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The Rotation Of The Mandible Resulting From Growth: Its Implications In Orthodontic Treatment
生长导致的下颌骨旋转：其对正畸治疗的影响

F. F. Schudy, D.D.S. F.F. Schudy, D.D.S.Houston, Texas 休斯顿

An intensive study of the growth of the human head will inevitably lead to the realization that it involves the most complicated anatomical complex in all creation. The interrelationships are infinite and the causes and effects of these relationships are almost imponderable. The more our knowledge increases the more our ignorance unfolds. The vast stretches of the unanswered and the unfinished still outstrip our collective comprehension. It is little wonder that the allied forces of medical science are making such slow progress in gaining an understanding of the growth of the jaws.
深入研究人类头部的生长过程，必然会认识到这是所有造物中最复杂的解剖结构。其中的相互关系无穷无尽，而这些关系的因果关系则几乎难以捉摸。我们的知识越丰富，我们的无知就越多。绵延不绝的未解之谜和未解之谜仍然超出了我们的集体理解能力。这也就难怪，医学界在了解颌骨生长方面进展如此缓慢了。
The rotation of the mandible resulting from an inharmony between vertical growth and anteroposterior or horizontal growth has important implications in orthodontic treatment (Figs. 1,2 and 3 ). It is well-recognized that the mandible rotates both clockwise and counterclockwise as the growth processes unfold. This is particularly true during the pubertal growth acceleration. Now, how does this rotation affect orthodontic treatment? Clockwise rotation (as viewed from the patient’s right side) is a result of excessive vertical growth as it relates to horizontal growth, and tends to cause a reduction of vertical overbite. Counterclockwise rotation is a result of a deficiency in vertical growth as related to horizontal growth, and tends to cause an increase of the vertical overbite. Rotation of the mandi-
垂直生长与前后或水平生长不协调导致的下颌骨旋转对正畸治疗有重要影响（图 1、2 和 3）。众所周知，随着生长过程的展开，下颌骨会顺时针和逆时针旋转。这在青春期生长加速期尤为明显。那么，这种旋转对正畸治疗有什么影响呢？顺时针旋转（从患者的右侧看）是垂直生长过快的结果，因为它与水平生长有关，往往会导致垂直咬合过大。逆时针旋转是垂直生长与水平生长不足的结果，往往会导致垂直过度咬合增加。下颌旋转
Read at the biennial meeting of the Edward H. Angle Society of Orthodontia, Phoenix, Arizona, October 1963.
1963 年 10 月，在亚利桑那州凤凰城举行的爱德华-H-角矫形协会两年一度的会议上宣读。
ble involves primarily the vertical growth of the dentocephalic complex. It is this growth on which we would like to focus your attention. Documented evidence will be presented in this study to corroborate the validity of this thesis.
这主要涉及到齿脑复合体的垂直生长。我们希望大家关注的正是这种生长。本研究将提供书面证据来证实这一论点的正确性。
For our purpose here we are dealing only with growth increments which cause positional changes of the chin. Some of these increments cause the chin to move vertically while others cause it to move anteroposteriorly. To those increments which cause the chin to move vertically we apply the term, “vertical growth”; to the one increment, namely the condyles, which causes the chin to move forward we apply the term “horizontal growth”. Vertical and horizontal growth are opposing forces competing for the control of the chin. The resultant of their effect is usually a downward and forward direction.
在这里，我们只讨论导致下巴位置变化的生长增量。其中一些增量会导致下巴垂直移动，而另一些则会导致下巴前后移动。对于导致下巴垂直移动的增量，我们称之为 "垂直生长"；对于导致下巴向前移动的增量，即髁状突，我们称之为 "水平生长"。垂直生长和水平生长是争夺下巴控制权的对立力量。它们作用的结果通常是向下和向前。

Purpose 目的

This study was initiated for the purpose of documenting the growth changes which produce rotation of the mandible. We hoped to identify the specific increments of growth responsible for this phenomenon and wished to point out that it is the relationship of increments one to another which is so important and which results in changes in proportion. A comprehensive documentation and a sound interpretation of these facts should be a worthwhile contribution toward better treatment procedures.
启动这项研究的目的是记录导致下颌骨旋转的生长变化。我们希望找出导致这一现象的特定生长增量，并希望指出，生长增量之间的关系非常重要，它导致了比例的变化。对这些事实进行全面的记录和合理的解释，将有助于改进治疗程序。
MAY MAY 五月 五月
1958 19bl
Fig. 1 Showing the growth of a female, age 11 to 14 years, in which the condyles grew out of proportion to vertical molar growth. This resulted in a 4 ∘ 4 ∘ 4^(@)4^{\circ} rotation and marked forward swing of the mandible, a 2 mm increase in vertical overbite, and an adverse effect on the facial profile. (From the U. of Texas growth study)
图 1 显示了一名 11 至 14 岁女性的生长情况，其髁突的生长与臼齿的垂直生长不成比例。这导致了下颌骨的 4 ∘ 4 ∘ 4^(@)4^{\circ} 旋转和明显前摆，垂直过咬合增加了 2 毫米，并对面部轮廓产生了不良影响。(来自德克萨斯大学的生长研究）

