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The medial axis branch point in the human mandible
ANNALS
or ANATOMY
=========
The medial axis branch point in the human mandible Kalevi Koski and Juha Varrela Department of Oral Development and Orthodontics, Institute of Dentistry, University of Turku, FIN-20S20 Thrku, Finland
Summary. The medial axis method was applied to radiocephalometric images of the mandible in 20 adults and 18 children and to panoramic X-ray images of these children, and also directly to 50 halves of dry mandibles. It was found that the location of the posterior branch point coincided almost invariably with the mandibular foramen/lingula. The foramen may be regarded as the posterior limit of the mandibular body, from which the condylar and coronoid processes branch off. The medial axis appears to reflect the developmental and functional anatomy of the human mandible.
Key words: Medial axis - Branch point - Human mandible
Introduction The mandible has often been seen as a complex bone consisting of several more or less independent parts (Moss 1962; Moore 1973; Luther 1993). Support for this view has been obtained from anthropometric (Cleaver 1937), radiocephalometric (Vinkka and Koski 1975), and experimental studies (Manson 1968). For the various analyses of this mosaic bone, the medial axis (Blum 1967; Bookstein 1981), which is also known as the median axis, the symmetrical axis, the skeleton or line skeleton (Straney 1990), has been employed. The medial axis can be defined as "the continuous, branching curve that in some well-defined sense lies in the middle of the outline" (Straney 1990). The method has been applied to the total outline of the human mandible (DeSouza and Houghton 1977; Webber and Blum 1979; Bookstein 1981) as well as, for example, to the symphyseal shape (Daegling 1993). Our preliminary visual observations seemed to suggest that the branch point of the medial axis in the human Correspondence to: K. Koski
Ann Anat (1997) 179: 273-276 © Gustav Fischer Verlag
mandible, i. e., the point where the single axis line of the mandibular body divides into two lines which form the median axes of the condylar and coronoid processes, coincides with the mandibular foramen or lingula. The mandibular nerve has been postulated as an element by which the growing mandible adjusts itself to the surrounding structures, such as, the skull base (Moss and Salentijn 1971), the role of the blood supply in osteogenesis being textbook knowledge and its influence in the growth of the craniofacial structures being well documented (e. g., Schumacher et al. 1988). The sphenomandibular ligament, attached to the lingula, has been seen as a factor limiting the movements of the mandible (Moss 1959). The location of the entrance of the neurovascular bundle serving the body of the mandible, protected by the lingula, is thus unlikely to be a matter of chance. In order to clarify the relationship between the medial axis and the human mandible, a series of radiocephalometric studies and measurements of skeletal material were undertaken, and will be reported here.
Materials and methods 1\vo samples of radiograms were used: 20 lateral cephalometric radiograms of young adult women, 22 to 28 years of age, and 180rthopantomographic films of children (9, girls, 9 boys), S8 years of age. In addition, SO mandibles from late medieval skulls were inspected and measured. The films and specimens were picked in sequence from existing files and from the skull collection at the Institute of Dentistry, University of Thrku. The outlines of the mandibular halves with the clearer image of the two visible ones were traced from the cephalometric films, as were also those of both halves from the orthopantomograms. The location of the lingula was marked on all tracings, together with the beginning of the mandibular canal. Pilot measurements of the skeletal mandibles had revealed that the lingula, as a marker of the mandibular foramen, was approximately symmetrically situated in relation to the dorsal border of the ramus and
the temporal crest. The temporal crest, which was always discernible in the skeletal material and visible as a separate line in most of the cephalograms of the adults and in about half of those of the children, was then identified as the ventral border
of the ramus. Using a template of circles of different sizes (Bookstein 1981; Straney 1990) the center point of the circle touching the borders and the lowest point of the incisura (sigmoid notch) was located and marked on the tracing (Fig. 1). This center point is, by definition, the branch point of the medial axis (Webber and Blum 1979; Bookstein 1981). In the radiograms, the location of the branch point was recorded either as coinciding with or being away from the lingula; in the latter case its distance from the tip of it was measured to the nearest 0.5 mrn. The location of the branch point in the skeletal mandibular left halves was determined by finding, with the help of dial calipers, the point equidistant from the dorsal border of the ramus, the temporal crest, and the lowest point of the incisura (sigmoid notch), i. e., the center of the circle touching the boundaries of the ramus: the branch point (Fig. 2). The total width of the ramus between the dorsal and ventral surfaces was also measured at the level of the branch point (Fig. 2). The width of the ventral flange could then be determined by subtracting the dorsal surface-temporal crest dimension from the total width. These dimensions were measured to the nearest 0.1 mrn. The method errors were tested by double measurement of 25 mandibles, using the formula 1:d2/2n, and were found to be 0.20 and 0.20 mrn, or 0.55 to 0.69% of the mean, for the smaller and larger ramus widths (vide infra) respectively, and were thus acceptable.
