The key variables in treatment planning optimization are the parameters of the **radiation beams** (e.g., beams' shape, angle, and intensity). However, the quality of a treatment is primarily measured by the **radiation dose** delivered to the patient’s body. We can connect the beam parameters to the radiation dose using a straightforward linear relationship. First, we divide the patient’s body into small three-dimensional units called **voxels** and each radiation beam into small two-dimensional sections called **beamlets**. By calculating how much radiation each beamlet (j) delivers to each voxel (i), and representing this with a value **aij**, we create what is known as the **dose deposition matrix (A)**. This matrix links the intensities of the beamlets (x) to the total radiation dose delivered (d) using the equation: **d=Ax**. A general radiotherapy optimization problem can be formulated as:
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