Preliminary Discussion of the Growth of the Jaws
关于颌骨生长的初步讨论

While many investigators have observed changes in the angulation of the mandibular plane, apparently the importance of relating these changes to overbite has not been fully recognized.
虽然很多研究者都观察到了下颌平面角度的变化，但显然这些变化与咬合过度之间的关系的重要性还没有得到充分认识。
If the condylar growth is greater than vertical growth in the molar area, the mandible rotates counterclockwise and results in more horizontal change of the chin and less increase in anterior facial height. Extremes of this condition cause closed bites (Fig. 1). Conversely, if vertical growth in the molar region is greater than that at the condyles, the mandible rotates clockwise resulting in more anterior facial height and less horizontal change of the chin. Extremes of this condition cause open bites (Fig. 2 ) 2 ) 2)2).
如果臼齿区的髁突生长大于垂直生长，下颌骨就会逆时针旋转，导致下巴的水平变化较大，面部前部高度增加较少。这种极端情况会导致闭合性咬合（图 1）。相反，如果臼齿区的垂直生长大于髁状突的垂直生长，下颌骨就会顺时针旋转，导致面部前高增加，而下巴的水平变化较小。这种极端情况会导致开放性咬合（图 2 ) 2 ) 2)2) ）。
Fig. 2 Here is a growth study from the files of U. of Mich. From age 6 to 10 years the chin grew downward and forward and the mandibular plane moved downward in a parallel manner. At age 10 the condyles almost completely ceased growing. Then the chin moved downward and backward, and the mandibular plane became 7 ∘ 7 ∘ 7^(@)7^{\circ} steeper ( 35.5 ∘ 35.5 ∘ 35.5^(@)35.5^{\circ} to 42.5 ∘ 42.5 ∘ 42.5^(@)42.5^{\circ} ). The posterior growth analysis showed that the condyles grew 4 mm while vertical growth in the molar area was 10.5 mm ( 5 + 2.5 + 3 ) ( 5 + 2.5 + 3 ) (5+2.5+3)(5+2.5+3).
图 2 这是密歇根大学档案中的一项生长研究。从 6 岁到 10 岁，下巴向下和向前生长，下颌平面以平行的方式向下移动。10 岁时，髁突几乎完全停止生长。然后，下巴向下和向后移动，下颌平面变得 7 ∘ 7 ∘ 7^(@)7^{\circ} 陡峭（ 35.5 ∘ 35.5 ∘ 35.5^(@)35.5^{\circ} 到 42.5 ∘ 42.5 ∘ 42.5^(@)42.5^{\circ} ）。后生长分析表明，髁突增长了 4 毫米，而臼齿区的垂直生长为 10.5 毫米 ( 5 + 2.5 + 3 ) ( 5 + 2.5 + 3 ) (5+2.5+3)(5+2.5+3) 。
The mandibular first molars moved backward about 3 mm ; thus, it would have been impossible to have corrected a Class II condition under these circumstances.
下颌第一臼齿向后移动了约 3 毫米；因此，在这种情况下不可能矫正 II 级状况。
We know that growth at the mandibular condyles produces a forward component of the chin, not a downward, nor a downward and forward component. It is only when the vertical increments of facial growth begin to assert their influence on condylar growth through occlusal contact that a downward and forward direction of the chin is produced. Thus, it can be said that condylar growth is pitted against the combined vertical elements of growth. The final vector of growth of the chin is a resultant of the struggle between horizontal growth and vertical
我们知道，下颌髁状突的生长会使下巴向前，而不是向下，也不是向下和向前。只有当面部生长的垂直增量开始通过咬合接触对髁突生长产生影响时，才会产生下颏向前的方向。因此，可以说髁突的生长是与垂直生长的综合因素相对抗的。下巴生长的最终矢量是水平生长和垂直生长斗争的结果。
growth, in other words, between condylar growth and vertical growth of molars.
换句话说，就是臼齿的髁突生长和垂直生长之间的关系。
What are these vertical “elements” of growth? Specifically where are the increments which produce an increase in facial height? They are as follows: (Fig. 3) (1) growth at nasion and in the corpus of the maxilla which produces an increase in the distance from nasion to anterior nasal spine and causes the maxillary molars and posterior nasal spine to move away from the sella-nasion plane, (2) growth of the
这些垂直生长的 "要素 "是什么？具体来说，脸部增高的增量在哪里？它们如下：图 3）(1) 鼻翼和上颌骨体部的生长使鼻翼到前鼻骨棘的距离增加，并使上颌臼齿和后鼻骨棘远离鼻翼平面，(2) 上颌骨体部的生长使鼻翼到前鼻骨棘的距离增加，并使上颌臼齿和后鼻骨棘远离鼻翼平面，(3) 上颌骨体部的生长使上颌臼齿和后鼻骨棘远离鼻翼平面。
A = { I II III IV A =  I   II   III   IV  A={[" I "],[" II "],[" III "],[" IV "]:}A=\left\{\begin{array}{l} \text { I } \\ \text { II } \\ \text { III } \\ \text { IV } \end{array}\right.
Fig. 3 In harmonious facial growth there is balance between increment A A AA and increments I, II, III, and IV.
图 3 在和谐的面部生长过程中， A A AA 增量与 I、II、III 和 IV 增量之间保持平衡。
maxillary posterior alveolar processes causing the molar teeth to move away from the palatal plane, and (3) growth at the mandibular posterior alveolar processes causing the molar teeth to move occlusally.
(3) 下颌后牙槽突的生长导致磨牙向咬合面移动。
The vertical growth of the anterior alveolar processes does not seem to have an appreciable effect on facial height. It is merely expressed in varying degrees of overbite.
前牙槽突的垂直生长似乎对面部高度没有明显影响。它只是表现为不同程度的咬合过度。
The dorsal migration of the glenoid fossa is a very real factor in many cases and tends to cancel out the growth of the condyles; thus, in a sense it is arrayed on the side of vertical growth. Surface additions of bone at pogonion usually have an insignificant effect, but occasionally we do see quite appreciable apposition in this area.
在许多病例中，盂窝的背移是一个非常实际的因素，它往往会抵消髁突的生长；因此，从某种意义上说，它是站在垂直生长一边的。髁状突表面增加的骨量通常影响不大，但我们偶尔也会在这一区域看到明显的骨量增加。
Clockwise rotation of the mandible is a result of more posterior vertical growth than condylar growth, the point of rotation being the condyles. We know that when vertical growth exceeds horizontal growth, (condylar growth) pogonion cannot keep pace with the forward growth of the upper face and the mandibular plane must become steeper (Fig. 2). What effect does this type of growth have upon treatment? Obviously this condition would not help reduce the ANB angle, and it would not aid in correction of a Class II molar relation. However, it would tend to help correct the vertical overbite of the incisors. Many such growth patterns actually do reduce the vertical overbite, perhaps the majority do not. There is ample evidence to show that a predominance of vertical growth of the face facilitates the correction and retention of vertical overbite.
下颌骨的顺时针旋转是后方垂直生长多于髁状突生长的结果，旋转点是髁状突。我们知道，当垂直生长超过水平生长时，（髁突生长）pogonion 无法跟上上面部向前生长的速度，下颌平面必须变得更加陡峭（图 2）。这种生长方式对治疗有什么影响？很明显，这种情况无助于减小 ANB 角，也无助于矫正 II 类臼齿关系。但是，它往往有助于矫正门牙的垂直过咬合。许多这样的生长模式实际上确实可以减少垂直咬合过度，但也许大多数并不能。有充分的证据表明，脸部以垂直生长为主有利于矫正和保持垂直咬合过度。
Counterclockwise rotation of the mandible is a result of more condylar growth than combined vertical growth. This type of rotation is nearly always accompanied by a forward movement of pogonion and an increase in the
下颌骨逆时针旋转是髁突生长多于垂直生长的结果。这种类型的旋转几乎总是伴随着舌骨的前移和髁突的增加。
facial angle. The point of rotation is the most distal mandibular molar in occlusal contact. This “flattening” of the mandibular plane tends to increase the vertical overbite and renders vertical overbite correction and retention more difficult (Fig. 1).
面角。旋转点是咬合接触最远端的下颌臼齿。下颌平面的这种 "扁平化 "倾向于增加垂直咬合过度，使垂直咬合过度的矫正和保持更加困难（图 1）。
The size of the gonion angle has an important influence upon the number of degrees of resultant counterclockwise rotation. The smaller the gonion angle, the greater rotation is produced for each mm of forward movement of pogonion. When this angle is extremely small it is almost a physical impossibility for the chin to move forward without a “flattening” of the mandibular plane. By the same token, when the corpus of the mandible undergoes excessive rotation, we may expect the chin to move forward markedly.
柱头角的大小对逆时针旋转的度数有重要影响。腮弓角度越小，腮弓每向前移动一毫米所产生的旋转就越大。当这个角度极小时，下巴几乎不可能向前移动而不使下颌平面 "变平"。同样，当下颌骨体发生过度旋转时，我们可以预期下巴会明显向前移动。
An obtuse gonion angle may compensate for a short corpus. Moreover, it may also compensate for a short ramus. In other words, the correct gonion angle helps to compensate for inharmonies of facial proportions. This angle has a correlation coefficient of .74 with the OM angle and .61 with the SN-MP angle (where significance starts at .27 ). Thus, it could be said that these three angles represent a closely interrelated anatomical complex.
钝的齿根角可以补偿短的齿冠。此外，钝角还可以补偿短小的臼齿。换句话说，正确的齿槽角有助于补偿面部比例的不协调。该角度与 OM 角度的相关系数为 0.74，与 SN-MP 角度的相关系数为 0.61（显著性从 0.27 开始）。因此，可以说这三个角度代表了一个密切相关的解剖复合体。
More knowledge is needed regarding the behavior of the gonion angle. We do not have sufficient information about the changes that this angle undergoes during the growing period and we do not fully understand the significance of these changes. We need to know whether or not treatment causes changes in this region. Obviously, when the gonion angle becomes more acute the mandibular plane tends to become flatter, and when this angle becomes more obtuse the mandible tends to become steeper. In a growth study of sixty-two individuals the gonion angle changed an average of .5 of a degree
我们还需要更多关于性腺角行为的知识。我们对该角度在生长期间发生的变化没有足够的信息，也不完全了解这些变化的意义。我们需要知道治疗是否会导致该区域发生变化。很明显，当腮腺角变得更锐利时，下颌平面往往会变得更平坦，而当这个角度变得更钝时，下颌往往会变得更陡峭。在一项对 62 人进行的生长研究中，颌角的平均变化幅度为 0.5 度
in the direction of acuteness. In a growth study of a group of fifty treated cases the average change was an increase of 1.5 degrees. This suggests that treatment causes this angle to become more obtuse.
在尖锐度方向上。在对一组 50 个接受过治疗的病例进行的生长研究中，平均变化增加了 1.5 度。这表明，治疗会使这个角度变得更加钝。
The recent work of Björk 2 2 ^(2){ }^{2} has a definite relationship to this subject. By the use of metal implants he has shown that the inclination of the inferior border of the mandible may change considerably by resorption at the gonial region and deposition in the region of the symphysis. Thus, the extremities of the inferior border of the corpus undergo changes while the central portion, in the region of the first molar, apparently changes very little. Since vertical measurements are made at the site of the first molar tooth, they are not appreciably affected by these changes.
比约克（Björk） 2 2 ^(2){ }^{2} 的最新研究成果与这一主题有明确的关系。通过使用金属植入物，他证明了下颌骨下缘的倾斜度可能会因龈沟区域的吸收和干骺端区域的沉积而发生显著变化。因此，牙冠下缘的两端会发生变化，而位于第一磨牙区域的中央部分显然变化很小。由于垂直测量是在第一臼齿部位进行的，因此不会受到这些变化的明显影响。
The degree of facial divergence (measured by the angle SN-Mandibular Plane) also has a significant bearing on mandibular rotation. The larger the SN-MP angle, the more the mandible tends to become steeper and the more the chin moves backward. The smaller the angle, the greater the tendency of the mandible to become flatter and the chin to grow forward.
面部发散程度（以 SN-Mandibular Plane 角度测量）对下颌旋转也有重要影响。SN-MP角度越大，下颌骨越倾向于变得陡峭，下巴越倾向于向后移动。角度越小，下颌骨越倾向于变平，下巴越倾向于向前生长。

