A minimal unified model of disease trajectories captures hallmarks of multiple sclerosis

Modeling and simulation for prediction of multiple sclerosis progression

In light of extensive work that has created a wide range of techniques for predicting the course of multiple sclerosis (MS) disease, this paper attempts to provide an overview of these approaches and put forth an alternative way to predict the disease progression. For this purpose, the existing methods for estimating and predicting the course of the disease have been categorized into clinical, radiological, biological, and computational or artificial intelligence-based markers. Weighing the weaknesses and strengths of these prognostic groups is a profound method that is yet in need and works directly at the level of diseased connectivity. Therefore, we propose using the computational models in combination with established connectomes as a predictive tool for MS disease trajectories. The fundamental conduction-based Hodgkin-Huxley model emerged as promising from examining these studies. The advantage of the Hodgkin-Huxley model is that certain properties of connectomes, such as neuronal connection weights, spatial distances, and adjustments of signal transmission rates, can be taken into account. It is precisely these properties that are particularly altered in MS and that have strong implications for processing, transmission, and interactions of neuronal signaling patterns. The Hodgkin-Huxley (HH) equations as a point-neuron model are used for signal propagation inside a small network. The objective is to change the conduction parameter of the neuron model, replicate the changes in myelin properties in MS and observe the dynamics of the signal propagation across the network. The model is initially validated for different lengths, conduction values, and connection weights through three nodal connections. Later, these individual factors are incorporated into a small network and simulated to mimic the condition of MS. The signal propagation pattern is observed after inducing changes in conduction parameters at certain nodes in the network and compared against a control model pattern obtained before the changes are applied to the network. The signal propagation pattern varies as expected by adapting to the input conditions. Similarly, when the model is applied to a connectome, the pattern changes could give an insight into disease progression. This approach has opened up a new path to explore the progression of the disease in MS. The work is in its preliminary state, but with a future vision to apply this method in a connectome, providing a better clinical tool.

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.

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.

Reaction-diffusion models in weighted and directed connectomes

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances.

Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway.

In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

[The role of mitochondria in pathological mechanisms of innate immunity in multiple]

The review discusses the role of mitochondria in multiple sclerosis (MS). Previously, damage to the mitochondria was regarded as a manifestation of secondary damage to axons and neurons, i.e. as a marker of neurodenegation. Recently, the role of mitochondria in the early stages of MS development, when they could participate in the activation of innate immunity and trigger activation of autoimmune responses of acquired immunity, has been increasingly discussed. The role of polymorphism mitochondrial DNA changes in MS is discussed.

The Potential of Computational Modeling to Predict Disease Course and Treatment Response in Patients with Relapsing Multiple Sclerosis

As of today, 20 disease-modifying drugs (DMDs) have been approved for the treatment of relapsing multiple sclerosis (MS) and, based on their efficacy, they can be grouped into moderate-efficacy DMDs and high-efficacy DMDs. The choice of the drug mostly relies on the judgment and experience of neurologists and the evaluation of the therapeutic response can only be obtained by monitoring the clinical and magnetic resonance imaging (MRI) status during follow up. In an era where therapies are focused on personalization, this study aims to develop a modeling infrastructure to predict the evolution of relapsing MS and the response to treatments. We built a computational modeling infrastructure named Universal Immune System Simulator (UISS), which can simulate the main features and dynamics of the immune system activities. We extended UISS to simulate all the underlying MS pathogenesis and its interaction with the host immune system. This simulator is a multi-scale, multi-organ, agent-based simulator with an attached module capable of simulating the dynamics of specific biological pathways at the molecular level. We simulated six MS patients with different relapsing-remitting courses. These patients were characterized based on their age, sex, presence of oligoclonal bands, therapy, and MRI lesion load at the onset. The simulator framework is made freely available and can be used following the links provided in the availability section. Even though the model can be further personalized employing immunological parameters and genetic information, we generated a few simulation scenarios for each patient based on the available data. Among these simulations, it was possible to find the scenarios that realistically matched the real clinical and MRI history. Moreover, for two patients, the simulator anticipated the timing of subsequent relapses, which occurred, suggesting that UISS may have the potential to assist MS specialists in predicting the course of the disease and the response to treatment.

