The Cranial Base in Fetal Macaca nemestrina: A Quantitative Analysis of Size and Shape PETE E. LESTREL* and ROBERT N. MOORE
Dental Research Unit, Dental Service, Veterans Administration Hospital, * Sepulveda, California 91343, USA, and Section of Orthodontics, School of Dentistry, University of California, Los Angeles, California 90024, USA The applicability of Fourier analysis to quantitate the midsagittal cranial base has been demonstrated utilizing fetal Macaca nemestrina. This methodology accurately measures the irregular form of the endocranial profile, minimizes the effects of size, and maximizes shape dijfferences. This method provides a quantitative dimension to the descriptive analysis of shape change prevnously observed with a combined histologic and cephalometric analysis. J Dent Res 57(2): 395401, February 1978.
Although shape differences play a significant role in the growth process, until recently measurements of craniofacial size and shape have been based on relatively few, isolated metrical and angular measurements which can be conveniently determined. The major limitations of such conventional procedures are the inability to accurately describe complex morphological forms and the difficulty of clearly distinguishing between the effects of size and shape. ' Thus a method which would accurately measure any irregular form, minimize the effect of size, and maximize shape differences would be highly desirable. Fourier analysis provides such a methodology which will quantify a substantial percentage of the variability present and also partition a complex form into size and shape components. Received for publicationJanuary 25, 1977. Accepted for publication August 29, 1977. This study was supported in part by USPHS Research Grants DE-02931 and BRSG Grant RR-05304, awarded by the Biomedical Research Support Grant Program, DRR, NIH.
Another desirable property of Fourier's series is that the coefficients are orthogonal and consequently can be treated as independent variables. Comparisons within and between groups are now possible by viewing the differences in coefficients between the equations since the latter can be viewed as analogs of the actual morphology. The procedural details of the Fourier method advocated here have been published elsewhere. 1.2 Fourier analysis has now been successfully applied to quantitatively characterize in two dimensions such varied morphological structures as the cranial vault and the femur.3'4 The sagittal endocranial profile of the fetal Macaca nemestrina was utilized to demonstrate the applicability of Fourier analysis to craniofacial growth. Also, Moss has presented the hypothesis that malrelations of the bones that comprise the cranial base, implying changes in shape, may be significant in the etiology of craniofacial abnormalities such as cleft palate.5 The cranial base represents a complex, irregular form not easily analyzed by conventional metrics such as the cranial base angle (Basion-Sella-Nasion). While a first approximation of cranial base shape may be obtained from conventional linear6 or angular measurements,7 these cannot effectively deal with the actual distinct changes in shape as well as size which have been observed in the various component structures of the M nemestrina cranial base.8 It is the purpose of this communication to present a methodology utilizing Fourier analysis which will provide (1) a quantitative function that accurately describes the 395
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
396
LESTREL & MOORE
j Dent
Res
FebTuary
1978
FIG 1. -Standardized cephalometric radiographs illustrating the size and shape differences in the fetal Macaca nremestrz'na cranial base. (a) Young specimen
(100 to 110 days gestation). (b) Specimen near term (160 to 170 days). The midsagittal cranial base has been painted with barium sulfate.
midsagittal endocranial profile of the cranial base, (2) a method for calculating apposition/resorption rates, and (3) a graphic illustration of the pattern of size and shape changes which occur during growth.
estimated gestational age from 100 to 170 days. To enhance the radiographic outline of the incompletely ossified cranial base, the midline of the endocranial surface was painted with a narrow band of barium sulfate paste. Specimens were then positioned in a cephalometer fitted with a primate headholder and cephalometrically radiographed (Fig 1). The correction factor for magnification was 0.947. Because of the small size of the fetal skull, the radiographs were photographically enlarged 2.5 x onto plastic-coated Kodabrome H paper
Materials and Methods
Sixteen fetal Macaca nemestrina specimens out of 43 were available from the collection of the Regional Primate Research Center at the University of Washington.8 The sample (Table 1) ranged in
TABLE I SAMPLE DISTRIBUTI ION
Group
Estimated Gestational Age (days)
Male
1*
101-110 121-130
III
131-140
IV
141-150
2
V
151-160
3
VI
161-170
1*
in
Figures
Foot Length (mm)
42-44
53-57
II
*Specimens illustrated
Female
3
1
2,
3
60-66 67-73
3
74-76 79-85
and 4.
