Bifurcation analysis of a mathematical model of atopic dermatitis to determine patient-specific effects of treatments on dynamic phenotypes.

Atopic dermatitis (AD) is a common inflammatory skin disease, whose incidence is currently increasing worldwide. AD has a complex etiology, involving genetic, environmental, immunological, and epidermal factors, and its pathogenic mechanisms have not yet been fully elucidated. Identification of AD risk factors and systematic understanding of their interactions are required for exploring effective prevention and treatment strategies for AD. We recently developed a mathematical model for AD pathogenesis to clarify mechanisms underlying AD onset and progression. This model describes a dynamic interplay between skin barrier, immune regulation, and environmental stress, and reproduced four types of dynamic behaviour typically observed in AD patients in response to environmental triggers. Here, we analyse bifurcations of the model to identify mathematical conditions for the system to demonstrate transitions between different types of dynamic behaviour that reflect respective severity of AD symptoms. By mathematically modelling effects of topical application of antibiotics, emollients, corticosteroids, and their combinations with different application schedules and doses, bifurcation analysis allows us to mathematically evaluate effects of the treatments on improving AD symptoms in terms of the patients' dynamic behaviour. The mathematical method developed in this study can be used to explore and improve patient-specific personalised treatment strategies to control AD symptoms.

Computational design of treatment strategies for proactive therapy on atopic dermatitis using optimal control theory.

Atopic dermatitis (AD) is a common chronic skin disease characterized by recurrent skin inflammation and a weak skin barrier, and is known to be a precursor to other allergic diseases such as asthma. AD affects up to 25% of children worldwide and the incidence continues to rise. There is still uncertainty about the optimal treatment strategy in terms of choice of treatment, potency, duration and frequency. This study aims to develop a computational method to design optimal treatment strategies for the clinically recommended 'proactive therapy' for AD. Proactive therapy aims to prevent recurrent flares once the disease has been brought under initial control. Typically, this is done by using an anti-inflammatory treatment such as a potent topical corticosteroid intensively for a few weeks to 'get control', followed by intermittent weekly treatment to suppress subclinical inflammation to 'keep control'. Using a hybrid mathematical model of AD pathogenesis that we recently proposed, we computationally derived the optimal treatment strategies for individual virtual patient cohorts, by recursively solving optimal control problems using a differential evolution algorithm. Our simulation results suggest that such an approach can inform the design of optimal individualized treatment schedules that include application of topical corticosteroids and emollients, based on the disease status of patients observed on their weekly hospital visits. We demonstrate the potential and the gaps of our approach to be applied to clinical settings.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'.

Mathematical modeling of atopic dermatitis reveals "double-switch" mechanisms underlying 4 common disease phenotypes.

BACKGROUND: The skin barrier acts as the first line of defense against constant exposure to biological, microbial, physical, and chemical environmental stressors. Dynamic interplay between defects in the skin barrier, dysfunctional immune responses, and environmental stressors are major factors in the development of atopic dermatitis (AD). A systems biology modeling approach can yield significant insights into these complex and dynamic processes through integration of prior biological data. OBJECTIVE: We sought to develop a multiscale mathematical model of AD pathogenesis that describes the dynamic interplay between the skin barrier, environmental stress, and immune dysregulation and use it to achieve a coherent mechanistic understanding of the onset, progression, and prevention of AD. METHODS: We mathematically investigated synergistic effects of known genetic and environmental risk factors on the dynamic onset and progression of the AD phenotype, from a mostly asymptomatic mild phenotype to a severe treatment-resistant form. RESULTS: Our model analysis identified a "double switch," with 2 concatenated bistable switches, as a key network motif that dictates AD pathogenesis: the first switch is responsible for the reversible onset of inflammation, and the second switch is triggered by long-lasting or frequent activation of the first switch, causing irreversible onset of systemic TH2 sensitization and worsening of AD symptoms. CONCLUSIONS: Our mathematical analysis of the bistable switch predicts that genetic risk factors decrease the threshold of environmental stressors to trigger systemic TH2 sensitization. This analysis predicts and explains 4 common clinical AD phenotypes from a mild and reversible phenotype through to severe and recalcitrant disease and provides a mechanistic explanation for clinically demonstrated preventive effects of emollient treatments against development of AD.