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Keywords = sinus septa

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14 pages, 1608 KiB  
Article
Changes in Maxillary Sinus Structure Due to Tooth Loss and the Effects of Sex and Aging on CBCT Before Maxillary Sinus Augmentation: A Cross-Sectional Study of 120 Patients
by Takumi Itokawa, Kikue Yamaguchi, Kotaro Yagi, Kazuyuki Araki, Daisuke Sato and Motohiro Munakata
Bioengineering 2025, 12(3), 240; https://doi.org/10.3390/bioengineering12030240 - 26 Feb 2025
Viewed by 1093
Abstract
Prosthesis for missing maxillary molars with dental implants often requires maxillary sinus augmentation owing to insufficient alveolar bone height. However, the anatomical structure of the maxillary sinus is a significant risk factor. This study used preoperative cone-beam computed tomography (CBCT) to investigate changes [...] Read more.
Prosthesis for missing maxillary molars with dental implants often requires maxillary sinus augmentation owing to insufficient alveolar bone height. However, the anatomical structure of the maxillary sinus is a significant risk factor. This study used preoperative cone-beam computed tomography (CBCT) to investigate changes in the anatomical structure of the maxillary sinus due to tooth loss and conducted an epidemiological survey of Japanese people to determine the effects of gender and age on these changes. Preoperative CBCT scans were analyzed in patients aged ≥ 50 years with free-end maxillary molar edentulism involving ≥ 2 missing teeth seeking implant treatment. Statistical analyses were performed. One hundred and twenty participants (46 males, 74 females; mean age, 62.1 ± 7.4 years) with 3.0 ± 0.9 missing teeth and an existing bone volume of 6.2 ± 3.1 mm were included. Lateral wall thickness, sinus angle, sinus membrane thickness, maxillary sinus length and width, and the presence of the sinus septa significantly differed between missing and non-missing sides. Maxillary sinus height and sinus membrane thickness on missing side and maxillary sinus height and width on non-missing side varied significantly. Aging was associated with maxillary sinus length and width changes on the non-missing side in males, whereas no age-associated effects were identified in females. To ensure the safe execution of maxillary sinus augmentation, a thorough understanding of maxillary sinus anatomy is crucial prior to surgery. Full article
(This article belongs to the Section Biomedical Engineering and Biomaterials)
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29 pages, 6503 KiB  
Review
Non-Thrombotic Filling Defects in Cerebral Veins and Sinuses: When Normal Structures Mimic a Disease
by Marialuisa Zedde and Rosario Pascarella
Neurol. Int. 2025, 17(1), 9; https://doi.org/10.3390/neurolint17010009 - 17 Jan 2025
Viewed by 2840
Abstract
Cerebral venous thrombosis (CVT) is a rare and potentially critical cerebrovascular disease involving intracranial dural sinuses and veins. The diagnosis is a stepwise pathway starting from clinical suspicion and employing several neuroradiological techniques, mainly Computed Tomography (CT)-based and Magnetic Resonance Imaging (MRI)-based modalities. [...] Read more.
Cerebral venous thrombosis (CVT) is a rare and potentially critical cerebrovascular disease involving intracranial dural sinuses and veins. The diagnosis is a stepwise pathway starting from clinical suspicion and employing several neuroradiological techniques, mainly Computed Tomography (CT)-based and Magnetic Resonance Imaging (MRI)-based modalities. The neuroradiological findings, both in the diagnostic phase and in the follow-up phase, may provide some results at risk for misdiagnosis. Non-thrombotic filling defects of intracranial dural sinuses are among them, and the potential sources are artefactual and or anatomical (venous septa and arachnoid granulations). The misdiagnosis of these findings as CVT is potentially linked to dangerous consequences. A potential strategy to avoid this is to increase the knowledge about technical and anatomical reasons for non-thrombotic filling defects of intracranial dural sinuses and their imaging features. The main aim of this review is to address these issues, including the variability of the intracranial venous pathways, providing the solutions for overcoming the above-cited potential misdiagnosis of non-thrombotic filling defects as CVT. Full article
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15 pages, 15721 KiB  
Article
Anatomy of Maxillary Sinus: Focus on Vascularization and Underwood Septa via 3D Imaging
by Sara Bernardi, Serena Bianchi, Davide Gerardi, Pierpaolo Petrelli, Fabiola Rinaldi, Maurizio Piattelli, Guido Macchiarelli and Giuseppe Varvara
Tomography 2024, 10(4), 444-458; https://doi.org/10.3390/tomography10040034 - 24 Mar 2024
Cited by 8 | Viewed by 2805
Abstract
The study of the maxillary sinus anatomy should consider the presence of two features of clinical importance. The arterial supply course and the presence of the so-called Underwood septa are two important factors to consider when planning surgical treatment to reduce the risk [...] Read more.