vi
Fig. 1. An illustration of the medial axis method as applied to the tracing of an orthopantomographic image of a child mandible. The branch point is the center of the circle which touches the three boundaries of the ramus. The centers of the other circles indicate points on the medial axis and its branches.
Fig. 2. The dimensions measured on dry mandibular halves. Two widths of the ramus, one between the dorsal surface and the temporal crest, the other between the dorsal and ventral surfaces of the ramus, are here shown along the bisector of a circle whose center is the branch point, in this case located on the lingula.
Results In the tracings of cephalometric images of the adult mandibular halves the branch point was found on the lingula in 8/20 instances. Its location in the rest of the sample was within 2.5 mm off the lingula, always towards the incisura. In all but one of the 36 traced orthopantomographic radiographic images of the children's mandibular halves, the branch point was located on the lingula; in one pan tomogram the point was just off the lingula in the mandibular canal. In the skeletal material the findings were as follows: The location of the branch point was found to be on the lingula in the majority of instances. In 17 of the 50 mandibles the point was 0.5-3.0 mm above the lingula. The total width of the ramus averaged 35.5 mm (SD 3.53, range 26.8-42.6 mm). The width between the dorsal surface and the temporal crest, at the level of the tip of the lingula averaged 29.7 mm (SD 2.91, range 23.236.3 mm). The width of the ventral flange of the ramus in front of the temporal crest, was then calculated to average out at 5.8 mm (SD 1.58, range 2.5-8.8 mm).
Discussion The medial axis method is a way of describing a two-dimensional image of an object (which in itself may be, and usually is, three-dimensional) with a simple line figure
274
containing all the necessary information about the shape, but which can be more easily manipulated than the shape itself (Oxnard 1973). Since its introduction (Blum 1967), it has been applied to studies of skeletal and other shapes, usually to their two-dimepsional projections (Oxnard 1973; Souza and Houghton 1977; Webber and Blum 1979; Bookstein 1979). Although computerized methods for determining the medial axis have been developed by many authors, a simple manual method has been stated to give equally reliable results (Straney 1990). We chose to use the manual method, especially since it was easy to apply to the study of skeletal mandibles directly. Cephalometric, orthopantomographic, and direct skeletal findings all essentially confirmed our preliminary observations regarding the location of the medial axis posterior branch point of the mandible at the lingula/ mandibular foramen, provided that the ventral limit of the ramus was set at the temporal crest. This appears justified from the viewpoint of functional anatomy. The flange ventral to the temporal crest which is part of the attachment area of the temporal muscle (Schumacher 1959; Romanes 1964) and quite variable in size, as found even in this study, has been included in the coronoid process (Humphry 1866; Simon and Moss 1973). The coronoid process develops simultaneously with the condylar process during fetal life, but the maintenance of its size and shape in postnatal life depends on the continuing attachment of the temporal muscle, as shown by numerous animal experiments (Washburn 1947; Boyd et al. 1967; Schumacher and Dokhidal 1968; Moss and Meehan 1970). The mandibles of edentulous old people leave hardly any reason to doubt the existence of a similar relationship between the temporal muscle and its attachment area even in the human. The ventral flange may thus not be regarded as a part of the intrinsic coronoid process. The practically invariable location of the branch point in the region of the mandibular foramen/lingula suggests a more than geometric role for the medial axis configuration as a representative of the mandible in the human. It has been postulated that the neural element is of primary importance for the growth of the mandible (Moss and Salentijn 1971; Kjaer 1990); a case of a relatively normal mandibular body without the mandibular foramen and canal described in the literature may be explained by the compensatory function of the mylohyoid nerve (Jakobsen