Wound Healing: Multi-Scale Modeling
This chapter is meant as an overview of our already published work that we carry out on modeling wound healing on the cellular, colony and tissue scale, though we detail the description of some stochastic principles that appear in our models. The relation
- PDF / 2,345,630 Bytes
- 25 Pages / 439.37 x 666.142 pts Page_size
- 64 Downloads / 228 Views
Abstract This chapter is meant as an overview of our already published work that we carry out on modeling wound healing on the cellular, colony and tissue scale, though we detail the description of some stochastic principles that appear in our models. The relation between the scales is described in terms of the underlying biological and mathematical concepts. We also present the implications and applicability of the mathematical models studied.
1 Introduction Wound healing is a very complicated process with the following partly overlapping phases: inflammation—proliferation—remodeling. During the post-bleeding inflammatory phase macrophages and white blood cells (leukocytes) enter the wound site to clear up invading harmful agents and bacteria through the broken network of capillaries. If a patient suffers from diabetes, then the capillary walls are suffering from an increased stiffness by which they can break down, and extend less due to a decreased flexibility, and thereby transport less blood containing oxygen and indispensable nutrients. Co-agulation of blood occurs to shut-off the wound. This is followed by angiogenesis, to restore the capillary network, dermal regeneration, which involves contraction due to traction forces exerted by F. J. Vermolen (&) Delft Institute of Applied Mathematics, Delft University of Technology, Mekelweg 4, 2628 Delft, The Netherlands e-mail: [email protected] A. Gefen Department of Biomedical Engineering, Tel Aviv University, Tel Aviv, Israel e-mail: [email protected]
Stud Mechanobiol Tissue Eng Biomater (2013) 14: 321–345 DOI: 10.1007/8415_2012_156 Springer-Verlag Berlin Heidelberg 2012 Published Online: 25 November 2012
321
322
F. J. Vermolen and A. Gefen
(myo-)fibroblasts, as well as wound closure by the keratinocytes that form the basis of the epidermis (epithelium). Many in-vitro experimental and clinical in-vivo studies have been carried out to scrutinize the biological mechanisms that take place during the very complex process of wound healing. Unfortunately, still many of the underlying biology is still unclear despite the long lasting research in wound healing. In order to improve and to prevent wounds, such as pressure ulcers or diabetic ulcers, it is important to quantify the influence of the related partial processes taking place during the healing of wounds. This quantification can be done using statistical analyses on raw data using for instance genetic algorithms or other forms of artificial intelligence such as neural networks. Since much data lack detailed quantitative aspects, this holds for in-vivo data in particular, mathematical modeling is also a very helpful tool for the quest of the interrelations between the parameters involved. The challenge is either to build a complicated mathematical model that contains as many of the biological parameters as possible, or to construct simple models that contain a minimum number of parameters such that only those parameters and processes that have the largest impact on the healing kinetics are taken int
Data Loading...
