Physics of the Ventricular Vortex in Dilated Cardiomyopathy Volume 3 - Issue 3

Trainini Jorge MD, PhD*¹,Lowenstein Jorge MD², Beraudo Mario MD³, Wernicke Mario MD⁴, Jesús Valle, PhD⁵, Lowenstein-Haber Diego MD², Labrada Luis MD⁶, Trainini Alejandro MD^1,3 and Bastarrica María Elena MD³

• ¹Department of Cardiac Surgery, Hospital Presidente Perón, Buenos Aires, Argentina.
• ²Department of Cardiology, Investigaciones Médicas, Buenos Aires, Argentina.
• ³Department of Cardiac Surgery, Clínica Güemes , Luján , Buenos Aires, Argentina.
• ⁴Department of Pathology, Clínica Güemes , Luján , Buenos Aires, Argentina.
• ⁵National Institute for Aerospace Technology - General Subdirectorate for Naval Systems, Madrid, España.
• ⁶Deparment of Cardiology, Clínica Havanamed. Medellín, Colombia

Received:April 08, 2021;   Published: April 20, 2021

Corresponding author: Trainini Jorge MD, PhD, Department of Cardiac Surgery, Hospital Presidente Perón, Buenos Aires, Argentina

DOI: 10.32474/ACR.2021.03.000165

 

Abstract PDF

Abstract

The role of the vortex in cardiac remodeling should be understood as an etiopathogenic factor in the myocardial wall with its consequent dilation and not as a cause of this wall’s alteration. It is not necessary to consider the random molecular behavior in the intraventricular vortex as maximum unpredictability. Randomness becomes uniformity. For example, in a balloon, particles move in all directions but exert the same pressure. This is analogous to the left ventricle: molecules collide against each other as a dense and anarchic crowd. A fluid applies pressure on the surface with which it makes contact, but if the chaotic elements become ordered, we have regularity. A milliliter of blood contains around one hundred trillion particles. It is impossible to combine their equations. Probability in statistics was used to find regularity in global and average behavior. The random state of molecular chaos (turbulence) that occurs in the intraventricular vortex alters the wall. Remodeling leading to volume overload starts when 20% of the ventricular mass is compromised. With increased volume there is more sphericity and vice versa. Thus, fluid becomes a sculptor of the ventricular wall through the velocity of fluid particles colliding against its walls.

Keywords: Intraventricular vortex; Dilated cardiomyopathy; Myocardial torsion

Ventricular Vortex

The blood vortex generated in the left ventricle resulting in systolic ejection can be explained through the theory of “dissipative structures”, developed by Ilya Prigogine[1]. The helical anatomy of the heart and the ensuing torsion arising from this structure determine the intraventricular vortex (Figures 1 to 3).[2,3] The ejected blood flow is derived from a source of instability. It occurs through the coexistence of structure (ventricular chamber) and function (ejection). This trinomial of structure, function and flow implies a feedback system in which flow is subjected to continuous fluctuations leading to the reorganization of the system. What happens with the origin and progression of the intraventricular vortex? The helical arrangement of the myocardium leads in its function to an opposite rotation between the apex and the base of the heart, a situation that allows ventricular twisting (systolic contraction) and untwisting (ventricular suction) (Figure 3).[4,5] The anatomical basis is determined by the arrangement of the descending and ascending segments, which rotate in opposite directions allowing ventricular twisting-untwisting. This divergent direction in the apical and base rotation produces ventricular blood content instability and the development of a vortex, a consequence arising from the need of the myocardial mass to generate the necessary force to pump blood throughout the whole system. Ventricular torsion is a functional requirement that correlates with the image in 8 adopted by the myocardium.

