## 1 Introduction  
The goal of radiation therapy is the delivery of a lethal radiation dose to cancer cells with minimum toxicity in surrounding healthy tissues. In recent years, radiopharmaceutical therapy (RPT) has been a promising method for the treatment of many cancer types [1]. In RPT, radiation is delivered to tumor cells and their microenvironment with the use of agents or through physiological mechanisms [2]. An important advantage of RPT is that, unlike external beam radiotherapy, the radiation can more effectively target disseminated and micrometastatic disease [3]. To that end, studies in the fields of radiobiology, radiochemistry, and pharmacology are important for selecting the proper combination of radionuclidesand chemical agents toward improving treatment outcomes [2]. The radionuclides that are used in RPT are mainly \(\beta\)-emitters (and less so \(\alpha\)-emitters). The advantage of \(\beta\)-emitters is that the irradiation range is commonly in the mm-cm range and, therefore, to a good approximation, they result in a uniform dose distribution in the tumor volume even when the emitter is non-uniformly distributed, as is most often the case due to its limited diffusion. In addition, in sharp contrast to \(\gamma\)-emitters, the shorter irradiation range of \(\beta\)-emitters offers much greater sparing of surrounding healthy tissues raising the therapeutic index [3; 4]. The response and the toxicity of any radiotherapeutic modality depend upon the absorbed dose to the tumor and the normal tissue. The standard approach for the calculation of absorbed dose in RPT follows the formalism provided by the Medical Internal Radiation Dose (MIRD) Committee of the American Society of Nuclear Medicine. The dosimetric formalism of the MIRD Committee was first presented in 1968 and since then a series of developments has been published in specialized publications (MIRD pamphlets) [5]. The central quantities in MIRD-based RPT dosimetry are the absorbed fraction and the S factor [1]. These quantities are determined by either Monte Carlo (MC) simulations or dose point kernels (DPKs). In turn, DPKs may be determined using either MC simulations or analytic techniques, such as range-energy relations. Information about absorbed fractions and S factors from the organ to the cellular scale for most radionuclides and monoenergetic photons or electrons is available in various MIRD publications [6; 7; 8; 9; 10; 11; 12; 13]. At the macroscopic scale of organs and tissues, absorbed fractions and S factors are mostly calculated [14; 12; 15; 16] by general-purpose MC codes, like ETRAN [17], EGS [18], MCNP [19], and Geant4 [20]. These codes are well benchmarked at the organ/tissue scale (\(\sim\)cm) and represent the gold standard in clinical dosimetry (both internal and external). At the other extreme of the (sub) cellular scale (<10 to 100 um), absorbed fractions and S factors are mostly determined [21; 22; 23; 24; 25] by specialized MC track-structure codes, like KURBUC [26], PARTRAC [27], and Geant4-DNA [28; 29; 30; 31], among others reviewed in [32]. At the intermediate scale (sub-mm to cm), which includes disseminated and micrometastatic disease, both general-purpose and track-structure codes may be applied with each approach having its pros and cons. However, irrespective of the code, MC simulations are generally time-consuming and require substantial software expertise to avoid systematic errors or simulation artifacts. Therefore, to facilitate the practical application of the absorbed fraction and S factor in RPT dosimetry, DPK-based analytic approaches offer a valuable theoretical alternative to MC simulations by reducing computational time. Using the ETRAN code, [PERSON] first provided the energy deposition of photon point sources in water [33] and afterward, the distribution of the absorbed dose of point sources of electrons and beta-emitting particles in water and other media [34; 35].