β函数拟合正常He牙弓形态的研究

目的本研究应用β函数，通过比较正常He的三种牙弓形态，评价其对不同牙弓形态的拟合程度。方法选择22副个别正常He模型(男4人，女18人)，平均年龄为13．6岁。分为三组：方圆形8副、卵圆形10副、尖圆形4副。将模型平行于He平面扫描到计算机。由中切牙接触点、双侧尖牙牙尖点和双侧第二恒磨牙远中颊尖点五个点确定个体弓形。计算模型上其他各点与曲线的拟合度一相关系数(r)以及各点到拟合曲线的垂直距离之和、平均距离。比较β函数对三组弓形的拟合程度。结果1β函数模拟22副模型的拟合度一相关系数(r)均大于0．96。三组曲线拟合度一相关系数(r)没有差别。2方圆组上、下颌牙弓各点到拟合曲线的垂直距离之和、平均距离均比尖圆组大，P<0．05。3三组弓形的e值具有显著性差异，P<0．01。4上颌磨牙宽度、深度分别比下颌大4．9mm、4．4mm，P<0．001。而上、下颌牙弓e值没有显著差异。结论β函数可以较好地拟合正常He弓形，对尖圆形牙弓比方圆形牙弓拟合更准确。β函数参数e值大小可以区分方圆、卵圆和尖圆三种牙弓形态。正常He个体上、下颌牙弓形态相似。     

骨性Ⅱ类错牙合下颌牙弓与基骨形态相关性的三维测量研究

目的 用三维数字化模型测量的方法探讨骨性Ⅱ类错牙合畸形患者的下颌牙弓弓形与基骨弓形间的相互关系。方法 对35例骨性Ⅱ类错牙合畸形患者治疗前下颌模型进行扫描,获得三维数字模型,对右侧第一磨牙至左侧第一磨牙的FA点（代表牙弓）、WALA点（代表基骨）进行标定并映射到参考平面得到FA和WALA的映射点,分析其牙弓弓形与基骨弓形及其相关性,并对牙弓和基骨弓形进行曲线拟合。结果 骨性Ⅱ类的下颌牙弓弓形曲线与基骨弓形曲线相关度在尖牙区为0.534,磨牙区为0.873。牙弓与基骨尖牙间宽度的差异无统计学意义（P=0.481）,而牙弓与基骨磨牙间宽度的差异具有统计学意义（P<0.01）。牙弓弓形拟合曲线的曲率半径r为15.194,回归系数R2为0.912;基骨弓形拟合曲线的r为20.250,R2为0.947。结论 骨性Ⅱ类错牙合畸形患者下颌牙弓弓形与对应的基骨弓形在磨牙区高度相关,在尖牙区中度相关;基骨尖牙间宽度与牙弓尖牙间宽度无明显差异,基骨磨牙间宽度则明显大于牙弓磨牙间宽度。     

舌侧正畸标准弓形的研究

目的　制作舌侧正畸标准弓形模板 ,探索一种拟合个体弓形的方法。方法　将普查所得的5 0副正常模型分为宽牙弓、普通牙弓、小牙弓 ,分别进行定点三维测量 ,用相应的软件处理数据并拟合牙弓曲线 ,再推算舌侧弓形。结果　得出宽牙弓、普通牙弓、小牙弓的舌侧标准弓形图。结论　 1 舌侧正畸标准弓形模板的拟合度在 0 95以上 ,可用于临床参考。 2 六次多项式用于弓形拟合 ,在舌侧正畸中是实用而准确的 ,且优于四次多项式。 3 本方法可制作舌侧正畸个体弓形。     

青年女性浅层嚼肌B超形态与牙弓形态关系的研究

目的　了解肌肉形态、功能与牙弓形态之间相互作用关系 ,探讨错畸形形成机理。方法　本研究采用超声成像技术测量 31例正常青年女性浅层嚼肌横截面的周长、面积、横径、平均厚度、最大厚度及纵截面的长度 ,并将测量结果与牙弓测量指标进行统计相关分析。结果　超声测量浅层嚼肌横截面的周长、面积、横径、平均厚度、最大厚度对下颌牙弓磨牙区宽度影响明显 ,且成负相关 ;横截面的周长、面积、横径与下颌牙弓前段长度关系显著 ,呈正相关 ,厚度与下颌牙弓前中段长度呈正相关 ,周长与下颌牙弓后段长度呈正相关 ;横截面的面积、周长与上颌牙弓长度成止相关 ;纵截面长度与上下颌尖牙角、下颌双尖牙角的负相关关系。结论　浅层嚼肌形态与下颌牙弓形态相关关系显著 ,浅层嚼肌形态越粗壮 ,功能越强 ,下颌牙弓形态越窄长 ;浅层嚼肌形态对面中份深度有一定影响 ;此外 ,浅层嚼肌长度越长 ,上下颌尖牙角、下颌双尖牙角越小 ,牙弓形态越尖。     