The “dissipative structures” theory is based on the concept of the physicist Henri Bénard (1874-1939), which describes the instability of a stationary system leading to its auto-organization. In this experiment, a thin fluid layer is submitted to a thermal difference between the heated inferior layer and the superior layer in contact with the environment. The instability is produced by a vertical temperature gradient in the horizontal fluid layer. The inferior layer attains a higher temperature than the superior one, producing an upward heat flow. For small gradients, heat diffuses by conduction, but if it reaches a critical value, there is convection. Upon achieving an adequate temperature threshold, the resting state of the fluid becomes unstable: there is convection, that is, the coherent movement of an enormous amount of molecules. The threshold is thus the critical value from which the system becomes unstable, producing fluctuations. If these go beyond the stability threshold, the system is transformed leading to its autoorganization, with the emergence of a qualitatively different mode of function.
Hydrodynamics, due to turbulence, constitutes a good example of Bénard’s instability. When convection appears in inestability it leads to the spatial auto-organization of the system. If the system is observed vertically (at its output), a regular hexagonal arrangement is seen, similar to the cells of a beehive. These fluctuations lead to an order, produced by non-equilibrium.

Blood flows from the left ventricle towards the aorta forming a vortex that presents two established shapes: spiral and funnel. Ventricular torsion produces this turbulence because of the different speed at both sides of its surface (Figure 4). The anatomical arrangement (structure) described by the myocardial band theory and the resulting function contributes to its development. This is echocardiographically supported by the presence of greater radial strain at the basal and medial levels of the left ventricle due to the prevalence of transverse fibers, while oblique fibers towards the apex are responsible of greater longitudinal and circumferential strain with a clear predominance of apical rotation. This opposing motion from the base to the apex gives origin to systolic torsion [6-8].
As a result, blood increases its speed as it gets near the aortic output orifice. At first, flow tends to be uniform, but does not preserve this condition due to the irregularities present in the ventricular chamber and in blood motion. This situation triggers an afference difference in the rotational spiral motion of blood flow, increasing radial as well as rotational speed as the vortex diameter decreases. Blood moves with a helical motion, describing a pipe of narrowing flow lines, called vortex. The pipe of this vortex is constrained by the blood that applies pressure on all its circumference This decreases its radius and increases rotation, thus developing instability in the initial uniform flow.
Ventricular muscle pressure and blood pressure and the progressively reduced radius combine to accelerate the helical motion of blood with the concomitant increase in velocity. Eventually, a miniature eddy is formed (Figure 5), generating linear and non-linear structures. The forces acting to shape the vortex feed back unto themselves allowing it to act as a unit. In this instability, there is rupture in the spatial symmetry of the vortex leading from chaos to coherence. The trapped molecules in this vortex are no longer independent of one another. Figures 6 and 7 show the change of the non-linear chaos, forming the blood vortex, to a linear orderliness of blood flow at the aortic output [9]. This linear aortic flow implies a reorganization throughout the non-linearity of the intraventricular vortex. The system’s turbulence leads it into a new state. It is an organizer. The price is a permanent creation of chaos.

