Correlation of Types of Cortical Grain Structure with Architectural Features of the Human Skull ’

WILFRID T. DEMPSTER Department of Anatomy, University of Michigan, Ann Arbor, Michigan

ABSTRACT Seven grain-form relationships, as indicated by the split-line patterns, are recognized in the cortical bone of the adult human skull: (1) random pattern of braincase, (2) planes and (3) ridges with elongated grain, (4) troughs with transverse grain, (5) concavities with circular grain, (6) edges, and (7) spines. Con- cavities may show superimposed trough or ridge structure, and troughs may be marked by localized ridges and planes. That is, trough patterns are dominant over concavity patterns, and ridge patterns are dominant over both trough and concaviby patterns. Finally, there are a few small cranial areas that are random distributions in some skulls and planes in others; the skull vault proper, however, except for the forehead region and internal sagittal markings, has a random pattern throughout. The mechanical significance of the various patterns and the areas on which they are found are discussed and explained on the basis of principles of mechanics and architecture. The form-texture relationships are discussed as architectural features of the skull, and their adequacy and limitations are analyzed in terms of their reaction to force systems and their proneness to fracture.

Does the grain structure of cortical ink; instead of round holes, the punctures bone make the human skull stronger or usually produced elongate, ink-marked weaker? An attempt to answer this ques- “split-lines’’ that indicated a grain direction brings to light several unrecognized tion in the organic matrix. They were sim- relationships. Distinctive patterns of grain ilar in appearance to Langer’s (1861) texture are found on the eminences, fos- split-lines of the skin, Hultzkranz’s (1898) sae, processes, and certain other markings split-lines in joint cartilage, Benninghoffs of the adult skull, and similar forms all (’34) split pattern in mucous membrane, over the skull have similar grain patterns. Buhler’s (’34) puncture patterns in laryn- These form-texture relationships at first geal cartilages, and Ilberg’s (’35) punc- sight suggest that some mechanical ad- ture patterns in nasal cartilages. vantage might accrue from the relation- Although Tappen (’53) published pho- ship. This paper, then, (1) examines the tographs showing split-line patterns in an several form-texture relationships to clar- adult human skull, Benninghoff’s original ify the various grain patterns that are re- study, including illustrations of the facial, peatedly found, (2) lists nearly 150 skull lateral, and interior basal regions, is the forms with their characteristic textures to most complete demonstration to date of attest to the generality of the finding, and the grain of the adult skull. Dowgjallo (3) examines the mechanical and archi- (’32) and Seipel (’48) reported more tectural features of these form-texture re- highly detailed split-line studies of the lationships with regard to the weak and mandible. (A study of vascular canals in strong features of skull architecture and the cortex of the mandible - Dempster to fracture mechanics. Finally, the cur- and Enlow, ’59-by an ink injection- rent interpretations of force “trajectories” clearing technique, revealed still more of the skull are criticized. elaborate patterns of 11 tracts.) Bruhnke Forty years ago, Benninghoff (’25) (’29) used the split-line technique on the demonstrated an architectural pattern or horse skull, Henckel (’31) on several “grain” in the fibromatrix of the cortex of mammalian skulls, Tappen (’53, ’54, ’64) several flat bones, including those of the on primate skulls, and Ahrens (’36) on skull. Bones were decalcified in acid and 1 This investigation was entirely supported by Na- punctured with a needle dipped in India tional Science Foundation grant GB-356.

AM. J. ANAT., 120: 7-32. 7 8 WILFRID T. DEMPSTER various child skulls. None of these studies, ately suggested itself. This recognition of however, covers the entire skull or cor- a few recurring patterns was ineffectual relates grain with structural features. until a fresh approach was used. The present study reports a more ex- Three skulls that had been sawed to tensive investigation than others have show the interior of the braincase were made into the grain patterns of the bones first painted neutral grey. Exterior and of the whole skull, excluding the mand- interior surface forms were then marked ible. The split-line technique was used on by painting them different colors, each six complete adult skulls (new commer- color corresponding to a different shape or cial osteological material) and on miscel- form. Initially, the colors were used mere- laneous parts of some damaged discards. ly to distinguish planar regions, elevated The skulls were soaked overnight in 10% (convex) areas, and depressed (concave) formalin to fix the protein constituents; surfaces. Later, further distinctions were then the skulls were decalcified for short made : elongate ridges were considered periods in 5% or 10% HC1. The material apart from domes and saddle-shaped in acid was tested with a needle at inter- areas; troughs were distinguished from vals until the thinnest regions could be circular basins, and so on. Some of the easily punctured. If left too long, exces- finer distinctions proved unnecessary sive decalcification resulted in blurring when the corresponding grain patterns and smudging of the split-lines. A sew- were compared; others, however, were ing needle, mounted in a jeweler’s pin vise consistently correlated with differences in and dipped in India ink, was used to punc- grain patterns. ture the decalcified bone; after each punc- As the split-line skulls were examined, ture, excess ink was wiped away with a seven patterns of grain, corresponding bit of wet cotton wool to avoid indiscrim- with seven skull forms, emerged as appar- inate staining. After the thin areas had ently the most basic. These seven pat- been treated, the skulls were returned to terns included almost all the surface of the acid for further decalcification of the the skull. Many of the forms in the seven thicker areas; these areas were then punc- categories of the new grouping have stan- tured as above, with little deterioration of dard anatomical names, but there are the split-lines in thin areas. others that have no specific names. Best results were obtained when the Since the new grouping of seven forms, specimens were decalcified in a buffer each with a specific grain pattern, applies mixture of formic acid (8N) and sodium to so many forms, both named and un- formate (1s).Most of the material was named, it will be important to develop a stored in 80% alcohol and could be pho- new terminology in which both form and tographed after draining. Other material texture are indicated, a terminology that was allowed to dry slowly and thoroughly cannot be confused with standard ana- to produce hard, and somewhat shrunken, t omical nomenclature. dry specimens. The latter could be han- The seven form-texture types are dia- dled and demonstrated more easily than grammed in figure 3; the illustration also the specimens stored in alcohol. includes an eighth type to be treated separ- ately. Each has a name and a code letter FORMS AND TEXTURE that will identify patterns in the photo- The three drawings of figure 1 show graphic illustrations. In the following dis- most of the formations of the skull. Figure cussion of these types, conventional ana- 2 shows the same views with a superim- tomical terms such as “eminence,” “crest,” posed grain pattern based on the foregoing and “fossa” are avoided, since they are material. However, before these summary generalized descriptive terms that apply drawings could be made, a number of equally to bones, viscera, and surface skull specimens marked with split-lines anatomy. The present need, rather, is for had to be examined. Although careful terms relating specifically to bone struc- study showed that certain form and texture and denoting both the physical forms ture relationships recurred in different and the grain architecture associated with regions, no clue to interpretation immedi- each. Thus, “ridge” and “trough” will be CORTICAL GRAIN AND SKULL ARCHITECTURE 9

Fig. 1 Three views of the adult skull showing by shading the principal forms, apart from those of the nasal cavity. A, intact skull; B, right zygomatic arch cut away; C, much of left side of cranial vault removed to show interior. used to designate both the specific forms tions, or saddle-shaped elevations. These they describe and the underlying micro- forms may lie on either plane or moderate- organization of the forms. ly curved surfaces. In each instance, the B, Braincase cortex (fig. 3) shows a dis- grain direction shown by split-lines runs persed pattern of random lines. This pat- parallel to the less convex axis of an eleva- tern is found on both convex and concave tion; that is, parallel to the crest of the surfaces that have relatively large radii of curvature; for example, in most of the ridge. The grain runs parallel to the ridge exterior and interior of the skull vault. whether the top of the ridge is straight, P, Plane surfaces show either a par- convex, concave, or sigmoid - but the allel grain or, in triangular areas, a radi- grain is always perpendicular to that cross ating, fanlike pattern of grain. section of the ridge having the smallest R, Ridges and crests show the most radius of curvature. (This is true even for clearly expressed pattern. They may be the occipital condyle, as shown in figs. 2, plano-convex elevations (like the “barrel 5, where the ridge lies obliquely across arches” of architecture), elliptical eleva- the length of the condyle.) 10 WILFRID T. DEMPSTER

Fig. 2 The same three views of the skull showing the common texture pattern of the cortical bone-as revealed by split-lines.

