Skip to main content
SpringerLink
Log in

A three-compartment non-linear model of myocardial cell conduction block during photosensitization

  • Original Article
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

This study constructed a new non-linear model of myocardial electrical conduction block during photosensitization reaction to identify the vulnerable cell population and generate an index for recurrent risk following catheter ablation for tachyarrhythmia. A three-compartment model of conductive, vulnerable, and blocked cells was proposed. To determine the non-linearity of the rate parameter for the change from vulnerable cells to conductive cells, we compared a previously reported non-linear model and our newly proposed model with non-linear rate parameters in the modeling of myocardial cell electrical conduction block during photosensitization reaction. The rate parameters were optimized via a bi-nested structure using measured synchronicity data during the photosensitization reaction of myocardial cell wires. The newly proposed model had a better fit to the measured data than the conventional model. The sum of the error until the time where the measured value was higher than 0.6, was 0.22 in the conventional model and 0.07 in our new model. The non-linear rate parameter from the vulnerable cell to the conductive cell compartment may be the preferred structure of the electrical conduction block model induced by photosensitization reaction. This simulation model provides an index to evaluate recurrent risk after tachyarrhythmia catheter ablation by photosensitization reaction.

Graphical abstract

A three-compartment non-linear model of myocardial cell conduction block during photosensitization

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data and/or code availability

Once and if the paper is accepted for publication, the production department will put the respective statements in a distinctly identified section clearly visible for readers.

References

  1. Gao B, Langer S, Corry P (1995) Application of the time-dependent Green's function and Fourier transforms to the solution of the bioheat equation. Int J Hyperth 11:267–285

    Article  CAS  Google Scholar 

  2. Lumry R, Eyring H (1954) Conformation changes of proteins. J Phys Chem 58:110–120

    Article  CAS  Google Scholar 

  3. Breen M, Chen X, Wilson D, Saidel G (2002) Modeling cellular thermal damage from radio-frequency ablation. In: Engineering in Medicine and Biology, 2002. 24th Annual Conference and the Annual Fall Meeting of the Biomedical Engineering Society EMBS/BMES Conference, 2002. Proceedings of the Second Joint. IEEE, p 715 vol. 711

  4. Sanchez-Ruiz JM (1992) Theoretical analysis of Lumry-Eyring models in differential scanning calorimetry. Biophys J 61:921

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. Bagaria H, Johnson D (2005) Transient solution to the bioheat equation and optimization for magnetic fluid hyperthermia treatment. Int J Hyperth 21:57–75

    Article  CAS  Google Scholar 

  6. Feng Y, Oden JT, Rylander MN (2008) A two-state cell damage model under hyperthermic conditions: theory and in vitro experiments. J Biomech Eng 130:041016

    Article  PubMed  PubMed Central  Google Scholar 

  7. Fenton FH, Gizzi A, Cherubini C, Pomella N, Filippi S (2013) Role of temperature on nonlinear cardiac dynamics. Phys Rev E 87:042717

    Article  Google Scholar 

  8. Barone A, Carlino MG, Gizzi A, Perotto S, Veneziani A (2020) Efficient estimation of cardiac conductivities: A proper generalized decomposition approach. J Comput Phys 423:109810

    Article  Google Scholar 

  9. Ramírez WA, Gizzi A, Sack KL, Guccione JM, Hurtado DE (2020) In-silico study of the cardiac arrhythmogenic potential of biomaterial injection therapy. Sci Rep 10:1–14

    Article  Google Scholar 

  10. Kappadan V, Telele S, Uzelac I, Fenton F, Parlitz U, Luther S, Christoph J (2020) High-Resolution Optical Measurement of Cardiac Restitution, Contraction, and Fibrillation Dynamics in Beating vs. Blebbistatin-Uncoupled Isolated Rabbit Hearts. Front Physiol 11:464

    Article  PubMed  PubMed Central  Google Scholar 

  11. Barone A, Gizzi A, Fenton F, Filippi S, Veneziani A (2020) Experimental validation of a variational data assimilation procedure for estimating space-dependent cardiac conductivities. Comput Methods Appl Mech Eng 358:112615

    Article  Google Scholar 

  12. Loppini A, Gizzi A, Ruiz-Baier R, Cherubini C, Fenton FH, Filippi S (2018) Competing mechanisms of stress-assisted diffusivity and stretch-activated currents in cardiac electromechanics. Front Physiol 9:1714

