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The Gliding Path of the Mandible along the Skull
SPECIAL C O N TRIBU TIO N
D
l
The gliding path of the mandible along the skull
F e r d in a n d G r a f S p e e ( 1 8 5 5 - 1 9 3 7 )
Prosector at the Anatomy Institute of Kiel Translated and reviewed by M aria A. Biedenbach, PhD M argaret Hotz, MD, DMD H. Perry H itchcock, DMD, MSD
T
he follow ing argum ents concern the path of the m andibular m ovem ents such as the gliding of the occlu sal surfaces of the dental arches against each other, either ju st in contact or in full occlusion, possibly w ith interposition of a thin layer of food. In other words, these are movem ents w hich could be selectively perform ed as w ell laterally and sagittally. Furtherm ore, a backward gliding of the m an dible often occurs at the end of an incising m ove ment. T he course of these specifically m asticatory m ovem ents does not depend only on the m echanical array of the m andibular joint in its narrower sense but also on the configuration of the m asticatory sur faces of the teeth. A ccordingly, there is harm onious interaction. However, up to now, no studies have disclosed this relationship. Langer’s view ,1 for in stance, w hich he derived from a study on the low er ing of the m andible is not correct. He stipulates that, during forward and backward gliding in sagittal direction, the m andibular condyle m oves around the lower surface of the tuberculum glenoidale in a curve supposed to be concentric to the surface cur vature of the tuberculum glenoidale, the axis of w hich is supposed to lie w ithin the tuberculum. T h is view, however, is incorrect, at least, for m ove m ents during w h ich dental arches are in full o cclu sion. 670 ■ JADA, Vol. 100, M ay 1980
M eyer,2 who used his com parative anatom ical studies successfully in order to establish the sign ifi cance of fine structural details of the hum an m an dibular joint, does not even m ention an axis for sagittal displacem ent. N either does H enke.3 However, a definite axis can be established at least in the m ajority of cases, if we consider the occlusal configuration of the teeth. The m andible rotates around this axis w hile perform ing the ordinary sagittal gliding, w ith maybe ju st a sligh t deviation to the left or the right. A profile view of a hum an skull usually shows that on both sides the m asticatory surfaces of the molars are aligned in a downward convex curve along the upper jaw and in an upward concave curve along the lower jaw. T h is relationship is not consid ered in anatom ical textbooks. O ccasionally, it is cor rectly reproduced in illu stratio n s, esp ecially in those made by artists according to nature, but gener ally it is not shown. It also received no reasonable consideration in plastic reconstructions of hum an dentitions by dental tech nician s, nor in the prepara tions o f hum an skulls w ith artificially inserted teeth w hich were made in Paris. W e rather frequently find an unjustified tendency to arrange the m asticatory surfaces of the teeth in a horizontal plane. A good illustration of the downward convex curve
A ll dentists have heard o f th e “Curve of Spee.” It has m eant d ifferen t things to d ifferen t dentists. S om e h a v e said that it is an an terop o sterio r cu rv e in the vertical p la n e o f the low er arch. O thers h a v e said th at it is an anteroposterior curve in the vertical p lane o f th e u p p er arch (with the opposite arch assum ing a com p en satin g curve). In trying to learn w hat F erd in an d G raf S p ee actu ally sa id , it w as fo u n d that a rea d ily available translation o f G raf S p e e ’s original work did not exist. Two tran slations were n e e d e d : on e fro m archaic G erm an to m odern G erm an, an d another from m odern G erm an to English. M aria B ied en b a ch , PhD, assistan t professor of physiology, U niversity of Texas H ealth Science Center at San A ntonio, tran slated th e origin al article. H ow ever, sh e was not en tirely sa tisfied that s h e h a d correctly in terpreted the den tal terms. Later, M argaret H otz, MD, DMD, Z ah nartzlich es Institut d er U niverstat Z urich, agreed to tran slate it using current den tal term in ology. Now, all E n glish-speakin g d en tists can b e aw are o f w hat G raf S p e e sa id ; an d on e no longer has to d ep en d on an oth er’s interpretation. I d id n on e o f th e tran slation but on ly served to p ersu ad e Dr. B ied e n b a c h an d Dr. H otz to interpret this fa m o u s w ork. H. PERRY HITCHCOCK, DMD, MSD
in the sagittal plane in w hich the m asticatory sur faces of upper and lower teeth occlude can be ob tained from the photographic profile of the skull in Figure 1. Here, as a consequence of attrition, the molars have lost all the cusps of the crow ns so that th e m u tu a lly abrad ed m a stic a to ry su rfa ces fit exactly on top of each other. Thus, the upward con cave curve describes a sm ooth line in the sagittal plane. T eeth with com pletely intact crown cusps fundam entally also present the same curvelike ar rangem ent of (masticatory) occlu sal surfaces, except that they show an irregularly em bossed profile line, w hose in d en tation s are clea rly reco g n izab le as sm all fluctuations on an assum ed curvilinear base (Zero line) (Fig 2). As an exact exam ination of the curve is more com plicated in a dentition w ith pre served cusps than in cases in w hich they are reduced by wear, it is preferable to choose the worn cases in order to discuss the basic findings. If, in such a special case, the curve is determ ined in a profile view of the skull, for exam ple, Figure 1, or w ith a com pass, on its geom etric projection on the sagittal plane, the findings are the follow ing: — That the total visible con tact lin e of the molar m asticatory surfaces lies on the same arc of a circle; furthermore, — That in the sagittal plane the posterior continu