T, Troughs are elongate, shallow transverse pattern of split-lines character- trenches having a transverse grain; their istic of troughs: this suggests that the margins, however, often show elongate trough pattern is dominant to the con- ridge patterns. Some troughs are elongate cavity pattern. Again, minor ridges run- plano-concave depressions. Others are ning through a concavity show the elon- doubly concave, and here the radius of gate ridge pattern that seems to be dom- curvature is markedly different for the inant to both the trough and concavity two axes. A minor ridge within a trough patterns. will show the characteristic elongate ridge E, Unsupported free edges such as pattern, and the interrupted transverse flanges, fins, and margins of thin foramina trough pattern will show on one or both have a simple pattern of grain that par- sides of the ridge. This suggests that the allels the free edge. ridge pattern is in some sense “dominant” S, Spines, hooks, and sharp processes to the trough pattern. have a grain pattern that follows the shape C, Concavities are basin-like depres- of the part and converges to an apex. sions with an irregular series of concentric A final, eighth category, D, Disconti- circles, whorls, or spirals of grain pat- nuities is, to some extent, a convenient tern. If the concavity is elongate, so that catchall for miscellaneous forms, an es- its deepest part is like a trough, the base sential one, however, for a balanced dis- of the concavity will be marked by the cussion of skull mechanics. In each of CORTICAL GRAIN AND SKULL ARCHITECTURE 11 the foregoing seven forms, grain is related are distinguished) were studied. The in a rather specific way that is suggestive grain patterns are those of fully adult of some structural significance. Discon- skulls. Growth patterns with markedly tinuities, in some instances, are merely a different textures predominate in the combination of edges and spines, already fetus, infant, and child (Ahrens, '36); listed, together with foramina and sharp these patterns usually radiate from ossifi- grooves. Although about 50 disconti- cation centers. In time, specializations of nuities are listed below, their character- form and texture give rise to definitive istics can best be considered in a later part adult patterns. A certain amount of vari- of this paper. ability is found: concavities in one specimen may show as troughs in another, or A classification of form-textures small plane areas of one specimen may of the skull show as a random pattern in the next; the With this introduction to the different pattern common to one area may encroach categories of form and texture relation- on an adjacent one; an infantile pattern ships in the skull, a classification of the may persist in a localized region. How- principal forms of the skull will be given. ever, most forms are found consistently, This will demonstrate how inclusive the and extreme variations are rare. The fol- relations are. In deriving this catalog of lowing classification arbitrarily lists pat- forms, from six to ten specimens (or near- terns that appear to be most common, and ly double these numbers if rights and lefts only a few variants are mentioned. Re-

BRAINCASE PLANE

Fig. 3 Diagrams of eight form-textures with their predominant grain direction. All but the last have a characteristic grain pattern. With each sketch is a name and a code letter. 12 WILFRID T. DEMPSTER presentative illustrations of the texture in tions of ridges and spines, and figure 6 different regions will also testify to the shows where troughs and edges are found. fact that anatomical structures in the skull The capital letters at the head of each do have a specified form and texture. Fol- category are the code letters used in label- lowing the classification, this paper dis- ing the photographs. The figure numbers cusses the associated forms and textural in parenthesis after the name of each part arrangements in terrns of their architec- refer to figures that illustrate the texture tural or mechanical implications. involved. If a structure illustrated in a Most features of the skull surface are photograph is labelled with a code letter, classified below with regard to both the that letter in brackets follows the figure form and the direction of the grain texture number, as: (fig. 7 [Cl). of the cortical bone. Figure 4 illustrates the B - BRAINCASE (figs. 2A, 2B, 2c, 3,4) : principal regions of the skull surface that the random pattern found in most of the show random braincase structure, planes, skull vault externally between the frontal and concavities. Figure 5 shows the loca- eminences and the superior nuchal line,

Fig. 4 Areas of the skull surface occupied by braincase texture, B; and by planes, P. The code numbers P1, P2, and so on correspond to the list of planes in the text. CORTICAL GRAIN AND SKULL ARCHITECTURE 13 extending laterally into the temporal fos- frontal process of maxillae, usually a sae; the interior of the skull vault except saddle-shaped ridge (figs. 2A, 5A [51, 8 BI). in the sagittal crests and fossae; also in 6. Lacrimal crest and adjacent slopes of the localized areas of the anterior and middle bone (fig. 2A, 5A [S]). cranial fossae of the base of the skull (figs. 7. The whole alveolar part of the maxilla, 4 [CI, 8 PI, 10 [BI). below the nasal aperture from the region P - PLANESand relatively flat surfaces of the first and second molar teeth on the side across the midline to the opposite (figs. 3,4): side (figs. 2A, 5A [71, 8 [RI). I. Exterior of the skull. 8. Posterolateral aspect of the body of the maxilla, anterior and parallel to the 1. Supraglabellar plane showing transverse pterygopalatine fissure (figs. 2B, 5B [81). grain (fig. 2A) above and between the superciliary arches; sometimes a random 9. Lower part, external face of the body of braincase pattern (fig. 4). the zygomatic bone, from the maxillary process to the temporal process (figs. 2A, 2. Frontal process of zygoma, superficial rl r-7, surface (figs. 2A, 2B, 8). LYJ I. 3. Triangular area anterior to superior tem- 10. Crest of maxilla between lower part of poral line, partly superior to lateral orbi- the zygomatic process and first and sec- tal margin (figs. 2A, 8 [PI). ond molar teeth (figs. 2A, 2B, 5A [lo], 4. Maxilla forming floor of the orbit, some- 8 [Rl). times random braincase pattern (fig. 11. Outer surface of zygomatic process of 2A). temporal bone (figs. 2A, 5A t111, 8 IRI, 5. Orbital surface of the ethmoid bone (fig. 11 [RI). 2A). 12. Articular tubercle of temporal bone along 6. Orbital surface of the greater wing of its whole width - a saddle-shaped ridge the sphenoid bone (fig. 2A). (figs. 2B, 9 [Rl). 7. Nasofrontal process and body of maxilla 13. Lateral surface of mastoid process-a between margins of orbit and piriform vertical ridge (figs. 2A, 2B, 2C, 11 [Rl). aperture (fig. 2A). 14. Ridge at lower border of zygomatic root, 8. Posteromedial part of the hard palate, superior to external acoustic meatus, palatine, and maxillary bones (figs. 2B, from postglenoid tubercle to mastoid 9 [PI). process (figs. 2B, 11). 9. Perpendicular plate of vomer (figs. 2A, 15. Transverse ridge - sometimes a plane 2B). area - on inferior surface of greater 10. Perpendicular plate of ethmoid bone (no sphenoid wing, anterior to the foramen fig. ) . ovale and between the base of the lateral 11. Interior surface of the cranial cavity. pterygoid lamina and the articular eminence (figs. 2B, 9). 1. Superior surface of the lesser wings of 16. Basal surface of petrous part of the tem- the sphenoid bone; the plane between the poral bone anterior to the carotid canal two lesser wings (figs. 2C, 10 [PI). (figs. 2B, 9). 2. Dorsum sellae (fig. 2C). 3. That portion of the petrous part of the 17. Basilar part of occipital and sphenoid temporal bone between its posterior mar- bones, between the vomer and the crest gin and the aqueductus vestibuli (fig. of the anterior margin of the foramen 2C). magnum (figs. 2B, 9 [Rl). 4. Localized areas of the sphenoid, tempo- 18. Articular surfaces of the occipital con- ral, and parietal bones in the lateral part dyles; grain runs obliquely across the of the skull vault (fig. 2C). narrow dimension in a mediolateral direction (figs. 2B, 9 [RI). R -RIDGES AND CRESTS (figs. 3, 5) : 19. Anterior margin of foramen magnum and anterior condylar crest (figs. 2B, 9). I. Exterior of the skull. 20. Lateral postcondylar and posterior mar- 1. Area across frontal bone between right gins of foramen magnum (fig. 2B). and left frontal eminences (figs. 2A, 21. Superior, inferior, and medial nuchal 5A 111). lines (fig. 2B). 2. Superciliary arches (figs. 2A, 5A [21). 22. Ridge between groove for occipital artery 3. Superior orbital margin from fronto- and digastric fossa; juxtamastoid emi- sphenoidal process of the zygomatic bone nence, Taxman, ('63) (no fig.). to supraorbital notch; also from the notch to the nasal process of the maxilla (figs. 11. Interior of the cranial cavity. 2A, 5A [31). 1. Frontal crest anterior to the crista galli 4. Portion of the inferior and lateral mar- and foramen cecum; also, continuing gin of the orbit formed by the zygomatic ridges at the right and left of the sulcus bone (figs. 2A, 5A [41, 8 [HI). for the superior sagittal sinus, especially 5. Bridge of nose and facial surfaces of on the frontal and occipital bones (fig. nasal bones, extending to adjacent naso- 2C). 14 WILFRID T. DEMPSTER

Fig. 5 Areas of the skull surface occupied by ridge form-textures - R. Numbers correspond to the list of ridges in the text.

