The nervous system is today recognized to play an important role in the development of cancer. Indeed, neurons extend long processes (axons) that grow and infiltrate tumors in order to regulate the progression of the disease in a positive or negative way, depending on the type of neuron considered. Mathematical modelling of this biological process allows to formalize the nerve-tumor interactions and to test hypotheses in silico to better understand this phenomenon. In this work, we introduce a system of differential equations modelling the progression of pancreatic ductal adenocarcinoma (PDAC) coupled with associated changes in axonal innervation. The study of the asymptotic behavior of the model confirms the experimental observations that PDAC development is correlated with the type and densities of axons in the tissue. In addition, we study the identifiability of the model parameters. This informs on the adequacy between the parameters of the model and the experimental data. It leads to significant insights such that the transdifferentiation phenomenon accelerates during the development process of PDAC cells. Finally, we give an example of a simulation of the effects of partial or complete denervation that sheds lights on complex correlation between the cell populations and axons with opposite functions.
翻译:事实上,神经系统延长了长过程(轴),生长和渗入肿瘤,以便根据所考虑的神经神经元的类型,以正或负的方式调节该疾病的蔓延。这一生物过程的数学建模使神经震动相互作用正规化,并测试硅质中的假设,以更好地了解这一现象。在这项工作中,我们引入了一种差异方程系统,模拟胰腺肾上腺瘤的进化,并随之而来的是轴心内分泌的变化。模型的无症状行为证实了实验性观察,即PDAC的发展与组织内轴的型态和密度相关联。此外,我们研究模型参数的可识别性,从而了解模型参数与实验数据之间的适当性。这导致一种重要的洞察力,即在PDAC细胞的开发过程中,反切换现象会加速。最后,我们举一个例子,对PDAC的无症状行为进行了模拟,模拟了部分或完全的复合细胞的反光度。