et al. 1991). The allegedly uniform shape, a logarithmic spiral, of the mandibular nerve in the human (Moss and Salentijn 1971) could be interpreted to indicate a kind of neutral position of this nerve in the mandible. As to the blood vessels sharing this neutral position, the situation brings to mind that of the main nutrient artery of long bones (Lacroix 1951; Brookes 1971). Although the posterior part of the mandibular canal has been used as a natural stable landmark in cephalometric studies of mandibular growth (Bjork 1969), the stability of the whole mandibular canal during growth is questionable. A parallelism between the canal and the postulated neutral zone in long bones subjected to stress (Pauwels 1965) remains
an open question. Even a cursory perusal of radiographic images of the mandibular canal reveals that they do not correspond to the medial axes. Nevertheless, the entrance area of the neurovascular bundle, protected by the lingula to which the sphenomandibular ligament attaches itself, may conceivably represent a kind of neutral area in the development and growth of the human mandible. In a comprehensive review of the diversity of the mammalian ramus (Moss 1968), this part was considered to consist of several micro-skeletal units, and the shape and position of the ramus to be independent of the body of the mandible. Interestingly enough, in the figure that illustrates this concept (Moss 1968, Fig. 1), the major skeletal units of the human mandible, the basal, angular, condylar, and coronoid units are depicted as meeting at the approximate level of the mandibular foramen. The line of the sigmoid notch, while depending on the shape and direction of the coronoid process (Simon and Moss 1973), and obviously equally dependent on the condylar process, seems to be rather invariably related to the location of the mandibular foramen. One wonders why the ventral and dorsal borders of the basic ramus and the notch between the two processes are so consistently equidistant from the mandibular foramen/lingula during postnatal growth. The mandibular foramen may be seen as the natural posterior limit for the human mandibular body. This is in line with both the phylogenetic (Colbert 1955; Moore 1981) and ontogenetic records (Low 1909; Arey 1965). During the embryonic period "the original primary centre of ossification produces the body of the mandible as far back as the mandibular foramen; - - -; this is - - the neural element" (Scott and Dixon 1972, p. 433). From that posterior point on, the condylar and coronoid processes, which arise as separate secondary cartilages and join the already ossifying body of the jaw, may be viewed to branching off, each governed by different factors, the one by an articulating function (coupled with cartilaginous growth), the other by muscular forces. This would explain why "only small portion of the ramus is unaccounted for as coronoid process or condyle" (Bookstein 1981). The medial axis configuration in the human mandible appears to reflect the development and functional anatomy of this bone. Acknowledgements. We thank Leena Tuomarila and Janno Koskinen for illustrations, and the anonymous referees for valuable suggestions.
References Arey LB (1965) Developmental Anatomy, 7th ed. WB Saunders, Philadelphia Avis V (1959) The relation of the temporal muscle to the form of the coronoid process. Am J Phys Anthropol17: 99-1004 Bjork A (1969) Prediction of mandibular growth. Am J Orthod 55: 585-599
275
Blum H (1967) A transformation for extracting new descriptors of shape. In: W Walthen-Dunn (ed): Models for the perception of speech and visual form. Proc Symp Data Sciences Lab Air Force Cambridge Res Lab, MIT Press, Boston, pp 362-380 Bookstein FL (1979) The line skeleton. Comp Graph Image Proc 11: 123-137 Bookstein FL (1981) Looking at the mandibular growth: some new geometric methods. In: DC Carlson (ed): Craniofacial biology, Monograph No 10, Craniofacial Growth Series, Center for Human Growth and Development, University of Michigan, Ann Arbor, pp 83-103 Brookes M (1971) The Blood Supply of Bone. Butterworths, London Cleaver FH (1937) A contribution to the biometric study of the human mandible. Biometrika 29: 80--112 Colbert EH (1961) Evolution of the Vertebrates. Science Editions, New York Daegling DJ (1993) Shape variation in the mandibular symphysis