The study of the maxillary sinus anatomy should consider the presence of two features of clinical importance. The arterial supply course and the presence of the so-called Underwood septa are two important factors to consider when planning surgical treatment to reduce the risk of surgical complications such as excessive bleeding and Schneiderian membrane perforations. This study aimed to investigate the above-mentioned anatomical structures to improve the management of eventual vascular and surgical complications in this area. This study included a total of 200 cone-beam computed topographies (CBCTs) divided into two groups of 100 CBCTs to evaluate the arterial supply (AAa) course through the lateral sinus wall and Underwood’s septa, respectively. The main parameters considered on 3D imaging were the presence of the AAa in the antral wall, the length of the arterial pathway, the height of the maxillary bone crest, the branch sizes of the artery in the first group, and the position of the septa, the length of the septa, and their gender associations in the second group. The CBCT analysis showed the presence of the arterial supply through the bone wall in 100% of the examined patients, with an average size of 1.07 mm. With regard to the septa, 19% of patients presented variations, and no gender difference was found to be statistically significant. The findings add to the current understanding of the clinical structure of the maxillary sinus, equipping medical professionals with vital details for surgical preparation and prevention of possible complications. Full article
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15 pages, 4838 KiB  
Article
The Effectiveness and Practicality of a Novel Barrier Membrane for the Open Window in Maxillary Sinus Augmentation with a Lateral Approach, with Risk Indicators for Bone Graft Displacement and Bone Height Decrease: A Prospective Study in Humans
by Kikue Yamaguchi, Motohiro Munakata, Daisuke Sato, Yu Kataoka and Ryota Kawamata
Bioengineering 2023, 10(10), 1110; https://doi.org/10.3390/bioengineering10101110 - 22 Sep 2023
Cited by 2 | Viewed by 1740
Abstract
Maxillary sinus augmentation with a lateral approach (MSA) is a well-established treatment. In this prospective study, we evaluated risk factors for postoperative bone graft displacement and reported the clinical application of long-term resorbable L-lactic acid/-caprolactone (PLA/PCL) as a barrier membrane to cover the [...] Read more.
Maxillary sinus augmentation with a lateral approach (MSA) is a well-established treatment. In this prospective study, we evaluated risk factors for postoperative bone graft displacement and reported the clinical application of long-term resorbable L-lactic acid/-caprolactone (PLA/PCL) as a barrier membrane to cover the open window in the lateral wall in MSA. Twenty-four patients underwent MSA according to the relevant criteria; CT data obtained before and 1 week (1 w) and 5–6 months (5 m) post-MSA, bone height changes, bone height reduction rates at 1 w and 5 m post-MSA, bone graft displacement measurements, and risk factors were examined. All patients showed bone height increments (p < 0.005). However, no difference was observed between 1 w and 5 m post-MSA. Bone graft displacement was observed in eight patients; the reduction rate from 1 w to 5 m post-MSA was 8.38% ± 4.88%. Sex, septa, maxillary sinus floor–palatal bone distance, and maxillary sinus floor–maxillary ostium distance were associated with bone graft displacement (p < 0.05). The height from the maxillary sinus floor to the palatal bone and the sinus angle influenced the augmentation degree (p < 0.05). The PLA/PCL membrane is compared favorably with other membranes and may be useful as a barrier membrane for the MSA open window. Full article
(This article belongs to the Special Issue Advances in Dental Implant Surgery)
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14 pages, 2537 KiB  
Article
The CBCT Retrospective Study on Underwood Septa and Their Related Factors in Maxillary Sinuses—A Proposal of Classification
by Kamil Nelke, Dorota Diakowska, Monika Morawska-Kochman, Maciej Janeczek, Edyta Pasicka, Marceli Łukaszewski, Krzysztof Żak, Jan Nienartowicz and Maciej Dobrzyński
J. Pers. Med. 2023, 13(8), 1258; https://doi.org/10.3390/jpm13081258 - 14 Aug 2023
Cited by 4 | Viewed by 1985
Abstract
Introduction. The presence of bone septum in the maxillary sinus is one of the most common anatomical findings. So-called Underwood septa (US) are an atypical bone formation in the maxillary sinuses. Mostly they are quite easily found in CBCT studies and have major [...] Read more.
