68
J. Cranio-Max.-Fac.Surg. 18 (1990)
J. Cranio-Max.-Fac.Surg. 18 (1990) 68-73 © GeorgThiemeVerlagStuttgart • New York
Three-Dimensional Analysis of Facial Morphology before and after Orthognathic Surgery Tadaharu Kobayashfl, Ken Ueda1, Katsuhiko Honmd, Hitoshi Sasakura2, Kooji Hanada2, Tamio Nakajimd 1First Departmentof Oral and Maxillofacia[Surgery(Head:Prof. T. Nakajima,D.D.S,PhD)and 2 Departmentof Orthodontics(Head:Prof. K. Hanada,D.D.S,PhD),School of Dentistry,Niigata University,Niigata,Japan Submitted 26.12.88; accepted 11.4.89
Introduction In orthognathic surgery, the acquisition of an harmonious profile as well as an improvement in occlusal function are important goals. Therefore, an objective and quantitative analysis of facial morphology before and after surgery is indispensable. Cephalometric analyses of the facial hard and soft tissues have been presented by many authors, but most of them were done on a two-dimensional basis (Pepersack and Chausse, 1978; Nakajima et al., 1979; Kajikawa, 1979; Kobayashi et al., 1986 a), although there have been several reports on three-dimensional analysis of the hard tissues attained by three-dimensional correction of cephalometric landmarks on frontal and lateral cephalograms (Savara, 1965; Vogel, 1967; Ueda, 1983; Motoyoshi et al., 1986; Ueda et al., 1986). On the other hand, the facial soft tissues have been analyzed in three-dimensions by stereophotogrammetry (Haga et al., 1964; Burke, 1971, 1984), Moir6 topography (Shioiri, 1978; Hojo, 1981; Fujita et al., 1984; Itoh et al., 1985; Nabetani, 1985), telecentric photogrammetry (Robertson and Volp, 1981), laser-ITV system (Saitoh et al., 1985) and so forth. The cost of equipment, the complex nature in operation and/or the lack of reproducibility are the problems inherent in these methods. In this paper, new methods for three dimensional analysis of the facial soft tissue and mandibular morphologies are introduced, and the results of their application to the analysis of 28 patients in whom mandibular prognathism was corrected by orthognathic surgery are described.
Materials and Methods The patient group comprised 9 males and 19 females in whom a skeletal class III malocclusion with or without open bite and lateral deviation of the mandible was surgically corrected in the First Department of Oral and Maxillofacial Surgery, Niigata University. The mean age at the time of surgery was 24 years 10 months for males and
Summary A method for three-dimensional analysis of the facial hard- and soft-tissue morphologies is described. The soft-tissue analysis consisted of calculating three-dimensional values of reference points on the face by perspective transformation of their values in two pairs of photographs, taken simultaneously, from the right and left sides of the face. The shape of the mandible was analyzed three-dimensionally by the simultaneously taken frontal and lateral cephalograms. The hard- and soft-tissue changes were analyzed with the method in 28 patients in whom mandibular prognathism had been corrected by orthognathic surgery. The magnitude of the surgically-produced soft tissue volumetric changes in the anterior mandibular region was proportional to the posterior movement of the mandible. Asymmetry of the face also improved in response to correction of lateral deviation of the mandible and a close correlation between the directional indices of asymmetry of the hard and soft tissues was observed. Thus, the method was found to be quite useful for the analysis of facial morphology in jaw deformity. Key words Mandibular prognathism - Orthognathic surgery Three-dimensional analysis
19 years 3 months for females with a range of 16 to 33 years. All patients were examined by oral surgeons and orthodontists to analyze the exact location and degree of deformity, to determine the treatment plan. After presurgical orthodontic treatment, the postoperative position of the mandible was planned on dental casts and cephalograms so that maximum intercnspidation, adequate overbite, and an harmonious profile could be attained during surgery. In addition, movement of the mandible that might occur following bilateral ramus osteotomies to obtain a new occlusion was assessed by three-dimensional analysis to see if the lateral movement of the mandible at the site of osteotomy was minimal (Ueda, 1983; Ueda et al., 1986). Bilateral sagittal split osteotomies were used for correction in 24 patients and bilateral mandibular body ostectomies in two patients. For the two other patients who had facial asymmetry resulting from severe lateral deviation of the mandible, correction was done by a combination of ramus osteotomy and mandibular body ostectomy to minimize lateral movement in the ramus. The method used in this study for the three-dimensional analysis of the facial soft-tissue morphology has been described in detail in a previous paper (Kobayashi, 1986 b). In brief, reference points were marked on the face with a black eye-liner and two pairs of photographs were taken simultaneously at an angle of approximately 25 degrees from the right and left sides of the face with the head in a reference metal frame on which the standard points of known three-dimensional values were set (Fig. 1). In general, a perspective transformation can be expressed as the following 4 x 4 matrix:
Three-Dimensional Analysis of Facial Morphology --'~ 1 [x y
z
1]
I ~2/1
T12 T22 732
L..~.4,
T42
0 0 0
J. Cranio-Max.-Fac. Surg. 18 (1990)
Fig, 1 Photograph used for three-dimensional analysis of facial soft tissues. Metal reference frame with standard points of known three-dimensional values is set around the face with reference points marked with black eye-liner.
