See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/306051060 Golden Ratio: A subtle regulator in our body and cardiovascular system? Article in International journal of cardiology · August 2016 DOI: 10.1016/j.ijcard.2016.08.147 CITATIONS READS 8 266 3 authors, including: Selcuk Ozturk Ertan Yetkin Ankara University Istinye University, LIV Hospital 56 PUBLICATIONS 121 CITATIONS 227 PUBLICATIONS 3,259 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: microbiology View project golden ratio View project All content following this page was uploaded by Ertan Yetkin on 23 August 2019. The user has requested enhancement of the downloaded file. International Journal of Cardiology 223 (2016) 143–145 Contents lists available at ScienceDirect International Journal of Cardiology journal homepage: www.elsevier.com/locate/ijcard Review Golden ratio: A subtle regulator in our body and cardiovascular system? Selcuk Ozturk a, Kenan Yalta b, Ertan Yetkin c,⁎ a Abant Izzet Baysal University, Faculty of Medicine, Department of Cardiology, Bolu, Turkey b Trakya University, Faculty of Medicine, Department of Cardiology, Edirne, Turkey c Yenisehir Hospital, Division of Cardiology, Mersin, Turkey article info abstract Article history: Golden ratio, which is an irrational number and also named as the Greek letter Phi (φ), is defined as the ratio be- Received 13 July 2016 tween two lines of unequal length, where the ratio of the lengths of the shorter to the longer is the same as the Accepted 7 August 2016 ratio between the lengths of the longer and the sum of the lengths. The so-called formula is a mathematical ratio Available online 10 August 2016 and there exist a variety of examples in natural and man-made structures of great beauty. Moreover, golden ratio is expressed throughout the human body in some ways, including digits, uterus, teeth, and cardiovascular sys- Keywords: tem. Although the association of Fibonacci series or golden ratio with systems and organs of human being has Golden ratio Fibonacci series not been assessed in depth yet, the mainstream regulation of cardiovascular system seems to be associated Heart with golden ratio. This raises the idea that there might have been a fine and subtle regulator in our body. In Cardiovascular system this article, we aimed to elaborate the relationship between the existence of golden ratio and the human body and to discuss the golden ratio and its association with cardiovascular system. © 2016 Elsevier Ireland Ltd. All rights reserved. 1. Introduction The golden ratio is also related with geometric shapes like triangles, rectangles and pentagrams, to the equiangular spiral and these golden The mathematician who lived in the thirteenth century, Leonardo of geometric shapes have the feature that the ratio between the lengths Pisa, nicknamed “Fibonacci” described a number series which was later of their sides is the golden ratio. Golden section governs the hole field named after him. The sequence follows 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, of pentagonal geometry which conforms to the golden section in its all etc. and it is easy to follow. It suggests that for the integer sequence limbs. It plays an essential role in the construction of the pentagon starting with 0 or 1, the sequential number is the sum of the two previ- and five-fold symmetry and is used extensively in ancient and modern ous numbers. This ratio has also been described by Euclid as an extreme architecture, painting and music. Long before then Leonardo Pisa, gold- and mean ratio. When a straight line (AC) is divided into two sections by en ratio was used in monumental architecture of Egypt and elsewhere such a point B, the smaller section of the line (BC) is related to the larger in the ancient world [5–8]. section of the line (AB) in the same ratio as the larger section is related to the whole line (AC) (Fig. 1). In principle, golden proportion is an ob- 2. Golden ratio and the human body servation that the ratio of any two sequential Fibonacci numbers ap- proximates to the value of 1.618 which is named as the Greek letter Although modern science has reduced the concept of human being Phi (φ). The larger the consecutive numbers in the sequence, the more to molecular level, there seems to be lacking bricks and it is insufficient precise the approximation of 1.618. This ratio, which is named as the to understand human condition in health and illness. Tremendous ad- golden ratio or golden number has been discussed as for its apparent vances have been achieved in anatomy, physiology, biology, molecular aesthetic pleasure [1,2]. Artists, scientists and biologists with a notion biology by modern medicine in recent decades. However evidences of of philosophy have become entranced by the golden section and many other subtle regulations also exist in our living or non-living