A dual-gradient chemotaxis system modeling the spontaneous aggregation of microglia in Alzheimer’s disease

2018 ◽  
Vol 16 (03) ◽  
pp. 307-338
Author(s):  
Hai-Yang Jin ◽  
Zhi-An Wang
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Pattern Formation ◽  
System Modeling ◽  
Neumann Boundary ◽  
Classical Solutions ◽  
Open Problems ◽  
Global Classical Solutions ◽  
Spontaneous Aggregation ◽  
Dual Gradient

In this paper, we consider the following dual-gradient chemotaxis model [Formula: see text] with [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], where [Formula: see text] is a bounded domain in [Formula: see text] with smooth boundary, [Formula: see text] and [Formula: see text]. The model was proposed to interpret the spontaneous aggregation of microglia in Alzheimer’s disease due to the interaction of attractive and repulsive chemicals released by the microglia. It has been shown in the literature that, when [Formula: see text], the solution of the model with homogeneous Neumann boundary conditions either blows up or asymptotically decays to a constant in multi-dimensions depending on the sign of [Formula: see text], which means there is no pattern formation. In this paper, we shall show as [Formula: see text], the uniformly-in-time bounded global classical solutions exist in multi-dimensions and hence pattern formation can develop. This is significantly different from the results for the case [Formula: see text]. We perform the numerical simulations to illustrate the various patterns generated by the model, verify our analytical results and predict some unsolved questions. Biological applications of our results are discussed and open problems are presented.

scholarly journals On the Existence of Global Smooth Solutions to the Parabolic–Elliptic Keller–Segel System with Irregular Initial Data

2021 ◽  
Author(s):  
Frederic Heihoff
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Three Dimensions ◽  
Classical Solutions ◽  
List Type ◽  
Smooth Solutions ◽  
Smooth Bounded Domain ◽  
Global Classical Solutions ◽  
Global Smooth Solutions

AbstractWe consider the parabolic–elliptic Keller–Segel system $$\begin{aligned} \left\{ \begin{aligned} u_t&= \Delta u - \chi \nabla \cdot (u \nabla v), \\ 0&= \Delta v - v + u \end{aligned} \right. \end{aligned}$$ u t = Δ u - χ ∇ · ( u ∇ v ) , 0 = Δ v - v + u in a smooth bounded domain $$\Omega \subseteq {\mathbb {R}}^n$$ Ω ⊆ R n , $$n\in {\mathbb {N}}$$ n ∈ N , with Neumann boundary conditions. We look at both chemotactic attraction ($$\chi > 0$$ χ > 0 ) and repulsion ($$\chi < 0$$ χ < 0 ) scenarios in two and three dimensions. The key feature of interest for the purposes of this paper is under which conditions said system still admits global classical solutions due to the smoothing properties of the Laplacian even if the initial data is very irregular. Regarding this, we show for initial data $$\mu \in {\mathcal {M}}_+({\overline{\Omega }})$$ μ ∈ M + ( Ω ¯ ) that, if either $$n = 2$$ n = 2 , $$\chi < 0$$ χ < 0 or $$n = 2$$ n = 2 , $$\chi > 0$$ χ > 0 and the initial mass is small or $$n = 3$$ n = 3 , $$\chi < 0$$ χ < 0 and $$\mu = f \in L^p(\Omega )$$ μ = f ∈ L p ( Ω ) , $$p > 1$$ p > 1 holds, it is still possible to construct global classical solutions to ($$\star $$ ⋆ ), which are continuous in $$t = 0$$ t = 0 in the vague topology on $${\mathcal {M}}_+({\overline{\Omega }})$$ M + ( Ω ¯ ) .

scholarly journals The Qualitative Scoring MMSE Pentagon Test (QSPT): A New Method for Differentiating Dementia with Lewy Body from Alzheimer’s Disease

2013 ◽  
Vol 27 (2) ◽  
pp. 213-220 ◽  
Author(s):  
Paolo Caffarra ◽  
Simona Gardini ◽  
Francesca Dieci ◽  
Sandra Copelli ◽  
Laura Maset ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Differential Diagnosis ◽  
Lewy Body ◽  
Dementia With Lewy Body ◽  
System Modeling ◽  
Scoring Method ◽  
Contractive Map ◽  
Two Phases ◽  
Method Of Assessment

