Measuring histological form change with finite element methods: an application using diazo-oxo-norleucine (DON)-treated rats

Morphometric Analysis of Mandibular Growth in Skeletal Class III Malocclusion

BACKGROUND

The craniofacial growth patterns of untreated individuals with skeletal Class III malocclusion have rarely been systemically investigated. This study used morphometric techniques to investigate the growth characteristics of the mandible in individuals with skeletal Class III malocclusion.

METHODS

Lateral cephalometric head films of 294 individuals with untreated skeletal Class III malocclusion (134 males, 160 females) were selected and divided into five triennial age groups (T1-T5) and by gender to identify the morphologic characteristics and sexual dimorphism in changes of mandibular growth. Procrustes, thin-plate spline, and finite element analyses were performed for localization of differences in shape and size changes. Maximum and minimum principal axes were drawn to express the directions of shape changes.

RESULTS

From T1 (age 6-8 years) to T4 (age 15-17 years), the distribution of localized size and shape changes of the mandible was very similar between the two genders. From T1 to T2 (age 9-11 years), significant lengthening of the condylar region was noted (23.4-39.7%). From T2 to T3 (age 12-14 years), the greatest size and shape change occurred at the condylar head (27.4-34.9%). From T3 to T4, the greatest size and shape changes occurred in the symphyseal region (23.6-42.1%). From T4 to T5 (age>or=18 years), significant sexual dimorphism was found in the distribution and amount of localized size and shape changes. Females displayed little growth increments during T4. Despite differences in the remodeling process, the whole mandibular configurations of both genders exhibited similarly significant upward and forward deformation from T4 to T5.

CONCLUSION

We conclude that thin-plate spline analysis and the finite element morphometric method are efficient for the localization and quantification of size and shape changes that occur during mandibular growth. Plots of maximum and minimum principal directions can provide useful information about the trends of growth changes.

Size and shape changes during late fetal growth (137-157 gestational days) in the pigtailed macaque (Macaca nemestrina) craniofacial complex: an application using three-dimensional coordinate data and finite element scaling analysis

Form changes within the fetal pigtailed macaque (Macaca nemestrina) craniofacial complex was documented using finite element scaling analysis (FESA) and three-dimensional (3D) coordinate data for 35 craniofacial landmarks. Coordinate data were digitized from 3D reconstructions of computed tomography (CT) images and 2D axial slices. Twenty-two fetal pigtailed macaques ranging in age from 137 to 157 gestational days were included (in this species, birth is estimated at 170 gestational days). The null hypothesis that the craniofacial complex grows with isometry during late fetal growth of the craniofacial complex was tested (P < 0.05), and the prediction that morphological change along an anteroposterior axis dominates late fetal growth was also investigated. The null hypothesis was rejected, indicating that allometric growth is present during late fetal growth. Growth along an anteroposterior axis is localized in the palate and mandible. The neurocranium grows along a superoinferior axis, while the neurofacial junction displays growth along both the anteroposterior and superoinferior axes. Mediolateral changes are localized between asterions, the external auditory meati, and maxillary and mandibular alveolar points. Finally, a 3D model of craniofacial growth for this species was created, localizing size and shape changes that occur during late fetal growth for each of the 35 craniofacial landmarks defined in this study.

Localization of mandibular changes in patients with class II division 1 malocclusions treated with twin-block appliances: finite element scaling analysis

Thirty mandibular landmarks were digitized from cephalographs of 46 children (prepubertal, approximately 10 years old) and 53 adolescents (pubertal, approximately 13 years old) to determine mandibular morphological changes in patients with Class II Division 1 malocclusions treated with Twin-block appliances. Procrustes superimposition computed average geometries and an analysis of variance were performed on the cephalographs. Prepubertal pretreatment and approximately 13-month-posttreatment profiles and pubertal pretreatment and approximately 22-month-posttreatment profiles were statistically different (P <.002). In male prepubertal configurations, a color-coded finite element scaling analysis revealed a conspicuous area of positive allometry ( approximately 12%) in the condylar neck and negative allometry ( approximately 17%) at the apex of the coronoid process. For the female prepubertal configuration, local increases in size were discernible in the condylar neck ( approximately 3%) and in the apex of the coronoid process ( approximately 4%). Comparing male pubertal configurations, finite element scaling analysis revealed marked positive allometry ( approximately 27%) in the condylar neck and negative allometry ( approximately 16%) at the apex of the coronoid process. For the female pubertal configurations, local increases in size were noticeable at the condylar neck ( approximately 15%), with negative allometry ( approximately 9%) in the coronoid process. For shape change, all configurations were highly isotropic over the entire mandibular nodal mesh. Therefore, in growing patients treated for Class II Division 1 malocclusions with Twin-block appliances, condylar growth, coronoid process remodeling, and osteogenesis in corpus and dentoalveolar regions may reflect the correction of the underlying skeletal dysmorphology.

