Store:Asse Cerniera verticale parte 1
Introduzione
Nel capitolo precedente, Transverse Hinge Axis, abbiamo introdotto la cinematica mandibolare concentrandoci sul piano sagittale, osservando come i movimenti di protrusione e retrusione della mandibola includano non solo traslazioni lungo l’asse Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} , ma anche rotazioni attorno all’asse Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y} . Questo movimento condilare si riflette in traiettorie curvilinee osservabili, ad esempio, nell'incisivo mandibolare, e rappresenta una combinazione di rotazioni e traslazioni nello spazio tridimensionale.
Cinematica Mandibolare a Sei Gradi di Libertà Il movimento mandibolare può essere descritto da un sistema tridimensionale con sei gradi di libertà: tre assi di traslazione (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X, Y, Z} ) e tre assi di rotazione. Ogni condilo è associato a:
- L'asse Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Y} (latero-mediale) per la rotazione sull'asse cerniera trasversale (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle tHA} ).
- L'asse Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z} (verticale) per la rotazione sull'asse cerniera verticale (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle vHA} ).
- L'asse Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X} (antero-posteriore) per la rotazione sull'asse cerniera orizzontale (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle oHA} ).
I piani anatomici fondamentali (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (X,Y)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (X,Z)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (Y,Z)} ) sono utilizzati per studiare le relazioni tra i movimenti articolari.
Coordinate dei Condili e Punti di Riferimento
Consideriamo le coordinate iniziali:
- Condilo laterotrusivo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{C}_L(0) = (0, 10, 0)} .
- Condilo mediotrusivo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{C}_M(0) = (0, -10, 0)} .
- Punto molare laterotrusivo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{M}_L(0) = (5, 5, -5)} .
- Punto incisale: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{I}(0) = (0, 0, -10)} .
Rotazione e Traslazione dei Condili
Condilo Laterotrusivo
La posizione al tempo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t} è: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{C}_L(t) = \mathbf{R}_Z(\theta_L) \cdot \left(\mathbf{C}_L(0) - \mathbf{P}\right) + \mathbf{P} + \mathbf{d}_L } Dove:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{R}_Z(\theta_L)} : matrice di rotazione attorno a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z} .
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{P}} : centro di rotazione (spesso origine del sistema).
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{d}_L = (-d_L, 0, 0)} : traslazione retrusiva.
Condilo Mediotrusivo
Il movimento include rotazioni e traslazioni, descritte dalla formula di Rodrigues: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{C}_M(t) = \mathbf{v} \cos(\theta) + (\mathbf{k} \times \mathbf{v}) \sin(\theta) + \mathbf{k} (\mathbf{k} \cdot \mathbf{v})(1 - \cos(\theta)) + \mathbf{d}_M } Dove:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{v}} : vettore da ruotare.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{k} = (0, 0, 1)} : asse di rotazione.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{d}_M} : traslazione mediale del condilo mediotrusivo.
Tracciati dei Punti di Interesse
Punto Molare Laterotrusivo
La posizione è influenzata dai condili e può essere descritta da: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{M}_L(t) = \mathbf{M}_L(0) + \alpha \cdot \mathbf{C}_L(t) + \beta \cdot \mathbf{C}_M(t) } Con Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \beta} come coefficienti di influenza.
Punto Incisale
Il tracciato incisale dipende dal movimento globale mandibolare: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{I}(t) = \mathbf{I}(0) + \gamma \cdot \mathbf{C}_L(t) + \delta \cdot \mathbf{C}_M(t) } Con Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \gamma} e Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \delta} che riflettono i contributi condilari.
Punto Molare Mediotrusivo
Il punto molare mediotrusivo si sposta secondo: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathbf{M}_M(t) = \mathbf{M}_M(0) + \alpha' \cdot \mathbf{C}_L(t) + \beta' \cdot \mathbf{C}_M(t) }
Sintesi dei Risultati
| Punto | Distanza da P1 (mm) | Direzione X | Direzione Y | Angolo (°) |
|---|---|---|---|---|
| Condilo laterotrusivo | 15.75 | Retrusiva | Laterale | 42.44 |
| Punto molare laterotrusivo | 9.1 | Laterale | Laterale | 73.32 |
| Punto incisale | 13.84 | Retrusiva | Laterale | 85.09 |
| Punto molare mediotrusivo | 8.99 | Protrusiva | Mediale | 91.33 |
Le distanze e gli angoli sono stati calcolati utilizzando la distanza euclidea e il prodotto scalare, descrivendo con precisione i movimenti lineari e angolari.
Discussioni e Conclusioni
La cinematica mandibolare a sei gradi di libertà mostra che i movimenti condilari influenzano in modo complesso i punti di riferimento mandibolari. In particolare: 1. Il condilo laterotrusivo segue un movimento combinato di rotazione retrusiva e traslazione. 2. Il condilo mediotrusivo contribuisce significativamente al movimento orbitante. 3. I tracciati dei punti molare e incisale riflettono l’interazione tra i condili.
La comprensione di queste dinamiche è cruciale per:
- Diagnosticare disfunzioni temporomandibolari.
- Pianificare interventi terapeutici e riabilitativi.
- Modellare i movimenti mandibolari per simulazioni biomeccaniche.
La cinematica mandibolare non può essere semplificata considerando l'asse verticale Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z} come un riferimento statico, poiché il movimento tridimensionale richiede un approccio integrato che tenga conto delle interazioni tra i condili.