In Bénard’s vortices there is a temporal symmetry rupture. The molecules abandon the incoherent motion they had to adopt coherence. There are new states far from equilibrium. Independently of gaseous, liquid or crystalline equilibrium states, they all respond to an essential trait that differentiates them from the non-equilibrium states described in vortices or turbulences.
Vorticity appears when there is a relative rotation of some particles of the fluid with respect to others. The dynamics established by ventricular torsion, due to the crossover of the descending and ascending segment, causes the intraventricular fluid to adopt the characteristics of a vortex with turbulent flow that tends to linearity when it is ejected. Laminar flow is irrotational, this means that there cannot be vorticity. Why is there an intraventricular turbulent flow which we call vortex? Turbulence modifies parameters such as resistance to friction, heat transmission and mixing ability. Maybe the answer is to homogenize the blood to be distributed throughout the body, but it should also be acknowledged that this turbulence is the result of the ventricular torsion necessary to eject the fluid at high velocity.
In the ventricle, there can be no laminar flow, as the flow velocity is high and the chamber diameter is not small, a situation that invalidates parallel currents, called laminar movements. As the fluid is disturbed by ventricular torsion, a turbulent motion is established. The characteristic of this flow is its irregular, dissipative nature. If no energy is delivered, turbulence declines and this is what happens with the energetic slope during the ejective period, between the more active and less active phases of the cardiac cycle.
These turbulent motions are always rotational and threedimensional. There are no two-dimensional flows. Turbulence is not a property of fluid but of flow and is produced by ventricular torsion. Small perturbations make flow unstable. Infinitesimal perturbations grow spontaneously. The process of vortex development is produced due to the radical change in speed as a result of ventricular torsion. This torsion not only has the effect of generating enough energy but also of avoiding the blood content from affixing in peripheral ventricular locations by thoroughly washing its walls with the vortex.
Turbulence is determined by a maze of eddies which are drawn by gradients of velocity and by the interaction with other eddies. This process of division continues until the scale of eddies is so small that, with logically low Reynolds numbers, they prevent the persistence of instability. To determine the regime in which a fluid is, in internal flows, the Reynolds number is used, (Re) which is a dimensionless number (without physical dimensions) that takes into account the speed of the fluid, the local diameter of the geometry, dynamic viscosity and fluid density: whenever Re <2300 the flow will be laminar, if Re> 4000 the flow will be turbulent, and between 2300 and 4000 the flow is transitional.

Molecular Chaos

Blood is a Brownian, non-Newtonian fluid; therefore, it is not homogeneous and subject to molecular chaos. Leucippus, in 440 BCE, introduced a word whose meaning implied “that it cannot be cut”. He thus inaugurated the concept of atom. Democritus (V-IV BCE) progressed in its study, leading to the existence of vacuum, denied by Anaxagoras (500-428 BCE) and defended by Epicurus (341-270 BCE). It was necessary to wait untilLucretius (95-55 BCE) to renew its interest, but the microscopic movement was only developed by Daniel Bernoulli (1700-1782) in 1738 when he sustained that gases were composed of small particles (a theory extended to fluids). In view of the possibility that the whole universe was composed of moving and colliding atoms, Pierre- Simon Laplace (1749-1827), established a determinist concept: “[For a superior intelligence]… the future, as well as the past, would be present before its eyes”.
The challenge was to extend this idea to mechanics, which was inaugurated by Nicholas Léonard Sadi Carnot (1796-1832), when he tried to optimize the efficiency of steam engines. In 1824 he established the efficiency of fuel in steam engines, laying the foundation of thermodynamics. Heat had to flow from a hot to a cold body. Benjamin Thompson (1753-1814) gave an essential step in heat compression by stating that this was produced by the random movement of atoms (Figure 8).

Rudolph Clausius (1822-1888) is a fundamental figure. He confirmed that heat goes from a hot to a cold body and progresses in a direction where, if processes are irreversible, time is an arrow. He developed the concept of the second law of thermodynamics called entropy, which comes from the Greek word “trope” and means evolution or transformation. Entropy measures the amount of molecular disorder in a system. Clausius also established the basis of the kinetic theory of gases. In 1854, Hermann von Helmholtz (1821-1894) explained the end of this dissipation of heat in the universe until reaching thermal death.
James Clerk Maxwell (1831-1879) introduced probability. He postulated that a distribution function is the practical characterization of a huge set of molecules. It was more logical to ask oneself how many particles are in a certain range of velocities than looking at each particle individually. He established that what is important is not the trajectory of each particle but their mean behavior. Fluids should be considered a collection of molecules with random behavior, colliding between them and against the walls of the receptacle (Figure 8). Pressure is no more than the effect of collisions between molecules and the walls of the container. Temperature is a measure of the energy of particles and the average kinetic energy behaves the same as temperature. The greater the turbulence, the greater the velocity of collision with temperature increase. The state of the system is given by the number of molecules and their energy charges.
The concept of Brownian motion belongs to Robert Brown (1773-1858), who observed the frenzied dance of pollen grains in water. Albert Einstein (1879-1955) explained this diffusion which was later corroborated by him and Jean Perrin (1870-1942). Thermodynamics was developed since the Industrial Revolution. Almost at the same time, Ludwig Boltzmann (1844-1906) was born, who applied probability to physics. He thus considered that thermodynamics was reduced to the complementarity between mechanics and probability. He supported this concept with the atomic theory, assuming that due to the reduced size and great number of atoms, the way of understanding a set of particles was through statistics. Boltzmann devoted all his life to explain the second law of thermodynamics in mechanical terms. He associated entropy with probability. The greater the probability, the higher the entropy. In 1866 he published “The mechanical significance of the second law of thermodynamics” and in 1872 “New studies on the thermal equilibrium of gas molecules”. He based his study in the law of the atomic theory and used Daniel Bernoulli’s kinetic theory of gases, who had declared that fluids were aggregates of particles in constant motion.

