Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments. This article is characterized under: Analytical and Computational Methods > Computational Methods Translational, Genomic, and Systems Medicine > Therapeutic Methods Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

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Nanotherapy may constitute a promising approach to target tumors with anticancer drugs while minimizing systemic toxicity. Computational modeling can enable rapid evaluation of nanoparticle (NP) designs and numerical optimization. Here, an optimization study was performed using an existing tumor model to find NP size and ligand density that maximize tumoral NP accumulation while minimizing tumor size. Optimal NP avidity lies at lower bound of feasible values, suggesting reduced ligand density to prolong NP circulation. For the given set of tumor parameters, optimal NP diameters were 288 nm to maximize NP accumulation and 334 nm to minimize tumor diameter, leading to uniform NP distribution and adequate drug load. Results further show higher dependence of NP biodistribution on the NP design than on tumor morphological parameters. A parametric study with respect to drug potency was performed. The lower the potency of the drug, the bigger the difference is between the maximizer of NP accumulation and the minimizer of tumor size, indicating the existence of a specific drug potency that minimizes the differential between the two optimal solutions. This study shows the feasibility of applying optimization to NP designs to achieve efficacious cancer nanotherapy, and offers a first step towards a quantitative tool to support clinical decision making.

Nanoparticle (NP)-based drug delivery is a promising method to increase the therapeutic index of anticancer agents with low median toxic dose. The delivery efficiency, corresponding to the fraction of the injected NPs that adhere to the tumor site, depends on NP size a and aspect ratio AR. Values for these variables are currently chosen empirically, which may not result in optimal targeted drug delivery. This study applies rigorous optimization to the design of NPs. A preliminary investigation revealed that delivery efficiency increases monotonically with a and AR. However, maximizing a and AR results in nonuniform drug distribution, which impairs tumor regression. Therefore, a multiobjective optimization (MO) problem is formulated to quantify the trade-off between NPs accumulation and distribution. The MO is solved using the derivative-free mesh adaptive direct search algorithm. Theoretically, the Pareto-optimal set consists of an infinite number of mathematically equivalent solutions to the MO problem. However, interesting design solutions can be identified subjectively, e.g., the ellipsoid with a major axis of 720 nm and an aspect ratio of 7.45, as the solution closest to the utopia point. The MO problem formulation is then extended to optimize NP biochemical properties: ligand-receptor binding affinity and ligand density. Optimizing physical and chemical properties simultaneously results in optimal designs with reduced NP sizes and thus enhanced cellular uptake. The presented study provides an insight into NP structures that have potential for producing desirable drug delivery.

The rapid spread of the coronavirus disease COVID-19 has imposed clinical and financial burdens on hospitals and governments attempting to provide patients with medical care and implement disease-controlling policies. The transmissibility of the disease was shown to be correlated with the patient’s viral load, which can be measured during testing using the cycle threshold (Ct). Previous models have utilized Ct to forecast the trajectory of the spread, which can provide valuable information to better allocate resources and change policies. However, these models combined other variables specific to medical institutions or came in the form of compartmental models that rely on epidemiological assumptions, all of which could impose prediction uncertainties. In this study, we overcome these limitations using data-driven modeling that utilizes Ct and previous number of cases, two institution-independent variables. We collected three groups of patients (n = 6296, n = 3228, and n = 12,096) from different time periods to train, validate, and independently validate the models. We used three machine learning algorithms and three deep learning algorithms that can model the temporal dynamic behavior of the number of cases. The endpoint was 7-week forward number of cases, and the prediction was evaluated using mean square error (MSE). The sequence-to-sequence model showed the best prediction during validation (MSE = 0.025), while polynomial regression (OLS) and support vector machine regression (SVR) had better performance during independent validation (MSE = 0.1596, and MSE = 0.16754, respectively), which exhibited better generalizability of the latter. The OLS and SVR models were used on a dataset from an external institution and showed promise in predicting COVID-19 incidences across institutions. These models may support clinical and logistic decision-making after prospective validation.