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Vol1. 5 7 No. 2
CRANIAL BASE SIZE e SHAPE
SPHENETH
397
fr
PRESPH
BASIOCC,
op
FIG 2. - Technique used to quantitatively characterize the cranial base with Fourier analysis. This particular geometry was required to reduce the effect of discontinuities at Basion, dorsum sellae, and the anterior aspects of the endocranial surface of the frontal bone. See text for details.
and the outline of the desired anatomical structure was traced on 0.003 inch dimensionally-stable matte acetate. To establish a geometric framework for Fourier analysis, a self-stick radial pattern (Letraset LT 196*) with one-degree intervals was attached to a sheet of 20-mil clear acetate. This template was superimposed with the zero degree line on the foramen magnum (Opisthion-Basion) plane and moved anteriorly until the 54-degree line on the radial-pattern template intersected the most anterior point of the endocranial curvature of the frontal bone. At that point a center, C, (Fig 2) was temporarily established. Utilizing this center, two *Letraset, USA, 33 New Bridge Road, Bergenfield, N.J. 07621.
points were marked on the endocranial base outline at 2 and 52 degrees. These two points (numbered 1 and 55) represent the limits of the cranial base to be measured. A second line was then constructed at 850 to the CLIVUS line through point 1 (Fig 2). The zero degree line of the radial template was now superimposed on this second line and moved anteroinferiorly until the 54-degree line coincided with point 55. This defined a new center, VCTR, from which 55 vectors were subsequently drawn at one-degree intervals to the endocranial profile. This rather involved geometry was required to reduce the effects of discontinuities (abrupt changes in curvature) arising at Basion, dorsum sellae, and the anterior aspect of the endocranial sur-
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j Dent
LESTREL & MOORE
398
face of the frontal bone. The 55 vectors were then measured using a modified Helios dial calipert accurate to 0.05 mm. Finally the measured vectors, or ranges in polar coordinates, were submitted as observed data to a specially written Fourier analysis program.9 This program calculates a Fourier function which quantitatively describes the entire midsagittal cranial base as defined by the measurements shown in Figure 2. Two M nemestrina specimens were selected, one the youngest and the other the oldest, and superimposed on VCTR. The increase in size with age is clearly evident in Figure 3. It is possible to correct for differences in size by scaling up or down the specimens to a common area."2 In the present instance, the specimens have been scaled up to an area equal to 10,000 r units which effectively minimizes differtModern Tools Corp., 56-02 Roosevelt Ave., Woodside,
Res
February
1978
: fr
ba
- YOUNG (est. 100- 110 days)
VCTR FIG 4. - Superimposition of area-standardized young and old specimens to illustrate shape changes that occur during fetal development.
NY 11377.
ba
-
YOUNG (est. 100-110 days) OLD (est. 160-170 days) VCTR
FIG 3. -Superimposition of actual young and old specimens. Curves depicted represent observed data points fitted with the Fourier series n
y(O)
=
a.
+
ai cos iO.
ences in size and facilitates comparisons based on shape. Since the Fourier function is a series solution, the curve-fit becomes more accurate as the number of terms increases. That is, the residual or difference between the observed data points and the predicted fit decreases. With respect to the cranial base, this residual, with 20 coefficients and the constant, was found to have a mean value of below 0.30 mm which is within the range of error inherent in the photographic, tracing, and measurement techniques. The fit for the entire midsagittal cranial base profile was satisfactory with the occasional exception of the superior portion of the dorsum sellae. This area, depicted by the dotted area in Figures 3 and 4, forms a double-valued function because of its pronounced curvature. Although another center (VCTR) could have been chosen to reduce the effect of this discontinuity, the fit would have been poorer in the vicinity of points 1 and 55. Results
Dotted line shows superior aspect of dorsum sellae which, because of its pronounced curvature, creates a double-valued function which could not be satisfactorily fitted by the Fourier series used.
