A mathematical model of the multiple sclerosis plaque

A Framework for Quantitative Systems Pharmacology Model Execution

A mathematical model can be defined as a theoretical approximation of an observed pattern. The specific form of the model and the associated mathematical methods are typically dictated by the question(s) to be addressed by the model and the underlying data. In the context of research and development of new medicines, these questions often focus on the dose-exposure-response relationship.The general workflow for model development and application can be delineated in three major elements: defining the model, qualifying the model, and performing simulations. These elements may vary significantly depending on modeling objectives. Quantitative systems pharmacology (QSP) models address the formidable challenge of quantitatively and mechanistically characterizing human and animal biology, pathophysiology, and therapeutic intervention.QSP model development, by necessity, relies heavily on preexisting knowledge, requires a comprehensive understanding of current physiological concepts, and often makes use of heterogeneous and aggregated datasets from multiple sources. This reliance on diverse datasets presents an upfront challenge: the determination of an optimal model structure while balancing model complexity and uncertainty. Additionally, QSP model calibration is arduous due to data scarcity (particularly at the human subject level), which necessitates the use of a variety of parameter estimation approaches and sensitivity analyses, earlier in the modeling workflow as compared to, for example, population modeling. Finally, the interpretation of model-based predictions must be thoughtfully aligned with the data and the mathematical methods applied during model development.The purpose of this chapter is to provide readers with a high-level yet comprehensive overview of a QSP modeling workflow, with an emphasis on the various challenges encountered in this process. The workflow is centered around the construction of ordinary differential equation models and may be extended beyond this framework. It includes the fundamentals of systematic literature reviews, the selection of appropriate structural model equations, the analysis of system behavior, model qualification, and the application of various types of model-based simulations. The chapter concludes with details on existing software options suitable for implementing the described methodologies.This workflow may serve as a valuable resource to both newcomers and experienced QSP modelers, offering an introduction to the field as well as operating procedures and references for routine analyses.

Mathematical modeling in autoimmune diseases: from theory to clinical application

The research & development (R&D) of novel therapeutic agents for the treatment of autoimmune diseases is challenged by highly complex pathogenesis and multiple etiologies of these conditions. The number of targeted therapies available on the market is limited, whereas the prevalence of autoimmune conditions in the global population continues to rise. Mathematical modeling of biological systems is an essential tool which may be applied in support of decision-making across R&D drug programs to improve the probability of success in the development of novel medicines. Over the past decades, multiple models of autoimmune diseases have been developed. Models differ in the spectra of quantitative data used in their development and mathematical methods, as well as in the level of "mechanistic granularity" chosen to describe the underlying biology. Yet, all models strive towards the same goal: to quantitatively describe various aspects of the immune response. The aim of this review was to conduct a systematic review and analysis of mathematical models of autoimmune diseases focused on the mechanistic description of the immune system, to consolidate existing quantitative knowledge on autoimmune processes, and to outline potential directions of interest for future model-based analyses. Following a systematic literature review, 38 models describing the onset, progression, and/or the effect of treatment in 13 systemic and organ-specific autoimmune conditions were identified, most models developed for inflammatory bowel disease, multiple sclerosis, and lupus (5 models each). ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others - as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. Despite covering a relatively wide range of diseases, most models described the same components of the immune system, such as T-cell response, cytokine influence, or the involvement of macrophages in autoimmune processes. All models were thoroughly analyzed with an emphasis on assumptions, limitations, and their potential applications in the development of novel medicines.

The effect of chemotaxis on T-cell regulatory dynamics

Autoimmune diseases, such as Multiple Sclerosis, are often modelled through the dynamics of T-cell interactions. However, the spatial aspect of such diseases, and how dynamics may result in spatially heterogeneous outcomes, is often overlooked. We consider the effects of diffusion and chemotaxis on T-cell regulatory dynamics using a three-species model of effector and regulator T-cell populations, along with a chemical signalling agent. While diffusion alone cannot lead to instability and spatial patterning, the inclusion of chemotaxis can result in multiple forms of instability that produce highly complicated spatiotemporal behaviour. The parameter regimes in which different instabilities occur are determined through linear stability analysis and the full dynamics is explored through numerical simulation.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries.

Dynamic Observation of the Effect of L-Theanine on Cerebral Ischemia-Reperfusion Injury Using Magnetic Resonance Imaging under Mathematical Model Analysis

This study was to use the partial differential mathematical model to analyze the magnetic resonance imaging (MRI) images of cerebral ischemia-reperfusion injury (CIRI) and to dynamically observe the role of L-theanine in CIRI based on this. 30 patients with cerebral ischemia in a hospital in a certain area were selected and divided into a cerebral ischemia group and a L-theanine treatment group. The two groups of patients were examined by MRI within 48 hours, and the relative apparent diffusion coefficient (rADC) of the cerebral ischemic part of the patients was determined. The partial differential mathematical model was used for data processing to obtain the function of cerebral ischemia time and infarct area, and the data of patients in the cerebral ischemia group and L-theanine treatment group were compared and analyzed. The results showed that the partial differential mathematical model could effectively analyze the linear relationship between the rADC value and time in the treatment of CIRI using L-theanine. The rADC values of the four points of interest in the L-theanine treatment group all increased with time, and there was a positive correlation between the variables X and Y. In observing the efficacy indicators of L-theanine, the L-theanine treatment group showed a significant advantage in the neurospecific enolase (NSE) content compared with the cerebral ischemia group (P < 0.01), and the neurological function score of the L-theanine treatment group gradually decreased and showed a statistically obvious difference on the 7th day of treatment (P < 0.05). In summary, it was verified in this study that the role of L-theanine in the treatment of CIRI was of a great and positive significance for the subsequent treatment of patients with cerebral ischemia, providing reliable theoretical basis and data basis for clinical treatment of CIRI.