    Article  PubMed  PubMed Central  Google Scholar 

  13. Quarteroni A, Lassila T, Rossi S, Ruiz-Baier R (2017) Integrated Heart—Coupling multiscale and multiphysics models for the simulation of the cardiac function. Comput Methods Appl Mech Eng 314:345–407

    Article  Google Scholar 

  14. Gizzi A, Cherubini C, Filippi S, Pandolfi A (2015) Theoretical and numerical modeling of nonlinear electromechanics with applications to biological active media. Commun Comput Phys 17:93–126

    Article  Google Scholar 

  15. Gizzi A, Cherry E, Gilmour RF Jr, Luther S, Filippi S, Fenton FH (2013) Effects of pacing site and stimulation history on alternans dynamics and the development of complex spatiotemporal patterns in cardiac tissue. Front Physiol 4:71

    Article  PubMed  PubMed Central  Google Scholar 

  16. O’Neill DP, Peng T, Stiegler P, Mayrhauser U, Koestenbauer S, Tscheliessnigg K, Payne SJ (2011) A three-state mathematical model of hyperthermic cell death. Ann Biomed Eng 39:570–579

    Article  PubMed  Google Scholar 

  17. Cusimano N, Gizzi A, Fenton F, Filippi S, Gerardo-Giorda L (2020) Key aspects for effective mathematical modelling of fractional-diffusion in cardiac electrophysiology: A quantitative study. Commun Nonlinear Sci Numer Simul 84:105152

    Article  PubMed  Google Scholar 

  18. Weinberg S (2017) Ephaptic coupling rescues conduction failure in weakly coupled cardiac tissue with voltage-gated gap junctions. Chaos 27:093908

    Article  CAS  PubMed  Google Scholar 

  19. Cherubini C, Filippi S, Gizzi A, Ruiz-Baier R (2017) A note on stress-driven anisotropic diffusion and its role in active deformable media. J Theor Biol 430:221–228

    Article  PubMed  Google Scholar 

  20. Hurtado DE, Castro S, Gizzi A (2016) Computational modeling of non-linear diffusion in cardiac electrophysiology: A novel porous-medium approach. Comput Methods Appl Mech Eng 300:70–83

    Article  Google Scholar 

  21. Bueno-Orovio A, Kay D, Grau V, Rodriguez B, Burrage K (2014) Fractional diffusion models of cardiac electrical propagation: role of structural heterogeneity in dispersion of repolarization. J R Soc Interface 11:20140352

    Article  PubMed  PubMed Central  Google Scholar 

  22. Ogawa E, Kurotsu M, Arai T (2017) Irradiance dependence of the conduction block of an in vitro cardiomyocyte wire. Photodiagn Photodyn Ther 19:93–97

    Article  Google Scholar 

  23. Baumeister PA, Lawen T, Rafferty SA, Taeb B, Uzelac I, Fenton FH, Quinn TA (2018) Mechanically-Induced Ventricular Arrhythmias during Acute Regional Ischemia. J Mol Cell Cardiol 124:87–88

    Article  Google Scholar 

  24. Chen DD, Gray RA, Uzelac I, Herndon C, Fenton FH (2017) Mechanism for amplitude alternans in electrocardiograms and the initiation of spatiotemporal chaos. Phys Rev Lett 118:168101

    Article  PubMed  Google Scholar 

  25. Chang M-C, Peng C-K, Stanley HE (2014) Emergence of dynamical complexity related to human heart rate variability. Phys Rev E 90:062806

    Article  CAS  Google Scholar 

  26. Qu Z, Hu G, Garfinkel A, Weiss JN (2014) Nonlinear and stochastic dynamics in the heart. Phys Rep 543:61–162

    Article  PubMed  PubMed Central  Google Scholar 

  27. Sato D, Clancy CE (2013) Cardiac electrophysiological dynamics from the cellular level to the organ level. Biomed Eng Comput Biol 5(BECB):S10960

    Article  Google Scholar 

  28. Cherry EM, Fenton FH (2004) Suppression of alternans and conduction blocks despite steep APD restitution: electrotonic, memory, and conduction velocity restitution effects. Am J Phys Heart Circ Phys 286:H2332–H2341

    CAS  Google Scholar 

  29. Cherry EM, Greenside HS, Henriquez CS (2000) A space-time adaptive method for simulating complex cardiac dynamics. Phys Rev Lett 84:1343

    Article  CAS  PubMed  Google Scholar 

  30. Rappel W-J, Fenton F, Karma A (1999) Spatiotemporal control of wave instabilities in cardiac tissue. Phys Rev Lett 83:456