Mechanism of Growth 增长机制

In Figure 4 is shown an edentulous individual. Three cephalograms were taken - one in centric occlusion with the dentures in place, one in a position of overclosure with dentures removed and one with a block of wax between the dentures.
图 4 显示的是一名无牙患者。我们拍摄了三张头像照片--一张是装有假牙的中心咬合照片，一张是取下假牙的过度咬合照片，还有一张是在假牙之间放置蜡块的照片。
You will note that as the molar height increases the chin swings downward and backward, the mandibular plane becomes steeper, the gonial angle moves posteriorly and the facial angle decreases. Thus, by varying the molar height we were able to change the facial angle fourteen degrees and the inclination of the ramus eleven degrees.
您会注意到，随着臼齿高度的增加，下巴向下和向后摆动，下颌平面变得更陡峭，盂角向后移动，面部角度减小。因此，通过改变臼齿的高度，我们可以改变面部角度 14 度，改变横梁倾斜 11 度。
Fig. 4 An edentulous individual showing variation in the facial angle caused by changing the molar height.
图 4 一个无牙患者的面部角度因臼齿高度的变化而变化。
It will readily be seen that molar height not only controls the vertical position of the chin, but also to a considerable extent the anteroposterior position. These principles have a very definite application to the treatment of Class II malocclusions. Obviously too much vertical growth of the molar teeth would prevent the forward positioning of the chin and thereby render Class II correction very difficult.
不难看出，臼齿的高度不仅控制着下巴的垂直位置，还在很大程度上控制着前后位置。这些原则在治疗二类错合畸形时有非常明确的应用。很明显，臼齿垂直生长过多会妨碍下巴的前倾，从而使二类畸形矫正变得非常困难。
In Figure 3 we have tried to illustrate the mechanism of the growth of the jaws. These five growth increments are the principal ones with which the orthodontist is concerned. The relationships of these increments control the behavior of the mandible. They determine whether pogonion shall move downward and forward or downward and backward and whether a Class II condition will be easy or difficult to correct.
在图 3 中，我们试图说明颌骨生长的机制。正畸医生主要关注这五个生长增量。这些增量的关系控制着下颌骨的行为。它们决定了下颌前突是向下向前移动还是向下向后移动，也决定了二级状况是容易矫正还是难以矫正。
When pogonion and nasion grow forward at an equal rate, increment A will equal the sum of increments I, II, III, and IV. In other words, growth
当鼻小柱和鼻翼以相同的速度向前生长时，增量 A 将等于增量 I、II、III 和 IV 的总和。换言之，增长
at the condyles must equal the anteroposterior growth at nasion, plus the vertical growth of the corpus of the maxilla, plus the vertical growth of the maxillary alveolar process, plus the vertical growth of the mandibular alveolar process. Then it may be said that the horizontal growth at the condyles is pitted against combined vertical growth. Growth at the condyles is trying to carry the chin forward and combined vertical growth in the molar area is trying to carry the chin downward. The result is usually downward and forward; however, it may be downward and backward as we shall see.
髁突处的水平生长必须等于鼻翼处的前后生长，加上上颌骨体的垂直生长，再加上上颌牙槽突的垂直生长，再加上下颌牙槽突的垂直生长。因此可以说，髁突的水平生长与垂直生长的结合是对立的。髁状突的生长试图将下巴向前托起，而磨牙区的合并垂直生长则试图将下巴向下托起。结果通常是向下和向前，但也可能是向下和向后，我们将看到这一点。
When growth at A exceeds I, II, III, and IV, the mandibular plane becomes flatter and pogonion moves forward more than nasion. When the sum of I, II, III, and IV appreciably exceeds A, pogonion will usually move backward with relation to nasion and the mandibular plane will become steeper. When growth at A equals the sum of II, III, and IV the mandibular plane moves down in a parallel manner. However, excessive mesial movement of the molar teeth causes difficulty in measuring vertical increments.
当 A 处的生长速度超过 I、II、III 和 IV 时，下颌平面会变得更平坦，舌骨向前移动的速度会大于鼻翼向前移动的速度。当 I、II、III 和 IV 的总和明显超过 A 时，舌骨通常会相对于鼻翼向后移动，下颌平面会变得更陡峭。当 A 处的生长量等于 II、III 和 IV 的总和时，下颌平面会平行向下移动。然而，臼齿的过度中向移动会给垂直增量的测量带来困难。
The ratio between horizontal and vertical growth increments is called the posterior growth analysis. It is an aid in explaining the postural behavior of the mandible (Fig. 2). Please bear in mind that it is the relationship of these increments one to another which controls the forward growth and the rotation of the mandible.
水平和垂直生长增量之间的比率称为后生长分析。它有助于解释下颌骨的姿势行为（图 2）。请记住，正是这些增量之间的关系控制着下颌骨的向前生长和旋转。
You will note that the anterior teeth are absent. This is because these teeth do not have an appreciable effect on anterior facial height. The posterior teeth literally force the jaws apart, thereby increasing anterior facial height. The vertical growth of the incisor teeth is expressed in varying amounts of overbite.
您会注意到，前牙是没有的。这是因为这些牙齿对面部前部高度没有明显影响。后牙实际上会迫使下颌分开，从而增加面部前部的高度。门牙的垂直生长表现为不同程度的咬合过度。
Now what is the clinical application?
临床应用是什么？
All investigators are agreed that orthodontic treatment does not stimulate growth at the mandibular condyles. If this is true we have only the vertical increments that we may possibly change to serve our purposes. If we can inhibit vertical growth it will have the same effect as stimulating growth at the condyles. We are quite sure that we can stimulate the vertical growth of the alveolar processes, and we think we can inhibit this growth. If vertical growth is deficient we try to stimulate it, and if vertical growth is excessive we try to inhibit it. The question now arises - how do we tell when vertical growth
所有研究者都认为，正畸治疗不会刺激下颌髁状突的生长。如果这是真的，我们就只有可能改变垂直方向的增量来达到我们的目的。如果我们能抑制垂直方向的生长，其效果将与刺激髁突的生长相同。我们可以肯定，我们可以刺激牙槽突的垂直生长，而且我们认为我们可以抑制这种生长。如果垂直生长不足，我们就设法刺激它；如果垂直生长过度，我们就设法抑制它。现在的问题是--我们如何判断垂直生长
B
Fig. 5 Showing two opposite facial types. A, A hyperdivergent individual in which vertical growth is excessive and/or condylar growth is deficient. B, A hypodivergent type where vertical growth is deficient.
图 5 显示两种相反的面部类型。A, 垂直生长过度和/或髁突生长不足的高分化型。B: 垂直生长不足的低发散型。
has been deficient and when it has been excessive? There are certain rather welldefined guide posts which we may learn to recognize (Fig. 5).
什么时候是不足，什么时候是过度？我们可以学习识别某些相当明确的指导原则（图 5）。

The Growth of the Mandible
下颌骨的生长

The mandible should not be considered as a single growth entity, but rather as four entities: (1) growth of the condyle and ramus; (2) of the corpus; (3) of the posterior alveolar process; and (4) of the anterior alveolar process (Fig. 6).
下颌骨不应被视为单一的生长实体，而应被视为四个实体：(1) 髁状突和臼齿的生长；(2) 牙冠的生长；(3) 后牙槽突的生长；以及 (4) 前牙槽突的生长（图 6）。
This unique bone grows in many different ways. It may grow quite uniformly in all directions or any one of its aspects may grow out of proportion to the rest of the bone. The condyles may grow rapidly while the corpus grows very little or none. The corpus
这种独特的骨骼有许多不同的生长方式。它可能向各个方向均匀生长，也可能任何一个方面的生长与骨骼的其他部分不成比例。髁状突可能生长迅速，而骨质则生长很少或不生长。骨骼
Fig. 6 Showing different types of mandibular growth. A, Much condylar growth but very little growth of corpus. B, Good corpus growth but almost no condylar growth. C, Molar grew vertically much more than incisor. D, Incisor grew more than molar. E, Arbitrary segments of mandible.
图 6 显示不同类型的下颌骨生长。A，髁突生长旺盛，但牙冠生长极少。B, 牙冠生长良好，但髁突几乎没有生长。C, 磨牙的垂直生长比门牙多得多。D，切牙比臼齿长得多。E，下颌骨的任意节段。
may increase considerably in length while the condyles may exhibit little or no growth. The vertical growth of the anterior alveolar process may exceed that of the posterior process. The converse also may be true. The condyles may grow out of proportion to the posterior alveolar processes and vice versa. All of these patterns have an effect upon vertical overbite and overjet.
髁突的长度可能会显著增加，而髁状突可能几乎没有增长。前牙槽突的垂直生长可能超过后牙槽突。反之亦然。髁突的生长可能与后齿槽突不成比例，反之亦然。所有这些模式都会对垂直方向的咬合过度和过咬合产生影响。
It has been said that the growth of the mandible is the principal determining factor of facial morphology. However, it is not the growth of the mandible per se which primarily determines its posture but instead the vertical growth of the maxilla. Once this concept is understood it can be applied clinically to much advantage.
有人说，下颌骨的生长是面部形态的主要决定因素。然而，决定面部形态的主要因素并不是下颌骨本身的生长，而是上颌骨的垂直生长。一旦理解了这一概念，就可以将其应用于临床，并取得很大的优势。

