Will the real ventricular architecture please stand up?

Ventricular twisting, essential for cardiac function, is attributed to the contraction of myocardial helical fibers. The exact relationship between ventricular anatomy and function remains to be determined, but one commonly used explanatory model is the helical ventricular myocardial band (HVMB) model of Torrent-Guasp. This model has been successful in explaining many aspects of ventricular function, (Torrent-Guasp et al. Eur. J. Cardiothorac. Surg., 25, 376, 2004; Buckberg et al. Eur. J. Cardiothorac. Surg., 47, 587, 2015; Buckberg et al. Eur. J. Cardiothorac. Surg. 47, 778, 2015) but the model ignores important aspects of ventricular anatomy and should probably be replaced. The purpose of this review is to compare the HVMB model with a different model (nested layers). A complication when interpreting experimental observations that relate anatomy to function is that, in the myocardium, shortening does not always imply activation and lengthening does not always imply inactivation

Nonaxisymmetric mathematical model of the cardiac left ventricle anatomy

We describe a mathematical model of the shape and fibre direction field of the cardiac left ventricle. The ventricle is composed of surfaces which model myocardial sheets. On each surface, we construct a set of curves corresponding to myocardial fibres. Tangents to these curves form the myofibres direction field. The fibres are made as images of semicircle chords parallel to its diameter. To specify the left ventricle shape, we use a special coordinate system where the left ventricle boundaries are coordinate surfaces. We propose an analytic mapping from the semicircle to the special coordinate system. The model is correlated with Torrent-Guasp’s concept of the unique muscular band and with Pettigrew’s idea of nested surfaces. Subsequently, two models of concrete normal canine and human left ventricles are constructed based on experimental Diffusion Tensor Magnetic Resonance Imaging data. The input data for the models is only the left ventricle shape. In a local coordinate system connected with the left ventricle meridional section, we calculate two fibre inclination angles, i.e. true fibre angle and helix angle. We obtained the angles found from the Diffusion Tensor Magnetic Resonance Imaging data and compared them with the model angles. We give the angle plots and show that the model adequately reproduces the fibre architecture in the majority of the left ventricle wall. Based on the mathematical model proposed, one can construct a numerical mesh that makes it possible to solve electrophysiological and mechanical left ventricle activity problems in norm and pathology. In the special coordinate system mentioned, the numerical scheme is written in a rectangular area and the boundary conditions can simply be written. By changing the model parameters, one can set a general or regional ventricular wall thickening or the left ventricle shape change, which is typical for certain cardiac pathologies

Generalized minimal principle for rotor filaments

To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G = det(D)D-1. The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes

Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity

It has become widely accepted that the most dangerous cardiac arrhythmias are due to re- entrant waves, i.e., electrical wave(s) that re-circulate repeatedly throughout the tissue at a higher frequency than the waves produced by the heart's natural pacemaker (sinoatrial node). However, the complicated structure of cardiac tissue, as well as the complex ionic currents in the cell, has made it extremely difficult to pinpoint the detailed mechanisms of these life-threatening reentrant arrhythmias. A simplified ionic model of the cardiac action potential (AP), which can be fitted to a wide variety of experimentally and numerically obtained mesoscopic characteristics of cardiac tissue such as AP shape and restitution of AP duration and conduction velocity, is used to explain many different mechanisms of spiral wave breakup which in principle can occur in cardiac tissue. Some, but not all, of these mechanisms have been observed before using other models; therefore, the purpose of this paper is to demonstrate them using just one framework model and to explain the different parameter regimes or physiological properties necessary for each mechanism (such as high or low excitability, corresponding to normal or ischemic tissue, spiral tip trajectory types, and tissue structures such as rotational anisotropy and periodic boundary conditions). Each mechanism is compared with data from other ionic models or experiments to illustrate that they are not model-specific phenomena. The fact that many different breakup mechanisms exist has important implications for antiarrhythmic drug design and for comparisons of fibrillation experiments using different species, electromechanical uncoupling drugs, and initiation protocols.Comment: 128 pages, 42 figures (29 color, 13 b&w

A Triple Protostar System Formed via Fragmentation of a Gravitationally Unstable Disk

Binary and multiple star systems are a frequent outcome of the star formation process, and as a result, almost half of all sun-like stars have at least one companion star. Theoretical studies indicate that there are two main pathways that can operate concurrently to form binary/multiple star systems: large scale fragmentation of turbulent gas cores and filaments or smaller scale fragmentation of a massive protostellar disk due to gravitational instability. Observational evidence for turbulent fragmentation on scales of $>$1000~AU has recently emerged. Previous evidence for disk fragmentation was limited to inferences based on the separations of more-evolved pre-main sequence and protostellar multiple systems. The triple protostar system L1448 IRS3B is an ideal candidate to search for evidence of disk fragmentation. L1448 IRS3B is in an early phase of the star formation process, likely less than 150,000 years in age, and all protostars in the system are separated by $<$200~AU. Here we report observations of dust and molecular gas emission that reveal a disk with spiral structure surrounding the three protostars. Two protostars near the center of the disk are separated by 61 AU, and a tertiary protostar is coincident with a spiral arm in the outer disk at a 183 AU separation. The inferred mass of the central pair of protostellar objects is $\sim$1 M$_{sun}$, while the disk surrounding the three protostars has a total mass of $\sim$0.30 M_{\sun}. The tertiary protostar itself has a minimum mass of $\sim$0.085 M$_{sun}$. We demonstrate that the disk around L1448 IRS3B appears susceptible to disk fragmentation at radii between 150~AU and 320~AU, overlapping with the location of the tertiary protostar. This is consistent with models for a protostellar disk that has recently undergone gravitational instability, spawning one or two companion stars.Comment: Published in Nature on Oct. 27th. 24 pages, 8 figure

Orbital Angular Momentum Waves: Generation, Detection and Emerging Applications

Orbital angular momentum (OAM) has aroused a widespread interest in many fields, especially in telecommunications due to its potential for unleashing new capacity in the severely congested spectrum of commercial communication systems. Beams carrying OAM have a helical phase front and a field strength with a singularity along the axial center, which can be used for information transmission, imaging and particle manipulation. The number of orthogonal OAM modes in a single beam is theoretically infinite and each mode is an element of a complete orthogonal basis that can be employed for multiplexing different signals, thus greatly improving the spectrum efficiency. In this paper, we comprehensively summarize and compare the methods for generation and detection of optical OAM, radio OAM and acoustic OAM. Then, we represent the applications and technical challenges of OAM in communications, including free-space optical communications, optical fiber communications, radio communications and acoustic communications. To complete our survey, we also discuss the state of art of particle manipulation and target imaging with OAM beams