NOLIN - Física No-Lineal i Sistemes Fora de l'Equilibri
http://hdl.handle.net/2117/635
2016-12-08T09:54:18ZLangevin equation approach for slow dynamics in magnetic systems
http://hdl.handle.net/2117/79563
Langevin equation approach for slow dynamics in magnetic systems
Sancho, Jose Maria; Lacasta Palacio, Ana María; Torrent Serra, Maria del Carmen; García Ojalvo, Jordi; Tejeda Gómez, José Arturo
We present a magnetic model based on a Langevin equation which exhibits slow relaxation dynamics of ln(t) type. The system is composed of magnetic particles which are under the influence of a local potential and interact through a mean field. Recent experimental data are interpreted within this model.
2015-11-23T12:56:01ZSancho, Jose MariaLacasta Palacio, Ana MaríaTorrent Serra, Maria del CarmenGarcía Ojalvo, JordiTejeda Gómez, José ArturoWe present a magnetic model based on a Langevin equation which exhibits slow relaxation dynamics of ln(t) type. The system is composed of magnetic particles which are under the influence of a local potential and interact through a mean field. Recent experimental data are interpreted within this model.Propagation malfunctions due to gap junction dysregulation
http://hdl.handle.net/2117/25114
Propagation malfunctions due to gap junction dysregulation
Rodríguez Cantalapiedra, Inma; Peñaranda Ayllón, Angelina; Echebarría Domínguez, Blas
Gap junctions are membrane channels that connect the cytoplasm of adjacent cells allowing the cell-to-cell electrical
coupling necessary for action potential propagation. Pathological conditions, such as malformations in connexins, mutations affecting phosphorylation of regulatory sites
of connexins, alterations in gap junction organization, and type and quantity of connexin expression, can impede the normal electrical propagation. All these malfunctions can produce a dispersion of repolarization, implicated in ventricular
arrhythmias. In fact, ventricular tachycardia and spontaneous ventricular arrhythmia occurred in more than twice as many connexin deficient hearts than wild-type
hearts.
We perform numerical simulations of a human ventricular model in order to mimic some of these pathological conditions. In particular, we consider a diminished Cx43
connexin expression, as well as altered connexin conductance dynamics, i.e., modified maximum and minimum conductances gmax and gmin, half-inactivation voltage
V1=2 and decay kinetics. Physiologically these modifications can appear due to mutations or to different connexin
configurations, i.e., forming heteromeric channels. Under these conditions we study the change in action potential duration (APD) and CV-restitution properties. We observe that, although CV diminishes with decreased connexin expression, the APD remains almost constant up to the point
of conduction block. Also, propagation differs for constant or time-dependent voltage conductance, conduction block
occurring earlier for the former. While mutations resulting in a stronger dependence of the delay time produced an appreciable change intercellular conductances, this effect was not so important when the mutations affected the overall delay time. Thus, our results suggest that a correct
description of gap junctional conductance is of big importance for understanding action potential propagation under pathological conditions.
2014-12-19T17:06:05ZRodríguez Cantalapiedra, InmaPeñaranda Ayllón, AngelinaEchebarría Domínguez, BlasGap junctions are membrane channels that connect the cytoplasm of adjacent cells allowing the cell-to-cell electrical
coupling necessary for action potential propagation. Pathological conditions, such as malformations in connexins, mutations affecting phosphorylation of regulatory sites
of connexins, alterations in gap junction organization, and type and quantity of connexin expression, can impede the normal electrical propagation. All these malfunctions can produce a dispersion of repolarization, implicated in ventricular
arrhythmias. In fact, ventricular tachycardia and spontaneous ventricular arrhythmia occurred in more than twice as many connexin deficient hearts than wild-type
hearts.
