Cant Of The Occlusal Plane And Axial Inclinations Of Teeth
牙齿咬合平面和轴向倾角的变化

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

There is a growing awareness on the part of many orthodontists that the occlusal plane is an important plane of reference. The cant of this plane is closely related to function and significantly related to treatment. It is the line along which the teeth function and the line with which functional balance must be established. We must consider the axial inclinations of the maxillary and mandibular incisor teeth in relation to the occlusal plane and in relation to each other since these relationships in turn are closely related to vertical overbite.
许多正畸医生越来越意识到，咬合平面是一个重要的参考平面。该平面的位置与功能密切相关，与治疗也有重要关系。它是牙齿发挥功能的基准线，也是必须建立功能平衡的基准线。我们必须考虑上颌和下颌切牙的轴向倾斜与咬合平面的关系以及相互之间的关系，因为这些关系反过来又与垂直咬合过度密切相关。

In this study we have chosen to relate the occlusal plane to the mandibular plane. The angle formed by these two planes we have called the occlusomandibular plane angle or the OM angle. This angle is important in diagnosis and treatment as we will try to point out later. The angles formed by the occlusal plane with the Frankfort plane and with the sella nasion plane are much less variable in opposite types than that formed by the occlusal plane with the mandibular plane. There is little value in measuring factors which have only a slight variation. The most variable aspects of the dentocephalic complex serve as the most significant and useful criteria. Hence, it is logical that the OM angle is more meaningful, more expressive of type, and more expressive of the vertical positions of teeth within the dentofacial complex.
在这项研究中，我们选择将咬合平面与下颌平面联系起来。我们将这两个平面形成的角度称为咬合下颌平面角或 OM 角。这个角度在诊断和治疗中非常重要，我们将在下文中指出。咬合平面与法兰克福平面和蝶鞍平面形成的角度在相反类型中的变化要比咬合平面与下颌平面形成的角度小得多。对仅有轻微变化的因素进行测量的价值不大。牙颅复合体中变化最大的方面是最重要和最有用的标准。因此，符合逻辑的是，OM 角更有意义，更能表达类型，也更能表达牙颌面复合体中牙齿的垂直位置。

The purpose of this presentation is threefold:
本报告的目的有三个：

To introduce the OM angle, (Figure 1) to show that it is related to
介绍 OM 角（图 1），说明它与
vertical dysplasia, and that it is important in diagnosis and treatment.
垂直发育不良，而且在诊断和治疗中非常重要。
To stress the importance of the interincisal angle.
强调齿间角的重要性。
To show that it is desirable to tip the occlusal plane in some cases and undesirable to do so in others.
说明在某些情况下咬合平面倾斜是可取的，而在另一些情况下则是不可取的。
An attempt will be made to distinguish situations in which it is desirable to tip the occlusal plane and others in which it is not. Suggestions will be given for the differential diagnosis and treatment of the two extreme types of facial morphology, namely, retrognathia and prognathia.
我们将尝试区分哪些情况下需要使咬合平面倾斜，哪些情况下不需要。对于面部形态的两种极端类型，即后腭和前腭，将提出鉴别诊断和治疗建议。

There seems to be considerable confusion concerning the terms “retrognathia” and “prognathia”. They have somehow assumed double meanings. In the strictest sense, they are merely low and high facial angle readings. However, in this study broader meanings have been applied to these terms.
关于 "reversgnathia "和 "prognathia "这两个术语，似乎存在着相当大的混淆。它们在某种程度上具有双重含义。从最严格的意义上讲，它们只是面部角度读数的低和高。然而，在本研究中，这些术语被赋予了更广泛的含义。

Fig. 1 Anatomical points, lines, and planes used in this study. The average for the OM angle is

16^{\circ}

.
图 1 本研究中使用的解剖点、线和平面。OM 角的平均值为

16^{\circ}

。

Retrognathia, for our purpose, means a face in which height is out of proportion to depth (a long narrow face). Prognathia means a face in which depth is out of proportion to height (a short wide face). In the author’s opinion too much importance has been placed on the facial angle. It is not the best expression of facial type and additions to the nomenclature are needed to more accurately describe varying characteristics.
就我们的目的而言，后凸指的是高度与深度不成比例的脸（狭长的脸）。前倾指的是脸的深度与高度不成比例（短而宽的脸）。作者认为，人们过于重视面部角度。这并不是面部类型的最佳表达方式，需要对术语进行补充，以便更准确地描述不同的特征。

Review of Literature 文献综述

A perusal of the literature reveals that very little has been written concerning the cant of the occlusal plane. Apparently the inclination of this plane has been measured in only a few studies and there has been no attempt to evaluate its significance in diagnosis and treatment.
查阅文献发现，有关咬合面倾斜度的文献很少。显然，只有少数研究对该平面的倾斜度进行了测量，而且也没有尝试对其在诊断和治疗中的意义进行评估。

Downs,

^{7}

in a study of twenty individuals ages 12 years to 17 years, related the occlusal plane to the Frankfort horizontal plane and found the average angle to be 9.3 degrees. Goldsman,

^{10}

at the University of Indiana, in a study of fifty adults related the occlusal plane to the Frankfort horizontal plane and found the average angle to be 8.6 degrees. This slight difference ( 9.3 and 8.6) in these two studies lends support to the thesis that this angle is relatively constant in widely varying types, while the OM angle varies greatly with different types. When we subtract the occlusal - Frankfort angle from the FM angle in the Downs study we get an OM angle of

{12.6}^{\circ}

while in the Goldsman study we get an OM angle of

{16.8}^{\circ}

. This variation of

{4.2}^{\circ}

is as would be expected since the OM angle is somewhat consistent with the FM angle, as we shall see later, and the average FM angle showed about 4 degrees difference. Björk

^{2}

measured the angle formed by the occlusal plane and the sella articulare line in a study of
Downs，

^{7}

在对20名12至17岁的人进行研究时，将咬合平面与法兰克福水平面联系起来，发现平均角度为9.3度。印第安纳大学的戈德曼（

^{10}

）在对 50 名成年人进行的一项研究中，将咬合平面与法兰克福水平面联系起来，发现平均角度为 8.6 度。这两项研究中的微小差异（9.3 和 8.6）支持了这一论点，即该角度在差异较大的类型中相对恒定，而 OM 角度在不同类型中差异很大。在 Downs 的研究中，当我们从 FM 角减去咬合-法兰克福角时，我们得到的 OM 角为

{12.6}^{\circ}

，而在 Goldsman 的研究中，我们得到的 OM 角为

{16.8}^{\circ}

。这种

{4.2}^{\circ}

的变化是意料之中的，因为 OM 角与调频角在某种程度上是一致的，我们稍后会看到，调频角的平均值相差约 4 度。Björk

^{2}

在一项对以下牙齿的研究中测量了咬合面和龈沟线形成的角度

322 males age 12 years. The average angle was found to be 37.6 degrees. Steiner has related the occlusal plane to the sella nasion line and has found the average to be

