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Journal of Orthodontics, Vol. 36, No. 1, 23-35, March 2009 doi:10.1179/14653120722896
© 2009 British Orthodontic Society

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Scientific Section

Comparison of the Bolton Standards to longitudinal cephalograms superimposed on the occipital condyle (I-point)

Richard Grant Standerwick, Eugene W. Roberts, James K. Hartsfield, Jr, William J. Babler and Thomas R. Katona

Transformation Orthodontics. Langley, BC.

Address for correspondence: Richard Grant Standerwick, 20159-88th Ave, Suite E207 Langley, BC, Canada Email: rjstanderwick{at}gmail.com

Received 23 April 2008; accepted 5 November 2008


    Abstract
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 
Objective: To compare traditional superimposition on sella turcica and the anterior cranial base (SACB) to superimposition referenced at the occipital condyle (I-point) for demonstrating craniofacial growth and development.

Materials and methods: Tracings for ages 8, 10, 12, 15 and 18 were chosen from the Bolton Standards of Dentofacial Developmental Growth to compare superimposition with the traditional longitudinal reference at SACB (anterior curvature of sella turcica and anterior cranial base) to reference at I-point on the antero-inferior contour of the occipital condyles in norma lateralis. The serial tracings were superimposed using both the sagittal and postero-anterior (PA) tracings. Incremental growth of landmarks was measured in relation to Cartesian coordinates and compared between the superimposition methods.

Results: Sagittal and PA tracing superimpositions displayed an average 7 mm greater cephalad movement of landmarks, an average 2.4 mm greater ventral movement, and comparable transverse dimension with superimposition referenced at I-point as compared to the SACB reference.

Conclusion: I-point superimposition demonstrates physiologic growth patterns concealed by traditional registration at sella turcica. The evolution of superimposition on SACB was based on convenience and reproducibility. Fundamental principles of bone development are consistent with the occipital condyles as a more biologic reference for relative craniofacial growth. Actual vertical growth is believed to be greater than displayed in this study, due to the cross-sectional and blended nature of the sample.

Key words: Cephalometrics, I-point, occipital condyle, superimposition, craniofacial growth


    Introduction
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 
‘The problem of biologically correct registration is a primary one in the field today’.1Go Moss illustrated his point with an example of a Down’s syndrome patient, observing that tracings superimposed on the endocranial contours of the cranial base displayed a growth pattern more consistent with observed clinical features, compared with a traditional pre-sella registration. Stable landmarks for superimposition are commonly associated with neural structures, e.g. cribriform plate olfactory, PT point foramen rotundum, sella turcica-pituitary hypophysis. Pre-sella superimposition was chosen based on: fusion of the anterior cranial base (ACB) synchondroses, that superimposition was reproducible, and the midline structures of the ACB were easily visualized. It was assumed that the ACB was stable because the brain had finished growing by the age of 8;2Go,3Go however, MRI technology has demonstrated continuing brain anterior lobe growth up to age 12.4Go,5Go This late brain growth combined with the knowledge that growth of lateral skull sutures and the ACB is restricted relatively early,2Go,6Go is a quandary for displacement of the brain with growth.

The separation of the anterior and posterior cranial base (PCB) by the sphenooccipital synchondrosis (SOS) must be considered as most facial structures are located ventral to the SOS while the mandibular condyle is dorsal to the SOS.7Go Incorporation of structures on the PCB have lead to the development of analyses, notably by Broadbent (Bolton point-nasion),8Go,9Go Coben (basion-ACB analysis)7Go,10Go and Frankel (O'; occipital point).11Go These structural landmarks are proximate the occipital condyles, in norma lateralis. The cephalometric landmark I-point,12Go the most antero-inferior point on the basi-occipital portion of the occipital condyles in norma lateralis (OC) was utilized for cephalometric superimposition in this study (Figure 1Go). This method is similar to the Coben analysis (the reference points basion and I-point are both located on the PCB: the ACB orientation is similar to Coben’s sella-nasion line which is stable relative to the ethmoid cribriform plate,5Go and both are oriented parallel) and based on the work of Kanomi (K-point). Observed apposition at basion3Go is not large relative to the occipital condyle, however the effect of relative positional change of other landmarks increases with distance from the reference, making the small amounts significant.