采用四点还原法进行牙弓弓形绘制

目的：寻找一种操作简单的个体化牙弓弓形绘制方法。方法：采用四点还原法个体化牙弓弓形绘制。确定下颌左右第二前磨牙托槽槽沟中心点,下颌左右第一磨牙托槽或颊管槽沟中心点,从而绘制出个体化牙弓弓形图。将四点还原法绘制的个体化牙弓弓形过程编程,实现自动化打印,将打印图形和数显游标模型直接测量的线距和角度比较。应用Medcalc9.3统计软件包进行准确性及可重复性检验。结果：四点还原法可绘制个体化牙弓弓形图,与数显游标模型直接测量比较,线距协相关系数为0.9909,角度协相关系数为0.8419。结论：采用四点还原法个体化牙弓弓形绘制,图形准确可靠,具有较好的可重复性。     

前部弓形的不同形态对弓形弧长影响的研究

目的探讨上颌前部弓形在其深度与宽度一定时,其形态的不同对牙弓弧长的影响。方法选用圆形、椭圆形、抛物线形、双曲线形、悬链形和多曲余弦函数弓形来模拟上颌前部牙弓的形态。在前部弓形的深度与宽度一定时建立数学模型。结果前部弓形深度与宽度不变时,采用不同形状的弓形所获得的前牙弓弧长是不同的。由大到小的依次排序为:多曲余弦函数、圆形、椭圆形、悬链形、抛物线形、双曲线形。结论使用不同形态的弓形可能在一定程度上影响牙弓弧长,从而可能影响牙弓的拥挤度。     

江苏地区正常的牙弓形态

目的:通过对125名江苏地区正常人群的模型测量,建立江苏地区正常牙弓宽度及长度的平均值,并分析牙弓形态特征,为正畸临床的诊断和治疗提供依据。方法:选取正常模型125副(男61副,女64副),用扫描仪输入电脑,运用Winceph 8.0软件测量牙弓宽度及长度,对测量结果进行统计分析。结果:确立了以Currier外侧曲线为参考点的正常各段牙弓宽度及长度的平均值,结果表明江苏地区正常人群中,男性牙弓宽度及长度均大于女性。构建了江苏地区正常的牙弓形态,并建立了牙弓形态的β函数。结论:牙弓形态存在种族、地区和性别的差异,临床上应参照本民族、本地区的标准。β函数有助于指导临床错的诊断和治疗。     

老年人动态咬合下的接触特征的初步研究

目的：通过研究老年人多种颌位的咬合观察及前伸咬合运动中前牙的接触模式与牙弓形状的关系,探讨老年人的动态咬合下的接触特征,为临床修复重建提供理论依据。方法：本研究共86例老年患者,通过口内视诊确定牙弓形态。采用厚度为8um的Bausch咬合测试膜检查下颌各个非正中颌位的接触：侧方移动至包括下颌0.5mm、尖对尖接触位置及前伸移动至前牙切对切接触位置。结果：下颌侧方移动至0.5mm时,30.2%受试者为双侧组牙功能,20.1%为混合尖牙保护和组牙功能。下颌侧方移动至尖对尖接触位置时,45.3%的受试者为双侧尖牙保护,17.4%为双侧组牙功能。下颌向前滑动至上、下前牙切对切接触位置时,80.2%的受试者前牙存在接触,后牙分离。前牙的牙合接触模式与牙列形状的关系：71.4%方圆型牙弓受试者是I型前牙接触模式;63.9%尖圆型牙弓受试者为II型前牙接触模式;对于卵圆型牙弓受试者,前牙接触模式I型和II型均占40%。结论：老年患者具有特殊的动态接触特征。前伸咬合运动中前牙的接触模式与牙弓形状关系密切,修复重建需要考虑这种关系。     

