Mathematical modeling in scheduling cancer treatment with combination of VEGF inhibitor and chemotherapy drugs

Mathematical modeling and analysis of cancer treatment with radiation and anti-PD-L1

In cancer treatment, radiation therapy (RT) induces direct tumor cell death due to DNA damage, but it also enhances the deaths of radiosensitive immune cells and is followed by local relapse and up-regulation of immune checkpoint ligand PD-L1. Since the binding between PD-1 and PD-L1 curtails anti-tumor immunities, combining RT and PD-L1 inhibitor, anti-PD-L1, is a potential method to improve the treatment efficacy by RT. Some experiments support this hypothesis by showing that the combination of ionizing irradiation (IR) and anti-PD-L1 improves tumor reduction comparing to the monotherapy of IR or anti-PD-L1. In this work, we create a simplified ODE model to study the order of tumor growths under treatments of IR and anti-PD-L1. Our synergy analysis indicates that both IR and anti-PD-L1 improve the tumor reduction of each other, when IR and anti-PD-L1 are given simultaneously. When giving IR and anti-PD-L1 separately, a high dosage of IR should be given first to efficiently reduce tumor load and then followed by anti-PD-L1 with strong efficacy to maintain the tumor reduction and slow down the relapse. Increasing the duration of anti-PD-L1 improves the tumor reduction, but it cannot prolong the duration that tumor relapses to the level of the control case. Under some simplification, we also prove that the model has an unstable tumor free equilibrium and a locally asymptotically stable tumor persistent equilibrium. Our bifurcation diagram reveals a transition from tumor elimination to tumor persistence, as the tumor growth rate increases. In the tumor persistent case, both anti-PD-L1 and IR can reduce tumor amount in the long term.

A comprehensive review of computational cell cycle models in guiding cancer treatment strategies

This article reviews the current knowledge and recent advancements in computational modeling of the cell cycle. It offers a comparative analysis of various modeling paradigms, highlighting their unique strengths, limitations, and applications. Specifically, the article compares deterministic and stochastic models, single-cell versus population models, and mechanistic versus abstract models. This detailed analysis helps determine the most suitable modeling framework for various research needs. Additionally, the discussion extends to the utilization of these computational models to illuminate cell cycle dynamics, with a particular focus on cell cycle viability, crosstalk with signaling pathways, tumor microenvironment, DNA replication, and repair mechanisms, underscoring their critical roles in tumor progression and the optimization of cancer therapies. By applying these models to crucial aspects of cancer therapy planning for better outcomes, including drug efficacy quantification, drug discovery, drug resistance analysis, and dose optimization, the review highlights the significant potential of computational insights in enhancing the precision and effectiveness of cancer treatments. This emphasis on the intricate relationship between computational modeling and therapeutic strategy development underscores the pivotal role of advanced modeling techniques in navigating the complexities of cell cycle dynamics and their implications for cancer therapy.

Different mechanisms of CD200-CD200R induce diverse outcomes in cancer treatment

The CD200 is a cell membrane protein expressed by tumor cells, and its receptor CD200 receptor (CD200R) is expressed by immune cells including macrophages and dendritic cells. The formation of CD200-CD200R inhibits the cellular functions of the targeted immune cells, so CD200 is one type of the immune checkpoint and blockade CD200-CD200R formation is a potential cancer treatment. However, the CD200 blockade has opposite treatment outcomes in different types of cancers. For instance, the CD200R deficient mice have a higher tumor load than the wild type (WT) mice in melanoma suggesting that CD200-CD200R inhibits melanoma. On the other hand, the antibody anti-CD200 treatment in pancreatic ductal adenocarcinoma (PDAC) and head and neck squamous cell carcinoma (HNSCC) significantly reduces the tumor load indicating that CD200-CD200R promotes PDAC and HNSCC. In this work, we hypothesize that different mechanisms of CD200-CD200R in tumor microenvironment could be one of the reasons for the diverse treatment outcomes of CD200 blockade in different types of cancers. We create one Ordinary Differential Equations (ODEs) model for melanoma including the inhibition of CCL8 and regulatory T cells and the switching from M2 to M1 macrophages by CD200-CD200R to capture the tumor inhibition by CD200-CD200R. We also create another ODEs model for PDAC and HNSCC including the promotion of the polarization and suppressive activities of M2 macrophages by CD200-CD200R to generate the tumor promotion by CD200-CD200R. Furthermore, we use these two models to investigate the treatment efficacy of the combination treatment between the CD200-CD200R blockade and the other immune checkpoint inhibitor, anti-PD-1. Our result shows that different mechanisms of CD200-CD200R can induce different treatment outcomes in combination treatments, namely, only the CD200-CD200R blockade reduces tumor load in melanoma and only the anti-PD-1 and CD200 knockout decrease tumor load in PDAC and HNSCC. Moreover, in melanoma, the CD200-CD200R mainly utilizes the inhibitions on M1 macrophages and dendritic cells to inhibit tumor growth, instead of M2 macrophages.

