scholarly journals REACTION-DIFFUSION MECHANISMS UNDERLYING HIRSCHPRUNG'S DISEASE AND THEIR PRACTICAL IMPICATIONS

2018 ◽  
Author(s):  
Arturo Tozzi

The erratic extent of aganglionic and hypoganglionic segments in Hirschsprung's disease (HD) makes it difficult to predict the amount of the intestine to remove in order to restore the proper functional motility. Our aim was to assess whether the embryonic rostro-caudal intestinal colonization by neuroblasts from the neural crest follows a predictable pattern in HD. In touch with Turing's reaction diffusion model (RD), which describes biological patterns (such as leopard spots and lung branching morphogenesis) in terms of interactions/competitions between activating and inhibiting factors, we hypothesized that intestinal neural density could be triggered by local gut factors that counteract the proximal-distal embryonic progression of neural progenitors. While the neuronal number is approximately the same throughout the whole intestine in healthy subjects, in HD neural density decreases rostro-caudally towards the rectal region, due to an augmented activity and concentration of distal local inhibitors. In order to prove our hypothesis of HD's nervous rostro-caudal adjustments driven by Turing-like processes, we compared the neuronal density patterns achieved through RD models' simulations with the neuronal numbers detected in different colonic regions from affected children. We showed that the virtual and the real plots display fully overlapping and matching features. The fact that neuronal decreases in impaired colons match Turing equations's previsions points towards the human intestine (both healthy and sick) as colonized through a diffusive proximal-distal neural pattern that is predictable, allowing us to straightforwardly calculate the length of the gut to resect during surgical procedures for HD.

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu

Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.


2021 ◽  
Vol 82 (6) ◽  
Author(s):  
Pawan Kumar ◽  
Jing Li ◽  
Christina Surulescu

AbstractGliomas are primary brain tumors with a high invasive potential and infiltrative spread. Among them, glioblastoma multiforme (GBM) exhibits microvascular hyperplasia and pronounced necrosis triggered by hypoxia. Histological samples showing garland-like hypercellular structures (so-called pseudopalisades) centered around the occlusion site of a capillary are typical for GBM and hint on poor prognosis of patient survival. We propose a multiscale modeling approach in the kinetic theory of active particles framework and deduce by an upscaling process a reaction-diffusion model with repellent pH-taxis. We prove existence of a unique global bounded classical solution for a version of the obtained macroscopic system and investigate the asymptotic behavior of the solution. Moreover, we study two different types of scaling and compare the behavior of the obtained macroscopic PDEs by way of simulations. These show that patterns (not necessarily of Turing type), including pseudopalisades, can be formed for some parameter ranges, in accordance with the tumor grade. This is true when the PDEs are obtained via parabolic scaling (undirected tissue), while no such patterns are observed for the PDEs arising by a hyperbolic limit (directed tissue). This suggests that brain tissue might be undirected - at least as far as glioma migration is concerned. We also investigate two different ways of including cell level descriptions of response to hypoxia and the way they are related .


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