Figure 1
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Figure 1 Dry Skull in norma lateralis radiograph; arrows pointing to the superimposition of the occipital condyles (bottom arrow) and remnant of the sphenooccipital synchondrosis (top arrow); (B) Tracing of the superimposed occipital condyles as seen on a lateral cephalometric radiograph (Figure from Ref. 12Go)

 
I-point is physiologically stable because there is no appositional growth along articulating surfaces due to the high pressure gradient of the head resting on the spinal column and the lack of an interstitial growth mechanism for the bone supporting the joint.12Go Enlow13Go notes that cartilage functions as a growth cartilage in conjunction with certain enlarging bones and specifies that these are synchondrosis, condylar cartilage and the epiphyseal plate cartilage. Furthermore, Enlow’s analysis was based on anatomical surface topography of dynamic histomorphometry with intravital labels. Enlow could only determine that bone formation and resorption had occurred at some point in time but he could not determine current activity or rate. This was the departure of Enlow and Frost in the early 1960s.14Go Dixon15Go justifies the growth of certain cartilages by describing them as similar to epiphyseal plates. Also, it must be noted that studies based on surface microscopy patterns are not applicable to the hyaline cartilage on the occipital condyles, and that there is no periosteum, nor muscle attachment compatible with the matrix theory of Moss.16Go I point/ I curve (Figure 1Go) superimposition reveals a more physiologic growth pattern that is consistent with the Bjork implant studies,12Go airway demands, speech development and microscopic observation of necropsy specimens.3Go,12Go,13Go,17Go

The objective of this study was to determine if the occipital condyle is a more physiologic superimposition reference for demonstrating the modelling and remodelling mechanisms of craniofacial growth.


    Methods and materials
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 
Tracings from the Bolton Standards of Dentofacial Developmental Growth18Go were chosen to compare the traditional longitudinal reference, the anterior curvature of sella turcica and anterior cranial base (SACB), to reference at I-point; because they are a readily available, high quality resource.13Go,19Go The Bolton Standards are comprised of cross-sectional data from 32 subjects (16 male and 16 female) chosen from the 93 participants.18Go The 8-, 10-, 12-, 15- and 18-year-old tracings were selected for lateral and frontal superimposition.

The following 31 landmarks were selected for analysis using Cartesian coordinates with the lateral cephalometric radiographs:


A-point ANS Soft Tissue Pogonion
I-point PNS n/a
Bolton point Antigonion Soft Tissue Menton
Inion Ethmoidale Sella
Ramus point Supra-orbitale R-point
Gonion Articulare PT-point
Pogonion Prosthion Nasion
B-point Infradentale Orbitale
Menton Nose Tip Porion
Glabella Upper Lip Basion
Key Ridge Lower Lip

The following 24 landmarks were selected for analysis using Cartesian coordinates with the frontal cephalometric radiographs:


Anterior cranial base Lateral skull surface: external (right and left) internal (right and left) Supra-orbitale (right and left)
Frontonasal suture Mastoid process (right and left) Orbitale (right and left)
Nasal floor Superior crest of the external sagittal suture Zygoma (right and left)
Lateral alveolar crest (right and left) Superior crest of the internal sagittal suture Menton
Antigonion (right and left) Jugum (right and left)

