Table 1.
Patient details for eight patients who consecutively underwent corrective surgery.
Fig 1.
Preoperative CBCT reconstruction of the soft tissues and bones as well as boundary conditions.
Boundary conditions are indicated by black arrows and the reference axis by the grey arrows. The soft tissue nodes evaluated in the design of experiments are also indicated: nose (N), upper lip (UL), lower lip (LL), right cheek (RC), and left cheek (LC).
Fig 2.
Flowchart of the methodology for the probabilistic finite element analysis.
Colour coding: variable correlation, design of experiments I, optimisation on material properties, and design of experiments II.
Table 2.
Input parameters, and minimum and maximum values of the material properties.
Table 3.
Variable correlation results for patient P1 between various input variables and output.
Fig 3.
Patient 1 soft tissue prediction minimum and maximum.
(A) Overall minimum soft tissue prediction displacements with Gsoft = 94.4%, Esoft = 0.1 MPa, νsoft = 0.45, Ecart = 0.5 MPa, xdisp = 3 mm, and (B) maximum soft tissue prediction displacements with Gsoft = 30.5%, Esoft = 1 MPa, νsoft = 0.49, Ecart = 5 MPa, xdisp = 7 mm. Blue depicts no change from the postoperative CBCT (0 mm), bright red depicts a maximum change (6 mm).
Fig 4.
Design of experiments I: Soft tissue soft prediction ranges in five points for all patients.
Points include nose tip, upper lip, lower lip, right cheek, and left cheek. The vertical bars depict the range of soft tissue prediction; the black dots represent the soft tissue displacement from the postoperative CBCT. The baseline (0 mm) is the preoperative CBCT.
Fig 5.
Soft prediction ranges from design of experiments I (green) and design of experiments II (blue) following optimisation.
Green (P2, P3, P5, P7, and P8): based on design of experiments I and subsequent optimisation on postoperative CBCT scans. Blue (P1, P4, and P6): soft tissue ranges from design of experiments II based on optimised material properties.
Fig 6.
Histogram depicting the distribution of material properties following optimisation.
Green bars display all training data from P2, P3, P5, P7 and P8, as well as a fitted Weibull curve (solid black line) and cumulative density (dotted black line). G: viscoelastic scale factor, E: Young’s Modulus, ν: Poisson’s ratio, soft: soft tissue, cart: cartilage.
Fig 7.
Patient 1: Soft tissue prediction probability histograms.
Showing the nose (N), upper lip (UL), lower lip (LL), right cheek (RC) and left cheek (LC), as well as cumulative density plots (dotted lines). The black arrows on the x-axis depict the CBCT postoperative soft tissue position; preoperative position is equal to 0 mm displacement. The histograms for P4 and P6 show similar probability curves.
Fig 8.
Midline 2D views for P1, P4, and P6.
For each patient, preoperative CBCT (solid black line), postoperative CBCT (dashed line), and probabilistic soft tissue prediction (blue area) are shown, as well as indications for the nose (N), upper lip (UL), and lower lip (LL) points.