A growth-fragmentation is a stochastic process representing cells with continuously growing mass and sudden fragmentation. Growth-fragmentations are used to model cell division and protein polymerisation in biophysics. A topic of wide interest is whether or not these models settle into an equilibrium, in which the number of cells is growing exponentially and the distribution of cell sizes approaches some fixed asymptotic profile. In this work, we present a new spine-based approach to this question, in which a cell lineage is singled out according to a suitable selection of offspring at each generation, with death of the spine occurring at size-dependent rate. The quasi-stationary behaviour of this spine process translates to the equilibrium behaviour, on average, of the growth-fragmentation. We present some Lyapunov-type conditions for this to hold. This is joint work with Denis Villemonais (École des Mines de Nancy/Université de Lorraine).