We perform numerical simulations of a human ventricular model in order to mimic some of these pathological conditions. In particular, we consider a diminished Cx43
connexin expression, as well as altered connexin conductance dynamics, i.e., modified maximum and minimum conductances gmax and gmin, half-inactivation voltage
V1=2 and decay kinetics. Physiologically these modifications can appear due to mutations or to different connexin
configurations, i.e., forming heteromeric channels. Under these conditions we study the change in action potential duration (APD) and CV-restitution properties. We observe that, although CV diminishes with decreased connexin expression, the APD remains almost constant up to the point
of conduction block. Also, propagation differs for constant or time-dependent voltage conductance, conduction block
occurring earlier for the former. While mutations resulting in a stronger dependence of the delay time produced an appreciable change intercellular conductances, this effect was not so important when the mutations affected the overall delay time. Thus, our results suggest that a correct
description of gap junctional conductance is of big importance for understanding action potential propagation under pathological conditions.The timing statistics of spontaneous calcium release in cardiac myocytes
http://hdl.handle.net/2117/24090
The timing statistics of spontaneous calcium release in cardiac myocytes
Asfaw, Mesfin; Álvarez Lacalle, Enrique; Shiferaw, Yohannes
A variety of cardiac arrhythmias are initiated by a focal excitation that disrupts the regular beating of the heart. In some
cases it is known that these excitations are due to calcium (Ca) release from the sarcoplasmic reticulum (SR) via propagating
subcellular Ca waves. However, it is not understood what are the physiological factors that determine the timing of these
excitations at both the subcellular and tissue level. In this paper we apply analytic and numerical approaches to determine
the timing statistics of spontaneous Ca release (SCR) in a simplified model of a cardiac myocyte. In particular, we compute
the mean first passage time (MFPT) to SCR, in the case where SCR is initiated by spontaneous Ca sparks, and demonstrate
that this quantity exhibits either an algebraic or exponential dependence on system parameters. Based on this analysis we
identify the necessary requirements so that SCR occurs on a time scale comparable to the cardiac cycle. Finally, we study
how SCR is synchronized across many cells in cardiac tissue, and identify a quantitative measure that determines the relative
timing of SCR in an ensemble of cells. Using this approach we identify the physiological conditions so that cell-to-cell
variations in the timing of SCR is small compared to the typical duration of an SCR event. We argue further that under these
conditions inward currents due to SCR can summate and generate arrhythmogenic triggered excitations in cardiac tissue.
2014-09-17T16:48:42ZAsfaw, MesfinÁlvarez Lacalle, EnriqueShiferaw, YohannesA variety of cardiac arrhythmias are initiated by a focal excitation that disrupts the regular beating of the heart. In some
cases it is known that these excitations are due to calcium (Ca) release from the sarcoplasmic reticulum (SR) via propagating
subcellular Ca waves. However, it is not understood what are the physiological factors that determine the timing of these
excitations at both the subcellular and tissue level. In this paper we apply analytic and numerical approaches to determine
the timing statistics of spontaneous Ca release (SCR) in a simplified model of a cardiac myocyte. In particular, we compute
the mean first passage time (MFPT) to SCR, in the case where SCR is initiated by spontaneous Ca sparks, and demonstrate
that this quantity exhibits either an algebraic or exponential dependence on system parameters. Based on this analysis we
identify the necessary requirements so that SCR occurs on a time scale comparable to the cardiac cycle. Finally, we study
how SCR is synchronized across many cells in cardiac tissue, and identify a quantitative measure that determines the relative
timing of SCR in an ensemble of cells. Using this approach we identify the physiological conditions so that cell-to-cell
variations in the timing of SCR is small compared to the typical duration of an SCR event. We argue further that under these
conditions inward currents due to SCR can summate and generate arrhythmogenic triggered excitations in cardiac tissue.Are SR Ca content fluctuations or SR refractoriness the key to atrial cardiac alternans?: insights from a human atrial model
http://hdl.handle.net/2117/23521
Are SR Ca content fluctuations or SR refractoriness the key to atrial cardiac alternans?: insights from a human atrial model
Lugo Vélez, Carlos Antonio; Rodríguez Cantalapiedra, Inma; Peñaranda Ayllón, Angelina; Hove-Madsen, Leif; Echebarría Domínguez, Blas
Despite the important role of electromechanical alternans in cardiac arrhythmogenesis, its molecular origin is not well understood. The appearance of calcium alternans has often been associated to fluctuations in the sarcoplasmic reticulum (SR) Ca loading. However, cytosolic calcium alternans observed without concurrent oscillations in the SR Ca content suggests an alternative mechanism related to a dysfunction in the dynamics of the ryanodine receptor (RyR2). We have investigated the effect of SR release refractoriness in the appearance of alternans, using a mathematical model of a single human atrial cell, based on the model by Nygren et al. (30), where we modified the dynamics of the RyR2 and of SR Ca release. The genesis of calcium alternans was studied stimulating the cell for different periods and values of the RyR2 recovery time from inactivation. At fast rates cytosolic calcium alternans were obtained without concurrent SR Ca content fluctuations. A transition from regular response to alternans was also observed, changing the recovery time from inactivation of the RyR2. This transition was found to be hysteretic, so for a given set of parameters different responses were observed. We then studied the relevance of RyR2 refractoriness for the generation of alternans, reproducing the same protocols as in recent experiments. In particular, restitution of Ca release during alternans was studied with a S1S2 protocol, obtaining a different response if the S2 stimulation was given after a long or a short release. We show that the experimental results can be explained by RyR2 refractoriness, arising from a slow RyR2 recovery from inactivation, stressing the role of the RyR2 in the genesis of alternans.
