Cardiologists and a musician join to discuss similarities between the non-linear arrangement of micro- and macro-cosmos phenomena, and their relation to philosophy (Pythagoras, Fibonacci), art, music (J.S. Bach and others), and analogies to the functional anatomy of cardiomyocytes
One of the oldest and most analytic mathematical approximations of nature has been presented in Plato’s dialogue Timaeus. Interestingly, the dialogue takes place the day after Socrates described his ideal state. It has been suggested that Timaeus was influenced by a book written by a Pythagorean philosopher Philolaus. In this work, Plato believes that cosmic harmony is based on formulas (archetypes) that are being used as construction models of everything.
A great philosophical similarity with this approach can be found in Johannes Kepler’s astronomical work. Kepler believed that since everything was designed by an intelligent creator, the laws of the universe had to follow some sort of logical pattern.1
Causality in micro- and macro-cosmos’ phenomena is almost impossible to be predicted by traditional mathematical models. Gas kinetics, epidemics, brain function instabilities, and even arrhythmias may only be predicted with the help of statistics. Thus, alternative endeavours to explain non-linear expressions in nature released new scientific terms and definitions, such as ‘self-similarity’, ‘fractals’, and ‘strange attractors’.
Helix is one of the ubiquitous manifestations in nature. The myocardial architecture has been described as having a helical fibre arrangement that is energetically efficient and necessary for uniform redistribution of stresses and strain in the heart.2 This muscle configuration was first recognized in 1660 by Lower,3 who compared the physiology of heart muscle contraction with squeezing the water out of a wet towel. Analogies of this non-linear architecture can be documented in DNA, fingerprints, shells, and galaxies.
An analytic description of helicoid configuration, called the Fibonacci sequence, was named after the Italian mathematician Leonardo of Pisa, later known as Fibonacci. He introduced the sequence in Western European mathematics, although the sequence was heralded by Pythagoras golden ratio (600 BC) and in Indian Sanskrit poetry (200 BC) (Figure 1).
Fibonacci sequence. Each number is the sum of the two preceding ones.
Art and Science
Many artists (painters, architects, composers) used mathematical series, such as spiral models and the golden ratio in an attempt to approximate the proportions of beauty. Numerous buildings and artworks incorporate the golden ratio. Great representatives are the monument of Parthenon (447 BC), and Mona Lisa (1519), one of the most famous paintings of Leonardo da Vinci. In music, several composers across centuries from the renaissance to the contemporary era included in their music mathematics based on Fibonacci, spiral, or more advanced archetypes.
Johann Sebastian Bach (1685–1750) in one of his latest compositions, ‘Musical Offering’, provides a clear relationship between his mental inventiveness intuition and natural complexity. The composer used the Möbius strip to develop the symmetry of this innovative musical piece. An example of a Möbius strip is the shape you get when you take a strip of paper, give it a twist, and then glue the ends together (Figure 2).
Möbius strip.
The score uses a glide reflection symmetry that means when you shift it along and then flip it, it looks the same, and if you shift it the same direction and flip it again, you will reach the beginning.
The avant-garde composer Iannis Xenakis (1922–2001) inserts many mathematical models into his music (set theory, game theory, stochastic processes, and Fibonacci numbers). He also pointed out affinities between music, architecture, mathematics, and physics, and he was also influencer to the development of electronic and computer music. In his work, Pithoprakta (1956) used the Maxwell Boltzmann distribution corresponding to music parameters. In physics, this distribution describes particle speeds in ideal gases, where the particles move freely inside a stationary container without interacting with one another. In this work, spiral geometry also appears by tone pitches oscillation (Figure 3).
Pithoprakta. Part of graphic score.
The contemporary Hungarian composer Bela Bartok (1881–1945) was also influenced by the golden ratio and the Fibonacci numbers when he composed the first movement of his masterpiece, music for strings, celesta, and percussions. In the rhythmic progress of the melodic theme, meticulous analysis can decipher an accurate Fibonacci sequence (Figure 4).
Music for strings, celesta, and percussions. Part of graphic score.
Helical cardiac imaging
The described concepts work similarly in life. Focusing on heart physiology, the myocardium twists in systole to assist ejection and reciprocally untwists in early diastole to promote filling. This complex motion is produced by the shortening and lengthening of the helically oriented myocardial fibres. The sequence can be observed in the operating room. Advances in modern imaging modalities have improved our understanding of myocardial architecture and the contribution of helix dynamics to the overall cardiac performance in the clinical setting.
New terms and definitions such as rotation, twist, torsion, and propagation angle have been described as metrics of myofibre curvature and helical function, complementing the conventional parameters both in research and in clinical practice.2,4
Cardiac magnetic resonance (CMR), with its precise tissue tagging, is the gold standard imaging technique to assess twisting physiology. The new technique of diffusion tensor CMR (DT-CMR) is based on water diffusion in the intramyocellular space, as well as the intra- and extravascular space.
This innovative imaging method reflects all three compartments along with the microstructure of the heart. Several relevant indices can be derived from DT-CMR, including mean diffusivity, fractional anisotropy, myofibre helix angle, and myofibre sheet angle, providing an improved non-invasive in vivo recognition of myocardial histology, fibre orientation, and torsional dynamics4,5 (Figure 5).
Fibre orientation of entire human heart revealed with diffusion tensor cardiac magnetic resonance. Reproduced with permission from Mekkaoui et al.5
Similar to CMR, speckle tracking echocardiography has emerged as an alternative technique to assess the rotational mechanics of the myocardium.2 Three-dimensional (3D) analysis of myocardial helical deformation has been shown to be advantageous because speckles can be tracked in 3D space irrespective of the direction of their motion. Standardization of acquisition and image post-processing and improvements in spatial and temporal resolution of 3D echocardiography are expected to make this assessment more accurate and easier to use in practice.
The assessment of helical function by advanced imaging may have a more prominent role in the evaluation and management of cardiac patients in the future. Torsion may further help in characterizing and phenotyping heart diseases beyond ejection fraction.
Further technical improvements in advanced imaging modalities are expected to open new horizons in measuring the ‘cosmic music’ of the heart and linking this to improved diagnosis and management.
Lina Tonia1, Alexandros Stefanidis2, Nick Mparmpatzas2, and Bogdan A. Popescu3
1Department of Music Science and Art, University of Macedonia, Salonica, Greece; 21st Department of Cardiology, Nikea General Hospital, Piraeus, Greece; and 3Department of Cardiology, University of Medicine and Pharmacy “Carol Davila” - Euroecolab, Emergency Institute for Cardiovascular Diseases “Prof. Dr C. C. Iliescu”, Sos. Fundeni 258, 022328 Bucharest, Romania
Conflict of interest: none declared.
References
References are available as supplementary material at European Heart Journal online.
