Treatment change comparisons between skeletal Class I and II white adolescents with 3 different vertical divergencies—Part 2: Holdaway difference

Introduction

The Holdaway difference represents the relationship of the NB line to the mandibular incisor (NB-L1) and the bony pogonion (NB-Pog). This study aimed to evaluate treatment changes of NB-L1, NB-Pog, and the Holdaway difference in patients with skeletal Class I and II relationships with 3 different skeletal divergencies.

Methods

This retrospective study was the second part of treatment outcome assessments of 135 white adolescent patients (females, n = 69; males, n = 66; mean age, 12.8 ± 1.4 years pretreatment and 15.0 ± 1.4 years posttreatment). The NB-L1, NB-Pog, and Holdaway differences (NB-L1 − NB-Pog) were measured. The mixed-model analysis of variance was used to assess within- and between-subject effects responding to horizontal and vertical skeletal discrepancies.

Results

For the group with favorable profile changes, the means of the Holdaway difference were maintained in the hypodivergent and normodivergent subgroups and reduced in the hyperdivergent subgroups for patients with skeletal Class I and II relationships. The means of NB-L1 and Holdaway difference were significantly larger in the skeletal Class II group and became greater as skeletal vertical divergencies increased. The NB-Pog means were significantly different only between the hypodivergent and hyperdivergent subgroups.

Conclusions

Based on the findings of this study, the Holdaway difference should be adjusted to individualize the incisor positions, considering not only the anteroposterior but also the vertical skeletal relationships of the patients.

Highligh ts

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Class I low-angle adolescents showed a Holdaway difference (HODIF) close to 0.
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HODIF became larger as horizontal and vertical discrepancies increased.
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HODIF should be maintained in low-/normal-angle skeletal Class I & II adolescents.
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Reducing HODIF was crucial in high-angle skeletal Class I & II adolescents.

Historically, the mandibular incisor position has been considered the key to determining the anterior limit of tooth movement in treatment planning. Holdaway ^, first applied the lines NA (nasion, A point) and NB (nasion, B point) to construct linear and angular measurements to evaluate maxillary and mandibular incisor positions. He found, in the cephalometric tracings, that the maxillary incisors (U1s) became more retroclined, and the mandibular incisors (L1s) proclined more as ANB increased, showing dental compensation to accommodate for the ANB discrepancy. ^, Holdaway used his Utah study sample and proposed that the distances from the incisal border of L1s and bony pogonion (Pog) perpendicular to the NB line should be equal (NB-L1:NB-Pog, 1:1) for pleasing faces. However, the use of Holdaway difference (HODIF) (NB-L1 − NB-Pog = HODIF) is indicated when the Holdaway ratio is off from 1:1. Generally, the HODIF of up to 2 mm reflects an acceptable relationship between L1s and chin prominence. The relationship is less desirable when the HODIF is 3 mm. The discrepancy between NB-L1 and NB-Pog needs to be reduced primarily by uprighting L1s when the HODIF is more than 4 mm. Therefore, the HODIF provides a quantitative judgment regarding L1s position relative to chin projection for diagnosis and treatment planning when the Holdaway ratio is not 1:1.

Steiner later incorporated the Holdaway ratio into his chevrons to create customized solutions for each patient. The initial step of this procedure is to create 2 chevrons as 2 sets of projections showing the desired U1 and L1 positions on the basis of estimated ANB and NB-Pog in 2 or 3 years of treatment time ( Fig 1 ). The U1 and L1 positions (NA-U1 and NB-L1) on the first chevron are determined by applying the estimated ANB value to the acceptable compromise chart, representing the mathematically derived dental compensation. For the second chevron, the desired L1 position (NB-L1) is obtained on the basis of estimated NB-Pog values using the ideal Holdaway ratio of 1:1. Once the 2 individual predictions are completed, the chevrons are combined into one, presenting optimal maxillary and mandibular incisor positions derived from estimated ANB and NB-Pog ( Fig 1 ). However, the influences of vertical skeletal divergences on the incisor positions were not considered in Steiner’s chevrons because both ANB and NB-Pog are associated with the sagittal plane, not the vertical dimension. In addition, because of a lack of follow-up studies, it is uncertain if using the Holdaway ratio of 1:1 as a generic guide for treatment prediction is adequate in various combinations of horizontal and vertical skeletal patterns.

In part 1 of this study, the Tweed diagnostic triangle and Z angle were used to examine treatment changes of 135 white adolescents. The data suggested that patients with skeletal Class I and Class II relationships should have different standards for Frankfort-mandibular incisor angle correction. This retrospective study is the second article of a series assessing treatment outcomes of white adolescent patients. This study aimed to evaluate treatment changes of NB-L1, NB-Pog, and the HODIF in patients with skeletal Class I and II relationships with 3 different divergent patterns. The working hypothesis was that the HODIF is correlated to skeletal vertical divergencies in patients with skeletal Class I and II relationships with favorable facial changes after treatment.

Material and methods

This retrospective study evaluated treatment records of 135 white adolescent patients comprising 70 females and 65 males (mean age pretreatment, 12.8 ± 1.4 years; mean age posttreatment, 15.0 ± 1.4 years) treated at the University of Detroit Mercy Orthodontic Clinic between 2006 and 2016. The approval number of the University of Detroit Mercy Institutional Review Board is 1819-58. Two hundred and seventy 2-dimensional cephalometric images were constructed from pretreatment and posttreatment cone-beam computed tomography images. NB-L1, NB-Pog, and HODIFs were measured. The details of sample selection, cone-beam computed tomography settings, 2-dimensional image construction, and cephalometric measurement software were listed in part 1.

