the heart, cardiac action potentials, and arrhythmias … and how … · 2008-06-13 · the heart,...
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The heart, cardiac action potentials, and arrhythmias … and how we
model them
Trine Trine KroghKrogh--Madsen Madsen ((ChristiniChristini lab)lab)
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Cardiac action potentials vary by region
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Cardiac action potentials• Upstroke of ventricular
AP is Na+ mediated.
• At the peak, Ca2+
channels open, causing an inward current that prolongs AP (plateau).
• Ca2+ influx triggers additional Ca2+ release from the sarcoplasmic reticulum.
• Cytoplasmic Ca2+
produces muscle contraction.
• Cardiac cells have many different types of K+ channels.
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Ito IK1 IKr IKs IKp
INaCa3 Na+
Ca2+
INaKK+
Na+
ICa ICa,bINa
Ip(Ca)ICa,K
INa
Jp(Ca)
Jleak
Jrelease
What is “computational modeling”?
Ii = gi ·(V - Ei )
CVM model of the canine ventricular myocyte~13 state variables and ~60 parameters
gi = f(V,t)
Pump
Exchanger
Voltage-gated ion channel
Non-voltage-gated ion channel
= ∑Ii /CmdVdt
courtesy of R. Gilmour
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Ito IK1 IKr IKs IKp
INaCa3 Na+
Ca2+
INaKK+
Na+
ICa ICa,bINa
Ip(Ca)ICa,K
INa
Jp(Ca)
Jleak
Jrelease
What is “computational modeling”?
Ii = gi ·(V - Ei )
CVM model of the canine ventricular myocyte~13 state variables and ~60 parameters
gi = f(V,t)
Pump
Exchanger
Voltage-gated ion channel
Non-voltage-gated ion channel
= f(∑Ii )dVdt
courtesy of R. Gilmour
INa = G Nam3hj(V − ENa)
dm
dt= αm(1− m)− βm
dh
dt= αh(1− h)− βh
dj
dt= αj(1− j)− βj
ENa =RT
Fln(
[ Na+ ]o
[ Na+ ]i
)
αm = .32V + 47.13
1− e−.1(V+47.13)
βm = .08e−
V
11
αh = .135e(V+80)
−6.8
βh =7.5
1+ e−.1(V+11)
αj =.175e
V+100
−23
1+ e.15(V+79)
βj =.3
1+ e−.1(V+32)
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Cardiac ionic models• Surge in development of models of cardiac myocyte
EP over the last 5-10 years.
• 37 models included on Cell ML website through 2004
• ~1/3 in most recent 3 years.
• Multiple models for same species/region.
2004
1995-1997
1960s
20001999
1970s
1990-1994
1980s
20011998
2002
2003
Number of Cardiac EP Models
37 Total Cell ML Site
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• Rodent cardiac myocytes have fundamentally different channel expression levels (especially repolarizing currents). Therefore, transgenic models are not always appropriate.
• Modeling allows one to monitor each component simultaneously – not possible in experiments.
Why use computational modeling for cardiac electrophysiology?
• Dynamics can be observed at resolutions that are unattainable experimentally or clinically.
• It is often cheaper and easier to do so
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Cardiac electrical activity: from one cell to many
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Gap junctions behave according to Ohm’s law
CELL 1 CELL 2I = V/R
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Normal and pathological electrocardiograms (ECG)
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The cause of ventricular arrhythmias• The majority of ventricular arrhythmias are a direct result of the
deterioration of heart tissue resulting from a myocardial infarction (commonly known as a heart attack).
• Arrhythmias are electrical events. Infarctions are mechanical/fluid events.
F. Netter, 1978
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How can scar tissue cause arrhythmias?
Wave propagating in presence of dense scar
Wave propagating in presence of scar with viable, but damaged, tissue within scar
Ventricular tachycardia is usually characterized by reentrant waves of excitation.
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How can scar tissue cause arrhythmias?
Wave propagates around, and into, scar
Wave propagates around, but not into, scar
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How can scar tissue cause arrhythmias?
Wave propagates through scar slowly because the tissue is poorly coupled
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
Waves from either side of the scar merge and propagate beyond scar
Waves from either side of the scar merge and propagate back into scar (excitable waves propagate into any tissue that is viable and non-refractory)
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How can scar tissue cause arrhythmias?
The two intra-scar waves, flowing in opposite directions, annihilate one another. No reentrant rhythm occurs.
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How can scar tissue cause arrhythmias?
Now let’s examine what can happen when an ectopic beat occurs at the “wrong place and wrong time”.
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How can scar tissue cause arrhythmias?
Because the slow conduction zone can also lengthen refractory period, the ectopic wave can block by running into the tail of the preceding wave
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
By the time the ectopic wave reaches the top of the scar, the slow pathway has recovered, and the wave can reenter the scar. A reentrant rhythm ensues.
