Mathematical Modelling of Aerosolised Skin Grafts Incorporating Keratinocyte Clonal Subtypes

Abstract

Severe burns can be very traumatic for the patient, and while burns caused by industrial or domestic accidents are common, there are also increasing numbers of burns associated with terrorism. A novel technique to assist in the healing process is to spray skin cells, keratinocytes, that are cultured from the patient's own tissue, directly onto the burn site. This process involves taking some undamaged skin from the patient, allowing the skin cells to proliferate rapidly in the laboratory over a period of 5-10 days, harvesting and separating the cells and then spraying them onto the burn. This paper deals with keratinocytes that have been cultured in vitro for a short period of time (early passage cultured cells). The spraying process has yet to be optimised with respect to the seeding density required for fastest re-epithelisation and thus there is a need for this process to be modelled. In this paper, we review some of the skin biology and develop a mathematical model of the growth patterns of cell colonies after they have been applied using a aerosolised technique. The model allows us to predict coverage over time and can be used as a decision support tool for clinicians.

Translational Systems Biology: Introduction of an Engineering Approach to the Pathophysiology of the Burn Patient

“…Rather, our main goal is to make the burn community aware of possible resources and approaches that can potentially augment ongoing avenues of research. Furthermore, we suggest that the application of TSB can provide an integrated engineering framework consistent with the burn community's tradition of a "research team approach" that has in the past already included mathematicians and modelers [33][34][35][36][37][38][39][40][41][42][43][44][45] to address these areas of interest.…”

“…TSB models exist for all three conditions, 24,28,31 but there is currently no complete model of the presumed inflammatory pathophysiology of a burn patient. Early efforts at applying mathematical models to diverse aspects of the burn response [33][34][35][36][37][38][39][40][41][42][43][44][45] could be coupled with the TSB models described above to define the mechanistic dynamics of burn injury and its response to resuscitation. Furthermore, the development of multiple TSB models of the acute response to burn injury and resuscitation might provide a means of rational, biologically mechanistic analysis of the genomic information generated by large-scale programs such as the Inflammation and Host Response to Injury "Glue Grant."…”

“…[33][34][35][36][37][38][39][40][41][42][43][44][45] This methodology consists of assigning variables to various parameters within a system and writing differential equations that describe how those parameters change over time. These equations are linked to reproduce the dynamics of the system with respect to the selected parameters.…”

“…As we begin to describe this potential integration, we note that mathematical models have been used for over 20 years in the study of burns, [33][34][35][36][37][38][39][40][41][42][43][44][45] and a large portion of these modeling studies might be termed directly translational. 34,37,39,[41][42][43][44][45] However, there is a paucity of mathematical modeling studies integrating the AIR and healing responses in burns.…”

“…34,37,39,[41][42][43][44][45] However, there is a paucity of mathematical modeling studies integrating the AIR and healing responses in burns. 38,40,41,45 In addition, the methods and platforms used for modeling complex systems have evolved over that period of time. In the sections below, we will first describe some of the methods currently used in TSB.…”