江苏地区正常的舌侧牙弓形态

目的：通过对125副江苏地区正常人群的模型测量,研究江苏地区正常舌侧牙弓形态特征。方法：选取正常模型125副（男61副,女64副）,用扫描仪输入电脑,运用Winceph 8.0软件测量舌侧牙弓宽度及长度。结果：本研究探讨了江苏地区正常舌侧牙弓宽度及长度的正常范围,发现江苏地区正常人群中,男性舌侧牙弓宽度及长度都大于女性,并绘出舌侧弓形图,男性较女性弓形宽大。结论：舌侧牙弓形态存在种族、地区和性别的差异,临床上应参照本民族、本地区的标准。     

骨性Ⅲ类错(牙合)畸形患者下颌牙弓与基骨形态的三维测量研究

目的 对骨性Ⅲ类错(牙合)患者下颌模型进行三维扫描并测量,评估其牙弓形态与基骨形态的相关性及个体差异,以期指导临床治疗.方法 选取29例骨性Ⅲ类错(牙合)患者下颌模型进行激光扫描,建立三维模型.对下颌右侧第一磨牙至下颌左侧第一磨牙的FA点(临床冠中心点)、WALA点(膜龈联合(牙合)方的软组织带处最凸点)进行标定,并分析FA曲线和WALA曲线所对应的牙弓形态与基骨形态.结果 骨性Ⅲ类错(牙合)的下颌FA曲线与WALA曲线显著正相关(r尖牙区=0.616;r磨牙区=0.818).前牙区WALA曲线的曲率半径(23.07)大于FA曲线的曲率半径(19.22).左右侧尖牙区和左右侧第一磨牙区FA点的变异系数(分别为10.00％、13.97％和5.99％、6.36％)均大于相应区域WALA点的变异系数(分别为7.57％、8.60％和3.78％、5.07％).FA点和WALA点尖牙区变异系数均大于第一磨牙区变异系数.结论 骨性Ⅲ类错(牙合)下颌牙弓形态与对应的基骨形态显著相关,且尖牙区的个体差异较磨牙区的个体差异大,因此正畸治疗时不能仅考虑牙弓形态,还应多考虑基骨形态对治疗的影响.     

The dental arch form revisited

Recently, the beta function has been shown to be an accurate mathematical model of the human dental arch. In this research, we tried to find the equation of a curve that would be similar to the generalized beta function curve and at the same time could represent tapered, ovoid, and square dental arches. A total of 23 sets of naturally well-aligned Class I casts were selected, and the depths and widths of the dental arches were measured at the canine and second molar regions. Using the mean depths and widths, functions in the form of Y = AXm + BXn were calculated that would pass through the central incisors, canines, and second molars. Each function was compared with the generalized beta function with the use of root mean square values. It was shown that the polynomial function Y = AX6 + BX2 was the nearest to the generalized beta function. Then the coordinates of the midincisal edges and buccal cusp tips of each dental arch were measured, and the correlation coefficient of each dental arch with its corresponding sixth order polynomial function was calculated. The results showed that the function Y = AX6 + BX2 could be an accurate substitute for the beta function in less common forms of the human dental arch.     

Evaluation of dental arch width and form changes after orthodontic treatment and retention with a new computerized method.

The purpose of this study was to evaluate longitudinal arch width and form changes and to define arch form types with a new computerized method. Maxillary and mandibular models of 21 Class II Division 1 patients were examined before treatment (T(0)), after treatment (T(1)), and an average of 3 years after retention (T(2)). Arch width measurements were made directly on scanned images of maxillary and mandibular models. Arch form changes at T(0)-T(1) and T(1)-T(2) were evaluated by superimposing the computer-generated Bezier arch curves with a computer program. Types of dental arch forms were defined by superimposing them with the pentamorphic arch system, which included 5 different types of arch forms: normal, ovoid, tapered, narrow ovoid, and narrow tapered. Maxillary arch widths were increased during orthodontic treatment. Mandibular posterior arch widths were also increased. The expansion of the mandibular arch forms was less than in the maxillary arch forms. Arch width changes were generally stable, except for reduction in maxillary and mandibular interlateral, inter-first premolar, and mandibular intercanine widths. Pretreatment maxillary arch forms were mostly tapered; mandibular arch forms were tapered and narrow tapered. In maxillary arch forms, 76% of the treatment changes were maintained. Mandibular arch form was maintained in 67% of the sample, both during treatment and after retention. In mandibular arches, 71% of orthodontically induced arch form changes were maintained.     

