# Effect of Ambient Temperature on Impedance-Based Physiological Activity Evaluation of Zelkova Tree
## 2 Impedance Measurement Method  
Impedance can be calculated by applying a current to the object being measured and measuring the voltage induced in the object being measured. Since the wood and the  
Figure 2: Shigometer: (**a**) a measuring device and (**b**) probes inserted into a tree. contact surface between the wood tissue and the measurement probe are expected to be composed of a combination of resistance and capacitance, the impedance measurement is performed using a flowing AC current rather than a DC current. Figure 3a shows the Hayden model, which is often applied as an electrical equivalent model for plant cells [11; 12]. The Hayden model represents a tree cell as three resistors and one capacitor. The symbol R\({}_{\rm I}\) represents the intercellular resistance and the symbol R\({}_{\rm E}\) represents the extracellular resistance. The symbol R\({}_{\rm M}\) represents the membrane resistance and the symbol C\({}_{\rm M}\) represents the membrane capacitance. The cell membrane is modeled as a parallel combination of capacitance C\({}_{\rm M}\) and resistance R\({}_{\rm M}\), the inside of the cell is modeled as a series-connected resistance value R\({}_{\rm I}\), and the material between cells is modeled as a resistance R\({}_{\rm E}\). Previous Shigometers were only able to measure impedance of DC currents, but since tree tissue can be modeled as a combination of resistance and capacitance, the TPAM system requires the ability to change the frequency of the applied current. To measure impedance, a probe is inserted into the tree, and a contact impedance is formed between the metal probe and the tree tissue, as shown in Figure 3b [13]. The symbol C\({}_{\rm PA}\) represents the interface capacitance, the symbol R\({}_{\rm ct}\) represents the charge transfer resistance, and the symbol R\({}_{\rm S}\) represents the solution resistance. The contact impedance Z\({}_{\rm c}\), which is composed of a combination of these components C\({}_{\rm PA}\), R\({}_{\rm ct}\), and R\({}_{\rm S}\), exists between the probe and the tree tissue. In the two-point impedance measurement method, the contact impedance Z\({}_{\rm c}\) component is included, so additional error cannot be avoided. Figure 4a shows the electrical model when measuring the impedance of a tree using the two-point measurement method. The impedance to be measured in the tree is denoted as Z\({}_{\rm t}\), and the contact impedance between the probe and the tree tissue is denoted as Z\({}_{\rm c1}\) and Z\({}_{\rm c2}\). There is also a resistance component of the probe itself, which is connected in series to the measuring instrument, but the resistance of a probe made of metal is so small that it is negligible compared to the contact impedance. Therefore, for simplicity, Z\({}_{\rm c1}\) and Z\({}_{\rm c2}\) were not drawn across the border between the probe and the tree, but were drawn as if they were the impedance of the probe itself. The current \(I_{d}\) applied from the current source flows through the contact impedance Z\({}_{\rm c1}\), the tree impedance Z\({}_{\rm t}\), and the contact impedance Z\({}_{\rm c2}\) connected in series between nodes \(M1\) and \(M2\). The voltage measured between nodes \(M1\) and \(M2\) also includes contact resistance in addition to the wood impedance, but there is no way to separate the values corresponding to these components. For these technical reasons, traditional Shigometers using a two-point measurement method are bound to be inaccurate. Moreover, when a single measurement is repeated, such as with the Shigometer, the state of the interface between the probe and the tree changes, so the contact impedance value also changes, which inevitably reduces the measurement reproducibility. Figure 3: Electrical impedance model: (**a**) Hayden model and (**b**) electrode–electrolyte interface model. Figure 4b is an electrical model showing the four-point impedance measurement method.