Сюняев Р.А., Алиев Р.Р. Биофизика, 54(1), 77

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Computer simulations of propagation and
reentry patterns in the sinoatrial node
Rubin R. Aliev & Roman A. Syunyaev
Email: [email protected]
www: http://lep.mipt.ru
Moscow Institute of Physics and Technology
Institute of Theoretical and Experimental Biophysics
Federal Medico-Biological Agency
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SAN pacemaker membrane model
Ach-modified currents
Zhang et al. Am. J. Physiol., 279, H397-421 (2000),
Zhang et al. J. Cardiovasc. Electrophysiol., 13, 465-474 (2002).
Model described in:
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Master equation for the transmembrane
current
 Cm
i  iCa ,L  iCa ,T  i f  iK ,r  iK ,s  ito  isus
 iK , ACh  ib ,Na  ib ,Ca  ib ,K  iNaK  iNaCa  i p ,Ca
dV

Na
dt
iNa – натриевый ток,
iCa,T, iCa,L – кальциевые токи Т и L типа,
if – активируемый при гиперполяризации ток,
ib,Na, ib,Ca, ib,K – фоновые токи,
iK,r, iK,s – быстрый и медленный калиевые токи задержанного выпрямления,
ito, isus – компоненты чувствительного к 4-AP тока,
iK,АCh – активируемый АЦХ калиевый ток,
iNaK – Na-K насос,
iNaCa – Na-Ca обменник,
ip,Ca – кальциевый насос.
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Membrane + intracellular
currents
From: Алиев РР, Чайлахян ЛМ. ДАН 402 (2005).
RR Aliev, LM Chailakhyan Doklady Acad Sci 402 (1), 236-239
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The effect of Ach on SAN cells
t |ACh| = D2|ACh| - k|ACh||AChE|
r
ACh
R
AChE
Алиев РР, Розенштраух ЛВ. Росс.Физиол.Ж. 92(9), 1069-1077 (2006).
Aliev Rozenshtraukh Rus Physiol J.
Experiment
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Stimulation electrode
Superior vena cava
Right atrium
СУ
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Effect of vagal stimulation on SAN pacemaker cells. CL increase by 14
%.
Алиев Р.Р., Абрамочкин Д., Розенштраух Л.В. Рос.Физиол.Ж., 95(1), 49-57 (2009).
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Phase response curves as function of stimuli number: from 1 to 10.
Алиев Р.Р., Абрамочкин Д., Розенштраух Л.В. Рос.Физиол.Ж., 95(1), 49-57 (2009).
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Close to membrane concentrations, currents and transmembrane potential.
Алиев Р.Р., Абрамочкин Д., Розенштраух Л.В. Рос.Физиол.Ж., 95(1), 49-57 (2009).
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PRL curves computed and experimental
Алиев Р.Р., Абрамочкин Д., Розенштраух Л.В. Рос.Физиол.Ж., 95(1), 49-57 (2009).
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Theoretical width of the zone of positive chronotropic affect as a function of number of
stimuli (а). Experiment for single stimulation (б). For phases 0.85 to 1.0 there is a
positive chronotropic effect.
Алиев Р.Р., Абрамочкин Д., Розенштраух Л.В. Рос.Физиол.Ж., 95(1), 49-57 (2009).
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Sync and De-sync od SAN cells
Desynchronization
Рассогласование:
T с Т о
r
То
Тс – Period of stimulation,
Т0 – Period of unperturbed oscillations
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(а) unperturbed oscillations, Т0=340 мс; (б-д) stimulation with the period 306, 323, 374, 510 ms, which
corresponds to r, -0.1, -0.05, 0.1, 0.5 (numbers left). It is seen that at positive r – increase CL; at r = –0.05 –
decrease CL, at r = -0.1 – desync.
Алиев Р.Р. Биофизика, т.53(6), c.1125–1128 (2008).
RR Aliev Biophysics 53 (6), 645-647
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Established averaged ratio of frequences (а) and phase shifts (б) as functions of r. sync
activity correspond to horisontal zones in (а) and monotonic parts in (б).
Алиев Р.Р. Биофизика, т.53(6), c.1125–1128 (2008).
RR Aliev Biophysics 53 (6), 645-647
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Two cells connected via gap junctions
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Сюняев Р.А., Алиев Р.Р. Биофизика, 54(1), 77-80 (2009).
RA Siuniaev, RR Aliev Biofizika 54 (1), 77-80
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Сюняев Р.А., Алиев Р.Р. Биофизика, 54(1), 77-80 (2009).
RA Siuniaev, RR Aliev Biofizika 54 (1), 77-80
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Сюняев Р.А., Алиев Р.Р. Биофизика, 54(1), 77-80 (2009).
RA Siuniaev, RR Aliev Biofizika 54 (1), 77-80
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Development of synchronization
Сюняев Р.А., Алиев Р.Р. Биофизика, 54(1), 77-80 (2009).
RA Siuniaev, RR Aliev Biofizika 54 (1), 77-80
Simulating 1D, 2D, 3D
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Conceptual models
Detail models
•PDE
• ODE
dV
C
 C( DE )   I ( g ,V )
dt
dV
C
  I j   I ( g ,V )
dt
Simulating SAN: 2D.
ACh results in a functional block of
conduction
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Syunyaev, Aliev Biophysics (rus.), 55(6), 1132 -7 (2010).
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Syunyaev, Aliev. RJNAMM 26(6) 575-587(2011)
Simulating SAN: 2D.
Inhomogeneity.
Из: Dobrzynski H et al., Circulation
2005; 111:846-854.
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Моделирование СУ: 3D.
Миграция водителя ритма
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Syunyaev, Aliev. RJNAMM 26(6) 575-587(2011)
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2D
Syunyaev, Aliev Biophysics (rus.), 55(6), 1132 -7 (2010).
3D
Syunyaev, Aliev. RJNAMM 26(6) 575-587(2011)
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Evolution of pacemaker density in the SAN. Note the initially
large number of pacemakers significantly drops during first few
seconds.
Syunyaev, Aliev. RJNAMM 26(6) 575-587(2011)
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Syunyaev, Aliev. RJNAMM 26(6) 575-587(2011)
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Syunyaev, Aliev. RJNAMM 26(6) 575-587(2011)
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Thank you for your patience!
Email: [email protected]
www: http://lep.mipt.ru
Moscow Institute of Physics and Technology
Institute of Theoretical and Experimental Biophysics
Federal Medico-Biological Agency