Once the Fourier coefficients have been calculated they have to be corrected for differences in size. Table 2 shows the coef-
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
Vol. 57 No. 2
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Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
400
LESTREL & MOORE
ficients (after size differences have been controlled) which uniquely define the shape of each of the 16 cranial base outlines in norma lateralis. No statistically significant shape differences (comparing the young specimens [n 5] with the older group [n 11]) between coefficients were found for either sex or gestational age. This is not surprising in view of the extremely small sample size unfortunately available and the variability present in the cranial base. Further, no statistically significant differences using angular measurements were discerned in a previous cephalometric study of the total M nemestrina sample (n = 43) from which these 16 were drawn. 8 Once the data have been corrected for size via the area-standardization procedure (Fig 4), the differences in shape can be readily visualized and translated into resorption/apposition changes. These shape differences, quantitatively determined (Fig 4), have also been independently observed in the coordinated histologic and cephalometric study just mentioned. In brief, the endocranial portion of the basioccipital bone shows resorptive activity and becomes less concave. There is continued ossification of the dorsum sellae and postsphenoid bone, superior aspect of the presphenoid bone, and posterior portion of the sphenoethmoid plane. In contrast, the anterior portion of the sphenoethmoid plane shows endocranial resorption and the sagittal profile of the anterior cranial base becomes more concave. These subtle remodeling changes, readily discernable in Figure 4, become apparent only after differences in size have been controlled for. The Fourier analytic procedures advocated here are necessary for this comparison (Fig 4). Apposition and resorption rates can now be calculated as differences per unit area per time for the whole cranial base or selected bones (work in progress). Although the comparison shown in Figure 4 is based on two individuals to illustrate the methodology, the patterns of resorption/apposition are representative. Nevertheless, accurate estimates will in all probability require a three-dimensional approach. =
=
Discussion and Conclusions
As a curve-fitting procedure, Fourier's
j Dent
Res
February
1978
series converges onto any arbitrary shape, subject only to the following constraints: (1) the number of data points, (2) the presence of irregularities (discontinuities), (3) the choice of vector center, and (4) the number of terms (harmonics) taken in the series.
Fourier analysis provides a quantitative approach which will measure a much larger percentage of the variability inherent in all biological forms than is possible with the conventional metric approach. Since a two-dimensional form requires standardization in both dimensions, the utilization of area is advocated rather than the usual approach of standardizing a complex form for size by a linear method. The results of the present study clearly illustrate the confounding effect of size. Shape changes which are due to a differential resorption/apposition pattern are able to be quantified and clearly displayed; thus, Fourier analysis lends an added quantitative dimension to the histologic approach and provides a methodology for determining bone remodeling rates as they affect the cranial base during development. The authors would like to thank Drs. Benjamin Moffett and Laura Newell-Morris for allowing us continued use of the fetal primate collection at the University of Washington.
References
1. LESTREL, P,E.: Some Problems in the Assessment of Morphological Size and Shape Differences, Yearbook Phys Anthrop 18:140-162, 1974. 2. LESTREL, P.E., and ROCHE, A.F.: Fourier Analysis of the Cranium in Trisomy 21, Growth 40:385-398, 1976. 3. LESTREL, P.E., and BROWN, H.D.: Fourier Analysis of Adolescent Growth of the Cranial Vault: A Longitudinal Study, Hum Biol 48:517-528, 1976. 4. LESTREL, P.E.; KIMBEL, W.H.; PRIOR, F.W.; and FLEISCHMANN, M.L.: Size and Shape of the Hominoid Distal Femur: Fourier Analysis, Am J Phys Anthrop 46:281290, 1977. 5. Moss, M.L.: Malformation of the Skull Base Associated with Cleft Palate Deformity, Plast Reconst Surg 17:226-234, 1956. 6. HOUPT, M.I.: Growth of the Craniofacial
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
Vol. 57 No. 2 Complex of the Human Fetus, Am J Orthod 58:373-383. 1970. 7. FORD, E.H.: The Growth of the Foetal SkullJAnat 90:63-72, 1956. 8. MOORE, R.N.: A Cephalometric and Histologic Study of the Cranial Base in Foetal
CRANIAL BASE SIZE & SHAPE
401
Monkeys, Macaca nemestrina, Arch Oral Biol23:57-67, 1978. 9. PARNELL, J.N., and LESTREL, P.E.: A Computer Program for Fitting Irregular Two-Dimensional Forms, Computer Programs in Biomedicine 7:145-161, 1977.