of apes: an application of a median axis method. Am J Phys Anthropol 91: 505-516 DeSouza PV, Houghton P (1977) Computer location of medial axis. Comp Biomed Res 10: 333-343 Humphry GM (1866) On the growth of jaws. Trans Cambridge Philos Soc XI:1. Cit. Brash JC (1924) The growth of the jaws and palate. In: The Growth of the Jaws, Normal and Abnormal, in Health and Disease. The Dental Board of the United Kingdom, pp 23-66 Jakobsen J, Jorgensen JB, Kjaer I (1991) Tooth and bone development in a Danish medieval mandible with unilateral absence of the mandibular canal. Am J Phys Anthropol 85: 15-23 Kjaer I (1990) Correlated appearance of ossification and nerve tissue in human fetal jaws. J Craniofac Genet Devel Bioi 10: 329-336 Lacroix P (1951) The Organization of Bones. J & A Churchill, London Low A (1909) Further observations on the ossification of the human lower jaw. J Anat 44: 83-95 Luther F (1993) A cephalometric comparison of medieval skulls with a modem population. Eur Orthod J 15: 315-325 Manson JD (1968) A comparative study of the postnatal growth of the mandible. Henry Kimpton, London Moore WJ (1973) An experimental study of the functional components of growth in the rat mandible. Acta Anat 85: 378-385 Moore WJ (1981) The Mammalian Skull. Cambridge University Press, Cambridge
Moss ML (1959) Functional analysis of the temporomandibular growth. In: L Schwarz (ed): Disorders of the Temporomandibular Joint. WB Saunders, Philadelphia, pp 73-88 Moss ML (1962) The functional matrix. In: BS Kraus, RA Riedel (eds): Vistas in Orthodontics. Lea & Febiger, Philadelphia, pp 85-98 Moss ML (1968) Functional cranial analysis of mammalian mandibular ramal morphology. Acta Anat 71: 423-447 Moss ML, Meehan MA (1970) Functional cranial analysis of the coronoid process in the rat. Acta Anat 77: 11-24 Moss ML, Salentijn L (1971) The unitary logarithmic curve descriptive of human mandibular growth. Acta Anat 78: 532-542 Oxnard CE (1973) Some problems in the comparative assessment of skeletal form. In: MH Day (ed): Human Evolution. Taylor & Francis, London, pp 103-125 Pauwels F (1965) Gesammelte Abhandlungen zur funktionellen Anatomie des Bewegungsapparates. Springer, Berlin-Heidelberg-New York Romanes GJ (ed) (1964) Cunningham's Textbook of Anatomy, 10th ed. Oxford University Press, London Schumacher GH (1959) Die Kaumuskulatur von menschlichen Friih- und Neugeborenen. Z Anat Entwickl-gesch 121: 304-321 Schumacher GH, Dokilidal M (1968) Uber unterschiedliche Sekundarverlinderungen am Schadel als Folge von Kaumuskelresektionen. Acta Anat 69: 378-392 Schumacher GH, Fanghanel J, Koster D Mierzwa J (1988) Kraniofaziales Wachstum unter dem Einfluss der Blutversorgung. 14. Theoretische Ableitungen und klinische Schlussfolgerungen (Schluss). Anat Anz 167: 17-22 Scott JH, Dixon AD (1972) Anatomy for Students of Dentistry, 3rd ed. Churchill Livingstone, Edinburgh & London Simon MR, Moss ML (1973) A functional cranial analysis of human sigmoid notch form. Acta Anat 85: 133-144 Straney DO (1990) Median axis method in morphometrics. In: FJ Rohlf, FL Bookstein (eds): Proceedings of the Michigan Morphometric Workshop, The University of Michigan Museum of Zoology, Ann Arbor, pp 179-200 Vinkka H, Koski K (1975) Variability of the craniofacial skeleton. II. Comparison between two age groups. Am J Orthod 67: 34-43 Washburn SL (1947) The relation of the temporal muscle to the form of the skull. Anat Rec 99: 239-248 Webber RL, Blum H (1979) Angular invariants in developing human mandibles. Science 206: 689-670 Accepted December 30,1996
276
or ANATOMY
=========
The medial axis branch point in the human mandible Kalevi Koski and Juha Varrela Department of Oral Development and Orthodontics, Institute of Dentistry, University of Turku, FIN-20S20 Thrku, Finland
Summary. The medial axis method was applied to radiocephalometric images of the mandible in 20 adults and 18 children and to panoramic X-ray images of these children, and also directly to 50 halves of dry mandibles. It was found that the location of the posterior branch point coincided almost invariably with the mandibular foramen/lingula. The foramen may be regarded as the posterior limit of the mandibular body, from which the condylar and coronoid processes branch off. The medial axis appears to reflect the developmental and functional anatomy of the human mandible.