The 8-, 10-, 12-, 15- and 18-year-old sagittal tracings were superimposed 3 times by referencing on the anterior curvature of sella and oriented to ACB (SACB), and then, superimposed 3 times referencing at I-point/I-curve while ACB was oriented parallel to subsequent superimposed ACB (Figure 2Go). Cartesian coordinates where designed for both superimposition methods using transparency graph paper (8.5'x11' transparency film 0.1 mm, SL5263, Staples Inc., Framingham, MA, USA; which was imprinted with a 1x1 cm grid). The x-axis was coincident with a line oriented through the anterior curvature of sella turcica midpoint and ethmoidale (the deepest point on the ACB outline) of the 8-year-old tracing (Figure 3Go). The y-axis was coincident with a perpendicular line originating from the x-axis and bisecting I-point on the 8-year-old tracing (Figure 3Go). Overlaying the acetate graph to match the created x-axis and y-axis, points were marked on the graph acetate with a permanent marker (Sharpie® ultra fine point, 0.3 mm, Model 37001). As subsequent tracings were superimposed, the graph acetate was reoriented over the superimpositions, aligned to the x- and y-axis of the 8-year-old tracing, and landmarks plotted for the subsequent tracings. Measurement between points was from the best approximation of the point centres using an electronic digital caliper (Orthopli, #0400-EEP, Philadelphia) recorded to two decimal places.


Figure 2
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Figure 2 Sagittal Superimposition of 8-, 10-, 12-, 15- and 18-year-old Bolton Standards referenced at (A) I-point oriented to ACB (in parallel) and (B) at the anterior curvature of sella turcica and oriented to anterior cranial base (Tracings from the Bolton Standards of Dentofacial Developmental Growth)18Go

 

Figure 3
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Figure 3 Cartesian co-ordinate system. X-axis formed by a line through the mid-contour of the anterior curvature of sella turcica and the anterior cranial base. The y-axis was formed by a line perpendicular to the x-axis and through I-point (Tracing from the Bolton Standards of Dentofacial Developmental Growth)18Go

 
The 8-, 10-, 12-, 15- and 18-year-old posterior-anterior tracings were superimposed 3 times on the ACB (to represent the SACB superimposition), and then superimposed 3 times on I-point by orienting the ACB parallel (Figure 4Go). The vertical distances between ACB on the posterior-anterior tracings were made equal to the vertical distances between ACB as measured from sagittal I-point superimpositions. For example, for the lateral superimposition at I-point, if the distance between the ACB for the 8- and 10-year tracing was 2 mm, the ACB for the PA tracing would be oriented so that the distance between the 8 year and 10 year ACB was also 2 mm, and so on for the age intervals. The Cartesian grid was arranged using the 8-year-old tracing with the origin at crista galli. The x-axis was parallel to the ACB and perpendicular to the y-axis. The y-axis was made perpendicular to the x-axis and through the mid-sagittal structures. For the sagittal tracings, movement in the dorsal or cephalad direction was registered as negative, while movement in the ventral or caudad direction was registered as positive. For the PA superimposition, movement cephalad or to the patient’s right were registered as negative, while movement caudad or to the patient’s left were registered as positive.


Figure 4
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Figure 4 PA superimposition of 8- to 18-year-old Bolton Standards referenced at (A) the I-point/I-curve by orienting ACB parallel, to subsequent superimposed ACB, maintaining ACB distances equal to the distance observed in the sagittal tracings; and (B) the SACB by superimposing on the ACB (Tracings from the Bolton Standards of Dentofacial Developmental Growth)18Go

 

    Statistical summary
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 
The mean of the distance between the landmarks (x-axis and y-axis) was calculated for the tracings referenced at I-point and SACB for both the sagittal cephalometric tracings and posterior-anterior cephalometric tracings. The standard deviation of the x-axis and y-axis measurements was calculated.

Inter-correlation coefficients (ICCs) were calculated for within-reference repeatability (I point or SACB) for each location, separately for x-axis and y-axis and ICCs for the agreement between measurements using I point and SACB as reference, separately for x-axis and y-axis, again using all of the measurements for that location.

The between-reference difference mean, standard error and P-value were calculated, separately for x-axis and y-axis, using I point and SACB as reference again for all of the measurements for that location.


    Results
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 
The interval results (between 8 and 10, 10 and 12, etc.) did not reveal an obvious growth pattern, and therefore were excluded. The 8- to 18-year-old observations are shown in Tables 1Go and 2Go. Differences (mean, SE, P value) between measurements using I point and SACB as reference revealed large differences between them as shown by the highly significant P values; therefore there is not agreement between the references.