Morphologic determinants in the etiology of class III malocclusions: a review

Morphospatial disharmony of the craniomaxillary and mandibular complexes may yield apparent mandibular prognathism, but Class III malocclusions can exist with any number of aberrations of the craniofacial complex. Deficient orthocephalization of the cranial base allied with a smaller anterior cranial base component has been implicated in the etiology of Class III malocclusions. Whereas the more acute cranial base angle may affect the articulation of the condyles resulting in their forward displacement, the reduction in anterior cranial size may affect the position of the maxilla. As well, intrinsic skeletal elements of the maxillary complex may be responsible for maxillary hypoplasia that may exacerbate the anterior crossbite seen in the Class III condition. Conversely, with an orthognathic maxilla, condylar hyperplasia and anterior positioning of the condyles at the temporo-mandibular joint may produce an anterior crossbite. Aside from the skeletal components, soft tissue matrices, particularly labial pressure from the circumoral musculature, may influence the final outcome of craniofacial growth of a child skeletally predisposed to Class III conditions. Indeed, as some Asian ethnic groups demonstrate an increased prevalence of Class III malocclusions, it is likely that the skeletal components and soft tissues matrices are genetically determined. Presumably, the co-morphologies of the craniomaxillary and mandibular complexes are likely dependent upon candidate genes that undergo gene-environmental interactions to yield Class III malocclusions. The identification of such genes is a desirable step in unraveling the complexity of Class III malocclusions. With this knowledge, the clinician may elect an early course of dentofacial orthopedic and orthodontic treatments aimed at preventing the development of Class III malocclusions.

Finite element analysis of the cranial base in subjects with Class III malocclusion

The association between cranial base morphology and Class III malocclusion is poorly understood. This study analyses local shape- and size differences in cranial base configurations of Class I and Class III subjects, employing finite element (FEM) analysis. Seventy-three prepubertal European-American children with Class III malocclusion were compared to their counterparts with a normal, Class I molar occlusion. Lateral cephalographs were traced, checked and subdivided into age- and sex-matched groups. Thirteen points on the cranial base were identified and digitized, providing a geometrical cranial base representation. Average cranial geometries were scaled to an equivalent size and a FEM analysis, capable of depicting and quantifying local shape- and size-change, employed to highlight regionalized, morphological differences. While the anterior cranial base was more homogeneous for shape-change, significant, localized anisotropy in the posterior regions of the cranial base and around sella turcica was evident. For size-change, areas of negative allometry were located posteriorly, but dilations in the mid- and anterior cranial base also were apparent. It is concluded that morphological alterations within the petro-occipital complex accompanied by changes in the sphenoidal and ethmoidal regions induce deviation from a normal cranial base configuration to one associated with deficient orthocephalization and an appearance of Class III malocclusion.

Morphometry of the cranial base in subjects with Class III malocclusion

The significance of the cranial base in the development of Class III malocclusion remains uncertain. The purpose of this study was to determine whether the form of the cranial base differs between prepubertal Class I and Class III subjects. Lateral cephalographs of 73 children of European-American descent aged between 5 and 11 years with Class III malocclusion were compared with those of their counterparts with a normal, Class I molar occlusion. The cephalographs were traced, checked, and subdivided into seven age- and sex-matched groups. Average geometries, scaled to an equivalent size, were generated based on 13 craniofacial landmarks by means of Procrustes analysis, and these configurations were statistically tested for equivalence. Bivariate and multivariate analyses utilizing 5 linear and angular measurements were undertaken to corroborate the Procrustes analysis. Graphical analysis, utilizing thin-plate spline and finite element methods, was performed for localization of differences in cranial base morphology. Results indicated that cranial base morphology differed statistically for all age-wise comparisons. Graphical analysis revealed that the greatest differences in morphology occurred in the posterior cranial base region, which generally consisted of horizontal compression, vertical expansion, and size contraction. The sphenoidal region displayed expansion, while the anterior regions showed shearing and local increases in size. It is concluded that the shape of the cranial base differs in subjects with Class III malocclusion compared with the normal Class I configuration, due in part to deficient orthocephalization, or failure of the cranial base to flatten during development.

