Mathematical Modelling and Analysis of the Tumor Treatment Regimens with Pulsed Immunotherapy and Chemotherapy

Oscillations in a Spatial Oncolytic Virus Model

Virotherapy treatment is a new and promising target therapy that selectively attacks cancer cells without harming normal cells. Mathematical models of oncolytic viruses have shown predator-prey like oscillatory patterns as result of an underlying Hopf bifurcation. In a spatial context, these oscillations can lead to different spatio-temporal phenomena such as hollow-ring patterns, target patterns, and dispersed patterns. In this paper we continue the systematic analysis of these spatial oscillations and discuss their relevance in the clinical context. We consider a bifurcation analysis of a spatially explicit reaction-diffusion model to find the above mentioned spatio-temporal virus infection patterns. The desired pattern for tumor eradication is the hollow ring pattern and we find exact conditions for its occurrence. Moreover, we derive the minimal speed of travelling invasion waves for the cancer and for the oncolytic virus. Our numerical simulations in 2-D reveal complex spatial interactions of the virus infection and a new phenomenon of a periodic peak splitting. An effect that we cannot explain with our current methods.

Novel Mathematical Modelling of Platelet-Poor Plasma Arising in a Blood Coagulation System with the Fractional Caputo–Fabrizio Derivative

This study develops a fractional model using the Caputo–Fabrizio derivative with order α for platelet-poor plasma arising in a blood coagulation system. The existence of solutions ensures that there are solutions to the considered system of equations. Approximate solutions to the recommended model are presented by selecting different numbers of fractional orders and initial conditions (ICs). For each case, graphs of solutions are supplied through different dimensions.

Mathematical Modeling and Analysis of Tumor Chemotherapy

Cancer diseases lead to the second-highest death rate all over the world. For treating tumors, one of the most common schemes is chemotherapy, which can decrease the tumor size and control the progression of cancer diseases. To better understand the mechanisms of chemotherapy, we developed a mathematical model of tumor growth under chemotherapy. This model includes both immune system response and drug therapy. We characterize the symmetrical properties and dynamics of this differential equation model by finding the equilibrium points and exploring the stability and symmetry properties in a range of model parameters. Sensitivity analyses suggest that the chemotherapy drug-induced tumor mortality rate and the drug decay rate contribute significantly to the determination of treatment outcomes. Numerical simulations highlight the importance of CTL activation in tumor chemotherapy.

A NEW MATHEMATICAL MODELING AND SUB-OPTIMAL CHEMOTHERAPY OF CANCER

The development of more accurate cancer mathematical models leads to present more realistic treatment protocols, especially in model-based treatment protocol design. Hence, a cancer mathematical model is presented by considering tumor cells, immune cells, interleukins, macrophages polarization, and chemotherapy based on biological concepts. Both local and global sensitivity analyses are done to examine the effect of changing the parameters on the final tumor population. Then, the tumor-free equilibrium points of the system are derived, and their stabilities are studied. The main target of chemotherapy is to eliminate the tumor while limiting drug toxicity. The SDRE method is used to construct a sub-optimal control strategy by using the developed nonlinear cancer model. For simulation, three patients are considered: a young patient, an old patient, and a pregnant patient. These cases have different immune system strengths. Also, three initial tumor sizes are regarded for each case. So, different treatment strategies are suggested. Eradication of tumor cells in a finite duration with a desired amount of chemo-drug is shown in the simulation results. The results confirmed that the immune system’s ability plays an important role in treatment success. It is shown that there are different treatment protocols for different patients, and the SDRE method is more flexible and effective than the others.

Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune Interactions

Mathematical modelling has been used to study tumor-immune cell interaction. Some models were proposed to examine the effect of circulating lymphocytes, natural killer cells, and CD8+T cells, but they neglected the role of CD4+T cells. Other models were constructed to study the role of CD4+T cells but did not consider the role of other immune cells. In this study, we propose a mathematical model, in the form of a system of nonlinear ordinary differential equations, that predicts the interaction between tumor cells and natural killer cells, CD4+T cells, CD8+T cells, and circulating lymphocytes with or without immunotherapy and/or chemotherapy. This system is stiff, and the Runge-Kutta method failed to solve it. Consequently, the "Adams predictor-corrector" method is used. The results reveal that the patient's immune system can overcome small tumors; however, if the tumor is large, adoptive therapy with CD4+T cells can be an alternative to both CD8+T cell therapy and cytokines in some cases. Moreover, CD4+T cell therapy could replace chemotherapy depending upon tumor size. Even if a combination of chemotherapy and immunotherapy is necessary, using CD4+T cell therapy can better reduce the dose of the associated chemotherapy compared to using combined CD8+T cells and cytokine therapy. Stability analysis is performed for the studied patients. It has been found that all equilibrium points are unstable, and a condition for preventing tumor recurrence after treatment has been deduced. Finally, a bifurcation analysis is performed to study the effect of varying system parameters on the stability, and bifurcation points are specified. New equilibrium points are created or demolished at some bifurcation points, and stability is changed at some others. Hence, for systems turning to be stable, tumors can be eradicated without the possibility of recurrence. The proposed mathematical model provides a valuable tool for designing patients' treatment intervention strategies.

