Revisiting Hanau’s Quint: a novel digital analysis of the laws of articulation in complete dentures

Abstract

PURPOSE

The purpose of this study was to evaluate the interrelationships among the determinants of Hanau’s Quint — condylar guidance, occlusal plane, compensating curve, incisal guidance, and cusp height — according to the laws of articulation, using a novel digital method.

MATERIALS AND METHODS

Fully edentulous casts with 9 sets of occlusion rims (7, 8, and 9 inches curvature; standard, +5°, and -5° inclination) were mounted on a semi-adjustable articulator to simulate analog experimental conditions (AECs). The same settings were reproduced in a 2-dimensional virtual articulator in a lateral view (Adobe Photoshop), with the addition of cusp height as a variable, to generate digital experimental conditions (DECs). Whenever an increase in one determinant produced occlusal disharmony, other factors were modified until bilateral balanced occlusion (BBO) was reestablished. The results were compared with Hanau’s predicted interactions.

RESULTS

Both analog and digital methods demonstrated consistent interrelationships among the occlusal plane, compensating curve, condylar guidance, and incisal guidance, as described in Hanau’s Quint. Cusp height, tested digitally, showed a predictable compensatory role.

CONCLUSION

The interrelationships among the determinants of Hanau’s Quint in achieving BBO were validated digitally using a simple and reproducible digital methodology confirmed by an analog articulator. This study may help clinicians better understand BBO and Hanau’s principles in complete denture treatment planning.

INTRODUCTION

Edentulism remains a global public health concern, with prevalence expected to increase as populations age.¹,² Complete dentures (CD) provide an accessible and non-invasive treatment option³,⁴; however, because they are mucosa supported, establishing an occlusion that harmonizes with functional movements is essential for long-term success.⁵,⁶,⁷ Ill-fitting CD may lead to patient insatisfaction,⁸ treatment failure,⁹ accelerated bone resorption¹⁰,¹¹ and traumatic ulcers,¹²,¹³ which may be associated with mucosal pathology.¹⁴ Therefore, accurate occlusal contacts and maxillomandibular relationships are critical factors in CD stability during speech and mastication.¹⁵

Hanau’s articulation quint¹⁶ — condylar guidance, plane of occlusion, compensating curve, incisal guidance, and cusp height — is a cornerstone in understanding occlusal concepts for CD.⁶ These interrelated determinants, as described by Hanau in his laws of articulation,¹⁶ explain how bilateral balanced occlusion (BBO) can be achieved and have been further refined in prosthodontic literature.¹⁷,¹⁸,¹⁹,²⁰,²¹,²²,²³ Condylar guidance inclination describes the anatomical pathway of the condyle and articular disc along the articular eminence, which can be reproduced in an articulator by the sagittal angle. The occlusal plane is defined by the incisal and occlusal surfaces of the teeth and is represented by occlusion rims in CD. The compensating curve refers to the anteroposterior and mediolateral curvatures of occlusal surfaces and incisal edges of artificial teeth, compensating for disocclusion during excursive movements. Incisal guidance is determined by the contact of mandibular and maxillary anterior teeth during protrusion and is reproduced in the articulator by the incisal pin and guide table angle. Cusp height corresponds to the perpendicular distance between a cusp tip and its base, being directly influenced by tooth anatomy.²⁰

Integration of these determinants guides tooth selection and arrangement, overbite and overjet, the individualization of compensating curves and occlusal adjustments. Although no consensus exists regarding the most suitable occlusal scheme for CD,⁷,¹⁵,²⁴,²⁵,²⁶,²⁷ BBO is generally recognized for improving stability by allowing simultaneous contact in lateral movement and protrusion¹⁵,²⁴ and facilitating patient adaptation.²⁷

Digital workflows now facilitate teeth assembly for CD. Nevertheless, clinical success continues to rely on the practitioner’s understanding of occlusal principles,²⁸ such as defined by Hanau. The present study aimed to investigate, through both analog and digital approaches, the elements in Hanau’s Quint — condylar guidance inclination, incisal guidance inclination, occlusal plane inclination, compensating curve prominence, and cusp height — and their interrelationships. The null hypothesis was that the experimental conditions evaluated in this study would not differ from the interactions described in Hanau’s Quint and the corresponding laws of articulation.