2. Ridges, usually longitudinal, between the 9. Posterior face of the petrous part of the digital fossae of the orbitobasal plate of temporal bone, superior to the aqueduc- the frontal bone (figs. 2C, 10 IR]). tus vestibuli (fig. 2C). 3. Transverse ridge anterior to chiasmatic 10. Ridge posterior to the sigmoid sulcus groove, joining anterior clinoid processes (fig. 2C). (figs. 2c, 10). 11. Ridges above and below the sulcus for 4. Tuberculum sellae, transverse pattern the transverse sinus (fig. 2C). between chiasmatic groove and hypo- 12. Median sagittal crest between right and physeal fossa (figs. 2C, 10 [R]). left cerebellar fossae (fig. 2C). 5. Parasagittal ridges on sphenoid body be- 13. Crest between the right and left posterior tween the floor of the sella turcica and cerebral fossae (fig. 2C). the carotid grooves (fig. 2C). 14. Minor ridges in the floor of the cerebellar 6. Ridges between digital fossae of the fossae, inconstant (fig. 2C). middle cranial fossa (figs. 2C, 10). 7. Ridges along the length of the anterior (Commentary: as in Langer's (1861) split- surface of the petrous part of the tem- lines in skin, three texture tracts associated with poral bone, including the arcuate emi- ridges and planes will merge, two by two, to nence (figs. 2C, lO[Rl). form a triradiate pattern with a tiny triangular 8. Ridges on the superior margin of the area or node at the focus. These are shown as petrous bone, bordering the superior black trigones in figure 2 as follows: figure 2A, petrosal sinus (figs. 2C, lo). (1) on the maxilla medial to the infraorbital CORTICAL GRAIN AND SKULL ARCHITECTURE 15 foramen, (2) on the anterior face of the zygo- 2. Posterior surface of the body and frontal matic process of the maxilla, and (3) on the ex- process of the zygomatic bone (bound- ternal surface of the zygoma at the junction of ing the temporal fossa) ; trough pattern, the frontal process with the body; figure 2B, the both above and below the level of the exterior basal aspect of the skull in the mid- infraorbital fissure (figs. 2A, 2B, 2C, sagittal planes: (1) on the basal part of the 6A IT21, 8 IT1 1. occipital bone anterior to the foramen magnum, 3. Groove on the upper surface of the junc- and (2) on the occipital squama posterior to the tion of the anterior root of the zygomatic foramen magnum; figure 2C, on the interior of arch with the adjacent squama of the the skull, on the midline, posterior to the fora- temporal bone - the groove acts as a men magnum.) pulley for the posteriormost fascicles of the temporalis muscle (figs. 2C, 11 [TI). 4. Infratempord fossa between lateral ptery- T - TROUGHS,grooves, furrow, gutters, goid wing and infratemporal crest (figs. or trenches (figs. 3,6): 26 9 [TI). 5. Gutters on the palate between the palatal I. Exterior of the skull. and alveolar processes of the maxilla - 1. Walls of the nasolacrimal canal proper, the anterior and superolateral arches of but not the continuous nasolacrimal the palatal vault (figs. 2B, 9 [TI). fossa of the lacrimal bone anterior to 6. Roof of the nasal cavity between the the lacrimal crest (no fig.). vomer bone and the medial pterygoid

Fig. 6 Areas of the skull surface with the form and textures of troughs - T, and spines - S. The troughs are numbered T1, T2, and so on to correspond to the list of troughs. The other numbers refer to spines as listed. 16 WILFRID T. DEMPSTER

plate and vertical part of the palatal 11. Interior of the cranial cavity. bone (fig. 2B). 1. The deeper digital fossae at the antero- 7. Inferior part of pterygoid fossa; trans- lateral margins of the anterior cranial verse grain across fossa (fig. 2B); grain fossa (figs. 2C, 10 [C]). aattern in suwrior uart of the fossa is 2. Floor of hypophyseal fossa (fig. 2C), partly or wholly that of a concavity (C) sometimes a transverse trough with an (figs. 2B, 9 [Cl). anteroposterior grain (fig. 10 [TI). 8. Inferolateral border of the floor of the 3. Superior concave surface of the greater nasal cavity (no fig.). wing of the sphenoid bone near the su- 9. Posterior digastric fossa (fig. 2B). perior orbital fissure - contacts the an- 10. Concave wall of the carotid canal (fig. terior pole of the temporal lobe (figs. 2C, 2B). 10 [CI ). Interior of the cranial cavity. 4. Cerebellar fossa of the posterior cranial 11. fossa - often crossed by a trough or 1. Hypophyseal fossa (fig. 10 [TI); some- ridge (fig. 2C). times the posterior portion or the whole 5. About 2 cm of the sigmoid sulcus near- is a concavity (C) (figs. 2C, 9). est the jugular foramen, below the over- 2. Wall of carotid canal and of the carotid hanging rear border of the petrous part groove on the body of the sphenoid bone of the temporal bone (fig. 2C). lateral to the sella turcica (figs. 2C, 10). 3. Grain tracts on lowest part of the clivus near the foramen magnum from the E - EDGES, thin flangelike or finlike medial side of one condyle to the other plates, or keels with unsupported free (figs. 2C, 10); aIthough most of the edges (figs. 3, 7): clivus to the dorsum sellae is concave, ridge tracts from the sides of the fora- I. Exterior of the skull. men magnum above the hypoglossal 1. Lateral margin of nasal (piriform) aper- canals converge to form a dominant ture on the face bounded by the maxil- ridge-type sagittal pattern of grain. The lae, but not including the free ends of dorsum sellae proper has a plane struc- the nasal bones (figs. 2A, 2B, 7A 111). ture; its upper margin shows an edge 2. Buccal and lingual alveolar margins - pattern, and the posterior clinoid proc- buccal grain tract - thin in the incisor- esses are spines. bicuspid region and wider in the molar 4. Transverse and sigmoid sulci, except in region; wider in the lingual than in the the region nearest the jugular foramen buccal region, especially posteriorly; buc- (fig. 2C). cal and lingual tracts are continuous behind last molar tooth (figs. 2A, 2B, C - CONCAVITIES,concave depressions, 7A 121, 7B, 8 [El, 9.[El). rounded fossae, bowls, or basins (figs. 3. Free margins of medlal and lateral ptery- 2,7): goid laminae of sphenoid bone (figs. 2A, 2B.~. 9). I. Exterior of the skull. 4. Posterior margin of palatal process of 1. Lacrimal fossa in the suoeriorlateral or- palatine bone (figs. 2B, 9 [El). bital roof (fig. 2A). 5. Posterior margin of the vertical plate of 2. The facial surface of the maxilla inferior the vomer bone (fig. 2B). to the infraorbital foramen (figs. 2A, 6. Anterior, superior, and lower margins of 7A [CZl). infraorbital fissure (figs. 2B, 9 [El). 3. Canine fossa, inconstant (no fig.). 7. Anterior border of the bony nasal septum 4. Variable fossae in the anterior part of - ethmoid, vomer (fig. 2A). the palatal arch between the alveolar 8. Margins of foramina with thin borders process, at the cuspid or bicuspid tooth, (as foramen ovale); in oblique foramina

and the midline (figs. 2B., 9 IC1).- _, (as internal acoustic meatus and infra- 5. Upper part of the pterygoid fossa (figs. orbital foramen), one side of the fora- 2B, 9ICl). men has a specialized margin (figs. 2A, 6. Mandibular fossa of temporal bone, 2B, 2C, 9 [El). sometimes troughlike (fig. 2B). 9. Free edge of lateral wall of the naso- 7. Bilateral areas on the inferior surface of lacrimal canal (no fig.). the basilar process of the occipital bone, 10. Free margins of the nasal conchae (no anterior to the roots of the occipital con- fig.). dyles, inconstant (no fig.). 8. Fossa of the posterior condyloid canal 11. In terior of the cranial cavity. (fig. 2B). 1. Margins of crista galli, ethmoid (fig. 2C). 9. Concave anterior wall of jugular fossa 2. Posterior border of lesser wing of sphe- (fig. 2B). noid, lateral to the anterior clinoid proc- 10. Fossae on the base of the occipital squa- ess (figs. 2C, 10 [El). ma for muscular attachment of sub- 3. Lower, outer margin of superior orbital occipital and semispinalis capitis mm fissure - greater wing of sphenoid (fig. (fig. 2B). 2C). CORTICAL GRAIN AND SKULL ARCHITECTURE 17