Material 材料

Growth was studied on sixty-two patients. On twenty-nine of these the growth period used was from 11 to 14 years. The other thirty-three subjects were studied from approximately 8 to 11 years.
对 62 名患者的生长情况进行了研究。其中 29 人的生长期为 11 至 14 年。其他 33 名受试者的生长期约为 8 至 11 年。
Fifty treated patients were selected and the period studied was approximately 11 to 14 years. Treatment was carried out during this three year period. The average treatment time was about 18 months. All patients were treated without removing dental units and all were of medium or average facial proportions.
选取了 50 名接受治疗的患者，研究时间约为 11 至 14 年。治疗在这三年期间进行。平均治疗时间约为 18 个月。所有患者在治疗过程中都没有移除牙齿单位，面部比例均为中等或一般。
Sixty-two measurements were made on each individual. Means and standard deviations were calculated on these measurements. Four thousand correlations coefficients and many " t t tt " tests were run on the data. Only a small part of the total information is used here.
对每个个体进行了 62 次测量。根据这些测量结果计算出平均值和标准偏差。对数据进行了四千次相关系数和许多" t t tt "测试。这里只使用了全部信息中的一小部分。
Three hundred and seven treated patients were selected and divided into three groups according to type (Fig. 7). These groups were studied with a view
选取了 37 名接受治疗的患者，并根据类型分为三组（图 7）。研究这些组别的目的是
GROUP TYPE OF THEATMENT 剧场类型 SN-MP S OF subjects showing change.
S OF 显示变化的对象。
EXT. NON-EXT. decreased 减少 INCAEASED NO CHANGE  NO   CHANGE  {:[" NO "],[" CHANGE "]:}\begin{gathered} \text { NO } \\ \text { CHANGE } \end{gathered}
untreated 未处理 62 33 ∘ 33 ∘ 33^(@)33^{\circ} Av.  33 ∘ 33 ∘ 33^(@)33^{\circ} Av. 745. 10% 164
treated 受过治疗的 134 52 29 ∘ .35 ∘ 29 ∘ .35 ∘ 29^(@).35^(@)29^{\circ} .35^{\circ} 464 30 % 30 % 30%30 \% 68
treated 受过治疗的 42 34 27 ∘ 27 ∘ 27^(@)27^{\circ} & BELOW  27 ∘ 27 ∘ 27^(@)27^{\circ} 及以下内容 118 245 58
TREATED 37 ∗ ∗ ^(**){ }^{*} 40 ∘ L ABOVE 40 ∘ L  ABOVE  {:[40^(@)L],[" ABOVE "]:}\begin{gathered} 40^{\circ} \mathrm{L} \\ \text { ABOVE } \end{gathered} 408 425 18%
GROUP TYPE OF THEATMENT SN-MP S OF subjects showing change. EXT. NON-EXT. decreased INCAEASED " NO CHANGE " untreated 62 33^(@) Av. 745. 10% 164 treated 134 52 29^(@).35^(@) 464 30% 68 treated 42 34 27^(@) & BELOW 118 245 58 TREATED 37 ^(**) "40^(@)L ABOVE " 408 425 18%| GROUP | TYPE OF THEATMENT | | SN-MP | S OF subjects showing change. | | | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | | EXT. | NON-EXT. | | decreased | INCAEASED | $\begin{gathered} \text { NO } \\ \text { CHANGE } \end{gathered}$ | | untreated | | 62 | $33^{\circ}$ Av. | 745. | 10% | 164 | | treated | 134 | 52 | $29^{\circ} .35^{\circ}$ | 464 | $30 \%$ | 68 | | treated | 42 | 34 | $27^{\circ}$ & BELOW | 118 | 245 | 58 | | TREATED | 37 | ${ }^{*}$ | $\begin{gathered} 40^{\circ} \mathrm{L} \\ \text { ABOVE } \end{gathered}$ | 408 | 425 | 18% |
Figure 7 图 7
to determining their differences in reaction to treatment, as revealed by changes in the SN-MP angle.
通过 SN-MP 角度的变化来确定它们对治疗反应的差异。

Method 方法

In order to determine the cause of mandibular rotation it was necessary to measure total vertical growth in the region of the first molar teeth, and relate this growth to that at the mandibular condyles.
为了确定下颌旋转的原因，有必要测量第一磨牙区域的总垂直生长，并将这种生长与下颌髁状突的生长联系起来。
To measure the effective growth of the condyles over a period of time we punch pin holes through both tracings at the approximate site of the head of the condyle. By superimposing on the mandibular plane, registering on the lingual cortical plate of the symphysis, and measuring between the two pin holes, we can determine the increase in the length of the mandible as well as the vertical and horizontal components of this growth. This method automatically eliminates any error in measuring the condyles and glenoid fossae. After all, we are not so much interested in the actual growth as in the effect that this growth has on the position of the chin.
为了测量髁突在一段时间内的有效生长情况，我们会在髁突头部的近似位置在两张描记图上打针孔。通过在下颌骨平面上叠加，在干骺端的舌侧皮质板上记录，并在两个针孔之间进行测量，我们就可以确定下颌骨长度的增长以及这种增长的垂直和水平部分。这种方法可以自动消除测量髁状突和盂窝时的误差。毕竟，我们感兴趣的不是实际的增长，而是这种增长对下巴位置的影响。
The vertical growth of the body of the maxilla is measured from the Frankfort plane to the palatal plane along a line perpendicular to the Frankfort plane through the distobuccal cusp of the maxillary first molar. The vertical growth of the maxillary alveolar process is measured from the palatal plane to the occlusal plane by a perpendicular to the Frankfort plane through the
上颌骨体的垂直生长是从法兰克福平面到腭平面，沿着一条垂直于法兰克福平面的线通过上颌第一磨牙的远颊尖测量的。上颌齿槽突的垂直生长是从腭平面到咬合平面，通过一条垂直于法兰克福平面的线测量的。
distobuccal of the first molar. The vertical growth of the mandibular alveolar process is measured from the occlusal plane at the site of the distobuccal cusp of the first molar. The second measurement was taken at the same anteroposterior site as the first. This growth is difficult to measure accurately if there is marked forward growth of the mandible or marked mesial drift of the molar teeth.
第一磨牙的远颊面。下颌牙槽突的垂直生长是从第一磨牙远颊尖部位的咬合平面开始测量的。第二次测量的位置与第一次测量的位置相同。如果下颌骨明显向前生长或臼齿明显向中偏移，则很难准确测量这一生长情况。