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
Dental Research Unit, Dental Service, Veterans Administration Hospital, * Sepulveda, California 91343, USA, and Section of Orthodontics, School of Dentistry, University of California, Los Angeles, California 90024, USA The applicability of Fourier analysis to quantitate the midsagittal cranial base has been demonstrated utilizing fetal Macaca nemestrina. This methodology accurately measures the irregular form of the endocranial profile, minimizes the effects of size, and maximizes shape dijfferences. This method provides a quantitative dimension to the descriptive analysis of shape change prevnously observed with a combined histologic and cephalometric analysis. J Dent Res 57(2): 395401, February 1978.
Although shape differences play a significant role in the growth process, until recently measurements of craniofacial size and shape have been based on relatively few, isolated metrical and angular measurements which can be conveniently determined. The major limitations of such conventional procedures are the inability to accurately describe complex morphological forms and the difficulty of clearly distinguishing between the effects of size and shape. ' Thus a method which would accurately measure any irregular form, minimize the effect of size, and maximize shape differences would be highly desirable. Fourier analysis provides such a methodology which will quantify a substantial percentage of the variability present and also partition a complex form into size and shape components. Received for publicationJanuary 25, 1977. Accepted for publication August 29, 1977. This study was supported in part by USPHS Research Grants DE-02931 and BRSG Grant RR-05304, awarded by the Biomedical Research Support Grant Program, DRR, NIH.
Another desirable property of Fourier's series is that the coefficients are orthogonal and consequently can be treated as independent variables. Comparisons within and between groups are now possible by viewing the differences in coefficients between the equations since the latter can be viewed as analogs of the actual morphology. The procedural details of the Fourier method advocated here have been published elsewhere. 1.2 Fourier analysis has now been successfully applied to quantitatively characterize in two dimensions such varied morphological structures as the cranial vault and the femur.3'4 The sagittal endocranial profile of the fetal Macaca nemestrina was utilized to demonstrate the applicability of Fourier analysis to craniofacial growth. Also, Moss has presented the hypothesis that malrelations of the bones that comprise the cranial base, implying changes in shape, may be significant in the etiology of craniofacial abnormalities such as cleft palate.5 The cranial base represents a complex, irregular form not easily analyzed by conventional metrics such as the cranial base angle (Basion-Sella-Nasion). While a first approximation of cranial base shape may be obtained from conventional linear6 or angular measurements,7 these cannot effectively deal with the actual distinct changes in shape as well as size which have been observed in the various component structures of the M nemestrina cranial base.8 It is the purpose of this communication to present a methodology utilizing Fourier analysis which will provide (1) a quantitative function that accurately describes the 395
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
396
LESTREL & MOORE
j Dent
Res
FebTuary
1978
FIG 1. -Standardized cephalometric radiographs illustrating the size and shape differences in the fetal Macaca nremestrz'na cranial base. (a) Young specimen
(100 to 110 days gestation). (b) Specimen near term (160 to 170 days). The midsagittal cranial base has been painted with barium sulfate.
midsagittal endocranial profile of the cranial base, (2) a method for calculating apposition/resorption rates, and (3) a graphic illustration of the pattern of size and shape changes which occur during growth.
estimated gestational age from 100 to 170 days. To enhance the radiographic outline of the incompletely ossified cranial base, the midline of the endocranial surface was painted with a narrow band of barium sulfate paste. Specimens were then positioned in a cephalometer fitted with a primate headholder and cephalometrically radiographed (Fig 1). The correction factor for magnification was 0.947. Because of the small size of the fetal skull, the radiographs were photographically enlarged 2.5 x onto plastic-coated Kodabrome H paper
Materials and Methods
Sixteen fetal Macaca nemestrina specimens out of 43 were available from the collection of the Regional Primate Research Center at the University of Washington.8 The sample (Table 1) ranged in
TABLE I SAMPLE DISTRIBUTI ION
Group
Estimated Gestational Age (days)
Male
1*
101-110 121-130
III
131-140
IV
141-150
2
V
151-160
3
VI
161-170
1*
in
Figures
Foot Length (mm)
42-44
53-57
II
*Specimens illustrated
Female
3
1
2,
3
60-66 67-73
3
74-76 79-85
and 4.
