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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

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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

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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. After ment of golden ratio. Recently Yetkin et al. [26] searched whether there this supposition in the early 1990s, it was proven that the human ge- is a relationship between the echocardiographic parameters and golden nome contains fractal behaviour and its organization pattern is related ratio in the healthy subjects. They included one thousand four hundred with Fibonacci series and the golden proportion. In 1991, Perez hypoth- and twelve patients in their study retrospectively, which fulfiltheir esized that gene coding region sequences in the DNA were strongly inclusion criteria. They found that the ratio between the left ventricular related to the golden ratio and Fibonacci series. In 2008, Yamagashi end-diastolic (LVEDd) and end-systolic (LVESd) diameters gives a ratio and his friends discovered that the whole human genome consists of a of 1.614 which is quite close to golden ratio, simulating the Euclid's Fibonacci series [16–19]. Accordingly it appears that golden proportion extreme and mean (Fig. 1c). Besides, they found that the ratio between or golden ratio manifests itself from the innermost structure of human (LVEDd-LVESd) and LVESd is 1.624. They stated in their study that the body, namely DNA to the outermost feature namely beauty, to maintain left ventricular diameters obey the rule of golden ratio [26]. a healthy and aesthetic human body. According to Gardiner et al. [27], the golden ratio is seen in normal foetal myocardium function development. They showed that between 3. Golden ratio and the heart 20 and 40 weeks of age, the heart muscle diastolic function matures 1.6 mm/s per week which is close to golden ratio [27]. Besides this growth The heart as a continuously pumping organ with an amazing harmo- pattern, between the age of 20 and 80, a healthy adult heart muscle ny and synchrony has gained an increasing interest in terms of golden loses velocity of 1.6 cm/s each decade [28]. In the light of these findings ratio. Studies assessing the presence of golden ratio in cardiovascular we can speculate that there is a close relationship between ageing and system mostly depend on the anatomy, physiology, hemodynamic ventricular myocardial function and this is linked with the golden ratio. effects, electrocardiographic and echocardiographic features of the The electrical features of the heart which is represented by electro- heart. Gibson et al. examined the distribution of lesions responsible for cardiography and its relationship with golden ratio have also been in- ST-segment elevation myocardial infarction (STEMI) in their study. vestigated by Yetkin et al. [29]. They included one hundred and sixty They hypothesized that the Fibonacci sequence would be observed two healthy subjects which were gathered from the hospital staff and in the location of coronary artery lesions relative to the length of the their healthy relatives and the electrocardiograms were recorded with epicardial artery. They collected the data from the Thrombolysis In 25 mm/s rate after 15 min of rest at supine position. By defining the sys- Myocardial Infarction (TIMI) 14, 20, 23 and 24 trials, retrospectively. tolic phase interval as the time between the tip of R wave and the end of They calculated the median length of all arteries 15.3 cm and they di- the T wave on electrocardiography, they have calculated the diastolic vided this length by the ratio of 4.236 (2.618 × 1.618 and 2.618/0.618) phase duration/systolic phase duration and R-R/diastolic phase dura- which is identified in Fibonacci Cascade. This calculation yielded a pre- tion for each subject. Subsequently they found the diastole/systole dicted value of 3.62 cm which is 24% of the distance down the artery ratio as 1.611 and R-R interval/diastole ratio as 1.618 which are very from the origin. They calculated that the coronary artery lesion respon- close to golden ratio (Fig. 1a) [29]. The representation of