Various embodiments of the present invention provide methods and systems for deterministic calculation of 
radiation doses, delivered to specified volumes within human tissues and organs, and specified areas within other organisms, by external and 
internal radiation sources. Embodiments of the present invention provide for creating and optimizing computational mesh structures for deterministic 
radiation transport methods. In general these approaches seek to both improve solution accuracy and computational efficiency. Embodiments of the present invention provide methods for planning 
radiation treatments using deterministic methods. The methods of the present invention may also be applied for 
dose calculations, 
dose verification, and 
dose reconstruction for many different forms of radiotherapy treatments, including: conventional beam therapies, 
intensity modulated radiation therapy (“IMRT”), 
proton, 
electron and other 
charged particle beam therapies, targeted 
radionuclide therapies, 
brachytherapy, stereotactic 
radiosurgery (“SRS”), Tomotherapy®; and other radiotherapy delivery 
modes. The methods may also be applied to radiation-dose calculations based on radiation sources that include linear accelerators, various delivery devices, 
field shaping components, such as jaws, blocks, flattening filters, and multi-leaf collimators, and to many other radiation-related problems, including radiation shielding, 
detector design and characterization; thermal or 
infrared radiation, 
optical tomography, 
photon migration, and other problems.