Findings and Their Implications
研究结果及其影响

The average effective condyle growth in the untreated sample was 7.2 mm ; in the treated group it was 6.7 mm . The average total vertical growth was 6.3 mm in the untreated cases, while in the treated individuals it was 7.1 mm . Since both untreated and treated groups had almost identical average growth of the condyles, it was thought that they could be compared, giving an opportunity to see differences in the behavior of the chin.
未治疗样本的髁状突平均有效生长量为 7.2 毫米，治疗组为 6.7 毫米。未治疗样本的平均总垂直生长量为 6.3 毫米，而治疗组为 7.1 毫米。由于未接受治疗组和接受治疗组的髁突平均生长速度几乎相同，因此我们认为可以将这两组进行比较，从而了解下巴行为的差异。
Of the 6.3 mm of total vertical growth in the untreated group, 73 % 73 % 73%73 \% ( 4.6 mm .) was in the maxilla and 27 % 27 % 27%27 \% ( 1.7 mm ) ( 1.7 mm ) (1.7mm)(1.7 \mathrm{~mm}) in the mandible. Two and six-tenths mm of the maxillary growth was in the body of the maxilla and 2.0 mm in the alveolar process. Of the total vertical growth in the treated group, 4.8 mm or 68 % 68 % 68%68 \% was contributed by the maxilla, and 2.3 mm or 32 % 32 % 32%32 \% by the mandible. The maxillary growth in this group was made up of 2.4 mm in the body and 2.4 mm in the alveolar process.
未经治疗组的总垂直生长量为 6.3 毫米，其中 73 % 73 % 73%73 \% （4.6 毫米.）位于上颌骨， 27 % 27 % 27%27 \% ( 1.7 mm ) ( 1.7 mm ) (1.7mm)(1.7 \mathrm{~mm}) 位于下颌骨。上颌骨增长的十分之二毫米位于上颌骨体，2.0 毫米位于牙槽突。在治疗组的总垂直生长量中，4.8 毫米或 68 % 68 % 68%68 \% 来自上颌骨，2.3 毫米或 32 % 32 % 32%32 \% 来自下颌骨。该组上颌骨的增长包括2.4毫米的牙体增长和2.4毫米的牙槽突增长。
Thus, it may be seen that the maxilla is responsible for about 70 % 70 % 70%70 \% of total vertical growth and therefore has an important effect on the “tilt” of the mandible. In the treated cases the amount and distribution of vertical growth was different from that of the nontreated cases. This difference was an increase principally in the mandibular alveolar process. This increase was
由此可见，上颌骨的垂直生长约占总垂直生长的 70 % 70 % 70%70 \% ，因此对下颌骨的 "倾斜 "有重要影响。在接受治疗的病例中，垂直生长的数量和分布与未接受治疗的病例不同。这种差异主要体现在下颌骨牙槽突的增加上。这种增长是
variable 变量
 Y 轴（NS-Gn）
Y AXIS
(NS-Gn)
Y AXIS (NS-Gn)| Y AXIS | | :--- | | (NS-Gn) |
 Y AXIS FRANKFORT Y 轴 法兰克福 X − Y AXIS X − Y AXIS {:[X-Y],[AXIS]:}\begin{aligned} & \mathrm{X}-\mathrm{Y} \\ & \mathrm{AXIS} \end{aligned} OM SN- MP
* DEPTH TO ANTERIOR VERTICAL HEIGHT
* 前部垂直高度的深度		 - 64 -. 49 - 78 - 46 - 63
% RAMUS TO ANTERIOR VERTICAL HEIGHT
臼齿与前部垂直高度的百分比		 . 07 − 10 − 10 -10-10 - 20 - 60 - 79
% RAMUS TO ANTERIOR DENTAL HEIGHT
臼齿与前牙高度的百分比		 - 25 − .10 − .10 -.10-.10 - 15 - ⋅ 65 ⋅ 65 *65\cdot 65 − .76 − .76 -.76-.76
SIGNIFICANCE 5 意义 5 5%. LEVEL - .27 5%.级别 - .27 1% LEVEL... 35 1% 等级...35
variable "Y AXIS (NS-Gn)" Y AXIS FRANKFORT "X-Y AXIS" OM SN- MP * DEPTH TO ANTERIOR VERTICAL HEIGHT - 64 -. 49 - 78 - 46 - 63 % RAMUS TO ANTERIOR VERTICAL HEIGHT . 07 -10 - 20 - 60 - 79 % RAMUS TO ANTERIOR DENTAL HEIGHT - 25 -.10 - 15 - *65 -.76 SIGNIFICANCE 5 5%. LEVEL - .27 1% LEVEL... 35 | variable | Y AXIS <br> (NS-Gn) | Y AXIS FRANKFORT | $\begin{aligned} & \mathrm{X}-\mathrm{Y} \\ & \mathrm{AXIS} \end{aligned}$ | OM | SN- MP | | :---: | :---: | :---: | :---: | :---: | :---: | | * DEPTH TO ANTERIOR VERTICAL HEIGHT | - 64 | -. 49 | - 78 | - 46 | - 63 | | % RAMUS TO ANTERIOR VERTICAL HEIGHT | . 07 | $-10$ | - 20 | - 60 | - 79 | | % RAMUS TO ANTERIOR DENTAL HEIGHT | - 25 | $-.10$ | - 15 | - $\cdot 65$ | $-.76$ | | SIGNIFICANCE 5 | 5%. LEVEL - .27 | | 1% LEVEL... 35 | | |
Figure 8 图 8
found to be significant at the 5 % 5 % 5%5 \% level with a " t t tt " test reading of 2.35 .
5 % 5 % 5%5 \% 水平上有意义，" t t tt "检验读数为 2.35。
Growth of anterior vertical height was found to have a correlation coefficient of .92 with growth of total vertical height in the molar region. This is an extremely high reading indicating that there is a very high degree of association between vertical height and molar height, and suggests a cause and effect relationship.
研究发现，前牙垂直高度的增长与臼齿区总垂直高度的增长之间的相关系数为 0.92。这是一个非常高的读数，表明垂直高度和臼齿高度之间存在着非常高的相关性，也表明两者之间存在着因果关系。
In a random sample of fifty individuals taken from a group of four hundred malocclusions, correlation coefficients were calculated on the Y-axis at SN , the Y axis at Frankfort, and the X-Y axis. The results may be found in Fig. 8. It can be seen that the relationship of facial height to depth has a high correlation (-64, -.49, and - 78 respectively) with all of these axes. Obviously, this would be true just as the diagonal of a rectangle varies as does the length of the sides. However, when we correlate these axes with lower face proportions, we find very low readings. Thus, it would appear that the Y -axis and the X - Y -axis are not closely associated with the morphology of the lower face, whereas both the SN-MP and OM angles are.
从四百个错颌畸形群体中随机抽取了五十个人，计算了SN的Y轴、法兰克福的Y轴和X-Y轴的相关系数。结果见图 8。可以看出，面部高度与深度的关系与所有这些轴都有很高的相关性（分别为-64、-.49 和-78）。很明显，这就像矩形的对角线会随着边长的变化而变化一样。然而，当我们将这些轴线与较低的脸部比例相关联时，我们发现读数非常低。由此看来，Y 轴和 X - Y 轴与下面部的形态关系并不密切，而 SN-MP 角和 OM 角却与下面部的形态关系密切。
Price 9 9 ^(9){ }^{9} made a study of twenty-five high angle cases (average 43.98 degrees SN-MP angle) treated by several orthodontists by conventional treatment procedures. In this study he found that 64 % 64 % 64%64 \% of the patients had an increase in the SN-MP angle. This increase varied
Price 9 9 ^(9){ }^{9} 对几位正畸医生通过传统治疗程序治疗的 25 个高角度病例（SN-MP 角度平均为 43.98 度）进行了研究。在这项研究中，他发现 64 % 64 % 64%64 \% 患者的SN-MP角度有所增加。这种增大的程度各不相同
from 1 to 7.5 degrees. It will be noted in Figure 7 that in forty-five high angle cases only 42 % 42 % 42%42 \% showed an increase in the SN-MP angle. These cases were treated by the author taking advantage of only a part of the principles of treatment expressed in this study. This suggests that the precepts are sound. It also suggests that treatment procedures should be varied when the SN-MP plane varies appreciably.
从 1 度到 7.5 度。从图 7 中可以看出，在 45 个高角度病例中，只有 42 % 42 % 42%42 \% 显示 SN-MP 角度增大。作者在治疗这些病例时，只利用了本研究中提出的部分治疗原则。这表明这些原则是正确的。这也表明，当 SN-MP 平面发生明显变化时，治疗程序应有所变化。

The Y Axis Y 轴

There exists at the present time considerable difference of opinion regarding the importance of the Y axis. Some feel that it is undesirable to increase the Y axis with treatment; however, a careful study of the facts do not confirm this opinion. It must be remem-
目前，对于 Y 轴的重要性存在着相当大的分歧。有些人认为，通过治疗增加 Y 轴是不可取的；然而，对事实的仔细研究并没有证实这种观点。必须记住
Fig. 9 Here is shown a treated case in which the Y-axis increased three degrees. This was a very favorable growth reaction from every standpoint (aesthetics, function, overbite, and stability). Increase in anterior facial height was four times greater than increase in facial depth. Condylar growth was ample to balance vertical growth and to keep the mandibular plane parallel to its original inclination.
图 9 这是一个经过治疗的病例，其 Y 轴增加了 3 度。从各方面（美学、功能、咬合过度和稳定性）来看，这都是一个非常有利的生长反应。面部前部高度的增加是面部深度增加的四倍。髁突的增长足以平衡垂直方向的增长，并使下颌平面与原来的倾斜度保持平行。
bered that the Y axis angle increases on an average from 8 to 15 years of age. Also it must be remembered that the average is made up of extremes in both directions. It can be said that most of these extremes represent normal growth for these individuals.
结果表明，从 8 岁到 15 岁，Y 轴角度平均增大。此外，必须记住，平均值是由两个方向的极端值组成的。可以说，这些极值中的大多数代表了这些人的正常生长。
If faces were square, that is, if depth and height were equal, and if faces normally grew equally in vertical and horizontal directions, then normal growth would in fact be down the Yaxis. However, we know that faces are not square but that depth is from 66 to 85 % 85 % 85%85 \% of height. Also we know anterior facial height increases from two to three times as much as facial depth. Figure 9 shows that the Y axis can only open when the face grows more vertically than horizontally. It illustrates why this angle does and should become more obtuse. The more vertical
如果面是正方形的，即深度和高度相等，而且面通常在垂直和水平方向上平均生长，那么正常生长实际上是沿着 Y 轴向下的。然而，我们知道脸部不是正方形的，但深度是高度的 66 到 85 % 85 % 85%85 \% 。我们还知道，面部前部高度的增长是面部深度的两到三倍。图 9 显示，只有当面部的垂直增长大于水平增长时，Y 轴才能打开。它说明了为什么这个角度会变得越来越钝。越垂直
Fig. 10 This 3.5 ∘ 3.5 ∘ 3.5^(@)3.5^{\circ} increase in the Y-axis was a very unfavorable growth reaction. There was very little increase in S-Gn distance, pogonion went downward and backward and the mandibular plane became 7 ∘ 7 ∘ 7^(@)7^{\circ} steeper. The cause of this was primarily a marked deficiency in condylar growth.
图 10 Y 轴上的 3.5 ∘ 3.5 ∘ 3.5^(@)3.5^{\circ} 增加是一种非常不利的生长反应。S-Gn间距几乎没有增加，pogonion向下和向后移动，下颌平面变得 7 ∘ 7 ∘ 7^(@)7^{\circ} 陡峭。造成这种情况的主要原因是髁突生长明显不足。
growth exceeds horizontal growth, the more the Y axis must drop posteriorly. If during treatment vertical growth far exceeds horizontal growth, the Y-axis must move backward just as it would do if the individual were not being treated orthodontically (Fig. 10).
如果垂直生长超过水平生长，则 Y 轴必须向后方移动。如果在治疗过程中，垂直生长远远超过水平生长，Y 轴就必须向后移动，就像没有接受正畸治疗时一样（图 10）。
Perhaps the most desirable behavior of the Y axis from the standpoint of vertical overbite correction is a backward swing, provided there is enough condylar growth to keep the mandibular plane parallel and enable the mandible to keep pace with the forward growth of the maxilla.
从垂直咬合过大矫正的角度来看，Y 轴最理想的状态可能是向后摆动，前提是有足够的髁突生长来保持下颌平面平行，并使下颌骨能够跟上上颌骨向前生长的步伐。
While it is important to note and record the anatomical changes which cause the Y axis to change, I do not feel that it is necessary to actually record the Y axis. There are other places at which these changes can be recorded more meaningfully. The Y axis angle merely tells us where the chin is situated with relation to the cranium, but does not tell us by what route it traveled to arrive there. It does not tell us whether we have a square or an obtuse gonial angle. An increase in the Y-axis angle may accompany normal growth as well as abnormal growth.
虽然注意并记录导致 Y 轴变化的解剖变化很重要，但我认为没有必要实际记录 Y 轴。在其他地方记录这些变化更有意义。Y 轴角度只是告诉我们下巴相对于头盖骨的位置，但并没有告诉我们下巴是通过什么路线到达那里的。它并不能告诉我们颌角是正角还是钝角。Y 轴角的增大可能伴随着正常生长，也可能伴随着异常生长。