Introduction. The presence of bone septum in the maxillary sinus is one of the most common anatomical findings. So-called Underwood septa (US) are an atypical bone formation in the maxillary sinuses. Mostly they are quite easily found in CBCT studies and have major importance in sinus lift procedures in dental surgery. Furthermore, the shape, location, and size of the bony septa are important in each maxillary sinus surgery. Material and methods. A retrospective study of 120CBCT scans from the authors’ own database was conducted. Results. Approximately 37.5% of each CBCT was associated with the occurrence of US, while just 25% had a full septum, and a total of only 14 patients had a half septa. More females have US, while healthy pneumatized maxillary sinus is most commonly found (82.22%). There is no correlation between the occurrence of silent sinus syndrome (p = 0.174), mucosal thickening (p = 0.325), or retention cyst formation (p = 0.272). Most sinuses are without any opacification in CBCT evaluation (91.11%), while other syndromes are not statistically relevant. Conclusions. It seems that the occurrence of Underwood septa is not statistically related to any clinical, radiological, or pathological condition within the sinus (p > 0.05). Furthermore, a more full or partial appearance of US was found in female patients. Full article
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11 pages, 2428 KiB  
Article
Anatomical Variants of Internal Carotid Artery—Results from a Retrospective Study
by Bogdan Mihail Cobzeanu, Vasilica Baldea, Victor Vlad Costan, Mihail Dan Cobzeanu, Octavian Dragos Palade, Liliana Gheorghe, Luminita Radulescu, Florentina Severin, Corina Lupascu Ursulescu, Geanina Bandol, Cristian Martu, Andrei Mihail Rosu and Maria Luiza Cobzeanu
Medicina 2023, 59(6), 1057; https://doi.org/10.3390/medicina59061057 - 31 May 2023
Cited by 1 | Viewed by 4995
Abstract
Background and Objectives: The internal carotid artery (ICA) is a vascular structure that can be easily injured during sinus endoscopic procedures, and surgeons should be familiar with its anatomic variants. The aim of this study was to describe the anatomical variations in [...] Read more.
Background and Objectives: The internal carotid artery (ICA) is a vascular structure that can be easily injured during sinus endoscopic procedures, and surgeons should be familiar with its anatomic variants. The aim of this study was to describe the anatomical variations in the internal carotid artery in relationship to sphenoidal sinuses, using computed tomography (CT). Materials and Methods: In this retrospective study, we evaluated the variations of the ICA in relationship to sphenoidal sinuses in a cohort of 600 patients who were assessed between January 2020 and December 2022 in ‘Saint Spiridon’ Emergency Hospital, Iasi, Romania. Descriptive statistics were used to characterize our data. Results: The most prevalent anatomical variant was represented by intrasinusal septa with posterior insertion on the ICA (58.6%), followed by procident ICA (58%) and dehiscent ICA (52%). We could not find any statistical significance regarding demographic characteristics among groups. Conclusions: A thorough CT examination should be performed before functional endoscopic sinus surgery, with the identification of anatomical variants of the ICA, in order to prevent its injury with potentially fatal consequences. Full article
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12 pages, 6715 KiB  
Review
The Use of CBCT in Evaluating the Health and Pathology of the Maxillary Sinus
by Andy Wai Kan Yeung, Kuo Feng Hung, Dion Tik Shun Li and Yiu Yan Leung
Diagnostics 2022, 12(11), 2819; https://doi.org/10.3390/diagnostics12112819 - 16 Nov 2022
Cited by 32 | Viewed by 14458
Abstract
The use of cone-beam computed tomography (CBCT) has been increasing in dental practice. This narrative review summarized the relevance and utilizations of CBCT to visualize anatomical structures of the maxillary sinus and common pathologies found in the maxillary sinus. The detection/visualization rate, the [...] Read more.
