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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.

This study is intended to find more effective and robust clinical diagnostic indices to characterize muscle strength and coordination alternation following anterior cruciate ligament (ACL) rupture. To evaluate angle-specific moments and hamstring (H)/quadriceps (Q) ratios, 46 male subjects with unilateral chronic ACL-rupture performed isokinetic concentric (c), eccentric (e) quadriceps and hamstring muscle tests respectively at 60°/s. Normalized moments and H/Q ratios were calculated for peak moment (PM) and 30°, 40°, 50°, 60°, 70°, 80° knee flexion angles. Furthermore, we introduced single-to-arithmetic-mean (SAM) and single-to-root-mean-square (SRMS) muscle co-contraction ratios, calculating them for specific angles and different contraction repetitions. Normalized PM and 40° specific concentric quadriceps, concentric hamstring strength in the ACL-deficient knee were reduced significantly (P ≤ 0.05). Concentric angle-specific moments together with Qe/Qc ratios at 40° (d = 0.766 vs. d = 0.654) identify more obvious differences than peak values in ACL ruptured limbs. Furthermore, we found SRMS-QeQc deficits at 40° showed stronger effect than Qe/Qc ratios (d = 0.918 vs. d = 0.766), albeit other ratio differences remained basically the same effect size as the original H/Q ratios. All the newly defined SAM and SRMS indices could decrease variance. Overall, 40° knee moments and SAM/SRMS ratios might be new potential diagnosis indices for ACL rupture detection.

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