Fig. 2

Model structures and workflow. A The structure of BP-ANN models. B The workflow to calculate the coefficients between SN-OP and FHR, FA respectively. Briefly, for FHR, patient-specific skeletal parameters (pn) were extracted to form a matrix where SN-OP varied from 9 to 25 (yellow box) while other variables as skeletal parameters remained constant (N-ANS, S-N, SNA, NA-FH, Ptm-A, PP-FH for cranio-maxilla complex, Go-Po, Go-Co, S-Go for mandible) (orange box). The matrix was put into the model FHR to predict patient-specific FHR values (FHRn9-FHRn25) in response to SN-OP changes. Subsequently, a regression function between SN-OPni and FHRni yielded slope (kn) and vertical intercepts (bn) for each patient. The FA model followed a similar process