The interactions of docetaxel with tumor microenvironment

There are several interactions within the tumor microenvironment (TME) that affect the response of cancer cells to therapy. There are also a large number of cells and secretions in TME that increase resistance to therapy. Following the release of immunosuppressive, pro-angiogenic, and metastatic molecules by certain cells such as tumor-associated macrophages (TAMs), cancer-associated fibroblasts (CAFs), and cancer cells, immune evasion, angiogenesis, and metastasis may be induced. However, natural killer (NK) cells and cytotoxic CD8 + T lymphocytes (CTLs) can responsively release anticancer molecules. In addition, anticancer drugs can modulate these cells and their interactions in favor of either cancer resistance or therapy. Docetaxel belongs to taxanes, a class of anti-tumor drugs, which acts through the polymerization of tubulin and the induction of cell cycle arrest. Also, it has been revealed that taxanes including docetaxel affect cancer cells and the other cells within TME through some other mechanisms such as modulation of immune system responses, angiogenesis, and metastasis. In this paper, we explain the basic mechanisms of docetaxel interactions with malignant cells. Besides, we review the diverse effects of docetaxel on TME and cancer cells in consequence. Lastly, the modulatory effects of docetaxel alone or in conjunction with other anticancer agents on anti-tumor immunity, cancer cell resistance, angiogenesis, and metastasis will be discussed.

Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future.

Assessing chemotherapy dosing strategies in a spatial cell culture model

Predicting patient responses to chemotherapy regimens is a major challenge in cancer treatment. Experimental model systems coupled with quantitative mathematical models to calculate optimal dose and frequency of drugs can enable improved chemotherapy regimens. Here we developed a simple approach to track two-dimensional cell colonies composed of chemo-sensitive and resistant cell populations via fluorescence microscopy and coupled this to computational model predictions. Specifically, we first developed multiple 4T1 breast cancer cell lines resistant to varying concentrations of doxorubicin, and demonstrated how heterogeneous populations expand in a two-dimensional colony. We subjected cell populations to varied dose and frequency of chemotherapy and measured colony growth. We then built a mathematical model to describe the dynamics of both chemosensitive and chemoresistant populations, where we determined which number of doses can produce the smallest tumor size based on parameters in the system. Finally, using an in vitro model we demonstrated multiple doses can decrease overall colony growth as compared to a single dose at the same total dose. In the future, this system can be adapted to optimize dosing strategies in the setting of heterogeneous cell types or patient derived cells with varied chemoresistance.

Replacement in angiogenesis research: Studying mechanisms of blood vessel development by animal-free in vitro, in vivo and in silico approaches

Angiogenesis, the development of new blood vessels from pre-existing ones, is an essential process determining numerous physiological and pathological conditions. Accordingly, there is a high demand for research approaches allowing the investigation of angiogenic mechanisms and the assessment of pro- and anti-angiogenic therapeutics. The present review provides a selective overview and critical discussion of such approaches, which, in line with the 3R principle, all share the common feature that they are not based on animal experiments. They include in vitro assays to study the viability, proliferation, migration, tube formation and sprouting activity of endothelial cells in two- and three-dimensional environments, the degradation of extracellular matrix compounds as well as the impact of hemodynamic forces on blood vessel formation. These assays can be complemented by in vivo analyses of microvascular network formation in the chorioallantoic membrane assay and early stages of zebrafish larvae. In addition, the combination of experimental data and physical laws enables the mathematical modeling of tissue-specific vascularization, blood flow patterns, interstitial fluid flow as well as oxygen, nutrient and drug distribution. All these animal-free approaches markedly contribute to an improved understanding of fundamental biological mechanisms underlying angiogenesis. Hence, they do not only represent essential tools in basic science but also in early stages of drug development. Moreover, their advancement bears the great potential to analyze angiogenesis in all its complexity and, thus, to make animal experiments superfluous in the future.