T14q
T24/ T34|
= [X Y 0
H]
T44_J =H[x'
y'
0
1]
Where (x, y, z) are the three-dimensional coordinate values of each landmark and (x', y') are the two-dimensional coordinate values projected on the XY-plane. Using this equation, transformation matrices of the photographs of the face enlarged close to the real size were calculated from the known three-dimensional coordinate values of six standard points on the metal frame and their two-dimensional coordinate values on the photographs, because the photographs can be regarded as perspective drawings. Then, the three-dimensional coordinate values of reference points on the face were calculated from the transformation matrices and their two-dimensional coordinate values in a pair of photographs (Rogers and Adams, 1979). The calculation was done by a personal computer and a wireframe model of a three-dimensional image of the face seen from any direction as well as its contour at any plane of section were displayed on a CRT or an X-Y plotter (Fig. 2). In addition, the following measurements were taken from the photographs which were taken immediately before surgery and at least six months after surgery:
Fig. 2 Wire-frame model of face displayed on CRT. Three-dimensional image of face seen from any direction can be shown.
1. Volumes of the facial soft tissues at eight sites divided by six planes (Fig. 3). 2. Directional index of asymmetry of the facial soft tissue defined by the formula: volume (3 + 7) - volume (4 + 8) volume (3 + 4 + 7 + 8)
x 100 (%)
The shape of the mandible was analyzed three-dimensionally by the method described by Savara (1965) using frontaX and lateral cephalograms which were taken simultaneously, with the patient in centric occlusion, immediately before surgery and at least six months after surgery. Fig. 4 shows the three-dimensional relationships between the frontal and lateral cephalograms. The ZY-plane defined by the coordinate axes is parallel to the frontal film, and the XY-plane lies parallel to the lateral film. Cephalometric landmarks appearing on the frontal and lateral cephalograms can be projected into the actual skull space by relating them to a three-dimensional coordinate system with its origin at the intersection of the two central X-ray beams. In our cephalometer, the focus-origin distance is 1500 m m and the focus-film distance is 1650 mm. If the coordinate values of a landmark on the lateral cephalogram are (xl, yl) and on frontal cephalogram (zf, yf), the true coordinate values (x, y, z) are calculated by the following formulae based on the proportionality of triangles formed by diverging X-rays. x 1500+z y 1500+z
xl 1650 _
69
z 1500+x
zf 1650
yl
y
yf
1650
1500+x
1650
In the actual analysis, bony points with various heights from the centre of the ear rods were set on the lateral and
D
C
E
F
Fig.3
Eight sites used for measurements of facial soft tissues. Planes A and B crossing Subnasale and left Cheilion, respectively, are parallel to FH plane. Plane C is XY-plane, and Planes D and E are parallel and 40 and -40mm lateral to Plane C, respectively. Plane F is perpendicular to XY-plane and FH plane and 40mm backward from left Orbitale.
frontal cephalograms (Fig. 5), and their three-dimensional coordinates were calculated and transformed by a personal computer system into a standard coordinate system in which the origin was Sella, the X-axis was set by the line
70
J. Cranio-Max.-Fac. Surg. 18 (1990)
T. Kobayashi et al. Fig.4 Diagram of three-dimensional relationships between frontal and lateral cephalograms. (x, y, z) are coordinate values of landmark P, and (xl, yl) and (zf, yf) are coordinate values on lateral and frontal films, respectively.
