S. binding capacity-based dosing. The rate of binding of drug to cancer cells depends on the total number of their specific receptors, which therefore can be estimated from the pharmacokinetic curve of diagnostic radioconjugates. Injection of doses significantly exceeding cancer binding capacity should be avoided since radioconjugates remaining in the bloodstream have negligible efficacy to toxicity ratio. 3) Particle range-guided multi-dosing. The use of short-range particle emitters and high-affinity antibodies allows for robust treatment optimization via initial saturation of cancer binding capacity, enabling redistribution of further injected radioconjugates and deposited dose towards still viable cells that continue expressing specific receptors. Introduction Biological background Targeted therapy is based on suppressing survival and proliferation of cancer cells through interactions with molecules specific to the cancer type under consideration. Large class of targeted brokers are monoclonal antibodies that specifically bind to receptors around the surfaces of cancer cells [1]. One such example is usually daratumumab, which targets CD38. These receptors are overexpressed in multiple myeloma, which is a white blood cell cancer resulting in about MDK a hundred thousand deaths worldwide annually [2]. The main mode of action of daratumumab is usually induction of cancer cell killing by the immune system [3]. Clinical trials have shown favorable safety profile of daratumumab [4]. However, its action results in highly heterogeneous outcomes, including frequent cancer relapse after initial response. Relevant studies suggest that the mechanisms of multiple myeloma resistance to daratumumab are associated with immune escape [5], as relapsing patients show stable expression of unmutated CD38 on cancer cells, which preserves their ability to be Pyraclonil targeted by daratumumab [6]. A way to enhance the efficacy of targeted therapy is usually to attach additional therapeutic payload to antibodies, ensuring its selective delivery to malignant cells. Conjugation of antibodies with cytotoxic brokers has already led to more than a dozen clinically approved drugs [1], and conjugation of antibodies with radioactive nuclides is usually gaining growing clinical interest [7]. Two main types of radionuclides are being investigated in trials: emitters of trials simulating treatment outcomes for heterogeneous virtual populations [15]. Robust conclusions gained by mathematical modeling can be verified in clinical trials and eventually be implemented into clinical decision-making Pyraclonil pipeline [16]. Mathematical Pyraclonil modeling of TRT relies on modeling of drug pharmacokinetics, which is an extensive research area [17], and on modeling of continuous exposure of cells to irradiation, which has a well-established mathematical foundation [18]. Yet, to date there exist only a few studies on mathematical modeling of TRT. The works by Kletting et al. present detailed pharmacokinetic models, designed with the goal of predicting the biologically effective doses received by tumors and healthy organs [19, 20] as well as the tumor response [21] for varying amounts of injected taking positive values for such cases. This reflects the presence of impurities that accompany the production of radioconjugates, which are unlabeled antibodies and antibodies conjugated with non-radioactive ions [35]. This can also reflect deliberate dilution of drug within unlabeled antibodies. The function of radiation damage accounts for three sources of radiation Pyraclonil that can affect viable cancer cells. The terms of self-damage and cross-fire stand for the damage of a cancer cell due to the decays taking place on its own receptors and on the receptors of neighboring cells, respectively. The numerator in each of these terms denotes the rate of decays within a certain volume, provided in the denominator. The relative significance of self-damage for should, however, increase with the decrease of cancer cells density. The third term of radiation damage corresponds to decays of unanchored nuclides. For brevity, we will refer to them as for time, for volume, for amounts of antibodies and receptors, for their concentrations. Table 1: Model parameters. for the basic set of parameters. A, dynamics of active antibodies and their fragments in plasma. B, dynamics of cancer cells. C, dependence of minimal single curative dose on relative significance of self-damage, is achieved when the rate of nuclear decays falls to the level at which they are not able to compensate for ongoing cell proliferation. The ratio can be regarded as of cancer.