Mathematical modeling of autoimmune diseases: a systematic review and analysis for advancing therapeutic development
Cristina Leon (1), Yaroslav Ugolkov (2,3), Antonina Nikitich (2,3), Gabriel Helmlinger (4), Kirill Peskov (1,2,3,5), Victor Sokolov (1,2), Alina Volkova (1,2)
(1) Modeling and Simulation Decisions FZ - LLC, Dubai, UAE, (2) Research Centre of Model-Informed Drug Development, I.M. Sechenov First Moscow State Medical University, Moscow, Russia, (3) Marchuk Institute of Numerical Mathematics RAS, Moscow, Russia, (4) Biorchestra Co., Ltd., Cambridge, MA, USA, (5) Sirius University of Science and Technology, Sirius, Russia
Introduction: The intricate pathogenesis and etiology of autoimmune diseases (ADs) pose challenges to the research and development of novel therapeutic agents. Despite autoimmune conditions becoming increasingly prevalent worldwide, there still are unmet needs for disease-modifying medicines. Pharmacometric modeling plays an essential role in support of the Drug Development process, in guiding dose selection, choices of dosing strategies, quantitative investigations of drug mechanism of action and pharmacodynamic (PD) responses, and translation of PK and/or PD across species and patient populations. Over the past decades, numerous models addressing ADs have emerged, showcasing the diversity in quantitative data, mathematical methodologies, and descriptive granularity of the immune system.
Objectives: This study aimed at performing a comprehensive review of mathematical models developed for various AD, analyzing model structures and the quantitative information used, and outlining perspectives on their applications in Model-Informed Drug Development.
Methods: A systematic literature search was conducted in the PubMed database to identify mechanistic mathematical models in ADs. The search query comprised two components: the first included 184 disease-specific terms [1] and general descriptors of autoimmunity, while the second focused on studies involving mechanistic or physiologically-based mathematical structures. Non-English records or articles related to clinical trial results, reviews, or meta-analyses were excluded. The systematic search yielded 500 potentially relevant publications (last accessed: October 20, 2023). Two authors independently screened articles for duplication and eligibility, with disagreements resolved through discussion with independent reviewers. In order to be considered for inclusion in our analysis, articles were required to present a mathematical description of autoimmune processes at any level of generalization, with interconnections between at least two components of the immune system. Next, the identified models were classified according to target organ or system, indication, mathematical methods, and associated data. Visualization and statistical analysis were performed using the R Statistics software.
Results: The systematic review identified 35 models that characterized disease onset, progression, and treatment effects across 13 systemic and organ-specific autoimmune conditions. The majority of records focused on modeling in inflammatory bowel disease, multiple sclerosis and lupus, with five models for each. Over 70% of the models used nonlinear systems of ordinary differential equations; others used partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. The identified models extensively explored the interconnections between subtypes of T-helper cells (Th1, Th2, Th17) and cytokines (TNFa, IL-1, IL-6, IL-17, IL-23, and IL-13). However, immune elements such as cytotoxic T cells, B cells and type 1 IFN pathway-related components, all involved in the development of multiple AD pathogenesis and targets of more recent therapeuties are still unrepresented. Furthermore, our study established a comprehensive list of model assumptions and limitations and assessed potential application fields for each model.
Conclusion: Mathematical modeling is indispensable for navigating the complexities of ADs in Drug Development. The vast majority of AD models we identified lack extensive model calibration and evaluation, including identifiability analyses, external validation, generation of realistic patient populations, which limit their quantitative predictive capabilities. These models were often developed in the absence of pharmacokinetic “driving modules” reflecting pharmacological intervention and lacked clinical endpoints, further restricting their relevance for drug development. Thus, the field of mechanistic models in ADs requires further efforts to proactively develop robust quantitative models that contribute to practical applications of mathematical modeling in this most challenging domain.
Supported by the Russian Science Foundation (Grant Number 23-71-10051) and Modeling & Simulation Decisions FZ - LLC, Dubai, UAE.
References: [1] Autoimmune Disease List. Global Autoimmune Institute https://www.autoimmuneinstitute.org/resources/autoimmune-disease-list/ [Accessed January 26, 2024]
