Mathematical Modeling of In Vivo Alpha Particle Generators and Chelator Stability

Background: Targeted α particle therapy using long-lived in vivo α particle generators is cytotoxic to target tissues. However, the redistribution of released radioactive daughters through the circulation should be considered. A mathematical model was developed to describe the physicochemical kinetics of 212Pb-labeled pharmaceuticals and its radioactive daughters. Materials and Methods: A bolus of 212Pb-labeled pharmaceuticals injected in a developed compartmental model was simulated. The contributions of chelated and free radionuclides to the total released energy were investigated for different dissociation fractions of 212Bi for different chelators, for example, 36% for DOTA. The compartmental model was applied to describe a 212Bi retention study and to assess the stability of the 212Bi-1,4,7,10-tetrakis(carbamoylmethyl)-1,4,7,10-tetraazacyclododecane (212Bi-DOTAM) complex after β- decay of 212Pb. Results: The simulation of the injection showed that α emissions contribute 75% to the total released energy, mostly from 212Po (72%). The simulation of the 212Bi retention study showed that (16 ± 5)% of 212Bi atoms dissociate from the 212Bi-DOTAM complexes. The fractions of energies released by free radionuclides were 21% and 38% for DOTAM and DOTA chelators, respectively. Conclusion: The developed α particle generator model allows for simulating the radioactive kinetics of labeled and unlabeled pharmaceuticals being released from the chelating system due to a preceding disintegration.

A population-based method to determine the time-integrated activity in molecular radiotherapy

BACKGROUND

The calculation of time-integrated activities (TIAs) for tumours and organs is required for dosimetry in molecular radiotherapy. The accuracy of the calculated TIAs is highly dependent on the chosen fit function. Selection of an adequate function is therefore of high importance. However, model (i.e. function) selection works more accurately when more biokinetic data are available than are usually obtained in a single patient. In this retrospective analysis, we therefore developed a method for population-based model selection that can be used for the determination of individual time-integrated activities (TIAs). The method is demonstrated at an example of [¹⁷⁷Lu]Lu-PSMA-I&T kidneys biokinetics. It is based on population fitting and is specifically advantageous for cases with a low number of available biokinetic data per patient.

METHODS

Renal biokinetics of [¹⁷⁷Lu]Lu-PSMA-I&T from thirteen patients with metastatic castration-resistant prostate cancer acquired by planar imaging were used. Twenty exponential functions were derived from various parameterizations of mono- and bi-exponential functions. The parameters of the functions were fitted (with different combinations of shared and individual parameters) to the biokinetic data of all patients. The goodness of fits were assumed as acceptable based on visual inspection of the fitted curves and coefficients of variation CVs < 50%. The Akaike weight (based on the corrected Akaike Information Criterion) was used to select the fit function most supported by the data from the set of functions with acceptable goodness of fit.

RESULTS

The function [Formula: see text] with shared parameter [Formula: see text] was selected as the function most supported by the data with an Akaike weight of 97%. Parameters [Formula: see text] and [Formula: see text] were fitted individually for every patient while parameter [Formula: see text] was fitted as a shared parameter in the population yielding a value of 0.9632 ± 0.0037.

CONCLUSIONS

The presented population-based model selection allows for a higher number of parameters of investigated fit functions which leads to better fits. It also reduces the uncertainty of the obtained Akaike weights and the selected best fit function based on them. The use of the population-determined shared parameter for future patients allows the fitting of more appropriate functions also for patients for whom only a low number of individual data are available.

A Whole-Body Physiologically Based Pharmacokinetic Model for Alpha Particle Emitting Bismuth in Rats

Introduction/Aim: α particle emitting bismuth (²¹²Bi) as decay product of ²¹²Pb-labeled pharmaceuticals has been effective in targeted α particle therapy (TAT). Estimating the contribution of ²¹²Bi released from its chelator to the absorbed doses in nontarget tissues is challenging in TAT. Physiologically based pharmacokinetic (PBPK) modeling can help overcome this limitation. Therefore, a whole-body ²¹²Bi-PBPK model was developed to describe the pharmacokinetics (PKs) of ²¹²Bi in rats. Materials and Methods: The rat ²¹²Bi-PBPK model was implemented using the modeling software SAAM II with data and parameter values from the literature. Besides other mechanisms, ²¹²Bi interactions with red blood cells, high molecular weight plasma protein, and intracellular biological thiols are described. Important PK parameters were fitted to time-activity data. Absorbed dose coefficients (ADCs) were calculated for injecting 0.774 fmol of ²¹²Bi. Results: ²¹²Bi uptake rates of liver, bone, small intestine, bone marrow, skin, and muscle were (0.86 ± 0.13), (3.85 ± 0.63), (0.27 ± 0.05), (1.44 ± 0.29), (0.04 ± 0.01), and (0.007 ± 0.007) per min with corresponding ADCs of 0.09, 0.03, 0.03, 0.07, 0.01, and 0.003 mGy/kBq, respectively. An ADC of 0.70 mGy/kBq was determined for kidneys. Conclusion: Kidneys are the dose-limiting organs in ²¹²Bi-based TAT. The ²¹²Bi-PBPK model is an effective tool to investigate the ²¹²Bi biodistribution in murine models. Integrating the ²¹²Bi-PBPK model into other murine and human PBPK models of α particle generators can help study the efficacy and safety of TAT.