14^{\circ}

.
322 名 12 岁的男性。发现平均角度为 37.6 度。斯坦纳（Steiner）将咬合平面与蝶鞍线联系起来，发现平均值为

14^{\circ}

。

Brodie

^{3}

states that when the occlusal plane is tipped as a result of orthodontic treatment, “it tends to return to its original position”. “Tending to return” and actually returning are two different things. There seems to be a general belief that, when tipped, this plane does actually return to its original position. This assumption may be due to an interpolation of Brodie’s statement. There also seems to be a prevalent belief that it is undesirable to change the occlusal plane in any type of malocclusion. Since I have observed many cases five years after treatment in which the tipped occlusal plane has remained tipped, and since in these cases excellent results were achieved, it seems quite desirable to change the cant of the occlusal plane by treatment in certain types of cases.
Brodie

^{3}

指出，当咬合面因正畸治疗而倾斜时，"它往往会回到原来的位置"。"倾向于恢复 "和实际恢复是两码事。人们似乎普遍认为，当咬合面倾斜时，它确实会回到原来的位置。这种假设可能是由于对布罗迪的陈述进行了插值。此外，人们似乎还普遍认为，在任何类型的错颌畸形中，改变咬合平面都是不可取的。我观察过许多病例，在治疗五年后，倾斜的咬合平面仍然保持倾斜，而且这些病例都取得了很好的效果，因此，在某些类型的病例中，通过治疗改变咬合平面的倾斜度似乎是非常可取的。

Improved appliances coupled with advanced knowledge in recent years have enabled us to make major tooth movements. The greater distances we move teeth, the greater effect our work has upon facial contour. Hence, there have been many studies on the esthetic effect of orthodontic treatment. Tweed

^{21}

has employed a triangle as an aid in determining the proper position of the mandibular incisor in the dentofacial complex. Steiner

^{19}

has gone a step farther and developed a formula for positioning both the mandibular incisors and the maxillary incisors with relation to their bases, with relation to the cranium and to one another. Holdaway

^{11}

has made recommendations for positioning the mandibular incisors to the osseous symphysis. Ricketts

^{18}

has norms for positioning the mandibular incisor with relation to the A-Po line, the line proposed by Downs. All of these
近年来，改进的矫治器和先进的知识使我们能够进行大范围的牙齿移动。我们移动牙齿的距离越远，我们的工作对面部轮廓的影响就越大。因此，有很多关于正畸治疗的美学效果的研究。特威德（Tweed）

^{21}

曾用三角形来辅助确定下颌切牙在牙面复合体中的正确位置。Steiner

^{19}

则更进一步，制定了一个公式来确定下颌切牙和上颌切牙与牙根、与颅骨以及相互之间的位置关系。Holdaway

^{11}

对下颌切牙与骨骺的定位提出了建议。Ricketts

^{18}

对下颌切牙与A-Po线（Downs提出的线）的关系提出了定位规范。所有这些
contributions are directed primarily toward positioning teeth anteroposteriorly and are closely associated with the esthetic effect of orthodontic treatment. None of them makes any attempt to locate teeth vertically within the head.
它们主要针对牙齿的前胸定位，与正畸治疗的美学效果密切相关。它们都没有尝试在头部垂直定位牙齿。

Now, the field of orthodontics needs to consider a vertical analysis of the posterior part of the face. Criteria are needed to enable us to assess the vertical positions of the teeth, particularly the posteriors, within the dentocephalic complex. This study is an attempt to establish such criteria. It represents only a beginning and more study is needed before conclusions can be drawn. It is an effort to better evaluate function as it relates to vertical growth; malocclusions are often the result of a dysplasia in the vertical dimension.
现在，正畸学领域需要考虑对面部后部进行垂直分析。我们需要一些标准来评估牙齿，尤其是后牙，在齿脑复合体中的垂直位置。本研究试图建立这样的标准。这只是一个开始，在得出结论之前还需要更多的研究。这项研究旨在更好地评估与垂直生长有关的功能；畸形往往是垂直方向发育不良的结果。

Why do we think the OM angle is important and why do we think it should be considered in diagnosis? It is important because it is a way of objectively expressing the vertical position of the mandibular posterior teeth as related to the vertical position of the mandibular anterior teeth. It is thought to be an indicator of the vertical growth of the alveolar process as related to the vertical growth of the ramus and condyle and significantly related to vertical overbite. Considerable documented evidence will be presented to substantiate the existence of these relationships.
为什么我们认为 OM 角很重要，为什么我们认为在诊断中应该考虑它？它之所以重要，是因为它是一种客观表达下颌后牙垂直位置与下颌前牙垂直位置关系的方法。它被认为是牙槽突垂直生长的一个指标，与臼齿和髁突的垂直生长有关，并与垂直咬合过度密切相关。大量的文献证据将证明这些关系的存在。

Explanation of Ocalusal Plane Ghanges
距骨平面变化的解释

Just what do we mean by “the cant of the occlusal plane”? What are we measuring? We are merely measuring the relative vertical heights of the anterior and posterior segments of teeth to the inferior border of the mandible.
我们所说的 "咬合平面的倾斜度 "是什么意思？我们在测量什么？我们只是在测量牙齿前段和后段与下颌骨下缘的相对垂直高度。

There are a number of relative movements of the maxillary and mandibular incisor and first molar teeth which can
上颌和下颌门牙和第一磨牙有一些相对运动，这些运动可以

Fig. 2 Showing five possible changes in the inclination of the occlusal plane.
图 2 显示咬合面倾斜度的五种可能变化。
cause a change in the occlusal plane, Fig. 2.
导致咬合面的改变，图 2。

If the maxillary and mandibular molars move occlusally equal distances, and the maxillary and mandibular incisor teeth also move incisally the same distance, the occlusal plane is unchanged.
如果上颌和下颌臼齿在咬合面上移动的距离相等，而上颌和下颌切齿也在切面上移动相同的距离，则咬合面保持不变。
If the first molars and maxillary incisors are unchanged vertically and the mandibular incisors are depressed, the plane tips downward anteriorly.
如果第一臼齿和上颌切牙垂直不变，而下颌切牙凹陷，平面就会向前方下方倾斜。
If the first molars are unchanged and the maxillary incisors are depressed, the plane tips upward anteriorly.
如果第一臼齿不变，而上颌门齿凹陷，平面就会向前方倾斜。
If the incisors are depressed equally and the mandibular first molars are elevated, the plane tips upward posteriorly.
如果切牙平均下凹，下颌第一臼齿抬高，则平面向后上方倾斜。
If the mandibular incisors are depressed more than the maxillary incisors and the mandibular first molars move occlusally more than do the maxillary first molars, then the plane tips upward on the posterior
如果下颌切牙的下凹程度大于上颌切牙，下颌第一磨牙的咬合移动程度大于上颌第一磨牙，那么平面就会在后方向上倾斜。
end and downward on the anterior end. This is the most common behavior of the occlusal plane as a result of orthodontic treatment.
前端向下。这是正畸治疗后咬合面最常见的表现。

Material 材料

A study was made of 400 random sample malocclusions. Means, ranges, and standard deviations were calculated for nineteen different measurements. Some of these measurements were angular; others were linear. Most were commonly accepted measurements; however, some were relatively new insofar as we could determine. The cases were not classified according to Angle’s classifications. The age range was from 9 years to 18 years, but a very high percentage fell within 11 years to 13 years. Both sexes were represented but the percentage of each was not determined. The findings are shown in Table I.
对 400 个畸形随机样本进行了研究。计算了 19 种不同测量的平均值、范围和标准偏差。其中一些是角度测量，另一些是线性测量。大多数测量值都是公认的，但也有一些是我们能确定的相对较新的测量值。这些病例没有按照 Angle 的分类标准进行分类。年龄范围从 9 岁到 18 岁，但 11 岁到 13 岁的比例非常高。男女患者均有，但比例不详。调查结果见表 I。

