Mathematical Modeling Unveils Optimization Strategies for Targeted Radionuclide Therapy of Blood Cancers

Abstract

Targeted radionuclide therapy is based on injections of cancer-specific molecules conjugated with radioactive nuclides. Despite the specificity of this treatment, it is not devoid of side-effects limiting its use and is especially harmful for rapidly proliferating organs well perfused by blood, like bone marrow. Optimization of radioconjugates administration accounting for toxicity constraints can increase treatment efficacy. Based on our experiments on disseminated multiple myeloma mouse model treated by ²²⁵Ac-DOTA-daratumumab, we developed a mathematical model which investigation highlighted the following principles for optimization of targeted radionuclide therapy. 1) Nuclide to antibody ratio importance. The density of radioconjugates on cancer cells determines the density of radiation energy deposited in them. Low labeling ratio as well as accumulation of unlabeled antibodies and antibodies attached to decay products in the bloodstream can mitigate cancer radiation damage due to excessive occupation of specific receptors by antibodies devoid of radioactive nuclides. 2) Cancer 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.

Figure 1:

Schematic view of the main processes considered in the mathematical model. Created with BioRender.

Figure 2:

Model simulations of treatment by pure radioconjugates $\left(\eta =0\right)$ 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, $k_s$. D, dynamics of occupied receptors on viable cells. E, dynamics of occupied receptors on damaged cells.

Figure 3:

Dependence of minimal single curative dose on the coefficient of drug impurity, $\eta$, i.e., the ratio of unlabeled antibodies to radioconjugates. A, moderate variation of $\eta$. B, extended variation of $\eta$.

Figure 4:

A, scatter plot of cancer binding capacity, i.e., total amount of specific receptors on cancer cells at the moment of drug injection, and minimal single curative dose produced by the global parameter sweep within the training set of one thousand virtual mice. Coefficient of drug impurity, $\eta$, corresponds to the labeling ratio of 1.85 kBq/µg. B, survival curves and C, toxicity curves for a single test set of one thousand virtual mice, treated by different approaches.

Figure 5:

Survival curves for the test set of virtual mice, grouped by relative significance of self-damage, $k_s$: A, low $k_s$; B, intermediate $k_s$; C, high $k_s$. Coefficient of drug impurity, $\eta$, corresponds to the labeling ratio of 1.85 kBq/µg.