# Identification, Control, and Characterization of Peristaltic Pumps in Hemodialysis Machines
## 3 Analysis of Results
### Characterization  
Characterizing peristaltic pumps is essential for optimizing performance and ensuring flow accuracy, particularly in applications requiring sterile handling, such as hemodialysis [27, 28]. These pumps operate by compressing and decompressing a flexible tube, minimizing contamination risk [2]. However, factors such as fluid-tubing interactions, influenced by properties like elasticity and viscosity, directly affect flow dynamics and accuracy [29]. Nonlinearities, such as oscillations caused by roller separation during operation, contribute to flow variability and performance reduction [30]. Similarly, non-Newtonian fluids, like synthetic blood, complicate flow dynamics due to shear-dependent viscosity and memory effects [25, 31]. Proper characterization accounting for these factors ensures realistic flow rate estimations [26]. This study characterizes a peristaltic pump over a flow range from 1.5 RPM, where system inertia is overcome, to 73 RPM, the maximum operating limit. The target flow rates include 20, 100, 200, 300, 400, 500, 600, 700, and 730 mL/min, as summarized in Table 2. The experimental setup (Figure 7) is designed to enable a robust evaluation of the developed system's performance. The setup integrates a peristaltic pump controlled via a LabVIEW interface, synthetic blood with clinically representative viscosity, and a hemodialysis filter to replicate real operational conditions. The LabVIEW interface synchronizes the pump's operation with real-time flow monitoring, allowing precise adjustments to ensure consistent fluid transport through the patient circuit hoses. Volume and mass measurements are recorded using graduated cylinders and a Sartorius weight scale, ensuring precise flow characterization. Once the experimental setup was complete, the patient circuit tubing was entirely filled with fluid to ensure no air remained in the system. The procedure began by setting a pump controller setpoint of 1.5 RPM, allowing the system to stabilize before placing the tubing into a graduated cylinder for timed measurements. The pump was kept running continuously during all repetitions to maintain flow consistency and avoid resetting the roller position, which could introduce variability. Flow rate calculations were derived by dividing the measured volume and mass by elapsed time. Measurement durations varied according to setpoint and cylinder capacity: 3 min for volumes of 20-300 mL, 2 min for 400-500 mL, and 1 min for 600-730 mL. To ensure accuracy and reliability, ten repetitions were conducted for each target flow rate. This methodology reduced variability, identified anomalies, and provided robust RMSE calculations, as shown in Table 2[32, 33]. The relationship between RPM and flow rate (mL/min) was determined by averaging the ten replicates for each setpoint and plotting the results. Figure 8 illustrates the fitted polynomial function, which provided the best experimental fit with an RMSE of 0.9193 mL/min. This function was estimated using the non-linear least squares method, as \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & **Target Flow** & \multirow{2}{*}{**RPM**} & **Average Flow** & **Standard** & \multirow{2}{*}{**RMSE**} \\  & **(mL/min)** & & **(mL/min)** & **Deviation** & \\ \hline
1 & 20 & 1.50 & 23.06 & 0.18 & 0.97 \\
2 & 100 & 8.50 & 101.35 & 0.45 & 0.45 \\
3 & 200 & 17.50 & 200.00 & 0.00 & 0.00 \\
4 & 300 & 27.49 & 297.55 & 1.03 & 0.84 \\
5 & 400 & 36.60 & 400.00 & 0.00 & 0.00 \\
6 & 500 & 46.70 & 500.00 & 0.00 & 0.00 \\
7 & 600 & 58.50 & 599.80 & 0.60 & 0.20 \\
8 & 700 & 69.90 & 697.40 & 0.18 & 0.97 \\
9 & 730 & 73.00 & 727.60 & 0.45 & 0.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Flow rate characterization in mL/min vs. RPM. detailed in _Section 3.3 Validation_. The polynomial model showed high accuracy in describing the relationship between RPM and flow, with minimal deviation between predicted and observed values. Figure 8: Fitted polynomial function of experimental data of peristaltic pump flow rate.