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
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How can scar tissue cause arrhythmias?
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The electrophysiology study
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EP study – an effort in signal processing and pattern recognition
• Catheters inserted via venous circulation are used to pace and record from localized areas.
• Pacing allows the physician to take control of the heart and probe its function, including:• Induction of arrhythmia via timed stimuli to confirm risk;• Entrainment mapping and pace mapping – techniques that
employ pattern matching to determine when an electrode has been properly positioned to within an arrhythmia circuit;
• CARTO mapping – GPS-like mapping system;• Endocardial Solutions – multielectrode basket catheter.
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One treatment: ablation
Tissue that shouldn’t conduct, sometime does Ablation is a cure !!!
Radiofrequency energy destroys tissue by resistive heating that creates a non-viable lesion.
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Ablation – engineering advances• Cryoablation - reversibly test the effectiveness of an
ablation site with moderately cold temperature; more extreme temperature makes lesion permanent.
• Ultrasound and microwave - which have better depth penetration than radiofrequency ablation.
• Diode lasers - can deliver controlled low energy through a variety of fiber configurations (such as loops) to achieve thin, continuous lesions in and around defined anatomical structures such as valve orifices.
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Implantable cardioverter defibrillator (ICD)
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Implantable CardioverterDefibrillator
(ICD)
Antitachycardia pacing therapy
Defibrillation therapy
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• ICDs don’t always work.• ICD shocks can be painful.• High-power shocks drain batteries quickly.
• The more “turbulent” a system becomes, the more difficult it is to alter that system’s dynamics.
• Can we detect the progression to arrhythmia onset and disrupt it?
• Can we improve the efficacy of low-power therapy (i.e., antitachycardia pacing)?
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ICDs – engineering advances• Size reduction; longevity increase.
• Arrhythmia detection improvement – reduction in false shocks, reducing pain and chronic anxiety.
• Indication expansion – e.g., biventricular pacing for heart failure.
• Incorporation of understanding of arrhythmia nonlinear dynamics into termination algorithms:• The more “turbulent” a system becomes, the more difficult it is
to alter that system’s dynamics.• Can we detect the progression to arrhythmia onset and disrupt
it?• Can we come up with better pacing algorithms?
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How can modeling help us understand cardiac arrhythmias?
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0-dimensional cardiac simulation
(i.e., single cell)
Can be used to investigate rate-
dependence of repolarization
“restitution”
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Restitution hypothesis of alternans
B
C
A
DI APDAPDn = f(DIn-1 )
Incomplete recovery of IK , ICa
Incomplete cycling of Ca2+
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Alternans controlBasic concept: control alternans by applying (small) electrical stimuli at well-timed intervals
Ionic model:
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Small pieces of ventricular tissue:
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Purkinje fiber experiments (length ~2 cm)
Small amplitude alternans: control everywhere
Larger amplitude concordant alternans: control at stimulus end plus some
Discordant alternans: control at stimulus end, concordant alternans
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One-dimensional virtual cardiac fiber
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Propagation of two closely-timed waves down a cable
Dynamical spatial heterogeneity
CV restitution
Incomplete recovery of INa
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Alternans in space
APD
i
i+1
DI
x
i+1
i
i i+1
x=0
x=a
a
a
0
0
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time →
propagationalong the
fiber↓
Why alternans is problematic:Discordant APD alternans to conduction block
modified from R. Gilmour
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Alternans control in spatially extended systems
Purkinje fiber model:
Control off
Control on
Control off
Control on
Alternans suppressed everywhere
Alternans suppressed at stimulus end
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Two-dimensional virtual cardiac tissue
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Reentry and tachyarrhythmias
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Conduction block can induce reentry
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Pastore & Rosenbaum, Circ. Res., 2000
Ionic heterogeneity and alternans
2D sheet
fiber
gto , gKs
Anisotropy
Ionic heterogeneity
Krogh-Madsen & Christini, Biophys. J., 2007
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w/o ionic heterogeneity: effect of SB is minimal
with ionic heterogeneity: presence of SB causes qualitative change in the dynamics
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Three-dimensional virtual cardiac tissue
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Whole organ computational modeling – 3D atria
3D model is built from 2.5-million sets of single-cell kinetic equations, and realistic human atrial geometry.
In addition to anatomical structures such as valves, the model incorporates heterogeneity in conduction characteristics (diffusion coefficient).
Bachmann’s bundle
pectinate muscle
isthmus region
fossa ovalis
Gong & Christini
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Discordant alternans produces a gradient of refractoriness, which causes conduction block and reentry
11
inferior view; isthmus region in green
PV ectopic focus initiation of AF
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Cardiac modeling is fun and worthwhile
Take-home message