| Abstract: |
| Lactate used to be known as a a molecular waste in the brain. But today it is fully accepted that lactate is an important source of energy for neurons. Like other cancers, gliomas lead to alterations of cells energy management. In particular, lactate creation, consumption, import and export of a glioma cell seem to play a key role in the cancer development.\
But because energy management in healthy and tumoral cells can be difficult to observe and explain experimentally, we use mathematical modeling to help to describe and understand cells energy changes. We present here a fast-slow system describing the locals mechanisms of interest. This model was first proposed by A. Aubert, R. Costalat, P.J. Magistretti \& L. Pellerin.\
In particular, we will give bounds on the solutions, compare global ($\varepsilon>0$) and limit ($\varepsilon =0$) dynamics and give simulations for several parameters of interest. We will also compare simulations with MRS data and discuss our results.\
Key words :\
lactate ; fast-slow systems ; stability ; simulations ; MRS data ; dynamical systems |
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