abstract: Cancer is one of the commonest causes of death in both developing and developed countries. Lung cancer kills more than breast and ovarian cancer combined in women and more than prostate, colon and rectal, pancreas, leukemia combined in man. In western Europe and the USA, out of 100 patients with cancer, approximately 22\% are cured by surgery, 18\% by radiotherapy (alone or associated with other agents in a combination in which radiotherapy has the prominent role) and 5\% by chemotherapy (alone or in combination but with the leading role to chemotherapy). Intensity- modulated radiotherapy is new method to deliver X-ray to the tumor, with lower dose to the neighbor normal structure. With IMRT, they have five beams angled at the tumor, each containing thousands of individual beamlets and there are many different constraints. The optimization process is time consuming. Inventing new algorithm to save time without reducing the accuracy is very necessary for medical physics. With the reference of incremental Computed Tomography (CT) to helical CT, the brand new radiotherapy machine, Tomotherapy, was created. The other aspect of mathematic application in radiotherapy is calculating the complication probability of radiotherapy, e.g. radiation pneumonitis, depending on the ratio of lung volume irradiated below and over a radiation dose, the radiation dose to the tumor, the patient gender, past history disease, etc. we are exploring a new mathematic model to mimic the lung cancer growth and regression after radiotherapy.
(The author wish to thank Dr Ming Jiang, Dr Anhui Shi for collaboration.)