Z
S
Y
Fig.5 Bony points on lateral and frontal cephalograms determined by height from centre of ear rods.
,S
! m
;
=
.,
,,
,,
:
;
N i,
ol J .... f
-
-
Before After
surgery surgery
Fig.6 Area(Area A)constructed on XY-plane by movement of anterior outline of mandible from L1 to Menton ~ surgery
-
-
Before After
surgery surgery
Fig.7 Right and left areas (Areas Br and BI) constructed on the preoperative mandibular plane by lateral outline of mandible, midline and line across Gonion and perpendicular to midline.
Three-Dimensional Analysis of Facial Morphology
J. Cranio-Max.-Fac. Surg. 18 (1990)
"l'eblel Pre- and post-operative facial soft-tissue volumes and their differences at eight sites in 28 patients Site
Before surgery
After surgery
Difference
1 2 3 4 5 6 7 8
37.5 ± 5.9 37.0± 5.8 63.5 ± 15.4 60.6±17,6 11.2± 4.1 10.6 ± 4.3 6 . 2 ± 4,0 5 . 7 ± 4.1
37.3 ± 6.2 36.9± 6.2 50.5 ± 11.5 49.4±12.5 11.1± 3.6 10.8 ± 4.0 4 . 6 ± 2.8 4 . 5 ± 2,9
-
Table3 Areas constructed by the anterior profile line of the mandible on the XY-plane and by the outer line of the mandible on the preoperative mandibular planes Before surgery
0.2 ±2.1 0 +1.6 - 13.0 ± 6.7* -11.1 ±7.7* - 0.1 ±1.7 0.2 ± 1.8 - 1.4±1.9" - 0.7±1.9"
71
area on X-Y plane (Area A) area on mandibular plane right (Area Br) left (Area BI)
After surgery
Difference
3.3 ± 1,2
25.4±3.6 24.1±3.6
21.5±3.1 21.0±3.3
-3.8±1.8" -3.1±2.0" (cm 2)
(cm 3) Values are shown as mean+SD. Values are shown as mean±SD.
* : P
J. Cranio-Max.-Fac.Surg. 18 (1990)
J. Cranio-Max.-Fac.Surg. 18 (1990) 68-73 © GeorgThiemeVerlagStuttgart • New York
Three-Dimensional Analysis of Facial Morphology before and after Orthognathic Surgery Tadaharu Kobayashfl, Ken Ueda1, Katsuhiko Honmd, Hitoshi Sasakura2, Kooji Hanada2, Tamio Nakajimd 1First Departmentof Oral and Maxillofacia[Surgery(Head:Prof. T. Nakajima,D.D.S,PhD)and 2 Departmentof Orthodontics(Head:Prof. K. Hanada,D.D.S,PhD),School of Dentistry,Niigata University,Niigata,Japan Submitted 26.12.88; accepted 11.4.89
Introduction In orthognathic surgery, the acquisition of an harmonious profile as well as an improvement in occlusal function are important goals. Therefore, an objective and quantitative analysis of facial morphology before and after surgery is indispensable. Cephalometric analyses of the facial hard and soft tissues have been presented by many authors, but most of them were done on a two-dimensional basis (Pepersack and Chausse, 1978; Nakajima et al., 1979; Kajikawa, 1979; Kobayashi et al., 1986 a), although there have been several reports on three-dimensional analysis of the hard tissues attained by three-dimensional correction of cephalometric landmarks on frontal and lateral cephalograms (Savara, 1965; Vogel, 1967; Ueda, 1983; Motoyoshi et al., 1986; Ueda et al., 1986). On the other hand, the facial soft tissues have been analyzed in three-dimensions by stereophotogrammetry (Haga et al., 1964; Burke, 1971, 1984), Moir6 topography (Shioiri, 1978; Hojo, 1981; Fujita et al., 1984; Itoh et al., 1985; Nabetani, 1985), telecentric photogrammetry (Robertson and Volp, 1981), laser-ITV system (Saitoh et al., 1985) and so forth. The cost of equipment, the complex nature in operation and/or the lack of reproducibility are the problems inherent in these methods. In this paper, new methods for three dimensional analysis of the facial soft tissue and mandibular morphologies are introduced, and the results of their application to the analysis of 28 patients in whom mandibular prognathism was corrected by orthognathic surgery are described.