2014-07-16T07:09:45ZLugo Vélez, Carlos AntonioRodríguez Cantalapiedra, InmaPeñaranda Ayllón, AngelinaHove-Madsen, LeifEchebarría Domínguez, BlasDespite the important role of electromechanical alternans in cardiac arrhythmogenesis, its molecular origin is not well understood. The appearance of calcium alternans has often been associated to fluctuations in the sarcoplasmic reticulum (SR) Ca loading. However, cytosolic calcium alternans observed without concurrent oscillations in the SR Ca content suggests an alternative mechanism related to a dysfunction in the dynamics of the ryanodine receptor (RyR2). We have investigated the effect of SR release refractoriness in the appearance of alternans, using a mathematical model of a single human atrial cell, based on the model by Nygren et al. (30), where we modified the dynamics of the RyR2 and of SR Ca release. The genesis of calcium alternans was studied stimulating the cell for different periods and values of the RyR2 recovery time from inactivation. At fast rates cytosolic calcium alternans were obtained without concurrent SR Ca content fluctuations. A transition from regular response to alternans was also observed, changing the recovery time from inactivation of the RyR2. This transition was found to be hysteretic, so for a given set of parameters different responses were observed. We then studied the relevance of RyR2 refractoriness for the generation of alternans, reproducing the same protocols as in recent experiments. In particular, restitution of Ca release during alternans was studied with a S1S2 protocol, obtaining a different response if the S2 stimulation was given after a long or a short release. We show that the experimental results can be explained by RyR2 refractoriness, arising from a slow RyR2 recovery from inactivation, stressing the role of the RyR2 in the genesis of alternans.Final architecture diploma projects in the analysis of the UPC buildings energy performance
http://hdl.handle.net/2117/22827
Final architecture diploma projects in the analysis of the UPC buildings energy performance
Bosch González, Montserrat; Rodríguez Cantalapiedra, Inma; López Plazas, Fabián; Ruiz Martorell, Galdric
Education is the base for achieving sustainable development. With the purpose
of introducing sustainable challenges in terms of climate change, water and
energy consumption, the Technical University of Catalonia (UPC) has promoted
the culture of energy efficiency in new generations of professionals that will
work in the field of building construction. A group of 29 students taking the final
official Diploma in Architecture were involved in a project of analysis of energy
performance of UPC buildings in order to identify and implement cost-effective
ways of promoting a greater environmental responsibility. The development of
works focused the attention on introducing energy audits in existing university
buildings, analysing the following aspects: surveying construction drawings,
building characteristics, energy consumption, and use of natural lighting, energysaving
lighting controls, water consumption, and high-efficiency HVAC
systems. The ultimate goal was to draft a proposal with greater respect for the
environment, and for corrective measures aimed at reducing the cities
environmental impact.
This paper has the objective of publicising the results, from an academic
standpoint, of a specific action carried out within the framework of the Energy
Efficiency Plan (UPC,* 2002) that is now being implemented and that will allow
the existing commitment to greening the university studies in Technical
Architecture School to be strengthened. The first stage was performed through
the energy audit of 24 UPC buildings, and, in view of the good results obtained,
the second stage has now been started through other public office, school and
sport buildings.
