This study presents a computational model to estimate the elasticity and viscosity of a medium with a simulated tumor region through vibrational wave propagation analysis. Using finite-difference time-domain (FDTD) methods, we simulate wave behavior across differing elasticity and viscosity profiles that represent healthy and tumor-affected tissues. An adaptive Least Mean Squares (LMS) filter reduces noise in velocity measurements, while Fast Fourier Transform (FFT) and Laplace transformations extract elasticity and viscosity values at specific points in the medium. To enhance convergence, we propose initializing the weight of each filter with the weight of its adjacent filter, leveraging spatial similarity in noise impact. Averaging results across simulations yields robust parameter estimates, effectively distinguishing between healthy and tumor-affected areas. This model shows potential for non-invasive tissue analysis, offering a promising tool for biomedical applications.