From this group of 400 malocclusions
在这 400 个畸形中
TABLE NO. I 表号I
Group I 第一组

Item 项目	Mean 平均值	S.D.	Range 范围
SNM	33.5	5.11	18	54
FM	28.6
SNA	80.9	3.34	67.5	92.5
SNB	76.2	2.92	66	87
ANB	4.4	1.65	-5	10
Occ. - NPo Occ.- NPo	85	2.36	73	95
OM	15.8	3.96	4	30.5
1-1	126.9	11.07	99.5	175
1-Occ. 1 角	58.5	6.32	39.5	87
1-Occ. 1 角	69.3	7.11	53	93
1-NA	23.1	7.81	-9	52
1-NA(mm)	) 5.7	2.33	-6	18
1-NB	24	6.11	0	41
i-NB(mm)	5.4	2.1	-1	14
1-MP	96.1	5.41	73	114
$\overset{―}{I} - APo$ (mm) $\overset{―}{I} - APo$ （毫米）	) 1.7	2.16	$- 7.5$	10
Po-NB (mm)	) 2.7	1.44	-2	9.5
Overbite 咬合过度	3.8	1.68	-4	10

two smaller groups were selected on the basis of the size of the OM angle. These two groups represent the two extremes of the OM angle. Fifty-seven cases with OM angles above

20^{\circ}

were placed in Group II, and forty-four cases with OM angles below

11^{\circ}

were placed in Group III. It was found that those with OM angles above

20^{\circ}

also comprised, in general, cases with high SN to mandibular plane (M) angles. The group composed of individuals with OM angles below

11^{\circ}

also comprised, in general, those with low SN to M angles. In other words, the two groups represented extreme facial types, retrognathia and prognathia. It was reasoned that since these two groups were at opposite ends of the pole it would be enlightening to contrast them in as many ways as possible.
根据 OM 角的大小选出两个较小的组。这两组代表了 OM 角的两个极端。57 例 OM 角大于

20^{\circ}

的病例被归入第二组，44 例 OM 角小于

11^{\circ}

的病例被归入第三组。研究发现，OM 角大于

20^{\circ}

的病例一般还包括 SN 与下颌平面（M）夹角较大的病例。而 OM 角低于

11^{\circ}

的一组人一般也是鼻窦与下颌平面（M）夹角较小的人。换句话说，这两组人代表了极端的面部类型，即后颌畸形和前颌畸形。我们认为，既然这两组人处于两极的两端，那么尽可能多地对他们进行对比会很有启发。

Glossary 术语表

Occlusal plane: The occlusal plane was established by bisecting the vertical overlapping of the distobuccal cusps of the first molars and bisecting the vertical overbite (or openbite) of the central incisor teeth. A point was chosen midway between the images of the right and left first molars.
咬合平面：咬合平面是通过将第一臼齿远颊尖的垂直重叠部分一分为二和将中切牙的垂直过度咬合（或开放咬合）部分一分为二来确定的。在左右第一磨牙图像的中间选取一个点。
Mandibular plane: This plane was established by using menton and the most inferior point on the outline of the mandible at the gonion angle. A point was chosen midway between the images of the right and left sides.
下颌骨平面：该平面通过使用门齿和门齿角处下颌骨轮廓的最下端点来确定。选取的点位于左右两侧图像的中间。
OM angle: The angle formed by the intersection of the occlusal plane and the mandibular plane.
OM 角：咬合平面与下颌平面的交点所形成的角度。
OF angle: The angle formed by the occlusal plane and the facial plane (nasion - pogonion). The posterior superior angle is used.
OF 角：咬合平面与面部平面（nasion - pogonion）形成的角度。使用后上角。
Actual symphysis: That portion of the mandible which lies anterior to a line perpendicular to the mandibular plane, passing through point $B$ .
实际骨骺：下颌骨的前部，位于垂直于下颌骨平面的一条线上，通过 $B$ 点。

This is measured parallel to the mandibular plane.
这是与下颌平面平行测量的结果。
6. Effective symphysis: That portion of the mandible which lies anterior to a continuation of line NB, measured perpendicular to line NB.
6.有效骨骺：垂直于 NB 线测量，位于 NB 线延长线前方的下颌骨部分。

Findings and Their Implications
研究结果及其影响

In Group I the average OM angle was found to be

16^{\circ}

and the average SN to M angle was 33 degrees. Thus, it will be noted that the OM angle was 47 percent of the SN to M angle. In Group II the average OM angle was 23 degrees and the average SN to M was 39 degrees, or 58.1 percent. In Group III the average OM angle was

{9.3}^{\circ}

while the SN to M angle was

26^{\circ}

, or 35.7 percent. In Group II the average OM angle was

13^{\circ}

higher than that of Group III. Strangely enough the SN to M angle was also

13^{\circ}

higher in Group II than in Group III. These percentages seem to indicate that there may exist a significant relationship between the OM angle and the SN to M angle.
在第一组中，OM 角的平均值为

16^{\circ}

，SN 与 M 角的平均值为 33 度。因此，可以看出 OM 角是 SN 与 M 角的 47%。在第二组中，OM 角的平均值为 23 度，SN 与 M 角的平均值为 39 度，即 58.1%。在第三组中，OM 角的平均值为

{9.3}^{\circ}

，而 SN 与 M 的夹角为

26^{\circ}

，即 35.7%。第二组的平均 OM 角为

13^{\circ}

，高于第三组。奇怪的是，第二组的 SN 与 M 的夹角也

13^{\circ}

高于第三组。这些百分比似乎表明，OM 角和 SN 与 M 的夹角之间可能存在显著的关系。
The occlusal plane and the facial plane (NPo) seem to be rather consistently related to one another in all types of malocclusion and in normal occlusions, Figure 3. We have chosen to call this the occlusofacial angle or the OF angle. The average for the OF angle in Group I was

85^{\circ}

, in Group II 87.4, and in Group III it was 84.3. The low standard deviation (

3^{\circ}

in Group II and

{2.2}^{\circ}

in Group II) and low coefficient of variation (Group I .027, Group II .034, and Group III .026) attest to the fact that the occlusal and facial planes generally have a rather consistent relationship to one another, thus giving importance to the diagnostic value of the occlusal plane.
在所有类型的错颌畸形和正常的咬合中，咬合平面和面部平面（NPo）似乎都有相当一致的相互关系，图 3。我们将其称为咬合面角或 OF 角。第一组的OF角平均值为

85^{\circ}

，第二组为87.4，第三组为84.3。低标准偏差（第二组为

3^{\circ}

，第二组为

{2.2}^{\circ}

）和低变异系数（第一组为 0.027，第二组为 0.034，第三组为 0.026）证明了咬合平面和面部平面之间通常具有相当一致的关系，因此咬合平面的诊断价值非常重要。

