# Modeling of Integrated Nanoneedle-Microfluidic System for Single Cell Temperature Measurement
## 2 Proposed Nanoneedle-Microfluidic System
### Simulation Analysis Setup  
In this work, the simulation analysis was done using ABAQUS (Version: 6.12, Dassault Systemes, Velizy-Villacoublay Cedex, France) finite element analysis software that performs multi-physics analysis. Different settings were implemented for each stage in the modeling process depending on the parameters and condition under study. For instance, in the designing (shape, gap and size) and electrical and mechanical characterization of the nanoneedle, the objectives of the simulation are to have an equally distributed current density within the nanoneedle, to obtain the nanoneedle that causes minimal damage to the cell under study. This is performed to have the same behavior as a positive RTD, and to have high strength to be able to penetrate the cell/cell wall. This involved the use of electrical-thermal and mechanical definition. The nanoneedle was modelled as a 3D solid deformable DC3D4E with a 4-node linear coupled thermal-electrical element for the nanoneedle shape and size optimization. The nanoneedle shape of either being square or a circular (Figure 2) and the gap length within the nanoneedle were studied (Figure 2b), the uniformity of current density distribution was the determining factor. The cross-sectional area size of the nanoneedle was analyzed based on the damage the nanoneedle caused a yeast cell after penetration (Figure 3a). The nanoneedle position on a 4 \(\upmu\)m yeast cell model is shown in Figure 3b. The yeast cell was modelled as a solid deformable C3 DSR with an 8-node linear brick 3D stress element for mechanical model. The cell model had two main components: the cell wall and cytoplasm. The size was varied between 4 and 6 \(\upmu\)m in diameter depending on the purpose of the simulation. Here a 4 \(\upmu\)m yeast cell was used. The cell wall was defined as a hyper-elastic material with properties defined from [22] and the cytoplasm as homogenous fluid. Figure 1: (**a**) Proposed microfluidic system design, the system concept and working principle; (**b**) Schematic diagram illustrating how cells penetrate the nanoneedle for measurement; (**c top**) The microfluidic channel when cells are inserted into the chip for measurement; (**c bottom**) The location and direction of water after the measurement and for waste collection. Figure 2: The nanoneedle design highlighting the shape and the gap to be studied. (**a**,**i**) Square (**a**,**ii**) Circular; (**b**) Gap length performed in the nanoneedle design optimization. The second stage in the modelling was to characterize the nanoneedle behavior prior to the integration. Firstly, it was the electrical characterization, which a deformable DC3D4E model was used to model the nanoneedle for the thermal-electric characterization with a 4-node linear coupled thermal-electric element definition. Density, specific heat, electrical and thermal conductivity of tungsten were defined and a 0.1 hexahedron meshing size was applied. The aim of this simulation was to observe the behavior of the current within the nanoneedle and if it complies with the behavior of a positive RTD. A constant voltage of 1 volts was applied at one surface of the electrodes and ground to the other (Figure 4a). The current density change was observed as the temperature varied. The temperature was defined at the surrounding in the pre-defined field as a preliminary step for the temperature to stabilize and have an even distribution within the needle prior to the application of the voltage. Secondly in the mechanical characterization, the nanoneedle was modeled as a 3D solid deformable C3D8R with an 8-node linear brick 3D stress element. Density, elastic, plastic and failure properties were defined for tungsten and a 0.1 hexahedron meshing size was applied. Ramp force was applied to the top surface of the needle where the penetration happens, and fixed at the bottom surface of the electrodes where it would attach to the glass plate in the microfluidic system (Figure 4b).