Restitution portrait:

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Restitution portrait
a new technique for investigating restitution
properties of periodically-paced cardiac tissue

• Elena Tolkacheva
• Duke University,
• Department of Physics
• Durham NC

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Talk Outline

• Introduction cardiac dynamics and
• APD restitution
• Memory in cardiac tissue
• Restitution Portrait
• experiment
• mathematical modeling
• Conclusions and future directions

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Cardiac dynamics
Major problem of cardiac dynamics is to
understand mechanisms causing cardiac electrical
instabilities (fibrillation) and sudden cardiac
death
Whole heart small pieces of cardiac
tissue fibrillation alternans
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Dynamics of periodically-paced cardiac tissue
Pacing protocol sequences of small external
stimulus
Responses transmembrane voltage
small pieces of cardiac tissue
time (s)
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Dynamics typical responses
Action Potential Duration Diastolic
Interval Basic Cycle Length
stimulus
stimulus
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Normal responses (11) and alternans (22)
Normal response (11)
Alternans
All action potentials identical
Long-short alternation of APD
Analysis Plot bifurcation diagram and
restitution curve
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Bifurcation diagram and restitution curve (RC)
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11
?
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22
Restitution relation alternans occur when slope
of restitution curve gt 1
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Restitution hypothesis

• Does it always work?
• No memory in cardiac tissue
• What can we do about it?
• New technique restitution portrait

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Memory in cardiac tissue
The presence of memory means that APD depends
not only on preceding DI but also on previous
history of the paced cardiac tissue

• Experimental results contradict theory
• failure of restitution relation
• slope of the RC does not predict the onset of
  alternans
• rate-dependent restitution
• RC depends on pacing protocol by which it is
  measured
• APD accommodation
• it take up to several minutes for APD to reach
  steady-state

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Failure of restitution relation

• Steep restitution
• stable 11 response
• Rabbit (Banville et al. JCE 131141,2002)
• Frog (G.M. Hall et al. PRL, 822995, 1999)
• Shallow restitution alternans
• Dog (Koller et al. AJP 44H1635, 1998., and
  others)

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Rate-dependent restitution
Pacing protocols
Dynamic (steady-state) Dynamic RC
S1-S2 (standard) S1-S2 RC

• Steady-state responses
• to a change in BCL
• Unique dynamic RC

• Immediate responses
• to a change in BCL
• Different S1 gt different RCs

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Rate-dependent restitution

• Different RCs have
• different slopes
• What slope we have to
• measure to predict
• alternans?

V. Elharrar, B.Surawicz, Am. J. Physiol. 244,
H782 (1983)
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More aspects of cardiac dynamics?

• S1-S2 RC Immediate response to a change in BCL
• Dynamic RC Steady-state response to a change in
  BCL
• What about the transient responses?
• CONSTANT-BCL RESTITUTION

Response to sustained change in BCL
Response to perturbation
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Wealth of Information

• Four types of restitution curves
• 1 Dynamic
• S1-S2s for different S1-S1 cycle lengths
• CBs for sustained changes in BCL (CB-D)
• CBs for perturbations in BCL (CB-S)
• How can we assess all this information?

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Cardiac dynamics in presence of memory new
approach
Present approach fails to describe cardiac
dynamics in presence of memory New approach
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New pacing protocol
design to measure all different RCs at each BCL
key information
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New pacing protocol
CB-D D S CB-S S CB-S

• Dynamic RC (D) at different B slope Sdyn
• S1S2 RC (S) slope S12
• Constant-BCL RC
• after change in B (CB-D) slope SCB-D
• after small perturbation (CB-S) slope SCB-S

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Experimental results responses at given BCL

• dynamic
• S1-S2
• CB-D
• CB-S

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Restitution portrait 11 responses
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Restitution portrait transient alternans
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Slopes of different restitution curves 11
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Modeling Restitution

• Problem
• Restitution condition was derived mathematically
  based
• on an incomplete model where there is only one
• restitution curve
• Our goal
• Find a similar model
• Reproduce experimental restitution
• Develop a criterion for stability (prediction of
  onset of alternans)

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Mapping models

• simple enough in compare to ionic models
• be derived on the basis of ionic models
• restitution relation can be derived directly

An1 function (previous states)
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Different types of mapping models

• One-dimensional mapping model without memory
• One-dimensional mapping model with memory
• Two-dimensional mapping model with memory

M E M O R Y
classical
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Restitution portraits
Experiment
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Stability of 11 response
Present restitution relation
Unique restitution curve
The slope of the restitution curve determines
stability of the 11 response
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New restitution relation
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New restitution relation
Individual slopes of the restitution curves do
not predict the onset of alternans
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Conclusions
We propose a new method for measuring multiple
aspects of cardiac dynamics in presence of
memory the restitution portrait
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Conclusions
We show that all RCs describe different aspects
of cardiac dynamics in presence of memory and
have to be measured simultaneously at each BCL
We derive a new restitution relation showing that
stability of the normal cardiac rhythm depends on
combination of the slopes of different types of
restitution curves measured simultaneously
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Future directions

• Develop methods to assess risk for cardiac
  arrhythmias
• Understand ionic mechanism of memory
• Obtain a restitution portrait for different
  species, including human heart
• cellular level
• tissue level
• whole heart

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Acknowledgements
Duke University

• Physics BME
• Dan Gauthier Wanda Krassowska
• Hana Dobrovolny Soma Kalb
• Mathematics Pediatric Cardiology
• David Schaeffer Salim Idriss
• John Cain