2014-05-05T15:30:30ZBosch González, MontserratRodríguez Cantalapiedra, InmaLópez Plazas, FabiánRuiz Martorell, GaldricEducation is the base for achieving sustainable development. With the purpose
of introducing sustainable challenges in terms of climate change, water and
energy consumption, the Technical University of Catalonia (UPC) has promoted
the culture of energy efficiency in new generations of professionals that will
work in the field of building construction. A group of 29 students taking the final
official Diploma in Architecture were involved in a project of analysis of energy
performance of UPC buildings in order to identify and implement cost-effective
ways of promoting a greater environmental responsibility. The development of
works focused the attention on introducing energy audits in existing university
buildings, analysing the following aspects: surveying construction drawings,
building characteristics, energy consumption, and use of natural lighting, energysaving
lighting controls, water consumption, and high-efficiency HVAC
systems. The ultimate goal was to draft a proposal with greater respect for the
environment, and for corrective measures aimed at reducing the cities
environmental impact.
This paper has the objective of publicising the results, from an academic
standpoint, of a specific action carried out within the framework of the Energy
Efficiency Plan (UPC,* 2002) that is now being implemented and that will allow
the existing commitment to greening the university studies in Technical
Architecture School to be strengthened. The first stage was performed through
the energy audit of 24 UPC buildings, and, in view of the good results obtained,
the second stage has now been started through other public office, school and
sport buildings.On the validity of Avrami formalism in primary crystallization
http://hdl.handle.net/2117/22789
On the validity of Avrami formalism in primary crystallization
Bruna Escuer, Pere; Crespo Artiaga, Daniel; González Cinca, Ricardo; Pineda Soler, Eloi
Calorimetric data of primary crystallization is usually interpreted in the framework of the
Kolmogorov Dokl. Akad. Nauk SSSR 1, 355 1937 , Johnson and Mehl Trans. AIME 135, 416
1939 , and Avrami J. Chem. Phys. 7, 1103 1939 ; 8, 212 1940 ; 9, 177 1941 KJMA theory.
However, while the KJMA theory assumes random nucleation and exhaustion of space by direct
impingement, primary crystallization is usually driven by diffusion-controlled growth with soft
impingement between the growing crystallites. This results in a stop of the growth before the space
is fully crystallized and induces nonrandom nucleation. In this work, phase-field simulations are
used to check the validity of different kinetic models for describing primary crystallization kinetics.
The results show that KJMA theory provides a good approximation to the soft-impingement and
nonrandom nucleation effects. Moreover, these effects are not responsible of the slowing down of
the kinetics found experimentally in the primary crystallization of glasses.
2014-04-30T12:39:03ZBruna Escuer, PereCrespo Artiaga, DanielGonzález Cinca, RicardoPineda Soler, EloiCalorimetric data of primary crystallization is usually interpreted in the framework of the
Kolmogorov Dokl. Akad. Nauk SSSR 1, 355 1937 , Johnson and Mehl Trans. AIME 135, 416
1939 , and Avrami J. Chem. Phys. 7, 1103 1939 ; 8, 212 1940 ; 9, 177 1941 KJMA theory.
However, while the KJMA theory assumes random nucleation and exhaustion of space by direct
impingement, primary crystallization is usually driven by diffusion-controlled growth with soft
impingement between the growing crystallites. This results in a stop of the growth before the space
is fully crystallized and induces nonrandom nucleation. In this work, phase-field simulations are
used to check the validity of different kinetic models for describing primary crystallization kinetics.
The results show that KJMA theory provides a good approximation to the soft-impingement and
nonrandom nucleation effects. Moreover, these effects are not responsible of the slowing down of
the kinetics found experimentally in the primary crystallization of glasses.Motor adaptation as a greedy optimization of error and effort
http://hdl.handle.net/2117/22787
Motor adaptation as a greedy optimization of error and effort
Emken, Jeremy L.; Benítez Iglesias, Raúl; Sideris, Athanasios; Bobrow, James E.; Reinkensmeyer, David J.
thought of as a process in which the nervous
system learns to anticipate the environmental forces to eliminate
kinematic error. Here we show that motor adaptation can more
generally be modeled as a process in which the motor system greedily
minimizes a cost function that is the weighted sum of kinematic error
and effort. The learning dynamics predicted by this minimization
process are a linear, auto-regressive equation with only one state,
which has been identified previously as providing a good fit to data
from force-field-type experiments. Thus we provide a new theoretical
result that shows how these previously identified learning dynamics
can be viewed as arising from an optimization of error and effort. We
also show that the coefficients of the learning dynamics must fall
within a specific range for the optimization model to be valid and
verify with experimental data from walking in a force field that they
indeed fall in this range. Finally, we attempted to falsify the model by
performing experiments in two conditions (repeated exposure to a
force field, exposure to force fields of different strengths) for which
the single-state, auto-regressive equation might be expected to not fit
the data well. We found however that the equation adequately captured
the pattern of errors and thus conclude that motor adaptation to
a force field can be approximated as an optimization of effort and
error for a range of experimental conditions.