Asymmetric vault modification in Hopi crania

Cradleboarding was practiced by numerous prehistoric and historic populations, including the Hopi. In this group, one result of cradleboarding was bilateral or asymmetric flattening of the posterior occipital. We test whether cradleboarding had significant effects on the morphology of the cranial vault, cranial base, and face. Additionally, we examine associations between direction of flattening and asymmetric craniofacial growth. A skeletal sample of Hopi from the Old Walpi site includes both nonmodified (N = 43) and modified individuals (N = 39). Three-dimensional coordinates of 53 landmarks were obtained using a diagraph. Thirty-six landmarks were used to define nine finite elements in the cranial vault, cranial base, and face. Finite element scaling was used to compare average nonmodified individuals, with averages of bilaterally, right, and left modified individuals. The significance of variation among "treatment" groups was evaluated using a bootstrap test. Pearson product-moment correlations test the association of asymmetry with direction of modification. Hopi cradleboarding has a significant effect on growth of the cranial vault, but does not affect morphology of the cranial base or face. Bilateral flattening of the cranial vault leads to decreased length and increased width of the cranial vault. Flattening of the right or left cranial vault results in ipsilaterally decreased length and width coupled with a corresponding increased length and width on the contralateral side of the cranial vault. There is a significant correlation of size asymmetry with direction of modification in the cranial vault, but not with size or shape change in the cranial base or face.

Effect of premature sagittal suture closure on craniofacial morphology in a prehistoric male Hopi

Scaphocephaly is caused by premature sagittal suture closure. It restricts medial-lateral growth of the cranial vault which appears longer and narrower than normal. We examined how this natural malformation affected morphology of the cranial base and face. A prehistoric adult male Hopi with scaphocephaly was compared to 19 normal male Hopi (Old Walpi Series, Field Museum of Natural History, Chicago, IL). Three-dimensional coordinates of 53 landmarks were recorded on the cranial vault, cranial base, and face. Finite element scaling analysis was used to test for significant differences between the scaphocephalic and normal individuals in craniofacial morphology. Finite element scaling results indicated that scaphocephaly has a profound effect on cranial vault morphology. However, morphology of the cranial base and face were only slightly affected and, typically, are within the normal range of variation for the sample. An abnormality in the cranial base is not associated with scaphocephaly in this individual.

Effects of annular cranial vault modification on the cranial base and face

Artificial modification of the cranial vault was practiced by a number of prehistoric and protohistoric populations, frequently during an infant's first year of life. We test the hypothesis that, in addition to its direct effects on the cranial vault, annular cranial vault modification has a significant indirect effect on cranial base and facial morphology. Two skeletal series from the Pacific Northwest Coast, which include both nonmodified and modified crania, were used: the Kwakiutl (62 nonmodified, 45 modified) and Nootka (28 nonmodified, 20 modified). Three-dimensional coordinates of 53 landmarks were obtained using a diagraph, and 36 landmarks were used to define nine finite elements in the cranial vault, cranial base, and face. Finite element scaling was used to compare average nonmodified and average modified crania, and the significance of the results were evaluated using a bootstrap test. Annular modification of the cranial vault produces significant effects on the morphology of the cranial base and face. Annular modification in the Kwakiutl resulted in restrictions of the cranial vault in the medial-lateral and superior-inferior dimensions and an increase in anterior-posterior growth. Similar dimensional changes are observed in the cranial base. The Kwakiutl face is increased anterior-posteriorly and reduced anterior-laterally to posterior-medially. Similar effects of modification are observed in the Nootka cranial vault and cranial base, though not in the face. These results demonstrate the developmental interdependence of the cranial vault, cranial base, and face.

