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Neuroimaging is a technique of examination of the brain with the help of devices such as MRI, fMRI, EEG, and DTI. Brain data is available in hospitals and research centers, which are however, not easily shared. The federated learning assists in training the computer models without the provision of raw data. The process is made safe and trustworthy with the aid of blockchain. The systemic review of the blockchain-based federated learning integration in neuroimaging indicates that it is used in disease prediction, multi-modal brain imaging, and cross-institutional studies. Among them are the technical process of FL in multi-site datasets, harmonization and preprocessing plan, and how blockchain can help to reduce security threats and improve regulatory conformity. Limitations that are present in the paper include, but are not limited to, computational overhead, network latency, and data heterogeneity, and emerging solutions such as lightweight blockchain, integration of edge computing, and federated models personalized. This survey assists scientists to realize the safe use of FL and blockchain in brain science.