Fig. 7 Areas occupied by edges-E (heavy black lines) and by concavities-C (concentric circles). The edges are designated by numbers corresponding to the list of forms. The concavities are coded C1, C2, and so on.

4. Margins of foramina with thin edges, as 11. Interior of the skull. foramina ovale, (fig. 2C) and cf. 1-8, 1. Anterior clinoid process (figs. 2C, 10 [S]). above. 2. Posterior clinoid process (fig. 2C). 3. Apex, petrous part of temporal bone (figs. S - SPINES, hooks, or sharp processes 2c, 10 [S]). (figs. 3, 6): D - DISCONTINUITIES: sharp edges, I. Exterior of the skull. holes, or foramina; projections; surfaces 1. Anterior nasal spine, maxillae (figs. 2A, meeting at sharp angles : the following list 6A 111). in part includes structures of the previous 2. Posterior nasal spine, palatine bones list when sharp breaks in surface continu- (figs. 2B, 9 IS]). ity or irregular congeries of forms are close 3. Pterygoid hamulus (fig. 2B). together. The discontinuities listed below 4. Spine of angle, sphenoid (fig. 2B). are not specifically identified in the illus- 5. Styloid process, temporal bone (fig. 2B). trations (fig. 3): 6. Spine of vaginal process, tympanic bone (fig. 2B). I. Exterio~of the skull. 7. Spine of infratemporal crest, sphenoid 1. Supraorbital notch or foramen (figs. lA, (fig. 2B). 2A). 18 WILFRID T. DEMPSTER

Fig. 8 Photograph of the facial view of a decalcified skull with split-lines. Code: B- braincase, C - concavity, E - edge, P - plane, R - ridge, S - spine, and T - trough.

Fig. 9 Photograph of split-line preparation of anterior-basal region of the skull. Code: C - concavity, E - edge, P - plane, R - ridge, S - spine, T - trough. Fig. 10 Photograph of a split-line preparation of anterior portion of interior-basal aspect of the skull. Code: B - braincase, C - concavity, E - edge, P - plane, R - ridge, and T - trough.

Fig. 11 Photograph of lateral aspect of temporal bone, split-line preparation. Code: B- braincase, E - edge, P -plane, R -ridge, and T - trough. 20 WILFRID T. DEMPSTER

2. Lacrimal crest and anterior margin of 27. Hypoglossal canal (no fig.). the 1acrimaI sulcus (figs. lA, 2A). 28. Posterior condyloid foramen (figs. lB, 3. Thin bone of the ethmoid bone; air cells 2B). and partitions; ethmoidal foramina (figs. 29. Mastoid foramen, especially anterior lA, 2A, 7). border (figs. lB, 2B). 4. Sharp borders of the infraorbital groove 30. Foramen ovale (figs. lB, 2B, 9). and fissure (figs. lB, 2B, 7, 8). 31. Foramen spinosum (figs, lB, 2B). 5. Inferior border of supraorbital fissure 32. Thin posteriormost portion of foramen (figs. lA, 2A). magnum (figs. lB, 2B, lC, 2C). 6. Sharp margin, superior and lateral bor- 33. Region of anterior palatal foramen; pal- ders of the orbital aditus from the supra- atal crest (fig. 1B). orbital notch laterally to the midlevel of 34. Foramen lacerum (figs. lB, 2B). the frontal process of the zygoma (figs. 35. Conchae and markings on the lateral 2A, 7). walI of the nasal cavity (figs. lA, 2A). 7. Superior margin of the infraorbital foramen (figs. lA, 2A, 7). 11. In terior of the cranial cavity. 8. Sharp edge bordering nasal aperture, 1. Free edge of crista galli (figs. lC, 2C). from nasal bones to anterior nasal spine 2. Foramen caecum (no fig.). (figs. lA, 2A, 7). 3. Cribriform plate and olfactory foramina 9. Margins of the tooth sockets (fig. 8). of ethmoid bone (figs. lC, 2C, 10). 10. Posterior margin of the incisive fora- 4. Posterior border of lesser wing of sphe- men (figs. lB, 2B, 9). noid (figs. lC, 2C, 10). 11. Posterior border of palatine bone from 5. Superior and postero-inferior margin of posterior nasal spine to pyramidal pro- optic canal (no fig.). cess of palatine bone (figs. lB, 2B, 9). 6. Edges of posterior clinoid process and 12. Posterior border of vomer bone; also ar- adjacent edges of dorsum sellae (figs. ticulation with sphenoid bone (figs. lB, lC, 2c, 10). 2B). 7. General region of sphenoid body bounded 13. Posterior edge of medial pterygoid plate by superior orbital fissure, foramen ro- (figs. lB, 2B, 9). tundum, foramen ovale, foramen spino- 14. Inferior and posterior edges of lateral sum, and intracranial carotid canal (figs. pterygoid lamina; pterygoid spine of lC, 2c, 10). Civinini (figs. lB, 2B, 9). 8. Sharp edges of hiatus of facial canal 15. The crest separating scaphoid from (figs. lC, 2C). pterygoid fossae (no fig.). 9. Posterior border of internal acoustic 16. Sharp margins of the spine of the angle meatus (figs. lC, 2C). of the sphenoid bone (figs. lB, 2B). 10. Superior margins of aqueductus vesti- 17. Infratemporal crest and spine (fig. 2B). buli (no fig.). 18. Keel at anterior edge of pterygoid pro- 11. Posterior sharp border of petrous part cess bordering pterygopalatine fossa (no of the temporal bone from apex to lateral fig.). terminus in the sigmoid sulcus (figs. 19. Sharp superior border of zygomatic arch; lC, 2C). also the continuous acute posterior bor- 12. Junction with sigmoid sulcus of mastoid der of the frontal process of the zygoma, foramen and posterior condyloid fora- including the angular process and the men (figs. lC, 2C). continuation to the frontal bone as the 13. The grooves for the middle meningeal anterior part of the superior temporal artery (no fig.). line (figs. lA, 2A, 7). 20. Free margin of the tympanic bone at Although the foregoing classification the external acoustic meatus; also con- covers most of the skull surface, certain tinuing sharp edge behind the postglenoid tubercle (figs. lA, lB, 2A, 2B). regions are not included, such as the laby- 21. Miscellaneous irregular edges for ten- rinth and tympanic cavity of the temporal dinous attachment (masseter m.), along bone, the paranasal sinuses, and details the lower border of the zygomatic arch of the nasal cavity. The reason in some and on the outer border of the mandibular fossa (figs. lB, 2B). cases was simply that not enough skulls 22. Lower free edge of tympanic plate in- were examined to permit definitive char- cluding the vaginal process (figs. lB, acterization of the features involved. In 2B). other instances, regions of very thin bone, 23. Inferior edge of the carotid canal (figs. lB, 2B). such as the ethmoid bone, after being 24. Inferior edge of jugular foramen; also cleaned and bleached, did not withstand vertical crest on anterior wall of the even moderate decalcification. When a jugular fossa (figs. lB, 2B). few split-lines were produced in very thin 25. foramen (figs. lB>2B). 26. Anteromedial, anterior, and lateral edges bone, they often deteriorated from further of articular surface of the occipital con- decalcification of surrounding thicker dyle (figs. lB, 2B). bony regions or from storage in alcohol. CORTICAL GRAIN AND SKULL ARCHITECTURE 21

