scholarly journals Evaluation of the Golden Ratio in Nasal Conchae for Surgical Anatomy

2019 ◽  
Vol 100 (1) ◽  
pp. NP57-NP61
Author(s):  
Emine Petekkaya ◽  
Mahinur Ulusoy ◽  
Hassan Bagheri ◽  
Şükrü Şanlı ◽  
Mehmet Seyit Ceylan ◽  
...  

Purpose: The golden ratio is reached by the fractal model of the number sequence which is known as the “Fibonacci series” and has a convergent ratio of approximately 1.618 between 2 consecutive Fibonacci numbers. Golden ratio relationships have been shown in several plants in the nature and several organs and structures in the human body. The conchae, which form an important part of the nasal valve, have a special geometric significant in terms of providing turbulence to the laminar airflow that passes to the nasal cavity. Methods: This study made golden ratio calculations on 34 adults aged 20 to 45 years over computed tomography (CT) images. Totally, 34 volunteers (male, n = 18 and female, n = 16) with no nasal pathologies participated in the study. Using Adobe Photoshop, golden ratio calculations were made by applying the Fibonacci spiral on the images that best showed the conchae and meatuses on the CT images. Results: The intersection points of the spiral that was projected on the inferior and middle nasal concha were determined as S0, S1, S2, S3, and S4. The distances of S0-S1, S1-S2, S2-S3, and S3-S4 were measured. The concha measurements of the women showed significantly similar values to the golden ratio constant of ∼1.618 in the RS3/S4 and LS3/S4 measurements. Conclusion: We found that the S3/S4 region that captured the golden ratio in our study corresponds to the base part of the inferior nasal concha, and its place of spiraling in the nasal cavity is observed to have an important role in creating vortices.

Author(s):  
Saifutdin Arifov ◽  
Alexey Rasulov

Among chronic forms of rhinitis of great importance is vasomotor rhinitis, which is the most common form of chronic non-allergic rhinitis and the clinician has to deal with it constantly. Treatment of vasomotor rhinitis is a complex and largely unresolved problem, which puts this disease among the important problems of modern rhinology. The variety of methods used in the treatment of patients with vasomotor rhinitis confirms the complexity of the task of choosing the optimal method for clinicians and the difficulty of obtaining a sustainable result from the chosen method. Surgical treatment of patients with of patients with various forms of chronic rhinitis is sometimes the only effective. Currently, the arsenal of methods and means of surgical treatment of the nasal concha is quite wide and varied. The purpose of this study – to study in a comparative aspect the functional state of the nasal cavity after carrying out some methods of surgical treatment ofvasomotor rhinitis. Materials and Methods: The study was conducted in the clinic of the Department of Otorhinolaryngology of the Tashkent institute of postgraduate medical education on 43 patients with vasomotor rhinitis in age from 20 to 46 years, average age 28,0±1,3 years. All patients with BP included in our study, after collecting complaints and anamnesis, underwent an endoscopic examination of the nasal cavity and nasopharynx, a computerized tomogram of the nose and paranasal sinuses, standard laboratory tests and microscopy of a smear from the nasal cavity on eosinophils.Investigated the respiratory (computer rhinopneumocotachometry), transport (saccharin test) functions of the nasal mucosa, performed an adrenaline test and the Flour test (determination of the consistency of inferior nasal concha and the response to pushing with a push-button probe). Results: Studies have shown the highest efficiency of laser coagulation with vasomotor rhinitis. After laser surgery, a long-lasting and sustained improvement in the functions of the nasal cavity was noted, while there was no adverse effect on the mucous membrane of the nasal cavity, which was reflected in the recovery rates of both nasal breathing and mucociliary clearance. Given the well-tolerated laser coagulation, the lack of the need for observation and care of the nasal cavity in the postoperative period, the possibility of outpatient treatment, allows us to recommend this type of exposure as the method of choice in the surgical treatment of patients with vasomotor rhinitis. The simplicity of submucosal vasotomy, the availability of instruments for carrying out, the restoration of free nasal breathing and the positive effect on the functional state of the nasal cavity, although slower than laser coagulation, minimal side effects put it on a par with the laser effect. The need to use tampons after surgery reduces the quality of life of patients, hospital stays and the need to monitor patients in the early postoperative period makes this operation strictly inpatient. Electrocautery of inferior nasal concha demonstrated in our study a negative effect on the function of the nasal cavity, although, of course, there was a definite improvement in nasal breathing, but the severity and speed of improvement was significantly less than during laser exposure and submucosal vasotomy. The slowest and most incomplete restoration of the mucociliary clearance of the nasal cavity once again underlines the disadvantage of this method. Conclusion: Evaluation of the long-term results of surgical treatment based on the combination of effects on the respiratory and transport functions of the nasal cavity, as well as on the clinical manifestations of BP, makes it possible to recommend laser coagulation as the most optimal method providing a long-lasting effect in treating patients with vasomotor rhinitis. Alternatively, you can take a submucosal vasotomy of the inferior nasal concha.


1926 ◽  
Vol 22 (4) ◽  
pp. 466-467
Author(s):  
V. S.

