Stimulus not properly stimulating

Question

Hi,
I have been working on a stimulus setup that is performing an extracellular stimulus (open or closed) of a large-tissue block submerged in a bath that is meant to mimic a piece of ventricular tissue. The mesh tissue has been tuned and has induced reentry using the psd function from the 02_EP_Tissue/21_reentry_induction example for 600ms, then I applied the stimulus to try to terminate the rotor. I have tried out the various configurations of both electrodes and types from the 02_EP_Tissue/02_stimulus example, but currently, the best result I got is seeing some slight effects on the tissue near the stimulation site, and they are not strong or sustained enough to significantly perturb or terminate the rotor. My current setup uses three different electrodes: a stimulus on the epicardial side selected from a grid based on electrical potential (crct type 2), some grounding electrodes across the bath face on the endocardial side (crct type 3), and aux electrodes on the endocardial side (crct type 0), and the stimulation strength is 1000 mV for 2ms, using Tomek20Land17_DynSarc ionic model, conduction velcority 0.57 and 0.24, tissue size 5cm by 5cm by 12mm, with 3mm bath, resolution 250 mircons. I wonder why my stimulation does not work and how the stimulation should be configured—whether through the electrode arrangement, grounding configuration, stimulation waveform, or other parameters—to produce a sufficiently strong and sustained effect that can successfully interrupt the rotor.

Answer 1

Hey,

Two things that come to my mind:

1. Are you actually solving bidomain?

The extracellular potential stimuli are only really active if you solve the bidomain equations. Check first if you set bidomain = 1 and that the bath/intra/extra regions are assigned properly.

2. Field strength is too low

Looking at the field gradient in the tissue (V/cm) is what matters here. If I understand it correctly, you want to defibrillate the tissue to stop or perturb the arrhythmia. Defibrillation scale capture needs somewhere in the area of 3-5 V/cm across the tissue. Your 1000mV across 5cm (assuming that's the endo-epi distance) is in the area of 0.2 V/cm, likely less since part of it drops across the bath and not the tissue.

So check if bidomain = 1. If yes, increase the voltage on your stimulating electrode quite a bit and measure the voltage drop across the tissue.

Best,

Tobias

Comments

Hi,

Thank you so much for the response. To answer your questions,
1. Yes, I have set it up using bidomain = 1 and I believe my regions are assigned properly.
2. I have tried to increase my stimulation strength, but somehow it always lead to a divergence error that will always make the simulation fail after the stimulation is applied. The error message I received is L5: parabolic PDE (PETSc) solver diverged. Reason: NaN or inf encountered. I wonder why is that happening and how could I fix it?

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Hey,

I reproduced your problem on a smaller mesh with the Tomek20Land17_DynSarc ionic model so numbers etc can differ for your setup.

What's happening:

The ODEs of the ionic model are blowing up under the electrode that hyper polarizes the tissue. That's why you see NaN values which causes the solver to fail. For this particular ionic model, it seems that IKr blows up first. Once Vm passes -150mV, IKr goes 0.53 → −5.5 → 57.5 → −627 → 6715 → −1.2e5 → −2.0e6 → −8.4e19 → NaN. That alternating-sign geometric growth is a classic explicit-integration instability. The cause: IKr is a Markov model, and its states are integrated with forward Euler (Rush-Larsen only covers the HH-type gates). One of the transition rates is

beta = 0.2442*exp(-1.604*vfrt) 

which doubles every 11.5 mV of hyperpolarization. Forward Euler requires dt < 2/beta. That limit is about 0.9 µs at −152 mV, 0.1 µs at −190 mV, and ~0.003 µs at −250 mV.

What you can try:

Lowering dt is not a practical solution. Without changing the ionic models ODE integration, your only option is limiting the hyperpolarization. You can do that by using a biphasic pulse. You get a comparable effect with lower peak polarization. But I am honestly not sure if that will be enough.

Either way, add a trace_node in the tissue close to your source and ground electrodes. Measure what kind of values you see in your setup.

Hope that helps a bit