Hybrid Equation/Agent-Based Model of Ischemia-Induced Hyperemia and Pressure Ulcer Formation Predicts Greater Propensity to Ulcerate in Subjects with Spinal Cord Injury

Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI). People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM) are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE) models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation.Author Summary: Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI). To gain insight into the pathogenesis and effective treatment of post-SCI pressure ulcers, we constructed a computer simulation in a hybrid modeling platform which combines both equation- and agent-based models. The model was calibrated using skin blood flow data and reactive hyperemia in response to pressure and predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects. The methodology we present in the paper may eventually be used as a novel platform to study post-SCI ulcer formation, as well as serving as a framework for other biological contexts in which agent-based models and mathematical equations can be integrated.