The upper-lower incisal angle of

127^{\circ}

for the entire study compares favorably with the 128.45 average found by Björk. In this group the upper in-
整个研究的上下切角为

127^{\circ}

，与比约克（Björk）发现的 128.45 的平均值相比毫不逊色。在这组研究中，上切角

127^{\circ}

的平均值为128.45。

Fig. 3 The OF angle (formed by occlusal and facial planes) varies only slightly in opposite types of normal occlusions.
图 3 OF 角（由咬合平面和面部平面形成）在不同类型的正常咬合中仅略有不同。
cisor to occlusal plane angle was

{58.5}^{\circ}

; the lower incisor to occlusal plane angle

{69.3}^{\circ}

; Björk found this to be

58^{\circ}

and

{70.5}^{\circ}

respectively. There was a difference of nine degrees in the incisal angle between the two subgroups, the high angle group being lower.
Björk发现，上切牙与咬合面的角度为

{58.5}^{\circ}

；下切牙与咬合面的角度为

{69.3}^{\circ}

；这两个角度分别为

58^{\circ}

和

{70.5}^{\circ}

。两个亚组的切角相差 9 度，高切角组的切角更小。

The average for the angle formed by the long axis of the maxillary central incisor and the line NA was

23^{\circ}

in Group I. The average for the angle formed by the long axis of the mandibular central incisor and line NB was 24 degrees, in Group No. II 24.4 and in Group III 25.3. These data strongly suggest that the mandibular incisor should be related to line NB in a rather definite manner.
上颌中切牙长轴与NA线形成的夹角在第一组中的平均值为

23^{\circ}

。下颌中切牙长轴与NB线形成的夹角在第二组中的平均值为24度，在第二组中为24.4度，在第三组中为25.3度。这些数据有力地表明，下颌切牙与 NB 线的关系是相当明确的。

The angle formed by the long axis of the mandibular incisor and the mandibular plane made an interesting study. In Group I the average for this angle was

{96.1}^{\circ}

. In Group II the average was

{90.6}^{\circ}

, while in Group III it was 101.8 , a difference of

11^{\circ}

. To us this is a clarion warning that we should leave these incisors tipped farther forward in prognathic cases as they are farther forward in the beginning.
下颌切牙长轴与下颌平面形成的角度是一项有趣的研究。在第一组中，该角度的平均值为

{96.1}^{\circ}

。第二组的平均值为

{90.6}^{\circ}

，而第三组为 101.8，相差

11^{\circ}

。对我们来说，这是一个明确的警告，我们应该让这些门牙在前牙畸形的病例中更靠前，因为它们一开始就更靠前。

However, this study indicates that the mandibular incisors should generally be related to the occlusal plane in a similar manner in all types of facial morphology. The readings for the lower incisor to occlusal plane angle were: Group I

{69.3}^{\circ}

, Group II

{66.2}^{\circ}

,
不过，这项研究表明，在所有面部形态类型中，下颌切牙与咬合平面的关系一般都应该是相似的。下切牙与咬合面角度的读数为第一组

{69.3}^{\circ}

，第二组

{66.2}^{\circ}

、

Fig. 4 Two malocelusions exhibiting opposite facial types. (A) Retrognathic type; (B) Prognathic type.
图 4 两种畸形表现出相反的面部类型。(A) 后突型；(B) 前突型。
and Group III

{68.7}^{\circ}

. These data clearly indicate that the lower incisor is more consistently related to the occlusal than to the mandibular plane.
和第三组

{68.7}^{\circ}

。这些数据清楚地表明，下切牙与咬合面的关系比与下颌平面的关系更加一致。

Ricketts has found that the ideal position of the mandibular incisor is 0.5 mm anterior to the APo line. In Group I this tooth was found to be 1.7 mm anterior to the APo line, Group II was 3.1 mm , while in Group III this reading was 1.3 mm .
Ricketts 发现，下颌切牙的理想位置是在 APo 线前方 0.5 毫米。在第一组中，这颗牙齿位于 APo 线前方 1.7 毫米，第二组为 3.1 毫米，而第三组为 1.3 毫米。

The average vertical overbite was found to be twice as great in Group III as in Group II. This suggests that vertical overbite is to a significant degree dependent upon facial morphology.
结果发现，第三组的平均垂直咬合过度程度是第二组的两倍。这表明垂直过咬在很大程度上取决于面部形态。

Comparison of Two Cases Representing Opposite Types
代表相反类型的两个案例的比较

In Figure 4 it will be noted that the angle formed by the sella nasion and the mandibular plane is extremely high in one case (A) and in the other, (B) extremely low. One is quite retrognathic with a steep mandibular plane; the other individual, representing an opposite type, has a square jaw, is prognathic and has an extremely low sella nasion and mandibular plane angle. One has a high OM angle with an open bite, while the other has a low OM angle with an extremely closed bite.
从图 4 中可以看出，在一个病例（A）中，蝶鞍与下颌平面形成的角度非常大，而在另一个病例（B）中，蝶鞍与下颌平面形成的角度非常小。其中一个人的下颌平面陡峭，是相当严重的后颌畸形；另一个人则是相反的类型，下颌呈方形，是前颌畸形，下颌角与下颌平面的夹角极小。一个人的OM角大，咬合开放，而另一个人的OM角小，咬合极度闭合。

One is characterized by a pronounced actual symphysis, the other by a small actual symphysis, Figures 5 and
其中一个的特点是实际干骺端明显，另一个的特点是实际干骺端较小，图 5 和图 6。

Fig. 5 Two malocclusions showing variation in the morphology of the mandibles, variation in OM angles and in the ratio of effective symphysis to actual symphysis.
图 5 显示下颌骨形态变化、OM 角变化以及有效骨骺与实际骨骺比例变化的两种错颌畸形。

Fig. 6 Two normal occlusions showing differences in the morphology of the mandibles, variation in the OM angles and in the ratio of effective symphysis to actual symphysis.
图 6 两个正常咬合显示下颌骨形态的差异、OM 角的变化以及有效骨骺与实际骨骺的比例。
6. The cross-sectional outlines of the two mandibles in the sagittal plane show a marked difference in morphology, (A) has a tall, narrow form while (B) is short and wide. One has a dental height measured from menton to anterior nasal spine of 75 mm , while the other has a height of 60 mm for this same dimension, Figure 7.
6.两个下颌骨在矢状面上的横截面轮廓显示出明显的形态差异，（A）高而窄，而（B）短而宽。图 7：从门齿到前鼻骨棘，一个的齿高为 75 毫米，而另一个的齿高为 60 毫米。

The mandibular incisors of (A) are at

75^{\circ}

to the mandibular plane while (B) has incisors quite procumbent at

104^{\circ}

. One has protrusive maxillary incisors, and the other retrusive.
(A)的下颌门齿位于下颌平面的

