Numerical study of ultrasonic propagation and shock wave formation in concentration dependent fibrin clots

<sec>Ultrasound thrombolysis stands out among various treatment methods due to its safety and high efficiency. Although the cavitation and mechanical mechanisms behind this technique have been well-established, the effect of the concentration-dependent strain hardening properties of thrombotic biomaterials on ultrasound-induced shockwave effects remains a subject of concern. Furthermore, the extremely short time window for effective clinical intervention requires precise spatial localization of rapidly formed shockwaves and determination of their energy thresholds for optimizing treatment protocols.</sec><sec>Considering that the main mechanical properties of blood clots are dominated by the fibrin network, their stress-strain relationship is significantly dependent on fibrin concentration. Based on the results obtained from quasi-static compression tests performed on clots with different fibrin concentrations, a power-law constitutive equation capable of characterizing the progressive hardening characteristics of clots is proposed in this work. By incorporating the changes in wave speed caused by strain-hardening characteristics into a third-order nonlinear ultrasound propagation wave equation, the dynamic characteristics of shock wave formation during ultrasound propagation in clot media are studied via numerical simulations. The results show that the significant stress discontinuity prior to this process is due to a sudden displacement change caused by the progressive hardening of the clot. In order to accurately locate the starting position, the average steepening factor (ASF) based on threshold limitation is used for localization. However, this method is severely limited by the problem of mesh convergence, and the improvement in finite accuracy leads to an exponential increase in computation time. In contrast, the total harmonic distortion (THD) using the extremum of frequency-domain energy for localization is less sensitive to truncation errors and provides computational efficiency advantages. Parametric analysis indicates that a maximum localization error between the two methods is 2.55%, and the peak stress determined by the THD criterion is much higher than that determined by the ASF method.</sec><sec>Based on experimental fitting of constitutive equations at different concentrations, numerical simulations of wave propagation show that according to the THD criterion, the increase in fibrin concentration from 10 mg/mL to 35 mg/mL delays the formation of shockwave by 91.7% and increases the peak stress by 60%. Corresponding fitting formulas are derived. Through real-time THD feedback and acoustic field parameter adjustment, a theoretical basis is provided for rapidly localizing and flexibly controlling shockwave effects in clinical ultrasound thrombolysis.</sec>