Defense Date

2013

Document Type

Thesis

Degree Name

Master of Science

Department

Mathematical Sciences

First Advisor

Segal Rebecca

Abstract

Dermal wound healing involves a myriad of highly regulated and sophisticated mechanisms, which are coordinated and carried out via several specialized cell types. The dominant players involved in this process include platelets, neutrophils, macrophages and fibroblasts. These cells play a vital role in the repair of the wound by orchestrating tasks such as forming a fibrin clot to stanch blood flow, removing foreign organisms and cellular debris, depositing new collagen matrix and establishing the contractile forces which eventually bridge the void caused by the initial infraction.\\[5pt] \indent Our current understanding of these mechanisms has been primarily based upon animal models. Unfortunately, these models lack insight into pathologic conditions, which plague human beings, such as keloid scar or chronic ulcer formation. Consequently, investigators have proposed a number of {\it in vivo} techniques to study wound repair in humans in order to overcome this barrier. One approach, which has been devised to increase our level of understanding of these chronic conditions, involves the cutaneous placement of a small cylindrical structure within the appendage of a human test subject.\\[5pt] \indent Researches have designed a variety of these implantable structures to examine different aspects of wound healing in both healthy subjects and individuals that experience some trauma related condition. In each case, several implants are surgically positioned at multiple locations under sterile conditions. These structures are later removed at distinct time intervals at which point they are histologically analyzed and biochemically assayed to deduce the presence of biological markers involved in the repair process. Implantable structures used in this way are often referred to as Human Implantable Models or Systems.\\[5pt] \indent Clinical studies with implantable models open up tremendous opportunities in fields such as biomathematics because they provide an experimentally controlled setting that aids in the development and validation of mathematical models. Furthermore, experiments carried out with implants greatly simplify the mathematics required to describe the repair process because they minimize the modeling of complex features associated with healing such as wound geometry and the evolution of contractile forces.\\[5pt] \indent In this work, we present a notional mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between the time response of the variables of our system and those reported by the literature for normal healing. Once a suitable choice of parameters has been made, we then compare simulation results with data obtained from clinical investigations. While more data is desired, we have a promising first step toward describing the primary events of wound repair within the confines of an implantable system.

Rights

© The Author

Is Part Of

VCU University Archives

Is Part Of

VCU Theses and Dissertations

Date of Submission

August 2013

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