Multi-Scale Modeling and Analysis of Left Ventricular Remodeling Post Myocardial Infarction: Integration of Experimental and Computational Approaches

Abstract

Progressive remodeling of the left ventricle (LV) following myocardial infarction (MI) involves spatiotemporal interactions among multiple cell types and the extracellular matrix environment. Despite the extensive experimental studies designed to elucidate the regulatory mechanisms, there is a growing recognition that the complexity of LV remodeling precludes the efficient identification of early diagnostic indicators after myocardial infarction. Currently, systemic approaches are needed to reduce this complexity. Previous studies in other systems demonstrate that establishing a multi-scale analytical model of LV remodeling response to MI will likely help in the development of prognostic therapies. In this review, we discuss the current approaches used for mathematical modeling of the LV, advantages and disadvantages of the approaches, and methods used to validate these models.

Mathematical modeling and stability analysis of macrophage activation in left ventricular remodeling post-myocardial infarction

“…A Hill equation is employed to represent this self-inhibition effect and parameter c 1 denotes the self-inhibition effect of IL-10 post-MI [6,17]. Parameter $d_{I{L}_{10}}$ denotes the decay rate of IL-10 determined by its half-life time [13]. …”

“…Cellular densities of M1 and M2 macrophages were considered as the outputs of the system. We chose IL-1, IL-10, and TNF- α as three molecules which regulate macrophage activations in this mathematical model since they were well-recognized as stimuli for macrophage activation [ 13 - 15 ]. M1 macrophages and myocytes secrete IL-1 and TNF- α .…”

“…Secretion function is denoted by thick arrow, activation and differentiation are denoted by thin arrow. The regulatory relationship shown in the framework was determined by published results [ 3 , 13 - 17 ].…”

Coupled Immunological and Biomechanical Model of Emphysema Progression

“…This literature (Ignotz and Massagué, 1986 ; Onozaki et al, 1988 ; Oliver et al, 1993 ; Bellingan et al, 1996 ; Tsutsumi et al, 1996 ; Darby et al, 1997 ; Meng and Lowell, 1997 ; Hehenberger et al, 1998 ; Horio et al, 1998 ; Cobbold and Sherratt, 2000 ; Steinmüller et al, 2000 ; Eberhardt et al, 2002 ; Huang et al, 2002 ; Maass et al, 2002 ; Zhang et al, 2003 ; Mantovani et al, 2004 ; Porcheray et al, 2005 ; Tanaka et al, 2005 ; Edwards et al, 2006 ; Lenga et al, 2008 ; Marino et al, 2008 ; Moro et al, 2008 ; Jin and Lindsey, 2010 ; Wang et al, 2012 ) is reported in Reference section and it is associated to the different biological parameteres considered in Table 1 . We focus mainly on the well-vetted interactions between different types of macrophages, pro- and anti-inflammatory cytokines, fibroblasts, collagen deposition and degradation, neutrophils and elastase production.…”