the systolic sible for STEMI from the origin of the artery is 3.78 cm (24.7%) which is and diastolic phases of the heart on the circulating blood and peripheral S. Ozturk et al. / International Journal of Cardiology 223 (2016) 143–145 145 vessels is the blood pressure. It refers to the force applied by circulating References blood on the blood vessels. It is defined as systolic, the peak pressure at [1] R.A. Dunlap, The Golden Ratio and Fibonacci Numbers, World ScientificPublishing, the contraction of the heart; diastolic, the lowest pressure in the arteries Singapore, 1997 Chapter 6. Lucas number and generalized Fibonacci numbers. at the time of rest. After they proved that the beating of the heart is [2] M. Livio, The Golden Ratio, Broadway Books, New York, 2002 1–11. linked with the golden ratio, Yetkin et al. [30] searched whether such [3] I. Adler, D. Barabe, R.V. Jean, A history of the study of phyllotaxis, Ann. Bot. 80 (1997) 231–244. a relationship is observed between the systolic and diastolic pressures [4] T.K. Garland, Charity, Math and Music-harmonious Connections, Dale Seymore of the heart. They planned their study retrospectively and four hundred Publications, White Plains, NY, 1995. and sixty two subjects were enrolled in the study. They included four [5] M. Bashour, An objective system for measuring facial attractiveness, Plast. Reconstr. – hundred and sixty two subjects who underwent ambulatory blood pres- Surg. 118 (3) (2006) 757 774. [6] R.M. Ricketts, Divine proportion in facial esthetics, Clin. Plast. Surg. 9 (4) (1982) sure monitoring in their study. They calculated systolic diastolic blood 401–422. pressure ratio and diastolic to pulse pressure ratio for each patient. [7] M.J. Seghers, J.J. Longacre, G.A. DeStefano, The golden proportion and beauty, Plast. – They defined the pulse pressure, systolic blood pressure minus diastolic Reconstr. Surg. 34 (4) (1964) 382 386. [8] F. Vegter, J.J. Hage, Clinical anthropometry and canons of the face in historical blood pressure. In their study, Yetkin and his friends found that the perspective, Plast. Reconstr. Surg. 106 (5) (2000) 1090–1096. twenty four hour, day time and night time systolic to diastolic and dia- [9] J.W. Littler, On the adaptability of man's hand (with reference to the equiangular stolic to pulse pressures were close to the golden ratio. They also ob- curve), Hand 5 (3) (1973) 187–191. [10] R. Hamilton, R.A. Dunsmuir, Radiographic assessment of the relative lengths of the served that night time proportions gave the closest results to golden bones of the fingers of the human hand, J. Hand. Surg. 27 (6) (2002) 546–548. ratio, however, during day time it was a bit far from the golden ratio [11] S. Marinkovic, P. Stankovic, M. Strbac, I. Tomic, M.S. Cetkovic, Cochlea and other [30]. This study demonstrates the relationship between the arterial spiral forms in nature and art, Am. J. Otolaryngol. 33 (2011) 80–87. [12] R.M. Ricketts, The Golden divider, J. Clin. Orthod. 15 (11) (1981) 752–759. pressure and golden ratio (Fig. 1b). The explanation why night time [13] R.M. Ricketts, The biologic significance of the divine proportion and Fibonacci series, measurements are closest to the golden ratio can be explained by the di- Am. J. Orthod. 81 (1982) 351–370. rect effect of sympathetic and parasympathetic nervous system to the [14] M.A. Elliott, J. Kelly, J. Friedel, J. Brodsky, P. Mulcahy, The golden section as optical limitation, PLoS One 10 (7) (2015), e0131045, http://dx.doi.org/10.1371/journal. heart. At night time, there is a tendency to decrease in blood pressure pone.0131045. and this is associated with reduction of sympathetic nervous system [15] J. Verguts, L. Ameye, T. Bourne, D. Timmerman, Normative data for uterine size ac- activation. Also, during the day time activity, peripheral vascular resis- cording to age and gravidity and possible role of the classical golden ratio, Ultrasound – tance, cardiac output and balance of sympathetic and parasympathetic Obstet. Gynecol. 