNA synthesis were both measured, and the results are reproduced in Figure 21. Cell viability is defined as the number of live, healthy cells in a sample.  
The data from [32] contains four different molecules analysed at two concentrations at three different times. The molecules were given numerical values based on their specific surface area, defined as the total surface area of a material per unit of mass. This can be seen in Table 4:  
The generator part of the WGAN was trained to produce four outputs: the specific surface area of the particles containing a specific molecule, the concentration level, the time level (we sample the response at 3 time levels: 4 h, 24 h and 72 h) and the response  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Molecule** & **Specific Surface Area m\({}^{2}\) g\({}^{-1}\)** \\ \hline Ag\({}^{+}\) & 4.4 \\ s-AgNWs & 4.6 \\
50 nm AgNSs & 6 \\
20 nm AgNSs & 40.4 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Specific surface area of the particles formed from different molecules which form independent variables for the WGAN regression.  
Figure 21: Concentration and time-dependent effect of AgNSs and AgNWs, and Ag\({}^{+}\) ions on ASM cell viability after 4 h, 24 h and 72 h. The bars represent mean values of 3 ASM cell donors and the whiskers indicate standard error of the mean (SEM). The data is expressed as percentage change with respect to the untreated control. This plot was formed from the dataset also reported in [32].  
(change in cell viability). All four outputs were scaled to be between 0 and 1. The WGAN architecture can be seen in Figure 22.  
Figure 23 contains the predictions made by the WGAN for cell viability, given time level, concentration level and surface area taken from the original study. For each combination of parameters (time level, concentration level and surface area), 10 predictions are made using the prediction Algorithm 1, minimising the error in the numerical value associated with a molecule, the concentration level and the time of interest. It can be observed that the mean of the predictions is close to the mean of the assessment. The average \(p\)-value for these predictions made is <0.2.