Key words: Medial axis - Branch point - Human mandible
Introduction The mandible has often been seen as a complex bone consisting of several more or less independent parts (Moss 1962; Moore 1973; Luther 1993). Support for this view has been obtained from anthropometric (Cleaver 1937), radiocephalometric (Vinkka and Koski 1975), and experimental studies (Manson 1968). For the various analyses of this mosaic bone, the medial axis (Blum 1967; Bookstein 1981), which is also known as the median axis, the symmetrical axis, the skeleton or line skeleton (Straney 1990), has been employed. The medial axis can be defined as "the continuous, branching curve that in some well-defined sense lies in the middle of the outline" (Straney 1990). The method has been applied to the total outline of the human mandible (DeSouza and Houghton 1977; Webber and Blum 1979; Bookstein 1981) as well as, for example, to the symphyseal shape (Daegling 1993). Our preliminary visual observations seemed to suggest that the branch point of the medial axis in the human Correspondence to: K. Koski
Ann Anat (1997) 179: 273-276 © Gustav Fischer Verlag
mandible, i. e., the point where the single axis line of the mandibular body divides into two lines which form the median axes of the condylar and coronoid processes, coincides with the mandibular foramen or lingula. The mandibular nerve has been postulated as an element by which the growing mandible adjusts itself to the surrounding structures, such as, the skull base (Moss and Salentijn 1971), the role of the blood supply in osteogenesis being textbook knowledge and its influence in the growth of the craniofacial structures being well documented (e. g., Schumacher et al. 1988). The sphenomandibular ligament, attached to the lingula, has been seen as a factor limiting the movements of the mandible (Moss 1959). The location of the entrance of the neurovascular bundle serving the body of the mandible, protected by the lingula, is thus unlikely to be a matter of chance. In order to clarify the relationship between the medial axis and the human mandible, a series of radiocephalometric studies and measurements of skeletal material were undertaken, and will be reported here.
Materials and methods 1\vo samples of radiograms were used: 20 lateral cephalometric radiograms of young adult women, 22 to 28 years of age, and 180rthopantomographic films of children (9, girls, 9 boys), S8 years of age. In addition, SO mandibles from late medieval skulls were inspected and measured. The films and specimens were picked in sequence from existing files and from the skull collection at the Institute of Dentistry, University of Thrku. The outlines of the mandibular halves with the clearer image of the two visible ones were traced from the cephalometric films, as were also those of both halves from the orthopantomograms. The location of the lingula was marked on all tracings, together with the beginning of the mandibular canal. Pilot measurements of the skeletal mandibles had revealed that the lingula, as a marker of the mandibular foramen, was approximately symmetrically situated in relation to the dorsal border of the ramus and
the temporal crest. The temporal crest, which was always discernible in the skeletal material and visible as a separate line in most of the cephalograms of the adults and in about half of those of the children, was then identified as the ventral border
of the ramus. Using a template of circles of different sizes (Bookstein 1981; Straney 1990) the center point of the circle touching the borders and the lowest point of the incisura (sigmoid notch) was located and marked on the tracing (Fig. 1). This center point is, by definition, the branch point of the medial axis (Webber and Blum 1979; Bookstein 1981). In the radiograms, the location of the branch point was recorded either as coinciding with or being away from the lingula; in the latter case its distance from the tip of it was measured to the nearest 0.5 mrn. The location of the branch point in the skeletal mandibular left halves was determined by finding, with the help of dial calipers, the point equidistant from the dorsal border of the ramus, the temporal crest, and the lowest point of the incisura (sigmoid notch), i. e., the center of the circle touching the boundaries of the ramus: the branch point (Fig. 2). The total width of the ramus between the dorsal and ventral surfaces was also measured at the level of the branch point (Fig. 2). The width of the ventral flange could then be determined by subtracting the dorsal surface-temporal crest dimension from the total width. These dimensions were measured to the nearest 0.1 mrn. The method errors were tested by double measurement of 25 mandibles, using the formula 1:d2/2n, and were found to be 0.20 and 0.20 mrn, or 0.55 to 0.69% of the mean, for the smaller and larger ramus widths (vide infra) respectively, and were thus acceptable.
vi
Fig. 1. An illustration of the medial axis method as applied to the tracing of an orthopantomographic image of a child mandible. The branch point is the center of the circle which touches the three boundaries of the ramus. The centers of the other circles indicate points on the medial axis and its branches.
