Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Image reconstruction in EIT is a nonlinear and ill-posed inverse problem. The Tikhonov method with L₂ regularization is always used to solve the EIT problem. However, the L₂ method always smoothes the sharp changes or discontinue areas of the reconstruction. Image reconstruction using the L₁ regularization allows addressing this difficulty. In this paper, a sum of absolute values is substituted for the sum of squares used in the L₂ regularization to form the L₁ regularization, the solution is obtained by the barrier method. However, the L₁ method often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive. In this paper, the projection method is combined with the L₁ regularization method to reduce the computational cost. The L₁ problem is mainly solved in the coarse subspace. This paper also discusses the strategies of choosing parameters. Both simulation and experimental results of the L₁ regularization method were compared with the L₂ regularization method, indicating that the L₁ regularization method can improve the quality of image reconstruction and tolerate a relatively high level of noise in the measured voltages. Furthermore, the projected L₁ method can also effectively reduce the computational time without affecting the quality of reconstructed images.

The extremely low frequency electromagnetic fields (ELF-EMFs) have been shown to have an environmentally negative effect on humans’ health; however, its treatment effect is beneficial for patients suffering from neurological disorders. Despite this success, the application of ELF-EMF has exceeded in the understanding of its internal mechanism. Recently, it was found that on-line magnetic stimulation may offer advantages over off-line magnetic exposure and has proven to be effective in activating the prefrontal cortex pyramidal neurons in vitro. Here, we perform computational simulations of the stimulation coils in COMSOL modeling to describe the uniformity of the distribution of the on-line magnetic field. Interestingly, the modeling data and actual measurements showed that the densities of the magnetic flux that was generated by the on-line stimulation coils were similar. The on-line magnetic stimulator induced sodium channel currents as well as field excitatory postsynaptic potentials of the rat hippocampal CA1 neurons and successfully demonstrated its extensive applications to activate neuronal tissue. These findings further raise the possibility that the instrument of on-line magnetic stimulation may be an effective alternative for studies in the field of bioelectromagnetics.

To investigate the effects of extremely low-frequency electromagnetic fields (ELF-EMFs) stimulation on sodium channel currents (I_Na), transient outward potassium channel currents (I_A) and delayed rectifier potassium channel currents (I_K) on hippocampal CA1 pyramidal neurons of young Sprague–Dawley rats. CA1 pyramidal neurons of rat hippocampal slices were subjected to ELF-EMFs stimulation with different frequencies (15 and 50 Hz), intensities (0.5, 1 and 2 mT) and durations (10, 20 and 30 min). The I_Na, I_A and I_K of neurons were recorded by a whole-cell patch-clamp method. ELF-EMFs stimulation enhanced I_Na densities, and depressed I_A and I_K densities. In detail, I_Na was more sensitive to the variation of intensities and frequencies of ELF-EMFs, whereas I_A and I_K were mainly affected by the variation of the duration of ELF-EMFs. ELF-EMFs stimulation altered activation and deactivation properties of I_Na, I_A and I_K. ELF-EMFs stimulation plays a role as a regulator rather than an inducer for ion channels. It might change the transition probability of ion channel opening or closing, and might also change the structure and function of the ion channel which need to be proved by the further technical method.