Consequence of Vortex in Dilated Cardiomyopathy

Diagnosis and treatment of heart failure is limited by the difficult acquisition of noninvasive quantitative indices of cardiac physiology. The study of velocity vectors, movable geometry, pressure-volume loops, left ventricular elastic wall stress-strain relationships, the importance of the vortex and its role as mechanical energy storage, together with the dependence of its properties, can provide accurate information for therapeutic decision-making, follow-up and prognosis [10].
Intraventricular blood fluid (molecular chaos) models the preservation of dilated cardiomyopathy though the vortex, which is the result of myocardial torsion. It must be understood that for the elastic walls of a container such as the myocardium, blood fluid in the ventricular chamber behaves in the vortex mechanism as a chaotic molecular state, perpetuating remodeling [11]. This process is due to the continuous collision of particles and their constant change of direction. The simulation of biological processes is an unexplored field with a limited number of devices that have started to develop computational simulation models almost always directed to a virtual visualization concept and lacking an adequate scientific model of fluid behavior.
It is not known how to model blood from a dynamic-fluid perspective. Blood is a much more complex fluid than any other homogeneous liquid. It is defined as a non-Newtonian fluid, whose viscosity changes with the gradient of tension applied to it, and whose frictional shear stresses are directly proportional to the velocity gradient. As a result, different from a Newtonian fluid, a non- Newtonian fluid does not have a constant defined viscosity. It is also necessary to couple fluid simulation to an elastic deformable system such as arteries and the heart. Studies carried out so far provided stiff geometries, so it is necessary to integrate fluid mechanics with elastic or deformable structures. Imaging techniques supply sufficient information for therapeutic decision-making. However, there are groups of patients with inadequate indication provided by these techniques to make therapeutic decisions based on scientific evidence. As examples we can mention patients with small diameter aneurysms but at risk of rupture or those with heart failure and preserved ejection fraction. The diagnosis can be enhanced with the development of simulation systems able to study intraventricular flow velocities and characteristics, pressure differences and quantitative myocardial contractility and distensibility indices. The characterization of these indices will deliver the necessary information for precise therapeutic decisionmaking, predict the behavior of a specific repair and assess the riskbenefits of a surgical intervention.
In fact, the role of the vortex in cardiac remodeling should be understood as an etiopathogenic factor in the myocardial wall with its consequent dilation and not as a cause of this wall’s alteration. It is not necessary to consider the random molecular behavior in the intraventricular vortex as maximum unpredictability. Randomness becomes uniformity. For example, in a balloon, particles move in all directions but exert the same pressure. This is analogous to the left ventricle: molecules collide against each other as a dense and anarchic crowd. A fluid applies pressure on the surface with which it makes contact, but if the chaotic elements become ordered, we have regularity. A milliliter of blood contains around one hundred trillion particles. It is impossible to combine their equations. Probability in statistics was used to find regularity in global and average behavior. The random state of molecular chaos (turbulence) that occurs in the intraventricular vortex alters the wall. Remodeling leading to volume overload starts when 20% of the ventricular mass is compromised. With increased volume there is more sphericity and vice versa. Thus, fluid becomes a sculptor of the ventricular wall through the velocity of fluid particles colliding against its walls.

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