In this follow-up study, the samples were sorted with the same method as in part 1. Moreover, 105 patients with favorable facial changes (increased Z angle) were statistically evaluated. The rest of the sample (30 patients) was used to illustrate the trends of the HODIF changes for unfavorable facial changes (decreased Z angle) after treatment. Figure 2 is a visual explanation of identifying the anatomic landmarks and measuring NB-L1 and NB-Pog. NB-L1 is the distance from the mandibular incisal border perpendicular to line NB, and NB-Pog is the distance from the bony pogonion perpendicular to line NB. The values of the HODIF were obtained by subtracting NB-Pog from NB-L1 in mm.

Statistical analysis

Two sets of NB-L1 and NB-Pog measurements were collected 2 weeks apart and tested by the Pearson correlation. The mixed-model analysis of variance (general linear model) assessed within- and between-subject effects on skeletal Class I and II groups with 3 different vertical divergencies. The post-hoc tests with Bonferroni correction were performed to confirm the significant differences among 3 divergent subgroups. The statistical significance was set at P <0.05.

Results

The results of the Pearson correlation showed 0.993 for NB-L1 and 0.998 for NB-Pog, reflecting excellent measurement reliability.

In the skeletal Class I and II groups with posttreatment favorable facial changes (increased Z angle), the initial HODIF showed minimal changes in the hypo- and normodivergent subgroups and decreased in the hyperdivergent subgroups ( Fig 3 ). The posttreatment means of the HODIF were close to 1, 2, and 3 mm for the skeletal Class I hypodivergent, normodivergent, and hyperdivergent subgroups, respectively, and close to 3, 5, and 7 mm for the skeletal Class II hypodivergent, normodivergent, and hyperdivergent subgroups respectively. Only the skeletal Class I hypodivergent subgroup showed a HODIF close to 0 before and after treatment ( Fig 3 ; Table I ). The treatment changes in NB-L1 were not statistically significant between patients with skeletal Class I and II relationships but significant according to skeletal vertical divergencies ( Table II ). Overall, NB-Pog increased significantly in all patients with favorable facial changes after treatment, with similar increments regardless of the horizontal and vertical skeletal classifications ( Table II ). The mixed-model analysis of variance results of between-subject effects demonstrated significant differences in all 3 variables between skeletal Class I and II groups and also among the 3 divergent patterns ( Table III ). The skeletal Class II group had significantly larger NB-L1 and smaller NB-Pog values than the skeletal Class I group, leading to larger HODIFs in the skeletal Class II group ( Table III ). The means of NB-L1 and HODIF were significantly larger as the skeletal vertical divergencies increased ( Table III and IV ). Although L1s were retroclined during treatment in the hyperdivergent subgroups, the posttreatment NB-L1 means were still the largest in the hyperdivergent subgroups compared with the 2 other subgroups ( Fig 3 ; Table I ). The NB-Pog mean values were significantly different only between the hypodivergent and hyperdivergent subgroups ( Table III and IV ).

Table I

Descriptive statistics for patients with skeletal Class I and II relationships with an increased Z angle postreatment

Variables	Skeletal Class I ^†				Skeletal Class II ^‡				Total
Variables	LA (n = 22)	NA (n = 21)	HA (n = 9)	Total (n = 52)	LA (n = 22)	NA (n = 23)	HA (n = 8)	Total (n = 53)	Skeletal Class I and II (n = 105)
NB-L1
T0	2.8 ± 1.4	4.1 ± 1.8	6.1 ± 1.7	3.9 ± 2.0	4.7 ± 1.9	5.2 ± 1.6	7.3 ± 1.4	5.3 ± 1.9	4.6 ± 2.1
T1	3.7 ± 1.7	4.4 ± 1.9	5.0 ± 2.3	4.2 ± 1.9	5.1 ± 1.7	6.0 ± 1.9	6.8 ± 0.9	5.8 ± 1.8	5.0 ± 2.0
T1-T0	0.9 ± 1.8	0.3 ± 1.4	−1.0 ± 1.6	0.3 ± 1.7	0.4 ± 1.3	0.8 ± 1.9	−0.5 ± 1.6	0.5 ± 1.7	0.4 ± 1.7
NB-Pog
T0	2.5 ± 1.3	1.9 ± 1.7	1.3 ± 1.7	2.0 ± 1.6	1.5 ± 1.6	1.0 ± 1.3	−0.2 ± 1.7	1 ± 1.6	1.5 ± 1.7
T1	3.1 ± 1.4	2.5 ± 2.2	2.4 ± 1.5	2.7 ± 1.8	2.0 ± 1.7	1.5 ± 1.7	0.2 ± 2.1	1.5 ± 1.9	2.1 ± 1.9
T1-T0	0.7 ± 0.9	0.6 ± 1.2	1.2 ± 0.8	0.7 ± 1.0	0.6 ± 0.7	0.5 ± 0.9	0.4 ± 1.2	0.5 ± 0.8	0.6 ± 0.9
Holdaway difference
T0	0.3 ± 2.3	2.3 ± 3.2	4.8 ± 3.1	1.9 ± 3.2	3.2 ± 3.1	4.2 ± 2.3	7.5 ± 2.7	4.3 ± 3.1	3.1 ± 3.3
T1	0.6 ± 2.2	1.9 ± 3.8	2.6 ± 3.4	1.5 ± 3.2	3.1 ± 2.8	4.5 ± 2.7	6.6 ± 2.4	4.3 ± 3.0	2.8 ± 3.3
T1-T0	0.2 ± 2.0	−0.3 ± 2.0	−2.2 ± 1.9	−0.4 ± 2.1	−0.1 ± 1.6	0.3 ± 2.1	−0.9 ± 1.9	−0.1 ± 1.9	−0.2 ± 2.0