We recently proposed a simplified model to empirically capture the effect of DNP on the collective and macroscopic aspects of the nuclear spin dynamics, and to reproduce experimental observations. In this model, the nuclear inverse spin temperature β n of the 1 H Zeeman reservoir relaxes exponentially with time constant γ n,ee , to the electron non-Zeeman spin temperature β ee , which also exponentially relaxes (with rate γ st ) to a stationary value that represents either its polarization upon µw irradiation, or the lattice temperature. This toy model of DNP is relevant to the case where 2 H nuclei are present in large quantities in the sample, as these provide a source of polarization to the 1 H nuclei by an indirect "cross-talk" mechanism through their interaction with the electron non Zeeman reservoir. Thus, the deuterium spins contribute to the repolarization of the protons and buildup of the nuclear magnetization, and compensate at least partially the 1 H Zeeman energy lost to the probe through radiation damping. In this model setup, the z component of the nuclear spin magnetization density at point r, m z (r, t), therefore tends to the time-varying value m th oz (r, t), that "relaxes" to a stationary value m st 0 (r). Again, the quantity m st 0 (r) pertains either to the stationary value of the 1 H magnetization upon µw irradiation, or to its thermal equilibrium, when µw irradiation is turned off. This model therefore writes: