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The human heart: Application of the golden ratio and angle. Michael Y. Henein and the Golden Ratio Collaborators: Ying Zhao, Rachel Nicoll , Lin Sun,Ashraf W. Khir , Karl Franklin, Per Lindqvist. Reporter:Shu-Hsiu,Yu Date: 2012/06/19. Volume 150, Issue 3, 4 August 2011, Pages 239–242.
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Michael Y. Henein and the Golden Ratio Collaborators: Ying Zhao, Rachel Nicoll, Lin Sun,Ashraf W. Khir, Karl Franklin, Per Lindqvist
Volume 150, Issue 3, 4 August 2011, Pages 239–242
It is expressed as an irrational mathematical constant phi (φ) of approximately1.618.
Allied to this is the golden angle, calculated by sectioning the circumference of a circle (c) into two arcs, such that the ratio of the length of the larger arc (a) to the length of the smaller arc (b) is the same as the ratio of the full circumference to the length of the larger arc (i.e. c/a = a/b).
The golden angle is the angle subtended by the smaller arc (b) and measures 137.5°. The golden ratio decimal (0.618) equates to an angle of 222.5°, the reverse of the golden angle, with the sum adding up to 360°.
Authors hypothesised that since the golden ratio and angle are so deeply rooted in nature, they must have some correspondence in the healthy heart structure and function.
Authors found that Chinese left ventricle dimensions were smaller by 8 ± 1 mm and 5 ± 0.5 mm, compared to Swedes but the golden ratio was maintained at approximately 1.618.
However, in end-stage heart failure, the left ventricular ratio was significantly reduced (p < 0.01) and this distorted the cardiac ratio to around 1.4 (p < 0.005), consistent with pathological remodeling resulting in a more spherical shape to the heart.
Consequently, it appears that as long as the cardiac ratio is maintained at approximately 1.618, survival is likely but a significant deviation from the golden ratio is associated with a poor outcome.
Authors have also previously demonstrated that the golden ratio is seen in normal foetal myocardial function development, where the heart muscle diastolic function matures at a rate of 1.6 mm/s per week between 20 and 40 weeks of age, while a healthy adult heart muscle loses velocity of 1.6 cm/s each decade between age 20 and 80 years, indicating a close relationship between ageing and ventricular myocardial function.
Finally, others have shown that the end product of normal cardiac function, the blood pressure ratio of 120/80 mmHg, also approximates to the golden ratio of 1.618 and carries significant prognostic value.
Additionally, myocardial muscle fibre orientation takes a helical shape, with the coils of each segment of the apical loop being of different lengths and having a harmonic proportion which conforms to the golden ratio.
This angle increased significantly to 160 ± 4° (p > 0.001) in right heart failure patients, as the right ventricle became cylindrical and lost its native shape, reducing the inflow-outflow tract angle to approximately 20° from 43° (unpublished).
Hence it can be seen that the complex anatomy of the right ventricle, as well as its myocardial fibre architecture, support the unique role of this angle in preserving the peristaltic circulation inside the right ventricle.
Normal systolic pressure in the aorta is almost six times that in the pulmonary artery, hence the need for a pressure recovery space between the two arteries to avoid pressure transmission across their thin walls. In hypertension, the pressure difference between the aorta and the pulmonary artery could increase to 10 times the norm.
In addition to these two great arteries, the same angle seems to be adopted by the central and peripheral arterial tree; early anatomical studies demonstrated the branching pattern of the coronary and peripheral arteries to be compatible with the golden angle.
Application of these ratios and angles in our daily clinical practice may lead to development of simple and reliable markers of early deviation from normality, which could be treated before irreversible alteration in cardiac structure and function develops.