A SIMPLIFIED MODEL OF PROPAGATION AND DISSIPATION OF EXCITATION FRONTS

2003 ◽  
Vol 13 (12) ◽  
pp. 3605-3619 ◽  
Author(s):  
V. N. BIKTASHEV
Keyword(s):  
Cardiac Tissue ◽  
Simplified Model ◽  
Excitation Wave ◽  
Temporal Gradient ◽  
Transmembrane Voltage ◽  
Front Solutions ◽  
Traveling Front ◽  
Order Of Magnitude ◽  
Na Inactivation ◽  
Simplified Mathematical Model

An excitation wave in nerve or cardiac tissue may fail to propagate if the temporal gradient of the transmembrane voltage at the front becomes too small to excite the tissue ahead of it. A simplified mathematical model is suggested, that reproduces this phenomenon and has exact traveling front solutions. The spectrum of possible propagation speeds is bounded from below. This causes a front to dissipate if it is not allowed to propagate quickly enough. A crucial role is played by the Na inactivation gates, even if their dynamics are by an order of magnitude slower than the dynamics of the voltage.

COSMIC ORIGIN OF QUANTIZATION

2004 ◽  
Vol 18 (04n05) ◽  
pp. 519-525 ◽  
Author(s):  
FRANCESCO CALOGERO
Keyword(s):  
Angular Momentum ◽  
Spatial Coherence ◽  
Simplified Model ◽  
Nucleon Mass ◽  
Universal Gravitation ◽  
Large Component ◽  
Missing Mass ◽  
Order Of Magnitude ◽  
The Universe ◽  
Cosmic Origin

An estimate is presented of the angular momentum associated with the stochastic cosmic tremor, which has been hypothesized to be caused by universal gravitation and by the granularity of matter, and to be itself the cause of quantization ("cosmic origin of quantization"). If that universal tremor has the spatial coherence which is instrumental in order that the estimated action associated with it have the order of magnitude of Planck's constant h, then the estimated order of magnitude of the angular momentum associated with it also has the same value. We moreover indicate how these findings (originally based on a simplified model of the Universe, as being made up only of particles having the nucleon mass) are affected (in fact, essentially unaffected) by the possible presence in the mass of the Universe of a large component made up of particles much lighter than nucleons ("dark", or "missing", mass).

scholarly journals Analysis and Simulation about a Simplified Model for Modulation and Demodulation of Ship-borne Single Channel Monopulse Radar

2018 ◽  
Vol 232 ◽  
pp. 04043
Author(s):  
Xudong Zhang ◽  
Haiyu Ji
Keyword(s):  
Mathematical Model ◽  
Single Channel ◽  
Simplified Model ◽  
Modulation And Demodulation ◽  
Pulse Radar ◽  
Factors Influencing ◽  
Simplified Mathematical Model

A simplified mathematical model for modulation and demodulation of a single channel monopulse (SCM) system is proposed, which is based on a ship-borne pulse radar S-band guided receiver. Using the proposed mathematical model, the modulation and demodulation of single-channel and multi-channel signals were simulated respectively, and the factors influencing the modulation and demodulation of the SCM system were analysed.

Cardiac Alternans Arising From an Unfolded Border-Collision Bifurcation

2007 ◽  
Author(s):  
Xiaopeng Zhao ◽  
David G. Schaeffer ◽  
Carolyn M. Berger ◽  
Wanda Krassowska ◽  
Daniel J. Gauthier
Keyword(s):  
Action Potential ◽  
Cardiac Tissue ◽  
Medical Literature ◽  
Period Doubling ◽  
Electrical Stimulus ◽  
Period Doubling Bifurcation ◽  
Small Interval ◽  
Border Collision Bifurcation ◽  
Transmembrane Voltage ◽  
Cardiac Alternans

Following an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. In principle, a period-doubling bifurcation may occur through either a smooth or a nonsmooth mechanism. Previous experiments reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which is due to large variations in the system’s properties over a small interval of bifurcation parameter. To reproduce the experimentally observed hybrid behaviors, we have developed a model of alternans that exhibits an unfolded border-collision bifurcation. Excellent agreement between simulation of the model and experimental data suggests that features of the unfolded border-collision model should be included in modeling cardiac alternans.

scholarly journals Dynamics of action potential head-tail interaction during reentry in cardiac tissue: ionic mechanisms

2000 ◽  
Vol 279 (4) ◽  
pp. H1869-H1879 ◽  
Author(s):  
Thomas J. Hund ◽  
Niels F. Otani ◽  
Yoram Rudy
Keyword(s):  
Action Potential ◽  
Wave Front ◽  
Cardiac Tissue ◽  
Excitation Wave ◽  
One Dimensional ◽  
Spatial Oscillations ◽  
Ionic Mechanisms ◽  
High Degree ◽  
Dynamics Of Action ◽  
Transient Oscillations