The use of cone-beam computed tomography (CBCT) has been increasing in dental practice. This narrative review summarized the relevance and utilizations of CBCT to visualize anatomical structures of the maxillary sinus and common pathologies found in the maxillary sinus. The detection/visualization rate, the location and the morphometric characteristics were described. For sinus anatomy, the reviewed features included the posterior superior alveolar artery, sinus pneumatization, sinus hypoplasia, sinus septa, and primary and accessory sinus ostia. For pathology, the following items were reviewed: membrane thickening associated with periapical lesions/periodontal lesions, mucous retention cyst, and antrolith. The visualization and assessment of the maxillary sinus is very important prior to procedures that take place in close proximity with the sinus floor, such as tooth extraction, implant insertion, and sinus floor elevation. Some sinus pathologies may be associated with odontogenic lesions, such as periapical diseases and periodontal bone loss. Full article
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11 pages, 1923 KiB  
Article
Incidence, Size and Orientation of Maxillary Sinus Septa—A Retrospective Clinical Study
by Laura Andreea Schiller, Horia Mihail Barbu, Stefania Andrada Iancu and Silviu Brad
J. Clin. Med. 2022, 11(9), 2393; https://doi.org/10.3390/jcm11092393 - 24 Apr 2022
Cited by 6 | Viewed by 3427
Abstract
Background: The purpose of this study is to analyze if there is any statistical correlation between the surgery’s complexity (easy to difficult—depending on the anatomical conditions) and the patient’s sex, type of edentulism, and left or right side of the maxilla. Methods: Cone [...] Read more.
Background: The purpose of this study is to analyze if there is any statistical correlation between the surgery’s complexity (easy to difficult—depending on the anatomical conditions) and the patient’s sex, type of edentulism, and left or right side of the maxilla. Methods: Cone beam computed tomography records of 1192 maxillary sinuses were evaluated, measured, and statistically analyzed with respect to patient sex, type of edentulism, and left or right side, taking into consideration Wen’s proposed sinus septum classification. Results: Our research suggests that most sinus augmentation procedures in patients presenting antral septum fall into the Moderate A category (31.94%) and that there is not a correlation between the surgery’s complexity (easy to difficult) and the patient’s sex, type of edentulism and left or right side of the maxilla. Conclusion: We suggest a minor modification to Wen’s classification in view of the fact that our findings revealed a combination of medio-lateral and antero-posterior septa that we could not classify in one of the existing categories. Full article
(This article belongs to the Topic State-of-the-Art Dentistry and Oral Health)
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2 pages, 572 KiB  
Proceeding Paper
External Approach to Bilaterally Septated Maxillary Sinuses: A Case Report
by Pedro Gameiro, Bernardo Saldanha, Francisco Santos, Jéssica Silva, João Norte, João Reis, Pedro Sottomayor, Rodolfo Vaz and Pedro Rodrigues
Med. Sci. Forum 2021, 5(1), 35; https://doi.org/10.3390/msf2021005035 - 22 Jul 2021
Viewed by 2782
Abstract
The careful planning of a sinus lift procedure is the key to avoiding surgical complications. In this clinical case, a female patient, 59 years old and totally edentulous in the maxilla, was referred to Egas Moniz’s Dental Clinic Implantology consultation with indication for [...] Read more.
The careful planning of a sinus lift procedure is the key to avoiding surgical complications. In this clinical case, a female patient, 59 years old and totally edentulous in the maxilla, was referred to Egas Moniz’s Dental Clinic Implantology consultation with indication for bilateral external sinus lift of the maxillary sinuses prior to implant placement. Both orthopantomography and cone-beam computed tomography were used to show the anatomy of the maxillary sinuses, which presented multiple sinus septa. A multiple anterolateral window approach was applied in order to avoid perforation of the Schneiderian membrane while accessing it. Full article
(This article belongs to the Proceedings of The 5th International Congress of CiiEM (IC CiiEM))
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8 pages, 2532 KiB  
Article
Sinus Mucosa Thickness Changes and Ostium Involvement after Maxillary Sinus Floor Elevation in Sinus with Septa. A Cone Beam Computed Tomography Study
by Shingo Kato, Yuki Omori, Masatsugu Kanayama, Atsuya Hirota, Mauro Ferri, Karol Alí Apaza Alccayhuaman and Daniele Botticelli
Dent. J. 2021, 9(8), 82; https://doi.org/10.3390/dj9080082 - 21 Jul 2021
Cited by 11 | Viewed by 4017
Abstract
Background: A thickening of the sinus mucosa is observed after sinus floor augmentation. The objective of this retrospective study was to evaluate the influence of the presence of septa in the dimensional variation and ostium involvement over time of the Schneiderian mucosa after [...] Read more.