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Table 1 Supper imposition Between-Reference Difference: 8 to 18 years of age; Sagittal tracings
 

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Table 2 Supper imposition Between-Reference Difference: 8 to 18 years of age; PA Tracings
 
Within reference repeatability for ICC was relatively large, but within the range usually observed for cephalometrics. Some data are misleading because the measured distances for specific landmarks were very small resulting in a lower ICC value. The sagittal tracings displayed with-in reference average ICC values for I-point which were nearly identical to SACB; 0.87/ 0.87 for the x-axis and 0.85/0.86 for the y-axis. The between reference average ICC was 0.58 for the x-axis and 0.26 for the y-axis. The PA tracings displayed similar with-in reference average ICC values for the y-axis, 0.95/I-point and 0.97/SACB; however the x-axis values displayed slight divergence with an I-point value of 0.88 compared to 0.78 for SACB. The between-reference average ICC was 0.74 for the x-axis and 0.23 for the y-axis.

A comparison of landmark movement and the corresponding superimpositions are shown in Figures 2Go and 4Go. For the ages 8 to 18, sagittal tracing superimpositions displayed an average 7 mm greater cephalad movement of landmarks and 2.4 mm greater ventral movement when superimposition was referenced at I-point as compared to the SACB reference. The PA tracings displayed an average 6.7 mm cephalad movement of landmarks and comparable transverse dimension (–0.4 mm) for I-point reference (Table 3).

Differences (mean, SE, P value) between measurements using I point and SACB as references, are shown by the highly significant P values; these were not an agreement between the references.


    Discussion
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 
Consistent with our earlier study which used angular measurements,12Go this study revealed quantitative values for the observed movements. Reference at the occipital condyle demonstrated a more biologically correct modelling pattern of craniofacial growth.

The use of stable internal landmarks (implants) were not available, however within the limitations of this study, the impact of the vertical cranial component of growth was revealed relative to the aponeurotic tension model of craniofacial growth.12Go,20Go

Also, there is an inability to observe mandibular rotation (Bjork)21Go with the Bolton Standards because the appropriate internal landmarks were not traced: mandibular condyle, internal symphysis and inferior alveolar canal.12Go For future studies using these stable structures, it is recommended that the inferior alveolar canal landmark point be transferred from the initial tracing to subsequent tracings (regional superimposition to locate the same point on the canal) when utilizing internal stable structures for superimposition with I-point.12Go,21Go

The cross-sectional sample of blended sex mean values used to create the Bolton Standards tracing are a limitation of this study; therefore the vertical component of growth for individuals may be have been underestimated. Additionally, the cross-sectional nature hindered any useful observation from the growth intervals between 8 and 18 years of age, hence they were excluded. The use of digitizing and relative superimposition would have negated superimposition error, but the equipment was unavailable.

Many previous observations were not consistent with ACB superimpositions, which evolved as a convenience because the ACB was easier than PCB to visualize on cephalograms. It is clear that a more biologically valid reference such as I-point is needed, and that it should be more easily located as cephalometrics enters the three-dimensional (3D) age. From a clinical perspective, the anterior rotation of the jaws can be demonstrated directly without the use of implants by way of internal stable structures.12Go,22Go The Bjork implant method was able to demonstrate jaw rotation during growth by compensating for the biological masking of craniofacial growth, due to ACB superimposition.23Go

Figure 2Go displays the disparity of airway growth and speech development associated with ACB superimposition. The expressed dorsal/caudad growth pattern of the mandible would constrict the airway, in conjunction with pharyngeal side bone apposition on the clivus,3Go and compress the hyolaryngeal complex.17Go Therefore, a growth pattern based on ACB superimposition is inconsistent with a physiologic progression of growth and development. Cranial rotation, airorhynchy (posterior and upper portions of the face rotate dorsally relative to the posterior cranial base by extension of the anterior cranial base relative to the posterior cranial base),17Go,24Go cephalad cranial growth (I-point reference), the expanding V-principal of mandibular growth13Go and forward jaw rotation tend to increase the airway space, cause a relative descent of the hyolaryngeal complex (to allow speech development)17Go and position the genial tubercles of the tongue ventrally. The present results demonstrate that the mandible and maxilla move ventrally to a greater degree with I-point, compared with SACB superimposition. I-point registration demonstrates a more biologically correct growth pattern.

