\begin{equation}
\epsilon_{SO_2,K1} = \frac{0.262}{1 + \left(\frac{28.17}{D_{SO_2}}\right)},
\tag{5}
\end{equation}

\begin{equation}
\epsilon_{SO_2,to} = \frac{0.374}{1 + \left(\frac{16.74}{D_{SO_2}}\right)},
\tag{6}
\end{equation}

In agreement with experimental data \cite{10}, the mathematical relationship between the concentration of NOx and the blocking of the current I$_{Na}$ is the following:

\begin{equation}
b_{NO,Na} = \frac{1}{1 + \left(\frac{523}{D_{NO}}\right)^{6.8}},
\tag{7}
\end{equation}

where D$_{NO}$ is the NO$_x$ concentration in nM. To simulate the effect of the NO$_x$ on the I$_{CaL}$ current, the Michaelis--Menten equation was implemented as follows:

\begin{equation}
\epsilon_{NO,CaL} = \frac{0.59(D_{NO})}{D_{NO} + 0.007},
\tag{8}
\end{equation}

where the values 0.59 nM and 0.007 nM are the values of $e_{max}$ and half-maximal effective concentration (EC$_{50}$) respectively. This equation was fitted using human atrial myocyte data from \cite{11}. The blocking and increasing factors were introduced to the I$_{CaL}$, I$_{Na}$, I$_{K1}$ and I$_{to}$ equations in the cell model, as follows:

\begin{equation}
I_{CaL} = (1 - b_{CO,CaL})(1 - b_{SO_2,CaL})(1 + \epsilon_{NO,CaL}) g_{CaL} d f f_{Ca}(V_m - 65),
\tag{9}
\end{equation}

\begin{equation}
I_{Na} = (1 + \epsilon_{SO_2,Na})(1 - b_{NO,Na}) g_{Na} m^3 h j (V_m - E_{Na}),
\tag{10}
\end{equation}

\begin{equation}
I_{K1} = \frac{(1 + \epsilon_{SO_2,K1}) g_{K1} (V_m - E_{K1})}{1 + e^{0.07(V + 80)}},
\tag{10}
\end{equation}

\begin{equation}
I_{to} = (1 + \epsilon_{SO_2,to}) g_{to} a^3 o i (V_m - E_{to}),
\tag{11}
\end{equation}

The modified model was incorporated into a 3D model of human atria to evaluate the dynamics of propagation.

\subsection{3D model of human atrial}

A 3D virtual model of human atria was implemented \cite{12}. The model comprises the main anatomical structures, it is composed of 515010 hexahedral elements with a spatial resolution of 300 $\mu$m. It includes realistic fiber orientation, electrophysiological heterogeneity, and anisotropy.

To simulate the cardiac action potential propagation through the 3D model, the monodomain model described by the following reaction-diffusion equation was used:

\begin{equation}
\frac{1}{S_v} \nabla \cdot (D \nabla V_m) = C_m \frac{dV_m}{dt} + I_{ion} - I_{est},
\tag{12}
\end{equation}

where V$_m$ is the transmembrane voltage, C$_m$ is the specific membrane capacitance (100 pF), I$_{ion}$ is the total ionic current that crosses the membrane, I$_{stim}$ is the stimulus current, S$_v$ is the surface/volume ratio and D stands for the conductivity tensor. This equation was numerically solved using the finite element method implemented in the EMOS$^{R}$ software, with a temporal resolution of 0.001 ms.

\subsection{Simulation protocol}

For single-cell simulations, an S1-S1 stimulation protocol was applied, which consists of a train of rectangular pulses of 2 ms duration and -2,000 pA to generate action potentials at a base cycle length (BCL) of 1000 ms. The APD at 90\% of the repolarization (APD$_{90}$) and the different currents were measured on the 10th beat.

To simulate arrhythmia in the 3D model, an S1-S2-S3 stimulation protocol was applied, where S1 simulates the sinus rhythm as a train of stimuli applied in the sinoatrial node at a BCL of 500 ms. S2 and S3 simulate two ectopic foci composed of 6 stimuli each. S2 is located at the interatrial septum near the coronary sinus and S3 at the posterior wall of the left atrium, in the base of the right pulmonary veins. The first S2 and S3 were applied at coupling intervals that generated a unidirectional block, with cycle lengths selected such that the second stimulus from each focus also generated a unidirectional block. The simulations ran for 5 seconds. To calculate the number of reentries, reentry is defined as the propagation activity that presents 2 or more consecutive turns.

Table 1 shows the concentrations defined for each polluting gas, where the high concentration corresponds to an approximate value of the IC$_{50}$, the medium is half of the high concentration and the low corresponds to 20\% of the high concentration.

\begin{table}[h]
\centering
\caption{Gaseous air pollutants concentrations.}
\label{table_1}
\begin{tabular}{lccc}
\hline
Concentration level & [CO] & [SO$_2$] & [NO$_x$] \\
\hline
Control & 0 $\mu$M & 0 $\mu$M & 0 nM \\
Low & 250 $\mu$M & 8 $\mu$M & 0.002 nM \\
Medium & 625 $\mu$M & 20 $\mu$M & 0.005 nM \\
High & 1250 $\mu$M & 40 $\mu$M & 0.01 nM \\
\hline
\end{tabular}
\end{table}

\section{Results}

The results of single-cell simulations indicate that individual gaseous pollutants exhibit pro-arrhythmic effects in a concentration-dependent manner by altering the action potential.

Under healthy conditions, as the CO concentration increased, a reduction in the magnitude of the maximum peak of the I$_{CaL}$ current was observed and consequently, a reduction in APD$_{90}$ of 23.6\% (Figure 1A).

As the SO$_2$ concentration increased, APD$_{90}$ was reduced up to 38.8\%, also presenting a loss of the dome of the plateau phase (Figure 1B). The above is a consequence of the alterations in the ionic currents, which include a reduction in the magnitude of the maximum peak of the I$_{CaL}$ current, and an increase in the maximum peaks of the I$_{Na}$, I$_{to}$, and I$_{K1}$ currents.

Finally, as the NO$_x$ concentration increased, an increase in the magnitude of the maximum peak of the I$_{Na}$ and I$_{CaL}$ currents was observed, an effect opposite to what was observed in the other two gases. This generated a more