The Freeway Spage 高速公路

Documented studies of the freeway space were not made in these investigations; however, we have made many observations of the behavior of teeth as related to this space. Usually molar teeth associated with large freeway spaces are very difficult to move occlusally; in the case of small spaces molars are often found to readily move occlusally thereby eliminating most or all of this space. These observations are not consistent with the popular belief that the freeway space is a dictatorial factor in vertical molar position. One encounters on every hand the belief that molars frequently are depressed into the bone by muscle pressure subsequent
在这些调查中，我们没有对自由空间进行记录研究；但是，我们已经观察到了许多与自由空间相关的牙齿行为。通常情况下，与大的自由空间相关的臼齿很难在咬合面上移动；而在小空间的情况下，臼齿往往很容易在咬合面上移动，从而消除了大部分或全部的自由空间。这些观察结果与人们普遍认为的 "高速公路间隙是臼齿垂直位置的决定性因素 "并不一致。我们经常会遇到这样的观点，即臼齿经常在肌肉压力的作用下向骨内凹陷。
to treatment and that this is accompanied by a decrease in the lower face height (ANS to menton). In hundreds of cases observed, the author has never seen more than a very slight reduction in ANS-menton height and that was in the first few days following band removal. It can be said that molars almost never are intruded into the bone subsequent to treatment. Thus, if molars can be induced to move occlusally, they will remain at that attained level in almost all instances.
在治疗过程中，脸部下部高度（ANS-menton）会降低。在观察的数百个病例中，作者从未见过ANS-menton高度仅有非常轻微的降低，而且还是在拆除矫治带后的最初几天。可以说，磨牙几乎从未在治疗后侵入过牙槽骨。因此，如果能诱导磨牙咬合移动，它们几乎在所有情况下都会保持在已达到的水平。

The Behavior of the Occlusal Plane During Mandibular Rotation
下颌旋转时咬合平面的行为

In discussing the plane of occlusion one is involved in an area in which it is difficult to communicate. Caution must be exercised lest we refer to this plane as though it were a tangible entity. It is not an anatomical part but a boundary between two parts. To be most accurate we really need two occlusal planes - one for the maxillary teeth and one for the mandibular teeth. However, this would perhaps be too complicated and impractical.
在讨论闭塞平面时，我们会涉及到一个难以沟通的领域。我们必须小心谨慎，以免把这个平面说成是一个有形的实体。它不是一个解剖部位，而是两个部位之间的边界。为了做到最准确，我们确实需要两个咬合平面--一个是上颌牙的咬合平面，另一个是下颌牙的咬合平面。然而，这可能过于复杂，而且不切实际。
It is not enough to speak of the occlusal plane as having tipped a given number of degrees in a given direction; we should qualify this by saying that a given segment of teeth moved a given number of mm vertically to cause this change. If we will always relate posterior and anterior segments of teeth to their respective bases, we will not become confused about occlusal plane changes. Our real interest is in just which dental units have undergone vertical changes to produce a tipping of the occlusal plane, just which segments moved to produce bite opening.
仅仅说咬合平面向某个方向倾斜了一定的度数是不够的，我们还应该说是某个牙段垂直移动了一定的毫米数才导致了这种变化。如果我们总是将牙齿的后段和前段与它们各自的基底联系起来，我们就不会对咬合平面的变化感到困惑。我们真正感兴趣的是，到底是哪些牙齿单位发生了垂直变化，从而导致咬合面倾斜，到底是哪些牙段发生了移动，从而导致咬合张开。
We must not think of posttreatment occlusal plane changes as a rebounding reaction, as though something returns to where it once was. This seldom if ever happens, but depressed incisors
我们不能把治疗后咬合面的变化看成是一种反弹反应，好像有什么东西又回到了原来的位置。这种情况很少发生，但凹陷的门牙
in some cases do subsequently extrude. The same kind of growth which causes this plane to flatten before treatment also causes it to flatten after treatment. In a high percentage of cases the occlusal plane does not change subsequent to treatment unless there is posttreatment growth (Figs. 11 and 12).
在某些情况下，它们随后会挤出。在治疗前导致该平面变平的生长也会在治疗后导致该平面变平。在很高比例的病例中，咬合平面在治疗后不会发生变化，除非治疗后出现生长（图 11 和图 12）。
Relating the occlusal plane to the palatal plane is not meaningful because the palatal plane frequently changes with relation to SN . It is possible to have a change in the palatal plane which in no way affects the vertical dimension of the dental area, for example, a downward tipping on only the anterior end of the palatal plane. Hence, such a change may not have any significance so far as facial height is concerned. It is the vertical changes in the molar area with which we primarily are concerned.
将咬合平面与腭平面联系起来是没有意义的，因为腭平面经常随着SN的变化而变化。腭平面的变化有可能丝毫不影响牙齿区域的垂直尺寸，例如，仅在腭平面的前端向下倾斜。因此，就面部高度而言，这种变化可能没有任何意义。我们主要关注的是臼齿区的垂直变化。
The inclination of the plane of occlusion seems to reflect Nature’s attempt to compensate for inharmonies of growth. The vertical growth of the anterior alveolar processes seems to try to compensate for the inharmonies between posterior alveolar growth and ramus growth.
咬合面的倾斜似乎反映了大自然试图弥补生长不协调的问题。前牙槽突的垂直生长似乎是为了弥补后牙槽突生长和臼齿生长之间的不协调。

Facial Types 面部类型

It is important that the profession agree upon the one most important criterion for selecting facial types (Fig. 5 ). Why is this so important? Because types of facial morphology are identified with specific types of malocclusions, a syndrome of dentofacial symptoms. We know that the face grows from two to three times as much vertically as anteroposteriorly; it seems logical to use such growth as the basis for facial typing.
重要的是，专业人员必须就选择脸型的一个最重要标准达成一致（图 5）。为什么这一点如此重要？因为面部形态的类型与特定类型的错颌畸形、牙面症状综合征相鉴别。我们知道，面部的垂直生长是前后生长的两到三倍；将这种生长作为面部分型的基础似乎是合乎逻辑的。
Angles formed by predominantly horizontal planes are our best registration of vertical variations. The angle SNMP should be our angle of choice for identifying types. The terms "hyper-
主要由水平面形成的角度是我们对垂直变化的最佳记录。SNMP角度应该是我们识别类型的首选角度。超

BEHAVIOR OF OCCLUSAL PLANE
咬合平面的行为

Fig. 11 This illustrates that condylar growth (as related to vertical growth) is the key to changes of the occlusal plane. The posterior growth analysis shows that the condyles grew 23 mm and the vertical growth in the molar area was 18 mm ( 9 + 6 + 3 ) 18 mm ( 9 + 6 + 3 ) 18mm(9+6+3)18 \mathrm{~mm}(9+6+3). The result was an 8 ∘ 8 ∘ 8^(@)8^{\circ} change of the occlusal plane. (From the growth study of the U. of Mich.)
图 11 这说明髁突的生长（与垂直生长相关）是咬合面变化的关键。后方生长分析表明，髁突生长了 23 毫米，臼齿区的垂直生长为 18 mm ( 9 + 6 + 3 ) 18 mm ( 9 + 6 + 3 ) 18mm(9+6+3)18 \mathrm{~mm}(9+6+3) 。结果是咬合面发生了 8 ∘ 8 ∘ 8^(@)8^{\circ} 的变化。(摘自密歇根大学的生长研究）。

BEHAVIOR OF OCCLUSAL PLANE
咬合平面的行为

Fig. 12 Again showing that condylar growth when related to vertical growth is the key to the behavior of the occlusal plane. Poor condylar growth ( 4 mm ) could not keep pace with 10 mm of vertical growth ( 4 + 2.5 + 3 ( 4 + 2.5 + 3 (4+2.5+3(4+2.5+3. 5). The result was a 5 ∘ 5 ∘ 5^(@)5^{\circ} change of the occlusal plane. (From the U. of Mich. growth study.)
图 12 再次表明，髁突生长与垂直生长的关系是咬合平面行为的关键。较差的髁突生长（4 毫米）无法与 10 毫米的垂直生长 ( 4 + 2.5 + 3 ( 4 + 2.5 + 3 (4+2.5+3(4+2.5+3 保持同步。5).结果是咬合面发生了 5 ∘ 5 ∘ 5^(@)5^{\circ} 变化。(来自密歇根大学的生长研究）。
divergence" and “hypodivergence” express the two extremes of the term “facial divergence”. The terms “brachycephalic” and “dolichocephalic” are of little value since they refer primarily to cranial proportions and to the relationship of width to length. The orthodontist is principally concerned with facial depth to height ratios. The terms “retrognathic” and “prognathic” are based on the wrong dimension of the face to be most meaningful. They are low and high facial angle readings and as such are measures of facial depth, nothing more. However, the term facial divergence in a very real way takes into account depth as well as height.
divergence "和 "hypodivergence "表达了 "面部分异 "一词的两个极端。畸形头 "和 "畸形头 "这两个术语的价值不大，因为它们主要指的是颅骨比例和宽度与长度的关系。正畸学家主要关注的是面部深度与高度的比例。后颌面 "和 "前颌面 "这两个术语是基于错误的面部尺寸，因此意义不大。它们是面部低角度和高角度的读数，因此是面部深度的测量，仅此而已。然而，"面部发散 "这个术语在很大程度上既考虑了深度，也考虑了高度。

