Algorithmic asymptotic analysis: Extending the arsenal of cancer immunology modeling

Studying the importance of regulatory T cells in chemoimmunotherapy mathematical modeling and proposing new approaches for developing a mathematical dynamic of cancer

Studying the mathematical dynamics of cancer has gained the attention of bioengineers in the past three decades. Different kinds of modelling considering various aspects of treatment have been proposed. In this paper, the key role of Regulatory T cells is discussed and a model in ordinary differential equation (ODE) form is proposed by adding this state to the system dynamics considering chemoimmunotherapy treatment. Regulatory T cells are considered as one of the main tumor cells' tactics to deceive the body's immune system. The improved model is verified mathematically and biologically and fits all criteria in both fields. The results show that entering Regulatory T cells state on cancer mathematical modelling for simulating body cells for chemoimmunotherapy provides a way to identify critical cases more carefully, which a simplified model is unable to accomplish. This point emphasizes the fact that this state must be present in cancer modelling to anticipate immune response more accurately. The advanced system fixed points are obtained by the Newton method and bifurcation diagrams are derived and discussed. New features and remarks are proposed during the journey of developing more accurate models that have the best fit with laboratory data. The sensitivity chart of the model is illustrated and novel aspects of discussions are made with the aim of personalizing a model for a patient and identifying critical conditions based on the chart before any treatment begins. This point enables physicians to determine whether critical conditions have occurred for a patient in a specific treatment or not.

From immune equilibrium to immunodynamics

Objective

The immunology field has long been short of a universally applicable theoretical model that can quantitatively describe the immune response, and the theory of immune equilibrium (balance) is usually limited to the interpretation of the philosophical significance of immune phenomena. Therefore, it is necessary to establish a new immunological theory, namely, immunodynamic theory, to reanalyze the immune response.

Methods

By quantifying the immune dynamic equilibrium as the ratio of positive and negative immune power, the immune dynamic equilibrium equation was established. Then, the area under the curve of the positive and negative immune power was assumed to be equal in the whole process of immune response (regardless of correct or not), and through thought experiments based on this key hypothesis, a series of new concepts and expressions were derived, to establish a series of immunodynamic equations.

Results

New concepts of immune force and immune braking force and their expression equations, namely, the theoretical equations of immunodynamics, were derived through thought experiments, and the theoretical curves of immunodynamics were obtained according to these equations. Via the equivalent transformation of the theoretical equations and practical calculation of functional data, and by the methods of curve comparison and fitting, some practical equations of immunodynamics were established, and these practical equations were used to solve theoretical and practical problems that are related to the immunotherapy of infectious diseases and cancers.

Conclusion

The traditional theory of immune equilibrium has been mathematized and transformed from a philosophical category into a new concrete scientific theory, namely the theory of immunodynamics, which solves the dilemma that the traditional theory cannot guide individualized medical practice for a long time. This new theory may develop into one of the core theories of immunology in the future.

Combined anti-angiogenic and cytotoxic treatment of a solid tumour: In silico investigation of a xenograft animal model's digital twin

Anti-angiogenic (AA) treatments have received significant research interest due to the key role of angiogenesis in cancer progression. AA agents can have a strong effect on cancer regression, by blocking new vessels and reducing the density of the existing vasculature. Moreover, in a process termed vascular normalisation, AA drugs can improve the abnormal structure and function of the tumour vasculature, enhancing the delivery of chemotherapeutics to the tumour site. Despite their promising potential, an improved understanding of AA treatments is necessary to optimise their administration as a monotherapy or in combination with other cancer treatments. In this work we present an in silico multiscale cancer model which is used to systematically interrogate the role of individual mechanisms of action of AA drugs in tumour regression. Focus is placed on the reduction of vascular density and on vascular normalisation through a parametric study, which are considered either as monotherapies or in combination with conventional/metronomic chemotherapy. The model is specified to data from a mammary carcinoma xenograft in immunodeficient mice, to enhance the physiological relevance of model predictions. Our results suggest that conventional chemotherapy might be more beneficial when combined with AA treatments, hindering tumour growth without causing excessive damage on healthy tissue. Notably, metronomic chemotherapy has shown significant potential in stopping tumour growth with minimal toxicity, even as a monotherapy. Our findings underpin the potential of our in silico framework for non-invasive and cost-effective evaluation of treatment strategies, which can enhance our understanding of combined therapeutic strategies and contribute towards improving cancer treatment management.

Algorithmic multiscale analysis for the FcRn mediated regulation of antibody PK in human

A demonstration is provided on how algorithmic asymptotic analysis of multi-scale pharmacokinetics (PK) systems can provide (1) system level understanding and (2) predictions on the response of the model when parameters vary. Being algorithmic, this type of analysis is not hindered by the size or complexity of the model and requires no input from the investigator. The algorithm identifies the constraints that are generated by the fast part of the model and the components of the slow part of the model that drive the system within these constraints. The demonstration is based on a typical monoclonal antibody PK model. It is shown that the findings produced by the traditional methodologies, which require significant input by the investigator, can be produced algorithmically and more accurately. Moreover, additional insights are provided by the algorithm, which cannot be obtained by the traditional methodologies; notably, the dual influence of certain reactions depending on whether their fast or slow component dominates. The analysis reveals that the importance of physiological processes in determining the systemic exposure of monoclonal antibodies (mAb) varies with time. The analysis also confirms that the rate of mAb uptake by the cells, the binding affinity of mAb to neonatal Fc receptor (FcRn), and the intracellular degradation rate of mAb are the most sensitive parameters in determining systemic exposure of mAbs. The algorithmic framework for analysis introduced and the resulting novel insights can be used to engineer antibodies with desired PK properties.