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. Rapid healing of severe burns is essential to preventing fluid loss and bacterial infection. At present, the most popular method to assist with skin repair in burn patients with large burn areas is to use cultured epithelial autografts (CEA). This technique involves taking epidermal cells from an unburnt area of the patient’s body and expanding the epidermal cells in culture by plating the cells onto a feeder layer of growth-arrested 3T3 cells (a mouse fibroblast cell line). An epithelial sheet is formed and then grafted onto the patient’s burn to provide permanent coverage. This procedure has several disadvantages. It may take 3 to 4 weeks for the graft to be available. In addition, the cell sheets are hard to handle, as they are very fragile and the sheets often have poor attachment in areas such as joints, hands and the face where there is complex topography or mechanical forces. The treatment is also prohibitively expensive - it has been estimated that the cost of treatment was around US $110,000 per adult during the period from 1990 to 1995.
An innovative method to assist in the repair of the epidermis (the outer layer of skin) is to use an aerosolised apparatus. This method involves taking skin cells known as keratinocytes from an area of the patient's undamaged skin, culturing the cells in a laboratory, encouraging them to rapidly proliferate over a period of 5-10 days, and then harvesting and separating the cells from each other. The cells are then suspended in aerosolization medium, and sprayed onto the wound surface, where they migrate and proliferate, eventually covering the wound. This method is claimed to result in faster healing and better quality re-epithelialisation than CEA, with better delivery of cells at a substantially reduced cost.
In order to optimise the spraying process with respect to the seeding density for fastest re-epithelisation, Paula Denman of the Queensland University of Technology is modelling the growth of skin cell colonies applied through this process. It is assumed that there are three different cell types present in the sprayed cells - based on the clonal subtypes found in the epidermis - each with a different rate of proliferation and motility. The highly active cell types undergo a transition to the moderately active cells, which undergo a similar transition to the least active cells. The least active cells undergo a transition to quiescent cells, which are assumed to neither migrate nor proliferate. The reverse transitions are not possible. Paula models the spread of the skin cells as a system of 4 differential equations, taking into account the proliferation and conversion rates, and modelling the motility of the cells as a diffusion process.
The spatial distribution of the cell colonies when applied with a spray apparatus is typically either fairly spatially uniform or spatially normally distributed. One aspect of Paula's research has focused on determining the initial distribution that provides the fastest rate of coverage, as rapid repair of skin is often critical to the survival of the patient.
Figures 1 and 2 show frames from simulations showing the coverage of skin cells over time, for different initial spatial distributions. Figure 1 shows the coverage assuming the initial positions of the colonies were chosen randomly from a normal distribution. Figure 2 shows the coverage assuming the initial positions of the colonies were chosen randomly from a uniform distribution. The wound area is 20 mm × 20 mm. In each case, there are 15 colonies initially - 3 highly active colonies (shown in red), 5 moderately active colonies (green) and 7 least-active colonies (blue). Black regions indicate quiescent cells. Frame 1 of each figure shows the initial distribution of colonies (t=0), while frames 2 to 4 show the coverage after 8, 16 and 24 days respectively.
For the case of the normal distribution, the wound is essentially completely healed after 21 days.
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Figure 1: Frames of a movie showing the coverage of skin cells over time, where the initial positions of the colonies was chosen randomly from a normal distribution. |
For the case of the uniform distribution, the wound is essentially completely healed after 20 days.
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Figure 1: Frames of a movie showing the coverage of skin cells over time, where the initial positions of the colonies was chosen randomly from a uniform distribution. |
This model can be further used to investigate a number of different situations - e.g. it may be used to study the efficiency of repeated application of cells, in order to see if this improves the time to confluence. Furthermore, it also has application as a decision support tool - specification of the number of cells, ratio of highly active, moderately active and least active cells, the spatial distribution of the cells and the wound size allows the evolution of the coverage to be predicted.
Paula was supported in her work by the HPC unit at QUT.
Contact
Paula Denman,
Professor
Sean McElwain
School of Mathematical Sciences,
Queensland University of Technology
Publications
Denman, P.K., McElwain, D.L.S., Harkin, D.G. and Upton, Z. "Mathematical Modelling of Aerosolised Skin Grafts Incorporating Keratinocyte Clonal Subtypes", Bulletin of Mathematical Biology, accepted 06/02/06, available online.
Denman, P.K., McElwain, D.L.S. and Norbury, J. "Analysis of Travelling Waves Associated with the Modelling of Aerosolised Skin Grafts", Bulletin of Mathematical Biology, accepted 04/05/06, available online.
Written by T. Curtis, November 2006.