2014-04-30T12:21:49ZEmken, Jeremy L.Benítez Iglesias, RaúlSideris, AthanasiosBobrow, James E.Reinkensmeyer, David J.thought of as a process in which the nervous
system learns to anticipate the environmental forces to eliminate
kinematic error. Here we show that motor adaptation can more
generally be modeled as a process in which the motor system greedily
minimizes a cost function that is the weighted sum of kinematic error
and effort. The learning dynamics predicted by this minimization
process are a linear, auto-regressive equation with only one state,
which has been identified previously as providing a good fit to data
from force-field-type experiments. Thus we provide a new theoretical
result that shows how these previously identified learning dynamics
can be viewed as arising from an optimization of error and effort. We
also show that the coefficients of the learning dynamics must fall
within a specific range for the optimization model to be valid and
verify with experimental data from walking in a force field that they
indeed fall in this range. Finally, we attempted to falsify the model by
performing experiments in two conditions (repeated exposure to a
force field, exposure to force fields of different strengths) for which
the single-state, auto-regressive equation might be expected to not fit
the data well. We found however that the equation adequately captured
the pattern of errors and thus conclude that motor adaptation to
a force field can be approximated as an optimization of effort and
error for a range of experimental conditions.Human-robot cooperative movement training: learning a novel sensory motor transformation during walking with robotic assistance-as-needed
http://hdl.handle.net/2117/22786
Human-robot cooperative movement training: learning a novel sensory motor transformation during walking with robotic assistance-as-needed
Emken, Jeremy L.; Benítez Iglesias, Raúl; Reinkensmeyer, David J.
Background
A prevailing paradigm of physical rehabilitation following neurologic injury is to "assist-as-needed" in completing desired movements. Several research groups are attempting to automate this principle with robotic movement training devices and patient cooperative algorithms that encourage voluntary participation. These attempts are currently not based on computational models of motor learning.
Methods
Here we assume that motor recovery from a neurologic injury can be modelled as a process of learning a novel sensory motor transformation, which allows us to study a simplified experimental protocol amenable to mathematical description. Specifically, we use a robotic force field paradigm to impose a virtual impairment on the left leg of unimpaired subjects walking on a treadmill. We then derive an "assist-as-needed" robotic training algorithm to help subjects overcome the virtual impairment and walk normally. The problem is posed as an optimization of performance error and robotic assistance. The optimal robotic movement trainer becomes an error-based controller with a forgetting factor that bounds kinematic errors while systematically reducing its assistance when those errors are small. As humans have a natural range of movement variability, we introduce an error weighting function that causes the robotic trainer to disregard this variability.
Results
We experimentally validated the controller with ten unimpaired subjects by demonstrating how it helped the subjects learn the novel sensory motor transformation necessary to counteract the virtual impairment, while also preventing them from experiencing large kinematic errors. The addition of the error weighting function allowed the robot assistance to fade to zero even though the subjects' movements were variable. We also show that in order to assist-as-needed, the robot must relax its assistance at a rate faster than that of the learning human.
Conclusion
The assist-as-needed algorithm proposed here can limit error during the learning of a dynamic motor task. The algorithm encourages learning by decreasing its assistance as a function of the ongoing progression of movement error. This type of algorithm is well suited for helping people learn dynamic tasks for which large kinematic errors are dangerous or discouraging, and thus may prove useful for robot-assisted movement training of walking or reaching following neurologic injury.
2014-04-30T12:05:06ZEmken, Jeremy L.Benítez Iglesias, RaúlReinkensmeyer, David J.Background
A prevailing paradigm of physical rehabilitation following neurologic injury is to "assist-as-needed" in completing desired movements. Several research groups are attempting to automate this principle with robotic movement training devices and patient cooperative algorithms that encourage voluntary participation. These attempts are currently not based on computational models of motor learning.
