Mathematical Modelling of Gamma Radiation Attenuation in Biological Tissues

Gamma radiation attenuation is one of the most important quantitative processes in medical physics,radiological protection, and diagnostic imaging. In this work, a mathematical model for photon attenuationin biological tissues is developed from an infinitesimal balance law. The classical exponential attenuationequation is derived through an ordinary differential equation, and the physical meaning of the linearattenuation coefficient is discussed in connection with absorption and scattering mechanisms. The modelis then extended to layered tissues, effective attenuation, transmission fraction, and absorbed intensityprofiles. The mathematical treatment uses derivatives, integrals, limits, and exponential functions todescribe how gamma beams lose intensity as they propagate through matter. The resulting frameworkis directly relevant to radiodiagnosis, shielding calculations, and treatment planning in radiation-basedmedical procedures.