Dosage optimization for reducing tumor burden using a phenotype-structured population model with a drug-resistance continuum

Drug resistance is a significant obstacle to effective cancer treatment. To gain insights into how drug resistance develops, we adopted a concept called fitness landscape and employed a phenotype-structured population model by fitting to a set of experimental data on a drug used for ovarian cancer, olaparib. Our modeling approach allowed us to understand how a drug affects the fitness landscape and track the evolution of a population of cancer cells structured with a spectrum of drug resistance. We also incorporated pharmacokinetic (PK) modeling to identify the optimal dosages of the drug that could lead to long-term tumor reduction. We derived a formula that indicates that maximizing variation in plasma drug concentration over a dosing interval could be important in reducing drug resistance. Our findings suggest that it may be possible to achieve better treatment outcomes with a drug dose lower than the levels recommended by the drug label. Acknowledging the current limitations of our work, we believe that our approach, which combines modeling of both PK and drug resistance evolution, could contribute to a new direction for better designing drug treatment regimens to improve cancer treatment.

Dose optimization of an adjuvanted peptide-based personalized neoantigen melanoma vaccine

The advancements in next-generation sequencing have made it possible to effectively detect somatic mutations, which has led to the development of personalized neoantigen cancer vaccines that are tailored to the unique variants found in a patient's cancer. These vaccines can provide significant clinical benefit by leveraging the patient's immune response to eliminate malignant cells. However, determining the optimal vaccine dose for each patient is a challenge due to the heterogeneity of tumors. To address this challenge, we formulate a mathematical dose optimization problem based on a previous mathematical model that encompasses the immune response cascade produced by the vaccine in a patient. We propose an optimization approach to identify the optimal personalized vaccine doses, considering a fixed vaccination schedule, while simultaneously minimizing the overall number of tumor and activated T cells. To validate our approach, we perform in silico experiments on six real-world clinical trial patients with advanced melanoma. We compare the results of applying an optimal vaccine dose to those of a suboptimal dose (the dose used in the clinical trial and its deviations). Our simulations reveal that an optimal vaccine regimen of higher initial doses and lower final doses may lead to a reduction in tumor size for certain patients. Our mathematical dose optimization offers a promising approach to determining an optimal vaccine dose for each patient and improving clinical outcomes.

A Retrospective Review of Center for Biologics Evaluation and Research Advisory Committee Meetings in the Context of the FDA's Benefit-Risk Framework

The US FDA Center for Biologics Evaluation and Research (CBER) is responsible for the regulation of biologically derived products. FDA has established Advisory Committees (AC) as vehicles to seek external expert advice on scientific and technical matters related to the development and evaluation of products regulated by the agency. We aimed to identify and evaluate common topics discussed in CBER AC meetings during the regulatory decision-making process for biological products and medical devices. We analyzed the content of 119 CBER-led AC meetings between 2009 and 2021 listed on the FDA AC webpage. We reviewed publicly available meeting materials such as briefing documents, summaries, and transcripts. Using a structured review codebook based on FDA benefit-risk guidance, we identified important considerations within the benefit-risk dimensions discussed at the AC meetings: therapeutic context, benefit, risk and risk management, and benefit-risk trade-off, where evidence and uncertainty are critical parts of the FDA benefit-risk framework. Based on a detailed review of 24 topics discussed in 23 selected AC meetings conducted between 2016 and 2021, the two most frequently discussed considerations were "Uncertainty about assessment of the safety profile" and "Uncertainty about assessment of the benefit based on clinical trial data" (16/24 times each) as defined in our codebook. Most of the reviewed meetings discussed Investigational New Drug or Biologics License Applications of products. This review could help sponsors better plan and design studies by contextualizing how the benefit-risk dimensions were embedded in the AC discussions and the considerations that went into the final AC recommendations.

