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Physical treatment planning systems in radiation oncology, in spite of high technology, do not provide a quantitative prediction about a biological response of tumours and adjacent normal tissues. Mathematical modelling biological effects (comprising physical parameters and radiobiological processes during and after therapy) offers a new paradigm for optimisation of treatment planning radiation therapy. Biophysical models BED, EUD, TCP and NTCP for external therapy, stereotactic therapy, brachytherapy and proton therapy with clinical cases and illustrative outcomes are described. For radiobiological optimisation imaging techniques (CT, MRI, PET), 3D-treatment plans and dose volume histograms (DVH) are used. Good news: The respected reader can become a user of a stand-alone program BioGray, to simulate his patient cases and confront them with his clinical experience. It promises him an attractive wayfaring from the 4th-dimensional space into the 5th-dimension of radiobiology and radiation oncology.