Materials and Methods The patient group comprised 9 males and 19 females in whom a skeletal class III malocclusion with or without open bite and lateral deviation of the mandible was surgically corrected in the First Department of Oral and Maxillofacial Surgery, Niigata University. The mean age at the time of surgery was 24 years 10 months for males and
Summary A method for three-dimensional analysis of the facial hard- and soft-tissue morphologies is described. The soft-tissue analysis consisted of calculating three-dimensional values of reference points on the face by perspective transformation of their values in two pairs of photographs, taken simultaneously, from the right and left sides of the face. The shape of the mandible was analyzed three-dimensionally by the simultaneously taken frontal and lateral cephalograms. The hard- and soft-tissue changes were analyzed with the method in 28 patients in whom mandibular prognathism had been corrected by orthognathic surgery. The magnitude of the surgically-produced soft tissue volumetric changes in the anterior mandibular region was proportional to the posterior movement of the mandible. Asymmetry of the face also improved in response to correction of lateral deviation of the mandible and a close correlation between the directional indices of asymmetry of the hard and soft tissues was observed. Thus, the method was found to be quite useful for the analysis of facial morphology in jaw deformity. Key words Mandibular prognathism - Orthognathic surgery Three-dimensional analysis
19 years 3 months for females with a range of 16 to 33 years. All patients were examined by oral surgeons and orthodontists to analyze the exact location and degree of deformity, to determine the treatment plan. After presurgical orthodontic treatment, the postoperative position of the mandible was planned on dental casts and cephalograms so that maximum intercnspidation, adequate overbite, and an harmonious profile could be attained during surgery. In addition, movement of the mandible that might occur following bilateral ramus osteotomies to obtain a new occlusion was assessed by three-dimensional analysis to see if the lateral movement of the mandible at the site of osteotomy was minimal (Ueda, 1983; Ueda et al., 1986). Bilateral sagittal split osteotomies were used for correction in 24 patients and bilateral mandibular body ostectomies in two patients. For the two other patients who had facial asymmetry resulting from severe lateral deviation of the mandible, correction was done by a combination of ramus osteotomy and mandibular body ostectomy to minimize lateral movement in the ramus. The method used in this study for the three-dimensional analysis of the facial soft-tissue morphology has been described in detail in a previous paper (Kobayashi, 1986 b). In brief, reference points were marked on the face with a black eye-liner and two pairs of photographs were taken simultaneously at an angle of approximately 25 degrees from the right and left sides of the face with the head in a reference metal frame on which the standard points of known three-dimensional values were set (Fig. 1). In general, a perspective transformation can be expressed as the following 4 x 4 matrix:
Three-Dimensional Analysis of Facial Morphology --'~ 1 [x y
z
1]
I ~2/1
T12 T22 732
L..~.4,
T42
0 0 0
J. Cranio-Max.-Fac. Surg. 18 (1990)
Fig, 1 Photograph used for three-dimensional analysis of facial soft tissues. Metal reference frame with standard points of known three-dimensional values is set around the face with reference points marked with black eye-liner.
T14q
T24/ T34|
= [X Y 0
H]
T44_J =H[x'
y'
0
1]
Where (x, y, z) are the three-dimensional coordinate values of each landmark and (x', y') are the two-dimensional coordinate values projected on the XY-plane. Using this equation, transformation matrices of the photographs of the face enlarged close to the real size were calculated from the known three-dimensional coordinate values of six standard points on the metal frame and their two-dimensional coordinate values on the photographs, because the photographs can be regarded as perspective drawings. Then, the three-dimensional coordinate values of reference points on the face were calculated from the transformation matrices and their two-dimensional coordinate values in a pair of photographs (Rogers and Adams, 1979). The calculation was done by a personal computer and a wireframe model of a three-dimensional image of the face seen from any direction as well as its contour at any plane of section were displayed on a CRT or an X-Y plotter (Fig. 2). In addition, the following measurements were taken from the photographs which were taken immediately before surgery and at least six months after surgery:
Fig. 2 Wire-frame model of face displayed on CRT. Three-dimensional image of face seen from any direction can be shown.
