Exploring the Formation of Alzheimer's Disease Senile Plaques in Silico

Edelstein‐Keshet, Leah; Spiros, Äthan

doi:10.1006/jtbi.2002.2540

Cited by 63 publications

(63 citation statements)

References 85 publications

(82 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present simulation, we used for the cytokine diffusivity the value d A = 10 −4 cm 2 /h. Indeed this value is the order of magnitude of TNF diffusivity in the extracellular space of the brain used in Edelstein- Keshet and Spiros (2002), and is also the order of magnitude of LDL diffusivity in the arterial walls taken in Vincent et al (2009). As for the immune cell diffusivity d M , we used a value smaller than d A , namely d M = 10 −5 cm 2 /h.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Reaction–diffusion model of atherosclerosis development

et al. 2011

View full text Add to dashboard Cite

Atherosclerosis begins as an inflammation in blood vessel walls (intima).The inflammatory response of the organism leads to the recruitment of monocytes. Trapped in the intima, they differentiate into macrophages and foam cells leading to the production of inflammatory cytokines and further recruitment of white blood cells. This self-accelerating process, strongly influenced by low-density lipoproteins (cholesterol), results in a dramatic increase of the width of blood vessel walls, formation of an atherosclerotic plaque and, possibly, of its rupture. We suggest a 2D mathematical model of the initiation and development of atherosclerosis which takes into account the concentration of blood cells inside the intima and of pro-and antiinflammatory cytokines. The model represents a reaction-diffusion system in a strip with nonlinear boundary conditions which describe the recruitment of monocytes as a function of the concentration of inflammatory cytokines. We prove the existence of travelling waves described by this system and confirm our previous results which suggest that atherosclerosis develops as a reaction-diffusion wave. The theoretical results are confirmed by the results of numerical simulations.

show abstract

Section: Numerical Simulationsmentioning

confidence: 99%

Reaction–diffusion model of atherosclerosis development

et al. 2011

View full text Add to dashboard Cite

show abstract

“…Through its functional specifications of cell behavior, our can potentially bridge the current gap between intracellular descriptions and infection dynamics models. Similar approaches have been used to model a variety of host-pathogen systems ranging from general immune system simulation platforms [12,13,14,15,16] to models of specific diseases including tuberculosis [17,18], Alzheimer's disease [19], cancer [20,21,22,23,24,25], and HIV [26,27].…”

Section: Agent-based Modelingmentioning

confidence: 99%

Modeling Influenza Viral Dynamics in Tissue

Beauchemin

Forrest

Koster

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…The mechanism of formation of Aβ fibrils has been modelled by several groups: Kinetics of Aβ aggregation has been described using mathematical models 12, 13, 14, 39, 54, 55.Activated microglia increases the production of Aβ through the secretion of Interleukin‐1 (IL‐1) whilst quiescent microglia helps to maintain Aβ production within a healthy range. Neuroinflammation associated with AD has been quantitatively investigated 41.…”

Section: Resultsmentioning

confidence: 99%

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Lloret-Villas

Varusai

Juty

et al. 2017

CPT Pharmacom & Syst Pharma

View full text Add to dashboard Cite

Neurodegenerative diseases are a heterogeneous group of disorders that are characterized by the progressive dysfunction and loss of neurons. Here, we distil and discuss the current state of modeling in the area of neurodegeneration, and objectively compare the gaps between existing clinical knowledge and the mechanistic understanding of the major pathological processes implicated in neurodegenerative disorders. We also discuss new directions in the field of neurodegeneration that hold potential for furthering therapeutic interventions and strategies.

show abstract

Exploring the Formation of Alzheimer's Disease Senile Plaques in Silico

Cited by 63 publications

References 85 publications

Reaction–diffusion model of atherosclerosis development

Reaction–diffusion model of atherosclerosis development

Modeling Influenza Viral Dynamics in Tissue

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Contact Info

Product

Resources

About