## 4 Discussion
For the stretching chamber used in this study, which had a size of 20 mm \(\times\) 20 mm, the maximum vertical shift was approximate 200 \(\upmu\)m, and for a miniaturized stretch chamber, the vertical shift may become a value smaller than 10 \(\upmu\)m [40; 42]; a small vertical shift only resulted from the thickness change of the membrane of a miniaturized stretch chamber. In this case, since the thickness changed gradually but not suddenly, stage linear movement (a trapezoidal waveform) should be effective for compensation. It is challenging to use the methodology established in this study in fluorescence observation of cell organelles nowadays. There are two reasons as follows. First, fluorescence is weak in comparison to transmitted light phase contrast, and long exposure time is always necessary to improve the signal-to-noise ratio when using a conventional fluorescence microscope [52]. An essential difference of the method in this study is that the feedforward method was used and no image processing was conducted at the lengthening/relaxation phases. Although a high-speed camera such as an Electron Multiplying Charge Coupled Device (EM-CCD) or scientific-grade CMOS (sCMOS) camera maybe suitable for high-speed imaging of fluorescently tagged cells (\(>\)100 fps) [53], for a conventional fluorescence microscope, because the vertical shift was compensated at a millisecond level, there is a time limit for the collection of real-time fluorescence images because of long exposure time. Second, to observe the cell organelles using the immunofluorescence method, the stability of the stretched membrane may be influenced heavily by the culture medium in a chamber with a size of 20 mm \(\times\) 20 mm and the lens is sensitive to the small vibration when the magnification is high. In the future study, for enhanced stability, a miniaturized chamber is recommended, and if such a large chamber is necessary anyway, the stability of the chamber membrane may be achieved by putting a cover glass into the area between the chamber membrane and the objective lens. The reasons are as follows. There is a weak adhesion force between the membrane and the cover glass, which may reduce the effect of vibration when using a lens with high magnifying power, although the displacement of the membrane may become smaller. Further, the adding of a cover glass is necessary for the experiments observing cell organelles using conventional silicone chambers because for the observation of organelles using high power lens immersion oil is necessary, but the silicone substrate swells with immersion oil and turns into non-uniform shape [41]. Therefore, a cover glass here not only protects the membrane from immersion oil but also stabilizes the membrane when a lens with high power is applied. The following can be conducted to further improve the performance of the system. Displacement waveforms were specific at a different position on the membrane. It will be valuable to establish a mathematical model about the relationship between the membrane position and the displacement values (compensation values) of these positions, and combine the mathematical model to Formula (1). The combined model will be capable of predicting compensation waveforms more precisely. Next, the volume of the culture medium was a crucial factor influencing the effect of the compensation. As shown in Figures 5b and 7, the vertical displacement of point 3 was larger in the chamber with medium addition compared to the chamber without medium addition. Indeed, a large volume of the culture medium may increase the steps of compensation and the accumulation of position deviation. On the other hand, the volume of the culture medium may also influence cell functions. For example, the volume of the culture medium influenced the differentiation of osteoblasts and osteoclasts [54]. Therefore, a trade-off is necessary. To make the system compatible with fluorescent imaging, several factors should be taken into consideration.