75^{\circ}

处，而(B)的门齿则位于

104^{\circ}

处。一个上颌门牙突出，另一个后退。

Fig. 7 Cross sections of mandibles superimposed on the occlusal plane. Each tooth and mandible is related to the horizontal line just as they were related to their own occlusal planes. It was found that in prognathic cases the apices of the mandibular central incisors were on an average 1.5 mm lingual to the center of the mandible at the level of point B , measured perpendicular to line NB. In retrognathic cases these apices were on an average .5 mm anterior to the center of the mandible. (A) Retrognathic mandibles, (B) prognathic mandibles, © variation in the dental height in the two types.
图 7 叠加在咬合平面上的下颌骨横切面。每颗牙齿和下颌骨与水平线的关系就像它们与各自的咬合平面的关系一样。研究发现，在前颌病例中，下颌中切牙的舌尖平均距离下颌骨中心 1.5 毫米，位于 B 点水平，垂直于 NB 线测量。在后龈病例中，这些切尖平均位于下颌中心前 0.5 mm 处。(A) 后腭下颌骨，(B) 前腭下颌骨，© 两种类型的牙齿高度存在差异。

The Occlusal Plane as 咬合平面作为
Related to The Symphysis 与干骺端相关
Heredity seems to make a strong effort to coordinate the cant of the occlusal plane with the size of the symphysis, that is the actual symphysis and to some extent the effective symphysis. The size of the symphysis tends to vary as the size of the OM angle and of the angle SN to mandibular plane. It was found in the 57 individuals in Group II that the average amount of actual symphysis was 9.1 mm while the effective symphysis was only 1.8 mm . In the 44 individuals of Group III the average amount of actual sym-
遗传似乎在努力使咬合面的倾斜度与骨骺的大小（即实际骨骺和一定程度上的有效骨骺）相协调。咬合面的大小往往随着OM角和SN角与下颌平面的大小而变化。在第二组的 57 个个体中发现，实际干骺端平均为 9.1 mm，而有效干骺端仅为 1.8 mm。在第三组的 44 人中，实际干骺端平均长度为 9.1 毫米，而有效干骺端仅为 1.8 毫米。
physis was 6.7 mm with an effective symphysis of 3.4 mm . In other words, in the latter group (with low OM angles) the symphysis was

50 %

effective while in the former group (with high OM angles) the symphysis was only

20 %

effective. In Group II the symphysis was

55 %

greater but

45 %

less effective. Thus it can be said that when the OM angle is large the actual symphysis tends to be large; when it is small the actual symphysis tends to be small, Figure 7. The relative proportion of effective symphysis to actual symphysis in any individual is largely dependent upon the cant of the mandibular plane; however, this proportion is somewhat influenced by the length of the mandible. Six mm of actual symphysis when accompanied by an SN to M angle of about

20^{\circ}

will result in enough effective symphysis to produce good facial harmony provided that the ANB angle is not too great. Twelve mm of actual symphysis are required to produce ample effective symphysis for good facial harmony when accompanied by an SN to M angle of

45^{\circ}

. The reason a given individual has pleasing proportions of facial morphology is not only because the mandibular incisors are in harmony with facial plane, but also because they are harmonized with the symphysis and the symphysis in turn with the line NB. It is a physical impossibility to have ideal facial contour unless the anterior limits of the teeth and the anterior limits of the symphysis are properly related to line NB.
前一组（OM 角大）的有效骨骺为

50 %

，而后一组（OM 角小）的有效骨骺为

20 %

有效，而前一组（OM 角大）的骨骺仅

20 %

有效。在第二组中，干骺端

55 %

较大，但

45 %

较小。因此可以说，当 OM 角较大时，实际干骺端往往较大；当 OM 角较小时，实际干骺端往往较小，图 7。任何个体的有效骨骺与实际骨骺的相对比例在很大程度上取决于下颌骨平面的倾斜度；但是，这一比例在一定程度上受到下颌骨长度的影响。实际干骺端为 6 mm，SN 与 M 的夹角约为

20^{\circ}

，如果 ANB 的夹角不太大，则有效干骺端足以产生良好的面部和谐。如果SN与M的夹角为

45^{\circ}

，则需要12毫米的实际干骺端才能产生足够的有效干骺端，从而实现良好的面部和谐。一个人的面部形态比例之所以令人满意，不仅是因为下颌切牙与面部平面相协调，还因为下颌切牙与干骺端相协调，而干骺端又与 NB 线相协调。除非牙齿的前缘和干骺端的前缘与 NB 线保持适当的关系，否则不可能有理想的面部轮廓。

The low angle Group III is characterized by an average interincisal angle of

131^{\circ}

and by an excessive overbite ( 5 mm ). Since large interincisal angles are so consistently associated with ex-
低角度 III 组的特点是平均颌间角度为

131^{\circ}

，过度咬合（5 毫米）。由于大的颌间角与前牙反咬合和后牙反咬合有如此一致的联系，因此，我们将其归入低角度Ⅲ组。
cessive overbites we may logically deduce that a large interincisal angle is a contributing cause of deep overbite. We may say that when the OM and SNM angles are small and the overbite is deep it is extremely important to produce an interincisal angle of about

135^{\circ}

. When this is done the maxillary and mandibular incisors each tend to prevent the extrusion of the other. The ideal components of this

135^{\circ}

seem to be

64^{\circ}

for the upper incisor to the occlusal plane and

71^{\circ}

for the lower to the occlusal plane. About

7^{\circ}

difference in the angles seems to be ideal; that is, the lower should be

7^{\circ}

more than the upper. In the case of open bites or slight overbites the

135^{\circ}

interincisal angle is not so important from the standpoint of function; however, it may be important from the standpoint of esthetics.
我们可以合乎逻辑地推断出，颌间距离过大是造成深覆颌的一个原因。我们可以说，当OM和SNM角度较小且咬合过深时，产生大约

135^{\circ}

的颌间距离是非常重要的。在这种情况下，上颌切牙和下颌切牙会各自阻止另一颗切牙的挤出。

135^{\circ}

的理想成分似乎是上切牙与咬合平面的

64^{\circ}

和下切牙与咬合平面的

71^{\circ}

。角度差约为

7^{\circ}

似乎比较理想；也就是说，下切牙的角度应

7^{\circ}

大于上切牙。对于开放性咬合或轻微的咬合过度，

135^{\circ}

咬合间角从功能的角度来看并不那么重要，但从美观的角度来看可能很重要。

The vertical overbite of the incisor teeth has been pointed out to vary directly with the OM angle and, therefore, with the inclination of the occlusal plane. However, it must be said that many exceptions to this rule can be found.
有学者指出，门牙的垂直咬合过度与 OM 角直接相关，因此也与咬合平面的倾斜度有关。然而，必须指出的是，这一规则也有许多例外。

The orthodontic problem seems to revolve largely around the vertical overbite or open bite of the anterior teeth. Greater insight into the overbite problem gives us greater insight into the physiology of the teeth. Since function is our basic responsibility, a study of the vertical overbite of teeth is extremely important.
正畸问题似乎主要围绕着前牙的垂直咬合或开放咬合。更深入地了解牙齿咬合过紧的问题，可以让我们更深入地了解牙齿的生理学。由于功能是我们的基本责任，因此对牙齿垂直咬合过度的研究极为重要。

