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Analysis of craniofacial asymmetry by multiplane cephalometry
Analysis of craniofacial asymmetry multiplane cephalometry
by Dr. Grayson
Barry H. Grayson, D.D.S., Joseph G. McCarthy, M.D., and Fred Bookstein, Ph.D. New
York,
N.Y.
A fhree-dimensional, multiplane cephalomefric analysis is presented. This analysis permits visualization of skeletal midlines at selected depths of the craniofacial complex. When the midlines and associated anatomic structures are studied sequentially, the individual midlines may be combined conceptually into a warped midsagiflal “plane.” This localizes craniofacial asymmetry in the posteroanterior and basilar views. The study of structures in various coronal and transverse planes makes it possible to measure and record the three-dimensional relationshios of anatomic structures to one another. A case of hemicraniofacial microsomia in which this analysis was used is presented.
C
onsiderable cephalometric data are required to define the complex skeletal pathology of craniofacial deformities. In fact, more information is needed than can be provided by the classic lateral-view cephalogram alone. The purpose of this report is to present a three-dimensional multiplane cephalometric analysis integrating information from both the posteroanterior and basilar cephalometric radiographs. Broadbent’s * placed emphasis on the complementary use of the lateral and frontal radiographs to study and measure growth of the head. He stated that the anterior film was to be studied not only for its own value but also for its contribution to an understanding of structures that appear in the lateral view. Sassouni3 described a method of correlating information from the lateral and posteroanterior views by horizontal orientation of the tracings side by side on graph paper. Both Broadbent and Sassouni attempted to achieve a three-dimensional understanding of the head through the study of both views. The basilar view was described as early as 1905 by Schuelle4 and later by Merrill .5 Bergefl proposed a method of aligning the basilar view with the lateral and posteroanterior views based on the Frankfort horizontal plane as a common factor. He demonstrated a method for determining the midline of the basilar view by drawing a line through the vomer, the posterior part of the nasal septum, and the crista galli. Nahoum and assoFrom The Institute of Reconstmctive Plastic Surgery, The New York University Medical Center. Preparation of this manuscript was supported by National Institutes of Health Grant DE 03568.
ciates7 described a technique to orient the structures of the lateral, posteroanterior, and basilar views, using drafting principles of three-dimensional projection to one plane. Marmary and co-workers8 proposed that a reliable midline could be derived by the study of neural foramina in the base of the skull (foramina spinosum) which might be relatively unaffected by environmental factors. These studies pointed to the value of the basilar-view midline construct in evaluation of asymmetry in the craniofacial skeleton. Through the study of structures located near specific coronal and transverse planes in the head, the observer may describe features of the midline at various depths. For the purpose of demonstration, a patient with unilateral craniofacial microsomia will be presented. This syndrome is characterized by unilateral underdevelopment of the mandible, maxilla, external and middle ear, zygoma, parotid gland, fifth and seventh cranial nerves, and associated musculature and soft tissue (Fig. 1). While the lateral cephalogram (Fig. 2,A andB) displays the asymmetry of the left and right mandibular body and ramus, it fails to describe the specific geometric deformation that is present in the craniofacial skeleton. In order to define and measure facial deformity, especially asymmetries, a method was developed to integrate the findings of the posteroanterior and basilar cephalometric views into the cephalometric analysis (Figs. 3 and 4). Examination of the posteroanterior cephalogram in a manner to be described enables the observer to visualize distinct regions of the craniofacial complex so as to apprehend the deformation of the structure from symmetry. In practice, three separate acetate tracings 217
Fig. 1. A patient C, Frontal view.
with right unilateral craniofacial D, Submental view.
are made on the same radiograph, corresponding to strut:tures of the lateral view in or near the three planes indiccated in Fig. 5. [n the first tracing, the orbital rims are outlined (Fig. 6), along with the pyriform aperture, the maxillary and mandibular incisors, and the midpoint of the
microsomia.
A, Right
lateral
view.
6, Left lateral
view.
symphysis. This acetate drawing represents the anatomy of the most superficial aspects of the face as transected by line A in Fig. 5. On a second acetate sheet are traced the greate:r and lesser wings of the sphenoid, the most lateral cross section of the zygomatic arch, the coronoid proces s, the
Analysis of craniofucial
Volume 84 Number 3
Fig. 2. A, Lateral cephalogram of patient with right unilateral tracing, right lateral view. Note asymmetry of left and right
Fig. 3. Posteroanterior cephalometric tracing. The mandible is deviated toward the affected side and the right orbit is displaced inferiorly. Note that the tracing is reversed so that the patient’s right side is on the viewer’s left.
craniofacial mandibular
microsomia. body, ramus,
Fig. 4. Basilar cephalometric maxilla are deviated toward
usymmetry
219
B, Cephalometric and orbits.
tracing. the right.
