Mathematical model of the anatomy and fibre orientation field of the left ventricle of the heart

Background: One of the main factors affecting propagation of electrical waves and contraction in ventricles of the heart is anisotropy of cardiac tissue. Anisotropy is determined by orientation of myocardial fibres. Determining fibre orientation field and shape of the heart is important for anatomically accurate modelling of electrical and mechanical function of the heart. The aim of this paper is to introduce a theoretical rule-based model for anatomy and fibre orientation of the left ventricle (LV) of the heart and to compare it with experimental data. We suggest explicit analytical formulae that allow us to obtain the left ventricle form and its fibre direction field. The ventricle band concept of cardiac architecture given by Torrent-Guasp is chosen as the model postulate. Methods: In our approach, anisotropy of the heart is derived from some general principles. The LV is considered as a set of identical spiral surfaces, each of which can be produced from the other by rotation around one vertical axis. Each spiral surface is filled with non-intersecting curves which represent myocardial fibres. For model verification, we use experimental data on fibre orientation in human and canine hearts. Results: LV shape and anisotropy are represented by explicit analytical expressions in a curvilinear 3-D coordinate system. The derived fibre orientation field shows good qualitative agreement with experimental data. The model reveals the most thorough quantitative simulation of fibre angles at the LV middle zone. Conclusions: Our analysis shows that the band concept can generate realistic anisotropy of the LV. Our model shows good qualitative agreement between the simulated fibre orientation field and the experimental data on LV anisotropy, and the model can be used for various numerical simulations to study the effects of anisotropy on cardiac excitation and mechanical function

Study of the possibility of increasing the intensity of photochemical processes of riboflavin/UV photocrosslinking of scleral collagen by means of tissue immersion clearing

The possibility of increasing the efficiency of light action during scleral collagen riboflavin/UV photocrosslinking by means of immersion clearing of tissue before UV irradiation is studied. The effectiveness of photo-action is assessed by a decrease in the relative content of the photocrosslinking sensitizer, riboflavin, which is determined from the decay times of tissue fluorescence at different stages of the photocrosslinking process. The fluorescence decay times are measured using a multiphoton tomograph in the mode of time-resolved two-photon fluorescence recording. Studies are performed in vitro on porcine sclera samples. An 88 % aqueous solution of glycerol is used as an immersion clearing agent. Optical clearing is shown to make it possible to increase the intensity of photoinduced conversion of riboflavin into non-fluorescent leukoforms during photochemical reactions preceding collagen crosslinking. According to the experimental data obtained for cases of photocrosslinking without optical clearing and with preliminary optical clearing of tissue under the same irradiation conditions, the content of riboflavin that has not undergone photoconversion in tissue, at depths from 40 to 75 mm, after UV irradiation in the first case is approximately 5.6 times (average over 15 regions of two samples) higher than in the second case

Interglobular Diffusion of an Energy Donor in Triplet-Triplet Energy Transfer in Proteins

The triplet-triplet energy transfer between polar molecules of luminescent probe (eosin) as an energy donor and nonpolar molecules of energy acceptor (anthracene) is studied. Both the donor and the acceptor are bound to human serum albumin by noncovalent bonds. A dependence of rate constant of triplet-triplet energy transfer on human serum albumin concentration is revealed. A rate constant of eosin output from protein globules is determined. It is shown that the energy transfer occurs as a result of interglobular diffusion of eosin. The obtained results indicate that a protein-luminescent probe based sensor can be used for testing a concentration of polycyclic aromatic hydrocarbons in proteins

Interglobular Diffusion of an Energy Donor in Triplet-Triplet Energy Transfer in Proteins

The triplet-triplet energy transfer between polar molecules of luminescent probe (eosin) as an energy donor and nonpolar molecules of energy acceptor (anthracene) is studied. Both the donor and the acceptor are bound to human serum albumin by noncovalent bonds. A dependence of rate constant of triplet-triplet energy transfer on human serum albumin concentration is revealed. A rate constant of eosin output from protein globules is determined. It is shown that the energy transfer occurs as a result of interglobular diffusion of eosin. The obtained results indicate that a protein-luminescent probe based sensor can be used for testing a concentration of polycyclic aromatic hydrocarbons in proteins

Electrical wave propagation in an anisotropic model of the left ventricle based on analytical description of cardiac architecture.

We develop a numerical approach based on our recent analytical model of fiber structure in the left ventricle of the human heart. A special curvilinear coordinate system is proposed to analytically include realistic ventricular shape and myofiber directions. With this anatomical model, electrophysiological simulations can be performed on a rectangular coordinate grid. We apply our method to study the effect of fiber rotation and electrical anisotropy of cardiac tissue (i.e., the ratio of the conductivity coefficients along and across the myocardial fibers) on wave propagation using the ten Tusscher-Panfilov (2006) ionic model for human ventricular cells. We show that fiber rotation increases the speed of cardiac activation and attenuates the effects of anisotropy. Our results show that the fiber rotation in the heart is an important factor underlying cardiac excitation. We also study scroll wave dynamics in our model and show the drift of a scroll wave filament whose velocity depends non-monotonically on the fiber rotation angle; the period of scroll wave rotation decreases with an increase of the fiber rotation angle; an increase in anisotropy may cause the breakup of a scroll wave, similar to the mother rotor mechanism of ventricular fibrillation

Progrès technique et inégalité

<p>The notation is the same as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0093617#pone-0093617-g004" target="_blank">Fig. 4</a>.</p