# Talk:Scroll wave turbulence

This mini-review provides a good survey of scroll wave turbulence. It could be completed by mentionning two further points.

The first one is the connection between the all-important sign of the scroll line tension and the direction of spiral drift in an external electric field (1,2). This is particularly interesting since the drift direction of a spiral in an electric field has been shown to change as a function of the medium excitability (3).

The second one is the control of scroll turbulence. In particular, possible control by a weak non-resonant modulation could be mentionned (4).

(1) Spiral drift in an external field was observed by

Agladze K I, de Kepper P, J Phys Chem 96 5239 (1992) and


Steinbock O et al Phys. Rev. Lett. 68, 248 (1992). (2) The connection between spiral drift in an external field

was noted in Hakim V,  Karma A Phys. Rev. E 60, 5073-5105 (1999)


and studied in detail in Henry H, Hakim V Phys Rev E 65, 046235 (2002) (3) This was pointed out in Krinsky V, Hamm E, Voignier V Phys. Rev. Lett. 76, 3854-3857 (1996). The exact location of this drift direction change has subsequently been understood as a resonance between the spiral rotation frequency and the meander instability frequency (the imaginary part of the meander modes)in H Henry Phys Rev E 70, 026204 (2004). (4) This was pointed out Alonso S, Sagues F, Mikhailov AS, Science 299, 1722-1725 (2003); a general review of control of turbulence in chemical systems is Mikhailov AS, Showalter K, Physics Reports 425, 79-194 (2006).

This is a nice review on scroll wave turbulence. However, I miss a few points, that could broaden the scope of the article.

Although the title of the review is "scroll wave turbulence", it is mostly centered on the instabilities that give rise to this state. I think that it could be worth to discuss what is known about the statistical properties of SWT, as for instance the change in time of the number and length of the filaments, their lifetime, etc. Also, how this state differs from 2D spiral break-up, and if its properties are different depending on the originating mechanism. Some work on this can be found in:

R.H. Clayton, A.V. Holden, Phys. Med. Biol. 47, 225 (2002); 47, 1777 (2002).

R.H. Clayton, CHAOS 18, 043127 (2008)

R.H. Clayton, E.A. Zhuchkovab, A.V. Panfilov, Prog. Bio. Mol. Bio. 90, 378 (2006)

R.M. Zaritski, S.F. Mironov, A.M. Pertsov, PRL 92, 168302 (2004)

J. Davidsen, M. Zhan, R. Kapral PRL 101, 208302 (2008)

As a second point, I wonder if the review should be focused only on excitable media, or it should include SWT found in oscillatory media. In fact, the definition that is given for SWF ("Self-sustained regime in excitable media mediated by three-dimensional instability of scroll waves") implies that this is a property of excitable systems, which I find too narrow. See, for instance:

J.C. Reid, H. Chate, J. Davidsen, EPL 94, 68003 (2011)

and also

G. Rousseau, H. Chaté, R. Kapral, Chaos 18, 026103 (2008)

This article gives a brief overview of what is currently known about scroll wave turbulence. There are two things I would suggest for consideration. The first one is to extend the list of the cited literature on controlling scroll wave turbulence (e.g. PRL 94, 188301 (2005)). The second one is that there seems to be a slight contradiction in what is stated with respect to the finite-wavenumber instability. In the introduction, it is stated that this instability is known to lead to SWT in excitable media, yet, in the corresponding subsection on the finite-wavenumber instability only SWT in oscillatory media are mentioned. This should be clarified. There are also some minor typos. Please check all double brackets and replace "However, it is now..." by "However, it is not..." in the section on the negative filament tension.

In my opinion this review on scroll wave turbulence is concise and correct. It is well written and it looks already complete. I would like to add only several corrections and suggestions.

I think that the main comment is the lack of motivation with respect the dynamics of arrhythmias in cardiac tissue. For example explain that cardiac tissue is excitable and 3D and reentrant waves may take the form of scroll waves. Scroll waves can produce tachycardia and unstable 3D waves are associated with fibrillation. Also it may be interesting to note that cardiac tissue is typically highly excitable. I recommend to add a couple of sentences at the end of the overview paragraph.

I miss the reference H. Dierckx and H. Verschelde Effective dynamics of twisted and curved scroll waves using virtual filaments Phys. Rev. E 88, 062907 (2013) where the theory of filament dynamics has been improved.

I would add that spiral waves rotate around a circular core in the 3rd line before write that "Scroll waves rotate around filaments".

Omega is not defined as the rotation frequency after eq.(2).

Two paragraphs after eq.(5) there is a equivalence between scroll rings and spiral waves in an electric field. Please note that is is only true for scroll rings with large radius.

In the section SWT mediated by negative filament tension, correct form "However, it is now known" to "However, it is not known".

At the end of the same paragraph change from "existing scrolls" to "existing scroll waves" because other types of scrolls (for example rings) will disappear with the forcing.

If references are organized by alphabetic order, Dierckx (2009) should be before Fenton's papers.

REFEREE 1


> The first one is the connection between the all-important sign of the > scroll line tension and the direction of spiral drift in an external > electric field (1,2).

DONE: the current text states "Filament tension can be defined via the asymptotic rate of collapse or expansion of scroll rings of large radius and exact axial symmetry, in which case the problem becomes mathematically equivalent to that of a drift of a spiral wave in an electric field"

> The second one is the control of scroll turbulence. In particular, > possible control by a weak non-resonant modulation could be mentionned > (4).

