A random walk approach to estimate the confinement of α-particle emitters in nanoparticles for targeted radionuclide therapy

Uwe Holzwarth, Isaac Ojea Jimenez, Luigi Calzolai

Targeted radionuclide therapy is a highly efficient but still underused treatment modality for various types of cancers that uses so far mainly readily available β-emitting radionuclides. By using α-particle emitters several shortcomings due to hypoxia, cell proliferation and in the selected treatment of small volumes such as micrometastasis could be overcome. To enable efficient targeting longer-lived α-particle emitters are required. These are the starting point of decay chains emitting several α-particles delivering extremely high radiation doses into small treatment volumes. However, as a consequence of the α-decay the daughter nuclides receive high recoil energies that cannot be managed by chemical radiolabelling techniques. By safe encapsulation of all α-emitters in the decay chain in properly sized nanocarriers their release may be avoided. The encapsulation of small core nanoparticles loaded with the radionuclide in a shell structure that safely confines the recoiling daughter nuclides promises good tumour targeting, penetration and uptake, provided these nanostructures can be kept small enough. A model for spherical nanoparticles is proposed that allows an estimate of the fraction of recoiling α-particle emitters that may escape from the nanoparticles as a function of their size. The model treats the recoil ranges of the daughter nuclides as approximately equidistant steps with arbitrary orientation in a three-dimensional random walk model. The presented model allows an estimate of the fraction of α-particles that are emitted from outside the nanoparticle when its size is reduced below the radius that guarantees complete confinement of all radioactive daughter nuclides. Smaller nanoparticle size with reduced retention of daughter radionuclides might be tolerated when the effects can be compensated by fast internalisation of the nanoparticles by the target cells.