In studying function we must constantly keep in mind, on one hand, the tendency of teeth to move occlusally and, on the other hand, the tendency of teeth to resist lateral movement. Simply stated, a balanced occlusion is a state of being in which the tendency of teeth to move vertically is in har-
在研究功能的过程中，我们必须始终牢记，一方面，牙齿咬合移动的趋势，另一方面，牙齿抵抗横向移动的趋势。简单地说，平衡的咬合是一种状态，在这种状态下，牙齿垂直移动的趋势与牙齿侧向移动的趋势保持一致。
mony with their tendency to move horizontally. Malocclusions are often the result of an imbalance between growth in these two directions. An overbite is but the result of the interplay of growth in a vertical direction versus growth in a horizontal direction. Too, we must always keep in mind the vertical growth of the alveolar process versus vertical growth of the rami and condyles. An excessive overbite is an expression of insufficient vertical growth of the alveolar process as related to condylar growth. Conversely, an open bite is an expression of insufficient condylar growth as related to vertical growth of the posterior alveolar bone.
牙齿的水平移动趋势。畸形通常是这两个方向的生长不平衡造成的。咬合过度就是垂直方向生长与水平方向生长相互作用的结果。同样，我们必须始终牢记牙槽突的垂直生长与嵴和髁突的垂直生长。过度咬合是牙槽突垂直生长不足的表现，与髁突生长有关。相反，开牙合是髁突生长不足的表现，与后牙槽骨的垂直生长有关。

Open bites and abnormal deglutition are closely related to morphology and growth. In other words the pattern of function of a complex of related structures is basically influenced by the morphology and interrelation of the structures.
张口咬合和异常脱臼与形态和生长密切相关。换句话说，由相关结构组成的复合体的功能模式基本上受这些结构的形态和相互关系的影响。

It was found in Group II that the average vertical distance between the anterior nasal spine and menton was eleven millimeters greater than in Group III, Figure 7. Thus, we could assume that the distance from the floor of the mouth to the vertex of the palatal vault is much greater in this group. Oddly enough, this is the group in which we find abnormal swallowing. We have always assumed that tongue habits are associated with abnormally large tongues. So, in view of these findings, we raise the question, is it not logical to assume that tongue habits are associated with tongues that are relatively too small? The tongue and contiguous structures seem to be trying to fill a cavity too large for them. They are trying to function in an area which is relatively too large in the vertical dimension. In view of these observations it seems logical to deduce that the pattern of function which is acquired by the individual is conditioned by the
在第二组中，我们发现鼻前棘与鼻翼之间的平均垂直距离比第三组大 11 毫米（图 7）。因此，我们可以推测该组患者从口腔底部到腭穹顶点的距离要大得多。奇怪的是，我们在这一组中发现了吞咽异常。我们一直认为，舌头习惯与异常大的舌头有关。因此，鉴于这些发现，我们提出了一个问题：假设舌习惯与相对过小的舌头有关，这难道不符合逻辑吗？舌头和毗连结构似乎试图填补一个对它们来说太大的空腔。它们试图在一个垂直维度相对过大的区域内发挥作用。根据这些观察结果，我们似乎可以合乎逻辑地推断出，个体所获得的功能模式是受以下因素制约的
morphology of the related parts as well as the converse.
相关部分的形态以及相反的情况。

Most orthodontists have observed abnormal swallowing at the end of treatment which was apparently not present at the beginning. This is perplexing and disturbing. If we will check our pretreatment and posttreatment head x-rays, I believe we will find in most such cases that there has been insufficient growth of the condyles resulting in an increase in the angle sella nasion to mandibular plane. This, in turn, increases the vertical dimension of the oral cavity and renders it impossible for the tongue to function normally forcing it to thrust between the teeth while swallowing.
大多数正畸医生在治疗结束时都会发现吞咽异常，而这在治疗开始时显然是不存在的。这是令人困惑和不安的。如果我们检查一下治疗前和治疗后的头部X光片，我相信我们会发现在大多数这样的病例中，髁状突生长不足，导致髁状突与下颌平面的夹角增大。这反过来又增加了口腔的垂直尺寸，使舌头无法正常运作，被迫在吞咽时伸入牙齿之间。

If one will try swallowing with a block five mm in thickness between the maxillary and mandibular molars, it will be readily noted that the process of deglutition is immediately altered for the tongue thrusts between the tecth. This seems to be a logical explanation of why we occasionally see a tongue habit develop during treatment. If this is true then we must avoid elevating the mandibular molars with Class II elastics. In other words we must not tip the occlusal plane by raising the posterior end when we start with an open bite.
如果在上颌臼齿和下颌臼齿之间放置一个厚度为 5 毫米的块状物来尝试吞咽，就会很容易发现，由于舌头在齿间的伸展，脱臼过程立即发生了改变。这似乎可以合理地解释为什么我们偶尔会在治疗过程中看到舌习惯的形成。如果情况属实，那么我们就必须避免使用第二类矫治器抬高下颌臼齿。换句话说，当我们开始进行开放咬合时，不能通过抬高后端来使咬合面倾斜。

We can now predict with some degree of accuracy which cases will tend to resist bite-opening; which cases will tend to give difficulty in retaining the corrected overbite and which will not. Moreover, we can now foresee with considerable accuracy which cases will tend to develop an open bite during treatment and which will not. We now have a sound basis for predicting in which cases we can expect a relapse of the corrected Class II relation. We have shown that the OM angle tends to vary directly with the SNM angle in most cases; in the 400 cases studied, on an average the OM angle was about

47 %

of the other angle. When this propor-
现在，我们可以在一定程度上准确地预测出哪些病例倾向于抵制咬合张开；哪些病例倾向于难以保持已矫正的咬合过度，哪些不会。此外，我们现在还能相当准确地预测出哪些病例在治疗过程中容易出现咬合张开，哪些不会。我们现在有了一个可靠的依据来预测哪些病例会复发矫正后的二类关系。我们已经证明，在大多数病例中，OM 角倾向于与 SNM 角直接变化；在研究的 400 个病例中，OM 角平均约为其他角度的

47 %

。当这一比例
tion varies markedly then we think we can attach some significance to it. In general, when the OM angle is disproportionately high (above

60 %

of SN to M) the bite should not be difficult to open and retain even if it were a marked overbite in the beginning. When the angle is markedly low (below

35 %

of SN to M) then we may expect difficulty in these procedures. In such cases bite correction is usually accomplished by depression of anterior teeth, as the molars are disinclined to move occlusally. When the OM angle is above

23^{\circ}

the tendency is toward an open bite or a small overbite and, if there is a marked overbite, in most cases it will not be difficult to correct and to remain corrected. When the angle is below

8^{\circ}

, the overbite tends to be excessive, is difficult to correct and when corrected will tend to return.
如果咬合角度有明显的变化，那么我们就可以认为它有一定的意义。一般来说，当OM角过高时（高于SN与M的

