Mechanisms and Points of Control in the Spread of Inflammation: A Mathematical Investigation.

Understanding the mechanisms that control the body's response to inflammation is of key importance, due to its involvement in myriad medical conditions, including cancer, arthritis, Alzheimer's disease and asthma. While resolving inflammation has historically been considered a passive process, since the turn of the century the hunt for novel therapeutic interventions has begun to focus upon active manipulation of constituent mechanisms, particularly involving the roles of apoptosing neutrophils, phagocytosing macrophages and anti-inflammatory mediators. Moreover, there is growing interest in how inflammatory damage can spread spatially due to the motility of inflammatory mediators and immune cells. For example, impaired neutrophil chemotaxis is implicated in causing chronic inflammation under trauma and in ageing, while neutrophil migration is an attractive therapeutic target in ailments such as chronic obstructive pulmonary disease. We extend an existing homogeneous model that captures interactions between inflammatory mediators, neutrophils and macrophages to incorporate spatial behaviour. Through bifurcation analysis and numerical simulation, we show that spatially inhomogeneous outcomes can present close to the switch from bistability to guaranteed resolution in the corresponding homogeneous model. Finally, we show how aberrant spatial mechanisms can play a role in the failure of inflammation to resolve and discuss our results within the broader context of seeking novel inflammatory treatments.

Defining vitamin D status using multi-metabolite mathematical modelling: A pregnancy perspective.

Vitamin D deficiency is linked to adverse pregnancy outcomes such as pre-eclampsia (PET) but remains defined by serum measurement of 25-hydroxyvitamin D3 (25(OH)D3) alone. To identify broader changes in vitamin D metabolism during normal and PET pregnancies we developed a relatively simple but fully parametrised mathematical model of the vitamin D metabolic pathway. The data used for parametrisation were serum vitamin D metabolites analysed for a cross-sectional group of women (n = 88); including normal pregnant women at 1 st (NP1, n = 25) and 3rd trimester (NP3, n = 21) and pregnant women with PET (n = 22), as well as non-pregnant female controls (n = 20). To account for the effects various metabolites have upon each other, data were analysed using an ordinary differential equation model of the vitamin D reaction network. Information obtained from the model was then also applied to serum vitamin D metabolome data (n = 50) obtained from a 2nd trimester pregnancy cohort, of which 25 prospectively developed PET. Statistical analysis of the data alone showed no significant difference between NP3 and PET for serum 25(OH)D3 and 24,25(OH)2D3 concentrations. Conversely, a statistical analysis informed by the reaction network model revealed that a better indicator of PET is the ratios of vitamin D metabolites in late pregnancy. Assessing the potential predicative value, no significant difference between NP3 and PET cases at 15 weeks gestation was found. Mathematical modelling offers a novel strategy for defining the impact of vitamin D metabolism on human health. This is particularly relevant within the context of pregnancy, where major changes in vitamin D metabolism occur across gestation, and dysregulated metabolism is evidenced in women with established PET.