Methods
Here we assume that motor recovery from a neurologic injury can be modelled as a process of learning a novel sensory motor transformation, which allows us to study a simplified experimental protocol amenable to mathematical description. Specifically, we use a robotic force field paradigm to impose a virtual impairment on the left leg of unimpaired subjects walking on a treadmill. We then derive an "assist-as-needed" robotic training algorithm to help subjects overcome the virtual impairment and walk normally. The problem is posed as an optimization of performance error and robotic assistance. The optimal robotic movement trainer becomes an error-based controller with a forgetting factor that bounds kinematic errors while systematically reducing its assistance when those errors are small. As humans have a natural range of movement variability, we introduce an error weighting function that causes the robotic trainer to disregard this variability.
Results
We experimentally validated the controller with ten unimpaired subjects by demonstrating how it helped the subjects learn the novel sensory motor transformation necessary to counteract the virtual impairment, while also preventing them from experiencing large kinematic errors. The addition of the error weighting function allowed the robot assistance to fade to zero even though the subjects' movements were variable. We also show that in order to assist-as-needed, the robot must relax its assistance at a rate faster than that of the learning human.
Conclusion
The assist-as-needed algorithm proposed here can limit error during the learning of a dynamic motor task. The algorithm encourages learning by decreasing its assistance as a function of the ongoing progression of movement error. This type of algorithm is well suited for helping people learn dynamic tasks for which large kinematic errors are dangerous or discouraging, and thus may prove useful for robot-assisted movement training of walking or reaching following neurologic injury.Mechanisms for initiation of cardiac discordant alternans
http://hdl.handle.net/2117/22783
Mechanisms for initiation of cardiac discordant alternans
Echebarría Domínguez, Blas; Karma, Alain
Electrical alternans, defined as a beat-to-beat change in the duration of the excited phase of cardiac cells, is among the known precursors of sudden cardiac death. It may appear as concordant (all the tissue presenting the same phase of oscillation) or discordant (with out-of-phase regions distributed among tissue). Spatially discordant alternans can lead to unidirectional block that initiates reentry and ventricular fibrillation. The role played by tissue heterogeneities and heart rate changes in their initiation remains, however, unclear. We study the mechanisms for initiation of spatially discordant alternans by numerical simulations of an ionic model spatially distributed in a one-dimensional cable and in an anatomical model of the rabbit heart. The effects of CV-restitution, ectopic beats, and the role of spatial gradients of electrical restitution properties are investigated. In homogeneous tissue, the origin of discordant alternans may be dynamical, through CV-restitution, or due to a localized change in the pacing period. We also find that a sudden change of stimulation rate can initiate discordant alternans in the presence of a spatial gradient of APD-restitution without necessitating CV-restitution. The mechanism of, and the conditions for, initiation are determined based on an iterated map analysis of beat to beat changes of APD. This analysis leads to the definition of a vulnerable window for initiation of discordant alternans. Moreover, the pattern of spatially discordant alternans is found to change slowly over several beats following initiation, as reflected in ECG recordings.
2014-04-30T11:10:55ZEchebarría Domínguez, BlasKarma, AlainElectrical alternans, defined as a beat-to-beat change in the duration of the excited phase of cardiac cells, is among the known precursors of sudden cardiac death. It may appear as concordant (all the tissue presenting the same phase of oscillation) or discordant (with out-of-phase regions distributed among tissue). Spatially discordant alternans can lead to unidirectional block that initiates reentry and ventricular fibrillation. The role played by tissue heterogeneities and heart rate changes in their initiation remains, however, unclear. We study the mechanisms for initiation of spatially discordant alternans by numerical simulations of an ionic model spatially distributed in a one-dimensional cable and in an anatomical model of the rabbit heart. The effects of CV-restitution, ectopic beats, and the role of spatial gradients of electrical restitution properties are investigated. In homogeneous tissue, the origin of discordant alternans may be dynamical, through CV-restitution, or due to a localized change in the pacing period. We also find that a sudden change of stimulation rate can initiate discordant alternans in the presence of a spatial gradient of APD-restitution without necessitating CV-restitution. The mechanism of, and the conditions for, initiation are determined based on an iterated map analysis of beat to beat changes of APD. This analysis leads to the definition of a vulnerable window for initiation of discordant alternans. Moreover, the pattern of spatially discordant alternans is found to change slowly over several beats following initiation, as reflected in ECG recordings.Amplitude equation approach to spatiotemporal dynamics of cardiac alternans
http://hdl.handle.net/2117/22782
Amplitude equation approach to spatiotemporal dynamics of cardiac alternans
Echebarría Domínguez, Blas; Karma, Alain
Amplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during
periodic pacing of one- B. Echebarria and A. Karma, Phys. Rev. Lett. 88, 208101 2002 and twodimensional
homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue.
