An equivalent astable multivibrator model to assess flow instability and dysfunction risk in in-vitro stenotic arteriovenous grafts

Narrowed vessel accesses produce blood flow changes, and induce flow instability and vessel wall vibration, resulting in blood pressure, flow velocity, and flow resistance increases. The vessel wall vibrates and propagates the low axial blood flow, as representing the resistance (R) to blood flow. The compliance is a blood pressure-blood volume relation, representing the systole and diastole capacity of the blood vessel. These dynamic behaviors increase blood flow resistances and reduce blood vessel compliances. Vibration phenomena result on the elastic vessel walls and induce simple harmonic motion due to transverse vibration pressure (TVP). The rise time, amplitude, and pulse duration of transverse waves are determined by the flow resistances (R) and vessel compliances (C). Thus, a stenotic arteriovenous access has high resistance and low compliance, which can be expressed an astable multivibrator as an equivalent model consisting of a lumped resistor (R) and a lumped capacitor (C). TVP's oscillation frequency, rise time, and amplitude are determined by the flow resistances and vessel compliances. Hence, an astable multivibrator is used to model TVP parameters to estimate negative time constants, τ(R× C), which are used to evaluate the flow instability and the dysfunction risk in in-vitro arteriovenous grafts (AVGs). Experimental results show the average negative time constants have the positive correlation as the degree of stenosis (DOS) increases (R² 0.8944), and their variations with the flow resistance and vessel compliance are also validated. Positive pole values, s(-1/τ), are used to show that the force responses of the vessel walls grow in a finite time, 0.5415 ± 7.60 × 10^-3 sec, and the equivalent model would be also unstable as DOS increases (R² 0.8802). By comparison with hemodynamic analysis, the finding of proposed model can be further carried out for screening AVG dysfunction risk during hemodialysis treatment.