Fig. 2. The dimensions measured on dry mandibular halves. Two widths of the ramus, one between the dorsal surface and the temporal crest, the other between the dorsal and ventral surfaces of the ramus, are here shown along the bisector of a circle whose center is the branch point, in this case located on the lingula.
Results In the tracings of cephalometric images of the adult mandibular halves the branch point was found on the lingula in 8/20 instances. Its location in the rest of the sample was within 2.5 mm off the lingula, always towards the incisura. In all but one of the 36 traced orthopantomographic radiographic images of the children's mandibular halves, the branch point was located on the lingula; in one pan tomogram the point was just off the lingula in the mandibular canal. In the skeletal material the findings were as follows: The location of the branch point was found to be on the lingula in the majority of instances. In 17 of the 50 mandibles the point was 0.5-3.0 mm above the lingula. The total width of the ramus averaged 35.5 mm (SD 3.53, range 26.8-42.6 mm). The width between the dorsal surface and the temporal crest, at the level of the tip of the lingula averaged 29.7 mm (SD 2.91, range 23.236.3 mm). The width of the ventral flange of the ramus in front of the temporal crest, was then calculated to average out at 5.8 mm (SD 1.58, range 2.5-8.8 mm).
Discussion The medial axis method is a way of describing a two-dimensional image of an object (which in itself may be, and usually is, three-dimensional) with a simple line figure
274
containing all the necessary information about the shape, but which can be more easily manipulated than the shape itself (Oxnard 1973). Since its introduction (Blum 1967), it has been applied to studies of skeletal and other shapes, usually to their two-dimepsional projections (Oxnard 1973; Souza and Houghton 1977; Webber and Blum 1979; Bookstein 1979). Although computerized methods for determining the medial axis have been developed by many authors, a simple manual method has been stated to give equally reliable results (Straney 1990). We chose to use the manual method, especially since it was easy to apply to the study of skeletal mandibles directly. Cephalometric, orthopantomographic, and direct skeletal findings all essentially confirmed our preliminary observations regarding the location of the medial axis posterior branch point of the mandible at the lingula/ mandibular foramen, provided that the ventral limit of the ramus was set at the temporal crest. This appears justified from the viewpoint of functional anatomy. The flange ventral to the temporal crest which is part of the attachment area of the temporal muscle (Schumacher 1959; Romanes 1964) and quite variable in size, as found even in this study, has been included in the coronoid process (Humphry 1866; Simon and Moss 1973). The coronoid process develops simultaneously with the condylar process during fetal life, but the maintenance of its size and shape in postnatal life depends on the continuing attachment of the temporal muscle, as shown by numerous animal experiments (Washburn 1947; Boyd et al. 1967; Schumacher and Dokhidal 1968; Moss and Meehan 1970). The mandibles of edentulous old people leave hardly any reason to doubt the existence of a similar relationship between the temporal muscle and its attachment area even in the human. The ventral flange may thus not be regarded as a part of the intrinsic coronoid process. The practically invariable location of the branch point in the region of the mandibular foramen/lingula suggests a more than geometric role for the medial axis configuration as a representative of the mandible in the human. It has been postulated that the neural element is of primary importance for the growth of the mandible (Moss and Salentijn 1971; Kjaer 1990); a case of a relatively normal mandibular body without the mandibular foramen and canal described in the literature may be explained by the compensatory function of the mylohyoid nerve (Jakobsen et al. 1991). The allegedly uniform shape, a logarithmic spiral, of the mandibular nerve in the human (Moss and Salentijn 1971) could be interpreted to indicate a kind of neutral position of this nerve in the mandible. As to the blood vessels sharing this neutral position, the situation brings to mind that of the main nutrient artery of long bones (Lacroix 1951; Brookes 1971). Although the posterior part of the mandibular canal has been used as a natural stable landmark in cephalometric studies of mandibular growth (Bjork 1969), the stability of the whole mandibular canal during growth is questionable. A parallelism between the canal and the postulated neutral zone in long bones subjected to stress (Pauwels 1965) remains