ation of this arc touches the m ost anterior point of the m andibular condyle. A ccordingly, the points of the m andible w hich glide in contact along the upper part of the skull are lying on the same cylin drical surface. The location of the axis of that cylin d er’s curvature could be de term ined by reconstruction and m easurem ent w ith the com pass at the level of the horizontal m idorbital plane, posteriorly from the crista lacrim alis poste rior. In the lateral view it appears as a point (Fig 1, a). The attritional configuration of the teeth develops through their respective gliding m ovem ents and thus conform s to the pathway w hich the teeth of the m andible follow. As the teeth in the jaw s have to be considered as fixed, this pathway is not only a m an ifestation of tooth m ovem ent but an effect of the displacem ent of the w hole m andible. C onsidering at the same tim e Figure 1, it follow s that the m ovem ent occurs in circular paths ju st as a pendulum m oves around an axis. T h is axis is given by a transverse connecting line from the sagittally projected centers of the masticatory curvature of both sides. From Figure 2, it further follow s that the m ost anterior part of the surface of the condyle also m oves on a circular path w ith the same length of radius as the occlu sal surfaces of the m olars. In other words, these parts move on the sam e cylin d ric surface. Spee : GLIDING PATH OF MANDIBLE ALONG SKULL ■ 671
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C O N T R IB U T IO N
Fig 1 a, b ■ Illustrations from same skull; l,a in exact profile view; 1 ,b from somewhat anterior view. Fig l,a shows curve for for ward movement of mandible; 1 ,b shows curve for occlusal surface without reduction in length. Di mensions of illustrations are comparable as they were repro duced at equal magnification (r indicates radius of curve for mas ticatory [occlusal] surfaces and c indicates center of curve).
Fig 2 ■ Dentition of adult with well-preserved crown cusps. Only surface of still-present sec ond deciduous molar (m) shows attrition. This surface prolongs occlusal line of articulatory sur faces of posteriorly located mo lars quite naturally.
Fig 3 ■ Mandible of child.
Fig 4 ■ Series of points of hu man, worn occlusal surface accu rately located in relative position to each other and to anterior sur face of mandibular condyle, k. Natural size. Two preparations a, b.
v'enag \e’d & Comp, e
The m ost prom inent anterior part of the m andibu lar condyle is also the most lateral. Thus, according to the explanations of M eyer,2 it belongs to that half of the condyle w hich during sym m etric forward and backward m ovem ents of the m andible is moving up and down very closely along the tuberculum. T he m asticatory surface of the upper teeth and the articulating surface of the glenoid tuberculum with its m eniscus form the analogous parts of a big cy lin drical curve around whose surface area the points of the low er jaw glide. The radius of the glenoid tuber672 ■ JADA, Vol. 100, M ay 1980
culum is m uch shorter than the radius of the cy lin der. Yet a con cen trically arranged series of basic points corresponding to its surface can be estab lished for the com plete lin e of m otion of the m an dibular condyle along the tuberculum , because the thicker part of the wedge-shaped m eniscus in terca lates betw een the two areas and com pensates the shorter radius of the tubercular curvature. As for ward and backward gliding of the m andible takes place in a path of circular m otion, such d isp lace m ents can occu r over longer distances w ithout any
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need for the arches to separate from each other. Thus, m asticatory efficiency is guaranteed. A sep aration of the occlusal surfaces is only inevitable in order to overcom e the contact of strongly protruding upper and lower canines. But this can also be elimi nated by wear. If the occlusal surfaces of the teeth were arranged on a plane, and, since the tuberculum articulare is present, parallel shifting of the closely apposed arches for purposes of crushing and grinding food would not be possible. This ought to be considered in the construction of dentures, not only to enable better m astication but also in order to avoid lever effects during chewing. These levering effects are less manifest with increased length of contact sur face in every position of the firmly occluded teeth. The backward gliding of the m andible, usually fol lowing an incising movement, is especially effective and m ainly responsible for sagittal attrition. Isolated backward m ovem ents of the mandible are rather unusual. In addition, as concerns wear, one has to consider alternating lateral rotation of the mandible around nearly vertical axes. During these m ovem ents, the grinding