CLC number: Q66; R540.4

On-line Access: 2014-03-04

Received: 2013-06-10

Revision Accepted: 2013-09-17

Crosschecked: 2014-02-21

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He-qing Zhan, Ling Xia, Guo-fa Shou, Yun-liang Zang, Feng Liu, Stuart Crozier. Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study[J]. Journal of Zhejiang University Science B, 2014, 15(3): 225-242.

@article{title="Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study",

author="He-qing Zhan, Ling Xia, Guo-fa Shou, Yun-liang Zang, Feng Liu, Stuart Crozier",

journal="Journal of Zhejiang University Science B",

volume="15",

number="3",

pages="225-242",

year="2014",

publisher="Zhejiang University Press & Springer",

doi="10.1631/jzus.B1300156"

}

%0 Journal Article

%T Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study

%A He-qing Zhan

%A Ling Xia

%A Guo-fa Shou

%A Yun-liang Zang

%A Feng Liu

%A Stuart Crozier

%J Journal of Zhejiang University SCIENCE B

%V 15

%N 3

%P 225-242

%@ 1673-1581

%D 2014

%I Zhejiang University Press & Springer

%DOI 10.1631/jzus.B1300156

TY - JOUR

T1 - Fibroblast proliferation alters cardiac excitation conduction and contraction: a computational study

A1 - He-qing Zhan

A1 - Ling Xia

A1 - Guo-fa Shou

A1 - Yun-liang Zang

A1 - Feng Liu

A1 - Stuart Crozier

J0 - Journal of Zhejiang University Science B

VL - 15

IS - 3

SP - 225

EP - 242

%@ 1673-1581

Y1 - 2014

PB - Zhejiang University Press & Springer

ER -

DOI - 10.1631/jzus.B1300156

**Abstract: **In this study, the effects of cardiac fibroblast proliferation on cardiac electric excitation conduction and mechanical contraction were investigated using a proposed integrated myocardial-fibroblastic electromechanical model. At the cellular level, models of the human ventricular myocyte and fibroblast were modified to incorporate a model of cardiac mechanical contraction and cooperativity mechanisms. Cellular electromechanical coupling was realized with a calcium buffer. At the tissue level, electrical excitation conduction was coupled to an elastic mechanics model in which the finite difference method (FDM) was used to solve electrical excitation equations, and the finite element method (FEM) was used to solve mechanics equations. The electromechanical properties of the proposed integrated model were investigated in one or two dimensions under normal and ischemic pathological conditions. fibroblast proliferation slowed wave propagation, induced a conduction block, decreased strains in the fibroblast proliferous tissue, and increased dispersions in depolarization, repolarization, and action potential duration (APD). It also distorted the wave-front, leading to the initiation and maintenance of re-entry, and resulted in a sustained contraction in the proliferous areas. This study demonstrated the important role that fibroblast proliferation plays in modulating cardiac electromechanical behaviour and which should be considered in planning future heart-modeling studies.

**
**

1. Introduction

Owing to the close relationship between myocardium electrical and mechanical activities, cardiac-coupled electromechanical models were developed, in from one to three dimensions, for both normal and pathological situations (Usyk and McCulloch,

However, these cardiac models describe only the properties of cardiac myocytes. Other types of cells, such as those in vasculature and connective tissues, (Manabe et al.,

In this study, a strongly coupled myocardial-fibroblastic electromechanical model is proposed to investigate the effect of fibroblasts on cardiac excitation conduction and contraction. The proposed model integrates the coupling between a fibroblast model (Xie et al.,

2. Materials and methods

Correspondingly, the cytosolic concentration of Ca

For fibroblast electrophysiology, two previously proposed models can simulate the main characteristics of the fibroblasts (Chilton et al.,

To the best of our knowledge, there is no well-defined mathematical model to describe the tension in fibroblasts. The main reasons are that: (1) There is lack of experimental data due to the small size of individual fibroblasts (Brown et al.,

At the tissue level, the fibroblasts and myocytes are assembled into a 2D tissue sheet and the electrophysiological and mechanical coupling is calculated to simulate the excitation conduction and deformation in the heart.