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
Vol1. 5 7 No. 2
CRANIAL BASE SIZE e SHAPE
SPHENETH
397
fr
PRESPH
BASIOCC,
op
FIG 2. - Technique used to quantitatively characterize the cranial base with Fourier analysis. This particular geometry was required to reduce the effect of discontinuities at Basion, dorsum sellae, and the anterior aspects of the endocranial surface of the frontal bone. See text for details.
and the outline of the desired anatomical structure was traced on 0.003 inch dimensionally-stable matte acetate. To establish a geometric framework for Fourier analysis, a self-stick radial pattern (Letraset LT 196*) with one-degree intervals was attached to a sheet of 20-mil clear acetate. This template was superimposed with the zero degree line on the foramen magnum (Opisthion-Basion) plane and moved anteriorly until the 54-degree line on the radial-pattern template intersected the most anterior point of the endocranial curvature of the frontal bone. At that point a center, C, (Fig 2) was temporarily established. Utilizing this center, two *Letraset, USA, 33 New Bridge Road, Bergenfield, N.J. 07621.
points were marked on the endocranial base outline at 2 and 52 degrees. These two points (numbered 1 and 55) represent the limits of the cranial base to be measured. A second line was then constructed at 850 to the CLIVUS line through point 1 (Fig 2). The zero degree line of the radial template was now superimposed on this second line and moved anteroinferiorly until the 54-degree line coincided with point 55. This defined a new center, VCTR, from which 55 vectors were subsequently drawn at one-degree intervals to the endocranial profile. This rather involved geometry was required to reduce the effects of discontinuities (abrupt changes in curvature) arising at Basion, dorsum sellae, and the anterior aspect of the endocranial sur-
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
j Dent
LESTREL & MOORE
398
face of the frontal bone. The 55 vectors were then measured using a modified Helios dial calipert accurate to 0.05 mm. Finally the measured vectors, or ranges in polar coordinates, were submitted as observed data to a specially written Fourier analysis program.9 This program calculates a Fourier function which quantitatively describes the entire midsagittal cranial base as defined by the measurements shown in Figure 2. Two M nemestrina specimens were selected, one the youngest and the other the oldest, and superimposed on VCTR. The increase in size with age is clearly evident in Figure 3. It is possible to correct for differences in size by scaling up or down the specimens to a common area."2 In the present instance, the specimens have been scaled up to an area equal to 10,000 r units which effectively minimizes differtModern Tools Corp., 56-02 Roosevelt Ave., Woodside,
Res
February
1978
: fr
ba
- YOUNG (est. 100- 110 days)
VCTR FIG 4. - Superimposition of area-standardized young and old specimens to illustrate shape changes that occur during fetal development.
NY 11377.
ba
-
YOUNG (est. 100-110 days) OLD (est. 160-170 days) VCTR
FIG 3. -Superimposition of actual young and old specimens. Curves depicted represent observed data points fitted with the Fourier series n
y(O)
=
a.
+
ai cos iO.
ences in size and facilitates comparisons based on shape. Since the Fourier function is a series solution, the curve-fit becomes more accurate as the number of terms increases. That is, the residual or difference between the observed data points and the predicted fit decreases. With respect to the cranial base, this residual, with 20 coefficients and the constant, was found to have a mean value of below 0.30 mm which is within the range of error inherent in the photographic, tracing, and measurement techniques. The fit for the entire midsagittal cranial base profile was satisfactory with the occasional exception of the superior portion of the dorsum sellae. This area, depicted by the dotted area in Figures 3 and 4, forms a double-valued function because of its pronounced curvature. Although another center (VCTR) could have been chosen to reduce the effect of this discontinuity, the fit would have been poorer in the vicinity of points 1 and 55. Results
Dotted line shows superior aspect of dorsum sellae which, because of its pronounced curvature, creates a double-valued function which could not be satisfactorily fitted by the Fourier series used.
