On the Mathematical Model of Drug Treatment of Rheumatoid Arthritis

Odisharia, Kakha; Odisharia, Vladimer; Tsereteli, P.; Janikashvili, Nona

doi:10.1007/978-3-030-10419-1_10

Cited by 3 publications

(4 citation statements)

References 7 publications

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“…Summary of models reviewed in [23] Systems of ordinary differential equations (ODEs), which are non-spatial deterministic continuous equations that describe the time evolution of a variable of interest, are the most common modelling approach used to describe the evolution of RA. Single compartment ODE models have been used to model joint erosion [24], the interactions between generic pro-and anti-inflammatory cytokines [25], the role of the cytokine TNF-α [26,27], the interactions of immune cells within the RA environment and the drug Tocilizumab [28]. More complex, multi-compartment ODE approaches have also been used to consider the circadian dynamics involved in the progression of rheumatoid arthritis [29] and the inflammatory and invasive processes occurring at the cartilage-pannus interface [30].…”

Section: Previous Mathematical Descriptions Of Ramentioning

confidence: 99%

Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Macfarlane

Chaplain

Eftimie

2021

Preprint

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Rheumatoid arthritis (RA) is a chronic inflammatory disorder that causes pain, swelling and stiffness in the joints, and negatively impacts the life of affected patients. The disease does not have a cure yet, as there are still many aspects of this complex disorder that are not fully understood. While mathematical models can shed light on some of these aspects, to date there are not many such models that can be used to better understand the disease. As a first step in the mechanistic understanding of RA, in this study we introduce a new hybrid mathematical modelling framework that describes pannus formation in a small proximal interphalangeal (PIP) joint. We perform numerical simulations with this new model, to investigate the impact of different levels of immune cells (macrophages and fibroblasts) on the degradation of bone and cartilage. Since many model parameters are unknown and cannot be estimated due to a lack of experiments, we also perform a sensitivity analysis of model outputs to various model parameters (single parameters or combinations of parameters). Finally, we connect our numerical results with current treatments for RA, by discussing our numerical simulations in the context of various drug therapies using, for example, methotrexate, TNF-inhibitors or tocilizumab, which can impact different model parameters.

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Section: Previous Mathematical Descriptions Of Ramentioning

confidence: 99%

Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Macfarlane

Chaplain

Eftimie

2021

Preprint

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“…The authors used the sigmoidal solution of this logistic-growth model to calculate the time-intervals Deterministic mathematical equations that describe the time evolution of a variable of interest; e.g., the density of immune cells involved in RA, the density of chondrocytes in the cartilage, the concentration of some cytokines, or the concentration of a therapeutic drug. These are the most common models used to describe the evolution of RA [118,9,45,68,86,94,99,49]. Advantages: These types of models require shorter simulation time, and are easily parametrised using experimental lab data or clinical patients data (because the large majority of collected data describes the temporal changes in some variable of interest; e.g., levels of pro-inflammatory cytokines).…”

Section: Deterministic Models For Disease Progression and Treatment: mentioning

confidence: 99%

“…An example of a slightly more complex ODE model for RA progression can be found in Odisharia et al [86], where the authors developed a system of 5 ODEs that was used to describe the interactions between B cells, T cells (i.e., T helper and T regulatory cells) and cells that form the cartilage, in the presence of a drug, tocilizumab (TCZ) (which we described in Section 2.3); see also Figure 5. The model incorporated the assumptions that (i) T helper cells stimulate B cell activity, (ii) T regulatory cells inhibit B cell activity, (iii) the drug TCZ blocks the growth of T helper cells and transforms them into T regulatory cells, (iv) B cells that reach levels higher than their normal values destroy the cartilage.…”

Section: Stochastic/probabilistic Modelsmentioning

confidence: 99%

“…The model incorporated the assumptions that (i) T helper cells stimulate B cell activity, (ii) T regulatory cells inhibit B cell activity, (iii) the drug TCZ blocks the growth of T helper cells and transforms them into T regulatory cells, (iv) B cells that reach levels higher than their normal values destroy the cartilage. The authors investigated numerically the dynamics of these different cells, including the degradation of the cartilage, as various model parameters Figure 5: Schematic describing the chemicals, cells and processes included in model described in [86]. The models considers five variables; B cells, T helper cells, T regulatory cells, cartilage and the drug TCZ, along with the interactions between these components.…”

Section: Stochastic/probabilistic Modelsmentioning

confidence: 99%

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Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis: A Brief Review

Macfarlane

Chaplain

Eftimie

2019

Cells

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Rheumatoid arthritis is a chronic autoimmune disease that is a major public health challenge. The disease is characterised by inflammation of synovial joints and cartilage erosion, which lead to chronic pain, poor life quality and, in some cases, mortality. Understanding the biological mechanisms behind the progression of the disease, as well as developing new methods for quantitative predictions of disease progression in the presence/absence of various therapies is important for the success of therapeutic approaches. The aim of this study is to review various quantitative predictive modelling approaches for understanding rheumatoid arthritis. To this end, we start by briefly discussing the biology of this disease and some current treatment approaches, as well as emphasising some of the open problems in the field. Then, we review various mathematical mechanistic models derived to address some of these open problems. We discuss models that investigate the biological mechanisms behind the progression of the disease, as well as pharmacokinetic and pharmacodynamic models for various drug therapies. Furthermore, we highlight models aimed at optimising the costs of the treatments while taking into consideration the evolution of the disease and potential complications.

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The Ratchet Model of Synovial Flares in Palindromic Rheumatism

Chakraborty,

Phatak,

Rath

et al. 2024

Preprint

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Synovial flares in palindromic rheumatism (PR) are aperiodic bursts of inflammation in the joints, which usually self-resolve in a times-scale hours or days. PR patients are believed to transit to a chronic auto-immune disease called rheumatoid arthritis (RA) in most cases, however, many patients remain palindromic indefinitely. We utilize and adapt a minimal ODE model of rheumatoid arthritis (RA) developed by Baker et al. to study PR in greater detail. We address questions characterizing the incidence, decay and sustenance of synovial flares in palindromic patients. A key question is to describe the nature of the transition from a palindromic to full RA. We show that PR flares ordinarily resolve spontaneously, however, there is a secondary equilibrium in the model into which the trajectory can sometimes get trapped. When this meta-stable locking occurs, it initiates an adaptation that helps rescue the flare. Furthermore, this adaptation in turn activates a secondary adaptation in response to fluctuations in the healthy steady state. Finally, we show that if metastable locking occurs frequently enough these adaptation sequences turn maladaptive and the system slowly progresses into fully developed RA.

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On the Mathematical Model of Drug Treatment of Rheumatoid Arthritis

Cited by 3 publications

References 7 publications

Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Modelling rheumatoid arthritis: A hybrid modelling framework to describe pannus formation in a small joint

Quantitative Predictive Modelling Approaches to Understanding Rheumatoid Arthritis: A Brief Review

The Ratchet Model of Synovial Flares in Palindromic Rheumatism

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