Numerical models developed to study high frequency ultrasound scattering during apoptosis require knowledge of mechanical properties of cells. Particle Tracking Microrheology (PTM) is a technique for studying the mechanical properties of soft materials. By tracking the Brownian movement of particles embedded in a material, its mechanical properties can be extracted. In this thesis, PTM is used to measure the relative changes in the viscoelasticity of apoptotic PC3 cells. PTM was first validated in purely viscous and viscoelastic phantoms. It was found to work well in viscous phantoms, but was limited to only measuring relative changes of the viscoelasticity of viscoelastic materials. After validation, PTM measurements in cells showed that the elastic and viscous modulus increased by over 50 Pa and 20 Pa respectively over the course of the treatment. Preliminary development of another technique known as Two-Point Particle Tracking Microrheology (TPM) is also presented in this thesis.