Cortical grain and bone properties in compression, the ratio of ultimate The tendency of decalcified cortical strengths being roughly three to five. bone to split in a specific direction when The foregoing findings imply that a cor- punctured is a distinctive property of the tical surface with a dominant grain pattern, which might be revealed by split- bony matrix; although articular surfaces lines or other techniques (decalcified and minor localized areas of long bones microscopic sections, ground sections, vas- may show round holes rather than splits, cular canal injection, or microradiog- this response in the skull-as may be raphy ) , withstands indenting pressures found at the summit of the frontal emin- and impacts better lengthwise than cross- ence - is exceptional. This results from wise. Grain direction thus becomes a fac- the fact that grain patterns are intimately tor - hitherto unrecognized - that influ- related to the orientation of the microscop- ences the initial response of the skull, or ic components of the osseous tissue. It was other bone, when it fractures. Benninghoff ('25) and Seipel ('48) who first showed that the direction of split-lines cor- Skull architectonics relates closely with the predominant direc- The problem of skull strength in relation of the fibrous tissue of the lamellae tion to environmental forces depends on of the bone, as in the Haversian systems. several different, though related, consider- A needle penetrating decalcified bone acts ations: (1) the physical characteristics of like a wedge and splits the matrix a short bone (including stiffness, yield strength, distance in the direction of least strength. and ultimate strength in tension, compres- Qlivo, Maj, and Toajari ('37) emphasize sion, and shear); (2) the force systems that although decalcified bone and intact that can act on the skull, including mag- bone have different properties, the pre- nitude and manner of application; and (3) dominant direction of split-lines in decal- the architectural features of the skull, in- cified bone correlates with the direction of cluding the quantity of bone in different greatest strength in intact bone. Tensile regions, the form of the different parts tests of single osteons (Haversian systems) (with concern for discontinuities), and by Ascenzi and Bonucci ('64) show that the direction of grain in each structure. the strongest osteons are those in which The type of response - for example, safe the fibrous bundles of successive lamellae transmission of forces, puncturing, chip- are arranged longitudinally rather than in ping, shearing, and so on -is entirely de- a strongly oblique (45") direction, and pendent on these three considerations. moreover, that the degree of natural cal- A number of the general physical cification and the action of chemical de- properties of bones as a material have calcifying agents are of limited influence been summarized (Evans, '57). Probably on the ultimate tensile strength of osteons. most important is the fact that the ulti- After testing pieces of femoral and mate compressive strength of human bone humeral cortex, Dempster and Liddicoat is about 25,000 PSI (pounds per square ('52) show that both the ultimate com- inch) in relation to an ultimate tensile pressive strength and the modulus of elas- strength of about 15,000 PSI; thus, bone ticity (stiffness) in compression, as in is more likely to be damaged by tensile wood, are greater along than across the failure than by compressive failure grain. Dempster and Coleman ('61), (Dempster and Liddicoat, '52). Secondly, using both bending and tensile tests, the tensile strength across the grain is demonstrate that tibia1 bone, mandibular much less the strength along the grain bone, and wood are all notably stronger (Dempster and Coleman, '61 ). in resisting deformations along rather The other two factors affecting strength than across the grain. Evans ('64) shows - force systems and architectural consid- the mean tensile strength of embalmed erations - must be discussed more fully wet cortical bone from tibiae is signifi- if the overall problem of skull strength is cantly greater than that from femora. to be understood. Many tests along the grain show that cor- Force systems on the skull. The head tical bone is much weaker in tension than and skull are subject to at least three types 22 WILFRID T. DEMPSTER of force systems. First, the skull acts as a tem of the proper kind and sufficient mag- container for the brain and other cranial nitude. contents, for the eye and orbital contents, A fracture in response to applied forces for the components of the inner and mid- must start at a particular millisecond of dle ear, and for the tongue mass. In a time at some localized area on the sur- static gravitational system, these parts, face of the cortical layer of bone and like a fluid, exert forces against certain spread from this point to produce a chip, containing bony walls. Under the influ- large cleavage, crushed area, or com- ence of rapid acceleration of centrifugal minuted fracture. In order to evaluate force acting on the head, or of impacts be- the cortical forms that were classified tween the head and other objects, the di- earlier, it will be necessary to examine rections of these container forces will some simple models of force systems on change, and the magnitudes of the forces beams, plates, and shells. may exceed the usual gravitational level Mechanics of cortical bone. Figure 12A for short periods. Such container forces introduces the basic mechanics of a de- are chiefly from the inside out, to be re- forming force (upper arrow) acting on a horizontal beam supported at each end. sisted by the containing bony surface. The total downward force (including the A second set of forces on the skull is weight of the beam) will be equaled by the intrinsic system of tensile and com- the sum of the two resisting forces. Part pressive forces associated with muscles, of the middle downward force in relation joints, and teeth. Muscle tensions are to the right end force tends to rotate the exerted on the exterior of the skull by the right half of the beam in a counterclock- neck muscles to the occipital and temporal wise direction; similarly, the middle down- bones and by the occlusal group of the ward and left end forces tend to rotate masticatory muscles. Other muscles (e.g., the left half in a clockwise direction. Each buccinator, superior pharyngeal constric- of these force arrangements is called a tor) exert lesser forces. Equal and op- force couple and the measure of its tend- posite compressive forces arise in reaction ency to bend is its moment or torque; in to the muscle tensions; for example, the the figure, the moments are designated by action of the atlas bone on the occipital the letter M and the curved arrows. The condyles and the forces on the teeth and amount the beam bends downward under on the temporomandibular joint. the influence of the two force couples de- Other forces, of an extrinsic nature, can pends on its stiffness. These force couples impinge on the exterior of the skull. Ex- shorten or compress the upper surface of amples of static loads on the skull and the beam as indicated by the arrows head such as bindings are rather special. (c = compression) and stretches the lower Impacts, however, are common. They may surface (t = tension); but the middle be caused, of course, by falls, blows of all plane of the beam (the neutral plane = sorts, collisions as with the dashboard of N. Pl.) retains its normal length. a decelerating automobile), bullets and If the beam in figure 12A were a bar of projectiles, and so on. When the head and cortical bone under a deforming force body form a battering ram, as in football, system having a magnitude that exceeded in bodies ejected to the ground from an the yield strength of the bone, a fracture automobile, or in diving accidents, the due to excessive force would be a tension crown of the head makes the impact but failure, since the ultimate tensile strength the vertebral column may also carry the of bone is only about 60% of the ultimate body inertia into the skull base. compressive strength (Dempster and Cole- The effect of any force on bone will be man, '61; Evans, '57). Thus, a fracture to bend the bone, to stretch it, compact it, would begin on the convex surface and cause it to shear, or some combination of spread toward the concave side as a deep- these types of deformation. The great ening split. variety of skull fractures reported in clin- Figures 12B and 12C show broad plates ical literature suggests that every skull of cortical bone instead of a narrow beam, bone can fail if subjected to a force sys- resting on two supports near opposite CORTICAL GRAIN AND SKULL ARCHITECTURE 23