action on the teeth on the side toward w hich the movement occurs is in alm ost transverse directions. During this, the teeth of the lower arch shift in a laterally descending direction below the m ost protruding lateral border of the upper crowns (Fig 2). Evidently the teeth of the other side w hich simultaneously move forward and m edially cannot remain in contact with the upper arch. This would also be a consequence of the unilateral protrusion of the condyle on top of the m edial half of the tuber culum (Meyer). The backward movement, during w hich the mandibular condyle slips back into the fossa, can occur by gliding of the arches (backward and outward), just as they are aligned. This m ove ment, of course, also follows the upw ard concave curve w hich was considered above in the sagittal projection (however slightly shortened), as the path of sagittal gliding of the mandible. But this time the movem ent occurs parallel to the greatest length of the curve w hich is visible only if view ed somewhat anteriorly and laterally, since it is flatter. From this perspective, the transverse distance between con dyle and lateral surfaces of the teeth does no longer appear shortened. Y et one finds that in spite of its longer radius the continuation of this curve also touches the lateral anterior surface of the condyle (Fig 1, b). Strictly speaking, the worn surfaces of the molars on each side form together, more or less, a rectangu lar area. Its diagonal line, slightly sagittally posi tioned, is curved spirally towards the opposite side; since the surfaces of the third molars have an inward slant, those of the second m olars are m ore horizontal and those of the first molars inclined outward. Thus
CO NTRIBUTIO N
it somewhat digresses from a cylindrical surface. This effect, aside from the difference in thickness of the enamel, is due to the tilted position of the teeth. As is well-known, the crow n of the second molar and even more so of the third is inclined lingually in the mandible and labially in the upper jaw in order to contact its antagonist. The resulting com plication for the occlusal surfaces is not significant enough to cause a relevant deviation from the path of m andibu lar motion just described. During sagittal sym m etric displacements, the com plication does not even ap pear, because all sym m etric m ovement effects in the direction of the m edian plane are mutually cancel led, the sam e as the medially directed forces of the external pterygoid muscles. Regarding the path for sagittal displacem ent, based on autographic curves about the m ovem ent of the lower incisor, Langer expressed the opinion that the mandible is shifting on very flat curves or rather on straight lines. As a rule, this is not the case. Furthermore, the photographic curve about jaw dis placem ent recently obtained by Luce,4 under Bowditch’s guidance, is not in accord with Langer’s views, but is in agreement with the results which derive from the modeling of the occlusal surfaces of the teeth in the path of sagittal displacement. It shows that the mandible glides forward in an up ward concave curve. However, the autographic curves are short, be cause the greatest possible forward gliding distance of the mandible amounts to about V-k cm (footnote, p 289). With this displacement, the lower incisors and canines usually enclose the upper ones from an teriorly and laterally. At the same time, the buccal edges of a lower molar move under the buccal edges of the next anterior upper tooth. For m astication, only about two thirds of this gliding distance is used, and for specific grinding movements, only a third. For m asticatory function, this rather small gliding distance is very efficient and m ost important because of its many repetitions on very long m asti catory surfaces. Along the whole length of these surfaces, the d irection of m ovem ent is clearly marked through the form of attrition, just as on a surface of a joint. Therefore, the form of the gliding surface of the molars offers the best information for evaluating the course of the movement. It is also the best criterion for analysis of the autographic curves. Within certain limits, the ligaments of the m andi ble generally adapt themselves to the new position of the shifted mandible without tension. A s Langer1 already found, only the fibers of the medial a c c e s s o r y lig a m e n t, w ith in th e f a s c ia b u c c o pharyngea, tighten very early during forward glid ing. Since it inserts on the anterior surface of the condyle, a force develops w hich would m ove the chin in the direction of the forehead. This is in accordance with the upward concave curve of the Spee: GLIDING PATH OF MANDIBLE ALONG SKULL ■ 673
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CO NTRIBUTIO N
m asticatory surfaces of the teeth. In case of a m aximal mandibular forward dis placem ent, the concordant movement of the m enis cus is restrained by its posterior attachm ents. Its anterior half being inserted like a strong wedge be tween condyle and tubercle, a further inhibition of condylar forward movement results in conjunction with the tension of the lateral ligament. I interpret the small dip at the end of the autographic glenoidal curve in L u ce’s Figure 4 as a consequence of a more pronounced interposition of the m eniscus between the bony parts of the temporomandibular joint.