These equations provide a simple physical understanding of arrhythmogenic patterns of period-doubling oscillations
of action potential duration with a spatially varying phase and amplitude, as well as explicit quantitative
predictions that can be compared to ionic model simulations or experiments. The form of the equations
is expected to be valid for a large class of ionic models but the coefficients are derived analytically only for a
two-variable ionic model and calculated numerically for the original Noble model of Purkinje fiber action
potential. In paced tissue, this theory explains the formation of “spatially discordant alternans” by a linear
instability mechanism that produces a periodic pattern of out-of-phase domains of alternans. The wavelength of
this pattern, equal to twice the spacing between nodes separating out-of-phase domains, is shown to depend on
three fundamental length scales that are determined by the strength of cell-to-cell coupling and conduction
velocity CV restitution. Moreover, the patterns of alternans can be either stationary, with fixed nodes, or
traveling, with moving nodes and hence quasiperiodic oscillations of action potential duration, depending on
the relative strength of the destabilizing effect of CV restitution and the stabilizing effect of diffusive coupling.
For the ring geometry, we recover the results of Courtemanche, Glass, and Keener Phys. Rev. Lett. 70, 2182
1993 with two important modifications due to cell-to-cell diffusive coupling. First, this coupling breaks the
degeneracy of an infinite-dimensional Hopf bifurcation such that the most unstable mode of alternans corresponds
to the longest quantized wavelength of the ring. Second, the Hopf frequency, which determines the
velocity of the node along the ring, depends both on the steepness of CV restitution and the strength of this
coupling, with the net result that quasiperiodic behavior can arise with a constant conduction velocity. In both
the paced geometries and the ring, the onset of alternans is different in tissue than for a paced isolated cell. The
implications of these results for alternans dynamics during two-dimensional reentry are briefly discussed.
2014-04-30T11:03:43ZEchebarría Domínguez, BlasKarma, AlainAmplitude equations are derived that describe the spatiotemporal dynamics of cardiac alternans during
periodic pacing of one- B. Echebarria and A. Karma, Phys. Rev. Lett. 88, 208101 2002 and twodimensional
homogeneous tissue and one-dimensional anatomical reentry in a ring of homogeneous tissue.
These equations provide a simple physical understanding of arrhythmogenic patterns of period-doubling oscillations
of action potential duration with a spatially varying phase and amplitude, as well as explicit quantitative
predictions that can be compared to ionic model simulations or experiments. The form of the equations
is expected to be valid for a large class of ionic models but the coefficients are derived analytically only for a
two-variable ionic model and calculated numerically for the original Noble model of Purkinje fiber action
potential. In paced tissue, this theory explains the formation of “spatially discordant alternans” by a linear
instability mechanism that produces a periodic pattern of out-of-phase domains of alternans. The wavelength of
this pattern, equal to twice the spacing between nodes separating out-of-phase domains, is shown to depend on
three fundamental length scales that are determined by the strength of cell-to-cell coupling and conduction
velocity CV restitution. Moreover, the patterns of alternans can be either stationary, with fixed nodes, or
traveling, with moving nodes and hence quasiperiodic oscillations of action potential duration, depending on
the relative strength of the destabilizing effect of CV restitution and the stabilizing effect of diffusive coupling.
For the ring geometry, we recover the results of Courtemanche, Glass, and Keener Phys. Rev. Lett. 70, 2182
1993 with two important modifications due to cell-to-cell diffusive coupling. First, this coupling breaks the
degeneracy of an infinite-dimensional Hopf bifurcation such that the most unstable mode of alternans corresponds
to the longest quantized wavelength of the ring. Second, the Hopf frequency, which determines the
velocity of the node along the ring, depends both on the steepness of CV restitution and the strength of this
coupling, with the net result that quasiperiodic behavior can arise with a constant conduction velocity. In both
the paced geometries and the ring, the onset of alternans is different in tissue than for a paced isolated cell. The
implications of these results for alternans dynamics during two-dimensional reentry are briefly discussed.