IM Krukover (Vesti. Rino-lyar-ot., 1925, No. 1) suggests using the measurement of t in the nose (under the inferior nasal concha) to diagnose diseases of the paranasal cavities (eg, sinusitis).


2020 ◽  
Vol 1 (3) ◽  
pp. 112-122
Author(s):  
Agung Prabowo

Fibonacci numbers, Lucas numbers and Mulatu numbers are built in the same method. The three numbers differ in the first term, while the second term is entirely the same. The next terms are the sum of two successive terms. In this article, generalizations of Fibonacci, Lucas and Mulatu (GFLM) numbers are built which are generalizations of the three types of numbers. The Binet formula is then built for the GFLM numbers, and determines the golden ratio, silver ratio and Bronze ratio of the GFLM numbers. This article also presents generalizations of these three types of ratios, called Metallic ratios. In the last part we state the Metallic ratio in the form of continued fraction and nested radicals.


Author(s):  
Jan C. A. Boeyens

The discovery of material periodicity must rank as one of the major achievements of mankind. It reveals an ordered reality despite the gloomy pronouncements of quantum philosophers. Periodicity only appears in closed systems with well-defined boundary conditions. This condition excludes an infinite Euclidean universe and all forms of a chaotic multiverse. Manifestations of cosmic order were observed and misinterpreted by the ancients as divine regulation of terrestrial events, dictated by celestial intervention. Analysis of observed patterns developed into the ancient sciences of astrology, alchemy and numerology, which appeared to magically predict the effects of the macrocosm on the microcosm. The sciences of astronomy and chemistry have by now managed to outgrow the magic connotation, but number theory remains suspect as a scientific pursuit. The relationship between Fibonacci numbers and cosmic self-similarity is constantly being confused with spurious claims of religious and mystic codes, imagined to be revealed through the golden ratio in the architecture of the Great Pyramid and other structures such as the Temple of Luxor. The terminology which is shared by number theory and numerology, such as perfect number, magic number, tetrahedral number and many more, contributes to the confusion. It is not immediately obvious that number theory does not treat 3 as a sacred number, 13 as unlucky and 666 as an apocalyptic threat. The relationship of physical systems to numbers is no more mysterious nor less potent than to differential calculus. Like a differential equation, number theory does not dictate, but only describes physical behavior. The way in which number theory describes the periodicity of matter, atomic structure, superconductivity, electronegativity, bond order, and covalent interaction was summarized in a recent volume. The following brief summary of these results is augmented here by a discussion of atomic and molecular polarizabilities, as derived by number theory, and in all cases specified in relation to the grand periodic function that embodies self-similarity over all space-time.


2019 ◽  
Vol 36 (9) ◽  
pp. 3164-3179
Author(s):  
Punjan Dohare ◽  
Amol P. Bhondekar ◽  
Anupma Sharma ◽  
C. Ghanshyam

Purpose The purpose of this paper is to understand the effect of airflow dynamics on vortices for different flow rates using the human nose three-dimensional model. Design/methodology/approach Olfaction originates with air particles travelling from an external environment to the upper segment of the human nose. This phenomenon is generally understood by using the nasal airflow dynamics, which enhances the olfaction by creating the vortices in the human nose. An anatomical three-dimensional model of the human nasal cavity from computed tomography (CT) scan images using the MIMICS software (Materialise, USA) was developed in this study. Grid independence test was performed through volume flow rate, pressure drop from nostrils and septum and average velocity near the nasal valve region using a four computational mesh model. Computational fluid dynamics (CFD) was used to examine the flow pattern and influence of airflow dynamics on vortices in the nasal cavity. Numerical simulations were conducted for the flow rates of 7.5, 10, 15 and 20 L/min using numerical finite volume methods. Findings At coronal cross-sections, dissimilar nasal airflow patterns were observed for 7.5, 10, 15 and 20 L/min rate of fluid flow in the human nasal cavity. Vortices that are found at the boundaries with minimum velocity creates deceleration zone in the nose vestibule region, which is accompanied by flow segregation. Maximum vortices were observed in the nasal valve region and the posterior end of the turbinate region, which involves mixing and recirculation and is responsible for enhancing the smelling process. Practical implications The proposed analysis is applicable to design the sensor chamber for electronic noses. Originality/value In this paper, the influence of airflow dynamics on vortices in the human nasal cavity is discussed through numerical simulations.


2008 ◽  
Vol 266 (2) ◽  
pp. 231-235 ◽  
Author(s):  
Mustafa F. Sargon ◽  
H. Hamdi Çelik ◽  
S. Sabri Uslu ◽  
Ö. Taşkın Yücel ◽  
Cem C. Denk ◽  
...  

1990 ◽  
Vol 3 (4) ◽  
pp. 307-316 ◽  
Author(s):  
C. M. Trotter ◽  
G. H. Hall ◽  
D. M. Salter ◽  
J. A. Wilson

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 426
Author(s):  
Noah Giansiracusa

There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie algebra g2 case of these bundles in three different ways, a family of summation formulas for Fibonacci numbers in terms of the golden ratio is derived.


2005 ◽  
Vol 19 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Bappaditya Ray ◽  
Lav Kumar Singh ◽  
Chandan Jyoti Das ◽  
T.S. Roy

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