  We describe a 3D percolation-type approach to modeling of the processes of
aging and certain other properties of tissues analyzed as systems consisting of
interacting cells. Lattice sites are designated as regular (healthy) cells,
senescent cells, or vacancies left by dead (apoptotic) cells. The system is
then studied dynamically with the ongoing processes including regular cell
dividing to fill vacant sites, healthy cells becoming senescent or dying, and
senescent cells dying. Statistical-mechanics description can provide patterns
of time dependence and snapshots of morphological system properties. The
developed theoretical modeling approach is found not only to corroborate recent
experimental findings that inhibition of senescence can lead to extended
lifespan, but also to confirm that, unlike 2D, in 3D senescent cells can
contribute to tissue's connectivity/mechanical stability. The latter effect
occurs by senescent cells forming the second infinite cluster in the regime
when the regular (healthy) cell's infinite cluster still exits.
