## 3 Results
### Effect of Cellular Density of Alginate Spheres on DPCs Proliferation  
To determine the effect of cellular density in the sphere on the proliferation of DPCs, we cultivated the spheres under the same spherical diameter but with different numbers of cells input. The diameter of each sphere was controlled approximately at 200 \(\upmu\)m, since the diameter of dermal papilla in human hair follicles is around 100-250 \(\upmu\)m depending on the bulb size and body location. To avoid generating alginate spheres with a tear drop shape, which resulted when the alginic acid was diluted, we also controlled the dilution ratio of the alginic acid and cellular media. As we expected, we could produce 3D alginate spheres containing different numbers of DPCs with a highly controlled size (Figure 3A-D). The average number of live cells were 31.8, 60.8, 115.3 and 214.4 per sphere immediately after making the sphere. Figure 3: Short-term and long-term cultivation of dermal papilla alginate spheres with different cellular densities. (**A**–**D**): Different densities of alginate spheres. (**A**) low density, (**B**) middle density, (**C**) moderate density and (**D**) high density of human DPCs in alginate spheres. (**E**) The live cell number per alginate sphere at different cellular densities. (**F**) The total cells included both the live cells and dead cells per alginate sphere at different cellular densities. (**G**) The ratio of live cells to total cells per alginate sphere at different cellular densities. (**H–K**): The live cell number with low density (**H**), middle density (**I**), moderate density (**J**), high density (**K**) of cells in a sphere (Cell number/mm\({}^{3}\)). Note. *: \(p\)-value <0.05, **: \(p\)-value <0.01. Compared to day 0 (control) as assessed by t-test. Scale bars: A–D: 100 \(\upmu\)m.  
After we distributed DPCs inside the spheres in different densities, we followed the cell proliferation and survival rate. Unlike the experiment related to the size of the spheres, we observed cellular growth in the lower density spheres, particularly in the 5 \(\times\) 10\({}^{4}\) and 1 \(\times\) 10\({}^{5}\) density spheres (30-60 cells/sphere). We found that there was no growth in the higher density spheres with more than 100 cells/sphere (Figure 3E). Considering that the total number of cells (including live and dead cells) increased under all conditions in these experiments, we could conclude that there were cellular proliferations in all of the spheres at early time point. (Figure 3F). The lower the cell density was, the greater the growth rate. However, the growth rate was insignificant compared to that produced through 2D cultivation. The total proportion of live cells decreased steadily as in the previous experiment (Figure 3G). To examine the effect of cellular density on the alginate spheres containing human DPCs, we cultivated them for 90 days. Unlike the size experiments, the cells inside the alginate spheres seemed to proliferate in the lower densities (Figure 3H,I). However, they tended to decrease in numbers after reaching a maximal number of cells at day 30. Compared to lower density, the live cells decreased as time passed in the higher densities (Figure 3J,K). The total number of live cells continued to decrease until 70 days after cultivation. Interestingly, the live cell number remained stable after 70 days and lasted until day 90 as in the size experiments. In the alginate spheres of every density, we observed a convergence phenomenon after 70 days (Figure 3H-K). Their diameters of each cellular density groups (5 \(\times\) 10\({}^{4}\), 1 \(\times\) 10\({}^{5}\), 2 \(\times\) 10\({}^{5}\), 5 \(\times\) 10\({}^{5}\)) were statistically similar, 203.4 \(\upmu\)m, 205.7 \(\upmu\)m, 203.3 \(\upmu\)m and 204.4 \(\upmu\)m respectively (\(p\)-value: 0.073, ANOVA). The number of live cells after convergence was around 10 cells per sphere in every condition, which inferred that the number of convergent cells was not dependent on the cell number we input but on the volume of the alginate sphere.