## 2 Idea and Concept  
The available hydrodynamic trapping techniques inside a microfluidic chip have improved and enhanced research study involving cells, moving from the population batch experiment towards individual cell analysis. The trapping method has been widely used [30; 31; 32; 33; 34; 35; 44; 45; 49; 50] as it enables high-throughput single cell trapping. However, currently available hydrodynamic trapping channels have limited capacity in providing a platform for individual cell manipulations for mechanical or electrical characterization. Realizing this need, researchers developed the idea to design T-channel single-cell trapping system with a microfluidic channel that could provide individual trapping site, thus enabling further single-cell characterization to be carried out. The T-channel trapping site is designed with two channels, a main and a trap channel. Figure 1 shows a schematic illustration of the hydrodynamic trapping concept with \(Rh_{\text{Trap}}\) and \(Rh_{\text{Main}}\) representing the flow resistance of the trap and the main channel, respectively. The \(Rh_{\text{Trap}}\) consists of the sum of three hydrodynamic resistances (\(Rh_{\text{T1}}\)+\(Rh_{\text{T2}}\)+\(Rh_{\text{T3}}\)). The yellow circle denotes a particle/cell to be trapped. For calculating the flow resistance of each channel, an analogous electrical circuit is considered, where the flow rate (\(Q\)) and the \(Rh\) are analogs of electric current and resistance, respectively. The main channel and trap channel's length are represented by \(L_{\text{Main}}\) and \(L_{\text{Trap}}\), respectively. \(W_{\text{Trap}}\) and \(W_{\text{Hole}}\) are the trap channel's and trap hole's width, respectively. The flow rate of whole fluid at the inlet could be assumed as an electric current source. The outlets could be assumed as grounds because they are at atmospheric pressure. This T-channel is a unique trapping site that allows single-cell manipulation to be performed using the trap channel's outlet port via a syringe pump. The hydrodynamic trapping concept can be summarized as follows: (a) the trapping channel has a lower \(Rh\) than the main channel when a trapping site is empty (Figure 2A); this will make the cells flow into the trapping stream and directed into the trap; (b) when a cell is trapped, it will act as a plug and increase the \(Rh\) along the trap channel (Figure 2B) drastically; and (c) the main flow will change from the trap channel to the bypass channel (main channel) and the next particles/cells will be directed to the bypass stream, passing by the filled trapping site [49]. The Darcy-Weisbach equation is used to determine the pressure drop or pressure difference in a microchannel to solve the continuity and momentum equations for the Hagen-Poiseuille flow problem. From the Hagen-Poiseuille equation, the flow rate (\(Q\)) can be defined by the following equation:  
\[\Delta P=Q\times Rh=Q\times\left(\frac{C\mu LP^{2}}{A^{3}}\right) \tag{1}\]  
where \(\Delta P\) is the pressure drop, \(Rh\) is the flow resistance of the rectangular channels, \(C\) is a constant that depends on the aspect ratio (ratio between height and width of the channel), \(\mu\) is the fluid's viscosity, and \(L\), \(P\), and \(A\) are the length, perimeter, and cross-sectional area of the channel, respectively.