Recent Advances in Bone Research 2022 Edition

More and more scientific and engineering applications in bone research make pivotal advances in treating patients with orthopedics issues. Hence, bone research in the 21st century combines, inter alia, biology, chemistry, mathematics, and mechanics with complementary characteristics that help a holistic approach to bone-related pathologies. Nowadays, it is hard to connect new evidence when jargoning and money remain two significant obstacles to sharing knowledge. “Recent Advances In Bone Research” is a free book – no money involved at any stage - that combines the most recent efforts in bone research from several experts with different backgrounds, every expert seeks to answer the same question: how my work can help the patients and the work of others scientists? This first book summarizes the BONe InTerdisciplinary sympOSium 2022 held in New York City, Staten Island May 20th, 202

A Mathematical Analysis of the Dynamics of Prion Proliferation

How do the normal prion protein (PrP(C)) and infectious prion protein (PrP(Sc)) populations interact in an infected host? To answer this question, we analyse the behavior of the two populations by studying a system of differential equations. The system is constructed under the assumption that PrP(Sc) proliferates using the mechanism of nucleated polymerization. We prove that with parameter input consistent with experimentally determined values, we obtain the persistence of PrP(Sc). We also prove local stability results for the disease steady state, and a global stability result for the disease free steady state. Finally, we give numerical simulations, which are confirmed by experimental data

Multi-Agent Systems and Blood Cell Formation

International audienceThe objective of this chapter is to give an insight of the mathematical modellng of hematopoiesis using multi-agent systems. Several questions may arise then: what is hematopoiesis and why is it interesting to study this problem from a mathematical point of view? Has the multi-agent system approach been the only attempt done until now? What does it bring more than other techniques? What were the results obtained? What is there left to do

Fragmentation and monomer lengthening of rod-like polymers, a relevant model for prion proliferation

The Greer, Pujo-Menjouet andWebb model [Greer et al., J. Theoret. Biol., 242 (2006), 598-606] for prion dynamics was found to be in good agreement with experimental observations under no-flow conditions. The objective of this work is to generalize the problem to the framework of general polymerization-fragmentation under flow motion, motivated by the fact that laboratory work often involves prion dynamics under flow conditions in order to observe faster processes. Moreover, understanding and modelling the microstructure influence of macroscopically monitored non-Newtonian behaviour is crucial for sensor design, with the goal to provide practical information about ongoing molecular evolution. This paper's results can then be considered as one step in the mathematical understanding of such models, namely the proof of positivity and existence of solutions in suitable functional spaces. To that purpose, we introduce a new model based on the rigid-rod polymer theory to account for the polymer dynamics under flow conditions. As expected, when applied to the prion problem, in the absence of motion it reduces to that in Greer et al. (2006). At the heart of any polymer kinetical theory there is a configurational probability diffusion partial differential equation (PDE) of Fokker-Planck-Smoluchowski type. The main mathematical result of this paper is the proof of existence of positive solutions to the aforementioned PDE for a class of flows of practical interest, taking into account the flow induced splitting/lengthening of polymers in general, and prions in particular.Comment: Discrete and Continuous Dynamical Systems - Series B (2012) XX-X

A qualitative analysis of a Aβ\beta-monomer model with inflammation processes for Alzheimer's disease

We introduce and study a new model for the progression of Alzheimer's disease incorporating the interactions of A$\beta$-monomers, oligomers, microglial cells and interleukins with neurons through different mechanisms such as protein polymerization, inflammation processes and neural stress reactions. In order to understand the complete interactions between these elements, we study a spatially-homogeneous simplified model that allows to determine the effect of key parameters such as degradation rates in the asymptotic behavior of the system and the stability of equilibriums. We observe that inflammation appears to be a crucial factor in the initiation and progression of Alzheimer's disease through a phenomenon of hysteresis, which means that there exists a critical threshold of initial concentration of interleukins that determines if the disease persists or not in the long term. These results give perspectives on possible anti-inflammatory treatments that could be applied to mitigate the progression of Alzheimer's disease. We also present numerical simulations that allow to observe the effect of initial inflammation and concentration of monomers in our model

Modeling the spatial propagation of Aβ oligomers in Alzheimer’s Disease

Recent advances in the study of Alzheimer’s Disease and the role of Aβ amyloid formation have caused the focus of biologists to progressively shift towards the smaller protein assemblies, the oligomers. These appear very early on in the disease progression and they seem to be the most infectious species for the neurons. We suggest a model of spatial propagation of Aβ oligomers in the vicinity of a few neurons, without considering the formation of large fibrils or plaques. We also include a simple representation of the oligomers neurotoxic effect. A numerical study reveals that the oligomers spatial dynamics are very sensitive to the balance between their diffusion and their replication, and that the outcome in terms of the progression of AD strongly depends on it

Contribution à l'étude d'une équation de transport à retards décrivant une dynamique de population cellulaire

mention très honorable avec félicitations du jury Rapporteurs : Glenn F. Webb et Michel LanglaisWe present a model of blood cell division based on two biological hypotheses : the presence of a factor called maturation and the division of the cycle into a resting and a proliferating phase It is represented by a system S of two age-maturity structured semi linear transport equations. Integrating with respect to the age, S becomes a system of maturity structured partial differential equations with delays. In chapter 1, we introduce the biological background motivating our work, and we present our model. In chapter 2, we study the model where the proliferating phase is constant and the cell division is equal. We prove a result of existence and uniqueness, then we show a result linking the solutions to the stem cells. We prove invariance, and asymptotic behaviour results and instability. In chapter 3, the proliferating phase depends on the cell maturity. We prove similar results as in chapter 2. In chapter 4, the proliferating phase is fixed but cells do not divide in an equal way. Using the Markov operator theory, we prove a global stability result.Nous présentons un modèle de division de cellules sanguines basé sur la présence d'un facteur appelé maturation et le partage du cycle en une phase de prolifération et une phase de repos. Il est représenté par un système S de deux équations de transport structuré en âge et maturité. En intégrant par rapport à l'âge, S devient un système d'équations aux dérivées partielles à retards structuré en maturité. Dans le chapitre 1, nous introduisons le contexte biologique, et nous présentons notre modèle. Dans le chapitre 2, nous étudions le modèle quand la phase de prolifération est fixe et la division est égale. Nous montrons l'existence et l'unicité puis un résultat liant les solutions aux cellules souches ainsi qu'un résultat d'invariance, de comportement asymptotique et d'instabilité. Dans le chapitre 3, nous supposons que la phase de prolifération varie suivant la maturité des cellules. Nous prouvons des résultats analogues au chapitre 2. Dans le chapitre 4, la phase de prolifération est fixe mais nous supposons la division inégale. En utilisant la théorie des opérateurs de Markov, nous prouvons un résultat de stabilité globale