Once the Fourier coefficients have been calculated they have to be corrected for differences in size. Table 2 shows the coef-
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
Vol. 57 No. 2
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400
LESTREL & MOORE
ficients (after size differences have been controlled) which uniquely define the shape of each of the 16 cranial base outlines in norma lateralis. No statistically significant shape differences (comparing the young specimens [n 5] with the older group [n 11]) between coefficients were found for either sex or gestational age. This is not surprising in view of the extremely small sample size unfortunately available and the variability present in the cranial base. Further, no statistically significant differences using angular measurements were discerned in a previous cephalometric study of the total M nemestrina sample (n = 43) from which these 16 were drawn. 8 Once the data have been corrected for size via the area-standardization procedure (Fig 4), the differences in shape can be readily visualized and translated into resorption/apposition changes. These shape differences, quantitatively determined (Fig 4), have also been independently observed in the coordinated histologic and cephalometric study just mentioned. In brief, the endocranial portion of the basioccipital bone shows resorptive activity and becomes less concave. There is continued ossification of the dorsum sellae and postsphenoid bone, superior aspect of the presphenoid bone, and posterior portion of the sphenoethmoid plane. In contrast, the anterior portion of the sphenoethmoid plane shows endocranial resorption and the sagittal profile of the anterior cranial base becomes more concave. These subtle remodeling changes, readily discernable in Figure 4, become apparent only after differences in size have been controlled for. The Fourier analytic procedures advocated here are necessary for this comparison (Fig 4). Apposition and resorption rates can now be calculated as differences per unit area per time for the whole cranial base or selected bones (work in progress). Although the comparison shown in Figure 4 is based on two individuals to illustrate the methodology, the patterns of resorption/apposition are representative. Nevertheless, accurate estimates will in all probability require a three-dimensional approach. =
=
Discussion and Conclusions
As a curve-fitting procedure, Fourier's
j Dent
Res
February
1978
series converges onto any arbitrary shape, subject only to the following constraints: (1) the number of data points, (2) the presence of irregularities (discontinuities), (3) the choice of vector center, and (4) the number of terms (harmonics) taken in the series.
Fourier analysis provides a quantitative approach which will measure a much larger percentage of the variability inherent in all biological forms than is possible with the conventional metric approach. Since a two-dimensional form requires standardization in both dimensions, the utilization of area is advocated rather than the usual approach of standardizing a complex form for size by a linear method. The results of the present study clearly illustrate the confounding effect of size. Shape changes which are due to a differential resorption/apposition pattern are able to be quantified and clearly displayed; thus, Fourier analysis lends an added quantitative dimension to the histologic approach and provides a methodology for determining bone remodeling rates as they affect the cranial base during development. The authors would like to thank Drs. Benjamin Moffett and Laura Newell-Morris for allowing us continued use of the fetal primate collection at the University of Washington.
References
1. LESTREL, P,E.: Some Problems in the Assessment of Morphological Size and Shape Differences, Yearbook Phys Anthrop 18:140-162, 1974. 2. LESTREL, P.E., and ROCHE, A.F.: Fourier Analysis of the Cranium in Trisomy 21, Growth 40:385-398, 1976. 3. LESTREL, P.E., and BROWN, H.D.: Fourier Analysis of Adolescent Growth of the Cranial Vault: A Longitudinal Study, Hum Biol 48:517-528, 1976. 4. LESTREL, P.E.; KIMBEL, W.H.; PRIOR, F.W.; and FLEISCHMANN, M.L.: Size and Shape of the Hominoid Distal Femur: Fourier Analysis, Am J Phys Anthrop 46:281290, 1977. 5. Moss, M.L.: Malformation of the Skull Base Associated with Cleft Palate Deformity, Plast Reconst Surg 17:226-234, 1956. 6. HOUPT, M.I.: Growth of the Craniofacial
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
Vol. 57 No. 2 Complex of the Human Fetus, Am J Orthod 58:373-383. 1970. 7. FORD, E.H.: The Growth of the Foetal SkullJAnat 90:63-72, 1956. 8. MOORE, R.N.: A Cephalometric and Histologic Study of the Cranial Base in Foetal
CRANIAL BASE SIZE & SHAPE
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Monkeys, Macaca nemestrina, Arch Oral Biol23:57-67, 1978. 9. PARNELL, J.N., and LESTREL, P.E.: A Computer Program for Fitting Irregular Two-Dimensional Forms, Computer Programs in Biomedicine 7:145-161, 1977.
Downloaded from jdr.sagepub.com at UCSF LIBRARY & CKM on March 11, 2015 For personal use only. No other uses without permission.
