Modeling of photoelastic imaging of mechanical stresses in transparent solids mimicking kidney stones

Theoretical and numerical models were developed to calculate the polariscopic integrated light intensity that forms a projection of the dynamic stress within an axisymmetric elastic object. Although the model is general, this paper addressed its application to measurements of stresses in model kidney stones from a burst wave lithotripter for stone fragmentation. The stress was calculated using linear elastic equations, and the light propagation was modeled in the instantaneous case by integrating over the volume of the stone. The numerical model was written in finite differences. The resulting images agreed well with measured images. The measured images corresponded to the maximum shear stress distribution, although other stresses were also plotted. Comparison of the modeled and observed polariscope images enabled refinement of the photoelastic constant by minimizing the error between the calculated and measured fields. These results enable quantification of the stress within the polariscope images, determination of material properties, and the modes and mechanisms of stress production within a kidney stone. Such a model may help in interpreting elastic waves in structures, such as stones, toward improving lithotripsy procedures.