Comparison of arch forms between Korean and North American white populations

The purpose of this study was to evaluate morphologic differences in the mandibular arches of Korean and North American white subjects. The subjects were grouped according to arch form (tapered, ovoid, and square) to compare the frequency distribution of the 3 arch forms between the ethnic groups in each Angle classification. The sample included 160 white (60 Class I, 50 Class II, and 50 Class III) and 368 Korean (114 Class I, 119 Class II, and 135 Class III) subjects. The most facial portion of 13 proximal contact areas was digitized from photocopied images of the mandibular dental arches. Clinical bracket points were calculated for each tooth according to mandibular tooth thickness data, and then 4 linear and 2 proportional measurements were taken. Arch width was statistically significantly smaller in the white group than in the Korean group, but arch depth did not differ. In the Korean group, the most frequent arch form was square, whereas in the white group the tapered arch form predominated. When the subjects were regrouped by arch form, the Korean arches had a tendency to be larger and deeper than the white arches within each of the 3 arch form types.     

A comparative study of Caucasian and Japanese mandibular clinical arch forms.

The purpose of this study was to clarify morphological differences between Caucasian and Japanese mandibular clinical arch forms in Class I, II, and III malocclusions. The study included 60 Class I, 50 Class II, and 50 Class III cases from each ethnic group. The most facial portion of 13 proximal contact areas was digitized from photocopied images of the mandibular dental arches. Clinical bracket points were calculated for each tooth based on mandibular tooth thickness data. Four linear and 2 proportional measurements were taken. The dental arches were classified into square, ovoid, and tapered forms to determine and compare the frequency distributions between the 2 ethnic groups. The Caucasian population had a statistically significant decreased arch width and increased arch depth compared with the Japanese population. When the subjects were regrouped by arch form, no statistically significant difference in arch dimension was observed between the 2 ethnic groups in any of the arch form samples. Our results suggest that there is no single arch form specific to any of the Angle classifications or ethnic groups. It appears to be the frequency of a particular arch form that varies among Angle classifications or ethnic groups.     

Tooth-position, arch-size, and arch-shape in the primary dentition

Tooth positions and dental arch forms are related to the growth of the cranio-facial complex. To determine the positions of primary teeth and size and shape of the primary dental arches, sixty dental casts of young children (thirty boys and thirty girls) with normal occlusions were examined. In all casts the coordinates of cusp tips of primary canines and molars, and mesial and distal line angles of primary canines and incisors were digitized. The computer-generated curves were made for the maxillary and mandibular arches using a polynomial model. The results show that there were three major cusp-to-fossa and one cusp-to-marginal ridge relations in primary molar intercuspation. On average, girl's dental arches were smaller than boy's dental arches. The mean curves of mandibular arches in anterior segments were gentler than those of maxillary arches.     

A computerized analysis of dental arch morphology in early permanent dentition

To determine the positions of teeth and the size and shape of the dental arches, 53 dental casts of children (29 boys and 24 girls) with their early permanent dentition and normal occlusions were examined. The coordinates of cusp tips and line angles of anterior teeth and cusp tips, contact points, and fossa of posterior teeth were digitized. Computer-generated curves were created for both arches using a polynomial model. There were 2 cusp-to-fossa relations and 4 cusp-to-marginal ridge relations for posterior segment intercuspation. Mean values of posterior arch lengths were statistically larger in boys than in girls. Mean curves of boys' dental arch forms were larger than those of girls and the ranges between the largest and smallest curves for both arches in boys were larger than those in girls. The boys' and girls' smallest curves for both arches were almost the same size.     

三种弓形的恒牙(牙合)初期正常(牙合)的Bolton指数分析

目的研究弓形对Bolton指数的影响。方法选择尖圆形、卵圆形、方圆形牙弓正常（牙合）模型各20例，测量计算Bolton指数值的前牙比、全牙比并作统计学分析。结果经方差分析3组前牙比有统计学差异（F=13．11，P〈0．01）。再经LSD检验，3组中每两组前牙比均有统计学差异（P〈0．01）。经方差分析3组全牙比有统计学差异（F=6．71，P〈0．01）。再经LSD检验，3组中每两组全牙比也有统计学差异（P〈0．01）。结论不同弓形应制定不同的Bolton指数正常值，以便指导临床。     

An evaluation of the curve of Spee in the maxilla and mandible of human permanent healthy dentitions