The
mandible
and
the
Fig. 7. Tracing 2. A, Greater and lesser wings of the sphenoid. i3, The most lateral cross section of the zygomatic arch. C, The coronoid process. 0, The maxillary and mandibular first permanent molars. 0, The body of the mandible. E, The body of the mandible. f, The mental foramina. Fig. 5. Separate acetate tracings are made on the same radiograph, corresponding to structures of the lateral view in or near the three planes indicated.
D Fig. 6. Tracing 1. A, Orbital rims. B, Pyriform aperture. C, Maxiilary and mandibular incisors. D, Inferior border of symphysis.
Fig. 6. Tracing 3. A, Superior surface of the petrous portion of the temporal bone. B, Mandibular condyles with outer border of the ramus. C, Mastoid process.
maxillary and mandibular first permanent molars, the body of the mandible, and the mental foramina (Fig. 7). These structures, all located on or near plane B (Fig. 5), represent a deeper coronal plane. The third acetate tracing, corresponding to line C of Fig. 5, includes the upper surface of the petrous portion
of the temporal bone, the mandibular condyles with the outer border of the ramus down to the gonial angle, and the mastoid processes with the arch of temporal and parietal bones connecting them (Fig. 8). When these three tracings are viewed separately, they reveal the degree of asymmetry at each of the three
Volume 84 Number 2
Analysis
Fig. 9. A, Straight
lines connecting M,,, MP, M,, and M, result in a segmented express the asymmetry of structures in this facial plane (A plane). 6, Midline C. Midline construct for the C plane.
Fig. 11. Three
/ II
Fig. 10. The midline as one
passes
from
constructs posterior
I
Posterior midsagittal
construct construct
horizontal
asymmetry
221
whose angles for the 6 plane.
planes
of the face.
cross sections of the craniofacial complex. A midline is constructed for each view as follows: In the A plane (the pyriform aperture, orbits, and incisors), the centrum* of each orbit is located (Fig. 9, A), and the point
3
ABC
of craniofacial
plane
progressively deviate laterally to anterior planes of the face.
*The centrum is the midpoint of two midpoints: the midpoint between the most superior and inferior points of the orbit and the midpoint between the most medial and most lateral point on the orbit.
222
Gruyson, MKarthy.
and Bookstein
6!!! 0 ::
0 Fig. 12. Key triangles midsagittal plane.
@ are constructed
in each
M,, halfway between them is identified. The most lateral point on the perimeter of each pyrifonn aperture is marked, and the point M, halfway between them is marked. The midpoint Mi, between the maxillary and the mandibular central incisors, and the gnathion M, are identified. All four of these points are “on the midline” in some sense. To view the midline with their aid, straight lines are constructed connecting M,, with M,, M, with Mi, and Mi with M,. This results in a segmented construct whose angles express the asymmetry of the structures of this plane. By the same method, a midline is constructed for the B plane (the sphenoid, zygomatic arch, etc.). The points Si, representing the intersection of the shadows of the greater and lesser wings of the sphenoid, are identified, and their bisector M,i is recorded (Fig 9, B). Similarly, we find midpoints M, for the centra of the zygomatic arches, M, for the tips of the coronoid processes, M, for maxillare* on the left and right zygomas, and Mr for the left and right mental foramina. Vertical line segments are constructed to link these points. Finally, in plane C, the heads of the condyles, the innermost inferior points on the mastoid processes, and the gonions yield bisecting points Md, M,, M,,, and segments Md - M,, M, - M,, (Fig. 9, C). If the midline constructs of A, B, and C planes are *Maxillare W&-Maximum concavity on the contour of the maxilla between the lower contour of the malar bone and the maxillary first molar.
