A three-dimensional mathematical and computational model of necrotizing enterocolitis

Area of Science:

• Neonatal gastrointestinal diseases
• Mathematical modeling in biology
• Inflammatory response

Background:

• Necrotizing enterocolitis (NEC) is a severe gastrointestinal disease impacting premature infants.
• Previous research on NEC pathogenesis, including inflammation, epithelial healing, and breastfeeding effects, remains fragmented.
• An integrated understanding of NEC is needed to advance treatment and prevention strategies.

Purpose of the Study:

• To synthesize current knowledge on NEC pathogenesis by developing a novel mathematical model.
• To incorporate spatial and transient effects in NEC modeling, moving beyond traditional ordinary differential equation approaches.
• To provide a platform for testing hypotheses and exploring intervention strategies for NEC.

Main Methods:

• Developed a mathematical model using nonlinear transient partial differential equations.
• Employed cell-centered finite differences and an explicit Euler method for numerical solutions.
• Simulated the evolution of intestinal wall injuries to assess NEC progression.

Main Results:

• The model produced pathophysiologically realistic outcomes for NEC.
• Reduced initial injury severity and inclusion of breastfeeding simulation led to healthier outcomes.
• The spatial distribution of initial injuries significantly influenced simulation results, highlighting the importance of spatial effects.

Conclusions:

• Mathematical modeling integrating inflammation, healing, and breastfeeding offers a novel approach to understanding NEC.
• Spatial dynamics are crucial for assessing patient outcomes in NEC.
• The model can guide future research, experimental design, and the development of NEC interventions.