# A Mathematical Model of Pressure Ulcer Formation to Facilitate Prevention and Management

## TL;DR

This paper presents a mathematical model to understand and predict pressure ulcer formation, helping prevent and manage the condition in immobilized patients.

## Contribution

A novel mathematical model integrating differential geometry and elasticity theory to predict pressure ulcer formation and cellular damage.

## Key findings

- The model simulates skin deformation and predicts cellular death rates under pressure.
- It incorporates blood flow changes due to skin geometry alterations.
- The model forecasts ulcer development time based on health conditions and treatment strategies.

## Abstract

Pressure ulcers are a frequent issue involving localized damage to the skin and underlying tissues, commonly arising from prolonged hospitalization and immobilization. This paper introduces a mathematical model designed to elucidate the mechanics behind pressure ulcer formation, aiming to predict its occurrence and assist in its prevention. Utilizing differential geometry and elasticity theory, the model represents human skin and simulates its deformation under pressure. Additionally, a system of ordinary differential equations is employed to predict the outcomes of these deformations, estimating the cellular death rate in skin tissues and underlying layers. The model also incorporates changes in blood flow resulting from alterations in skin geometry. This comprehensive approach provides new insights into the optimal bed surfaces required to prevent pressure ulcers and offers a general predictive method to aid healthcare personnel in making informed decisions for at-risk patients. Compared to existing models in the literature, our model delivers a more thorough prediction method that aligns well with current data. It can forecast the time required for an immobilized individual to develop an ulcer in various body parts, considering different initial health conditions and treatment strategies.