BackgroundWhile mathematical models are often used to predict progression of cancer and treatment outcomes, there is still uncertainty over how to best model tumor growth. Seven ordinary differential equation (ODE) models of tumor growth (exponential, Mendelsohn, logistic, linear, surface, Gompertz, and Bertalanffy) have been proposed, but there is no clear guidance on how to choose the most appropriate model for a particular cancer.MethodsWe examined all seven of the previously proposed ODE models in the presence and absence of chemotherapy. We derived equations for the maximum tumor size, doubling time, and the minimum amount of chemotherapy needed to suppress the tumor and used a sample data set to compare how these quantities differ based on choice of growth model.ResultsWe find that there is a 12-fold difference in predicting doubling times and a 6-fold difference in the predicted amount of chemotherapy needed for suppression depending on which growth model was used.ConclusionOur results highlight the need for careful consideration of model assumptions when developing mathematical models for use in cancer treatment planning.

In order to determine correct dosage of chemotherapy drugs, the effect of the drug must be properly quantified. There are two important values that characterize the effect of the drug: ε max is the maximum possible effect of a drug, and IC 50 is the drug concentration where the effect diminishes by half. There is currently a problem with the way these values are measured because they are time-dependent measurements. We use mathematical models to determine how the ε max and IC 50 values depend on measurement time and model choice. Seven ordinary differential equation models (ODE) are used for the mathematical analysis; the exponential, Mendelsohn, logistic, linear, surface, Bertalanffy, and Gompertz models. We use the models to simulate tumor growth in the presence and absence of treatment with a known IC 50 and ε max. Using traditional methods, we then calculate the IC 50 and ε max values over fifty days to show the time-dependence of these values for all seven mathematical models. The general trend found is that the measured IC 50 value decreases and the measured ε max increases with increasing measurement day for most mathematical models. Unfortunately, the measured values of IC 50 and ε max rarely matched the values used to generate the data. Our results show that there is no optimal measurement time since models predict that IC 50 estimates become more accurate at later measurement times while ε max is more accurate at early measurement times.

Background: The pathologic complete response (pCR) rate in inflammatory breast cancer (IBC) patients is worse than in non-IBC patients; new drug combinations are warranted to improve pCR rates across all IBC molecular subtypes. Based on our preclinical data, we added neratinib to standard neoadjuvant chemotherapy in both HER2+ (synergy) and HER2-/hormone receptor (HR)+ (high frequency of ERBB2 mut) untreated IBC, as a single-center, non-randomized phase I/II trial. Patients and Method: This study enrolled three cohorts: Cohort I phase Ib (C1P1B), Cohort I Phase II (C1P2) and Cohort II (C2). In C1P1B to determine the recommended phase 2 dose (RP2D), we enrolled patients with HER2+ metastatic or locally advanced breast cancer. Patients received paclitaxel/trastuzumab/pertuzumab (THP) + neratinib x 4 cycles (up to 8 cycles per physician’s discretion). For C1P2 and C2, we enrolled Stage III – IV primary IBC patients. In C1P2, patients with HER2+ IBC received neratinib (RP2D) combined with THP x 4 cycles followed by doxorubicin/cyclophosphamide (AC) x 4 cycles. Per stage I design, 11 patients were enrolled with plan to enroll 20 more patients in Stage II if at least 6 had a pCR. In C2, patients with HER2-/HR+ IBC received neratinib 200 mg/day combined with paclitaxel x 4 cycles followed by AC x 4 cycles. Stage I design planned for enrollment of 16 patients with enrollment of 15 more patients on stage II, if at least 2 Stage I patients had pCR. In all three cohorts, patients initiated prophylactic anti-diarrheal medication (loperamide & budesonide) with the first dose of neratinib. Results: From 2018 to 2022, thirty-four patients were enrolled and treated (n=4 C1P1B, n=14 C1P2, n=16 C2). In C1P1B, observed DLTs (dose limiting toxicities) were Grade (Gr) 2 Diarrhea, n=2 (50%); Gr3 diarrhea, n=2 (50%); 2 patients had a serious adverse event (SAE); 3 patients (55%) had Gr2 nausea. The RP2D was established at 80 mg/day (dose level 0). For patients in C1P2, the most frequently occurring adverse events (AEs) included Gr2 Alopecia, n=14 (100%); Gr2&3 Diarrhea, n=14 (100%); Gr2/3 Nausea, n=12 (86%); Gr2/3 Anemia, n=7 (50%); Gr2/3 Fatigue, n=8 (57%); Gr2/3 Hypokalemia, n=6 (57%); and Gr2/3 Neutrophil count decreased, n= 7 (50%). 6 patients had an SAE. Of the first 11 patients, 5 (46%) had pCR, 1 (9%) RCB-1, 1 (9%) RCB-II and 1 (9%) RCB-III. Three patients stopped study treatment for toxicity (27%), were non-evaluable and replaced. Of these, one had RCB-III (33.3%), one progression of disease (PD) (33.3%), and one came off study for toxicity (33.3%). Rather than replacing additional non-evaluable patients, the study was closed to new patient accrual. In C2, the most frequently occurring AEs were Gr2 diarrhea, n=7(44%); Gr3 diarrhea, n=8 (50%); Gr2 alopecia, n=14 (88%); Gr2/3 Anemia, n=10 (63%); Gr2/3 Nausea, n=7 (44%); Gr2/3 Neutropenia, n= 7 (44%). 3 patients had an SAE. Of 16 patients in this cohort, 1 had pCR (6%), 5 RCB-II (31%), 4 RCB-III (25%), 3 came off study for toxicity (19%) and 3 had PD (19%). C2 also closed to new patient accrual given the high toxicity profile. Conclusion: The addition of neratinib did not improve the pCR rate in HER2+ or HER2-/HR+ subtypes of IBC, and increased toxicities were observed. The trial closed to new patient entry March 2022. However, some patients achieved significant response. Biomarker analysis is ongoing. Evaluable participants will continue long-term follow-up per protocol. Acknowledgments: This study is supported by PUMA Biotechnology. Citation Format: Angela N. Marx, Megumi Kai, Min Fu, Hope E. Murphy, Jie S. Willey, Huiming Sun, Angela Alexander, Roland L. Bassett, Gary J. Whitman, H. T. Carisa Le-Petross, Miral Patel, Banu K. Arun, Sausan Abouharb, Parijatham S. Thomas, Carlos H. Barcenas, Nuhad K. Ibrahim, Vicente Valero, Naoto T. Ueno, Rachel M. Layman, Bora Lim, Wendy Woodward, Anthony Lucci. A phase 1b study of neratinib with THP in metastatic and locally advanced breast cancer, and phase II study of THP followed by AC in HER2 + primary inflammatory breast cancer (IBC), and neratinib with taxol followed by AC in HR+/HER2- IBC [abstract]. In: Proceedings of the 2022 San Antonio Breast Cancer Symposium; 2022 Dec 6-10; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2023;83(5 Suppl):Abstract nr P4-06-09.

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