In this study, a method is proposed to image magnetohydrodynamic (MHD) flow of ionic solutions, which is caused by externally injected electrical current to an imaging media, during MRI scans. A multi-physics (MP) model is created by using the electrical current, laminar flow, and MR equations. The conventional spoiled gradient echo MRI pulse sequence with bipolar flow encoding gradients is utilized to encode the MHD flow. Using the MP model and the MRI pulse sequence, relationship between the MHD flow related phase in the acquired MR signal, the injection current, and the MRI pulse sequence parameters is stated. Numerical simulations and physical experiments are performed to validate the proposed method. The simulation and experimental results are in agreement and show that the MHD flow related MR phase depends on the amplitude and duration of the flow encoding gradient and the injected current. This method may be used to evaluate the MHD flow of conductive liquid media during MRI scans with simultaneous electrical current injections. The MHD flow related MR phase is 1.5 radian for an injected current of 1 mA amplitude, 30 ms duration and a flow encoding gradient amplitude of 24 mT/m. This large MR phase range exhibits potential use of this method for clinical applications such as investigation of highly conductive cerebrospinal fluid (CSF) during clinical use of electrical current based neuromodulation in MRI. However, very high and time varying velocities of typical CSF flow compared to the MHD flow velocities should also be considered. (C) 2019 Elsevier Inc. All rights reserved.