Purkinje on Opencarp

Question

Hi everyone,

In the last openCARP user meeting I asked the question regarding how to make a conduction / purkinje system work in openCARP. I got the answer that a 1D mesh (Purkinje) connected with 1D elems to the myocardial tetrahedral mesh might do the trick and I promised to give some updates about this. So, as a man of my word, I tried to make it work but sadly I could not propagate the stimulus from the Purkinje fiber to the myocardium, as it halted in the purkinje-muscular-junction (PMJ). As myocardium I used a parallelepiped with 100 um resolution and as purkinje a line of 1D elems with the same 100 um mesh. As said, I connected both in an unique mesh and simulated with the monodomain equation. 

Here there are all my files:

opencarp purkinje

in /indiv_meshes you can find all the myocardium meshes I tried with different overall sizes. 

in /opencarp you'll find the small and simple sample already assemble with its .elem .pts .lon files and the .vtx stimulation file. Moreover there is the .par file with all settings. 

in /opencarp/results there are the results for the example simulation and in /opencarp/paraview there are the results in paraview .case format

the python script "setup_opencarp.py" basically combines the selected purkinje and myocardial meshes in /indiv_meshes with 1D elems from an extreme of the purkinje line to the myocardial nodes near a certain distance and puts all files in /opencarp

Obviously I tried different things that's why it took my so long to report here (sorry). I tried the following:

- I incremented the conductivity difference between the purkinje and myocardium above 100 times (default was ten times) =>  block in the PMJ.

- I incremented the stimulation magnitude as well as the duration => divergence or really deformed AP was reached.

- I tried the same cell type for purkinje-myo: tenTusscher-tenTusscher or Steward-Steward rather than Steward-tenTusscher, for avoiding the Vm gradient around the PMJ. In Steward-Steward myocardium depolarized simultaneously thanks to the automaticity in the cell model but did not followed the depolarization from the purkinje. On tenTusscher-tenTusscher  stimulus blocked in the PMJ.

- I set the purkinje-contacting tetrahedrons in the myocardium with the Steward model => block in the PMJ.

- I set isotropic conductivities in both domains and in both tissues => block in the PMJ

- I tried a more complex biventricular model with realistic conduction / purkinje system with coarse and thin resolution with all the aforementioned tests =>  same results.

- I played with gNa, gK in Steward and tenTusscher to try to reduce the source-sink mismatch =>  block in the PMJ

- I tried different myocardium overall size meshes to reduce the source sink mismatch =>  block in the PMJ even in the case with a cube of 100 um side-length.

- I tried, to use a Boltzmann curve to gracefully switch the monodomain conductivity in the last ten nodes of the purkinje from 1.2 to 0.12 as done in Dux-Santoy et al "Modeling the Different Sections of the Cardiac Conduction System to

Obtain Realistic Electrocardiograms" =>  block in the PMJ

- Moreover, I stimulated the myocardium => the stimulus traveled to the purkinje fiber (this tells me the mesh generation and simulation setting might be all right I guess) but it was impossible to get this in the other way around :(.

Maybe I am missing something or mistaking some configuration. If you have any ideas on what can be the problem or how to debug/analyse this better please let me know :D.

Thank you in advance.

 

Answer 1

Hello

It may be impossible to stimulate myocardium from a single node. There is a liminal length concept which says a certain amount of tissue needs to be excited before it is self sustaining.

So, you could try branching the Purkinje system and form several junctions. Maybe test before with a simple stimulus to see how many you need.

---

Cheers

Ed

Comments

Thanks, Ed.

I will follow your suggestion and get back to this thread as soon as possible.

Maxi

---

Hi!

Finally I got back to this and I did some experiments.

First of all, I saw the other question raised in the Q&A regarding this, where the depolarization halted when propagating from a Line (Ln elems) to a Cuboid (Tt elems) (https://opencarp.org/q2a/1124/the-problem-of-excitation-conduction-from-line-to-cuboid) I replicated the results obtained in this question, so I was able to propagate from a line to a cuboid but the cuboid had to be really small and made by just a few Tt elems.

I will try to summarize the results I obtained testing on this simple line+cuboid and on a more realistic conduction system + myocardium domain:

