Mathematical modeling of the fibrosis process in the implantation of inferior vena cava filters

Nicolás, M.; Peña, Estefanía; Malvè, Mauro; Martı́nez, Miguel Ángel

doi:10.1016/j.jtbi.2015.09.028

Cited by 9 publications

(7 citation statements)

References 40 publications

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“…The synthetic SMC evolution equation is as follows: where c ssmc (r, z, t) is the synthetic SMC concentration, D ssmc is the diffusion coefficient of synthetic SMCs in order to simulate the migration process, k prolif,ssmc is the proliferation rate of synthetic SMCs in response to GFs and k apop,ssmc is the apoptosis rate at which synthetic SMCs die. The initial density of synthetic SMCs in the arterial wall, c ssmc,0 , is assumed to be equal to zero [38].…”

Section: Synthetic Smooth Muscle Cellsmentioning

confidence: 99%

“…where r ec is the typical radius of an EC, and r smc and l smc are the typical radius and the length of an SMC, respectively as shown in table 3. This growth process has been defined following the method described for the development of atherosclerotic plaque in [36] and the fibrosis process after the implantation of an inferior vena cava filter in [38], respectively.…”

Section: Tissue Growthmentioning

confidence: 99%

“…Other continuum mathematical biological models typically comprise a series of coupled diffusion-reaction equations for describing the biological interaction between several species. Such models have been developed to describe phenomena such as neointimal hyperplasia formation [32], atherosclerotic plaque formation [33][34][35][36], fibrotic tissue formation surrounding medical implants [37,38] and, more recently, ISR [39] and arterial physiopathology [40]. In contrast to discrete models where cell behaviour is usually described by a set of rules, continuum models offer a mechanistic description, featuring physical parameters which may in principle be measured.…”

Section: Introductionmentioning

confidence: 99%

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Mathematical modelling of the restenosis process after stent implantation

Escuer

Martı́nez

McGinty

et al. 2019

J. R. Soc. Interface.

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The stenting procedure has evolved to become a highly successful technique for the clinical treatment of advanced atherosclerotic lesions in arteries. However, the development of in-stent restenosis remains a key problem. In this work, a novel two-dimensional continuum mathematical model is proposed to describe the complex restenosis process following the insertion of a stent into a coronary artery. The biological species considered to play a key role in restenosis development are growth factors, matrix metalloproteinases, extracellular matrix, smooth muscle cells and endothelial cells. Diffusion–reaction equations are used for modelling the mass balance between species in the arterial wall. Experimental data from the literature have been used in order to estimate model parameters. Moreover, a sensitivity analysis has been performed to study the impact of varying the parameters of the model on the evolution of the biological species. The results demonstrate that this computational model qualitatively captures the key characteristics of the lesion growth and the healing process within an artery subjected to non-physiological mechanical forces. Our results suggest that the arterial wall response is driven by the damage area, smooth muscle cell proliferation and the collagen turnover among other factors.

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Section: Synthetic Smooth Muscle Cellsmentioning

confidence: 99%

Section: Tissue Growthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mathematical modelling of the restenosis process after stent implantation

Escuer

Martı́nez

McGinty

et al. 2019

J. R. Soc. Interface.

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“…The TrapEase filter was found to capture smaller volumes of annular thrombi against the vessel wall that subsequently decreased the wall shear stress patterns. Intimal hyperplasia and decreased hemodynamic clot lysis are posited as the results of low wall shear stress due to recirculating flow patterns and struts that contact larger areas of IVC wall (12).…”

Section: Predicting Ivc Filter Functionmentioning

confidence: 99%

Computational evaluation of inferior vena cava filters through computational fluid dynamics methods