Discussion 讨论

The eternal search continues for the answer to the two most perplexing questions in orthodontics. They are: (1) why are Class I and Class II so much alike in basic jaw structure, and (2) why does orthodontic treatment retard the normal forward positioning of the chin?
对于牙齿矫正学中最令人困惑的两个问题，人们仍在继续永恒的探索。它们是(1) 为什么 I 类和 II 类在基本颌骨结构上如此相似，以及 (2) 为什么正畸治疗会延缓下巴的正常前倾？
Through the years many investigators have futilely pondered these questions; yet they have never explored the vertical dimension of the posterior aspect of the face. Here the secrets are to be found. For the most part the first question remains almost completely unanswered. As for the second question, the efforts to explain this phenomenon are somewhat inadequate.
多年来，许多研究人员徒劳地思考着这些问题，但他们从未探索过面部后侧的垂直维度。秘密就在这里。在大多数情况下，第一个问题几乎完全没有答案。至于第二个问题，为解释这一现象所做的努力有些不足。
In 1962 Maj and Luzi 8 Luzi 8 Luzi^(8)\mathrm{Luzi}^{8} stated, “Since it is not possible at present to pin point the predominant factor in skeletal disharmony for the individual case, no useful conclusions can be drawn from the cephalometric analysis as far as treatment planning and prognosis are concerned.”
1962 年，Maj 和 Luzi 8 Luzi 8 Luzi^(8)\mathrm{Luzi}^{8} 指出："由于目前无法确定造成个别病例骨骼不协调的主要因素，因此就治疗计划和预后而言，无法从头颅测量分析中得出有用的结论"。
An understanding of the mechanism of growth as described by this study is sufficient to completely explain why
了解了这项研究描述的生长机制，就足以完全解释为什么
positioning of the mandible. The same principles also fill in the “missing link” in the quest for the answer to why Class I and II malocclusions are so much alike in basic osseous structure. When the first molar teeth erupt to an end-to-end cuspal relationship, a little variation in vertical height can make the difference between Class I and Class II interdigitation. As little as two mm reduction in molar height could at this point result in a Class I molar relationship without any mesial or distal movement of the molars, without any increase in the length of the mandible, and without any forward movement of the condyle in the glenoid fossa.
下颌骨的定位。同样的原理也填补了 "缺失的一环"，即为什么 I 类和 II 类错合畸形在基本骨性结构上如此相似。当第一磨牙萌出到端对端尖牙关系时，垂直高度上的一点变化就会造成 I 类和 II 类咬合关系的不同。此时，臼齿高度只要减少两毫米，就会导致Ⅰ类臼齿关系，而臼齿的中轴或远轴均不会发生任何移动，下颌骨的长度也不会增加，髁状突在盂窝内也不会向前移动。
In a study of sixty-two untreated and fifty treated cases Creekmore 4 4 ^(4){ }^{4} compared forward movement of the chin. The former group had an average SN-MP angle of 34 degrees and the latter 31.5 degrees. In the untreated group pogonion moved forward an average of 3.48 mm , while in the treated group this reading was 2.49 mm . Again this shows that treatment retards the forward positioning of the chin. The cause of this difference was a difference in the amount of vertical development of the molar area (see findings).
Creekmore 4 4 ^(4){ }^{4} 在一项对 62 例未治疗和 50 例已治疗病例的研究中对下巴前移进行了比较。前者的 SN-MP 角度平均为 34 度，后者为 31.5 度。未治疗组的下巴平均前移 3.48 毫米，而治疗组为 2.49 毫米。这再次表明，治疗会延缓下巴的前移。造成这种差异的原因是臼齿区的垂直发育程度不同（见研究结果）。
A number of investigators have found that there is little or no difference between mandibular length in Class I and II malocclusions. In a comparison of retrognathia and prognathia Björk 1 1 ^(1){ }^{1} states that, “a comparison between the two extreme percentiles indicates that the mean length of the lower jaw is practically the same in both.” In discussing Class II, Division 1 malocclusions, Maj and Luzi 8 8 ^(8){ }^{8} state, “in most instances, the component parts (maxilla and mandible) are normal by themselves but their association results in a disharmony.” They further say, "No significant variations in shape and total length of the mandible have been
许多研究者发现，在 I 类和 II 类畸形中，下颌长度几乎没有差别。Björk 1 1 ^(1){ }^{1} 在比较后天畸形和前天畸形时指出："两个极端百分位数的比较表明，两者的下颌骨平均长度实际上是相同的。Maj 和 Luzi 8 8 ^(8){ }^{8} 在讨论第二类第一组错颌畸形时指出："在大多数情况下，各组成部分（上颌骨和下颌骨）本身是正常的，但它们的组合却导致了不协调"。他们还说："下颌骨的形状和总长度没有明显的变化。
Fig. 13 This is a treated case in which there was no appreciable condylar growth, necessitating the removal of two maxillary bicuspids. In four years of posttreatment observation there was no reduction of the SN-MP angle.
图 13 这是一个经过治疗的病例，该病例的髁突没有明显的生长，因此需要切除两个上颌双尖牙。在治疗后的四年观察中，SN-MP 角没有减小。
Thus, it can be said that most Class II cases have had average horizontal growth. Their principal shortcoming is that they have had too much vertical growth. Herein lies the crux of the orthodontic problem, namely, the relation of vertical to horizontal growth. The difficulty is in the fact that the vertical component of growth limits the horizontal component. This in turn prevents the forward movement of the chin.
因此，可以说大多数二级案例的横向增长都很一般。他们的主要缺点是垂直生长过快。这就是正畸问题的关键所在，即垂直生长与水平生长的关系。困难在于垂直生长限制了水平生长。这反过来又阻碍了下巴的前移。
Thus, we must not think of the growth of the jaws merely as a concentric enlargement of the face, but as definite amounts of growth in millimeters occurring in specific areas resulting in specific effects on overbite
因此，我们不能把下颌的生长仅仅看作是脸部的同心增大，而应看作是在特定部位以毫米为单位的一定量的生长，从而对咬合过大产生特定的影响
The implications in the literature are that when the mandibular plane becomes steeper as a result of treatment it subsequently returns to its original position. Just how this happens is not stated but it is implied that this occurs much as a rotated tooth returns to its original position. Reidel 12 12 ^(12){ }^{12} wrote, “If it is noted at the completion of orthodontic treatment that the mandibular plane has increased, it can be expected to return to its former angulation or less” (Fig. 13).
文献中的含义是，当下颌平面因治疗而变得更陡峭时，它随后会恢复到原来的位置。虽然没有说明这种情况是如何发生的，但隐含的意思是这种情况的发生就像旋转的牙齿恢复到原来的位置一样。Reidel 12 12 ^(12){ }^{12} 写道："如果在正畸治疗结束时注意到下颌平面增大了，可以预期它会恢复到以前的角度或更小"（图 13）。
It is important that we understand the cause of this mandibular rotational change. If growth has ceased to be active the mandible will permanently remain at the steeper inclination caused by treatment. If, subsequent to treatment, the condyles grow faster than total vertical growth then the mandibular plane will flatten accordingly. Not just any growth but growth at the condyles causes the mandible to return to its original inclination. Fortunately for the orthodontist the mandibular condyles usually are the last portion of the facial complex to stop growing, particularly in males.
我们必须了解这种下颌旋转变化的原因。如果生长不再活跃，下颌骨将永久保持在治疗所造成的较陡的倾斜度上。如果在治疗后，髁突的生长速度快于总的垂直生长速度，那么下颌平面就会相应变平。不仅仅是任何生长，髁突的生长也会导致下颌骨恢复到原来的倾斜度。对于正畸医生来说，幸运的是下颌髁状突通常是面部复合体中最后停止生长的部分，尤其是男性。
As Holdaway 6 6 ^(6){ }^{6} pointed out, the mandibular incisor must be harmonized with line NB, always taking into consideration the size of the effective symphysis (Figs. 14, 15, and 16). As the mandible rotates counterclockwise the mandibular incisors move posteriorly in relation to a vertical plane and the incisor-effective symphysis ratio is changed in favor of the symphysis. The more posteriorly the incisors are situated on the mandible, the greater this ratio changes for each degree of rotation. It is extremely important to keep these considerations in mind as we try to reach a judgment regarding the future position of the mandibular incisors.
正如 Holdaway 6 6 ^(6){ }^{6} 所指出的，下颌切牙必须与 NB 线协调，并始终考虑到有效骨骺的大小（图 14、15 和 16）。当下颌骨逆时针旋转时，下颌切牙相对于垂直面向后移动，切牙-有效骨骺的比例会发生有利于骨骺的变化。切牙在下颌骨上的位置越靠后，每旋转一度，这一比率的变化就越大。当我们试图对下颌切牙的未来位置做出判断时，将这些因素牢记在心是非常重要的。
There is a good possibility that one
很有可能
Fig. 14 Here the posterior growth analysis shows a ratio of 22 mm to 17 mm . This accounts for the marked forward positioning of the chin.
图 14 此处的后部生长分析显示，22 毫米与 17 毫米之比。这就是下巴明显前移的原因。
Fig. 15 Same case shown in Figure 14. Note 2 mm of appositional growth at pogonion.
图 15 与图 14 相同。注意到在舌骨处有 2 毫米的附着生长。
be induced to make a greater contribution to bite corrections. It seems likely that in the future a systematic approach to the application of differential inhibition and stimulation of vertical growth will play an important role in orthodontic therapy.
诱导对咬合矫正做出更大的贡献。看来，在未来的正畸治疗中，系统地应用不同的抑制和刺激垂直生长的方法将发挥重要作用。