Recent advances in primary palate and midface morphogenesis research

During the sixth week of human development, the primary palate develops as facial prominences enlarge around the nasal pits to form the premaxillary region. Growth of craniofacial components changes facial morphology and affects the extent of contact between the facial prominences. Our recent studies have focused on developing methods to analyze growth of the primary palate and the craniofacial complex to define morphological phases of normal development and to determine alterations leading to cleft lip malformation. Analysis of human embryos in the Carnegie Embryology Collection and mouse embryos of cleft lip and noncleft strains showed that human and mouse embryos have similar phases of primary palate development: first, an epithelial seam, the nasal fin, forms; then a mesenchymal bridge develops through the nasal fin and enlarges rapidly. A robust mesenchymal bridge must form between the facial prominences before advancing midfacial growth patterns tend to separate the facial components as the medial nasal region narrows and elongates, the nasal pits narrow, and the primary choanae (posterior nares) open posterior to the primary palate. In mouse strains with cleft lip gene, maxillary growth, nasal fin formation, and mesenchymal replacement of the nasal fin were all delayed compared with noncleft strains of mice. Successful primary palate formation involves a sequence of local cellular events that are closely timed with spatial changes associated with craniofacial growth that must occur within a critical developmental period.

Effects of fronto-occipital artificial cranial vault modification on the cranial base and face

Artificial reshaping of the cranial vault has been practiced by many human groups and provides a natural experiment in which the relationships of neurocranial, cranial base, and facial growth can be investigated. We test the hypothesis that fronto-occipital artificial reshaping of the neurocranial vault results in specific changes in the cranial base and face. Fronto-occipital reshaping results from the application of pads or a cradle board which constrains cranial vault growth, limiting growth between the frontal and occipital and allowing compensatory growth of the parietals in a mediolateral direction. Two skeletal series including both normal and artificially modified crania are analyzed, a prehistoric Peruvian Ancon sample (47 normal, 64 modified crania) and a Songish Indian sample from British Columbia (6 normal, 4 modified). Three-dimensional coordinates of 53 landmarks were measured with a diagraph and used to form 9 finite elements as a prelude to finite element scaling analysis. Finite element scaling was used to compare average normal and modified crania and the results were evaluated for statistical significance using a bootstrap test. Fronto-occipitally reshaped Ancon crania are significantly different from normal in the vault, cranial base, and face. The vault is compressed along an anterior-superior to posterior-inferior axis and expanded along a mediolateral axis in modified individuals. The cranial base is wider and shallower in the modified crania and the face is foreshortened and wider with the anterior orbital rim moving inferior and posterior towards the cranial base. The Songish crania display a different modification of the vault and face, indicating that important differences may exist in the morphological effects of fronto-occipital reshaping from one group to another.

Diagnosis of skeletal form on the lateral cephalogram with a finite element-based expert system

Orthodontic diagnosis depends largely on the current methods of cephalometric analysis and categorization. It is therefore unfortunate that such analyses tend to use inappropriate metrical systems that lack a rigorous scientific basis. As a consequence, the resultant data have questionable validity, as well as being subject to observer bias. In this study, an alternative, more rigorous, approach is described. A random sample of 126 pretreatment lateral cephalograms were analyzed with the finite element method. These data were then classified to form a training set or reference data base for the subsequent objective diagnosis of new, previously unclassified cases. This new case-classification system was based on matching the new cases to similar cases within the existing training set. The degree of concordance between such computer-matched cases was then evaluated by their subsequent conventional cephalometric analyses.

Growth of the cranial base in craniosynostosis

The configuration of the neurocranium has long been used as a diagnostic tool in assessing infants with abnormal head shape. In the case of craniosynostosis, a characteristic shape is caused by a constraint placed on growth of the neurocranium by prematurely closed sutures and secondary accommodation to that constraint. This investigation is a preliminary test of our hypotheses of growth of the cranial base under these constraints. Three dimensional landmark coordinate data were collected from pre-, peri-, and postoperative CT scans of eleven patients from The Cleft Palate and Craniofacial Deformities Institute, St. Louis, MO. These data were used in two sets of analytical comparisons. Comparisons of preoperative and perioperative morphology were taken to represent preoperative growth, while comparisons of perioperative to postoperative CT scans represent postoperative growth. Finite-element scaling analysis (FESA) and Euclidean distance matrix analysis (EDMA) were used to make these comparisons. Our results show that in cases involving premature closure of the metopic, sagittal, and bilateral coronary sutures, predictions about growth of the cranial base made prior to analysis prove correct. In these forms of craniosynostosis there are characteristic and consistent changes in the cranial base in both pre- and postoperative growth. Preoperative and postoperative growth in patients diagnosed with unicoronal synostosis show a greater degree of individual variability and do not follow a predictable pattern.