DONE: the current text states "They focused on super-resonant case with stimulation frequency higher than that of the scrolls. Such stimulation can sometimes effectively reverse the sign of filament tension from negative to positive, thus stopping the breeding of scroll waves and "taming" the SWT."

> (1) Spiral drift in an external field was observed by > Agladze K I, de Kepper P, J Phys Chem 96 5239 (1992) and > Steinbock O et al Phys. Rev. Lett. 68, 248 (1992).

good references; but they belong to the article "Spiral wave drift", not here.

> (2) The connection between spiral drift in an external field (and > the filament tension? - VNB) was noted in Hakim V, Karma A > Phys. Rev. E 60, 5073-5105 (1999) and studied in detail in Henry H, > Hakim V Phys Rev E 65, 046235 (2002)

> This is particularly interesting since the drift direction of a spiral > in an electric field has been shown to change as a function of the > medium excitability (3). > (3) This was pointed out in Krinsky V, Hamm E, Voignier V Phys. Rev. > Lett. 76, 3854-3857 (1996).

DONE: added Krinsky et al 1996, but also Panfilov and Rudenko 1987 and Brazhnik et al 1987.

> The exact location of this drift direction change has subsequently > been understood as a resonance between the spiral rotation frequency > and the meander instability frequency (the imaginary part of the > meander modes)in H Henry Phys Rev E 70, 026204 (2004).

DONE: added a paragraph saying nearly that.

> The second one is the control of scroll turbulence. In particular, > possible control by a weak non-resonant modulation could be mentionned > (4). > (4) This was pointed out Alonso S, Sagues F, Mikhailov AS, Science > 299, 1722-1725 (2003); a general review of control of turbulence in > chemical systems is Mikhailov AS, Showalter K, Physics Reports 425, > 79-194 (2006).

DONE. First, mentioned possible link to fibrillation, to motivate elimination as a goal. Then mentioned both resonant and non-resonant approaches.

REFEREE 2

> Although the title of the review is "scroll wave turbulence", it is > mostly centered on the instabilities that give rise to this state. I > think that it could be worth to discuss what is known about the > statistical properties of SWT, as for instance the change in time of > the number and length of the filaments, their lifetime, etc. Also, how > this state differs from 2D spiral break-up, and if its properties are > different depending on the originating mechanism. Some work on this > can be found in: ...

DONE: added two new sentences, starting with "Comparative statistical analalysis of numerical solutions of SWT..." and a few references to support.

As a second point, I wonder if the review should be focused only on excitable media, or it should include SWT found in oscillatory media. In fact, the definition that is given for SWF ("Self-sustained regime in excitable media mediated by three-dimensional instability of scroll waves") implies that this is a property of excitable systems, which I find too narrow. See, for instance ...

DONE: (i) mention oscillatory media in the topmost definition; (ii) ditto, in the introductory paragraph, (iii) new section "SWT due to finite wavenumber instability" is mostly about oscillatory media, and the two suggested references included there.

REFEREE 3

> The first one is to extend the list of the cited literature on > controlling scroll wave turbulence (e.g. PRL 94, 188301 (2005)).

> The second one is that there seems to be a slight > contradiction in what is stated with respect to the finite-wavenumber > instability. In the introduction, it is stated that this instability > is known to lead to SWT in excitable media, yet, in the corresponding > subsection on the finite-wavenumber instability only SWT in > oscillatory media are mentioned. This should be clarified.

DONE: the offending phrase in the introduction replaced by "three-dimensional mechanisms of SWT in excitable and oscillatory media"; and the term autowave in the short definition is spelled out as "excitable or oscillatory").

> There are also some minor typos. Please check all double brackets and > replace "However, it is now..." by "However, it is not..." in the > section on the negative filament tension.

DONE.

REFEREE 4

> I think that the main comment is the lack of motivation with respect > the dynamics of arrhythmias in cardiac tissue. For example explain > that cardiac tissue is excitable and 3D and reentrant waves may take > the form of scroll waves. Scroll waves can produce tachycardia and > unstable 3D waves are associated with fibrillation. Also it may be > interesting to note that cardiac tissue is typically highly > excitable. I recommend to add a couple of sentences at the end of the > overview paragraph.

DONE; comment re high excitability of cardiac tissue inserted not to the overview paragraph but to where its context is more evident.

> I miss the reference > H. Dierckx and H. Verschelde > Effective dynamics of twisted and curved scroll waves using virtual filaments > Phys. Rev. E 88, 062907 (2013) > where the theory of filament dynamics has been improved.

> I would add that spiral waves rotate around a circular core in the 3rd > line before write that "Scroll waves rotate around filaments".

DONE; only without 'circular', not to exclude meander.

> Omega is not defined as the rotation frequency after eq.(2).

DONE, "rotation frequency" for omega added.

> Two paragraphs after eq.(5) there is a equivalence between scroll > rings and spiral waves in an electric field. Please note that is is > only true for scroll rings with large radius.

DONE: "large scroll rings" replaced with "scroll rings of large radius"

> In the section SWT mediated by negative filament tension, correct form > "However, it is now known" to "However, it is not known".

DONE.

> At the end of the same paragraph change from "existing scrolls" to > "existing scroll waves" because other types of scrolls (for example > rings) will disappear with the forcing.

DONE, "scrolls" replaced with "scroll waves if they are not scroll rings topologically."

> If references are organized by alphabetic order, Dierckx (2009) should > be before Fenton's papers.

DONE.