The fractal derivative wave equation: Application to clinical amplitude/velocity reconstruction imaging

This paper proposes a dissipative acoustic wave equation in which the fractal derivative is employed to represent dissipation. The proposed model is derived from the viscoelastic constitutive relationship via the fractal derivative. It is noted that the fractal derivative is a local operator and avoids the expensive computational costs of non-local fractional derivative, which is popular in recent decades to describe frequency-dependent dissipation in acoustic wave propagation in soft materials. The proposed model is tested to simulate the clinical amplitude/velocity reconstruction imaging of breast tumors, where the reflecting plate is imaged as an elevated line in correspondence to tumor. Numerical experiments show that the present model is capable of indicating the size, position and quantity of tumors. The comparative study confirms that the fractal derivative acoustic wave equation has an advantage over the fractional derivative model regarding computational costs.