Target-wave to spiral-wave pattern transition in a discrete Belousov-Zhabotinsky
reaction driven by inactive resin beads
Guanqun Wang,
1
Qingsheng Wang,
2,
*
Peng He,
1
Srinivasa Pullela,
1
Manuel Marquez,
3,4
and Zhengdong Cheng
1,†
1
Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122, USA
2
Department of Fire Protection and Safety, Oklahoma State University, Stillwater, Oklahoma 74078-8016, USA
3
YNano LLC, 14148 Riverdowns South Drive, Midlothian, Virginia 23113-3796, USA
4
Escuela de Ingenierıas, Universidad de Malaga, C/Pedro Oritz Ramos, s/n 29071 Malaga, Spain
Received 22 June 2010; published 13 October 2010
Wave pattern formation and transition in chemical and biochemical reaction systems can reveal the system
properties. We investigate the pattern transition from target waves to spiral waves upon the increment of
inactive beads in a discrete system model, where ion-exchange resin loaded with Belousov-Zhabotinsky cata-
lyst corresponds to the active beads. The results show that inactive beads slow the propagation speed of target
waves and increase the wave frequency. As the population of inactive beads increases, clusters are formed,
which then break waves into segments where bounded spiral pairs are generated and separated into individual
spirals. From this observation, we conclude that the population of inactive resin beads acts as the bifurcation
parameter controlling the wave pattern transition from targets to spirals.
DOI: 10.1103/PhysRevE.82.045201 PACS numbers: 89.75.Kd, 82.40.Bj, 47.54.-r, 05.45.-a
I. INTRODUCTION
Spiral and target waves appear spontaneously in biologi-
cal excitable media e.g., heart tissue 1–3, in disordered
media 4, and in nonlinear chemical reactions e.g., the
Belousov-Zhabotinsky BZ reaction 5,6. Wave pattern
transition phenomena in excitable media reveal how dynam-
ics are organized in a system 7,8. Due to the heterogene-
ities of biological systems, discrete systems with nonlinear
chemical elements would be closely related analogs 9–11.
Research on nonlinear waves in discrete systems, however, is
less common than that on homogeneous excitable media
5,6. Inactive elements, specifically, heterogeneous features,
frequently exist in discrete excitable systems. For example,
fibrotic nonexcitable “dead” tissue normally presents at a
small percentage of normal heart tissue. As a result of aging,
after a myocardial infarction heart attack, or in the case of
cardiac myopathies, the percentage of fibrotic tissue in-
creases dramatically, up to 30– 40 % 12,13.
Interesting observations show that there is a wave-form
change from plane wave to multiple spiral wavelets accom-
panying the procession from normal sinus rhythm to ven-
tricular tachycardia, and finally to ventricular fibrillation
14. Also, in a monolayer of chick embryonic heart cells,
transition has been observed from target to spiral waves 7.
Both wave pattern transitions might be caused by increased
heterogeneities of the environment on which the wave pat-
terns are generated and propagated, but the mechanism
which gives rise to arrhythmias is still not clear. Insight into
the dynamics of spirals in bioexcitable media and the under-
standing of the genesis of spiral waves and their interactions
would offer insight into the development of effective ap-
proaches to interrupt arrhythmias. In this Rapid Communica-
tion, we address such wave pattern transitions using a simple
heterogeneous BZ reaction as a system model. Due to the
poor understanding of the transition between different wave
patterns, it would be of great interest to investigate how the
wave pattern transition is driven by inactive resin beads.
II. EXPERIMENTS
Belousov-Zhabotinsky active beads were fabricated by
immersion of polystyrene ion-exchange beads Acros Organ-
ics, Morris Plains, NJ in a 0.025 M aqueous solution of
ferroin Sigma-Aldrich, Milwaukee, WI in a capped glass
bottle. Ferroin, with the molecular formula as
Feo-phen
3
SO
4
, where o-phen is an abbreviation for 1,10-
phenanthroline, serves as the catalyst for BZ reactions. The
loading of ferroin into the resin beads was completed in 10 h,
yielding a colorless solution. The beads were then filtered
and dried in an oven at 50 ° C overnight. The concentration
of catalyst in active beads was 25 mol / g based on the
assumption that 100% catalyst was immobilized. The BZ
reactants for all experiments are aqueous solutions of sulfuric
acid J. T. Baker, Philipsburg, NJ0.25 M, malonic acid
Sigma-Aldrich, Milwaukee, WI0.025 M, and sodium
bromate 0.25 MSigma-Aldrich, Milwaukee, WI, which
are typical excitable systems based on previous experiments
by Maselko et al. 11,15,16.
In our experiments, an amount of 10 g of polystyrene ion
exchange resin beads 11 was added to 50 mL of the BZ
reactants in which the percentage of active beads was var-
ied from 0.2 to 1. In detail, active beads, inactive beads, and
50 mL of the BZ reactants were well mixed and the beads
precipitated. The mixture was placed in a 9-cm-diameter
beaker. The thickness of bead bed was about 5 mm and the
depth of the reactants plus the beads, about 1.5 cm. The size
of the beads was between 75 to 150 m. A camera installed
1.5 m directly above the beaker took images every 10 s in a
dark room maintained at 15 ° C. The wavelength of the ob-
served wave in the beads layer is about 2 mm. Three-
dimensional effects might affect the dynamics of the waves,
but were not explored in our experiments.
*
qingsheng.wang@okstate.edu
†
Corresponding author; cheng@chemail.tamu.edu
PHYSICAL REVIEW E 82, 045201R2010
RAPID COMMUNICATIONS
1539-3755/2010/824/0452014 ©2010 The American Physical Society 045201-1