Fig. 12 Force patterns on thin plates with resultant deformations. A: A section through a plate resting on two supports with a deforming load at its middle. N.P1., the neutral plane with short- ened (c - compressed) material on the concave side and elongated (t - tensed) material on the convex side. The curved arrows (M) imply bending moments. B: A plate with a lengthwise grain spanning the supports. C: A cortical plate of bone having grain oriented crosswise to the first is notably weaker to bending loads. D: A thin plate of indeterminate dimensions resting on an elastic substrate, as diploe. A concentrated deforming force, just short of a breaking force, is resisted over a wide area by the substrate. Inward bending moments about the deforming compressive force tend to cause a depressed deformation with a compressed (c) and tensed (t) side. Compensatory outward bending moments with reversed compressed and tensed deformations appear at a distance. edges; neglecting the weight of the plate In fact, the experiments of Dempster in each case, the downward force (wedge and Coleman ('61) showed clearly that and arrow) across the middle is exactly plates of tibial and mandibular bone (and balanced by the sum of the opposite up- birchwood) subjected to bending force ward forces (arrows). The bending mo- systems are indeed much stronger in the ments, the neutral plane, and the com- lengthwise direction of the grain (as in pressive (c) and tensile (t) forces are fig. 12B) than in the crosswise direction similar to those of the beam (fig. 12A). (as in fig. 12C). In these studies, dry In figure 12B, the length of the middle specimens of tibial cortex, mandibular wedge is perpendicular to the grain of the cortex, and birchwood showed ultimate bone; this force system causes bending bending strengths crosswise to the grain along (parallel to) the grain. In figure (as in fig. 12C), that, in whole numbers, 12C, the wedge is parallel to the grain; were only 17%, 43%, and 8%, respec- this system causes bending across (per- tively of the parallel-to-grain (fig. 12B) pendicular to) the grain. Practical ex- strength. The crosswise strength of water- perience with wood suggests that the plate soaked tibial pieces - more like fresh in 12B is less likely to split under a given bone - was also 17% of the parallel-to- force than that in 12C, since resistance to grain strength shown by wet pieces. bending along the grain (fig. 12B) is Mechanics of cortical bone in the greater than resistance to bending across skull. The skull, of course, is not formed the grain (fig. 12C). of simple machined plates of cortical bone. 24 WILFRID T. DEMPSTER

Most of the cranial and facial parts of the forces. If the surface being considered skull have inner and outer cortical bone has a parallel grain pattern, an elliptical and a middle layer of spongiosa or diploe. deformation or failure should be produced. Air sinuses and pneumatic bone are also This woud be true for plane areas (P) of recognized specializations of the skull. the skull with an oriented grain. A more Local areas of the bone in the temporal broadly applied force should be trans- fossa, in the occipital base, and in the mitted through the spongiosa to the inner orbital and nasal walls have no spongiosa cortex, without localized deformation, and and consist of cortex alone. It will be the whole thickness (all layers) of the convenient first to discuss cortical areas bone should respond like a uniform plate. resembling plates or shells. Cranial fractures commonly cross su- Many features of the mechanics of tures from bone to bone. The interlocking plates and shells, presented by Timo- types of suture rarely separate. Doubt- shenko and Woinowsky-Krieger (’59) re- less, however, a suitable force applied late to relatively thin, flat and curved en- directly over a simple (harmonic) suture gineering structures of sheet metal, con- should cause depression, separation, and crete and other structural materials. One possibly fracture. A consideration of the situation, in particular, applies to much of effect of force systems on the different the inner and outer cortex of the skull: types of sutures and synchondroses, how- most of the cortex of the face and brain- ever, leads away from the major concern case may be viewed, in effect, as a con- of this paper with the texture and form of tinuous plate with indefinite limits (i.e., skull bone. where edges may be ignored), supported Architectural forms of the cortex. More by an elastic foundation. The plate may specialized forms in the skull can be com- be viewed as having a large area relative pared with common architectural and to its thickness, and in this sense, it is like other structures for an evaluation of their the paving of the runways of an airport characteristics. The Italian architect, or a public plaza. In such a system, local- Nervi (’56), and other architects of the ized forces cause localized deformations. past quarter century have pioneered with This concept (figure 12D) is illustrated “form-resistant” structures; these incIude by a layer of cortex supported by a founda- curved membranelike domes and roofs tion of spongiosa. A localized downward with a thickness that is small compared deforming force is balanced by equal and to the other dimensions. Unlike more opposite forces of the spongiosa. The usual framed structures, the strength of tendency is to depress the cortex locally these structures, like that of boat hulls (much as a person’s foot depresses part and aeroplane wings, is a consequence of of a rubber mat); bending moments (M) the curvature of surfaces. Skull forms of cause a downward bending about the cortical bone are closely related; they dif- downward force, with compressive stresses fer largely because of the underlying at the free surface and tensile stress on spongiosa. Figure 13 shows five forms the spongiosa surface of the cortex. This that recur in parts of the skull other than deformation in turn produces, at a more the skull vault. At A, B, and C, ridges outward position, compensating bending are shown in representative cross sections moments (M) in an opposite direction. of skull bones and in corresponding archi- The latter moments, in contrast to those tectural models. Typically, ridges are near the applied force, produce a tension caused by undulations of the whole cor- deformation of the cortex at the free sur- tical layer and are not mere localized face and a compressive deformation at thickenings of cortex. The characteristic the spongiosa. In an isotropic material, grain direction is indicated in the models. a concave, circular depression results, and Sketch A is a barrel arch; as an architec- this is surrounded by a ring of radially tural form it might exist as a free stand- tensed material. For a material like bone ing structure, or it could be a viaduct be- that is more susceptible to tensile than low a roadway or the archway to a build- compressive failure, the initial fracture re- ing. In such structures, both the weight sponse would be tangential to the tensile of the masonry and any superimposed CORTICAL GRAIN AND SKULL ARCHITECTURE 25 downward load act to maintain the form; transversely to the direction of the ridges thus, wedge-shaped pieces (called vous- and the grain of the ridges; in each in- soir and keystone) are firmly pressed to- stance, the ridge is relatively thick bone - gether by external pressures. In a bony an external pressure would tend to com- ridge, the matrix grain is always length- pact the material into a firm arch rather wise to the arch, so that whatever bony than cause it to collapse. structure is responsible for the grain Troughs, (fig. 3T), such as the sulcus (lamellar bone, osteons, and so on) must for the sigmoid and transverse sinus, the be oriented in a predominantly length- grooves for the internal carotid artery, and wise direction. Such elements, like the the arched part of the palatal arch, can elements of the arch, would resist external be visualized as resisting pressure from forces efficiently. The elliptical dome or within the curvature. Troughs are ordin- shell at €3 and the saddle-shaped ridge at arily much thinner-walled than bony C have similar cross sections and compar- ridges, and their structure is comparable able fibrous patterns of the bony matrix; to “membrane” structures in architecture again, these patterns of grain represent (Nervi, ’56; Timoshenko and Woinowsky- mechanically advantageous arrangements Krieger, ’59; Salvadori and Heller, ’63). for resisting external loads and pressures. A cloth or membrane draped over two The sections (mastoid process, frontal supports sags, but it will support weight boss, and articular eminence) are all cut in its concavity (fig. 13D). The sketches

