Skip to main content
Top

2017 | OriginalPaper | Chapter

Image-Based Modeling of the Heterogeneity of Propagation of the Cardiac Action Potential. Example of Rat Heart High Resolution MRI

Authors : Anđela Davidović, Yves Coudière, Yves Bourgault

Published in: Functional Imaging and Modelling of the Heart

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper we present a modified bidomain model, derived with homogenization technique from assumption of existence of diffusive inclusions in the cardiac tissue. The diffusive inclusions represent regions without electrically active myocytes, e.g. fat, fibrosis etc. We present the application of this model to a rat heart. Starting from high resolution (HR) MRI, geometry is built and meshed using image processing techniques. We perform a study on the effects of tissue heterogeneities induced with diffusive inclusions on the velocity and shape of the depolarization wavefront. We study several test cases with different geometries for diffusive inclusions, and we find that the velocity might be affected by \(5\%\) and up to \(37\%\) in some cases. Additionally, the shape of the wavefront is affected.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
2.
go back to reference Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures. North-Holland Publishing Company, Amsterdam (1978)MATH Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures. North-Holland Publishing Company, Amsterdam (1978)MATH
3.
go back to reference Camelliti, P., Borg, T.K., Kohl, P.: Structural and functional characterisation of cardiac fibroblasts. Cardiovasc. Res. 65(1), 40–51 (2005)CrossRef Camelliti, P., Borg, T.K., Kohl, P.: Structural and functional characterisation of cardiac fibroblasts. Cardiovasc. Res. 65(1), 40–51 (2005)CrossRef
4.
go back to reference Clayton, R.H., Bernus, O., Cherry, E.M., Dierckx, H., Fenton, F.H., Mirabella, L., Panfilov, A.V., Sachse, F.B., Seemann, G., Zhang, H.: Models of cardiac tissue electrophysiology: progress, challenges and open questions. Prog. Biophys. Mol. Biol. 104(1), 22–48 (2011)CrossRef Clayton, R.H., Bernus, O., Cherry, E.M., Dierckx, H., Fenton, F.H., Mirabella, L., Panfilov, A.V., Sachse, F.B., Seemann, G., Zhang, H.: Models of cardiac tissue electrophysiology: progress, challenges and open questions. Prog. Biophys. Mol. Biol. 104(1), 22–48 (2011)CrossRef
5.
go back to reference Coudiere, Y., Davidovic, A., Poignard, C.: The modified bidomain model with periodic diffusive inclusions. In: Computing in Cardiology Conference (CinC), pp. 1033–1036. IEEE (2014) Coudiere, Y., Davidovic, A., Poignard, C.: The modified bidomain model with periodic diffusive inclusions. In: Computing in Cardiology Conference (CinC), pp. 1033–1036. IEEE (2014)
7.
go back to reference Ethier, M., Bourgault, Y.: Semi-implicit time-discretization schemes for the bidomain model. SIAM J. Numer. Anal. 46(5), 2443–2468 (2008)MathSciNetCrossRefMATH Ethier, M., Bourgault, Y.: Semi-implicit time-discretization schemes for the bidomain model. SIAM J. Numer. Anal. 46(5), 2443–2468 (2008)MathSciNetCrossRefMATH
8.
go back to reference Gilbert, S.H., Benoist, D., Benson, A.P., White, E., Tanner, S.F., Holden, A.V., Dobrzynski, H., Bernus, O., Radjenovic, A.: Visualization and quantification of whole rat heart laminar structure using high-spatial resolution contrast-enhanced MRI. Am. J. Physiol. Heart Circulatory Physiol. 302(1), H287–H298 (2012)CrossRef Gilbert, S.H., Benoist, D., Benson, A.P., White, E., Tanner, S.F., Holden, A.V., Dobrzynski, H., Bernus, O., Radjenovic, A.: Visualization and quantification of whole rat heart laminar structure using high-spatial resolution contrast-enhanced MRI. Am. J. Physiol. Heart Circulatory Physiol. 302(1), H287–H298 (2012)CrossRef
9.
go back to reference Mitchell, C.C., Schaeffer, D.G.: A two-current model for the dynamics of cardiac membrane. Bull. Math. Biol. 65(5), 767–793 (2003)CrossRefMATH Mitchell, C.C., Schaeffer, D.G.: A two-current model for the dynamics of cardiac membrane. Bull. Math. Biol. 65(5), 767–793 (2003)CrossRefMATH
11.
go back to reference Neu, J.C., Krassowska, W.: Homogenization of syncytial tissues. Crit. Rev. Biomed. Eng. 21(2), 137–199 (1992) Neu, J.C., Krassowska, W.: Homogenization of syncytial tissues. Crit. Rev. Biomed. Eng. 21(2), 137–199 (1992)
12.
go back to reference Ngoma, D.V., Bourgault, Y., Nkounkou, H.: Parameter identification for a non-differentiable ionic model used in cardiac electrophysiology. Appl. Math. Sci. 9(150), 7483–7507 (2015)CrossRef Ngoma, D.V., Bourgault, Y., Nkounkou, H.: Parameter identification for a non-differentiable ionic model used in cardiac electrophysiology. Appl. Math. Sci. 9(150), 7483–7507 (2015)CrossRef
13.
go back to reference Pandit, S.V., Clark, R.B., Giles, W.R., Demir, S.S.: A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys. J. 81(6), 3029–3051 (2001)CrossRef Pandit, S.V., Clark, R.B., Giles, W.R., Demir, S.S.: A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys. J. 81(6), 3029–3051 (2001)CrossRef
14.
go back to reference Pennacchio, M., Savare, G., Franzone, P.C.: Multiscale modeling for the bioelectric activity of the heart. SIAM J. Math. Anal. 37(4), 1333–1370 (2005)MathSciNetCrossRefMATH Pennacchio, M., Savare, G., Franzone, P.C.: Multiscale modeling for the bioelectric activity of the heart. SIAM J. Math. Anal. 37(4), 1333–1370 (2005)MathSciNetCrossRefMATH
15.
go back to reference Rioux, M., Bourgault, Y.: A predictive method allowing the use of a single ionic model in numerical cardiac electrophysiology. ESAIM Math. Model. Numer. Anal. 47(4), 987–1016 (2013)MathSciNetCrossRefMATH Rioux, M., Bourgault, Y.: A predictive method allowing the use of a single ionic model in numerical cardiac electrophysiology. ESAIM Math. Model. Numer. Anal. 47(4), 987–1016 (2013)MathSciNetCrossRefMATH
16.
go back to reference Relan, J., Pop, M., Delingette, H., Wright, G.A., Ayache, N., Sermesant, M.: Personalization of a cardiac electrophysiology model using optical mapping and MRI for prediction of changes with pacing. IEEE Trans. Biomed. Eng. 58(12), 3339–3349 (2011)CrossRef Relan, J., Pop, M., Delingette, H., Wright, G.A., Ayache, N., Sermesant, M.: Personalization of a cardiac electrophysiology model using optical mapping and MRI for prediction of changes with pacing. IEEE Trans. Biomed. Eng. 58(12), 3339–3349 (2011)CrossRef
Metadata
Title
Image-Based Modeling of the Heterogeneity of Propagation of the Cardiac Action Potential. Example of Rat Heart High Resolution MRI
Authors
Anđela Davidović
Yves Coudière
Yves Bourgault
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-59448-4_25

Premium Partner