Comparison between two finite-element modelling methods for measuring change in craniofacial form

Finite-element modelling of form change is a useful morphometric technique for measuring differences between anatomical patterns. Two different finite-element algorithms currently are used. One method requires normalized coordinates as input data, while the second method uses globalized coordinates as input data. This study determines whether the two finite-element methods provide equivalent measures of three-dimensional form change when applied to the nasal septa of embryonic mice. Computer models of the nasal septa from mice of 15 and 17 days gestation were generated. Homologous landmarks were identified so that each nasal septum was represented by a tetrahedral finite-element. These elements were subjected to both finite-element modelling methods. Results show that the two algorithms use different interpolation functions and yield dissimilar intermediate results, but generate identical strain matrices as well as equivalent principal extensions, directions of form change, variables of form change, and graphical displays. Therefore, results are directly comparable from studies using either finite-element modelling method.

An evaluation of the changes in soft-tissue profile form induced by orthodontic therapy

In view of the growing concensus that traditional cephalometric appraisals yield data of dubious scientific value, the changes in soft-tissue profile forms were evaluated by an alternative technique. This involved dividing the soft-tissue profile form into a series of triangular finite elements spanning homologous datum points. With the use of techniques derived from continuum mechanics, the changes in soft-tissue profile form were evaluated by computing the degree of distortion in each triangle after treatment (target element) compared with the triangle before treatment (reference element) in terms of specific size and shape parameters. In a comparison of samples of patients with Class I and II malocclusion, varying patterns of facial profile change were noted, depending on the parameters analyzed. The results, therefore, showed that although such techniques offer rigorous cephalometric potential, further investigation is required to identify more appropriate datum points.

A computer graphics program for measuring two- and three-dimensional form change in developing craniofacial cartilages using finite element methods

Allometric analysis of chondrocranial growth seeks to provide objective measures of morphogenetic form change during ontogeny of the primordial skull. Linear measures, typically employed to study differential growth, become problematic at the histological level since an external referencing system is impossible to achieve for microscopic anatomies in embryos. The purpose of this paper is to describe a computer graphics program which generates spatially invariant measures of two- and three-dimensional form change using finite element methods. Anatomical form change is viewed as a continuous deformation of an initial finite element representing an anatomical unit into a second configuration. The algorithm consists of isoparametric scaling of finite elements, strain matrix formulation, and size/shape variable derivation. The routine includes four segments serving to extract nodal data, generate the strain matrix relating the two morphologies as well as deriving corresponding size/shape variables, reference the major and minor axes of form change, and provide graphic display of the anatomical geometries. Applications are provided measuring two- and three-dimensional form change in the developing craniofacial cartilages of rats subjected to treatment with the known teratogen diazo-oxo-norleucine (DON). The finite element routine provides craniofacial form change variables which are expected in light of cellular alterations induced by DON administration. Finally, computational differences between this routine and similar approaches using finite element methods for analyzing biological form change are examined.

Comparative study of normal, Crouzon, and Apert craniofacial morphology using finite element scaling analysis

Finite element scaling analysis is used to study differences in morphology between the craniofacial complex of normal individuals and those affected with the syndromes of Apert and Crouzon. Finite element scaling quantifies the differences in shape and size between forms without reference to any fixed, arbitrary registration point or orientation line and measures the amount of form change required to deform one object into another. Two-dimensional coordinates of landmarks digitized from annual sets of cephalometric radiographs were used in the analysis. A simple tabulation shows no difference in variances between the normal and pathological samples. A test of mean differences depicts the Apert and Crouzon morphologies as significantly different from normal. The Apert palate differs from normal in shape in the older age groups analyzed, and palatal size differences are most common at the posterior nasal spine. The Apert pituitary fossa and basi-occiput are significantly larger than normal. The Crouzon pituitary fossa is also larger than normal, but the difference is not always significant. The typical morphology of the Crouzon nose is due more to differences in shape than size. The Crouzon basi-occiput is significantly smaller than normal. An age association of the differences between the normal and pathological craniofacies was found in Apert syndrome but not in Crouzon syndrome. Apert syndrome is characterized by a more homogeneous pattern of craniofacial dysmorphology from 6 months to 18 years of age than Crouzon syndrome.