MATERIALS AND METHODS

Fully edentulous maxillary and mandibular stone casts were used to develop a maxillary wax rim with anterior height of 20 mm, posterior height of 6 mm, and a thickness of 12 mm; the mandibular wax rim was adjusted according to the maxillomandibular relationship of a phantom head model. The casts and wax rims were scanned with a 3D scanner (HandySCAN 3D; Creaform Inc., Quebec, Canada), and the resulting images were imported into a software program (MeshMixer; Autodesk Inc., California, USA) to digitally design 9 occlusion rims, which were constructed by varying the occlusal curvature (spherical caps with diameters of 7, 8, and 9 inches) and the occlusal plane inclination (standard, +5°, and -5°). The curvature of the occlusion rim was defined according to Monson’s spherical theory, using an 8-inch sphere as the reference compensating curve, with 7-inch and 9-inch spheres representing more pronounced and flatter curvatures, respectively. The occlusal plane was initially established relative to the Camper’s plane of the mannequin and then increased or decreased by 5° in the posterior inclination.

Subsequently, the casts were manufactured using selective laser sintering (SinterStation HiQ; 3D Systems Corporation, South Carolina, USA) in 9 pairs of occlusion rims. The casts and initial occlusion rims (9-inches, standard) were mounted on a semi-adjustable non-arcon articulator (Bio-Art Soluções Inteligentes, São Paulo, Brazil) (Fig. 1). A non-arcon articulator was used due to its experimental flexibility in the sequence of adjustments during protrusion simulation, in which the condylar and incisal guidance were defined according to the occlusion rim in the experimental conditions.

Fig. 1. Occlusal rims mounted on articulator with individualized sagittal guidance.

From this baseline, each of the following factors were sequentially increased and observed: condylar guidance, compensating curve prominence, occlusal plane inclination, and incisal guidance – generating 6 analog experimental conditions (AECs). Whenever an increase in one factor resulted in loss of occlusal contact between the occlusion rims (Fig. 2), or loss of contact between the incisal pin and the incisal table, the remaining factors were adjusted until contact was reestablished in BBO.

Fig. 2. Occlusal disharmony in AEC (analog experimental condition).

For the digital method, a 2-dimensional lateral view of the articulator was reproduced in a software program (Adobe Photoshop CS3; Adobe Systems Inc., California, USA) based on reference measures of the analog articulator recorded with a digital caliper (Mitutoyo; Mitutoyo Corporation, Kanagawa, Japan). Artificial anterior and posterior teeth were virtually arranged over the occlusal plane. The posterior teeth simulated first molars, with the maxillary tooth positioned 7 mm from the most distal portion of the occlusion rims, whereas the mandibular tooth was initially positioned in intercuspation with its antagonist. Cusp height was calculated based on edges with a 33° inclination using the angular distance tool of the software. The anterior teeth were positioned in the most anterior region, with the incisal edge of the mandibular incisor initially contacting the palatal slope of the maxillary incisor.

The fulcrum of the articulator was positioned at the most anterosuperior region of the occlusion rims. Using the “Free Transform” tool, with the corresponding layers selected, the assembly was rotated to modify the inclination of the occlusal plane, thereby allowing adjustment of the condylar and incisal guidance of the articulator. This was performed by simulating protrusive movement, moving the upper member of the articulator until an incisal edge relationship of the anterior teeth and cusp tip contact of the posterior teeth were obtained. Under this condition, the guides were adjusted until contact with the condylar spheres and the incisal pin was established (Fig. 3).

Fig. 3. Lateral view of virtual articulator with individualized sagittal guidance.

From this baseline, the same factors tested in the analog method were sequentially modified, with the addition of cusp height as an experimental variable, generating 10 digital experimental conditions (DECs). Whenever an increase in one factor resulted in occlusal disharmony during protrusive movement, the other factors were modified until proper contact was reestablished in BBO. In this context, occlusal disharmony was defined as loss of contact between the cusp tips of the posterior teeth and the incisal edges of the anterior teeth (Fig. 4), as well as occlusal interferences that restricted movement, represented by overlapping of the edges of the posterior or anterior teeth (Fig. 5).

Fig. 4. Occlusal disharmony in DEC. (A) Lack of posterior contact, (B) Lack of anterior contact.

Fig. 5. Occlusal interferences in DEC. (A) Posterior teeth interference, (B) Anterior teeth interference.

The results obtained from the AECs and DECs were summarized in tabular form, in which the symbol “+” indicates an increase in the factor, whereas “-” denotes a reduction. These results were compared with each scenario described in Hanau’s Quint for correspondence analysis (Fig. 6).

Fig. 6. Modified representation of Hanau’s Quint based on the original publication.¹⁶ The effect of increased condylar guidance inclination on the other factors is highlighted in green.

RESULTS

For the analog method, the increase of condylar guidance was tested in AEC1, AEC2 and AEC3. Occlusion rims with 9-inch curvature and standard inclination were mounted on the articulator, with settings of 55° for the condylar guidance and -10° for the incisal guidance. Increasing condylar guidance to 60° resulted in loss of contact in BBO, which was reestablished by replacement with 8-inch rims. Therefore, the increase in condylar guidance (+) was compensated by greater occlusal curvature prominence (+) in AEC1.

