Experimental evidence for self-organised criticality (SOC) in non-conservative systems has recently been found in studies of rat cortical slices. The size distribution of observed neuronal avalanches has been attested to obey $3/2$ power-law scaling. A mean-field sandpile model of a noisy neuronal system is proposed to refute the irreconcilability between non-conservation and criticality put forward by longstanding SOC hypotheses. The model predicts that neuronal networks achieve and maintain criticality despite non-conservation due to the presence of background activity originating from membrane potential fluctuations within individual neurons. Furthermore, small networks are demonstrated to tip towards epileptiform activity when background activity is strong. This finding ties in redundancy, an intriguing feature of brain networks, to robustness of SOC behaviour
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