Self-Similar Functional Circuit Models of Arteries and Deterministic Fractal Operators: Theoretical Revelation for Biomimetic Materials

In this paper, the self-similar functional circuit models of arteries are proposed for bioinspired hemodynamic materials design. Based on the mechanical-electrical analogous method, the circuit model can be utilized to mimic the blood flow of arteries. The theoretical mechanism to quantitatively simulate realistic blood flow is developed by establishing a fractal circuit network with an infinite number of electrical components. We have found that the fractal admittance operator obtained from the minimum repeating unit of the fractal circuit can simply and directly determine the blood-flow regulation mechanism. Furthermore, according to the operator algebra, the fractal admittance operator on the aorta can be represented by Gaussian-type convolution kernel function. Similarly, the arteriolar operator can be described by Bessel-type function. Moreover, by the self-similar assembly pattern of the proposed model, biomimetic materials which contain self-similar circuits can be designed to mimic physiological or pathological states of blood flow. Studies show that the self-similar functional circuit model can efficiently describe the blood flow and provide an available and convenient structural theoretical revelation for the preparation of in vitro hemodynamic bionic materials.