Background: A thickening of the sinus mucosa is observed after sinus floor augmentation. The objective of this retrospective study was to evaluate the influence of the presence of septa in the dimensional variation and ostium involvement over time of the Schneiderian mucosa after sinus floor augmentation. Materials and Methods: Fifteen sinuses with septa (septa group) and 15 without (control group) were selected. CBCTs taken before surgery, and were analyzed after 1 week and after 9 months. Schneiderian membrane thickness changes over time and involvement of the ostium were evaluated. Results: Four perforations occurred in the septa group and none in the control group. After 1 week of healing, the sinus mucosa thickness increased in height by 5.7 mm and 7.1 mm in the septa and control groups, respectively. In this period, the patency of the ostium decreased in both groups, and three infundibula were obstructed in the septa group, and five in the control group. The mucosa was thicker and the edema was closer to the ostium in the control compared to in the septa group. After 9 months of healing, the dimensions regressed to normal pattern and no obstruction of the infundibula were observed. No statistically significant differences were found between septa and control groups. Conclusions: after one week of healing, the sinus mucosa increased in dimensions in both septa and control groups. However, the sinus mucosa presented a tendency of being thicker and closer to the ostium, resulting in a higher number of infundibula obstructions, in the control group compared to in the septa group. After 9 months, the sinus mucosa regressed to normal dimensions and no obstructions of the infundibula were observed in any group. Full article
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16 pages, 1094 KiB  
Article
Influence of Anatomical Parameters on the Dimensions of the Subantral Space and Sinus Mucosa Thickening after Sinus Floor Elevation. A Retrospective Cone Beam Computed Tomography Study
by Yuki Omori, Yasushi Nakajima, Hideki Imai, Daichi Yonezawa, Mauro Ferri, Karol Alí Apaza Alccayhuaman and Daniele Botticelli
Dent. J. 2021, 9(7), 76; https://doi.org/10.3390/dj9070076 - 24 Jun 2021
Cited by 7 | Viewed by 3829
Abstract
Background: Various anatomical parameters might influence the surgical approach for maxillary sinus floor elevation. The objective of the present study was to retrospectively evaluate the influence of anatomical parameters on the dimensions of the subantral space and of the sinus mucosa thickening after [...] Read more.
Background: Various anatomical parameters might influence the surgical approach for maxillary sinus floor elevation. The objective of the present study was to retrospectively evaluate the influence of anatomical parameters on the dimensions of the subantral space and of the sinus mucosa thickening after sinus floor elevation. Material and Methods: Seventy-eight maxillary sinuses in sixty-five patients were evaluated on cone beam computed tomographies taken before surgery and after one week (t1w) and nine months (t9m). Several parameters such as the distance XF between an axis parallel to the base of the nose (X-axes) and the sinus floor (F) were correlated with the height gain (IF) at t1w and t9m and the post-surgical edema. Results: A weak significant positive correlation was observed between height gain vs. sinus height of interest (XF), the balcony, and the sinus floor angle. The post-surgical edema was influenced by the initial mucosa thickness and the xenograft used. Conclusions: Various parameters might affect height gain and sinus mucosa thickening after sinus floor elevation. The height of interest, the balcony, and the sinus floor angle showed significant correlations with height gain. The initial thickness of the mucosa and the biomaterial used influenced the post-surgical edema. Full article
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10 pages, 2612 KiB  
Article
Anatomographic Variants of Sphenoid Sinus in Ethiopian Population
by Tizita K. Degaga, Abay M. Zenebe, Amenu T. Wirtu, Tequam D. Woldehawariat, Seife T. Dellie and Jickssa M. Gemechu
Diagnostics 2020, 10(11), 970; https://doi.org/10.3390/diagnostics10110970 - 19 Nov 2020
Cited by 17 | Viewed by 14016
Abstract
Neurosurgeons often neglect the sphenoid sinus due to its deep location and difficulties in accessing during surgical interventions. Disease of the sphenoid sinus is difficult to diagnose since its presenting symptoms are difficult to recognize. Moreover, compared with other paranasal sinuses, the sphenoid [...] Read more.