Specific findings in different dentitions Among anim als, as far as my experience goes, the ruminating and hoofed species as well as some pri m ates show the sam e upw ard con cave occlusal curves in their dentition without exception. The posterior continuation of the curve touches the an terior surface of the condyle just as in humans. The radius of the cylindric surface on w hich the concave curve lies, is longer in larger animals and more prognathic skulls. Different lengths were: horse, 21.9 cm ; Cervus elephas, 18.0 cm ; Cervus dama, 12.9 cm ; small monkey, 8.5 cm; and adult man, 6.5 to 7.0 cm. A com parison of the measurements found in ani mals w ith those found in man shows that, aside from body size, the relative sm allness of the visceral cranium coincides w ith a shorter radius and a larger curvature. This appears to point tow ard an increase of the m asticatory surface within a lim ited special area and therefore it seems appropriate. Rodents and carnivores do not show curves of the m asticatory surfaces. The tuberculum articulare, present in all the former anim als, is missing. Therefore, develop ment of curved occlusal surfaces as well as the circu lar path during sagittal forward displacem ent seems to depend on the presence of the tuberculum . Based on this recognition, several human cases w hich de viate from the rule can be explained. These cases w ill be discussed at the end of this paper. I under took the specific exam ination of hum an jaws on as m any sp ecim ens as possible, in order to avoid p u re ly in d iv id u a l v a ria tio n s . H o w e v e r, th e ir number w as not very large because only beautifully preserved and com pletely developed jaws could be used. Skeletal jaws w ith indiscrim inately and artifi cially inserted teeth were rejected. But, since good jaws of different races yielded the same findings just described, they have a general significance. The observations had to establish the positional relationship between the occlusal surfaces of the teeth and the surface of the mandibular condyle. They w ere made in various ways. The sim plest way to obtain the necessary m ea surements is to evaluate exact geom etric sagittal 674 ■ JADA, Vol. 100, May 1980
projections. Since, in adults, the alignm ent of m o lars does not decidedly deviate from the sagittal plane (on the average less than 20°), projections through large lenses, for exam ple, photographs, can be used w ithout relevant errors. By measuring the crowns w ith calipers, I determined the radius of the curve approxim ately if strong cusps were present (in ruminants). In abraded m asticatory surfaces in hu mans I did it more accurately: the vertical distances of a line of arbitrary points on the occlusal surface and of the m ost anterior point of the condylar sur face of the mandible were determined from the hori zontal plane and correctly entered in a system of coordinates. Through accurate reconstruction, the center of a circle touching as many of the points as possible was determined; the results could not be anticipated, but in most cases such a center could be obtained approxim ately. In some cases with decided abrasion all points were located exactly on the same circle (Fig 4). Such exact circular attrition is not explainable by simple wear. Specific effects or form relationships, which continuously acted toward this kind of development, m ust have existed from the beginning. As mentioned at the beginning, this is partly reflected from the fact, that even in nonabrad ed molars, cusps are arranged along a downward convex circle, w hich already shows in a ch ild ’s jaw with deciduous teeth at the same time as the tuber culum articulare develops. U ltim ately, develop mental relationships peculiar to a species m ust be considered (Fig 2, 4). In the beginning, the curve of the m asticatory surface of the mandible is sometimes not very clear and is m uch flatter than in the upper jaw where it is seldom missing. In such cases, the varying pressure exerted on the teeth appears to gradually induce com pensation of the curve difference. In general, it appears that teeth whose antagonists are missing are more and more elongated by new bone formation in the alveoli. Roots of teeth with intact antagonists remain deeply set in the alveolus. Therefore, we may assume that teeth, as long as they are subject to little pressure, will continue to grow more than those exposed to stronger pressure. This would be a continuously acting m echanism in order to adjust the curves of the masticatory surfaces of both arches. In adults, the radius of the curve of mandibular motion had a length of 6.5 to 7.0 cm, usually equal on both sides. Variations within these limits depend on the angular position of the ramus to the arch and on the width and height of the ramus. In children with complete sets of deciduous teeth, the radius is shorter than in adults, because of the generally smaller dimensions, despite the obtuse position of the still short ramus to the arch. In a special case the radius measured approxim ately 4.6 cm. Among the m any individual variations of the
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fixed parts of the m asticatory “ array,” we have to consider those in w hich the upward concave curve of the m asticatory surface did not exist. They are not especially rare. For all of them , it appears that the effect of the tuberculum articulare is elim inated (blocked). I have observed the following: — An extrem ely low or almost nonexisting tuber culum (several cases). — Shortening of the sagittal and vertical dimen sions of the ramus on one side so that its condyle could never have been in the fossa, while the other side showed the usual configuration (one case). — Unusual bulk of the condyle with so short a distance between tuberculum and anterior wall of the external auditory canal that the condyle of either side could never have been in the fossa (one case). — The m ost protruding part of the condyle does not lie laterally but opposite the posteriorly tilted medial part of the tuberculum, with the middle of its anterior surface on its m edial half, so that it does not stay as deep in the fossa as usual (three cases). Extrem e thickness of the m eniscus, w hich I, how ever, have not observed, w ould also eliminate the action of the tuberculum.
CONTRIBUTION
W ith s u c h c o n f ig u r a tio n of th e te m p o r o m and ib ular joint, the m a stica to ry m ovem en ts would have to occu r through level forward and backward gliding within the joints as in rodents. — K ie l, th e 2 4 th o f M a rc h , 1 8 9 0 .
Originally published in the Archives of Anatomy and Physiology, 16:285-294, 1890. Translation rights and illustrations use granted by Springer Verlag, Heidelburg. Dr. Biedenbach is associate professor, department of physiology, Uni versity of Texas Health Science Center at San Antonio. Dr. Hotz is founder of the cleft palate program, department of orthodontics, Zahnartzliches Institut der Universtat Zurich. Dr. Hitchcock is professor and chairman, department of orthodontics, University of Texas Dental School at San Antonio, 7703 Floyd Curl Dr, San Antonio, 78229. Address requests for reprints to Dr. Hitchcock. 1. Langer, Das Kiefergelenk des Menschen. Sitzungsberichte der kaiserl. Akademie der Wissenchaften zu Wien 1880. S. 457. 2. Meyer, H. Das Kiefergelenk VH. Beitrag zur Statik und Mechanik des menschlichen Knochengerüstes. Dies Archiv 1865. S. 719. 3. Henke, Handbuch der Anatomie und Mechanik der Gelenke, 1863. 4. Luce, C.E. The movements of the lower jaw. Boston Med Surg J, 1889, Figure 4.
