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

Abstract

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.

Fractal Operators and Fractional Dynamics with 1/2 Order in Biological Systems

“…We carefully compare the basic ideas in the literature [1][2][3]. We find that the three papers are exactly based on the same idea of fractalization.…”

“…The three types of problems addressed in the literature [1][2][3] are not novel. In the past, all these problems have been studied systematically [7][8][9][10][11][12][13][14].…”

“…However, the fractals in the literature [1][2][3] are not purely geometric. The structure in Figure 1b is abstracted as follows.…”

“…This paper focuses on fractal operators and fractional dynamics in biomaterials, biological structures and motions. In recent years, we have studied the following problems in biomechanics and biophysics: the first one is the constitutive response of muscle and ligament fibers [1]; the second one is the electrical signal transduction within nerve fibers [2], and the third one is the blood flow in arterial vessels [3]. Ultimately, it was astonishing to find that the three types of problems show surprising commonality, i.e., their basic laws can all be inscribed by fractal operators, and their mechanics are all 1/2-order fractional dynamics.…”

The cause of vasomotor symptoms: Resonance phenomena in the vascular bed

“…The resonance phenomena of the vascular system are based on the principle of physics and have been studied using electric circuit analogs. [ 2 3 4 ] However, a lower frequency than the cardiac frequency and time transition of the compliance/inertance have not been investigated in detail.…”