Mathematical Modeling and Analysis of CD200-CD200R in Cancer Treatment

CD200 is a cell membrane protein that binds to its receptor, CD200 receptor (CD200R). The CD200 positive tumor cells inhibit the cellular functions of M1 and M2 macrophages and dendritic cells (DCs) through the CD200-CD200R complex, resulting in downregulation of Interleukin-10 and Interleukin-12 productions and affecting the activation of cytotoxic T lymphocytes. In this work, we provide two ordinary differential equation models, one complete model and one simplified model, to investigate how the binding affinities of CD200R and the populations of M1 and M2 macrophages affect the functions of the CD200-CD200R complex in tumor growth. Our simulations demonstrate that (i) the impact of the CD200-CD200R complex on tumor promotion or inhibition highly depends on the binding affinity of the CD200R on M2 macrophages and DCs to the CD200 on tumor cells, and (ii) a stronger binding affinity of the CD200R on M1 macrophages or DCs to the CD200 on tumor cells induces a higher tumor cell density in the CD200 positive tumor. Thus, the CD200 blockade would be an efficient treatment method in this case. Moreover, the simplified model shows that the binding affinity of CD200R on macrophages is the major factor to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are significantly different to each other. On the other hand, both the binding affinity of CD200R and the population of macrophages are the major factors to determine the treatment efficacy of CD200 blockade when the binding affinities of CD200R on M1 and M2 macrophages are close to each other. We also analyze the simplified model to investigate the dynamics of the positive and trivial equilibria of the CD200 positive tumor case and the CD200 deficient tumor case. The bifurcation diagrams show that when M1 macrophages dominate the population, the tumor cell density of the CD200 positive tumor is higher than the one of CD200 deficient tumor. Moreover, the dynamics of tumor cell density change from tumor elimination to tumor persistence to oscillation, as the maximal proliferation rate of tumor cells increases.

Intratumoral VEGF nanotrapper reduces gliobastoma vascularization and tumor cell mass

Glioblastoma multiforme (GBM) is the most aggressive and invasive malignant brain cancer. GBM is characterized by a dramatic metabolic imbalance leading to increased secretion of the pro-angiogenic factor VEGF and subsequent abnormal tumor vascularization. In 2009, FDA approved the intravenous administration of bevacizumab, an anti-VEGF monoclonal antibody, as a therapeutic agent for patients with GBM. However, the number of systemic side effects and reduced accessibility of bevacizumab to the central nervous system and consequently to the GBM tumor mass limited its effectiveness in improving patient survival. In this study, we combined experimental and computational modelling to quantitatively characterize the dynamics of VEGF secretion and turnover in GBM and in normal brain cells and simultaneous monitoring of vessel growth. We showed that sequestration of VEGF inside GBM cells, can be used as a novel target for improved bevacizumab-based therapy. We have engineered the VEGF nanotrapper, a cargo system that allows cellular uptake of bevacizumab and inhibits VEGF secretion required for angiogenesis activation and development. Here, we show the therapeutic efficacy of this nanocargo in reducing vascularization and tumor cell mass of GBM in vitro and in vivo cancer models.

Optimization assisted Kalman filter for cancer chemotherapy dosage estimation

Cancer is regarded to be the earth's most deadly disease, with one of the highest mortality rates among people. "Surgery, radiotherapy, chemotherapy, hormone therapy, and immunotherapy" were all options for treat cancer. Chemotherapy is a medication that is most often deployed for treating cancer, as cancer cells develop and proliferate faster than other cells in the body. Even though chemotherapy is an effective method to treatment various kinds of cancers, the treatment includes risk as it causes side effects due to improper drug usage. The application of a controller-based strategy for determining the optimal rate of drug injection during treatment has risen dramatically in recent years. Thereby, this work develops a robust controller for controlling the dosage of drugs that is carried out under parameter estimation. In addition, a Modified Regularized Error Function-based Extended Kalman filter (MREF-EKF) is introduced for estimating the tumor cells and it can be exploited for diverse conditions. Moreover, the overfitting issue that occurs during drug dosage estimation is also solved using this approach. Further, to improve the performance of the developed approach, the initial state of EKF is fine-tuned via Mean fitness-based Particle Swarm Update (MF-PSU), which is the enhanced version of Particle Swarm Optimization (PSO). At last, the supremacy of the presented approach is proved with respect to convergence analysis and error analysis. For instance, our method outperforms existing GWO + e_k + m, AGWO + e_k + m, and PSO + e_k + m approaches in convergence analysis at noise level 0.41 by 0.009%, 0.002%, and 4.9% respectively. In error analysis, the error values for tumor cells have reached a minimum error value of zero for all noise levels (0.41, 0.43, and 0.55). The findings of this study can help for a better understanding of our presented robust controller's effectiveness in controlling the dosage of drugs.