The differential diagnosis across different variants of degenerative diseases is sometimes controversial. This study aimed to validate a qualitative scoring method for the pentagons copy test (QSPT) of Mini-Mental State Examination (MMSE) based on the assessment of different parameters of the pentagons drawing, such as number of angles, distance/intersection, closure/opening, rotation, closing-in, and to verify its efficacy to differentiate dementia with Lewy Body (DLB) from Alzheimer's disease (AD). We established the reliability of the qualitative scoring method through the inter-raters and intra-subjects analysis. QSPT was then applied to forty-six AD and forty-six DLB patients, using two phases statistical approach, standard and artificial neural network respectively. DLB patients had significant lower total score in the copy of pentagons and number of angles, distance/intersection, closure/opening, rotation compared to AD. However the logistic regression did not allow to establish any suitable modeling, whereas using Auto-Contractive Map (Auto-CM) the DLB was more strongly associated with low scores in some qualitative parameters of pentagon copying, i.e. number of angles and opening/closure and, for the remaining subitems of the MMSE, in naming, repetition and written comprehension, and for demographic variables of gender (male) and education (6–13 years). Twist system modeling showed that the QSPT had a good sensitivity (70.29%) and specificity (78.67%) (ROC-AUC 0.74). The proposed qualitative method of assessment of pentagons copying used in combination with non-linear analysis, showed to be consistent and effective in the differential diagnosis between Lewy Body and Alzheimer’s dementia.

scholarly journals Global existence and boundedness of solutions in a Lotka-Volterra reaction-diffusion system of predator-prey model with nonlinear prey-taxis

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 5023-5035
Author(s):  
Demou Luo
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Classical Solutions ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Global Classical Solutions ◽  
Prey Model

In this paper, we investigate a diffusive Lotka-Volterra predator-prey model with nonlinear prey-taxis under Neumann boundary conditions. This system describes a prey-taxis mechanism that is an immediate movement of the predator u in response to a change of the prey v (which lead to the collection of u). We apply some methods to overcome the substantial difficulty of the existence of nonlinear prey-taxis term and prove that the unique global classical solutions of Lotka-Volterra predator-prey model are globally bounded.

scholarly journals A 3D human triculture system modeling neurodegeneration and neuroinflammation in Alzheimer’s disease

2018 ◽  
Vol 21 (7) ◽  
pp. 941-951 ◽  
Author(s):  
Joseph Park ◽  
Isaac Wetzel ◽  
Ian Marriott ◽  
Didier Dréau ◽  
Carla D’Avanzo ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
System Modeling

Cognitive control constrains memory attributions

2019 ◽  
Vol 42 ◽  
Author(s):  
Colleen M. Kelley ◽  
Larry L. Jacoby
Keyword(s):  
Alzheimer’S Disease ◽  
Older Adults ◽  
Alzheimer's Disease ◽  
Traumatic Brain Injury ◽  
Brain Injury ◽  
Cognitive Control

Abstract Cognitive control constrains retrieval processing and so restricts what comes to mind as input to the attribution system. We review evidence that older adults, patients with Alzheimer's disease, and people with traumatic brain injury exert less cognitive control during retrieval, and so are susceptible to memory misattributions in the form of dramatic levels of false remembering.

Formation of paired helical filaments in Alzheimer's disease

1984 ◽  
Vol 42 ◽  
pp. 302-303
Author(s):  
J. Metuzals ◽  
D. F. Clapin ◽  
V. Montpetit
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Frontal Lobe ◽  
Giant Axon ◽  
Paired Helical Filaments ◽  
Normal Brain ◽  
Protein Assemblies ◽  
Electron Microscopic ◽  
Helical Symmetry ◽  
Structural Levels

Information on the conformation of paired helical filaments (PHF) and the neurofilamentous (NF) network is essential for an understanding of the mechanisms involved in the formation of the primary lesions of Alzheimer's disease (AD): tangles and plaques. The structural and chemical relationships between the NF and the PHF have to be clarified in order to discover the etiological factors of this disease. We are investigating by stereo electron microscopic and biochemical techniques frontal lobe biopsies from patients with AD and squid giant axon preparations. The helical nature of the lesion in AD is related to pathological alterations of basic properties of the nervous system due to the helical symmetry that exists at all hierarchic structural levels in the normal brain. Because of this helical symmetry of NF protein assemblies and PHF, the employment of structure reconstruction techniques to determine the conformation, particularly the handedness of these structures, is most promising. Figs. 1-3 are frontal lobe biopsies.

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