Location of I-point is as reliable as other commonly used landmarks.12Go The I-point reference method is a more biologically correct superimposition method, which demonstrates the jaw rotation observed by the implant reference method of Bjork.1Go,25Go I-point reference is consistent with the pubertal growth spurt in brain growth, continued enlargement of the occipital lobe up to 20 years of age,4Go airorhynchy17Go,24Go and brain flexure.17Go,20Go Previously it was known that the brain temporal lobe grows for several more years following completion of the anterior lobe.13Go This temporal lobe growth was believed to cause secondary displacement of the anterior lobes, driving facial growth. However, middle cranial fossa elongation nearly ceases by 10 years of age2Go and the nasal septum as a conduit of force to the midface has been discounted.13Go Asymmetric separation of the SOS26Go is a problem for any model of ‘downward and forward’ growth, as the separation rotates the ACB and midface ‘up and forward’ as observed with the facial block and airorhynchy.17Go,20Go,24Go The dural ‘slings’ which cradle the brain and emerging cranial nerves tend to restrict bone growth that might compromise neurologic function.20Go

The dura (desmocranial capsule) connective tissue around the brain is anisotropic. At its base, it becomes thick, grows slowly and resists brain enlargement in the developing cranial base in contrast to the thinner less resistant calvarial region.15Go This allows the cerebral hemispheres and to a lesser extent the cerebellar hemispheres, to expand more rapidly.15Go It is this dural attachment that is thought to cause early restriction of lateral cranial expansion,6Go,15Go necessitating vertical displacement of the brain. The weight of the brain and the dural sling attachment restrict lateral displacement, but the cross-sectional arch form and brain expansion with growth prevent the lateral skull from imploding from tension in the dural slings.

The observed vertical growth complies with the apposition pattern at sella turcica observed by Enlow13Go and the pubertal apposition on the anterior curvature of sella turcica observed by Melsen.3Go,20Go Significant growth of the head occurs between 5 and 20 years of age, when 2 inches of increased average head circumference is achieved, and between 10 and 20 years, an inch of growth occurs.27Go It can be seen from our sample that the vertical component is probably greater than the circumferential.

Cranial rotation1Go,5Go and airorhynchy,17Go in a pattern consistent with the fetal head unfolding associated with brain flexure,17Go explains some previously opaque growth observations.20Go For instance, when analyzed with implant radiographic markers the mesial surface of the maxillary first permanent molar in an adult is located ventral to the infrazygomatic crest. In comparison, the distal surface of the deciduous maxillary second molar lies dorsal to the crest in the absence of bone modelling.28Go Also, the distance between the anterior nasal spine and the zygomatic process increases in the absence of pronounced resorption on the anterior zygomatic process (Figures 2Go and 4Go),28Go,29Go which may be attributable to cranial rotation.

Figure 5Go illustrates a typical observation of mandibular rotation when superimposition is referenced at I-point/I-curve, and is more representative of the Bjork implant study observations.21Go,22Go,30Go Articulare in Figures 2Go and 6Go display the patterns seen in Figure 5Go. Notable is the condylar growth pattern observed with the I-point reference as shown in Figure 5Go.