Analysis of tumor-immune functional responses in a mathematical model of neoantigen cancer vaccines

Cancer neoantigen vaccines have emerged as a promising approach to stimulating the immune system to fight cancer. We propose a simple model including key elements of cancer-immune interactions and conduct a phase plane analysis to understand the immunological mechanisms of cancer neoantigen vaccines. Analytical results are obtained for two widely used functional forms that represent the killing rate of tumor cells by immune cells: the law of mass action (LMA) and the dePillis-Radunskaya Law (LPR). Using the LMA, our results reveal that a slowly growing tumor can escape the immune surveillance and that there is a unique periodic solution. The LPR offers richer dynamics, in which tumor elimination and uncontrolled tumor growth are both present. We show that tumor elimination requires sufficient number of initial activated T cells in relationship to the malignant cells, which lends support to using the neoantigen cancer vaccine as an adjuvant therapy after the primary tumor is surgically removed or treated using radiotherapy. We also derive a sufficient condition for uncontrolled tumor growth under the assumption of the LPR. The juxtaposition of analyses with these two different choices for the killing rate function highlights their importance on model behavior and biological implications, by which we hope to spur further theoretical and experimental work to understand mechanisms underlying different functional forms for the killing rate.

Mathematical model of a personalized neoantigen cancer vaccine and the human immune system

Cancer vaccines are an important component of the cancer immunotherapy toolkit enhancing immune response to malignant cells by activating CD4⁺ and CD8⁺ T cells. Multiple successful clinical applications of cancer vaccines have shown good safety and efficacy. Despite the notable progress, significant challenges remain in obtaining consistent immune responses across heterogeneous patient populations, as well as various cancers. We present a mechanistic mathematical model describing key interactions of a personalized neoantigen cancer vaccine with an individual patient’s immune system. Specifically, the model considers the vaccine concentration of tumor-specific antigen peptides and adjuvant, the patient’s major histocompatibility complexes I and II copy numbers, tumor size, T cells, and antigen presenting cells. We parametrized the model using patient-specific data from a clinical study in which individualized cancer vaccines were used to treat six melanoma patients. Model simulations predicted both immune responses, represented by T cell counts, to the vaccine as well as clinical outcome (determined as change of tumor size). This model, although complex, can be used to describe, simulate, and predict the behavior of the human immune system to a personalized cancer vaccine.

Personalized cancer vaccines have gained attention in recent years due to the advances in sequencing techniques that have facilitated the identification of multiple tumor-specific mutations. This type of individualized immunotherapy has the potential to be specific, efficacious, and safe since it induces an immune response to protein targets not found on normal cells. This work focuses on understanding and analyzing important mechanisms involved in the activity of personalized cancer vaccines using a mechanistic mathematical model. This model describes the interactions of a personalized neoantigen peptide cancer vaccine, the human immune system and tumor cells operating at the molecular and cellular level. The molecular level captures the processing and presentation of neoantigens by dendritic cells to the T cells using cell surface proteins. The cellular level describes the differentiation of dendritic cells due to peptides and adjuvant concentrations in the vaccine, activation, and proliferation of T cells in response to treatment, and tumor growth. The model captures immune response behavior to a vaccine associated with patient-specific factors (e.g., different initial tumor burdens). This model enables the simulation of a complex biological system, the human immune system, by performing in silico experiments that may become the input for further analysis such as the identification of key parameters or mechanisms and/or interpretation of data.

Nutritional regulation influencing colony dynamics and task allocations in social insect colonies

In this paper, we use an adaptive modeling framework to model and study how nutritional status (measured by the protein to carbohydrate ratio) may regulate population dynamics and foraging task allocation of social insect colonies. Mathematical analysis of our model shows that both investment to brood rearing and brood nutrition are important for colony survival and dynamics. When division of labour and/or nutrition are in an intermediate value range, the model undergoes a backward bifurcation and creates multiple attractors due to bistability. This bistability implies that there is a threshold population size required for colony survival. When the investment in brood is large enough or nutritional requirements are less strict, the colony tends to survive, otherwise the colony faces collapse. Our model suggests that the needs of colony survival are shaped by the brood survival probability, which requires good nutritional status. As a consequence, better nutritional status can lead to a better survival rate of larvae and thus a larger worker population.