of the horizontal
planes
and
related
to the posterior
superimposed on the posteroanterior tracing, one can observe a phenomenon we call warping within the craniofacial skeleton (Fig. 10). The midline constructs deviate progressively laterally as one passes from plane C, through plane B, to plane A toward the anterior of the face to the P-A composite. In patients with facial asymmetry, the posterior and middle cranial structures appear less severely affected. (For this reason, they are used to guide the observer in the construction of a midsagittal plane.) In each of the basilar-view planes (Fig. ll), key triangles are constructed (Fig. 12, A, B, and C), each of which may be referred to this primary (posterior) midsagittal plane. Superpositioning of the triangles clearly demonstrated the warping of the craniofacial complex in this patient (Fig. 13). The craniofacial skeleton is most severely deviated from the midsagittal plane at the level of the mandible; the severity of asymmetry decreased in a cephalic direction. DISCUSSION
Our three-dimensional cephalometric analysis permits visualization of skeletal midlines at selected depths of the craniofacial complex. When midlines and associated anatomic structures are studied sequentially, individual midlines may be combined conceptually into a warped midsagittal “plane. ” This localizes craniofacial asymmetry in posteroanterior and basilar views. Bilateral structures in the “symmetrical” head do not superimpose in the lateral cephalogram. The fan of
Analysis
of craniofacial
asymmetry
223
Fig. 14. A, Right lateral cephalometric tracing of a symmetrical mandible. The inferior border of the right body is below the left body. B, Right lateral cephalometric tracing of an asymmetrical mandible. The inferior border of the right body is above the left body.
Fig. 13. Superimposition of the triangles shows that the greatest amount of deviation from the midline occurs at the level of the mandible (A). decreasing in a cephalic direction. B, Maxilla. C, Cranial base.
the x-ray beam expands as it passes through the head, causing a divergence between the images of all bilateral structures except those along the central beam. Structures whose images are doubled and exhibit an apparent asymmetry (ramus, mandibular body, pterygoid space, orbits) are conventionally averaged and traced as a single image. This type of tracing is inadequate to describe the head that is truly asymmetrical. It would be more useful to trace bilateral structures separately if one were able to determine the contributions of beam geometry and skeletal asymmetry to the image. In the tracing of a symmetrical head, the right ramus appears anterior to the left while the right body appears inferior to the left (Fig. 14, A). In the lateral tracing of the patient with mandibular deviation to the
right and asymmetry of the body and ramus, this is not the case (Fig. 14, B). In this lateral tracing, combining the effect of beam geometry and skeletal asymmetry, the positions of left and right mandibular structures appear reversed. Similarly, right orbitale in the lateral tracings of the symmetrical head should be anterior to and on the same horizontal plane as left orbitale. In the asymmetrical patient right orbitale is displaced inferiorly and posteriorly. Examination of the worm’seye and frontal photographs (Fig. 1, B and C) shows the downward and posterior displacement of the right orbit. Owing to the compounding beam geometry and skeletal asymmetry, the posteroanterior and basilar cephalograms become vital to an understanding of the lateral cephalogram. The study of structures in various coronal and transverse planes makes it possible to measure and record the three-dimensional relationship of anatomic structures to one another. The composite basilar and posteroanterior tracing becomes more easily under-
224
Grctywn.
McCtrrthy.
and Brookstcin
stood when superimposed anatomic structures are studied both alone and in relation to the midline at various depths.
Berger, H.: Progress with basilar view cephalograms, Tran\. F.ur Onhod. Sot. 40: 159.164. 1964. Nahoum, H. I.. Fiasconaro, J., and DiSalvo. N. A.: The vcr ticosubmental roentgenogram in cephalometrics, J Am Dent Assoc. 69: 132-150, 1964. Marmary, Y., Zilkerman, Y.. and Mirsky, Y.: Use of foramrna spinosa to determine skull midlines, Angle Orthod. 49: 263-268. 1979.
REFERENCES 1. Broadbent, B. H., Sr.: A new x-ray technique and its application to orthodontia, Angle Otthod. 1: 45-66, 1931. 2. Broadbent, B. H., Sr., Broadbent, B. H.. Jr., and Golden, W. H.: Bolton standards of dentofacial developmental growth, St. Louis, 1975, The C. V. Mosby Company. 3. Sassouni, V.: Archial analysis in three dimensions, AM. J. ORTHOD. 44: 433-463, 19.58. 4. Schueller, A.: Die Schaedelbasis in Roentgenbid, Fortschr. Geb. Roentgenstr. 11: 1905 (quoted after Merrill”). 5. Merrill, V .: Atlas of roentgenographic positions, St. Louis, 1949, The C. V. Mosby Company.