Fig. 13 Mechanical models illustrating certain structural characteristics. A: An arch made of elongate members resists downward external forces. B and C: The same is true for an elongate dome and a saddle-shaped arch. Below each model, the bone sections show (A) a transverse cut through mastoid process, (B) a vertical cut through the frontal boss, and (C) a sagittal cut through the articular eminence. D: Tubing subjected to internal pressure, a membrane hanging across two supports, a section through the thin-walled sulcus for the transverse venous sinus - in all these instances, pressure against the concave side of the trough is resisted by transverse, curved tensile fibers. E: A rubber balloon containing fluid, a rubber membrane sagging over a hole, and a section through the thin-walled lacrimal fossa of the orbit; in each instance, pressures are resisted by tensile fibers. In bony concavities, the circular grain predominates. 26 WILFRID T. DEMPSTER at D also show rubber tubing subjected section. For engineering or mechanical to internal pressure; the rubber yields pri- structures that have uniform cross sec- marily by stretching its circumference. tions, the average stress to be borne by a A transverse circular covering, lining, or particular structure whether tensile, com- cordage, will effectively limit this yielding pressive, or shear stress) serves quite suit- of the rubber and provide greater resist- ably as a criterion for evaluating the ing strength. This is the direction of the strength and the margin of safety of the grain in bony troughs. Thus, by analogy, structure. Experience has shown, how- the transverse grain pattern found in bony ever, that even small discontinuities in the troughs should be suited for the type of surface or in the homogeneity of a mem- strength needed in a trough. ber will increase the stress in one or more Biconcave depressions (fig. 3C) can al- regions, the increase being out of all pro- so be considered as membranes. Sketch portion to the mean stress across the struc- E (fig. 3) shows a rubber balloon contain- ture. Thus, the part will fail more readily ing fluid. The fluid exerts an outward than might be assumed from the average pressure on the surface “membrane” stress values alone. which is under tension in the directions In this regard, there are two fields of shown; that is, both vertically and trans- physical science, namely, photoelasticity versely along the lines encircling the fluid. (Frocht, ’41; Heywood, ’52; Coker and As the volume and circumference increase Filon, ’57) and the theory of plates and with more fluid, each circular tension line shells (Timoshenko and Woinowsky-Krie- must stretch. Likewise, a thin rubber ger, ’59), that have supplied much evi- membrane tacked to a board with a cir- dence that discontinuities such as holes, cular hole in it will resist the pressure of sharp angles, notches, fillets, sudden fluid through both circular and radial ten- changes in thickness, and so on-re- sions (like those at the lowest part of the gardless of the material involved - cause drop of fluid). In fact, the circular resist- great concentrations of stress. Regions of ance will be greater than that across the high stress concentration are regions of surface, since for every unit that a diam- weakness and potential failure. Converse- eter is increased, the circumference of the ly, it has been pointed out (Heywood, corresponding circle on the membrane ’52) that mechanically sound designs must increase by r[ times the diameter. avoid discontinuities and the likelihood Grain in the floor of bony concavities is of dangerous levels of stress. generally circular and will thus resist such In bones, discontinuities such as fora- circumferential stretching, effectively tend- mina, notches, edges, and sharp angles all ing to prevent outward deformation of concentrate stress much beyond average the concavities. values, and it is here that fractures may As indicated in the classification, thin, begin to form. Discontinuities of skull unsupported edges and spines (figs. 3E bones, such as the mental foramina of the and S) consistently have an elongate mandible or the cribriform plate of the grain pattern that either parallels the edge ethmoid bone, may thus account for the or runs lengthwise in the spine to con- frequency of fractures traversing these verge at the apex. This grain pattern, like structures. Any of the discontinuities in the grain of an elongate wooden beam, the list above is presumptively a “weak” since it lies in the direction of greatest feature of the skull. Some discontinuities strength, contributes to the resistance to in the skull occur in groups as such com- bending. This is equally true for a canti- plex congeries of edges, spines, and fora- lever beam, like a spine, and also for an mina as to defy systematic analysis. The unsupported edge. region on each side of the skull bounded Discontinuities as weak regions. Dis- by the pterygoid process, the occipital con- continuities require special consideration dyle, the mastoid process, and the articu- in the evaluation of the strength of the lar eminence of the temporal bone is such skull. The force borne by a structure is a region. ordinarily treated in terms of a mean Spines and edges, as noted, have an stress - the force per unit area of a cross elongate grain structure; foramina with CORTICAL GRAIN AND SKULL ARCHITECTURE 27 thin edges are bordered by a region of cranial part of the skull acts as an oval circular grain texture. In each instance, container for the cranial contents. It is the part is strengthened by its texture, bounded, except for part of the basal re- but it cannot be said whether or not the gion, by braincase bone consisting of inner mechanical advanage due to texture fully and outer tables of cortex separated by a compensates for the stress-concentrating layer of diploe. The inner and outer cor- effect of the discontinuity. A spine that tical plates, except in old age, are general- has an effective texture may show a stress ly thicker than facial-bone cortex in parts concentrating discontinuity at the angle other than the mandible. between its stem and its base. No doubt Figure 14B shows a saw-cut cross sec- a force system that is potentially large tion of the skull, representing an approxi- enough will damage the skull somewhere, mate two-dimensional model that applies, and some region of discontinuity is a like- more or less, to most of the skull vault. ly site for fracture initiation. Under a compressive force system (fig. Massive regional fractures. In addi- 14C) the skull section flattens like a ring. tion to the localized fractures discussed The inner cranial surface opposite the ap- above, certain regions of the face or plied compressive forces shows tensile de- cranium may exhibit extensive fractures. formations; at 90" around the section For example, there are greater masses of from the applied force, the deformations bone at the level of the palate, at the level are reversed with tension acting on the of the orbital floor, and at the brow level external table and compression on the in- than in the regions between. As a re- ternal. Gurdjian and Lissner ('45) have sponse to impacts, the teeth and the entire demonstrated this type of skull deforma- alveolar arch may be sheared across below tion in experimental impacts. Thus, ten- the palate, separating the region from the sile fractures arising, contracoup, at a dis- rest of the skull. There may be trans- tance from an impact site on the skull nasal-maxillary sinus shearing fractures vault may spread widely. Because they or transorbital fractures. These are mas- often extend widely from the site of frac- sive responses to impacts across the face ture initiation, the fractures may reach in- at different levels. The fractures, basically, to the foramina at the base of the skull or are at right angles to the cortical grain to the middle meningeal artery at the thin of the bone. bone of the temporal fossa, resulting in Architectural and mechanical aspects hemorrhage or serious soft-tissue damage to cranial nerves. This tendency is in- of the skull vault creased by the stress-concentrating, bone- The architecture of the skull vault as a weakening effect of discontinuities at the gross form may be evaluated profitably in base of the skull. different ways. As indicated previously, The cranium should also be viewed braincase cortex is characterized predom- as a three-dimensional structure; a barrel inantly by a random arrangement of provides a satisfactory model (fig. 14D). fibrous matrix. Except in responding to A barrel may carry a load on its top, form- a sharp localized force, like a grazing bul- ing with the floor a compressive force sys- let, the whole cranial wall tends to react tem. The staves transmit compression as a unit. A localized compressive force while tending to bend outward; the hoops, to the outer surface (fig. 14A) may result however, are subjected to tensile forces in tensile deformation of the underlying which oppose the deformation of the inner table, or possibly comminuted frac- staves. Similarly, an uncooked hen's egg tures of the inner table; but little or no may withstand a compressive force of 75 damage may occur to the outer table, be- pounds if its ends are suitably padded cause the compressive strength of the (fig. 14E). Again, as compressive forces bone is much greater than the tensile are transmitted from end to end, the sides strength. tend to bulge like the hoop at C, and in- A more extensive group of fractures internal stresses transverse to the length of volves the cranium as a whole, irrespec- the egg exerting tension to counteract the tive of surfaces. As noted above, the bowing outward. The egg, like the barrel, 28 WILFRID T. DEMPSTER

