Parkinson's disease is one of the most diffuse neurodegenerative diseases. While the aetiology of Parkinson's disease remains elusive, the degeneration of the dopamine - producing nigrostriatal neurons, along with the accumulation of alpha-synuclein, are pathophysiological hallmarks. The impairment of motor functions, a consequence of the involvement of the thalamic-frontal loop, dominates the overt clinical picture. However, more recent findings clarified that the symptoms are more widespread, and cognitive and/or behavioral dysfunctions are also common. Accordingly, neuroimaging studies show that, even in early disease, structural and functional alterations are not confined to the motor areas. This suggests that the effects of the nigro-striatal neurodegeneration are not restricted to the motor areas alone but, rather, they modify the behavior of the brain on a large scale. Understanding how the local degeneration of dopaminergic neurons affects the whole brain dynamics remains an open question. The purpose of this study is to understand how the ability of the nigrostriatal pathways to support a dopaminergic stimulation affects the brain as a whole. To this end, we leverage simultaneous recordings from EEG and deep electrodes placed near the subthalamic nuclei (STN) from 10 Parkinsonian patients, acquired before and after L-Dopa administration. We used the topography of the spreading of aperiodic waves over a large scale (i.e. neuronal avalanches), utilizing the recently described avalanche transition matrix (ATM), to characterize the brain dynamics. To simulate the effect of L-Dopa in silico, we deployed a mechanistic neural-mass model derived from the adaptive quadratic integrate-and-fire model (aQIF) of individual neurons that has been extended to include dopamine concentration as a variable. Each parcelled brain region is equipped with a neural mass and then coupled according to the empirical connectomes, where connections can be either excitatory, inhibitory, or dopaminergic. Then, the whole-brain dynamics have been simulated for different configurations, i.e., for different dopaminergic tones. This way, we obtained a numerical prediction of the expected dynamics (in terms of properties of the ATMs), as observed in the deep electrodes and the EEG, given different dopaminergic tones. Then, in a Bayesian set-up, we used a class of deep neural networks to "invert" the model and infer the most likely dopaminergic tone given the empirically observed dynamics. For all ten patients, we correctly inferred that the dopaminergic tone was higher given the dynamics observed after administration of L-Dopa, and lower before. In other words, we could distinguish and quantify the dopaminergic tone from the electrophysiological data if the subjects had orally taken L-Dopa. This was achieved by integrating the background (anatomical and dynamical) knowledge into model prediction about the physiology of dopamine (as opposed to training a classifier to distinguish empirical data). Finally, we carried out a diagnostic for the validation of the model, as well as a further description of the simulated dopamine dynamics.