42 (2013) 713 717. [16] B. Mandelbot, The Fractal Geometry of Nature, WH Freeman and Company, nervous system affect blood pressure variability very much [31,32]. New York, USA, 1982. This situation explains why night time blood pressure ratio measure- [17] J.C. Perez, Chaos, DNA, and neuro-computers: a golden link: the hidden language ments are more closer to golden ratio. One of the most notable concept of genes, global language and order in the human genome, Specul. Sci. Technol. 14 (1991) 336–346. that might be drawn from these studies is that stimulation, contraction [18] M.E. Yamagishi, A.I. Shimabukuro, Nucleotide frequencies in human genome and diameters and pumping pressure of heart obey the rule of Fibonacci se- fibonacci numbers, Bull. Math. Biol. 70 (2008) 643–653. ries or golden proportions. And it seems that this harmony has been [19] D. Persaud-Sharma, J.P. O'Leary, Fibonacci series, golden proportions, and the human biology, Austin J. Surg. 2 (5) (2015) 1066. programmed and regulated by subtle forces or God. Future perspectives [20] C.M. Gibson, W.J. Gibson, S.A. Murphy, et al., Association of the Fibonacci Cascade of golden ratio and relation of golden ratio with divine aesthetics have with the distribution of coronary artery lesions responsible for ST-segment eleva- been reviewed by our group recently [33]. tion myocardial infarction, Am. J. Cardiol. 92 (2003) 595–597. [21] J.W. Thüroff, W. Hort, H. Lichti, Diameter of coronary arteries in 36 species of mam- malian from mouse to giraffe, Basic Res. Cardiol. 79 (1984) 199–206. [22] H. Ashrafian, T. Athanasiou, Fibonacci series and coronary anatomy, Heart Lung Circ. 4. Conclusion 20 (7) (Jul 2011) 483–484. [23] M.Y. Henein, Y. Zhao, R. Nicoll, et al., The human heart: application of the golden ratio and angle, Int. J. Cardiol. 150 (2011) 239–242. What makes golden ratio very interesting is that we really don't [24] C. Mihl, W.R. Dassen, H. Kuipers, Cardiac remodelling: concentric versus eccentric know whether there is an interaction between the spiritual things or hypertrophy in strength and endurance athletes, Neth. Hear. J. 16 (4) (2008) – subtle regulators with our body. In another way, we still lack certain 129 133. [25] G.D. Buckberg, Basic science review: the helix and the heart, J. Thorac. Cardiovasc. proofs in this regard. To understand the beautiful harmony of our Surg. 124 (5) (2002) 863–883. body with spiritual or subtle regulators would help us to understand [26] E. Yetkin, T. Celik, M. Arpaci, M. Ileri, Left ventricular diameters as a reflection of our physiology or pathophysiology with a new aspect and would im- “extreme and mean ratio”, Int. J. Cardiol. 198 (2015) 85–86. [27] H.M. Gardiner, L. Pasquini, J. Wolfenden, et al., Myocardial tissue Doppler and long prove our physiological and physicological wellbeings. Accordingly axis function in the fetal heart, Int. J. Cardiol. 113 (2006) 39–47. golden proportions might inherently yield a variety of diagnostic and [28] M. Henein, P. Lindqvist, D. Francis, S. Morner, A. Waldenstrom, E. Kazzam, Tissue prognostic implications in cardiovascular era with the support of further doppler analysis of age-dependency in diastolic ventricular behaviour and filling: fi a cross-sectional study of healthy hearts (the Umea General Population Heart studies. Explaining this relationship will help us to gure out the regu- Study), Eur. Heart J. 23 (2002) 162–171. larity of universe which is designed by God. An insight into the inner [29] G. Yetkin, N. Sivri, K. Yalta, E. Yetkin, Golden Ratio is beating in our heart, Int. J. realm of human beings by subtle regulators or spirituality would be Cardiol. 168 (2013) 4926–4927. ş able to arrive at a more integrated concept of human well being. [30] E. Yetkin, U. Topba , A. Yanik, G. Yetkin, Does systolic and diastolic blood pressure follow Golden Ratio? Int. J. Cardiol. 176 (3) (2014) 1457–1459. [31] K. Kario, J.E. Schwartz, T.G. Pickering, Ambulatory physical activity as a determinant of diurnal blood pressure variation, Hypertension 34 (1999) 685–691. Conflict of interest [32] G. Mancia, G. Grassi, Mechanisms and clinical implications of blood pressure variability, J. Cardiovasc. Pharmacol. 35 (4) (2000) 15–19. [33] K. Yalta, S. Ozturk, E. Yetkin, Golden Ratio and the heart: review of divine aesthetics, The authors declare no conflict of interest. Int. J. Cardiol. 214 (2016) 107–112.

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