t t

t Fig. 14 A: Bone of the skull vault in section; exterior compressive force induces tensile deformation on inner table. B and C: Transverse section of skull under compressive force deforms like circular ring with four regions of high tensile (t) and compressive (c) strains. D and E: In a three- dimensional sense, the skull deforms like the barrel at D and the egg at E. Vertical compression is transmitted from end to end and there are transverse circumferential tensions (suggested by the hoops in the barrel) and a three-dimensional force system analogous to that shown in the section at C. F: A dome on a horizontal support acts like the half of an egg above its equator. G: For a dome on pillars, the stresses focus toward the supports. H: In the case of the cranial vault, the braincase with its random-patterned texture continues the grain pattern shown, both in the base and in several external (and internal) pillars. (Sketches F and G from Salvadori and Heller, '63, with permission. ) exerts both tensile and compressive forces fig. 14G), and is partly continuous with (along lines such as those shown) to re- the base of the skull as in fig. 14F). The sist the external load; yet the egg shell cortical tables of most of the skull vault has no grain structure. have a random pattern of grain, forming Figure 14F is an architectural dome cor- a rough equivalent to the grainless struc- responding to the broad end of the egg. ture of the egg. The buttresses (fig. 14H) Its mode of resisting a vertical force (its are: on the external table of the skull own weight, or an external force) is the vault - the two mastoid processes later- same as that of the egg. If a dome is sup- ally with a vertical ridge grain; the two ported on pillars (fig. 14G), however, its zygomatico-frontal buttresses laterally weight must be counterbalanced at the with a vertical fan of plane grain pattern; support points where stress will be con- anteriorally, the frontal boss with a trans- centrated at higher levels. verse ridge grain. Not shown on the inner In the skull the cranial vault is partly table are vertical ridges or crests, with supported by ridges of bone with definite elongate grain, flanking the frontal and grain forming pillars or buttresses (as in occipital parts of the superior sagittal CORTICAL GRAIN AND SKULL ARCHITECTURE 29 sinus. An eccentric force on the skull vault in the skull. Most random patterned bone would result in one pillar or another trans- (fig. 4) gets its strength from the oval mitting much of the load to the base of shape of the braincase, from the three the skull and vertebral column. The layered structure, including diploe, of stress distribution through the skull could most of the skull vault, and from the be much more complex than that of a thickness of the cortical tables. The other comparable force system on an egg. forms contribute less to total skull strength. Edges (fig. 7) and spines (fig. DISCUSSION 6) have a grain pattern that provides Seven grain-form relationships are rec- localized reinforcement. Troughs (fig. 6) ognized in the adult skull: (1) a random and concavities (fig. 7) are usually local- pattern of braincase cortex, (2) planes ized areas of thin bone; the arrangement and (3) ridges with elongate grain, (4) of the texture, however, best resists sur- troughs with transverse grain, (5) con- face pressures. cavities with circular patterns, (6) edges, An eighth relationship - discontinuity and (7) spines. Concavities may show a - is recognized; this contains regions of superimposed trough or ridge structure, potentially high stress concentration and and troughs may be marked by localized weakness in the skull, even though certain ridges and planes. That is, trough pat- discontinuities such as edges, spines, and terns are dominant over concavity pat- thin foramina may show an effective use terns, and ridge patterns are dominant of texture. over both trough and concavity patterns. In the mechanics and engineering field Finally, there are a few small cranial known as “strength of materials” homo- areas that are random distributions in geneous bars of test materials are sub- some skulls and planes in others; the skull jected to detailed analyses of strains under vault proper, however, except for the fore- force systems of different types. For many head region and internal sagittal mark- force situations, as a beam in bending or ings, has a random pattern throughout. a column in torsion, the stresses vary Bone resists deformation and fracture from point to point, and maps or diagrams best in the long direction of its grain tex- showing the directions of the maximum ture but is a relatively weak material and minimum, or principal, stresses have crosswise. The classification of form-tex- been made. Sets of compression and ten- ture relationships presented in this paper sion lines always cross at right angles; the includes most of the parts of the adult curves show the direction of stresses only, skull. They are discussed as architectural and the magnitudes of the stresses along features of the skull, and their adequacy the lines vary. For more than a hundred and limitations are analyzed in terms of years, these lines of principal stress in their reaction to force systems and their homogeneous material have been desig- proneness to fracture. All seven form-tex- nated “trajectories.” ture relationships over localized areas This term trajectory has now been taken show grain directions that are in accord over by some students of bone, and its with the best mechanical use of the ma- original and only coherent meaning has terial of which they are made. Moreover, been seriously distorted. In particular, as shown in figure 5, the various ridges since Meyer’s demonstration of the tra- appear to be deployed over the upper- and becular patterns of the spongiosa of the mid-face and over the skull base, both femur and other bones (1867), the tra- exterior and interior, so as to provide rib- beculae of the spongiosa have even been bing and buttressing that should add regarded as specializations, or as trajec- strength. Plane areas (fig. 4), strong in tories, for carrying tensile or compressive the direction of the grain and weak cross- forces, ignoring completely the weakness wise, are typically bounded by ridges, of the spongiosa as a material. Koch edges, or random braincase bone; the (’17), however, showed that in the femur, grain direction may be assumed to con- the trabecular pattern parallels the lines tribute more to strength than if it were of maximum stress as the bone bears oriented at 90” to the grain actually seen loads and transmits forces and thus serves 30 WILFRID T. DEMPSTER as the most effective distribution of That is, the bone is resorbed, redeposited, spongiosa. But Koch did not even men- and reconstructed until the multitude of tion the term trajectory. eminences, processes, and fossae attain In the traditional armchair view of the structural forms and textures ex- the mechanics of the skull, the mastica- hibited by an adult skull. Most of the tory apparatus with its mobile jaw, teeth, texture of infantile bone is suppressed by and muscles, has been emphasized more secondary growth changes. This study than any other system for transmitting points out that the grain of bone (as re- stresses. Pressure-carrying specializations presented by the fibromatrix of the decal- in the form of pillars, beam, and but- cified bone) and the form of bone in adult tresses have been postulated from the skulls are closely correlated. The work, teeth to the upper skull; these extend ver- however, suggests no clues as to how or tically between the nose and orbit, through why these relations came to be. the zygoma, both through the zygomatic An alternate interpretation to the pres- arch and the lateral orbital margin, and sure line or trajectory idea of skull texture from the last molar region through the can be suggested. Since bone is especially pterygoid process to the skull base. MUS- weak crosswise to the grain for tension, cular tensions bridge between the jaw compression, bending, and torsion, one angle and the zygomatic arch, and from may assume that crosswise properties, the coronoid process to the temporal fossa when not specifically arranged to best ad- with the bones transmitting forces to the vantage (because of growth changes and teeth (Weinmann and Sicher, ’47). The new functional demands), present a weak pillar idea is based on the general appear- feature to be modified by osteoblast and ance of skull ridges and is not based on osteoclast activity as the bone grows under any bone measurements showing thick the stresses of normal functioning. Tex- columns of increased cross-sectional area tures, thus, should reorient from infantile acting to reduce stress values (force per patterns as a response to bone growth in- unit area). fluenced by the increasing size of the When split-line patterns in the skull brain, orbital contents, and tongue, the appeared to parallel the buttresses and formation of more cortex, more spongiosa, pillars, the idea that these tracts served and more marrow space, the development as cortical trajectories, or “cortical pres- of diploe, the formation of air sinuses, the sure lines,” was formulated (Benninghoff, adaptation to growing tooth germs, the ’25; Seipel, ’48; Tappen, ’53). No mechan- superimposition of sexual specialization, ically coherent interpretation involving and so on. force or stress was given to tell what these It is reasonable to propose that weak terms really meant. The implication, how- and inefficient bony tissues are replaced ever, is that the tracts developed in the during bone reconstruction under the in- individual as response to functional fluence of intermittent stresses by bone stresses (Wolffs Law). This explanation textures of more effective orientation. En- must be speculative, since we know of no low and Bang (’65) have shown that gross mechanism at the molecular level through form changes and growth of the maxilla which the processes of bone reorganiza- involve complex reconstructive changes, tion and growth might form pillars or periosteal deposition on certain surfaces, pressure tracts under the influence of periosteal resorption on others, with either stresses transmitted along the pillars. The endosteal deposition or endosteal resorp- so-called masticatory pillars could be tion on still other surfaces. The adult genetically determined growth specializa- form-texture relationship presented in this tions; the orientation of grain along them paper should arise in time, as a compensa- might or might not be a secondary me- tion for mechanically weaker features of chanical adaptation. a grain oriented initially by embryonic and The skull of an infant grows and fetal growth. Such a view further proposes changes its shape and form through child- that a randomly oriented braincase texture hood and adolescence, eventually acquir- should be stronger in all directions under ing adult architectural characteristics. tensile and compressive loads than is bone CORTICAL GRAIN AND SKULL ARCHITECTURE 31 in the cross grain direction. The skull 1964 Significant differences in the vault, like the egg, gains strength through tensile strength of adult human compact bone. Proc. European Bone and Tooth Symp. (Ox- its form and through the use of a struc- ford, 1963), I: 319-331. tural material that is equally strong in all Evans, F. G., and H. R. Lissner 1957 Tensile directions. Strength tests on parietal bone and compressive strength of human parietal by Evans and Lissner (’57) suggest an in- bone. J. Appl. Physiol., 10: 493-497. Frocht, M. M. 1941 Photoelasticity. 2 vols. J. termediate level of tensile strength; the Wiley and Sons, New York. test, however, related to whole thickness Gurdjian, E. S., and H. R. Lissner 1945 De- bone and not to single tables of cortical formation of the skull in head injury: a study bone. with the “stresscoat” technique. Surg., Gynec. and Obstet., 81: 679-687. Editor’s note Henckel, K. 0. 1931 Vergleichend-anatomische Untersuchungen iiber die Struktur der Knoch- This manuscript was edited from the encompakta nach der Spaltlinienmethode. Mor- final rough draft which Dr. W. T. Demp- phol. Jahrb., 66: 22-45. Heywood, R. 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