Overcoming Channel Uncertainties in Touchable Molecular Communication for Direct-Drug-Targeting-Assisted Immuno-Chemotherapy

OBJECTIVE

The performance of targeted immuno-chemotherapy of tumor is highly exposed to drug absorption in systemic circulation, which reduces its efficiency and increases side-effects. Direct drug targeting (DDT) combined with immuno-chemotherapy has the potential to mitigate the undesired systemic exposure, by using drug-loaded nanorobots to target cancer cells with the shortest possible physiological routes. This process can be modeled by the "touchable" (i.e., externally controllable and trackable) molecular communication system. However, such a complex process still suffers from various pharmacokinetic uncertainties caused by diffusion, degeneration, and branching of nanorobots (DDT pharmacokinetic uncertainties), as well as tumor/immune system modeling errors. The current work aims at identifying optimal drug administration plans by overcoming such challenges.

METHODS

A revisited tumor-immune interaction model is proposed to incorporate randomness of the drug concentration in the tumor site. Then, a robust multiple model predictive control (MMPC) scheme for the proposed tumor-immune interaction model is designed that uses multiple system models and an adaptive switch to identify the optimal plans for mixed drug administration via drug-loaded nanorobots. Furthermore, a wide range of prediction horizons under different loss scenarios of drug-loaded nanorobots and system model mismatches have been investigated in order to identify safe operating regions. From the molecular communications paradigm, this can be considered as a more robust information transmission system with feedback of channel state information to the transmitter implemented in the control unit.

RESULTS

The efficacy of the proposed MMPC is illustrated through identification of globally optimized drug administration schedules subject to various controller operation imperfections, which lead to successful cancer treatment as demonstrated through computational experiments.

CONCLUSION

By combining DDT with conventional mixed immunotherapy and chemotherapy, the proposed robust MMPC offers promising performance in controlling tumor growth while keeping the immune cell density higher than a specific level in the presence of both DDT pharmacokinetic uncertainties and system model mismatches.

SIGNIFICANCE

We believe that the proposed design framework represents an important first step towards clinically relevant DDT in the combined immunotherapy and chemotherapy of tumor given its robust performance.

Modelling of some aspects of a biomedical process: application to the treatment of digestive cancer (HIPEC)

Usual therapies against malignant tumors, such as surgery, chemotherapy, radiation, is severe and when repeated their efficiency may decrease because tumorous cells may become resistant. Contrarily, hyperthermia has been known for some time as an effective auxiliary treatment, which can be applied repeatedly. In some cases of abdominal carcinomatosis, particularly those of digestive origin, HIPEC is considered as an promising therapeutic option. Chemotherapy and hyperthermia are combined via the perfusion of the abdominal cavity with hot fluids containing chemotherapeutic agents, thus, augmenting the influence of appropriate chemotherapeutic agents with heat. The paper deals with in vivo temperature measurements during the treatment and the identification and development of a heat transfer model of the treatment and consequently its optimization. First, the focus is on in vivo acquisition and monitoring of temperatures. Temperature probe characteristics are identified. Next, a dynamic model for the heat transfer in the patient's body during the HIPEC is outlined. Then model is validated using experimental data collected by the medical partners (St-Etienne Bellevue and Lyon-Sud, France) during in vivo HIPEC. Finally, the concluding comments are reported, including the current perspectives. Since the effectiveness of HIPEC is based on the achievement of a uniform hyperthermic intracavity temperature, properly modelling and developing supervising/monitoring methods for heat transfer for this procedure is the motivation for this research. The paper presents some preliminary groundwork for an eventual simulator and decision aid related to HIPEC.

Role of mathematical medicine in gastrointestinal carcinoma: Current status and perspectives

Mathematical medicine has already played an important role in clinical and basic research as a major interdisciplinary branch of medicine. Mathematical medicine has an important role not only in imaging diagnosis, image storage and transmission in gastrointestinal (GI) cancer, but also in tumor precision therapy. Specifically, in the field of minimally invasive treatment such as precise ablation, 3-dimension modeling, navigation, and surgical simulation significantly improve the therapeutic safety and efficiency in GI cancer. In addition, in the era of big data, data analysis and individualized therapy using mathematical medicine will become a trend in the future, offering an effective method for diagnosing and treating GI cancer and promoting clinical and scientific research.