1. Volumes of the facial soft tissues at eight sites divided by six planes (Fig. 3). 2. Directional index of asymmetry of the facial soft tissue defined by the formula: volume (3 + 7) - volume (4 + 8) volume (3 + 4 + 7 + 8)
x 100 (%)
The shape of the mandible was analyzed three-dimensionally by the method described by Savara (1965) using frontaX and lateral cephalograms which were taken simultaneously, with the patient in centric occlusion, immediately before surgery and at least six months after surgery. Fig. 4 shows the three-dimensional relationships between the frontal and lateral cephalograms. The ZY-plane defined by the coordinate axes is parallel to the frontal film, and the XY-plane lies parallel to the lateral film. Cephalometric landmarks appearing on the frontal and lateral cephalograms can be projected into the actual skull space by relating them to a three-dimensional coordinate system with its origin at the intersection of the two central X-ray beams. In our cephalometer, the focus-origin distance is 1500 m m and the focus-film distance is 1650 mm. If the coordinate values of a landmark on the lateral cephalogram are (xl, yl) and on frontal cephalogram (zf, yf), the true coordinate values (x, y, z) are calculated by the following formulae based on the proportionality of triangles formed by diverging X-rays. x 1500+z y 1500+z
xl 1650 _
69
z 1500+x
zf 1650
yl
y
yf
1650
1500+x
1650
In the actual analysis, bony points with various heights from the centre of the ear rods were set on the lateral and
D
C
E
F
Fig.3
Eight sites used for measurements of facial soft tissues. Planes A and B crossing Subnasale and left Cheilion, respectively, are parallel to FH plane. Plane C is XY-plane, and Planes D and E are parallel and 40 and -40mm lateral to Plane C, respectively. Plane F is perpendicular to XY-plane and FH plane and 40mm backward from left Orbitale.
frontal cephalograms (Fig. 5), and their three-dimensional coordinates were calculated and transformed by a personal computer system into a standard coordinate system in which the origin was Sella, the X-axis was set by the line
70
J. Cranio-Max.-Fac. Surg. 18 (1990)
T. Kobayashi et al. Fig.4 Diagram of three-dimensional relationships between frontal and lateral cephalograms. (x, y, z) are coordinate values of landmark P, and (xl, yl) and (zf, yf) are coordinate values on lateral and frontal films, respectively.
Z
S
Y
Fig.5 Bony points on lateral and frontal cephalograms determined by height from centre of ear rods.
,S
! m
;
=
.,
,,
,,
:
;
N i,
ol J .... f
-
-
Before After
surgery surgery
Fig.6 Area(Area A)constructed on XY-plane by movement of anterior outline of mandible from L1 to Menton ~ surgery
-
-
Before After
surgery surgery
Fig.7 Right and left areas (Areas Br and BI) constructed on the preoperative mandibular plane by lateral outline of mandible, midline and line across Gonion and perpendicular to midline.
Three-Dimensional Analysis of Facial Morphology
J. Cranio-Max.-Fac. Surg. 18 (1990)
"l'eblel Pre- and post-operative facial soft-tissue volumes and their differences at eight sites in 28 patients Site
Before surgery
After surgery
Difference
1 2 3 4 5 6 7 8
37.5 ± 5.9 37.0± 5.8 63.5 ± 15.4 60.6±17,6 11.2± 4.1 10.6 ± 4.3 6 . 2 ± 4,0 5 . 7 ± 4.1
37.3 ± 6.2 36.9± 6.2 50.5 ± 11.5 49.4±12.5 11.1± 3.6 10.8 ± 4.0 4 . 6 ± 2.8 4 . 5 ± 2,9
-
Table3 Areas constructed by the anterior profile line of the mandible on the XY-plane and by the outer line of the mandible on the preoperative mandibular planes Before surgery
0.2 ±2.1 0 +1.6 - 13.0 ± 6.7* -11.1 ±7.7* - 0.1 ±1.7 0.2 ± 1.8 - 1.4±1.9" - 0.7±1.9"
71
area on X-Y plane (Area A) area on mandibular plane right (Area Br) left (Area BI)
After surgery
Difference
3.3 ± 1,2
25.4±3.6 24.1±3.6
21.5±3.1 21.0±3.3
-3.8±1.8" -3.1±2.0" (cm 2)
(cm 3) Values are shown as mean+SD. Values are shown as mean±SD.
* : P