STATEMENT OF PROBLEM: The characteristics of the curve of Spee in the mandibular arch have been extensively investigated. However, few studies have examined the characteristics of the curve of Spee in the maxillary arch. PURPOSE: The purpose of this study was to examine the differences in the curve of Spee between the maxillary and mandibular arches. The effects of gender on the curve of Spee were also investigated. Material and methods Fifty Japanese adults (25 men and 25 women) with permanent healthy dentitions participated. Standardized digital pictures of the right side of maxillary and mandibular dental casts were made with a digital camera. The cusp tips of the molars, premolars, and canines of the maxilla and mandible were identified. The radius and the depth of the curve of Spee were measured on the dental casts by means of computer software (Occlcircle). The Mann-Whitney test and the Wilcoxon signed rank test were used to test the statistical significance (alpha=.05). RESULTS: The curve of Spee showed a mean radius of approximately 106.4 mm in the maxillary arch and 83.4 mm in the mandibular arch. Radii of the curves of Spee in the maxillary arch were significantly larger than those in the mandibular arch (P <.0001) and had a depth of approximately 1.6 mm in the maxillary arch and 1.9 mm in the mandibular arch. The depth of the curve of Spee in the mandibular arch was significantly deeper than that in the maxillary arch (P =.0326). CONCLUSIONS: The curve of Spee was not influenced by the gender of the subjects investigated. The shape of the curve of Spee in the maxillary arch was significantly flatter than that in the mandibular arch.     

Mathematical beta function formulation for maxillary arch form prediction in normal occlusion population

The aim of this study was to assess the dental arch curvature in subjects with normal occlusion in an Iranian population and propose a beta function formula to predict maxillary arch form using the mandibular intermolar widths (IMW) and intermolar depths (IMD). The materials used were study casts of 54 adolescents with normal occlusion and mean age of 14.1 years (25 males, 29 females, age range 12–16 years). Curve-fitting analyses were carried out and the curves passing through the facial-axis point of the canines, premolars, first molars, and the incisal edges of the anterior teeth were studied using a 3D laser scanner. Using the measured IMW and IMD of the dental arches at the maxillary and mandibular first molar region, a beta function formula proposed for predicting maxillary arch form. The accuracy of the proposed formula was assessed on 10 randomly selected dental casts. The mean (SD) of the maxillary and mandibular IMW and IMD were 57.92 (4.75), 54.19 (5.31), and 31.59 (2.90) and 28.10 (2.59) mm, respectively. There was no gender dimorphism (P > 0.05) for both variables (IMW, IMD). There was a strong positive association (n = 10, Pearson r = 0.98, P < 0.05) between the measured (actual) maxillary arch length and proposed arch length derived from generated formula. The goodness of fit (whole arch) for the proposed beta function formula, using adjusted r square measure and root mean square in 10 patients averaged 0.97 and 1.49 mm, respectively. The corresponding figures for the maxillary anterior arch (canine to canine) were 0.90 and 0.92 mm, respectively. The proposed beta function formula used for predicting maxillary arch form based on two mandibular measures (IMW, IMD) was found to have a high accuracy for maxillary arch prediction in the Iranian population and may be used as a guide to fabricate customized arch wires or as an aid in maxillary reconstructive surgery.     

Dermatoglyphic Assessment in Subjects with Different Dental Arch Forms: An Appraisal

Successful rehabilitation of edentulous individuals involves selection and arrangement of artificial teeth in accordance with the patient’s original arch form. Various criteria exist for harmonious tooth arrangement but none is accepted universally. Finger and palm prints are unique to an individual and once formed in the sixth week of intra-uterine life, remain constant thereafter. Since dental arches are also formed during the same prenatal period, it is believed that the similar genetic factors may be involved in formation of dental arches and dermal patterns. This study was conducted to identify the association if any between type of dental arch forms and type of dermatoglyphic patterns. If specific dermal characteristics exist in individuals with specific dental arch forms, dermatoglyphic assessment of long standing edentulous subjects may help identify the patients preexisting dental arch form and thus aid in proper tooth arrangement. Ninety dentulous subjects were categorized into three groups on the basis of dental arch form (square, tapering or ovoid) and their finger and palm prints were recorded. The type of fingertip patterns, distribution of palmar patterns, Total Finger Ridge Count and angle atd were assessed. Subjects with square arches demonstrated a significantly high frequency of loops and a large atd angle with palmar patterns being most frequent in I₃ region. Subjects with tapering arches showed a high frequency of whorls, a small atd angle and greatest distribution of palmar patterns in I₄ region. In ovoid arched subjects, loops were the most common and palmar patterns were mostly observed in I₄. Since distinctive dermal patterns were observed in subjects with different dental arch forms, it is believed that dermatoglyphics may be used as a reliable tool for identifying original arch form in edentulous patients.