# Finger-Actuated Microneedle Array for Sampling Body Fluids
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Target Fluid**} & **BC 1** & **BC 2** & **BC 3** \\  & & **(Pressure Input by Finger)** & **(Reservoir)** & **(Fluid Inlet from MNs)** \\ \hline \multirow{2}{*}{1} & Human & \multirow{2}{*}{\(P(t)=2250\times\text{cos}\Big{(}\frac{2\pi}{5}\times t\Big{)}+2250\ \left[Pa\right]\)} & \multirow{2}{*}{\(P=0\)} & \multirow{2}{*}{\(P=135\ mmHg\)} \\  & blood & & & \\ \hline \multirow{2}{*}{2} & Human & \multirow{2}{*}{\(P(t)=2250\times\text{cos}(2\pi\times t)+2250\ \left[Pa\right]\)} & \multirow{2}{*}{\(P=0\)} & \multirow{2}{*}{\(P=135\ mmHg\)} \\  & blood & & & \\ \hline \multirow{2}{*}{3} & Human & \multirow{2}{*}{\(P(t)=2250\times\text{cos}\Big{(}\frac{2\pi}{5}\times t\Big{)}+2250\ \left[Pa\right]\)} & \multirow{2}{*}{\(P=0\)} & \multirow{2}{*}{\(P(t)=4000\times\text{cos}\Big{(}\frac{13\pi}{5}\times t\Big{)}+14000\ \left[Pa\right]\)} \\  & blood & & & \\ \hline \multirow{2}{*}{4} & Human & \multirow{2}{*}{\(P(t)=2250\times\text{cos}(2\pi\times t)+2250\ \left[Pa\right]\)} & \multirow{2}{*}{\(P=0\)} & \multirow{2}{*}{\(P(t)=4000\times\text{cos}\Big{(}\frac{13\pi}{5}\times t\Big{)}+14000\ \left[Pa\right]\)} \\  & blood & & & \\ \hline \multirow{2}{*}{5} & Interstitial & \multirow{2}{*}{\(P(t)=2250\times\text{cos}\Big{(}\frac{2\pi}{5}\times t\Big{)}+2250\ \left[Pa\right]\)} & \multirow{2}{*}{\(P=0\)} & \multirow{2}{*}{\(P=4\ mmHg\)} \\  & fluid (ISF) & & & \\ \hline \multirow{2}{*}{6} & Interstitial & \multirow{2}{*}{\(P(t)=2250\times\text{cos}(2\pi\times t)+2250\ \left[Pa\right]\)} & \multirow{2}{*}{\(P=0\)} & \multirow{2}{*}{\(P=4\ mmHg\)} \\  & fluid (ISF) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The simulated cases of the present study for two different fluids and various boundary conditions (BCs). The function in Equation (4) was also simulated. Cases 3 and 4 in Table 3 used this equation for the incoming human blood along with slow finger pressure input (Equation (1)) and fast finger pressure input (Equation (2)), respectively. The mass flow-time curves at the reservoir for these two cases are presented in Figures S1 and S2, respectively. Among two states of using a constant pressure for the human blood inlet and heartbeat imitation function of Equation (4), a small amount of difference in the mass flow rate was detected. While the pressure function imitated the heartbeat action and offered a more realistic study condition, the resulting mass flow rate, and hence the amount of the extracted blood, was smaller. Figure 2: Representation of the created mesh and results of the velocity field. (**a**) The mesh that was created for the study is represented here. In the highlighted area in yellow, the velocity field results in the direction perpendicular to the cross section of the channels are shown, with the function of the heartbeat imitation for the incoming human blood and pressing the mechanical pressure input button every 5 s (study case 3 in Table 3). In the fifth second, the velocity reached its maximum amount of around 0.25 m.s\({}^{-1}\). (**b**) The velocity field for one of the MNs in the patch from time = 0 to 5 s and (**c**) its corresponding velocity-time curve. The color bar shows velocity in m/s. In another series of simulations, ISF was used as the target fluid. First, Equation (1) was used as the BC for the finger pressing dome (case 5 in Table 3), followed by a second run with Equation (2) (case 6 in Table 3) to study the effect of the force input speed by pressing with fingers. The mass flow curve results at the reservoir are shown with the yellow color in Figure 4b,c for the state of slow (case 5, Table 3) and fast (case 6, Table 3), respectively. Figure 3: Pressure distribution results. (**a**) For interstitial fluid (ISF) and pressing the mechanical pressure input button every 5 s (study case 5 in Table 3), the pressure distribution in the fifth second is represented here along with (**b**), the magnified view of the microneedle array (MNA) area.