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7)
Mathematical modeling in wound healing
Principal organiser: Dr. Richard Schugart,
Mathematical Biosciences Institute, The Ohio State University
Summary
of Minisymposium:
Wound
healing is an extremely complex, yet dynamic process. The use
of mathematical models for wound healing can provide insights
into the complex nature of the biology that would otherwise
be difficult to capture experimentally or in a clinical setting.
Typically, the mathematical models address one aspect of the
healing process. These areas include, but are not limited to,
epidermal healing, wound angiogenesis, and repair of the dermal
extracellular matrix. The models may attempt to address issues
with healing abnormalities or impairment, such as the effects
of infection or keloid scarring, and look at different therapeutic
treatments to improve the healing process, such as the use of
oxygen or engineered skin substitutes to treat diabetic wounds.
Speakers in this minisymposium will discuss current research
on the modeling of wound healing.
Speakers
A
Mathematical Model for Wound Angiogenesis as a Function of Tissue
Oxygen Tension
Richard Schugart, Mathematical Biosciences Institute The
Ohio State University
CoAuthors: Avner Friedman, Chandan Sen, Rui Zhao
Wound
healing represents a wellorchestrated reparative response
that is induced by injuries. Angiogenesis, the formation of
blood vessels from existing vasculature, plays a central role
in wound healing. In this talk, I will present a mathematical
model that addresses the role of tissue oxygen tension in
cutaneous wound healing. Key components of the developed model
include capillary tips, capillary sprouts, fibroblasts, inflammatory
cells, chemoattractants, oxygen, and the extracellular matrix.
The model consists of a system of nonlinear partial differential
equations describing the interactions in space and time of
the above variables. The simulated results agree with the
reported literature on the biology of wound healing. The proposed
model represents a useful tool to analyze strategies for improved
healing and can be used to generate novel hypotheses for experimental
testing.
Mathematical
modelling of tissueengineered angiogenesis
Greg Lemon, University of Nottingham
Coauthors: Daniel Howard, Matthew J Tomlinson, Felicity R A
J Rose, Sarah L Waters, John R King
The
process by which porous biomaterials become vascularised after
being implanted in vivo has enormous clinical significance.
In this talk I will present a mathematical model for the fibrovascular
ingrowth into a porous scaffold under a variety of preseeding
conditions. The central mechanism in the model is the response
of cells to hypoxia, which controls the rate of angiogenesis
inside the implant. The model is given as a set of coupled
nonlinear ODEs which describe the evolution in time of the
amounts of the different tissue constituents inside the scaffold.
Bifurcation analyses reveal how the extent of vascularisation
changes as a function of the parameter values. It is shown
how the loss of seeded cells arising from the slow infiltration
of vascular tissue can be overcome using a prevascularisation
strategy consisting of seeding the implant with vascular cells.
Limited comparison is also given of the model solutions with
experimental data from the chick chorioallantoic membrane
(CAM) angiogenesis assay.
Localized
Wound Healing Techniques Using Conducting Nanofiber Adhesives
for Diabetic Patients
Subramaniya Hariharan, Department of Electrical and Computer
Engineering, The University of Akron
In
this talk, we consider a new methodology for accelerated wound
healing process for diabetic patients. Particular emphasis is
placed on foot ulcers. It is known in medical community that
heating (7 10 degrees higher than human body temperature) and
medications accelerate the healing process. This talk focuses
on the heating aspect only. While heating is a task that can
be achieved by several means including trivial solutions such
as heating pads, it is difficult to control the temperature
rise within a desired range. Moreover, any external heat that
is applied will not only heat the affected area, but also will
affect surrounding area, thus killing living cells. This motivated
us to investigate localized heating. This is accomplished with
the aid of metallically coated or metallic nanofiber bandages
that cover only the affected areas. It is also known that the
conducting nanofibers have large surface areas that can capitalize
heat produced by electromagnetic induction. We show a simple
mathematical model to demonstrate the fundamental concepts.
Limitations on frequencies and other biomechanisms will be discussed.
Also will be discussed are issues related to developing appropriate
electrospun nanofibers and possible design of an electromagnetic
field device.
TwoDimensional
Elastic Continuum Model of Enterocyte Layer Migration
David Swigon, University of Pittsburgh, Department of Mathematics
CoAuthors: Qi Mi, Beatrice Riviere, Yoram Vodovotz, David Hackam
We
have developed a mathematical model of migration of enterocytes
during experimental necrotizing enterocolitis, which is based
on a novel assumption of elastic deformation of the cell layer
and incorporates the following effects (i) mobility promoting
force due to lamellipod formation, (ii) mobility impeding adhesion
to the cell matrix, and (iii) enterocyte proliferation. This
1D model successfully reproduces migration of enterocytes with
straightedge on glass coverslips, namely the dependence of
migration speed on the distance from the wound edge, and the
finite propagation distance in the absence of proliferation
which results in an occasional failure to close the wound. It
also qualitatively reproduces the dependence of migration speed
on integrin concentration. We have recently extended the model
to twodimensions and using balance equations of continuum mechanics
we obtained a second order PDE model with moving boundary. To
numerically solve the problem, we designed a computational algorithm
based on the classical finite element method for parabolic equation.
The models allows us to predict the timedependent geometry
of the wound edge.
A
Mathematical Model of Chronic Epidermal Wound Healing
Ephraim Agyingi, School of Mathematical Sciences, Rochester
Institute of Technology
CoAuthors: Sophia Maggelakis, David Ross
A
chronic wound is one in which the normal process of healing
has been disrupted at one or more points in the phases of inflammation,
proliferation, and remodeling. All chronic wounds contain bacteria
whose potency and interaction with the host determine whether
the wound will heal or deteriorate. In this talk we will present
a mathematical model of the healing rate of a chronic wound
. The model accounts for oxygen availability, production of
macrophagederived growth factors, reconstruction of capillaries,
and bacteria burden in the wound. The model is expressed as
a system of reactiondiffusion equations. We will present computational
results for onedimensional problems.
Mathematical
Model for Inflammation in Wound Healing
Rebecca Segal, Department of Mathematics and Applied Mathematics,
Virginia Commonwealth University
As medical data collection techniques become more detailed,
mathematical models can serve to put the information into a
framework. This talk explores the current state of spatially
dependent modeling efforts in the area of wound healing and
the development of a new model of inflammation to account for
the numerous biochemical pathways initiated following an injury.
Ultimately, the inclusion of additional systemic parameters
will be added to the model to predict the outcome of the wound
and of the patient.