Regularized error function-based extended Kalman filter for estimating the cancer chemotherapy dosage: impact of improved grey wolf optimization

Objectives

The main aim of this work is to introduce a robust controller for controlling the drug dosage.

Methods

The presented work establishes a novel robust controller that controls the drug dosage and it also carried out parameters estimation. Along with this, a Regularized Error Function-based EKF (REF-EKF) is introduced for estimating the tumor cells that could be adapted for different conditions. It also assists in solving the overfitting problems, which occur during the drug dosage estimation. Moreover, the performance of the adopted controller is compared over other conventional schemes, and the attained outcomes reveal the appropriate impact of drug dosage injection on immune, normal, and tumor cells. It is also ensured that the presented controller does a robust performance on the parameter uncertainties. Moreover, to enhance the performance of the proposed system and for fast convergence, it is aimed to fine-tune the initial state of EKF optimally using a new Improved Gray Wolf Optimization (GWO) termed as Adaptive GWO (AGWO). Finally, analysis is held to validate the betterment of the presented model.

Results

The outcomes, the proposed method has accomplished a minimal value of error with an increase in time, when evaluated over the compared models.

Conclusions

Thus, the improvement of the proposed REF-EKF-AGWO model is proved from the attained results.

Robust controller for cancer chemotherapy dosage using nonlinear kernel-based error function

It is well-known that chemotherapy is the most significant method on curing the most death-causing disease like cancer. These days, the use of controller-based approach for finding the optimal rate of drug injection throughout the treatment has increased a lot. Under these circumstances, this paper establishes a novel robust controller that influences the drug dosage along with parameter estimation. A new nonlinear error function-based extended Kalman filter (EKF) with improved scaling factor (NEF-EKF-ISF) is introduced in this research work. In fact, in the traditional schemes, the error is computed using the conventional difference function and it is deployed for the updating process of EKF. In our previous work, it has been converted to the nonlinear error function. Here, the updating process is based on the prior error function, though scaled to a nonlinear environment. In addition, a scaling factor is introduced here, which considers the historical error improvement, for the updating process. Finally, the performance of the proposed controller is evaluated over other traditional approaches, which implies the appropriate impact of drug dosage injection on normal, immune and tumor cells. Moreover, it is observed that the proposed NEF-EKF-ISF has the ability to evaluate the tumor cells with a better accuracy rate.

Analysis of a mathematical model of rheumatoid arthritis

Rheumatoid arthritis is an autoimmune disease characterized by inflammation in the synovial fluid within the synovial joint connecting two contiguous bony surfaces. The inflammation diffuses into the cartilage adjacent to each of the bony surfaces, resulting in their gradual destruction. The interface between the cartilage and the synovial fluid is an evolving free boundary. In this paper we consider a two-phase free boundary problem based on a simplified model of rheumatoid arthritis. We prove global existence and uniqueness of a solution, and derive properties of the free boundary. In particular it is proved that the free boundary increases in time, and the cartilage shrinks to zero as [Formula: see text], even under treatment by a drug. It is also shown in the reduced one-phased problem, with cartilage alone, that a larger prescribed inflammation function leads to a faster destruction of the cartilage.

Multiscale modeling of tumor response to vascular endothelial growth factor (VEGF) inhibitor

Vascular endothelial growth factor (VEGF) has been known as a key mediator of angiogenesis in cancer. Bevacizumab is anti-VEGF monoclonal antibody that has been approved by the FDA as a first-line treatment in many types of cancer. In this paper, we extend a previously validated multiscale tumor model to comprehensively include the multiple roles of VEGF during the course of angiogenesis and its binding mechanism with bevacizumab. We use the model to simulate tumor system response under various bevacizumab concentrations, both in stand-alone treatment and in combination with chemotherapy. Our simulation indicates that periodic administration of bevacizumab with lower concentration can achieve greater efficacy than a single treatment with higher concentration. The simulation of the combined therapy also shows that the continuous administration of bevacizumab during the maintenance phase can lead to antitumor activity which further suppresses its growth. Agreement with experimental results indicates the potential of the model in predicting the efficacy of anti-VEGF therapies and could therefore contribute to developing prospective clinical trials.