Burnup and k-eff

Hi guys, i was trying to simulate the delpletion of a fuel pin in a fast reactor context, I started from the main example regarding the depletion module of openMC. I added the nuclides that describe the fuel pin. Now I was wandering how to retrieve the burn-up in MWd/ton starting from the k-eff plot. I was thinking of calculating the reactivity loss:

\rho(t)=\frac{k_{eff}-1}{k_{eff}}

And then in somehow the power trend p(t)=P(0)e^{\rho(t)\Delta t/\Lambda} using point kinetics (very simplified). P(0) is imposed. Following then

B(t)=\int_0^{t} \frac{p(t)}{m}

where B(t) is the burn-up, m fuel mass (I would say the initial mass of the fuel).
But I’m not getting some useful results, do you know any other method to calculate the Burn-up in openMC?