Spee : GLIDING PATH OF MANDIBLE ALONG SKULL ■ 675
D
l
The gliding path of the mandible along the skull
F e r d in a n d G r a f S p e e ( 1 8 5 5 - 1 9 3 7 )
Prosector at the Anatomy Institute of Kiel Translated and reviewed by M aria A. Biedenbach, PhD M argaret Hotz, MD, DMD H. Perry H itchcock, DMD, MSD
T
he follow ing argum ents concern the path of the m andibular m ovem ents such as the gliding of the occlu sal surfaces of the dental arches against each other, either ju st in contact or in full occlusion, possibly w ith interposition of a thin layer of food. In other words, these are movem ents w hich could be selectively perform ed as w ell laterally and sagittally. Furtherm ore, a backward gliding of the m an dible often occurs at the end of an incising m ove ment. T he course of these specifically m asticatory m ovem ents does not depend only on the m echanical array of the m andibular joint in its narrower sense but also on the configuration of the m asticatory sur faces of the teeth. A ccordingly, there is harm onious interaction. However, up to now, no studies have disclosed this relationship. Langer’s view ,1 for in stance, w hich he derived from a study on the low er ing of the m andible is not correct. He stipulates that, during forward and backward gliding in sagittal direction, the m andibular condyle m oves around the lower surface of the tuberculum glenoidale in a curve supposed to be concentric to the surface cur vature of the tuberculum glenoidale, the axis of w hich is supposed to lie w ithin the tuberculum. T h is view, however, is incorrect, at least, for m ove m ents during w h ich dental arches are in full o cclu sion. 670 ■ JADA, Vol. 100, M ay 1980
M eyer,2 who used his com parative anatom ical studies successfully in order to establish the sign ifi cance of fine structural details of the hum an m an dibular joint, does not even m ention an axis for sagittal displacem ent. N either does H enke.3 However, a definite axis can be established at least in the m ajority of cases, if we consider the occlusal configuration of the teeth. The m andible rotates around this axis w hile perform ing the ordinary sagittal gliding, w ith maybe ju st a sligh t deviation to the left or the right. A profile view of a hum an skull usually shows that on both sides the m asticatory surfaces of the molars are aligned in a downward convex curve along the upper jaw and in an upward concave curve along the lower jaw. T h is relationship is not consid ered in anatom ical textbooks. O ccasionally, it is cor rectly reproduced in illu stratio n s, esp ecially in those made by artists according to nature, but gener ally it is not shown. It also received no reasonable consideration in plastic reconstructions of hum an dentitions by dental tech nician s, nor in the prepara tions o f hum an skulls w ith artificially inserted teeth w hich were made in Paris. W e rather frequently find an unjustified tendency to arrange the m asticatory surfaces of the teeth in a horizontal plane. A good illustration of the downward convex curve
A ll dentists have heard o f th e “Curve of Spee.” It has m eant d ifferen t things to d ifferen t dentists. S om e h a v e said that it is an an terop o sterio r cu rv e in the vertical p la n e o f the low er arch. O thers h a v e said th at it is an anteroposterior curve in the vertical p lane o f th e u p p er arch (with the opposite arch assum ing a com p en satin g curve). In trying to learn w hat F erd in an d G raf S p ee actu ally sa id , it w as fo u n d that a rea d ily available translation o f G raf S p e e ’s original work did not exist. Two tran slations were n e e d e d : on e fro m archaic G erm an to m odern G erm an, an d another from m odern G erm an to English. M aria B ied en b a ch , PhD, assistan t professor of physiology, U niversity of Texas H ealth Science Center at San A ntonio, tran slated th e origin al article. H ow ever, sh e was not en tirely sa tisfied that s h e h a d correctly in terpreted the den tal terms. Later, M argaret H otz, MD, DMD, Z ah nartzlich es Institut d er U niverstat Z urich, agreed to tran slate it using current den tal term in ology. Now, all E n glish-speakin g d en tists can b e aw are o f w hat G raf S p e e sa id ; an d on e no longer has to d ep en d on an oth er’s interpretation. I d id n on e o f th e tran slation but on ly served to p ersu ad e Dr. B ied e n b a c h an d Dr. H otz to interpret this fa m o u s w ork. H. PERRY HITCHCOCK, DMD, MSD
in the sagittal plane in w hich the m asticatory sur faces of upper and lower teeth occlude can be ob tained from the photographic profile of the skull in Figure 1. Here, as a consequence of attrition, the molars have lost all the cusps of the crow ns so that th e m u tu a lly abrad ed m a stic a to ry su rfa ces fit exactly on top of each other. Thus, the upward con cave curve describes a sm ooth line in the sagittal plane. T eeth with com pletely intact crown cusps fundam entally also present the same curvelike ar rangem ent of (masticatory) occlu sal surfaces, except that they show an irregularly em bossed profile line, w hose in d en tation s are clea rly reco g n izab le as sm all fluctuations on an assum ed curvilinear base (Zero line) (Fig 2). As an exact exam ination of the curve is more com plicated in a dentition w ith pre served cusps than in cases in w hich they are reduced by wear, it is preferable to choose the worn cases in order to discuss the basic findings. If, in such a special case, the curve is determ ined in a profile view of the skull, for exam ple, Figure 1, or w ith a com pass, on its geom etric projection on the sagittal plane, the findings are the follow ing: — That the total visible con tact lin e of the molar m asticatory surfaces lies on the same arc of a circle; furthermore, — That in the sagittal plane the posterior continu