Treatment 治疗

The results of eight years of intensive investigations have led to improved treatment procedures. This consists
经过八年的深入研究，我们改进了治疗程序。这包括
Fig. 16 Same case shown in Figure 14. Note that the incisor - effective symphysis ratio changed from 5-4 to 3.5 − 9 3.5 − 9 3.5-93.5-9. Only 2 mm of this 9 were due to apposition growth and the rest due primarily to the rotation of the mandible. (Some of this ratio change was due to a change in point B.)
图 16 与图 14 中的病例相同。注意切牙-有效干骺端比率从 5-4 变为 3.5 − 9 3.5 − 9 3.5-93.5-9 。其中只有 2 mm 是由于附着生长造成的，其余主要是由于下颌骨的旋转造成的。(该比率的部分变化是由于 B 点的变化造成的）。
This is done with a view to forming good judgment regarding possible response to treatment.
这样做的目的是为了对可能的治疗反应形成良好的判断。
In order to take advantage of these new concepts in treatment it was necessary to design headgears to apply forces in desired directions. At the suggestion of my associate, Dr. Tom Creekmore, we designed a high pull face-bow for extraoral anchorage. The outer bow is terminated at the site of the maxillary first molar teeth to prevent their tipping. Elastic traction is then applied in an upward and backward direction to a conventional type high-pull headgear. This upward and backward directional force is applied for the purpose of inhibiting the downward growth of the maxillary alveolar process and possibly the body of the maxilla. This type of traction is used primarily on open-bite cases and individuals with high SN-MP angles.
为了在治疗中利用这些新概念，有必要设计头架，以便向所需的方向施力。在我的助手 Tom Creekmore 医生的建议下，我们设计了一种用于口外固位的高拉力面弓。外弓的末端位于上颌第一磨牙的位置，以防止其倾斜。然后将弹性牵引力以向上和向后的方向施加到传统型高拉力头套上。这种向上和向后方向的牵引力是为了抑制上颌牙槽突的向下生长，也可能是为了抑制上颌骨体的向下生长。这种牵引主要用于开放性咬合病例和SN-MP角度较大的患者。
When facial morphology indicates that vertical growth has been excessive
当面部形态显示垂直生长过度时
growth of the maxillary molars. When it has been determined that vertical growth is deficient, resulting in a deep overbite, we try to stimulate the vertical growth of the alveolar processes with Class II elastics and/or the conventional face-bow headgear with cervical traction.
上颌臼齿的生长。当确定垂直生长不足导致深咬合时，我们会尝试使用 II 类弹性矫治器和/或带有颈部牵引的传统面弓头套来刺激牙槽突的垂直生长。

Summary 摘要

  1. Variation in growth at the condyles and at the molar area is responsible for the rotation of the corpus of the mandible.
    髁状突和臼齿区的生长变化是下颌骨体旋转的原因。
  2. Clockwise rotation, viewed from the patient’s right side, is a result of more vertical growth at the molar area than at the mandibular condyles. Extremes of this condition cause open bites.
    从患者的右侧看，顺时针旋转是臼齿部位的垂直生长多于下颌髁状突的结果。这种情况的极端表现会导致开放性咬合。
  3. Counterclockwise rotation is a result of more condylar growth than vertical growth at the molars. Extremes of this condition cause closed bites.
    逆时针旋转是臼齿髁突生长多于垂直生长的结果。这种情况的极端会导致闭合性咬合。
  4. The size of the gonion angle affects the amount of rotation.
    楔角的大小会影响旋转量。
  5. The degree of facial divergence has an effect upon the degree of rotation of the mandible.
    面部发散程度对下颌骨的旋转程度有影响。
  6. The facial angle is influenced by vertical as well as horizontal growth.
    面部角度受垂直和水平生长的影响。
  7. The orthodontic profession needs to decide just which criterion is most important as a basis for facial type.
    正畸专业需要确定哪种标准作为面部类型的依据最为重要。
  8. The posterior growth analysis was presented as a method of analyzing the growth of the posterior aspect of the face.
    面部后侧生长分析是一种分析面部后侧生长的方法。

Bibliography 参考书目

  1. Björk, A.: The Face in Profile, Svensk Tandläkare-Tidskrift Volym 40, No. 5B, translated into English, Lund, 1947, Berlingska Boktrycheriet.
    Björk, A.: The Face in Profile, Svensk Tandläkare-Tidskrift Volym 40, No. 5B, transl into English, Lund, 1947, Berlingska Boktrycheriet.
  2. Björk, A.: Variations in the Growth Pattern of the Human Mandible:
    Björk, A.：人类下颌骨生长模式的变异：
400, 1963.
3. Brodie, A. G.: On the Growth Pattern of the Human Head, From the Third Month to the Eighth Year of Life, Am. J. Anat. 68: 209-262, 1941.
3.Brodie, A. G.: On the Growth Pattern of the Human Head, From the Third Month to the Eighth Year of Life, Am. J. Anat.Anat.68: 209-262, 1941.
4. Creekmore, T. D.: “Inhibition or Stimulation of Vertical Growth of the Facial Complex.” Unpublished.
4.Creekmore, T. D.: "Inhibition or Stimulation of Vertical Growth of the Facial Complex." 未发表。未发表。
5. Downs, W. B.: Variation in Facial Relationships, Their Significance in Treatment and Prognosis, A. J. Ortho. 34: 812-840, 1948.
5.Downs, W. B.: Variation in Facial Relationships, Their Significance in Treatment and Prognosis, A. J. Ortho.34: 812-840, 1948.
6. Holdaway, R.: Changes in Relationships of Points A and B During Orthodontic Treatment, A. J. Ortho. 42: 176-193, 1956.
6.Holdaway, R.: Changes in Relationships of Points A and B During Orthodontic Treatment, A. J. Ortho.42: 176-193, 1956.
7. Lande, Milton: Growth Behavior of the Human Bony Facial Profile as Revealed by Serial Cephalometric Roentgenology, Angle Ortho. 22: 78 90 , 1952 90 , 1952 90,195290,1952.
7.Lande, Milton：连续头颅X线摄影揭示的人类骨性面部轮廓的生长行为》，Angle Ortho.22: 78 90 , 1952 90 , 1952 90,195290,1952 .
8. Maj, G., and Luzi, C.: The Role of Cephalometrics in the Diagnosis and Prognosis of Malocclusions, A A AA. J. Ortho. Vol. 48, page 911-923: Dec., 1962.
8.Maj, G. 和 Luzi, C..： A A AA ，《头颅测量学在错颌畸形诊断和预后中的作用》。J. Ortho.第 48 卷，第 911-923 页：1962年12月。
9. Price, L.: “Comparison of Treatment Reaction in High and Low Angle Cases.” Unpublished.
9.Price, L.: "Comparison of Treatment Reaction in High and Low Angle Cases." Unublished.未发表。
10. Ricketts, R. M.: Facial and Denture Changes During Orthodontic Treatment as Analyzed from the Temporomandibular Joint, A. J. Ortho. 41: 163-179, 1955.
10.Ricketts, R. M.：从颞下颌关节分析正畸治疗期间面部和义齿的变化》，A. J. Ortho.41: 163-179, 1955.
11. : The Influence of Orthodontic Treatment on Facial Growth and Development, Angle Ortho. 30: July, 1960.
11. : 正畸治疗对面部生长发育的影响，Angle Ortho.30：1960 年 7 月。
12. Reidel, R. A.: A Review of Retention Problems, Angle Ortho. October, 1960, page 179.
12.Reidel, R. A.: A Review of Retention Problems, Angle Ortho.1960 年 10 月，第 179 页。
13. Schudy, Fred F.: The Cant of the Occlusal Plane and the Axial Inclinations of Teeth as Related to Diagnosis and Treatment, Angle Ortho. April, 1963.
13.Schudy, Fred F.: The Cant of the Occlusal Plane and the Axial Inclinations of Teeth as Related to Diagnosis and Treatment, Angle Ortho.1963年4月。
14. Schudy, Fred F.: Vertical Growth Versus Anteroposterior Growth as Related to Function and Treatment, Angle Ortho. Vol. 34: April, 1964.
14.Schudy, Fred F.: Vertical Growth Vers Anteroposterior Growth as Related to Function and Treatment, Angle Ortho.第 34 卷：1964 年 4 月。
15. Steiner, C.: Cephalometrics for You and Me, A. J. Ortho. 39: 729-755, 1953.
15.Steiner, C.：你我的头颅测量学》，A. J. Ortho.39: 729-755, 1953.
16. - : Cephalometrics In Clinical Practice, Angle Ortho. 22: 8-29, January, 1959.
16.- 头颅测量学在临床实践中的应用》（Cephalometrics In Clinical Practice），Angle Ortho.22：8-29，1959 年 1 月。

AcknowledgMENT 致谢

The author wishes to express appreciation to his associate, Dr. Tom Creekmore, for the preparation of the data and illustrations. Also, I would like to express appreciation to Dr. Cecil Steiner and Dr.
作者希望对他的同事 Tom Creekmore 博士表示感谢，感谢他为我们准备了数据和插图。此外，我还想对 Cecil Steiner 博士和 Dr. H. M. S. 博士表示感谢。
  1. 3-55 2X YEARS BEFORE TREATMENT 12 − 612 12 − 612 12-61212-612 YEARS POST TREATMENT
    3-55 2 倍 治疗前 12 − 612 12 − 612 12-61212-612 治疗后数年