The equation of myocyte-fibroblast electrophysiological modeling is expressed as (Xie et al.,

For tissue mechanics, the mechanical model of cardiac tissue should contain the mechanics of normal myocyte tissue and fibroblast proliferous tissue. The mechanical model proposed by Nash and Panfilov (

Because fibroblast proliferation occurs after a myocardial infarction and cardiac fibroblast proliferous remodeling leads to a progressive increase in ventricular passive stiffness (Conrad et al.,

The main framework of the proposed coupling model has been described in detail. It integrates two kinds of models (electrophysiological and mechanical models), two kinds of cells (myocytes and fibroblasts), and two spatial levels (cellular and tissue levels). The proposed model includes the sum of the ordinary differential equations (ODEs) and partial differential equations (PDEs), which requires a large computational effort.

The system was solved numerically using custom software written in Fortran language. At the cellular level, all state variables were updated by the forward Eular method. The FDM was applied to solve the reaction-diffusion equation. Following each time integration step, all parameters of cells were updated. The active stress was then interpolated at the four-node rectangle isoparametric element Gaussian points. The stresses of these active Gaussian points served as the inputs to the governing equations of the tissue mechanics model. The stress equilibrium equation was solved by a nonlinear least square iteration method with different material constants from different tissues.

In simulations, the electromechanical properties of a single human myocardial cell and a fibroblast were first computed using the proposed integrative model, and were then compared to the original characteristics of the corresponding electrophysiological and mechanic models—ten Tusscher and the Rice models. Second, the influence of diffuse fibroblast proliferation on plane wave propagation in 2D tissue was investigated. Third, the electromechanical coupling of a central point stimulus with two spatial resolutions, two temporal resolutions, two gap junction conductances, and two fibroblast membrane conductances was simulated and compared, to investigate the effect of various parameters on depolarization and repolarization times, APD, strain maps, and temporal traces of strain in different points of the tissue. Finally, the electromechanical coupling of the re-entry and strain maps was simulated. The spatial configuration of normal tissue and fibroblast proliferous tissue is illustrated in Fig.

3. Results

The AP and Ca

Model |
V
_{rest} (mV) |
V
_{max_plateau} (mV) |
dV/dt
_{max} (mV/ms) |
APD (ms) | Ca_{i_max} (μmol/L) |

Proposed | −86.20 | 20.18 | 287 | 289 | 0.59 |

ten Tusscher | −87.30 | 22.68 | 288 | 279 | 0.70 |

As given in Eq. (

Compared to the AP of the uncoupled myocyte, the peak of the myocyte AP of the coupled model decreased from 36.3 to 26.5 mV, with the coupled ventricular APD increasing from 289 to 335 ms (Fig.

Fig.

Figs.

Temporal resolution, Δt (ms) |
Depolarization dispersion (ms) |
Repolarization dispersion (ms) |
APD dispersion (ms) |
|||

Normal | Fibroblast proliferation | Normal | Fibroblast proliferation | Normal | Fibroblast proliferation | |

0.005 | 32 | 40 | 25 | 30 | 8 | 10 |

0.01 | 45 | 55 | 40 | 45 | 8 | 10 |

From Fig.

The histograms of APD dispersions shown in Fig.

Fig.

Figs.

In Fig.

4. Discussion

Coupling the human ventricular myocyte with fibroblasts in this study also modulated APD. In previous studies, both “passive” and “active” fibroblasts resulted in diverse effects on APD. Xie et al. (

In addition to the effect on human ventricular myocyte electrophysiology, coupled fibroblasts had implications for changes in

For spiral wave simulations, once fibroblast proliferation presented in the 2D tissue, the spiral wave did not propagate along its inherent directions and had to bypass fibroblast proliferous tissues. In this way, the fibroblast proliferation changed the form of the re-entry. In addition, because of the presence of the fibroblasts, the CV slowed (Miragoli et al.,

5. Conclusions

* Project supported by the National Basic Research Program (973) of China (No. 2007CB512100) and the National Natural Science Foundation of China (Nos. 81171421 and 61101046)Compliance with ethics guidelines He-qing ZHAN, Ling XIA, Guo-fa SHOU, Yun-liang ZANG, Feng LIU, and Stuart CROZIER declare that they have no conflict of interest.

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