Figure 5
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Figure 5 (A) Growth changes shown by superimposition referenced on the I-point/I-curve and anterior cranial fossa/base in a representative subject; (B) Growth changes shown by superimposition referenced at Sella and anterior cranial fossa/base in the same representative subject in (A). 4y9m (black) 6y6m (blue) 10y6m (red) 14y0m (green) (Figure from Ref. 12)

 

Figure 6
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Figure 6 Growth changes in norma lateralis, shown by superimposition referenced on I-point/I curve; ages 2, 5, 8, 14 and 18. Notice the cranial contour with growth (Tracings from the Bolton Standards of Dentofacial Developmental Growth)18Go

 
These results are directly comparable to those of Trenouth.19Go Trenouth reviewed traditional views of cranial proportions and found, based on the Bolton Standards,18Go the infant to adult cranial-facial ratios were less than traditionally reported; which is better represented by the greater proportionality of growth seen with superimposition at I-point. Campers line was also discussed and illustration displays clear cranial rotation relative to Campers line (porion to nasal spine);19Go although nasal spine is not neural related. The present data conflict with the observation that the cranium largely ceases growing by the age of 9.19Go The latter observation is inconsistent with continuing brain growth,4Go,31Go and probably reflects the difficulty with direct measurement of blended means and sagittal measurement of midline structures.32Go Future study is needed to determine the relationship of cranial morphology to peak height velocity of brain growth and volumetric change.

Therefore, brain temporal lobe growth reflects a vertical component of brain growth, concomitant with asymmetric growth at the SOS,26Go creates tension on the galea aponeurotica, which is transmitted through the craniofacial musculoaponeurotic system (CFMAS). This mechanism drives facial growth and associated rotations and is the essence of the aponeurotic tension model of craniofacial growth.12Go,20Go

A more biologically correct reference and orientation, based upon the occipital condyle will lead to greater insight into cranial rotation relative to the synergistic development of muscle, connective tissue, airway, and mandibular position. The increased accuracy of landmark definition in 3D will allow craniofacial orientation that will be more consistent with influence of neural structures and development of bone trabecular patterns. In two-dimensional the occipital condyles are viewed in norma lateralis as midline structures. CBCT will allow triangulation of the right and left I-points to the superior aspect of the sphenooccipital synchondrosis. It is believed that the basioccipital portion anterior to the inter-occipital synchondrosis is most stable to modelling due to the higher pressure gradient; dorsal to the synchondrosis, the exo-occipital portion anecdotally, seems prone to modelling with age.

Referencing these basilar structures will allow detection of asymmetric growth patterns and the determination of therapeutic responses in all three planes of space. This will be particularly important for realistic assessment of hyperdivergent and hypodivergent rotational growth patterns; sella turcica movement is believed more ventral and less cephalad, relative to I-point, for hypodivergent individuals compared with hyperdivergent. It is believed that the present method will be applicable for accurate description of growth and therapeutic changes prior to the ACB achieving stability at about age 8–12 years (this stability is valid only for the ethmoid portion).2Go,5Go Thus, superimposition on I-point will be applicable to subjects of all ages. (Figure 6Go Notice the growth superior to inion).

This study displays a quantitative vertical component of brain growth that is consistent with observation in literature not observable with ACB superimposition.

The occipital condyle is a more physiologic superimposition reference for demonstrating the modelling and remodelling mechanisms of craniofacial growth.


    Conclusions
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 


    Acknowledgments
 
Our thanks to George Eckert for providing the statistical analysis for this study.


    References
 Top
 Abstract
 Introduction
 Methods and materials
 Statistical summary
 Results
 Discussion
 Conclusions
 References
 
1 Moss ML. Ontogenetic aspects of craniofacial growth. In Moyers RE, Krogman WM (eds.). Craniofacial growth in man. Oxford, New York: Pergamon Press, 1971.

2 Hoyte DA: The cranial base in normal and abnormal skull growth. Neurosurg Clin N Am 1991; 2(3): 515–37.[Medline]

3 Melsen B. The cranial base: the postnatal development of the cranial base studied histologically on human autopsy material. Copenhagen: Arhus, 1974.