    Article  CAS  Google Scholar 

  31. Kimura T, Takatsuki S, Miyoshi S, Takahashi M, Ogawa E, Nakajima K, Kashimura S, Katsumata Y, Nishiyama T, Nishiyama N (2016) Electrical superior vena cava isolation using photodynamic therapy in a canine model. Europace 18:294–300

    Article  PubMed  Google Scholar 

  32. Kimura T, Takatsuki S, Miyoshi S, Fukumoto K, Takahashi M, Ogawa E, Ito A, Arai T, Ogawa S, Fukuda K (2013) Non-thermal cardiac catheter ablation using photodynamic therapy. Circ Arrhythm Electrophysiol 6:1025–1031

    Article  CAS  PubMed  Google Scholar 

  33. Kimura T, Takatsuki S, Miyoshi S, Takahashi M, Ogawa E, Katsumata Y, Nishiyama T, Nishiyama N, Tanimoto Y, Aizawa Y (2015) Optimal conditions for cardiac catheter ablation using photodynamic therapy. Europace 17:1309–1315

    Article  PubMed  Google Scholar 

  34. Wada K-I, Itoga K, Okano T, Yonemura S, Sasaki H (2011) Hippo pathway regulation by cell morphology and stress fibers. Development 138:3907–3914

    Article  CAS  PubMed  Google Scholar 

  35. Tunggal JK, Ballinger JR, Tannock IF (1999) Influence of cell concentration in limiting the therapeutic benefit of P-glycoprotein reversal agents. Int J Cancer 81:741–747

    Article  CAS  PubMed  Google Scholar 

  36. Pohlit W (1973) Radiation sensitivity and repair capacity dependent on cell concentration? Biophysik 10:33–37

    Article  CAS  PubMed  Google Scholar 

  37. Broman H, Bilotto G, De Luca CJ (1985) A note on the noninvasive estimation of muscle fiber conduction velocity. IEEE Trans Biomed Eng 32(5):341–344

    Article  CAS  PubMed  Google Scholar 

  38. Silvani A, Bastianini S, Berteotti C, Martire VL, Zoccoli G (2012) Control of cardiovascular variability during undisturbed wake-sleep behavior in hypocretin-deficient mice. Am J Phys Regul Integr Comp Phys 302:R958–R964

    CAS  Google Scholar 

  39. Cohen-Karni T, Timko BP, Weiss LE, Lieber CM (2009) Flexible electrical recording from cells using nanowire transistor arrays. Proc Natl Acad Sci 106:7309–7313

    Article  CAS  PubMed  Google Scholar 

  40. Nakayama S, Sawamura K, Mohri K, Uchiyama T (2011) Pulse-driven magnetoimpedance sensor detection of cardiac magnetic activity. PLoS One 6:e25834

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Ostojic S, Brunel N, Hakim V (2009) How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. J Neurosci 29:10234–10253

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Meyer C, Cv V (2002) Temporal correlations in stochastic networks of spiking neurons. Neural Comput 14:369–404

    Article  PubMed  Google Scholar 

Download references

Acknowledgments

We thank J. Ludovic Croxford, PhD, from Edanz Group (https://en-author-services.edanz.com/ac) for editing a draft of this manuscript.

Author information

Authors and Affiliations

  1. School of Allied Health Science, Kitasato University, Sagamihara, Kanagawa, Japan

    Emiyu Ogawa

  2. Institute of Statistical Mathematics, Tokyo, Japan

    Eitaro Aiyoshi

  3. School of Science and Technology, Keio University, Tokyo, Kanagawa, Japan

    Tsunenori Arai

Authors
  1. Emiyu Ogawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eitaro Aiyoshi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tsunenori Arai
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection, and analysis were performed by Emiyu Ogawa, Eitaro Aiyoshi, and Tsunenori Arai. The first draft of the manuscript was written by Emiyu Ogawa, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Funding

This work was supported in part by the Japan Agency for Medical Research and Development.

Corresponding author

Correspondence to Emiyu Ogawa.

Ethics declarations

Ethics approval

This study had no human participants.

Consent

This study had no human participants.

Conflicts of interest

A research grant from the Japan Agency for Medical Research and Development was awarded to Tsunenori Arai (16im0210204h0002).

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ogawa, E., Aiyoshi, E. & Arai, T. A three-compartment non-linear model of myocardial cell conduction block during photosensitization. Med Biol Eng Comput 59, 703–710 (2021). https://doi.org/10.1007/s11517-021-02329-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11517-021-02329-7

Keywords

Search

Navigation