ation of this arc touches the m ost anterior point of the m andibular condyle. A ccordingly, the points of the m andible w hich glide in contact along the upper part of the skull are lying on the same cylin drical surface. The location of the axis of that cylin d er’s curvature could be de term ined by reconstruction and m easurem ent w ith the com pass at the level of the horizontal m idorbital plane, posteriorly from the crista lacrim alis poste rior. In the lateral view it appears as a point (Fig 1, a). The attritional configuration of the teeth develops through their respective gliding m ovem ents and thus conform s to the pathway w hich the teeth of the m andible follow. As the teeth in the jaw s have to be considered as fixed, this pathway is not only a m an ifestation of tooth m ovem ent but an effect of the displacem ent of the w hole m andible. C onsidering at the same tim e Figure 1, it follow s that the m ovem ent occurs in circular paths ju st as a pendulum m oves around an axis. T h is axis is given by a transverse connecting line from the sagittally projected centers of the masticatory curvature of both sides. From Figure 2, it further follow s that the m ost anterior part of the surface of the condyle also m oves on a circular path w ith the same length of radius as the occlu sal surfaces of the m olars. In other words, these parts move on the sam e cylin d ric surface. Spee : GLIDING PATH OF MANDIBLE ALONG SKULL ■ 671
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C O N T R IB U T IO N
Fig 1 a, b ■ Illustrations from same skull; l,a in exact profile view; 1 ,b from somewhat anterior view. Fig l,a shows curve for for ward movement of mandible; 1 ,b shows curve for occlusal surface without reduction in length. Di mensions of illustrations are comparable as they were repro duced at equal magnification (r indicates radius of curve for mas ticatory [occlusal] surfaces and c indicates center of curve).
Fig 2 ■ Dentition of adult with well-preserved crown cusps. Only surface of still-present sec ond deciduous molar (m) shows attrition. This surface prolongs occlusal line of articulatory sur faces of posteriorly located mo lars quite naturally.
Fig 3 ■ Mandible of child.
Fig 4 ■ Series of points of hu man, worn occlusal surface accu rately located in relative position to each other and to anterior sur face of mandibular condyle, k. Natural size. Two preparations a, b.
v'enag \e’d & Comp, e
The m ost prom inent anterior part of the m andibu lar condyle is also the most lateral. Thus, according to the explanations of M eyer,2 it belongs to that half of the condyle w hich during sym m etric forward and backward m ovem ents of the m andible is moving up and down very closely along the tuberculum. T he m asticatory surface of the upper teeth and the articulating surface of the glenoid tuberculum with its m eniscus form the analogous parts of a big cy lin drical curve around whose surface area the points of the low er jaw glide. The radius of the glenoid tuber672 ■ JADA, Vol. 100, M ay 1980
culum is m uch shorter than the radius of the cy lin der. Yet a con cen trically arranged series of basic points corresponding to its surface can be estab lished for the com plete lin e of m otion of the m an dibular condyle along the tuberculum , because the thicker part of the wedge-shaped m eniscus in terca lates betw een the two areas and com pensates the shorter radius of the tubercular curvature. As for ward and backward gliding of the m andible takes place in a path of circular m otion, such d isp lace m ents can occu r over longer distances w ithout any
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need for the arches to separate from each other. Thus, m asticatory efficiency is guaranteed. A sep aration of the occlusal surfaces is only inevitable in order to overcom e the contact of strongly protruding upper and lower canines. But this can also be elimi nated by wear. If the occlusal surfaces of the teeth were arranged on a plane, and, since the tuberculum articulare is present, parallel shifting of the closely apposed arches for purposes of crushing and grinding food would not be possible. This ought to be considered in the construction of dentures, not only to enable better m astication but also in order to avoid lever effects during chewing. These levering effects are less manifest with increased length of contact sur face in every position of the firmly occluded teeth. The backward gliding of the m andible, usually fol lowing an incising movement, is especially effective and m ainly responsible for sagittal attrition. Isolated backward m ovem ents of the mandible are rather unusual. In addition, as concerns wear, one has to consider alternating lateral rotation of the mandible around nearly vertical axes. During these m ovem ents, the grinding action on the teeth on the side toward