Mila Gorobets – Schulich School of Engineering

Faculty Mentor: Dr. A Nygren

Setup of Reentrant Activity in Diabetic Cardiac Tissue

OutlineIntroduction: What is this all about?Methods: models, software and parametersProceduresResultsObservations and DiscussionConclusionsLimitations of this study

IntroductionType I diabetes presents additional cardiac

risks, such as arrhythmiasIrregular excitation can cause reentrant

activity to occur, potentially resulting in arrhythmias

IntroductionSeveral components can vary in cardiac

myocytes:

Gap junction lateralization: migration of gap junctions from ends of cells to the sides

ATP-dependent potassium current (IKATP ): opens in response to situations where ATP is lacking (eg ischemia)

Extracellular potassium concentration: rise in concentration will present several risk factors, such as action potential duration (APD) prolongation and elevation in resting voltage

Methods: ModelMyocyte models by Pandit et al were used

for healthy and diabetic tissuesThe models are based on systems of

differential equations describing gating variables and currents

Formulation for IKATP was obtained from Shaw & Rudy and added to the model

Methods: Software2D tissue simulations were done using the

Cardiac Arrhythmia Research Package (CARP)

1cm x 1cm piece of tissue was used

Single cell simulations carried out with an implementation in C using the Sundial’s CVODE package

Methods: Parameters: [K+]o Values of 5.4 mM and 9.0 mM used in

simulationsSteady-state values of gating variables at

different levels of extracellular K were obtained using single-cell implementation to speed up 2D simulations

Methods: Parameters: ConductanceConductance was used to represent gap

junction lateralization

gL refers to the longitudinal conductance

gT refers to the transverse conductance

Methods: Parameters: ConductanceThree setups used:

Normal: 90/10% split between gL and gT

Functional lateralized: 50/50% split between gL and gT

Nonfunctional lateralized: 50/10% split between gL and gT

Healthy myocytes always had 90/10% conductance ratio

Methods: Parameters: IKATPConductance of the

channel was chosen based on critical values obtained: 0.002 µS at 5.4 mM [K+]o, 0.006 µS at 9.0 mM [K+]o.

Simulations were done with the channel open and closedHealthy

5.4 mM [K+]o

Diabetic

5.4 mM [K+]o

Methods: Simulation Sets

[K+]o = 5.4 mM

[K+]o = 9.0 mM

Diabetic

Healthy

Diabetic

Healthy

No IKATP

No lateralization

Lateralization (non functional)

Lateralization (functional)

With IKATP

No lateralization

Lateralization (non functional)

Lateralization (functional)

Procedure: Stimulus deliveryS1-S2 protocol was usedS1 propagated transversely through the

tissue (downward)S2 originated in the top right corner of the

tissueOccupied ¼ of the tissue in areaS1 S2

Procedure: ReentryReentry considered successful when S2

travelled around at least once to its originDelay between S1 and S2 initiations was

notedValue was called the window of vulnerabilityDefined by range tL ≤ t ≤ tU, where t is time

where reentry is possible

Procedure: Reentry

Procedure: Lack of reentry

t<tL

t> tU

Results: Reentry at 5.4 mM

Results: Reentry at 5.4 mM

Results: Reentry at 9.0 mM No reentry was observed at this

concentration of extracellular potassiumWave propagation did not occur with IKATP

Waveform below was observed between t<tL and t>tU

Observations: Reentry at 5.4 mM No IKATP

Greatest risk: Healthy tissue – 13 ms window of vulnerability

Lowest risk: Diabetic tissue, functional lateralized gap junctions (1 ms)

IKATP

Greatest risk: Healthy tissue, and diabetic with nonfunctional lateralized gap junctions – 22 ms window of vulnerability

Lowest risk: Diabetic tissue, functional lateralized gap junctions (8 ms)

Discussion: Reentry at 5.4 mM Isotropic tissue (ie, diabetic tissue with 50/50%

functional gap junctions) is at constant advantageIsotropic tissue has been reported to be less prone

to reentry

Possible reason:Increase in transverse conductance leads to an

increase in conduction velocity in that directionLess time for tissue to become excitable following

S2’s originationS2 spiral bumps into its refractory tail and cannot

propagate

Discussion: Reentry at 5.4 mM Diabetic tissue has smaller window of

vulnerability than healthy tissueCan be due to the fact that while it has

slower conduction velocity, it also has a greater action potential duration – greater wavelengthLower susceptibility to reentry

Discussion: Reentry at 5.4 mM Diabetic tissue with nonfunctional

lateralized gap junctions is at a slight disadvantage compared to diabetic tissue with regular conductanceLateralization of gap junctions reduced

longitudinal conduction velocityLower conduction velocity means more time

for tissue to become excitableExcitable tissue can facilitate APs and

reentrant circuits

Discussion: Reentry at 5.4 mM Delays between S1 and S2 become smaller

as IKATP is introducedIKATP reduces APD, hence decreasing

wavelengthS2 needs to arrive sooner after S1 than

without IKATP to encounter refractory boundary

Discussion: Reentry at 5.4 mM Elevation of the resting potential could

account for the small difference in lower bracket values between healthy and diabetic tissuesThreshold voltage could be surpassed sooner

after S1 than expectedRequired sufficient stimulus current

Discussion: Reentry at 9.0 mM Propagation was possible, but no reentry

was achievedReentry could have occurred within a very

small window (time step used was 1 ms)Reentry might require other cardiac events

In simulations, elevation of potassium resulted in an environment that did not favour reentrant circuits

ConclusionsDiabetic tissues are not necessarily at a

disadvantage with respect to facilitating reentry in certain conditions

Lateralization of functional gap junctions results in an advantageous environment

Anisotropic tissue facilitates reentry more readily than isotropic does

Opening of the IKATP channel increases the risk of instantiating reentrant circuits in cardiac tissue

LimitationsTime step was taken to be 1 ms: could add

inaccuracies

Investigated a narrow band of parametersMultiple cardiac events could take place

Rat ventricular myocyte models were used – applications to studies of humans are limited

Acknowledgements- Dr Nygren for the mentoring over the past

10 months- Dr Vigmond and Patrick Boyle for help with

CARP

- Markin USRP in Health & Wellness for providing this valuable studentship