Related papers: Reaction-Diffusion-Delay Model for EPO/TNF-$\alpha…
We present a model of articular cartilage lesion formation to simulate the effects of cyclic loading. This model extends and modifies the reaction-diffusion-delay model by Graham et al. 2012 for the spread of a lesion formed though a single…
In previous works, the author and collaborators establish a mathematical model for injury response in articular cartilage. In this paper we use mathematical software and computational techniques, applied to an existing model to explore in…
Mounting evidence for the role of oxidative stress in the degeneration of articular cartilage after an injurious impact requires our modeling & simulation efforts to temporarily shift from just describing the effect of mechanical stress and…
The initial reaction of the body to pathogenic microbial infection or severe tissue trauma is an acute inflammatory response. The magnitude of such a response is of critical importance, since an uncontrolled response can cause further…
Epithelial tissues form physically integrated barriers against the external environment protecting organs from infection and invasion. Within each tissue, epithelial cells respond to different challenges that can potentially compromise…
A severe application of stress on articular cartilage can initiate a cascade of biochemical reactions that can lead to the development of osteoarthritis. We constructed a multiscale mathematical model of the process with three components:…
Recent experiments in epithelial wound healing have demonstrated the necessity of Mitogen-activated protein kinase (MAPK) for coordinated cell movement after damage. This MAPK activity is characterized by two wave-like phenomena. One MAPK…
Mechanical stress-induced damage to the articular cartilage can result in fracture imitation or significant tissue degeneration leading to osteoarthritis (OA) compromising joint mobility. Despite the clinical significance, a comprehensive…
Multiple Sclerosis is a chronic autoimmune disorder characterized by the degradation of the myelin sheath in the central nervous system, leading to neurological impairments. In this work, we analyze a reaction-diffusion model derived from…
We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines,…
Degradation of joint cartilages can result in osteoarthritis (OA) affecting about 10\% of the US population and responsible for significant hospitalization costs. While observations show that low dose radiation treatments (LDRT) bring…
We present a mathematical study for the development of Multiple Sclerosis in which a spatio-temporal kinetic { theory} model describes, at the mesoscopic level, the dynamics of a high number of interacting agents. We consider both…
Endovenous laser therapy (ELT) as a minimally invasive procedure for ablation of large superficial veins, nevertheless, can cause complications of thrombotic nature. In this regard, the study of the main patterns of thrombus formation…
Periodic hematological diseases such as cyclical neutropenia or cyclical thrombocytopenia, with their characteristic oscillations of circulating neutrophils or platelets, may pose grave problems for patients. Likewise, periodically…
When they are damaged or injured, soft biological tissues are able to self-repair and heal. Mechanics is critical during the healing process, as the damaged extracellular matrix (ECM) tends to be replaced with a new undamaged ECM supporting…
We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis…
Atherosclerosis is a chronic inflammatory disease of the artery wall. The early stages of atherosclerosis are driven by interactions between lipids and monocyte-derived-macrophages (MDMs). The mechanisms that govern the spatial distribution…
Coordinated motion of cell monolayers during epithelial wound healing and tissue morphogenesis involves mechanical stress generation. Here we propose a model for the dynamics of epithelial expansion that couples mechanical deformations in…
In this paper, we study a modification of the mathematical model describing inflammation and demyelination patterns in the brain caused by Multiple Sclerosis proposed in [Lombardo et al. (2017), Journal of Mathematical Biology, 75,…
In the framework of the recently developed asymptotic models for tibio-femoral contact incorporating frictionless elliptical contact interaction between thin elastic, viscoelastic, or biphasic cartilage layers, we apply an asymptotic…