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author:("Wang, kunji")
1.  Mathematical modeling of left ventricular dimensional changes in mice during aging 
BMC Systems Biology  2012;6(Suppl 3):S10.
Cardiac aging is characterized by diastolic dysfunction of the left ventricle (LV), which is due in part to increased LV wall stiffness. In the diastolic phase, myocytes are relaxed and extracellular matrix (ECM) is a critical determinant to the changes of LV wall stiffness. To evaluate the effects of ECM composition on cardiac aging, we developed a mathematical model to predict LV dimension and wall stiffness changes in aging mice by integrating mechanical laws and our experimental results. We measured LV dimension, wall thickness, LV mass, and collagen content for wild type (WT) C57/BL6J mice of ages ranging from 7.3 months to those of 34.0 months. The model was established using the thick wall theory and stretch-induced tissue growth to an isotropic and homogeneous elastic composite with mixed constituents. The initial conditions of the simulation were set based on the data from the young mice. Matlab simulations of this mathematical model demonstrated that the model captured the major features of LV remodeling with age and closely approximated experimental results. Specifically, the temporal progression of the LV interior and exterior dimensions demonstrated the same trend and order-of-magnitude change as our experimental results. In conclusion, we present here a validated mathematical model of cardiac aging that applies the thick-wall theory and stretch-induced tissue growth to LV remodeling with age.
doi:10.1186/1752-0509-6-S3-S10
PMCID: PMC3524011  PMID: 23281647
2.  Mathematical modeling and stability analysis of macrophage activation in left ventricular remodeling post-myocardial infarction 
BMC Genomics  2012;13(Suppl 6):S21.
Background
About 6 million Americans suffer from heart failure and 70% of heart failure cases are caused by myocardial infarction (MI). Following myocardial infarction, increased cytokines induce two major types of macrophages: classically activated macrophages which contribute to extracellular matrix destruction and alternatively activated macrophages which contribute to extracellular matrix construction. Though experimental results have shown the transitions between these two types of macrophages, little is known about the dynamic progression of macrophages activation. Therefore, the objective of this study is to analyze macrophage activation patterns post-MI.
Results
We have collected experimental data from adult C57 mice and built a framework to represent the regulatory relationships among cytokines and macrophages. A set of differential equations were established to characterize the regulatory relationships for macrophage activation in the left ventricle post-MI based on the physical chemistry laws. We further validated the mathematical model by comparing our computational results with experimental results reported in the literature. By applying Lyaponuv stability analysis, the established mathematical model demonstrated global stability in homeostasis situation and bounded response to myocardial infarction.
Conclusions
We have established and validated a mathematical model for macrophage activation post-MI. The stability analysis provided a possible strategy to intervene the balance of classically and alternatively activated macrophages in this study. The results will lay a strong foundation to understand the mechanisms of left ventricular remodelling post-MI.
doi:10.1186/1471-2164-13-S6-S21
PMCID: PMC3481436  PMID: 23134700
3.  A conceptual cellular interaction model of left ventricular remodelling post-MI: dynamic network with exit-entry competition strategy 
BMC Systems Biology  2010;4(Suppl 1):S5.
Background
Progressive remodelling of the left ventricle (LV) following myocardial infarction (MI) is an outcome of spatial-temporal cellular interactions among different cell types that leads to heart failure for a significant number of patients. Cellular populations demonstrate temporal profiles of flux post-MI. However, little is known about the relationship between cell populations and the interaction strength among cells post-MI. The objective of this study was to establish a conceptual cellular interaction model based on a recently established graph network to describe the interaction between two types of cells.
Results
We performed stability analysis to investigate the effects of the interaction strengths, the initial status, and the number of links between cells on the cellular population in the dynamic network. Our analysis generated a set of conditions on interaction strength, structure of the network, and initial status of the network to predict the evolutionary profiles of the network. Computer simulations of our conceptual model verified our analysis.
Conclusions
Our study introduces a dynamic network to model cellular interactions between two different cell types which can be used to model the cellular population changes post-MI. The results on stability analysis can be used as a tool to predict the responses of particular cell populations.
doi:10.1186/1752-0509-4-S1-S5
PMCID: PMC2880411  PMID: 20522255

Results 1-3 (3)