Quantification of biochemical PSA dynamics after radioligand therapy with [¹⁷⁷Lu]Lu-PSMA-I&T using a population pharmacokinetic/pharmacodynamic model

Background: There is an unmet need for prediction of treatment outcome or patient selection for [Lu-177]Lu-PSMA therapy in patients with metastatic castration-resistant prostate cancer (mCRPC). Quantification of the tumor exposure-response relationship is pivotal for further treatment optimization. Therefore, a population pharmacokinetic (PK) model was developed for [Lu-177]Lu-PSMA-I&T using SPECT/CT data and, subsequently, related to prostate-specific antigen (PSA) dynamics after therapy in patients with mCRPC using a pharmacokinetic/pharmacodynamic (PKPD) modelling approach. Methods: A population PK model was developed using quantitative SPECT/CT data (406 scans) of 76 patients who received multiple cycles [Lu-177]Lu-PSMA-I&T (+/- 7.4 GBq with either two- or six-week interval). The PK model consisted of five compartments; central, salivary glands, kidneys, tumors and combined remaining tissues. Covariates (tumor volume, renal function and cycle number) were tested to explain inter-individual variability on uptake into organs and tumors. The final PK model was expanded with a PD compartment (sequential fitting approach) representing PSA dynamics during and after treatment. To explore the presence of a exposure-response relationship, individually estimated [Lu-177]Lu-PSMA-I&T tumor concentrations were related to PSA changes over time. Results: The population PK model adequately described observed data in all compartments (based on visual inspection of goodness-of-fit plots) with adequate precision of parameters estimates (< 36.1% relative standard error (RSE)). A significant declining uptake in tumors (k(14)) during later cycles was identified (uptake decreased to 73%, 50% and 44% in cycle 2, 3 and 4-7, respectively, compared to cycle 1). Tumor growth (defined by PSA increase) was described with an exponential growth rate (0.000408 h(-1) (14.2% RSE)). Therapy-induced PSA decrease was related to estimated tumor concentrations (MBq/L) using both a direct and delayed drug effect. The final model adequately captured individual PSA concentrations after treatment (based on goodness-of-fit plots). Simulation based on the final PKPD model showed no evident differences in response for the two different dosing regimens currently used. Conclusions: Our population PK model accurately described observed [Lu-177]Lu-PSMA-I&T uptake in salivary glands, kidneys and tumors and revealed a clear declining tumor uptake over treatment cycles. The PKPD model adequately captured individual PSA observations and identified population response rates for the two dosing regimens. Hence, a PKPD modelling approach can guide prediction of treatment response and thus identify patients in whom radioligand therapy is likely to fail.