w hich the movement occurs is in alm ost transverse directions. During this, the teeth of the lower arch shift in a laterally descending direction below the m ost protruding lateral border of the upper crowns (Fig 2). Evidently the teeth of the other side w hich simultaneously move forward and m edially cannot remain in contact with the upper arch. This would also be a consequence of the unilateral protrusion of the condyle on top of the m edial half of the tuber culum (Meyer). The backward movement, during w hich the mandibular condyle slips back into the fossa, can occur by gliding of the arches (backward and outward), just as they are aligned. This m ove ment, of course, also follows the upw ard concave curve w hich was considered above in the sagittal projection (however slightly shortened), as the path of sagittal gliding of the mandible. But this time the movem ent occurs parallel to the greatest length of the curve w hich is visible only if view ed somewhat anteriorly and laterally, since it is flatter. From this perspective, the transverse distance between con dyle and lateral surfaces of the teeth does no longer appear shortened. Y et one finds that in spite of its longer radius the continuation of this curve also touches the lateral anterior surface of the condyle (Fig 1, b). Strictly speaking, the worn surfaces of the molars on each side form together, more or less, a rectangu lar area. Its diagonal line, slightly sagittally posi tioned, is curved spirally towards the opposite side; since the surfaces of the third molars have an inward slant, those of the second m olars are m ore horizontal and those of the first molars inclined outward. Thus
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it somewhat digresses from a cylindrical surface. This effect, aside from the difference in thickness of the enamel, is due to the tilted position of the teeth. As is well-known, the crow n of the second molar and even more so of the third is inclined lingually in the mandible and labially in the upper jaw in order to contact its antagonist. The resulting com plication for the occlusal surfaces is not significant enough to cause a relevant deviation from the path of m andibu lar motion just described. During sagittal sym m etric displacements, the com plication does not even ap pear, because all sym m etric m ovement effects in the direction of the m edian plane are mutually cancel led, the sam e as the medially directed forces of the external pterygoid muscles. Regarding the path for sagittal displacem ent, based on autographic curves about the m ovem ent of the lower incisor, Langer expressed the opinion that the mandible is shifting on very flat curves or rather on straight lines. As a rule, this is not the case. Furthermore, the photographic curve about jaw dis placem ent recently obtained by Luce,4 under Bowditch’s guidance, is not in accord with Langer’s views, but is in agreement with the results which derive from the modeling of the occlusal surfaces of the teeth in the path of sagittal displacement. It shows that the mandible glides forward in an up ward concave curve. However, the autographic curves are short, be cause the greatest possible forward gliding distance of the mandible amounts to about V-k cm (footnote, p 289). With this displacement, the lower incisors and canines usually enclose the upper ones from an teriorly and laterally. At the same time, the buccal edges of a lower molar move under the buccal edges of the next anterior upper tooth. For m astication, only about two thirds of this gliding distance is used, and for specific grinding movements, only a third. For m asticatory function, this rather small gliding distance is very efficient and m ost important because of its many repetitions on very long m asti catory surfaces. Along the whole length of these surfaces, the d irection of m ovem ent is clearly marked through the form of attrition, just as on a surface of a joint. Therefore, the form of the gliding surface of the molars offers the best information for evaluating the course of the movement. It is also the best criterion for analysis of the autographic curves. Within certain limits, the ligaments of the m andi ble generally adapt themselves to the new position of the shifted mandible without tension. A s Langer1 already found, only the fibers of the medial a c c e s s o r y lig a m e n t, w ith in th e f a s c ia b u c c o pharyngea, tighten very early during forward glid ing. Since it inserts on the anterior surface of the condyle, a force develops w hich would m ove the chin in the direction of the forehead. This is in accordance with the upward concave curve of the Spee: GLIDING PATH OF MANDIBLE ALONG SKULL ■ 673
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m asticatory surfaces of the teeth. In case of a m aximal mandibular forward dis placem ent, the concordant movement of the m enis cus is restrained by its posterior attachm ents. Its anterior half being inserted like a strong wedge be tween condyle and tubercle, a further inhibition of condylar forward movement results in conjunction with the tension of the lateral ligament. I interpret the small dip at the end of the autographic glenoidal curve in L u ce’s Figure 4 as a consequence of a more pronounced interposition of the m eniscus between the bony parts of the temporomandibular joint.
