Are PBPK Models Enough to Scale Between Mice and Humans?

Introduction: Prostate-specific membrane antigen (PSMA) is an over-expressed protein in prostatic cancer (up to a thousandfold) and has been investigated for both diagnostic and treatment purposes. A common approach throughout the scientific community to help understand the biokinetics of a new drug is the use of xenograft models. However, scaling radiopharmaceutical biokinetics between mice and humans is a well-known problem that still makes the translation from pre-clinic to clinic challenging. Although different methods have been suggested, a clear path on how and what to use is yet to come. In this work, we investigate using a physiologically based pharmacokinetic (PBPK) model for humans and mice and whether modifying parameters, such as organ masses, is enough for scaling ¹⁷⁷Lu-PSMA biodistribution. Additionally, we assess if, with the abovementioned modifications, the time scale of the time-activity curve (TAC) agrees with a commonly used allometric factor.

Methods: A ¹⁷⁷Lu-PSMA whole-body PBPK model developed in Simbiology (MATLAB) was used to simulate mice and human biokinetics with respective values of metabolic rates and organ masses. The models connect organs via blood flow, where labeled and unlabeled peptides compete for binding to free receptors. It includes, among other parameters, blood flow distribution, clearance, internalization rates, release, degradation, recycling, and physical decay. A standard activity of 7.4 GBq was used for the human model and a range of 0.1 to 30 MBq for the mouse model. The models were compared regarding the time-integrated-activity curves (TIACs) of the whole body, kidneys, liver, and spleen, and the number of free receptors in the kidneys. Lastly, a comparison with the allometric time equation (eq. 1) was used to assess if the model falls within the calculated time frame.

Time Factor = (mass Human/mass Mouse)^0.25 (Eq. 1)

Results: The TACs of mice demonstrate much faster uptake and washout than in humans. The PBPK model inherently “adjusts” the time scale through the metabolic rates and organ volumes. Using the time factor to rescale the TAC, humans, and mice normalized TACs can be overlaid. This shows that the PBPK model can scale between humans and mice, provided the correct input data are used. The relative difference of TIACs between men and mice varies across all organs, with the lowest mean relative difference of 36% for 3 MBq (highest of 70% with 0.1 MBq and 48% with the often-used activity of 30 MBq). After infusion was complete, at 5 min and 43 s, the number of free receptors kept dropping, reaching 23% and 2% of the maximum for humans and mice (30 MBq), respectively, and then recovers. In humans, it steadily increases, taking 20% of the total time to reach 90% of the maximum, while in mice, it slowly recovers, reaching the same value at 2/3 of the experiment time. Results closer to humans were observed with 3 MBq that drops to 34% and reaches 90% of the maximum at half of the experiment time. The receptor density in the organs, especially the kidneys, plays an essential role in the model. A higher value in the mouse model (which is expected) could shift the results into a higher activity.

Conclusions: The PBPK model inherently applies an allometric time factor, suggesting that a PBPK model may be sufficient to perform a translation between mice and humans, provided correct input data. In addition, 3 MBq administrations in mice better represent the therapeutic activity used in humans. This work focused on demonstrating the capability of a PBPK model to describe scaling human and mouse models by modifying the necessary parameters. Specific receptor density, as well as internalization and recycling rates, were considered part of a “fine-tuning” of the model that will be further investigated and implemented, along with the inclusion of absorbed doses, experimental measurements, and the extension of the model to other radiopharmaceuticals.