## 2 Composition and Pressure Measurement Principle of the Compact Pressure Measurement Catheter  
As shown in Figure 2, the compact pressure measurement catheter consists of four main components: the compact catheter body, high-precision pressure sensor, wireless communication circuit, and shell. The catheter body is made from PDMS, which has hydrophobic properties and a compact structure. The high-precision pressure sensor and its casing are made biocompatible and fluid-resistant through the deposition of Parylene C for surface modification. When using the compact high-precision interventional pressure measurement catheter, the catheter is filled with saline. It is then inserted into the body at the pressure measurement point (such as blood vessels, urethra, etc.) through a minimally interventional approach. At this location, the pressure inside the body cavity is transmitted to the high-precision pressure sensor through the small amount of saline in the catheter, and the pressure signal is transmitted to the computer system via the communication circuit. Since most of the pressure inside the human body fluctuates, monitoring in vivo pressure not only requires high-precision static measurement but is also necessary to achieve precise measurement of dynamic signals, such as changes in in-body pressure. The following theoretical analysis in Figure 3 addresses the different dynamic and static pressure measurement scenarios in response to the above conditions. Figure 1: Measurement method and structure of the compact pressure measurement catheter. When the pressure at the test point remains stable, as shown in Figure 3a, the fluid inside the catheter is in a static state, and at this time, the sensor's measured value is  
Figure 3: Theoretical analysis of the dynamic and static pressure measurement process of the pressure measurement catheter: (**a**) Measurement situation when the test point is under static pressure; (**b**) measurement situation when the test point is under dynamically varying pressure. Figure 2: Components of the Compact Pressure Measurement Catheter. equivalent to the total static pressure, \(P\). The mechanical relationship in this connected part is as follows:  
\[P=P_{0}+\rho gh, \tag{1}\]  
where \(P\) is the static pressure part at the sensor's location, \(P_{0}\) is the pressure at the front end of the pressure catheter connected to the internal fluid surface (equal to the pressure of the inner wall of the cavity to be measured, which is the target measurement value for the pressure sensor), \(\rho\) is the density of the liquid, \(g\) is the acceleration due to gravity, and \(h\) is the vertical distance from the location of the monitoring system to the position of \(P_{0}\). Under this condition, it can be regarded as the sensor directly measuring the liquid pressure, without the influence of vascular walls, muscle layers, fat layers, and skin or other surface tissues. Its measurement accuracy far exceeds that of indirect measurement devices, and the structure and materials of the pressure catheter do not affect the measurement results. When the pressure increases or decreases, the walls of the compact pressure measurement catheter deform, causing the fluid inside the catheter to flow due to this deformation. Most of the fluid flow inside the body is laminar, so the flow speed of the fluid in the pressure measurement catheter connected to the body is also very low, and its Reynolds number is far less than 2000, which can be considered as laminar flow.