请将下方内容用更为地道、更为科学的英文表达出来：To further optimize the physical properties of the brin- based hydrogel for intestinal organoid culturing we next modulated the stiffness of the gel by varying the concentrati

To optimize the physical properties of the hydrogel based on fibrin for culturing intestinal organoids, we conducted experiments to modulate its stiffness by adjusting the concentration of fibrin. Our results, as shown in Figure 2A, indicate that fibrin concentrations ranging from 1.5 to 6 mg/mL, which correspond to stiffness between 24 ± 10 Pa (SD, n = 6) and 270 ± 8 Pa (SD, n = 3), allowed for efficient formation of round cysts (Figure 2B,F) in the colony formation assay. However, increasing the fibrin concentration to 7.5 mg/mL, which generated a hydrogel with a stiffness of 492 ± 78 Pa (SD, n = 3), resulted in the formation of dense spheroids that did not continue to grow into budding organoids. Conversely, a lower fibrin concentration of 1.5 mg/mL led to gel degradation after only four days and impaired organoid expansion (Figure 2C). Based on these findings, we conclude that fibrin hydrogels ranging from 3 to 4.5 mg/mL (77 ± 25 Pa (SD, n = 3) and 140 ± 47 Pa (SD, n = 4)) provide optimal physical properties for organoid expansion