Neurosurgeons often neglect the sphenoid sinus due to its deep location and difficulties in accessing during surgical interventions. Disease of the sphenoid sinus is difficult to diagnose since its presenting symptoms are difficult to recognize. Moreover, compared with other paranasal sinuses, the sphenoid sinus is considered the most variable air sinus in terms of its degree of pneumatization, number and position of inter-sinus septa, and its relationship with the surrounding anatomical structures. Anatomical variations of the sphenoid sinus are significant from a neurosurgical point of view. Understanding of these variations and its relationships with surrounding structures such as the internal carotid artery, optic nerve, and pituitary gland are clinically relevant to minimize injuries associated with surgical procedures that involve sphenoid sinus. We implemented principles of imaging using computed tomography to elucidate any anatomical variations of the sphenoid sinus in the Ethiopian population. We conducted a prospective study in 200 patients with ages 18–79, who underwent scans of the sphenoid sinus at the Tikur Anbessa Referral Teaching Hospital in 2017–2018. Our findings revealed an incidence of anatomographical variations in terms of pneumatization that varied between 2–50%. These variants include 2% conchal, 25.5% presellar, 50% sellar, and 22.5% postsellar pneumatization. We also demonstrated anatomographic variants in terms of septation, 77.5% single complete septa, 11.5% single incomplete, 10% double septa, and 1% absence of septa. In summary, the sellar pneumatization was found to be the most clinically relevant anatomographic variant among Ethiopians participating in the study, of which 90% were tomographically single septated. These variants must be taken into consideration during trans-sphenoidal surgery and knowledge of the variations has clinical implication in minimizing injuries during invasive surgical procedures involving the sphenoid sinus. Full article
(This article belongs to the Special Issue Anatomical Variation and Clinical Diagnosis)
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11 pages, 2851 KiB  
Article
Anatomical Considerations and Study of the Fractal Dimension around the Posterior Superior Alveolar Artery
by Yolanda Guerrero-Sánchez, Francisco José Gómez García, Manuel Fernández-Martínez, Blanca Pallarés Martínez and Pia López-Jornet
Symmetry 2020, 12(7), 1177; https://doi.org/10.3390/sym12071177 - 16 Jul 2020
Cited by 2 | Viewed by 2626
Abstract
The Posterior Superior Alveolar Artery (PSAA) provides vascular support to molars, gingiva, and maxillary sinus. A tear of the PSAA may cause profuse hemorrhages which may lead to complications at a surgical level. As such, it becomes crucial to anatomically analyse several features [...] Read more.
The Posterior Superior Alveolar Artery (PSAA) provides vascular support to molars, gingiva, and maxillary sinus. A tear of the PSAA may cause profuse hemorrhages which may lead to complications at a surgical level. As such, it becomes crucial to anatomically analyse several features regarding the PSAA as well as the area surrounding it. In this paper, we are particularly interested in the study of the complexity of the periodontal tissue structure which appears close to the location of the PSAA. A total amount of 400 cone beam computed tomography (CBCT) scans (two per subject) were performed to explore the presence of the PSAA, the thickness of the Schneider’s membrane, and the existence of septa. Several parameters were evaluated including the location of the artery in the maxillary sinus, the distance from the PSAA to the alveolar ridge, the thickness of the membrane, the diameter of the cavities produced by the septa, and the fractal dimension of the trabecular tissue that surrounds the PSAA. They were found strong linear relationships between Distal and Central Measures (a Pearson’s R 2 = 0.9952 ), Mesial and Central Measures ( R 2 = 0.9950 ), and Distal and Mesial Measure ( R 2 = 0.997 ). We hypothesised that the loss of dental pieces would imply a distinct complexity of the trabecular tissue structure surrounding the PSAA. In this way, a p-value equal to 0.001 was provided by the Mann-Whitney test, which supports our hypothesis. Furthermore, the mean of the fractal dimensions of the group of edentulous patients (equal to 1.56 ) was found to be lower than the one of the group of non-edentulous patients (equal to 1.61 ) with small standard deviations in both cases. Our study suggests that accurate calculations of the fractal dimension combined with the use of CBCT do provide valuable information regarding the area that surrounds the PSAA. Full article
(This article belongs to the Special Issue Advances in Nonlinear, Discrete, Continuous and Hamiltonian Systems)
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