Setting-up of the calculation model for sagittal diameter of bulbo-medullary junction

Objective To develop a calculation model for normal sagittal diameter (SD) of bulbo-medullary junction with the change of distance above the measurement baseline(the line connecting the anterior lower margin of the C2 vertebral body and the posterior upper margin of the C3 vertebral body), and to investigate its calculation error. Methods All of 164 patients with cervical disc herniation or cervical spinal stenosis who underwent cervical MRI between April 2018 and August 2018 in Beijing Jishuitan Hospital were included in this study. The normal bulbo-medullary junction was divided into two parts from top to bottom, and the dividing line was defined factitiously (the line parallel to the measurement baseline and through the lower margin of cancellous bone of the anterior arch of atlas). On the middle sagittal MRI images of 100 cases of normal bulbo-medullary junction, the change rate of the SD along the distance above the measurement baseline was counted on the upper and lower segments separately. The calculation model for SD of bulbo-medullary junction was established, with the SD of spinal cord at level of the lower margin of axis and the distance above the measurement baseline as independent variables. After setting-up of the calculation model, the actual SD at the lower margin of the C1 anterior arch and 10 mm above and below it was measured on other 64 cases of normal bulbo-medullary junction. The actual SD and calculation value were compared for calculating the error and error rate. The SD at the dividing line was estimated using the substituted estimation (the actual SD at level of the lower margin of axis) and mean-value estimation (the mean SD of the first 100 cases). Calculation value, substituted estimation and mean-value estimation were compared, and their calculation error and the occurrence rate of significant error (no less than 1 mm) were also compared. Results Calculation formula for SD of bulbo-medullary junction: (below the dividing line) SD=sagittal diameter at level of the lower margin of axis (SDA)+0.0472×height above the measurement baseline (HAB), (above the dividing line) SD=SDA+0.0472×height of dividing line above the measurement baseline (HDL)+0.298×(HAB-HDL). The error of calculation model increased with the distance above the measurement baseline. The error at the topmost level was 1.06±0.72 mm, and the error rate was 10.52%± 8.26%. Compared with the estimation method using the mean value, the calculation model was accompanied with a significantly lower ratio of significant error (Z=-3.527, P<0.001). Compared with the estimation method using a substitute, the error of the calculation model was significantly smaller (Z=-4.88, P<0.001) and the ratio of significant errors was significantly lower (Chi-Square= 6.015, P=0.024). Conclusion The SD calculation model could accurately estimate the SD of a normal bulbo-medullary junction, and has great significance for the quantitative imaging assessment and decompression strategy in patients with atlantoaxial instability. Key words: Medulla oblongata; Cervical vertebrae; Spinal cord; Magnetic resonance imaging; Photogrammetry; Linear models