  Diffusion of molecules within biological cells and tissues is strongly
influenced by crowding. A key quantity to characterize diffusion is the
particle lifetime, which is the time taken for a diffusing particle to exit by
hitting an absorbing boundary. Calculating the particle lifetime provides
valuable information, for example, by allowing us to compare the timescale of
diffusion and the timescale of reaction, thereby helping us to develop
appropriate mathematical models. Previous methods to quantify particle
lifetimes focus on the mean particle lifetime. Here, we take a different
approach and present a simple method for calculating the maximum particle
lifetime. This is the time after which only a small specified proportion of
particles in an ensemble remain in the system. Our approach produces accurate
estimates of the maximum particle lifetime, whereas the mean particle lifetime
always underestimates this value compared with data from stochastic
simulations. Furthermore, we find that differences between the mean and maximum
particle lifetimes become increasingly important when considering diffusion
hindered by obstacles.
