An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors

Glick, Adam; Mastroberardino, Antonio

doi:10.3390/math5040049

Cited by 20 publications

(12 citation statements)

References 39 publications

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“…Further, a multicriteria treatment design could provide a useful approach to the broad field of mathematical oncology. Studies have been performed to find protocols considering other factors that include in addition to tumor burden and tumor targeting, drug resistance 46 , total drug dose (toxicity) 47 , and immune response 48 . Using multiobjective optimization, two or more (2020) 10:8294 | https://doi.org/10.1038/s41598-020-65162-2 www.nature.com/scientificreports www.nature.com/scientificreports/ criteria could be incorporated in treatment planning or drug discovery, enabling the tackling of prognostic and toxicologic challenges.…”

Section: Discussionmentioning

confidence: 99%

Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles

Chamseddine

Frieboes

Kokkolaras

2020

Sci Rep

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the pharmacokinetics of nanoparticle-borne drugs targeting tumors depends critically on nanoparticle design. Empirical approaches to evaluate such designs in order to maximize treatment efficacy are timeand cost-intensive. We have recently proposed the use of computational modeling of nanoparticlemediated drug delivery targeting tumor vasculature coupled with numerical optimization to pursue optimal nanoparticle targeting and tumor uptake. Here, we build upon these studies to evaluate the effect of tumor size on optimal nanoparticle design by considering a cohort of heterogeneously-sized tumor lesions, as would be clinically expected. the results indicate that smaller nanoparticles yield higher tumor targeting and lesion regression for larger-sized tumors. We then augment the nanoparticle design optimization problem by considering drug diffusivity, which yields a twofold tumor size decrease compared to optimizing nanoparticles without this consideration. We quantify the tradeoff between tumor targeting and size decrease using bi-objective optimization, and generate five Paretooptimal nanoparticle designs. the results provide a spectrum of treatment outcomes-considering tumor targeting vs. antitumor effect-with the goal to enable therapy customization based on clinical need. this approach could be extended to other nanoparticle-based cancer therapies, and support the development of personalized nanomedicine in the longer term. Chemotherapy is the treatment of choice to control metastatic cancer-a stage often reported in patients at the time of clinical presentation. Unfortunately, patients undergoing chemotherapy may have low median survival, especially for pancreatic, lung, and liver cancer 1. Negative response to treatment is attributed to a number of factors, including tumor microenvironmental barriers, evolution of resistance to drug, and chemotherapeutic toxicity. It has been shown that nanoparticle-mediated drug delivery may substantially enhance the pharmacokinetics of anticancer drugs while addressing some of these factors 2. However, while many nano-based formulations have undergone pre-clinical and clinical evaluation, few have been translated to the clinic 3. The targeting potential of nanotherapy is strongly associated with nanoparticle biophysical and biochemical properties 4-6. These properties include size 7 , shape (e.g., sphere or ellipsoid) 5 , stiffness 4,8 , and binding affinity of nanoparticle surface ligands to receptors upregulated in cells in tumors 5. Computational studies have investigated the effect of these properties on treatment efficacy in an attempt to find nanoparticles optimized for maximal anti-tumor activity. Nanoparticle margination 6 and adhesion to tumor vasculature 5 have been modeled as a function of nanoparticle properties (size, aspect ratio, ligand surface density, and ligand-receptor binding affinity). Uncertainties in ligand surface density and ligand-receptor affinity have been quantified and incorporated in a nanoparticle-tumor adhesion model using a Bayesian hierarc...

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Section: Discussionmentioning

confidence: 99%

Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles

Chamseddine

Frieboes

Kokkolaras

2020

Sci Rep

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“…Clearly, there are six roots of (26) counting multiplicity, and thus, at most six biologically relevant equilibrium values for the endothelial cell count or twelve possible biologically relevant equilibrium solutions since the host cell count is either zero or nonzero as displayed in (23a)−(23b). By Descartes rule of signs, there is always the possibility of a positive root of (26) since A 6 > 0 and A 5 < 0, and any positive root of (26) must also yield positive values of host, immune, and tumor cell counts in (23a)− (25). To this end, we present the following theorem.…”

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confidence: 91%

“…The carrying capacity of the vasculature in this model is defined to be the maximum tumor volume sustainable by the vascular network -a varying quantity predominantly determined by the volume of endothelial cells. Ledzewicz and Schattler [35], [36], [21], [34], [51], Benzekry et al [6], and Glick and Mastroberardino [25] provided studies of the Hahnfeldt model or its variations [22], [20] in order to determine optimal drug and dosing protocols.…”

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confidence: 99%

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Combined therapy for treating solid tumors with chemotherapy and angiogenic inhibitors

Glick¹,

Mastroberardino²

2020

DCDS-B

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Anti-angiogenesis therapy has been an emerging cancer treatment which may be further combined with chemotherapy to enhance overall survival of cancer patients. In this paper, we investigate a system of nonlinear ordinary differential equations describing a microenvironment consisting of host cells, tumor cells, immune cells and endothelial cells while incorporating treatment combination with chemotherapy and anti-angiogenesis therapy. We perform a dynamical systems analysis demonstrating that our model is able to capture the three phases of cancer immunoediting: elimination, equilibrium, and escape. In addition, we present transcritical bifurcations for relevant parameter values that correspond to the progression from the elimination phase to the equilibrium phase. A range of medically useful tumor doubling times were simulated to determine how combined therapy affects the tumor microenvironment over the course of a 250 day treatment. This analysis found two additional bifurcation parameters that move the system of equations from the equilibrium phase to the elimination phase. We determine that the most important aspect of an effective therapy is the activation of the anti-tumor immune response.

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“…Moreover, in the context of thermostatted kinetic theory, the correlations between the immune system and a tumor are defined at cell scales [22]. Ordinary differential equations (ODEs) [23][24][25], partial differential equations (PDEs) [26,27], and delay differential equations (DDEs) [28,29] have been used to suggest cancer models and study the effects of tumor growth on the dynamics of other cells or dynamics of brain diseases [30].…”

Section: Introductionmentioning

confidence: 99%

A New ODE-Based Model for Tumor Cells and Immune System Competition

Alharbi

Rambely

2020

Mathematics

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Changes in diet are heavily associated with high mortality rates in several types of cancer. In this paper, a new mathematical model of tumor cells growth is established to dynamically demonstrate the effects of abnormal cell progression on the cells affected by the tumor in terms of the immune system’s functionality and normal cells’ dynamic growth. This model is called the normal-tumor-immune-unhealthy diet model (NTIUNHDM) and governed by a system of ordinary differential equations. In the NTIUNHDM, there are three main populations normal cells, tumor cell and immune cells. The model is discussed analytically and numerically by utilizing a fourth-order Runge–Kutta method. The dynamic behavior of the NTIUNHDM is discussed by analyzing the stability of the system at various equilibrium points and the Mathematica software is used to simulate the model. From analysis and simulation of the NTIUNHDM, it can be deduced that instability of the response stage, due to a weak immune system, is classified as one of the main reasons for the coexistence of abnormal cells and normal cells. Additionally, it is obvious that the NTIUNHDM has only one stable case when abnormal cells begin progressing into early stages of tumor cells such that the immune cells are generated once. Thus, early boosting of the immune system might contribute to reducing the risk of cancer.

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An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors

Cited by 20 publications

References 39 publications

Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles

Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles

Combined therapy for treating solid tumors with chemotherapy and angiogenic inhibitors

A New ODE-Based Model for Tumor Cells and Immune System Competition

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