1- Tentusscher cellular model for line and cuboid (same result with DrouhardRoberge)

stim_amp = 120 uA/cm2 (on two nodes in the beginining of the line)

cuboid size = 5um

cuboid resolution = 5um

line size = 300um

line resolution = 50um

conductivity: isotropic in all domain and magnitude matching in line and cuboid (same result with transversal isotropy)

one extra Ln elem for connection between line a cuboid

PROPAGATION

2- Tentusscher cellular model for line and cuboid (same result with DrouhardRoberge)

stim_amp = 120/250 uA/cm2

cuboid size = 10um

cuboid resolution = 5um

line size = 300um

line resolution = 50um

conductivity: isotropic in all domain and magnitude matching in line and cuboid (same results with transverse isotropy)

one extra Ln elem for connection between line a cuboid

BLOCK

3- Tentusscher cellular model for cuboid and Stewart for Line

stim_amp = 250 uA/cm2

cuboid size = 10um

cuboid resolution = 5um

line size = 300um

line resolution = 50um

conductivity: isotropic in all domain and magnitude matching in line and cuboid

one extra Ln elem for connection between line a cuboid

PROPAGATION

4- Tentusscher cellular model for cuboid and Stewart for Line

stim_amp = 250 uA/cm2

cuboid size = 50um

cuboid resolution = 5um

line size = 300um

line resolution = 50um

conductivity: isotropic in all domain and magnitude matching in line and cuboid (same results for isotropic conductivities 10 and 100 times higher for the line with respect to the cuboid)

one extra Ln elem for connection between line a cuboid (same results for increased number of connections between the line and the cuboid)

BLOCK

Then, as conduction seems to block in such a tiny cuboid (50um side). I tried Edward's suggestion. Basically, I created a simplified but more realistic domain (https://drive.google.com/file/d/1QRuAPNNGU4mxzrU4MN7QArozgiVjBo6U/view?usp=sharing) consisting the conduction system (CS) and a finer apex-like myocardium mesh. Here, I branched the CS in order to have high density of pmjs (see image). The results are:  

5- Tentusscher cellular model for Myo and Stewart for CS

stim_amp = 250 uA/cm2 on the tip of the CS

myo resolution = 320um mean edge length

CS resolution = 200um mean edge length

conductivity: isotropic in all domain and magnitude = 0.24, myo_g_mult = 0.01 and CS_g_mult = 10

Endnodes of the CS are connected to nodes in the myocardium if they are located as near as 1 mm.

BLOCK

6- Tentusscher cellular model for Myo and Stewart for CS

stim_amp = 250 uA/cm2

myo resolution = 320um mean edge length

CS resolution = 200um mean edge length

conductivity: isotropic in all domain and magnitude = 0.24, myo_g_mult = 0.1 and CS_g_mult = 300

Endnodes of the CS are connected to nodes in the myocardium if they are located as near as 1 mm.

BLOCK

7- Tentusscher cellular model for Myo and Stewart for CS

stim_amp = 250 uA/cm2

myo resolution = 320um mean edge length

CS resolution = 200um mean edge length

conductivity: isotropic in all domain and magnitude = 0.24, myo_g_mult = 0.01 and CS_g_mult = 300

Endnodes of the CS are connected to nodes in the myocardium if they are located as near as 0.09 mm (CS end node connected with only one myocardial node).

BLOCK

Then, as I read the comment from Axel (https://opencarp.org/q2a/1124/the-problem-of-excitation-conduction-from-line-to-cuboid) and the paper he referred, I applied a conductivity gradient in the endbranches of the CS similarly to Dux-Santoy et al, "Modeling the different sections of the cardiac conduction system to obtain realistic electrocardiograms" (see Figure showing the elem tags of the domain https://drive.google.com/file/d/1jEDqG5L4zzOWhdEX28w7lnIbnnx4PSa3/view?usp=sharing))

8- Tentusscher cellular model for Myo and Stewart for CS

stim_amp = 250 uA/cm2

myo resolution = 320um mean edge length

CS resolution = 200um mean edge length

conductivity: isotropic in all domain and magnitude varied from 2.4 in the CS to 0.24 in myo. The gradient was applied in the CS endbranches as mentioned.

Endnodes of the CS are connected to nodes in the myocardium if they are located as near as 1 mm.

BLOCK

As summary, I only could obtain actual propagation of the depolarization when the myocardium/cuboid was extremely small. This does not seem realistic for me, so if you have any suggestion on what can I be doing wrong or what else to try I will try to solve this.

Thank you in advanced for yor feedback :D

Maxi

Answer 2

Just for the record,

There is this paper 10.1109/TBME.2011.2162841, where they use a fast marching method formulation for modelling wave propagation only through element edges in both the conduction system (purkinje) and the myocardium. This gave me the (probably naive) idea to use line elements in the myocardium which avoided the source-sink mismatch. This idea is supported by the authors stating that with their formulation "the data pass through the connecting edges across nodes, similar to what happens at cell level for intercellular ionic exchange". So I tried to have a myocardium made of tets and lines far and near the pmjs, respectively, but as soon as you put tets (even if more than 50% of the myo is modelled with lines) the block seems inevitable.

Videos of the results can be seen in the following presentation

pmj_line_myo_results_presentations

Comments

Hi Maxi,

it seems like the source-sink-mismatch to go from a line to a 3d element is always too big bc the amount of current delivered to the myocardium is not enough to stimulate it. I think @jorge.sanchez solved this by introducing a resistance in the PMJs. There is a branch (316-add-purkinje-system) in the openCARP git. It's a work in progress and not yet finished but maybe you can look into that.