Spontaneous Initiation and Termination of Reentry (SITR) Patterns

In a Loop of Cardiac Ventricular Tissue

Project Dated 2004-2008

 

The centerpiece of the project is a discrete, threshold model of reentrant circulation of an action potential in a loop of ventricular tissue subject to pacing by natural or artificial mechanisms. The project was initiated by Mark Wood (now deceased) and Hassan Sedaghat of the Virginia Commonwealth University and was partially funded by Medtronic, Inc.

 

Project participants in alphabetical order:

            Clive M. Baumgarten, Ph.D., Pauley Heart Center, VCU Health System

            John W. Cain, Ph.D., Department of Mathematics, University of Richmond

            David M. Chan, Ph.D., Department of Mathematics and the Center for the Study of Biological Complexity

            Chao-Kun Cheng, Ph.D., Department of Computer Science, VCU

            Candace M. Kent, Ph.D., Department of Mathematics and the Center for the Study of Biological Complexity

            Hassan Sedaghat, Ph.D., Department of Mathematics and the Center for the Study of Biological Complexity

            Mark A. Wood, M.D., Pauley Heart Center, VCU Health System

            Ena Y. Xiao, undergraduate student and research assistant

 

Project Publications:

·         Sedaghat, H., Wood, M.A., Cain, J.W., Cheng, C.K., Baumgarten, C.M., Chan, D.M. (2008) “Complex patterns of spontaneous initiation and termination of reentry in a loop of cardiac tissue,” J. Theo. Biol. 254, 14-26 http://arxiv.org/abs/0803.2698

·         Sedaghat, H., Kent, C.M., Wood, M.A. (2005) “Criteria for the convergence, oscillations and bistability of pulse circulation in a ring of cardiac tissue,” SIAM J. Appl. Math., 66, 573-590

 

The Model’s Description (PDF)

            (Notes on the project background and the model, plus various case-studies and simulations some of which appear in the aforementioned paper)

 

Supplements to case-studies in Model’s Description (additional runs)

 

 

Note: In the following simulations files “T4” refers to the TC threshold and “T3” is TP. See the Model’s Description above for definitions of TC and TP. “T2” is also TC but when the current beat is in paced mode (T2 is not reflected in mode sequences as T3 and T4 are). Also UDC or UDCP means the paced mode in the Model’s Description.

 

Numerical Simulation Files using C-K. Cheng’s code:

  1. Fixed period pacing, homogeneous loop and graphs
  2. Fixed period pacing-Effects of delta, homogeneous loop and graphs
  3. Fixed period pacing, heterogeneous loop and graphs with corrections
  4. Variable period pacing-Multistability effects, homogeneous loop
  5. Slow pacing rate, heterogeneous loop
  6. Effects of increasing the length of pacing cycle, homogeneous loop

 

Numerical Experiments:

  1. Runs summaries with graphs by J.W. Cain
  2. Runs summaries 1 by Ena Xiao and David Chan (Excel file, general study)
  3. Runs summaries 2 by Ena Xiao and David Chan (Excel file, slow pacing, various loop lengths)
  4. Mathcad worksheets showing 4 different stable patterns depending on initial DI values only (all other parameter values unchanged):

·         Multistable reentry, quasiperiodic pattern, all cells’ initial DI = 80

·         Multistable reentry, aperiodic pattern, all cells’ initial DI = 70

·         Multistable reentry, convergent pattern, all cells’ initial DI = 60

·         Multistable reentry, periodic pattern, all cells’ initial DI = 50

·         The Mathcad worksheet to create the above patterns and more (needs the Mathcad software to run)

 

Notes:

·         Taking Math to the Heart: Reentrant Pulse in a Discrete Loop  

(Reentrant circulation in a loop of cardiac tissue as a discrete dynamical system)

 

 

Email hsedagha@vcu.edu with comments or requests.

 

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