Reprint requests to: Dr. The The 560 New
Barry H. Grayson Institute of Reconstructive Plastic Surgery New York University Medical Center First Ave. York, N. Y. 10016
by Dr. Grayson
Barry H. Grayson, D.D.S., Joseph G. McCarthy, M.D., and Fred Bookstein, Ph.D. New
York,
N.Y.
A fhree-dimensional, multiplane cephalomefric analysis is presented. This analysis permits visualization of skeletal midlines at selected depths of the craniofacial complex. When the midlines and associated anatomic structures are studied sequentially, the individual midlines may be combined conceptually into a warped midsagiflal “plane.” This localizes craniofacial asymmetry in the posteroanterior and basilar views. The study of structures in various coronal and transverse planes makes it possible to measure and record the three-dimensional relationshios of anatomic structures to one another. A case of hemicraniofacial microsomia in which this analysis was used is presented.
C
onsiderable cephalometric data are required to define the complex skeletal pathology of craniofacial deformities. In fact, more information is needed than can be provided by the classic lateral-view cephalogram alone. The purpose of this report is to present a three-dimensional multiplane cephalometric analysis integrating information from both the posteroanterior and basilar cephalometric radiographs. Broadbent’s * placed emphasis on the complementary use of the lateral and frontal radiographs to study and measure growth of the head. He stated that the anterior film was to be studied not only for its own value but also for its contribution to an understanding of structures that appear in the lateral view. Sassouni3 described a method of correlating information from the lateral and posteroanterior views by horizontal orientation of the tracings side by side on graph paper. Both Broadbent and Sassouni attempted to achieve a three-dimensional understanding of the head through the study of both views. The basilar view was described as early as 1905 by Schuelle4 and later by Merrill .5 Bergefl proposed a method of aligning the basilar view with the lateral and posteroanterior views based on the Frankfort horizontal plane as a common factor. He demonstrated a method for determining the midline of the basilar view by drawing a line through the vomer, the posterior part of the nasal septum, and the crista galli. Nahoum and assoFrom The Institute of Reconstmctive Plastic Surgery, The New York University Medical Center. Preparation of this manuscript was supported by National Institutes of Health Grant DE 03568.
ciates7 described a technique to orient the structures of the lateral, posteroanterior, and basilar views, using drafting principles of three-dimensional projection to one plane. Marmary and co-workers8 proposed that a reliable midline could be derived by the study of neural foramina in the base of the skull (foramina spinosum) which might be relatively unaffected by environmental factors. These studies pointed to the value of the basilar-view midline construct in evaluation of asymmetry in the craniofacial skeleton. Through the study of structures located near specific coronal and transverse planes in the head, the observer may describe features of the midline at various depths. For the purpose of demonstration, a patient with unilateral craniofacial microsomia will be presented. This syndrome is characterized by unilateral underdevelopment of the mandible, maxilla, external and middle ear, zygoma, parotid gland, fifth and seventh cranial nerves, and associated musculature and soft tissue (Fig. 1). While the lateral cephalogram (Fig. 2,A andB) displays the asymmetry of the left and right mandibular body and ramus, it fails to describe the specific geometric deformation that is present in the craniofacial skeleton. In order to define and measure facial deformity, especially asymmetries, a method was developed to integrate the findings of the posteroanterior and basilar cephalometric views into the cephalometric analysis (Figs. 3 and 4). Examination of the posteroanterior cephalogram in a manner to be described enables the observer to visualize distinct regions of the craniofacial complex so as to apprehend the deformation of the structure from symmetry. In practice, three separate acetate tracings 217
Fig. 1. A patient C, Frontal view.
with right unilateral craniofacial D, Submental view.
are made on the same radiograph, corresponding to strut:tures of the lateral view in or near the three planes indiccated in Fig. 5. [n the first tracing, the orbital rims are outlined (Fig. 6), along with the pyriform aperture, the maxillary and mandibular incisors, and the midpoint of the
microsomia.
A, Right
lateral
view.
6, Left lateral
view.
symphysis. This acetate drawing represents the anatomy of the most superficial aspects of the face as transected by line A in Fig. 5. On a second acetate sheet are traced the greate:r and lesser wings of the sphenoid, the most lateral cross section of the zygomatic arch, the coronoid proces s, the
Analysis of craniofucial
Volume 84 Number 3
Fig. 2. A, Lateral cephalogram of patient with right unilateral tracing, right lateral view. Note asymmetry of left and right
Fig. 3. Posteroanterior cephalometric tracing. The mandible is deviated toward the affected side and the right orbit is displaced inferiorly. Note that the tracing is reversed so that the patient’s right side is on the viewer’s left.
craniofacial mandibular
microsomia. body, ramus,
Fig. 4. Basilar cephalometric maxilla are deviated toward
usymmetry
219
B, Cephalometric and orbits.
tracing. the right.
