There is a need for quantitative CT data in radiation therapy. Currently there are only few algorithms that address this issue, for instance the commercial DirectDensity algorithm. In scientific literature, an example of such an algorithm is DIRA. DIRA is an iterative model-based reconstruction method for dual-energy CT whose goal is to determine the material composition of the patient from accurate linear attenuation coefficients. It has been implemented in a two dimensional geometry, i.e., it could process axial scans only.  There was a need to extend DIRA so that it could process projection data generated in helical scanning geometries. The newly developed algorithm (DIRA-3D) implemented (i) polyenergetic semi-parallel projection generation, (ii) mono-energetic parallel projection generation and (iii) the PI-method for image reconstruction. The computation experiments showed that the accuracies of the resulting LAC and mass fractions were comparable to the ones of the original DIRA. The results converged after 10 iterations.