Since arterial blood has both fluidity and conductivity, the arterial blood flow area is equivalent to an electric current source under the action of a static magnetic field, thus forming an electric field within a certain range of the human body. Therefore, the distribution of arterial blood flow can be reconstructed by using electrodes to obtain the potential difference signal on the skin's surface. In this paper, firstly, a three-dimensional (3D) finite element simulation model of a human forearm artery was established in COMSOL to simulate the potential distribution under a uniform magnetic field and extract the potential difference data. Then, based on the integral equation of the electromagnetic reciprocity theorem and the Maxwell equation, a numerical model of the reconstructed arterial flow profile was derived in detail. Finally, the arterial location, velocity resolution and flow volume were reconstructed and analyzed respectively. The simulation results show that the correlation between the reconstructed image and the given image is above 0.82 and the highest is 0.91, the resolution of velocity imaging is 0.046 m s−1, and the mean relative error of the volume of the reconstructed blood flow is 0.820%. The above results showed good numerical accuracy, indicating the theoretical feasibility of using a uniform electromagnetic field to reconstruct the distribution of arterial blood flow.

This paper presents a mathematical model of measuring blood flow based on electromagnetic induction for predicting the rate of arterial stenosis. Firstly, an electrode sensor was used to collect the induced potential differences from human skin surface in a uniform magnetic field. Then, the inversion matrix was constructed by the weight function theory and finite element method. Next, the blood flow volume inversion model was constructed by combining the induction potential differences and inversion matrix. Finally, the rate of arterial stenosis was predicted based on mathematical relationship between blood flow and the area of arterial stenosis. To verify the accuracy of the model, a uniform magnetic field distribution of Helmholtz coil and a 3D geometric model of the ulnar artery of the forearm with different rates of stenosis were established in COMSOL, a finite element analysis software. Simulation results showed that the inversion model had high accuracy in the measurement of blood flow and the prediction of rate of stenosis, and is of great significance for the early diagnosis of arterial stenosis and other vessel diseases.