environ- different ways in which it determines the form and patterns in every ment and human body as well. If we start from the anatomy and beauty manifestation of life. Occurrence of Fibonacci numbers in the spiral which have been investigated for many years, it might have subtle arrangement of leaves around a plant's stem (called phyllotaxis) is concerns. Golden ratio or Fibonacci sequences occur in human body one of the main interests of scientists [3]. Fibonacci series have also as in every manifestation of life. The superimposed human hand ap- been used in the modelling of biological and financial systems as well proximates to the golden spiral which resembles golden rectangle [9]. as in electronics and music [4]. Additionally, phalangeal lengths of the digits indicate the Fibonacci values [10]. Such an observation can be seen in the human ear which approximates to the dimensions of the golden spiral [11]. ⁎ Corresponding author. The investigations about facial beauty mostly depend on mouth and E-mail addresses: [email protected], [email protected] (E. Yetkin). teeth which are the main features of the human face and the starting http://dx.doi.org/10.1016/j.ijcard.2016.08.147 0167-5273/© 2016 Elsevier Ireland Ltd. All rights reserved. 144 S. Ozturk et al. / International Journal of Cardiology 223 (2016) 143–145 nearly at the predicted distance [20]. This is the first study in the liter- ature demonstrating the presence of the Fibonacci Cascade in the dis- tribution of the culprit lesions in coronary arteries. The existence of this ratio may be related to the location of the branches in the coronary anatomy. In terms of beauty in nature, minimization of wasted space and the need for energy, golden ratio seems to be an important player for the regulation of harmony in our universe. We can state that there is a propensity for this ratio to appear in the nature because this ratio provides minimizing of the wasted space and the need for energy and nutrients is optimized. We cannot associate such a sequence to the coro- nary tree directly because of the complexity of the coronary anatomy but if the Fibonacci sequence is essential for the branch location, then we can speculate that this relation may optimize the branching pattern of the vessels. Thus, coronary tree maximizes myocardial perfusion like plant leaves and seed heads. Likewise, Ashrafian and his friends hypothesized that the structure of the coronary arterial branching system is analogous to the leaf branching seen in trees as described above. They studied data from 36 mammalian Fig. 1. Schematic view of cardiac stimulation (a); systolic blood pressure (SBP), diastolic species [21] and found that the association of cardiac diameters by the blood pressure (DBP) (b); and contraction diameters of left ventricle (c); AC/AB = sum of the diameters of all 13 branches is in the order of the golden AB/BC = 1618. ratio. They suggest that Fibonacci number series can be used to develop a bio-mathematical model of the coronary arterial system. Thus, we can point of these studies is the rule of golden proportions. Rickets investi- demonstrate myocardial metabolic maps and predict disease location gated the aesthetic smile and its relationship with golden ratio and and geometry. Also, this model can be used in the development of car- Fibonacci sequence in 1982. He applied the use of golden proportions diac radionuclide or magnetic resonance imaging techniques [22]. in the treatment of patients [6,12,13]. Elliot and his friends investigated The diameters of cardiac chambers have been evaluated by means the relationship between the aesthetic preference and the golden ratio. of transverse and vertical cardiac chamber measurements in each par- In their study, they found that golden sectioning affects the efficiency of ticipant of Swedish and Chinese population. Although the diameter of visual processing [14]. Golden ratio has also been investigated by Chinese population is found to be lower than that of Swedish popula- gynaecologists to document normal measurements and proportions of tion, golden proportions have been maintained in both population at the non-pregnant uterus according to age and gravity. They found that 1618. Additionally, significant deviation of vertical to transvers diame- at the age of peak fertility, the uterus measurements were equal to the ters ratio as 1,4 and increased mortality have been demonstrated in golden ratio [15]. end stage heart failure patients [23]. When the heart's contractile The relationship between Fibonacci sequence, fractals and human force and myocardial wall thickness reduce, the heart's shape becomes genome was first studied in 1982 by Benoit Mandelbot. He supposed dilated and spherical [24,25]. This remodelling process results in impair- that the structure of DNA and its organization pattern is fractal.