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A three-dimensional method to calculate mechanical advantage in mandibular function

Intra- and interexaminer reliability study

Eine dreidimensionale Methode zur Berechnung des mechanischen Vorteils der Unterkieferfunktion

Studie zur Intra- und Inter-Untersucher-Reliabilität

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Journal of Orofacial Orthopedics / Fortschritte der Kieferorthopädie Aims and scope Submit manuscript

Abstract

Purpose

Masticatory muscles are physically affected by several skeletal features. The muscle performance depends on muscle size, intrinsic strength, fiber direction, moment arm, and neuromuscular control. To date, for the masticatory apparatus, only a two-dimensional cephalometric method for assessing the mechanical advantage, which is a measure for the ratio of the output force to the input force in a system, is available. This study determined the reliability and errors of a three-dimensional (3D) mechanical advantage calculation for the masticatory system.

Methods

Using cone-beam computed tomography images from teenage patients undergoing orthodontic treatments, 36 craniofacial landmarks were identified, and the moment arms for seven muscles and their load moment arms (biomechanical variables) were determined. The 3D mechanical advantage for each muscle was calculated. This procedure was repeated by three examiners. Reliability was verified using the intraclass correlation coefficient (ICC) and the errors by calculating the absolute differences, variance estimator and coefficient of variation (CV).

Results

Landmark coordinates demonstrated excellent intra- and interexaminer reliability (ICC 0.998–1.000; p < 0.0001). Intraexaminer data showed errors < 1.5 mm. Unsatisfactory interexaminer errors ranged from 1.51–5.83 mm. All biomechanical variables presented excellent intraexaminer reliability (ICC 0.919–1.000, p < 0.0001; CV < 7%). Interexaminer results were almost excellent, but with lower values (ICC 0.750–1.000, p < 0.0001; CV < 10%). However, the muscle moment arm and 3D mechanical advantage of the lateral pterygoid muscles had ICCs < 0.500 (p < 0.05) and CV < 30%. Intra- and interexaminer errors were ≤ 0.01 and ≤ 0.05, respectively.

Conclusions

Both landmarks and biomechanical variables showed high reliability and acceptable errors. The proposed method is viable for the 3D mechanical advantage measure.

Zusammenfassung

Zielsetzung

Die Kaumuskulatur wird körperlich von mehreren Skelettmerkmalen beeinflusst. Die Muskelleistung hängt ab von der Muskelgröße, der intrinsischen Kraft, der Richtung der Muskelfasern, dem Impulsarm und der neuromuskulären Kontrolle. Bisher gibt es für den Kauorganapparat nur eine zweidimensionale kephalometrische Methode zur Beurteilung des mechanischen Vorteils, der ein Maß für das Verhältnis von Ausgangskraft zu Eingangskraft in einem System ist. In der vorliegenden Untersuchung wurden die Zuverlässigkeit und die Fehler einer dreidimensionalen (3-D) Berechnung des mechanischen Vorteils für den Kauapparat ermittelt.

Methoden

Anhand von digitalen Volumentomographie-Aufnahmen jugendlicher Kieferorthopädie-Patienten wurden 36 kraniofaziale Orientierungspunkte identifiziert und die Momentenarme für 7 Muskeln und ihre Lastmomentarme (biomechanische Variablen) bestimmt. Der mechanische 3‑D-Vorteil für jeden Muskel wurde berechnet. Dieses Verfahren wurde von 3 Untersuchern wiederholt. Die Zuverlässigkeit wurde anhand des Intraklassen-Korrelationskoeffizienten (ICC) überprüft, die Fehler durch Berechnung der absoluten Differenzen, des Varianzschätzers und des Variationskoeffizienten (CV).

Ergebnisse

Die Koordinaten der Referenzpunkte wiesen eine ausgezeichnete Intra- und Inter-Untersucher-Reliabilität auf (ICC 0,998–1,000; p < 0,0001). Die Intra-Untersucher-Daten zeigten Fehler < 1,5 mm. Unbefriedigende Inter-Untersucher-Fehler reichten von 1,51‑5,83 mm. Alle biomechanischen Variablen wiesen eine ausgezeichnete Intra-Untersucher-Reliabilität auf (ICC 0,919–1,000, p < 0,0001; CV < 7%). Die Inter-Untersucher-Ergebnisse waren fast hervorragend, jedoch mit niedrigeren Werten (ICC 0,750–1,000, p < 0,0001; CV < 10%). Der Drehmomentarm des Muskels und der mechanische 3‑D-Vorteil der seitlichen Pterygoidmuskeln wiesen jedoch ICCs < 0,500 (p < 0,05) und CV < 30% auf. Intra- und Inter-Untersucher-Fehler waren ≤ 0,01 bzw. ≤ 0,05.

Schlussfolgerungen

Sowohl die Referenzpunkte als auch die biomechanischen Variablen zeigten eine hohe Reliabilität und akzeptable Fehler. Die hier vorgeschlagene Methode ist für die Messung des mechanischen 3‑D-Vorteils geeignet.

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Authors and Affiliations

  1. Department of Dentistry, University of Ponta Grossa, Avenida General Carlos Cavalcanti n° 4748, Bloco M, Sala 64A, 84030-900, Ponta Grossa, Paraná, Brazil

    Alejandro Sánchez-Ayala DDS MS,  Alfonso Sánchez-Ayala DDS MS PhD, Rafaela Cristina Kolodzejezyk DDS,  Vanessa Migliorini Urban DDS MS PhD &  Manuel Óscar Lagravère DDS MS PhD

  2. Orthodontic Graduate Program, University of Alberta, 116 St & 85 Ave, T6G 2R3, Edmonton, Alberta, Canada

    Nara Hellen Campanha DDS PhD

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Correspondence to Alfonso Sánchez-Ayala DDS MS PhD.

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Conflict of interest

A. Sánchez-Ayala, A. Sánchez-Ayala, R.C. Kolodzejezyk, V.M. Urban, M.Ó. Lagravère and N.H. Campanha declare that they have no competing interests.

Ethical standards

All procedures performed in studies involving human participants or on human tissue were in accordance with the ethical standards of the institutional and/or national research committee and with the 1975 Helsinki declaration and its later amendments or comparable ethical standards. This work was approved by the Health Research Ethics Board at the University of Alberta (#5563). All subjects who participated in the study signed written informed consent to participate.

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Supplemental figures 1–3

Supplemental video 1: Identification of the 36 craniofacial landmarks, and determination of the spatial reference planes, moment arms for seven muscles (superficial masseter, anterior and posterior deep masseter, anterior and posterior temporal, and medial and lateral pterygoid), and their corresponding load moment arms at the incisor and molar position

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Sánchez-Ayala, A., Sánchez-Ayala, A., Kolodzejezyk, R.C. et al. A three-dimensional method to calculate mechanical advantage in mandibular function. J Orofac Orthop 84, 321–339 (2023). https://doi.org/10.1007/s00056-022-00378-7

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