A Systematic Review of the Efforts and Hindrances of Modeling and Simulation of CAR T-cell Therapy

Chimeric antigen receptor (CAR) T-cell therapy is an immunotherapy that has recently become highly instrumental in the fight against life-threatening diseases. A variety of modeling and computational simulation efforts have addressed different aspects of CAR T-cell therapy, including T-cell activation, T- and malignant cell population dynamics, therapeutic cost-effectiveness strategies, and patient survival. In this article, we present a systematic review of those efforts, including mathematical, statistical, and stochastic models employing a wide range of algorithms, from differential equations to machine learning. To the best of our knowledge, this is the first review of all such models studying CAR T-cell therapy. In this review, we provide a detailed summary of the strengths, limitations, methodology, data used, and data gap in currently published models. This information may help in designing and building better models for enhanced prediction and assessment of the benefit-risk balance associated with novel CAR T-cell therapies, as well as with the data need for building such models.

Predicting the results of competition between two breast cancer lines grown in 3-D spheroid culture

This study develops a novel model of a consumer-resource system with mobility included, in order to explain a novel experiment of competition between two breast cancer cell lines grown in 3D in vitro spheroid culture. The model reproduces observed differences in monoculture, such as overshoot phenomena and final size. It also explains both theoretically and through simulation the inevitable triumph of the same cell line in co-culture, independent of initial conditions. The mobility of one cell line (MDA-MB-231) is required to explain both the success and the rapidity with which that species dominates the population and drives the other species (MCF-7) to extinction. It is shown that mobility directly interferes with the other species and that the cost of that mobility is in resource usage rate.

A Quantitative Evaluation of COVID-19 Epidemiological Models

Quantifying how accurate epidemiological models of COVID-19 forecast the number of future cases and deaths can help frame how to incorporate mathematical models to inform public health decisions. Here we analyze and score the predictive ability of publicly available COVID-19 epidemiological models on the COVID-19 Forecast Hub. Our score uses the posted forecast cumulative distributions to compute the log-likelihood for held-out COVID-19 positive cases and deaths. Scores are updated continuously as new data become available, and model performance is tracked over time. We use model scores to construct ensemble models based on past performance. Our publicly available quantitative framework may aid in improving modeling frameworks, and assist policy makers in selecting modeling paradigms to balance the delicate trade-offs between the economy and public health.

Dynamical implications of bi-directional resource exchange within a meta-ecosystem

The exchange of resources across ecosystem boundaries can have large impacts on ecosystem structures and functions at local and regional scales. In this article, we develop a simple model to investigate dynamical implications of bi-directional resource exchanges between two local ecosystems in a meta-ecosystem framework. In our model, we assume that (1) Each local ecosystem acts as both a resource donor and recipient, such that one ecosystem donating resources to another results in a cost to the donating system and a benefit to the recipient; and (2) The costs and benefits of the bi-directional resource exchange between two ecosystems are correlated in a nonlinear fashion. Our model could apply to the resource interactions between terrestrial and aquatic ecosystems that are supported by the literature. Our theoretical results show that bi-directional resource exchange between two ecosystems can indeed generate complicated dynamical outcomes, including the coupled ecosystems having amensalistic, antagonistic, competitive, or mutualistic interactions, with multiple alternative stable states depending on the relative costs and benefits. In addition, if the relative cost for resource exchange for an ecosystem is decreased or the relative benefit for resource exchange for an ecosystem is increased, the production of that ecosystem would increase; however, depending on the local environment, the production of the other ecosystem may increase or decrease. We expect that our work, by evaluating the potential outcomes of resource exchange theoretically, can facilitate empirical evaluations and advance the understanding of spatial ecosystem ecology where resource exchanges occur in varied ecosystems through a complicated network.