The
mandible
and
the
Fig. 7. Tracing 2. A, Greater and lesser wings of the sphenoid. i3, The most lateral cross section of the zygomatic arch. C, The coronoid process. 0, The maxillary and mandibular first permanent molars. 0, The body of the mandible. E, The body of the mandible. f, The mental foramina. Fig. 5. Separate acetate tracings are made on the same radiograph, corresponding to structures of the lateral view in or near the three planes indicated.
D Fig. 6. Tracing 1. A, Orbital rims. B, Pyriform aperture. C, Maxiilary and mandibular incisors. D, Inferior border of symphysis.
Fig. 6. Tracing 3. A, Superior surface of the petrous portion of the temporal bone. B, Mandibular condyles with outer border of the ramus. C, Mastoid process.
maxillary and mandibular first permanent molars, the body of the mandible, and the mental foramina (Fig. 7). These structures, all located on or near plane B (Fig. 5), represent a deeper coronal plane. The third acetate tracing, corresponding to line C of Fig. 5, includes the upper surface of the petrous portion
of the temporal bone, the mandibular condyles with the outer border of the ramus down to the gonial angle, and the mastoid processes with the arch of temporal and parietal bones connecting them (Fig. 8). When these three tracings are viewed separately, they reveal the degree of asymmetry at each of the three
Volume 84 Number 2
Analysis
Fig. 9. A, Straight
lines connecting M,,, MP, M,, and M, result in a segmented express the asymmetry of structures in this facial plane (A plane). 6, Midline C. Midline construct for the C plane.
Fig. 11. Three
/ II
Fig. 10. The midline as one
passes
from
constructs posterior
I
Posterior midsagittal
construct construct
horizontal
asymmetry
221
whose angles for the 6 plane.
planes
of the face.
cross sections of the craniofacial complex. A midline is constructed for each view as follows: In the A plane (the pyriform aperture, orbits, and incisors), the centrum* of each orbit is located (Fig. 9, A), and the point
3
ABC
of craniofacial
plane
progressively deviate laterally to anterior planes of the face.
*The centrum is the midpoint of two midpoints: the midpoint between the most superior and inferior points of the orbit and the midpoint between the most medial and most lateral point on the orbit.
222
Gruyson, MKarthy.
and Bookstein
6!!! 0 ::
0 Fig. 12. Key triangles midsagittal plane.
@ are constructed
in each
M,, halfway between them is identified. The most lateral point on the perimeter of each pyrifonn aperture is marked, and the point M, halfway between them is marked. The midpoint Mi, between the maxillary and the mandibular central incisors, and the gnathion M, are identified. All four of these points are “on the midline” in some sense. To view the midline with their aid, straight lines are constructed connecting M,, with M,, M, with Mi, and Mi with M,. This results in a segmented construct whose angles express the asymmetry of the structures of this plane. By the same method, a midline is constructed for the B plane (the sphenoid, zygomatic arch, etc.). The points Si, representing the intersection of the shadows of the greater and lesser wings of the sphenoid, are identified, and their bisector M,i is recorded (Fig 9, B). Similarly, we find midpoints M, for the centra of the zygomatic arches, M, for the tips of the coronoid processes, M, for maxillare* on the left and right zygomas, and Mr for the left and right mental foramina. Vertical line segments are constructed to link these points. Finally, in plane C, the heads of the condyles, the innermost inferior points on the mastoid processes, and the gonions yield bisecting points Md, M,, M,,, and segments Md - M,, M, - M,, (Fig. 9, C). If the midline constructs of A, B, and C planes are *Maxillare W&-Maximum concavity on the contour of the maxilla between the lower contour of the malar bone and the maxillary first molar.