60 %

），即使一开始是明显的咬合过大，咬合也不应该难以打开和保持。如果咬合角度明显偏低（低于SN与M的

35 %

），那么我们可能会在这些过程中遇到困难。在这种情况下，咬合矫正通常是通过压低前牙来完成的，因为臼齿不愿意向咬合面移动。当OM角高于

23^{\circ}

时，倾向于开放性咬合或小的咬合过度，如果有明显的咬合过度，在大多数情况下不难矫正并保持矫正。当角度低于

8^{\circ}

时，过度咬合倾向于过度，很难矫正，而且矫正后容易复发。

There seems to be a logical explanation for this. When the SNM angle is low and the OM angle is also proportionately low, we can assume that there has been ample vertical growth of the rami and condyles and there has been no abnormal mechanical obstruction to the vertical growth of the alveolar process, due to the force of occlusion. We may further assume that the mandibular molars have already moved vertically to their full potential since they are already positioned high in the mandible when related to the mandibular incisors and, therefore, we cannot induce them to move occlusally. When the OM angle is high then the mandibular molars are positioned relatively low in the mandible, may not have reached their potential height, and may be moved occlusally to aid bite-opening.
这似乎有一个合乎逻辑的解释。当SNM角较低，OM角也相应较低时，我们可以认为牙突和髁突已经充分垂直生长，并且由于咬合力量的作用，牙槽突的垂直生长没有受到异常的机械阻碍。我们还可以进一步假设，下颌臼齿已经充分发挥了其垂直生长的潜力，因为当它们与下颌切牙相连时，它们在下颌骨中的位置已经很高，因此我们无法诱导它们咬合移动。当 OM 角较高时，下颌臼齿在下颌中的位置相对较低，可能尚未达到其潜在高度，因此可能需要咬合移动以帮助咬合张开。

The diagnostic value of the cant of the occlusal plane seems to lie in the upper and lower limits of its inclina-
咬合平面的倾斜度的诊断价值似乎在于其倾斜度的上限和下限。
tions. The average OM angle is about

16^{\circ}

; five to six degrees below and above

16^{\circ}

could be considered the medium range for this angle. Within this range little clinical significance is to be found; however, above and below we generally find two diametrically opposed types of individuals with quite different orthodontic problems. Since these two types of individuals are completely opposite in almost every respect, it seems inconceivable that the same treatment procedures can be used for both of them.
角度。OM角的平均值约为

16^{\circ}

；低于

16^{\circ}

和高于

16^{\circ}

五到六度可以被认为是这个角度的中等范围。在这一范围内，临床意义不大；然而，我们通常会发现在这一范围上下有两种截然相反的类型的人，他们的牙齿矫正问题也大相径庭。由于这两种类型的人在几乎所有方面都完全相反，因此似乎无法想象同样的治疗程序可以用于他们两个人。

To find logical reasons why we should use different treatment procedures for these two types of problems we must first consider treatment problems associated with the group exhibiting a high average OM angle:
为了找到对这两类问题采用不同治疗程序的逻辑原因，我们必须首先考虑与平均 OM 角偏高的组别相关的治疗问题：

Tipping the occlusal plane appreciably upward on the posterior end is undesirable.
后端咬合面明显向上倾斜是不可取的。
Increasing the angle SNM is not recommended as it will encourage a relapse of the corrected molar relation in Class II cases.
不建议增大SNM角，因为这会促使II类病例中已矫正的臼齿关系复发。
Class II elastics are disastrous when the angle SNM is above $45^{\circ}$ and the OM angle is above $25^{\circ}$ unless there is phenomenal growth occurring which is indeed rare. Under these circumstances the pull of the elastics causes an elevation of the mandibular molars. This in turn causes Point B and pogonion to go downward and backward resulting in an open bite and an increase rather than a decrease of the ANB angle, Figure 8. When the angle SNM is $40^{\circ}$ or above Class II elastics must be used sparingly. Occasionally we will find vigorous growth in boys which reduces this angle; here Class II elastics can be used for an extended period without undesirable effects.
当SNM角大于 $45^{\circ}$ 和OM角大于 $25^{\circ}$ 时，第二类矫治器是灾难性的，除非出现惊人的生长，而这种情况确实很少见。在这种情况下，弹力袜的拉力会导致下颌臼齿抬高。这反过来又会导致 B 点和舌骨向下和向后移动，从而造成开放性咬合和 ANB 角的增大而不是减小（图 8）。当ANB角为 $40^{\circ}$ 或以上时，必须慎用II类矫治器。有时，我们会发现男孩的生长发育旺盛，从而减小了这一角度；在这种情况下，可以长期使用 II 类矫治器，而不会产生不良影响。
Maxillary incisors should be retracted with a head gear. All distal movement of the maxillary denture should
上颌门牙应戴头套后缩。上颌义齿的所有远端活动均应

Fig. 8 Pretreatment and posttreatment tracings superimposed on SN registered at N . The ANB angle increased

2^{\circ}

, mandibular plane steepened 3.5 degrees and pogonion moved posteriorly 4 mm . The occlusal plane was markedly tipped upward on the posterior end. This case should not have had the use of Class II elastics; the elastic pull was responsible for the marked elevation of the mandibular molars and for the posterior movement of pogonion.
图 8 在 N 处记录的 SN 上叠加的治疗前和治疗后轨迹。ANB 角增大

2^{\circ}

，下颌平面变陡 3.5 度，pogonion 后移 4 毫米。咬合平面在后端明显向上倾斜。这个病例不应该使用 II 类弹性矫治器；弹性拉力是导致下颌臼齿明显抬高和pogonion后移的原因。
be done principally with extraoral anchorage in most instances.
在大多数情况下，主要采用口外固定。
5. If an open bite becomes a problem near the end of treatment, an acrylic splint over the occlusal surfaces of the mandibular second molars, accompanied by anterior vertical elastics and a high-pull head gear, is usually effective in eliminating the open bite and preventing excessive tipping of the occlusal plane.
5.如果开牙合咬合在治疗接近尾声时成为问题，在下颌第二磨牙的咬合面上使用丙烯酸夹板，同时使用前方垂直弹力带和高拉头架，通常能有效消除开牙合咬合，防止咬合面过度倾斜。
6. Many extreme Class II cases should have two bicuspids removed from the maxillary arch.
6.许多极端的 II 类病例应该从上颌牙弓中拔除两个双尖牙。
7. In Class II open-bite cases, one of the most common and most disastrous mistakes is moving the mandibular in-
7.在二类开放性咬合的病例中，最常见也是最严重的错误之一就是移动下颌前突。

Fig. 9 Tracings superimposed on SN at N. Mandibular molars moved occlusally. This was undesirable, but unavoidable; it was thought to be due to the growth of the alveolar process since no Class II elastics were used. The occlusal plane tipped upward on the posterior end. This was also undesirable. The mandibular plane became only slightly steeper indicating good condylar growth.
图 9 下颌臼齿向咬合方向移动，与 N 处的 SN 相叠加。这是不可取的，但也是不可避免的；由于没有使用 II 类矫治器，我们认为这是由于牙槽突的生长造成的。咬合平面在后端向上倾斜。这也是不理想的。下颌平面仅略微变陡，表明髁突生长良好。
cisors lingually. When this happens the resultant increase in overjet calls for Class II elastics. Class II elastics, in turn, elevate the mandibular molars, steepen the mandibular plane, and cause pogonion and B point to move downward and backward. The final result is usually a relapse of the corrected Class II condition.
臼齿的舌侧。当出现这种情况时，就需要使用 II 类矫治器来增加过咬合。二类矫治器反过来又会抬高下颌臼齿，使下颌平面变陡，并导致pogonion和B点向下和向后移动。最终的结果通常是矫正后的 II 类情况复发。

I should like to make the following recommendations for the treatment of the group which is characterized by a low OM angle:
针对 OM 角偏低的人群，我想提出以下治疗建议：

