Modeling to capture bystander-killing effect by released payload in target positive tumor cells.

BACKGROUND: Antibody-drug conjugates (ADCs) are intended to bind to specific positive target antigens and eradicate only tumor cells from an intracellular released payload through the lysosomal protease. Payloads, such as MMAE, have the capacity to kill adjacent antigen-negative (Ag-) tumor cells, which is called the bystander-killing effect, as well as directly kill antigen-positive (Ag+) tumor cells. We propose that a dose-response curve should be independently considered to account for target antigen-positive/negative tumor cells. METHODS: A model was developed to account for the payload in Ag+/Ag- cells and the associated parameters were applied. A tumor growth inhibition (TGI) effect was explored based on an ordinary differential equation (ODE) after substituting the payload concentration in Ag+/Ag- cells into an Emax model, which accounts for the dose-response curve. To observe the bystander-killing effects based on the amount of Ag+/Ag- cells, the Emax model is used independently. TGI models based on ODE are unsuitable for describing the initial delay through a tumor-drug interaction. This was solved using an age-structured model based on the stochastic process. RESULTS: ß∈(0,1] is a fraction parameter that determines the proportion of cells that consist of Ag+/Ag- cells. The payload concentration decreases when the ratio of efflux to influx increases. The bystander-killing effect differs with varying amounts of Ag+ cells. The larger ß is, the less bystander-killing effect. The decrease of the bystander-killing effect becomes stronger as Ag+ cells become larger than the Ag- cells. Overall, the ratio of efflux to influx, the amount of released payload, and the proportion of Ag+ cells determine the efficacy of the ADC. The tumor inhibition delay through a payload-tumor interaction, which goes through several stages, may be solved using an age-structured model. CONCLUSIONS: The bystander-killing effect, one of the most important topics of ADCs, has been explored in several studies without the use of modeling. We propose that the bystander-killing effect can be captured through a mathematical model when considering the Ag+ and Ag- cells. In addition, the TGI model based on the age-structure can capture the initial delay through a drug interaction as well as the bystander-killing effect.

Aiding early clinical drug development by elucidation of the relationship between tumor growth inhibition and survival in relapsed/refractory multiple myeloma patients.

Early prognosis of clinical efficacy is an urgent need for oncology drug development. Herein, we systemically examined the quantitative approach of tumor growth inhibition (TGI) and survival modeling in the space of relapsed and refractory multiple myeloma (MM), aiming to provide insights into clinical drug development. Longitudinal serum M-protein and progression-free survival (PFS) data from three phase III studies (N = 1367) across six treatment regimens and different patient populations were leveraged. The TGI model successfully described the longitudinal M-protein data in patients with MM. The tumor inhibition and growth parameters were found to vary as per each study, likely due to the patient population and treatment regimen difference. Based on a parametric time-to-event model for PFS, M-protein reduction at week 4 was identified as a significant prognostic factor for PFS across the three studies. Other factors, including Eastern Cooperative Oncology Group performance status, prior anti-myeloma therapeutics, and baseline serum ß2-microglobulin level, were correlated with PFS as well. In conclusion, patient disease characteristics (i.e., baseline tumor burden and treatment lines) were important determinants of tumor inhibition and PFS in MM patients. M-protein change at week 4 was an early prognostic biomarker for PFS.

Development of a quantitative relationship between CAR-affinity, antigen abundance, tumor cell depletion and CAR-T cell expansion using a multiscale systems PK-PD model.

The development of mechanism-based, multiscale pharmacokinetic-pharmacodynamic (PK-PD) models for chimeric antigen receptor (CAR)-T cells is needed to enable investigation of in vitro and in vivo correlation of CAR-T cell responses and to facilitate preclinical-to-clinical translation. Toward this goal, we first developed a cell-level in vitro PD model that quantitatively characterized CAR-T cell-induced target cell depletion, CAR-T cell expansion and cytokine release. The model accounted for key drug-specific (CAR-affinity, CAR-densities) and system-specific (antigen densities, E:T ratios) variables and was able to characterize comprehensive in vitro datasets from multiple affinity variants of anti-EGFR and anti-HER2 CAR-T cells. Next, a physiologically based PK (PBPK) model was developed to simultaneously characterize the biodistribution of untransduced T-cells, anti-EGFR CAR-T and anti-CD19 CAR-T cells in xenograft -mouse models. The proposed model accounted for the engagement of CAR-T cells with tumor cells at the site of action. Finally, an integrated PBPK-PD relationship was established to simultaneously characterize expansion of CAR-T cells and tumor growth inhibition (TGI) in xenograft mouse model, using datasets from anti-BCMA, anti-HER2, anti-CD19 and anti-EGFR CAR-T cells. Model simulations provided potential mechanistic insights toward the commonly observed multiphasic PK profile (i.e., rapid distribution, expansion, contraction and persistence) of CAR-T cells in the clinic. Model simulations suggested that CAR-T cells may have a steep dose-exposure relationship, and the apparent Cmax upon CAR-T cell expansion in blood may be more sensitive to patient tumor-burden than CAR-T dose levels. Global sensitivity analysis described the effect of other drug-specific parameters toward CAR-T cell expansion and TGI. The proposed modeling framework will be further examined with the clinical PK and PD data, and the learnings can be used to inform design and development of future CAR-T therapies.

Advanced Non-linear Mathematical Model for the Prediction of the Activity of a Putative Anticancer Agent in Human-to-mouse Cancer Xenografts.

BACKGROUND/AIM: Mathematical models have long been considered as important tools in cancer biology and therapy. Herein, we present an advanced non-linear mathematical model that can predict accurately the effect of an anticancer agent on the growth of a solid tumor. MATERIALS AND METHODS: Advanced non-linear mathematical optimization techniques and human-to-mouse experimental data were used to develop a tumor growth inhibition (TGI) estimation model. RESULTS: Using this mathematical model, we could accurately predict the tumor mass in a human-to-mouse pancreatic ductal adenocarcinoma (PDAC) xenograft under gemcitabine treatment up to five time periods (points) ahead of the last treatment. CONCLUSION: The ability of the identified TGI dynamic model to perform satisfactory short-term predictions of the tumor growth for up to five time periods ahead was investigated, evaluated and validated for the first time. Such a prediction model could not only assist the pre-clinical testing of putative anticancer agents, but also the early modification of a chemotherapy schedule towards increased efficacy.