Rajan

Makary

Martyn

et al. 2021

Diagn Interv Radiol

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A dvanced computing technology increasingly allows the expeditious calculation of solutions to complex problems. Three-dimensional (3D) finite element modeling and computational fluid dynamics, although historically time consuming and expensive, are becoming more accessible and thus more frequently utilized in improving medical devices (1).Finite element analysis (FEA) involves first modeling the system being analyzed with discrete elements, each of which allows for the variable being studied (e.g., stress, temperature, flow) to be approximated within its domain. After modeling is complete, a numerical matrix is assembled, which represents both the properties of the individual elements and the inter-relationships between the surrounding elements. Finally, known constraints on the problem (e.g., internal pressures) are applied as boundary conditions, and numerical techniques are used to solve the system of equations represented by the matrix. This solution leads to an approximation of the variable being studied (Fig. 1). This method is particularly useful for finding solutions in complex geometries for which closed-form solutions may not exist. Computational fluid dynamics (CFD) is a similar numerical technique used to estimate the behavior of fluids in complex geometries. CFD can be used to model blood flow through the vasculature and around intravascular devices to aid in decision making (2). Computational methods are typically less time-consuming and more cost-effective than some of the current alternatives to testing medical devices in vitro.Today, 3D simulation is used for designing, positioning, and testing devices (3). One such device is the inferior vena cava (IVC) filter, used to trap emboli from the lower extremities when medical anticoagulation is contraindicated. Complications of IVC filter placement include cava wall perforation, intimal hyperplasia, thrombosis, strut fracture, and embolization. Understanding the dynamic environment that IVC filters are placed in, in a patient-specific manner, could potentially decrease the occurrences of these complications (Fig. 2). Evaluating credibility of CFD in medical device designComplex CFD methods have the potential to change how we practice patient centered medicine; however, they must first be shown to accurately reflect the scenarios that they model. The reliability of these methods must be verified before they can be used to affect biomedical design and clinical practice. The American Society of Mechanical Engineers (ASME) recently released the V&V 40, a set of standards that outlines a framework to assess ABSTRACT Numerical simulation is growing in its importance toward the design, testing and evaluation of medical devices. Computational fluid dynamics and finite element analysis allow improved calculation of stress, heat transfer, and flow to better understand the medical device environment. Current research focuses not only on improving medical devices, but also on improving the computational tools themselves. As methods and computer technology allow ...

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“…Discrete and continuous models of SMC behaviour during in-stent restenosis have been developed by several research groups (Lally and Prendergast, 2006;Evans et al, 2008;Zahedmanesh et al, 2014;Tahir et al, 2015). Researchers have also developed models of the vascular SMC response to surgical interventions such as vein grafting (Budu-Grajdeanu et al, 2008;Garbey et al, 2017) and blood filter insertion (Nicolas et al, 2015). The tissue repair carried out by artery wall SMCs in response to vascular injury also shares several similarities with the process of dermal wound healing.…”

Section: Introductionmentioning

confidence: 99%

A Multiphase Model of Growth Factor-Regulated Atherosclerotic Cap Formation

Watson¹,

Byrne²,

Macaskill³

et al. 2019

Preprint

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Atherosclerosis is characterised by the growth of fatty plaques in the inner (intimal) layer of the artery wall. In mature plaques, vascular smooth muscle cells (SMCs) are recruited from the adjacent medial layer to deposit a cap of fibrous collagen over the fatty plaque core. The fibrous cap isolates the thrombogenic content of the plaque from the bloodstream and prevents the formation of blood clots that cause myocardial infarction or stroke. Despite the important protective role of the cap, the mechanisms that regulate cap formation and maintenance are not well understood. It remains unclear why certain caps become stable, while others become vulnerable to rupture.We develop a multiphase PDE model with non-standard boundary conditions to investigate collagen cap formation by SMCs in response to growth factor signals from the endothelium. Diffusible platelet-derived growth factor (PDGF) stimulates SMC migration, proliferation and collagen degradation, while diffusible transforming growth factor (TGF)-β stimulates SMC collagen synthesis and inhibits collagen degradation. The model SMCs respond haptotactically to gradients in the collagen phase and have reduced rates of migration and proliferation in dense collagenous tissue. The model, which is parameterised using a range of in vivo and in vitro experimental data, reproduces several observations from studies of plaque growth in atherosclerosis-prone mice. Numerical simulations and model analysis demonstrate that a stable cap can be formed by a relatively small SMC population and emphasise the critical role of TGFβ in effective cap formation and maintenance. These findings provide unique insight into the cellular and biochemical mechanisms that may lead to plaque destabilisation and rupture. This work represents an important step towards the development of a comprehensive in silico plaque.

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Mathematical modeling of the fibrosis process in the implantation of inferior vena cava filters

Cited by 9 publications

References 40 publications

Mathematical modelling of the restenosis process after stent implantation

Mathematical modelling of the restenosis process after stent implantation

Computational evaluation of inferior vena cava filters through computational fluid dynamics methods

A Multiphase Model of Growth Factor-Regulated Atherosclerotic Cap Formation

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