4 Giedd JN, Blumenthal J, Jeffries NO, et al. Brain development during childhood and adolescence: a longitudinal MRI study. Nature Neuroscience 1999; 2(10): 861–3.[CrossRef][Medline]

5 Bjork A. Cranial base development. A follow-up x-ray study of the individual variation in growth occuring between the ages of 12 and 20 years and its relation to brain case and face development. Am J Orthod 1955; 41:198–225.[CrossRef]

6 Ranly DM. Craniofacial growth. Dent Clin North Am 2000; 44 (3): 457–70.[Medline]

7 Coben SE. The spheno-occipital synchondrosis: the missing link between the profession’s concept of craniofacial growth and orthodontic treatment. Am J Orthod Dentofacial Orthop 1998; 114(6): 709–12; discussion 13–4.[CrossRef][Medline]

8 Broadbent BH. The Fface of the normal child. Angle Orthod 1937; 7(4): 183–208.

9 Broadbent BH. Bolton Standards and technique in orthodontic practice. Angle Orthod 1937; 7(4): 209–33.

10 Coben SE. Growth concepts. Angle Orthod 1961; 31(3): 194–201.

11 Frankel R. The applicability of the occipital reference base in cephalometrics. Am J Orthod 1980; 77(4): 379–95.[CrossRef][Medline]

12 Standerwick R, Roberts E, Hartsfield J, Jr, Babler W, Kanomi R. Cephalometric superimposition on the occipital condyles as a longitudinal growth assessment reference I-point and I-curve. Anat Rec, in press.

13 Enlow DH, Hans MG. Essentials of facial growth. Philadelphia, PA: Saunders, 1996.

14 Roberts WE, Roberts JA, Epkep BN, Burr DB, Hartsfield Jr JK. Remodeling of mineralized tissues, Part I: the Frost legacy. Semin Orthod 2006; 12(4): 216–37.[CrossRef]

15 Dixon AD, Hoyte DAN, Rönning O. Fundamentals of craniofacial growth. Boca Raton, FL: CRC Press, 1997.

16 Moss ML. A theoretical analysis of the functional matrix. Acta Biotheor 1968; 18(1): 195–202.[CrossRef][Medline]

17 Lieberman DE, Ross CF, Ravosa MJ. The primate cranial base: ontogeny, function, and integration. Am J Phys Anthropol 2000; Suppl 31:117–69.

18 Broadbent BH, Broadbent BH, Golden WH. Bolton standards of dentofacial developmental growth. Saint Louis, MO: Mosby, 1975.

19 Trenouth MJ, Joshi M. Proportional growth of craniofacial regions. J Orofac Orthop 2006; 67(2): 92–104.[CrossRef][Medline]

20 Standerwick RG, Roberts WE. The aponeurotic tension model of craniofacial growth, submitted.

21 Bjork A. Prediction of mandibular growth rotation. Am J Orthod 1969; 55(6): 585–99.[CrossRef][Medline]

22 Skieller V, Bjork A, Linde-Hansen T. Prediction of mandibular growth rotation evaluated from a longitudinal implant sample. Am J Orthod 1984; 86(5): 359–70.[CrossRef][Medline]

23 Bjork A, Skieller V. Facial development and tooth eruption: an implant study at the age of puberty. Am J Orthod 1972; 62 (4): 339–83.[CrossRef][Medline]

24 McCarthy RC, Lieberman DE. Posterior maxillary (PM) plane and anterior cranial architecture in primates. Anat Rec 2001; 264(3): 247–60.[CrossRef][Medline]

25 Bjork A. Facial growth in man, studied with the aid of metallic implants. Acta Odontol Scand 1955; 13(1): 9–34.[CrossRef][Medline]

26 Melsen B. The postnatal growth of the cranial base in Macaca rhesus analyzed by the implant method. Tandlaegebladet 1971; 75(12): 1320–9.[Medline]

27 Lowrey GH. Growth and Development of Children. 8th Edn. Chicago, IL: Year Book Medical Publishers, 1986.

28 Bjork A, Skieller V. Postnatal growth and development of the maxillary complex. In McNamara JA, Jr, et al. (eds.). Factors affecting the growth of the midface, Monograph No. 6 Craniofacial growth series. Ann Arbor: Center for Human Growth and Development, University of Michigan, 1976.

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