In a sufficiently short reentry pathway, the excitation wave front (head) propagates into tissue that is partially refractory (tail) from the previous action potential (AP). We incorporate a detailed mathematical model of the ventricular myocyte into a one-dimensional closed pathway to investigate the effects of head-tail interaction and ion accumulation on the dynamics of reentry. The results were the following: 1) a high degree of head-tail interaction produces oscillations in several AP properties; 2) Ca2+-transient oscillations are in phase with AP duration oscillations and are often of greater magnitude; 3) as the wave front propagates around the pathway, AP properties undergo periodic spatial oscillations that produce complicated temporal oscillations at a single site; 4) depending on the degree of head-tail interaction, intracellular [Na+] accumulation during reentry either stabilizes or destabilizes reentry; and 5) elevated extracellular [K+] destabilizes reentry by prolonging the tail of postrepolarization refractoriness.

scholarly journals Simplified model of the number of Covid-19 patients in the ICU: update April 6, 2020

2020 ◽  
Author(s):  
A. Cividjian ◽  
F Wallet ◽  
C. Guichon ◽  
O. Martin ◽  
S. Couray-Targe ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Intensive Care ◽  
Length Of Stay ◽  
Simplified Model ◽  
Icu Patients ◽  
Icu Length Of Stay ◽  
Patient Turnover ◽  
Official Data ◽  
Existing Data ◽  
Simplified Mathematical Model

ABSTRACTINTRODUCTIONPredicting the number of Covid-19 patients in the Intensive Care Units (ICU) could be useful to avoid the breaking point. We attempted to deduce a formula in order to model the number of the ICU patients in France from the official data and patient turnover in the ICU.METHODSThe Covid-19 ICU patient turnover was calculated using a recurrence relation from the internal data provided by Hospices Civils de Lyon. The number of new Covid-19 cases detected daily was modelized to fit with the last known data in France and extrapolated for the coming days using two scenarios following the existing data in China (best scenario) and Italy (worst scenario). The number of daily admissions in ICU was calculated as the sum of 13.7% of the new Covid-19 cases detected on a given day and 7.8% of the average of the total new Covid-19 cases recorded in the last week. Approximately 39.7% of patients admitted to the ICU were non-intubated with an average ICU length of stay of 4 days. Conversely, 60.3% of patients were intubated and for those who died among them (14.44%) the ICU length of stay was of 4 days for 78.3% of them and of 15 days for 21.7% of them. For the intubated patients that were discharged alive, the ICU length of stay was of 6 days for 44.4% of them and of 20 days for 55.6% of them.RESULTSWe predict a peak of 7072 – 8043 patients for the overall French territory.CONCUSIONDespite a simplified mathematical model, the strength of our study is a narrow possible range of predicted total number of ICU patients.

Excitation wave propagation in a patterned multidomain cardiac tissue

JETP Letters ◽  
2015 ◽  
Vol 101 (11) ◽  
pp. 772-775
Author(s):  
N. N. Kudryashova ◽  
A. S. Teplenin ◽  
Y. V. Orlova ◽  
K. I. Agladze
Keyword(s):  
Wave Propagation ◽  
Cardiac Tissue ◽  
Excitation Wave

scholarly journals Tunable Human Myocardium Derived Decellularized Extracellular Matrix for 3D Bioprinting and Cardiac Tissue Engineering

Gels ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 70
Author(s):  
Gozde Basara ◽  
S. Gulberk Ozcebe ◽  
Bradley W. Ellis ◽  
Pinar Zorlutuna
Keyword(s):  
Mechanical Properties ◽  
Tissue Engineering ◽  
Extracellular Matrix ◽  
Connexin 43 ◽  
Cardiac Tissue ◽  
Myocardial Infarct ◽  
Cardiac Tissue Engineering ◽  
3D Bioprinting ◽  
Decellularized Extracellular Matrix ◽  
Order Of Magnitude

The generation of 3D tissue constructs with multiple cell types and matching mechanical properties remains a challenge in cardiac tissue engineering. Recently, 3D bioprinting has become a powerful tool to achieve these goals. Decellularized extracellular matrix (dECM) is a common scaffold material due to providing a native biochemical environment. Unfortunately, dECM’s low mechanical stability prevents usage for bioprinting applications alone. In this study, we developed bioinks composed of decellularized human heart ECM (dhECM) with either gelatin methacryloyl (GelMA) or GelMA-methacrylated hyaluronic acid (MeHA) hydrogels dual crosslinked with UV light and microbial transglutaminase (mTGase). We characterized the bioinks’ mechanical, rheological, swelling, printability, and biocompatibility properties. Composite GelMA–MeHA–dhECM (GME) hydrogels demonstrated improved mechanical properties by an order of magnitude compared to the GelMA–dhECM (GE) hydrogels. All hydrogels were extrudable and compatible with human induced pluripotent stem cell derived cardiomyocytes (iCMs) and human cardiac fibroblasts (hCFs). Tissue-like beating of the printed constructs with striated sarcomeric alpha-actinin and connexin 43 expression was observed. The order of magnitude difference between the elastic modulus of these hydrogel composites offers applications in in vitro modeling of the myocardial infarct boundary. Here, as a proof of concept, we created an infarct boundary region with control over the mechanical properties along with the cellular and macromolecular content through printing iCMs with GE bioink and hCFs with GME bioink.

Sign in / Sign up

Export Citation Format

Share Document