In AEC2, occlusion rims with 9-inch diameter and -5° inclination were mounted on the articulator, with settings of 50° for the condylar guidance and -10° for the incisal guidance. Increasing condylar guidance to 55° (+) again led to loss of contact in BBO, which was corrected by increasing the inclination of the occlusal plane through replacement with standard occlusion rims (+).

In AEC3, occlusion rims with 9-inch curvature and standard inclination were mounted on the articulator with settings of 50° for the condylar guidance and -10° for the incisal guidance. Further increasing of condylar guidance to 60° (+) caused loss of contact in BBO, which was resolved by reducing incisal guidance to -15° (-).

Next, the increase of the compensating curve prominence was evaluated in AEC4 and AEC5. In AEC4, 8-inch rims with +5° inclination were mounted on the articulator, with condylar guidance at 60° and incisal guidance at -15°. Increasing the compensating curve prominence by replacement for 7-inch rims (+) caused loss of contact in BBO, which was corrected by reducing the occlusal plane inclination to standard rims (-). In AEC5, the articulator was initially adjusted with 9-inch rims and then replaced by 7-inch rims, increasing curvature prominence (+), and the resulting occlusal disharmony was corrected by raising incisal guidance from -15° to -10° (+).

Finally, the increase of incisal guidance was analyzed in AEC6. Occlusion rims with 8-inch diameter and -5° inclination were mounted on the articulator at -15° incisal guidance. Replacement for standard occlusion rims with greater inclination (+) caused loss of contact between the incisal pin and table, which was corrected by increasing incisal guidance to -10° (+).

The interrelationships between the AECs results are summarized in Table 1.

Table 1. Results of AECs.

	Condylar guidance inclination	Compensanting curve prominence	Occlusal plane inclination	Incisal guidance inclination
Condylar guidance inclination		AEC1: ++	AEC2: ++	AEC3: +-
Compensating curve prominence	AEC1: ++		AEC4: +-	AEC5: ++
Occlusal plane inclination	AEC2: ++	AEC4: -+		AEC6: ++
Incisal guidance inclination	AEC3: -+	AEC5: ++	AEC6: ++

“+” indicates an increase and “-” a decrease. Blue cells represent experimental results; others are duplicated and inferred by analogy.

For the digital method, the increase of condylar guidance was tested in DEC1, DEC2, DEC3 and DEC4. A 3° increase in condylar guidance (+) caused loss of posterior contact, which was corrected by increasing the compensating curve prominence (+) in DEC1, or by increasing occlusal plane inclination (+) in DEC2. The increased condylar guidance created anterior interference, solved by reducing incisal guidance (-) in DEC3. It also induced the loss of contact in posterior teeth, which was reestablished by increasing cusp height (+) in DEC4. Distal cusps required a greater increment (0.45 mm) than mesial cusps (0.41 mm).

Next, the increase of the compensating curve prominence was evaluated in DEC5, DEC6 and DEC7. Occlusion rims with 9-inch diameter were replaced with 7-inch rims, thereby increasing the compensating curve prominence (+). This modification produced posterior interference in DEC5, which was corrected by reducing occlusal plane inclination (-). In DEC6, loss of anterior contact was observed, reestablished by increasing the incisal guidance (+). In DEC7, posterior interference was eliminated by reducing cusp height (-).

The increase of the occlusal plane inclination (+) was analyzed in DEC8 and DEC9. This modification resulted in loss of anterior contact and was compensated by increasing the incisal guidance (+) in DEC8. Posterior interference was observed, which was corrected by reducing cusp height (-) in DEC9.

Finally, the increase of cusp height was observed in DEC10. An increase in incisal guidance (+) caused loss of posterior contact, which was corrected by increasing cusp height (+), returning to BBO.

The interrelationships between DECs results are summarized in Table 2.

Table 2. Results of the DECs.

	Condylar guidance inclination	Compensating curve prominence	Occlusal plane inclination	Incisal guidance inclination	Cusp height
Condylar guidance inclination		DEC1: ++	DEC2: ++	DEC3: +-	DEC4: ++
Compensating curve prominence	DEC1: ++		DEC5: +-	DEC6: ++	DEC7: +-
Occlusal plane inclination	DEC2: ++	DEC5: -+		DEC8: ++	DEC9: +-
Incisal guidance inclination	DEC3: -+	DEC6: ++	DEC8: ++		DEC10: ++
Cusp height	DEC4: ++	DEC7: -+	DEC9: -+	DEC10: ++

“+” indicates an increase and “-” a decrease. Blue cells represent experimental results; the others are duplicated and inferred by analogy.

