Mathematical model of the dependence between cerebral ventricular size and capillary pressure in laboratory animals

Aim: To adapt a mathematical model describing the interaction between fluid media and brain matter for the purpose of definition of the dependence between brain ventricle size and capillary pressure in laboratory animals of two genotypes, BALB/c and C57BL/6. Material and methods. The study included 4 male mice of each inbred strain C57BL/6 and BALB/c at the age of 12 weeks. The brain and cerebrospinal fluid system images were obtained using an 11.7 T horizontal MR scanner (Bruker, BioSpec 117/16 USR, Germany). An axial section at the level of -0.5 mm from bregma was chosen as the geometry for mathematical modelling. To describe the data obtained, the mathematical model was adapted by selecting a scale factor based on the known values of the cerebrospinal fluid formation rate for humans and mice. Results and discussion. The same qualitative pattern of relationship between capillary pressure and mean ventricular wall displacement was observed for all animals considered. Although the selected genetic strains of BALB/c and C57Bl mice differ significantly in terms of cerebral ventricle size, these differences in animal genotype did not affect the nature of this relationship. Changing the parameters of the fluid media interaction in the area of compression or moderate ventricular dilation almost does not lead to an exit from the physiologically acceptable capillary pressure value. In this case, the size of the ventricles changes significantly. In the area of large ventricular dilation, in contrast, there is little change in ventricular size, and this is accompanied by a dramatic increase in capillary pressure far beyond physiologic limits. Thus, the change in ventricular size is an adaptive process associated with pressure fluctuations caused by changes in intracranial fluid flow. The mere fact that some of the values reach the zone of physiologically unacceptable pressures associated, in fact, with death, provided that there is practically no change in ventricular size indicates that such a situation is rarely realized and is possible in case of violation of intracranial fluid media flows associated with the fact that the increase in ventricular size limits adaptive capabilities. Conclusions. The presented animal model will further increase the understanding of the pattern we have established and allow us to move on to attempts at prediction.

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