an open question. Even a cursory perusal of radiographic images of the mandibular canal reveals that they do not correspond to the medial axes. Nevertheless, the entrance area of the neurovascular bundle, protected by the lingula to which the sphenomandibular ligament attaches itself, may conceivably represent a kind of neutral area in the development and growth of the human mandible. In a comprehensive review of the diversity of the mammalian ramus (Moss 1968), this part was considered to consist of several micro-skeletal units, and the shape and position of the ramus to be independent of the body of the mandible. Interestingly enough, in the figure that illustrates this concept (Moss 1968, Fig. 1), the major skeletal units of the human mandible, the basal, angular, condylar, and coronoid units are depicted as meeting at the approximate level of the mandibular foramen. The line of the sigmoid notch, while depending on the shape and direction of the coronoid process (Simon and Moss 1973), and obviously equally dependent on the condylar process, seems to be rather invariably related to the location of the mandibular foramen. One wonders why the ventral and dorsal borders of the basic ramus and the notch between the two processes are so consistently equidistant from the mandibular foramen/lingula during postnatal growth. The mandibular foramen may be seen as the natural posterior limit for the human mandibular body. This is in line with both the phylogenetic (Colbert 1955; Moore 1981) and ontogenetic records (Low 1909; Arey 1965). During the embryonic period "the original primary centre of ossification produces the body of the mandible as far back as the mandibular foramen; - - -; this is - - the neural element" (Scott and Dixon 1972, p. 433). From that posterior point on, the condylar and coronoid processes, which arise as separate secondary cartilages and join the already ossifying body of the jaw, may be viewed to branching off, each governed by different factors, the one by an articulating function (coupled with cartilaginous growth), the other by muscular forces. This would explain why "only small portion of the ramus is unaccounted for as coronoid process or condyle" (Bookstein 1981). The medial axis configuration in the human mandible appears to reflect the development and functional anatomy of this bone. Acknowledgements. We thank Leena Tuomarila and Janno Koskinen for illustrations, and the anonymous referees for valuable suggestions.
References Arey LB (1965) Developmental Anatomy, 7th ed. WB Saunders, Philadelphia Avis V (1959) The relation of the temporal muscle to the form of the coronoid process. Am J Phys Anthropol17: 99-1004 Bjork A (1969) Prediction of mandibular growth. Am J Orthod 55: 585-599
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Blum H (1967) A transformation for extracting new descriptors of shape. In: W Walthen-Dunn (ed): Models for the perception of speech and visual form. Proc Symp Data Sciences Lab Air Force Cambridge Res Lab, MIT Press, Boston, pp 362-380 Bookstein FL (1979) The line skeleton. Comp Graph Image Proc 11: 123-137 Bookstein FL (1981) Looking at the mandibular growth: some new geometric methods. In: DC Carlson (ed): Craniofacial biology, Monograph No 10, Craniofacial Growth Series, Center for Human Growth and Development, University of Michigan, Ann Arbor, pp 83-103 Brookes M (1971) The Blood Supply of Bone. Butterworths, London Cleaver FH (1937) A contribution to the biometric study of the human mandible. Biometrika 29: 80--112 Colbert EH (1961) Evolution of the Vertebrates. Science Editions, New York Daegling DJ (1993) Shape variation in the mandibular symphysis of apes: an application of a median axis method. Am J Phys Anthropol 91: 505-516 DeSouza PV, Houghton P (1977) Computer location of medial axis. Comp Biomed Res 10: 333-343 Humphry GM (1866) On the growth of jaws. Trans Cambridge Philos Soc XI:1. Cit. Brash JC (1924) The growth of the jaws and palate. In: The Growth of the Jaws, Normal and Abnormal, in Health and Disease. The Dental Board of the United Kingdom, pp 23-66 Jakobsen J, Jorgensen JB, Kjaer I (1991) Tooth and bone development in a Danish medieval mandible with unilateral absence of the mandibular canal. Am J Phys Anthropol 85: 15-23 Kjaer I (1990) Correlated appearance of ossification and nerve tissue in human fetal jaws. J Craniofac Genet Devel Bioi 10: 329-336 Lacroix P (1951) The Organization of Bones. J & A Churchill, London Low A (1909) Further observations on the ossification of the human lower jaw. J Anat 44: 83-95 Luther F (1993) A cephalometric comparison of medieval skulls with a modem population. Eur Orthod J 15: 315-325 Manson JD (1968) A comparative study of the postnatal growth of the mandible. Henry Kimpton, London Moore WJ (1973) An experimental study of the functional components of growth in the rat mandible. Acta Anat 85: 378-385 Moore WJ (1981) The Mammalian Skull. Cambridge University Press, Cambridge
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