DISCUSSION

The null hypothesis was accepted, as the analog and digital methods demonstrated the interrelationship among the occlusal plane, compensating curve, condylar guidance, and incisal guidance in achieving BBO, consistent with Hanau’s Quint. Cusp height was assessed digitally, and since the first four determinants showed similar behavior across both methods, it may be inferred that cusp height would present comparable effects in an analog articulator.

The results obtained through the AEC and DEC confirmed Hanau’s summarized articulation laws¹⁶: (a) increasing condylar guidance inclination increases the prominence of the compensating curve (AEC1 and DEC1); (b) increasing condylar guidance inclination increases occlusal plane inclination (AEC2 and DEC2); (c) increasing condylar guidance inclination decreases incisal guidance inclination (AEC3 and DEC3); (d) increasing condylar guidance inclination progressively increases posterior cusp height (DEC4); (e) increasing the prominence of the compensating curve decreases occlusal plane inclination (AEC4 and DEC5); (f) increasing the compensating curve increases incisal guidance inclination (AEC5 and DEC6); (g) increasing the compensating cur ve prominence progressively decreases posterior cusp height (DEC7); (h) increasing occlusal plane inclination increases incisal guidance inclination (AEC6 and DEC8); (i) increasing occlusal plane inclination decreases cusp height equally or slightly less (DEC9); and ( j) increasing incisal guidance inclination progressively increases cusp height (DEC10).

These findings reinforce that clinical understanding of mandibular movements, articulator calibration, and an accurate occlusion rim are fundamental during CD fabrication. The occlusion rim should present predefined compensating curve prominence and occlusal plane inclination, established according to individual patient needs. The occlusal plane may be oriented parallel to Camper’s plane or the interpupillary line, while compensating curves can be established with an occlusal template, the Broadrick flag, or other techniques.²² These occlusion rim characteristics subsequently guide tooth arrangement within the selected occlusal scheme for the CD. BBO may improve prosthesis stability during function,¹⁵,²⁴ and there is some evidence for increased alveolar bone loss with CD without balanced occlusion.²⁴ However, patient satisfaction, stability, and masticatory efficiency have also been reported with canine guidance,²⁴,²⁵,²⁶ while lingualized balanced occlusion is often chosen for patients with severe residual ridge resorption,²³ despite esthetic compromises.¹⁵ Anatomical posterior teeth may enhance esthetics, function and patient acceptance,⁷,¹⁵ but higher cusps increase horizontal forces and can destabilize dentures in severely resorbed ridges,⁷ in which case lower cusps or cuspless teeth may be indicated.¹⁵ Therefore, tooth selection and occlusal scheme must be individualized to balance esthetic and biomechanical considerations, relying on the clinician’s skill in teeth arrangement according to the occlusal plane and compensating curve of each patient.

Other authors have expanded or challenged Hanau’s Quint. Trapozzano¹⁹ emphasized only three determinants — protrusive incisal guidance, cusp height, and condylar guidance — while Boucher¹⁷ and Levin¹⁸ highlighted the role of the compensating curve, in which the occlusal plane should be oriented as in natural dentition and cusp height may be modified through tooth positioning without altering tooth anatomy. The findings of the present study reinforce the interrelationships observed for BBO in Hanau’s original work, although alternative interpretations reported in the literature should also be considered. Additional factors with clinical relevance should likewise be analyzed; more recently, imbalances among anatomic guidances have been identified as potential contributors to temporomandibular dysfunction.²¹ Despite the importance of these topics, most studies evaluating Hanau’s principles are dated, highlighting the importance of revisiting and validating them with digital methodologies.

Under the inherent limitations of in vitro research in fully reproducing intraoral conditions affecting complete denture stability, such as soft tissue resilience and neuromuscular control, the present findings demonstrate that Hanau’s articulation laws can be confirmed digitally using a methodology validated with an analog articulator. A two-dimensional digital articulator was created based on the dimensions of an analog articulator in a lateral view, as the interrelationships of Hanau’s Quint can be effectively visualized during protrusive simulation. This simple and easily reproducible method allows the user to visualize compensatory effects of occlusion rim and artificial teeth characteristics, as well as articulator adjustments, which may help clinicians better understand BBO in complete denture treatment planning. Future studies may validate this method using three-dimensional articulators in CAD software programs, incorporating complete artificial dentitions with different cusp heights and angulations. The findings of the present study regarding variations in compensating curve prominence and occlusal plane inclination may also contribute to the refinement of digital planning workflows.

CONCLUSION

Within the limitations of this in vitro study, the interrelationships among condylar guidance, plane of occlusion, compensating curve, incisal guidance, and cusp height, as described in Hanau’s Quint for achieving bilateral balanced occlusion (BBO) in complete dentures, were demonstrated through a digital approach validated against an analog method.