Comparing the size indices (Table 1), Pre ostia had an average area of 15.52 (± 3.51) mm2, with values ranging from 9.14 to 20.61 mm2, and FU ostia had an average area of 13.30 (± 2.27) mm2, ranging from 10.18 to 16.55 mm2. Three out of seven ostia were larger after treatment (Table 2), but on average, ostium area of the FU data was 10% smaller than Pre data, with an average absolute shrinkage of 2.22 (± 4.22) mm2 and an average yearly shrinkage rate of 0.58 (± 4.88) mm2, which makes -2 (± 0.26) % per year.

Pre ostia had an average width of 5.01 (± 0.54) mm and FU ostia 4.49 (± 0.45) mm, with an average difference of 0.51 (± 0.68) mm, making FU ostia width 9% smaller than that of Pre ostia. This mirrors results for mean diameter, where average difference was 0.39 (± 0.62) mm, and FU had a 8% smaller mean diameter on average. For yearly rate of difference, max diameter had one of \(-\)0.59 (± 0.87) mm, making -12 (± 19) %, and mean diameter one of \(-\)0.24 (± 0.78) mm, making -4 (± 18) %.

Distances denoted by mean SSD between the Pre and FU ostia ranged from 0.35 mm to 1.69 mm, with a mean of 0.74 (± 0.42) mm. Strength of deformation from Pre to FU ostia varied between individual cases, where some cases had a maximum deformation of 2.32 mm, and others had one of 0.78 mm (Fig. 3). Deformation seemed to be biggest around the edges of the neck curve and smaller in the middle of the ostium.

Example of the deformation of the ostia of three ostia from Pre (pink) to FU (blue) scans. Color-coded arrows pointing from Pre to FU data highlight areas of low (blue) and high (red) deformations

Correlating the time passed between the Pre and FU scans with the rate of change, we found a positive correlation between time passed and changes in area, width, and mean diameter. The Pearson correlation coefficient (PCC) for time and area change was 0.80 and had a p-value of 0.03, making it the only correlation with p-value < 0.05. PCC for width and mean diameter was 0.68 and 0.69, respectively.

As ostia are complex shapes that can be concave, we started the comparison of shape indices with the CHs. Here, we observed an average absolute increase in volume of 0.43 (± 3.08) mm3 and a rate of 1.11 (± 3.02) mm3 per year. However, when looking at average relations between Pre and FU scans, CHs of FU ostia were 4% larger. Average CH volume was 6.81 (± 2.41) mm3 and 6.38 (± 1.83) mm3 for Pre and FU ostia, respectively.

The Pre ostia EI was higher than FU ostia EI in four out of seven cases (Table 2), with respective average EIs of 0.59 (± 0.02) and 0.54 (± 0.07) (Table 1). On average, the Pre EI was 8% larger than the FU EI, with a yearly rate of change of \(-\)0.06 (± 0.15), which is −10 (± 26) % per year. This means that ostia were more elongated before treatment with the CNS.

We applied the 2D-adapted formula for UI2D (Eq. 4) to both the original ostium data and the 2D-projected data, as the latter would lose information about convexity in the z-dimension. For projected ostia, both Pre and FU ostia had small values, 0.01 (± 0.01) and 0.03 (± 0.02), respectively, meaning they were overall convex shapes with low changes after treatment. The original ostia had a nearly identical UI2D of 0.53 (± 0.01), with an average difference of 0.004 and FU ostia being 0.7% less convex on average.

The projected Pre ostia had an average NCI of 0.04 (± 0.02), and FU ostia 0.06 (± 0.04). The non-projected ostia showed a similar trend, with Pre ostia having an average NCI of 0.08 (± 0.02) and FU ostia having one of 0.10 (± 0.04). These differences seem small, but when put in relation, the NCI of projected FU ostia was three times larger on average than for Pre ostia and the 3D NCI 52% larger. Overall, both Pre and FU ostia’s NCI is close to 0 and therefore rather circular, but slightly less so for FU ostia.

Lastly, we assessed mean and Gaussian curvature of the ostia. Pre ostias’ mean curvature was 0.02, and FU was 0.00. While an average difference of 0.02 (± 0.06) is small, the differences in individual ostium curvature from Pre to FU ostia go up to seven times larger. Gaussian curvature was \(-\)0.09 (± 0.07) for Pre ostia and \(-\)0.16 (± 0.13) for FU ostia on average, with an average difference of 0.08 (± 0.17), and FU observations being three times larger.