Comparison of Reported Spinal Cord Lesions in Progressive Multiple Sclerosis with Theiler's Murine Encephalomyelitis Virus Induced Demyelinating Disease

BACKGROUND

Spinal cord (SC) lesions in Theiler's murine encephalomyelitis virus induced demyelinating disease (TMEV-IDD) resemble important features of brain lesions in progressive multiple sclerosis (MS) including inflammation, demyelination, and axonal damage. The aim of the present study was a comparison of SC lesions in MS and TMEV-IDD focusing on spatial and temporal distribution of demyelination, inflammation, SC atrophy (SCA), and axonal degeneration/loss in major descending motor pathways.

METHODS

TMEV and mock-infected mice were investigated clinically once a week. SC tissue was collected at 42, 98, 147, and 196 days post infection, and investigated using hematoxylin and eosin (HE) staining, immunohistochemistry targeting myelin basic protein (demyelination), Mac3 (microglia/macrophages), phosphorylated neurofilaments (axonal damage) and transmission electron microscopy.

RESULTS

Demyelination prevailed in SC white matter in TMEV-IDD, contrasting a predominant gray matter involvement in MS. TMEV-infected mice revealed a significant loss of axons similar to MS. Ultrastructural analysis in TMEV-IDD revealed denuded axons, degenerative myelin changes, axonal degeneration, as well as remyelination. SCA is a consistent finding in the SC of MS patients and was also detected at a late time point in TMEV-IDD.

CONCLUSION

This comparative study further indicates the suitability of TMEV-IDD as animal model also for the investigation of progressive SC lesions in MS.

Dynamics and heterogeneity of brain damage in multiple sclerosis

Multiple Sclerosis (MS) is an autoimmune disease driving inflammatory and degenerative processes that damage the central nervous system (CNS). However, it is not well understood how these events interact and evolve to evoke such a highly dynamic and heterogeneous disease. We established a hypothesis whereby the variability in the course of MS is driven by the very same pathogenic mechanisms responsible for the disease, the autoimmune attack on the CNS that leads to chronic inflammation, neuroaxonal degeneration and remyelination. We propose that each of these processes acts more or less severely and at different times in each of the clinical subgroups. To test this hypothesis, we developed a mathematical model that was constrained by experimental data (the expanded disability status scale [EDSS] time series) obtained from a retrospective longitudinal cohort of 66 MS patients with a long-term follow-up (up to 20 years). Moreover, we validated this model in a second prospective cohort of 120 MS patients with a three-year follow-up, for which EDSS data and brain volume time series were available. The clinical heterogeneity in the datasets was reduced by grouping the EDSS time series using an unsupervised clustering analysis. We found that by adjusting certain parameters, albeit within their biological range, the mathematical model reproduced the different disease courses, supporting the dynamic CNS damage hypothesis to explain MS heterogeneity. Our analysis suggests that the irreversible axon degeneration produced in the early stages of progressive MS is mainly due to the higher rate of myelinated axon degeneration, coupled to the lower capacity for remyelination. However, and in agreement with recent pathological studies, degeneration of chronically demyelinated axons is not a key feature that distinguishes this phenotype. Moreover, the model reveals that lower rates of axon degeneration and more rapid remyelination make relapsing MS more resilient than the progressive subtype. Therefore, our results support the hypothesis of a common pathogenesis for the different MS subtypes, even in the presence of genetic and environmental heterogeneity. Hence, MS can be considered as a single disease in which specific dynamics can provoke a variety of clinical outcomes in different patient groups. These results have important implications for the design of therapeutic interventions for MS at different stages of the disease.

Multiple Sclerosis (MS) is an autoimmune disease in which inflammatory and degenerative processes damage the brain. We tested the hypothesis that the variability in disease progression and the clinical heterogeneity observed in MS is driven by a single mechanism, namely the autoimmune attack on the CNS that provokes this chronic inflammation and degeneration. As such, it is the difference in the intensity of these processes at distinct times that is responsible for establishing each of the disease subtypes defined to date. Mathematical models of brain damage and disease course were generated that were fitted to clinical data. We found that the phenotypes of the different MS subtypes were reproduced by the model, supporting the concept of a common pathogenesis and thus, that of a single disease in which specific dynamics can produce a variety of clinical outcomes in different groups of patients. These results are likely to be helpful when designing new therapies for this disease.