of the horizontal
planes
and
related
to the posterior
superimposed on the posteroanterior tracing, one can observe a phenomenon we call warping within the craniofacial skeleton (Fig. 10). The midline constructs deviate progressively laterally as one passes from plane C, through plane B, to plane A toward the anterior of the face to the P-A composite. In patients with facial asymmetry, the posterior and middle cranial structures appear less severely affected. (For this reason, they are used to guide the observer in the construction of a midsagittal plane.) In each of the basilar-view planes (Fig. ll), key triangles are constructed (Fig. 12, A, B, and C), each of which may be referred to this primary (posterior) midsagittal plane. Superpositioning of the triangles clearly demonstrated the warping of the craniofacial complex in this patient (Fig. 13). The craniofacial skeleton is most severely deviated from the midsagittal plane at the level of the mandible; the severity of asymmetry decreased in a cephalic direction. DISCUSSION
Our three-dimensional cephalometric analysis permits visualization of skeletal midlines at selected depths of the craniofacial complex. When midlines and associated anatomic structures are studied sequentially, individual midlines may be combined conceptually into a warped midsagittal “plane. ” This localizes craniofacial asymmetry in posteroanterior and basilar views. Bilateral structures in the “symmetrical” head do not superimpose in the lateral cephalogram. The fan of
Analysis
of craniofacial
asymmetry
223
Fig. 14. A, Right lateral cephalometric tracing of a symmetrical mandible. The inferior border of the right body is below the left body. B, Right lateral cephalometric tracing of an asymmetrical mandible. The inferior border of the right body is above the left body.
Fig. 13. Superimposition of the triangles shows that the greatest amount of deviation from the midline occurs at the level of the mandible (A). decreasing in a cephalic direction. B, Maxilla. C, Cranial base.
the x-ray beam expands as it passes through the head, causing a divergence between the images of all bilateral structures except those along the central beam. Structures whose images are doubled and exhibit an apparent asymmetry (ramus, mandibular body, pterygoid space, orbits) are conventionally averaged and traced as a single image. This type of tracing is inadequate to describe the head that is truly asymmetrical. It would be more useful to trace bilateral structures separately if one were able to determine the contributions of beam geometry and skeletal asymmetry to the image. In the tracing of a symmetrical head, the right ramus appears anterior to the left while the right body appears inferior to the left (Fig. 14, A). In the lateral tracing of the patient with mandibular deviation to the
right and asymmetry of the body and ramus, this is not the case (Fig. 14, B). In this lateral tracing, combining the effect of beam geometry and skeletal asymmetry, the positions of left and right mandibular structures appear reversed. Similarly, right orbitale in the lateral tracings of the symmetrical head should be anterior to and on the same horizontal plane as left orbitale. In the asymmetrical patient right orbitale is displaced inferiorly and posteriorly. Examination of the worm’seye and frontal photographs (Fig. 1, B and C) shows the downward and posterior displacement of the right orbit. Owing to the compounding beam geometry and skeletal asymmetry, the posteroanterior and basilar cephalograms become vital to an understanding of the lateral cephalogram. The study of structures in various coronal and transverse planes makes it possible to measure and record the three-dimensional relationship of anatomic structures to one another. The composite basilar and posteroanterior tracing becomes more easily under-
224
Grctywn.
McCtrrthy.
and Brookstcin
stood when superimposed anatomic structures are studied both alone and in relation to the midline at various depths.
Berger, H.: Progress with basilar view cephalograms, Tran\. F.ur Onhod. Sot. 40: 159.164. 1964. Nahoum, H. I.. Fiasconaro, J., and DiSalvo. N. A.: The vcr ticosubmental roentgenogram in cephalometrics, J Am Dent Assoc. 69: 132-150, 1964. Marmary, Y., Zilkerman, Y.. and Mirsky, Y.: Use of foramrna spinosa to determine skull midlines, Angle Orthod. 49: 263-268. 1979.
REFERENCES 1. Broadbent, B. H., Sr.: A new x-ray technique and its application to orthodontia, Angle Otthod. 1: 45-66, 1931. 2. Broadbent, B. H., Sr., Broadbent, B. H.. Jr., and Golden, W. H.: Bolton standards of dentofacial developmental growth, St. Louis, 1975, The C. V. Mosby Company. 3. Sassouni, V.: Archial analysis in three dimensions, AM. J. ORTHOD. 44: 433-463, 19.58. 4. Schueller, A.: Die Schaedelbasis in Roentgenbid, Fortschr. Geb. Roentgenstr. 11: 1905 (quoted after Merrill”). 5. Merrill, V .: Atlas of roentgenographic positions, St. Louis, 1949, The C. V. Mosby Company.
Reprint requests to: Dr. The The 560 New
Barry H. Grayson Institute of Reconstructive Plastic Surgery New York University Medical Center First Ave. York, N. Y. 10016