## 2 Materials and Methods
### Design of the Cyclic Stretch System
#### 2.2.2 Developed System
After the design of the compensation waveform, the next was to establish the methodology to determine the maximum local displacement in the horizontal and vertical direction. Here, we have developed a method to determine the maximum volume of compensation online for the first cycle by pressing the PC ENTER button, and after that, the cyclic stretch starts automatically and immediately, as shown in Figure 8. The process was performed at the beginning of all experiments, and the details are as follows. First, before stretching, adjust the focus, recognize and select the targets (a marker or cell for live imaging) by human eyes at any point on the membrane. After pressing the enter key to start stage 1, the chamber stretches at the desired speed and leads to membrane displacement in the horizontal and vertical directions. Second, stage 2 moves slowly at a speed of 10 \(\upmu\)m/s in the opposite direction of stage 1. Since the speed can be changed easily in the control program of stage 2, a sufficiently slow speed is achieved, and the targeting point can be recognized by human eyes during the period stage 2 movement. When the recognized target comes back to the center of the microscope's  
Figure 6: Vertical displacement trajectories of targets on the chamber membrane exposed to a stretching waveform different from that in Figures 4 and 5. (**a**) Layout of targets on the chamber membrane and the waveform for the control of stage 1/chamber stretching. (**b,c**) Upper: a typical waveform of points 1 and 2 when the chamber was stretched. Lower: the fit results of the stretching/holding/relaxation phases of the corresponding upper waveform. In (**b,c**), original data is in light blue and filtered data in orange. The lines with color in purple, blue, and black are the lines fitting for the lengthening, holding, and relaxation phases, respectively. field of view, the movement of stage 2 is stopped by pressing the ENTER key, and the displacement of stage 2 is used as the maximum compensation value in the horizontal direction. The target is out of focus due to the vertical shift of the chamber membrane. Next, push the enter key to start the movement of stage 3 to adjust the focus. Normally, since it is necessary to lower the position of the stretched chamber, stage 3 moves in the lower direction. After the target is brought into focus, press the enter key to stop stage 3, and the maximum compensation in the vertical direction is obtained. Since the stretching, holding, and relaxation time periods are fixed, moving speeds of stage 2 and 3 are calculated as the maximum compensation values divided by the time period. Therefore, moving speeds are obtained for the three stages, and cyclic stretch starts immediately with the desired stretching speed. Figure 7: The vertical displacement trajectory of point 3. 1 mL water was added to the stretch chamber before measuring. Lower: the fit results of the stretching/holding/relaxation phases. Original data is in light blue and filtered data in orange. The lines with color in purple, blue, and black are the lines fitting for the lengthening, holding, and relaxation phases, respectively.