Specific findings in different dentitions Among anim als, as far as my experience goes, the ruminating and hoofed species as well as some pri m ates show the sam e upw ard con cave occlusal curves in their dentition without exception. The posterior continuation of the curve touches the an terior surface of the condyle just as in humans. The radius of the cylindric surface on w hich the concave curve lies, is longer in larger animals and more prognathic skulls. Different lengths were: horse, 21.9 cm ; Cervus elephas, 18.0 cm ; Cervus dama, 12.9 cm ; small monkey, 8.5 cm; and adult man, 6.5 to 7.0 cm. A com parison of the measurements found in ani mals w ith those found in man shows that, aside from body size, the relative sm allness of the visceral cranium coincides w ith a shorter radius and a larger curvature. This appears to point tow ard an increase of the m asticatory surface within a lim ited special area and therefore it seems appropriate. Rodents and carnivores do not show curves of the m asticatory surfaces. The tuberculum articulare, present in all the former anim als, is missing. Therefore, develop ment of curved occlusal surfaces as well as the circu lar path during sagittal forward displacem ent seems to depend on the presence of the tuberculum . Based on this recognition, several human cases w hich de viate from the rule can be explained. These cases w ill be discussed at the end of this paper. I under took the specific exam ination of hum an jaws on as m any sp ecim ens as possible, in order to avoid p u re ly in d iv id u a l v a ria tio n s . H o w e v e r, th e ir number w as not very large because only beautifully preserved and com pletely developed jaws could be used. Skeletal jaws w ith indiscrim inately and artifi cially inserted teeth were rejected. But, since good jaws of different races yielded the same findings just described, they have a general significance. The observations had to establish the positional relationship between the occlusal surfaces of the teeth and the surface of the mandibular condyle. They w ere made in various ways. The sim plest way to obtain the necessary m ea surements is to evaluate exact geom etric sagittal 674 ■ JADA, Vol. 100, May 1980
projections. Since, in adults, the alignm ent of m o lars does not decidedly deviate from the sagittal plane (on the average less than 20°), projections through large lenses, for exam ple, photographs, can be used w ithout relevant errors. By measuring the crowns w ith calipers, I determined the radius of the curve approxim ately if strong cusps were present (in ruminants). In abraded m asticatory surfaces in hu mans I did it more accurately: the vertical distances of a line of arbitrary points on the occlusal surface and of the m ost anterior point of the condylar sur face of the mandible were determined from the hori zontal plane and correctly entered in a system of coordinates. Through accurate reconstruction, the center of a circle touching as many of the points as possible was determined; the results could not be anticipated, but in most cases such a center could be obtained approxim ately. In some cases with decided abrasion all points were located exactly on the same circle (Fig 4). Such exact circular attrition is not explainable by simple wear. Specific effects or form relationships, which continuously acted toward this kind of development, m ust have existed from the beginning. As mentioned at the beginning, this is partly reflected from the fact, that even in nonabrad ed molars, cusps are arranged along a downward convex circle, w hich already shows in a ch ild ’s jaw with deciduous teeth at the same time as the tuber culum articulare develops. U ltim ately, develop mental relationships peculiar to a species m ust be considered (Fig 2, 4). In the beginning, the curve of the m asticatory surface of the mandible is sometimes not very clear and is m uch flatter than in the upper jaw where it is seldom missing. In such cases, the varying pressure exerted on the teeth appears to gradually induce com pensation of the curve difference. In general, it appears that teeth whose antagonists are missing are more and more elongated by new bone formation in the alveoli. Roots of teeth with intact antagonists remain deeply set in the alveolus. Therefore, we may assume that teeth, as long as they are subject to little pressure, will continue to grow more than those exposed to stronger pressure. This would be a continuously acting m echanism in order to adjust the curves of the masticatory surfaces of both arches. In adults, the radius of the curve of mandibular motion had a length of 6.5 to 7.0 cm, usually equal on both sides. Variations within these limits depend on the angular position of the ramus to the arch and on the width and height of the ramus. In children with complete sets of deciduous teeth, the radius is shorter than in adults, because of the generally smaller dimensions, despite the obtuse position of the still short ramus to the arch. In a special case the radius measured approxim ately 4.6 cm. Among the m any individual variations of the
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fixed parts of the m asticatory “ array,” we have to consider those in w hich the upward concave curve of the m asticatory surface did not exist. They are not especially rare. For all of them , it appears that the effect of the tuberculum articulare is elim inated (blocked). I have observed the following: — An extrem ely low or almost nonexisting tuber culum (several cases). — Shortening of the sagittal and vertical dimen sions of the ramus on one side so that its condyle could never have been in the fossa, while the other side showed the usual configuration (one case). — Unusual bulk of the condyle with so short a distance between tuberculum and anterior wall of the external auditory canal that the condyle of either side could never have been in the fossa (one case). — The m ost protruding part of the condyle does not lie laterally but opposite the posteriorly tilted medial part of the tuberculum, with the middle of its anterior surface on its m edial half, so that it does not stay as deep in the fossa as usual (three cases). Extrem e thickness of the m eniscus, w hich I, how ever, have not observed, w ould also eliminate the action of the tuberculum.
CONTRIBUTION
W ith s u c h c o n f ig u r a tio n of th e te m p o r o m and ib ular joint, the m a stica to ry m ovem en ts would have to occu r through level forward and backward gliding within the joints as in rodents. — K ie l, th e 2 4 th o f M a rc h , 1 8 9 0 .
Originally published in the Archives of Anatomy and Physiology, 16:285-294, 1890. Translation rights and illustrations use granted by Springer Verlag, Heidelburg. Dr. Biedenbach is associate professor, department of physiology, Uni versity of Texas Health Science Center at San Antonio. Dr. Hotz is founder of the cleft palate program, department of orthodontics, Zahnartzliches Institut der Universtat Zurich. Dr. Hitchcock is professor and chairman, department of orthodontics, University of Texas Dental School at San Antonio, 7703 Floyd Curl Dr, San Antonio, 78229. Address requests for reprints to Dr. Hitchcock. 1. Langer, Das Kiefergelenk des Menschen. Sitzungsberichte der kaiserl. Akademie der Wissenchaften zu Wien 1880. S. 457. 2. Meyer, H. Das Kiefergelenk VH. Beitrag zur Statik und Mechanik des menschlichen Knochengerüstes. Dies Archiv 1865. S. 719. 3. Henke, Handbuch der Anatomie und Mechanik der Gelenke, 1863. 4. Luce, C.E. The movements of the lower jaw. Boston Med Surg J, 1889, Figure 4.
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