The molars should be moved occlusally as much as possible and the occlusal plane should be raised on the posterior end as much as possible. Thus; Class II elastics are very desirable.
臼齿应尽可能向咬合面移动，咬合面应尽可能向后端抬高。因此，二类矫治器是非常理想的。
The mandibular incisors should not be markedly depressed if it can be avoided.
如果可以避免，下颌切牙不应明显凹陷。
In most instances the maxillary incisors should be depressed as much as possible as they are often excessively elongated due to a large interincisal angle, Figure 10.
在大多数情况下，上颌门牙应尽量下压，因为它们通常会因为颌间距离过大而过度伸长（图 10）。
These cases should be treated without the extraction of teeth if at all possible.
在治疗这些病例时，应尽可能不拔牙。
Labial root torque on the mandibular incisors, accompanied by Class III elastics, while leveling the mandibular arch will prevent the apices of the mandibular incisors from moving lingually. These apices are usually already too far lingually. Class III elastics help move the maxillary posterior teeth occlusally and at the same time prevent depression of the mandibular incisors; both actions are desirable. In many of these
在调平下颌牙弓的同时，对下颌切牙进行唇根扭转，同时使用 III 类弹性矫治器，可以防止下颌切牙尖向舌侧移动。这些尖通常已经向舌侧移动过多。III类松紧带有助于上颌后牙向咬合方向移动，同时防止下颌切牙凹陷；这两种作用都是可取的。在许多这类

Fig. 10 Prognathic case in which maxillary incisors were depressed and their apices moved lingually helping to improve the interincisal angle. The mandibular molars moved occlusally to reduce the vertical overbite. Thus Class II elastics were very desirable.
图 10 前牙反咬合病例，上颌切牙下凹，牙尖向舌侧移动，有助于改善颌间距离。下颌臼齿向咬合侧移动，以减少垂直咬合过度。因此，第二类矫治器是非常理想的。
cases the mandibular incisors are quite procumbent, in good alignment, and we do not choose to retract them because of a large effective symphysis. A careful study of pretreatment and posttreatment head x-rays reveals that labially inclined mandibular incisors are almost impossible to depress without moving their apices lingually, unless labial root torque is used during the leveling off process. This labial root torque is not for the purpose of moving the apices labially but to prevent them from moving lingually.
在一些病例中，下颌切牙相当前倾，排列整齐，由于有效骨骺较大，我们不选择牵引它们。仔细研究治疗前和治疗后的头部X光片可以发现，唇侧倾斜的下颌切牙几乎不可能在不移动其舌尖的情况下被压低，除非在矫治过程中使用唇侧牙根扭力。这种唇侧牙根扭力的目的不是为了移动唇侧的牙尖，而是为了防止它们向舌侧移动。
6. Usually it is our objective in treatment to adjust all angles and measurements toward the mean but the OM angle is an exception. When the angle is below average we elevate the mandibular molars and the result is a very low OM angle. When the angle is high we should in most cases not reduce it appreciably for fear of an open bite.
6.通常，我们的治疗目标是将所有角度和测量值调整到平均值，但 OM 角是个例外。当角度低于平均值时，我们会抬高下颌臼齿，结果就是OM角度非常低。当角度偏高时，我们在大多数情况下不应该明显降低角度，以免造成开放性咬合。

General Discussion 一般性讨论

According to the pronouncements of the Research Work Shop on Cephalometrics in July 1959, all horizontal planes have an important relationship to the mandibular plane except the occlusal plane. Moreover, this same official body reached the conclusion that it is desirable to relate the occlusal plane to

SN, FH

, and the Bolton plane. No reference was made to relating the occlusal plane to the mandibular plane and we may assume that those present considered this of no value.
根据 1959 年 7 月头颅测量学研究工作小组的声明，除咬合平面外，所有水平面都与下颌平面有重要关系。此外，该官方机构还得出结论：最好将咬合平面与

SN, FH

和博尔顿平面联系起来。没有人提到将咬合平面与下颌平面联系起来的问题，我们可以认为与会人员认为这没有任何价值。

This same Work Shop stated that: 'Skeletal analysis has for its major purpose recognition of facial type and an appraisal of anteroposterior apical base relationship, particularly important in Class II and Class III malocclusions". No criteria were given by which we may recognize different facial types. Apparently the inference is that the important difference in facial types is in the anteroposterior dimension.
该工作坊还指出骨骼分析的主要目的是识别面部类型和评估前后牙尖基底关系，这对二类和三类畸形尤为重要"。但没有给出识别不同面部类型的标准。显然，推论认为面部类型的重要区别在于前胸维度。

I should like to proclaim that the real difference, of importance to orthodontists, between facial types lies in the vertical dimension. Of course, there are infinite differences in all planes of space which distinguish one type from another. The ANB angle per se is not a reliable criterion by which we can distinguish between types, Figure 11. In our Group II (retrognathia) the average ANB angle was

5^{\circ}

while in Group III (prognathia) the average ANB angle was

{4.3}^{\circ}

. This subject is deserving of further study and further discussion. It is hoped that a future work shop will
我想说的是，对于正畸医生来说，面部类型之间的真正区别在于垂直维度。当然，在空间的所有平面上都存在着无限的差异，这些差异可以将一种类型与另一种类型区分开来。ANB角本身并不是区分类型的可靠标准，如图11所示。在我们的第二组（后腭）中，ANB 角的平均值为

5^{\circ}

，而在第三组（前腭）中，ANB 角的平均值为

{4.3}^{\circ}

。这个问题值得进一步研究和讨论。希望未来的工作坊能够

Fig. 11 Above, -

1^{\circ}

ANB angle with Class II molar relationship. Below,

+ 9^{\circ}

ANB angle with Class I molar relationship.
图 11 上图，-

1^{\circ}

ANB 角与 II 类臼齿关系。下图，

+ 9^{\circ}

ANB 角与 I 类臼齿的关系。

Cant Of The Occlusal Plane And Axial Inclinations Of Teeth 牙齿咬合平面和轴向倾角的变化

Review of Literature 文献综述

Explanation of Ocalusal Plane Ghanges距骨平面变化的解释

Material 材料

Glossary 术语表

Findings and Their Implications研究结果及其影响

Comparison of Two Cases Representing Opposite Types代表相反类型的两个案例的比较

The Cant of the Occlusal Plane as Related to the Interinatsal Angle咬合平面的坎特 与胫骨间夹角的关系

The Occlusal Plane as Related to the Vertical Overbite咬合平面与垂直过咬合的关系

The Cant of the Occlusal Plane as Related to Treatment与治疗有关的咬合平面的坎特

General Discussion 一般性讨论

Cant Of The Occlusal Plane And Axial Inclinations Of Teeth
牙齿咬合平面和轴向倾角的变化

Explanation of Ocalusal Plane Ghanges
距骨平面变化的解释

Findings and Their Implications
研究结果及其影响

Comparison of Two Cases Representing Opposite Types
代表相反类型的两个案例的比较

The Cant of the Occlusal Plane
as Related to the Interinatsal Angle
咬合平面的坎特与胫骨间夹角的关系

The Occlusal Plane as Related to the Vertical Overbite
咬合平面与垂直过咬合的关系

The Cant of the Occlusal Plane as Related to Treatment
与治疗有关的咬合平面的坎特