Tissue Skin 3 layers: A thin outer Epidermis A thicker layer of
Dermis A thick subcutaneous fatty tissue (Hypodermis) First-,
Second-, and Third-Degree Burns How is heat transferred in the
system?
Slide 4
Temperature Field Three-dimensional Non-uniform So A
mathematical formulation of burns is difficult to obtain But.
Difficult, but not impossible
Slide 5
Slide 6
is density is heat capacity is the conductivity of tissue is an
index for the physical properties of blood is the normalized blood
perfusion of tissue is the heat from metabolism is the body core or
deep tissue temperature is the temperature of the skin at the burn
site
Slide 7
Cellular Level Free Energy Distributions Thermal Protein
Denaturation
Slide 8
Burn Trauma at the Cellular Level Which cellular structures are
most vulnerable? Which are most critical in cell viability?
Kinetics of damage ought to depend on multiple factors in the
chemical environment Moritz and Henriques (1947): Time Temperature
relationship for scald burning of forearm skin was Arrhenius
Slide 9
Arrhenius Process Observed in thermally activated reactions
Collision Theory: Molecules react if they collide with kinetic
energy that exceeds E A Explains temperature dependence of reaction
rates Boltzmann: probability of reactive collisions
Slide 10
Application of Arrhenius How is Thermal Injury explained by
Arrhenius? Two Hypotheses: 1. Statistical Mechanics. Central Limit
Theorem 2. Specific Denaturation.
Slide 11
Statistical Thermodynamics Free Energy Distribution in
Proteins
Slide 12
Energetics of Denaturation Thermodynamics forces drive changes
in protein conformations Central Limit Theorem: infinite number of
different processes behave like single Arrhenius process Gibbs Free
Energy (G): max energy available for work
Slide 13
Free Energy Distribution in Proteins Douglas Poland Protein in
aqueous solutions Fluctuations in conformation and molecular
vibrations broad distribution of enthalpy states Approximate
distribution function using maximum entropy method from moments G m
becomes the central function: describes thermal behavior of a
protein in the enthalpy neighborhood of the denaturation
maximum.
Slide 14
At normal physiological temperatures, proteins are in a folded,
three- dimensional conformation. When a burn injury occurs, tissue
is heated to well above physiological pH, and components of a
proteins 3-D structures are damaged, resulting in an unfolding and
eventual denaturing of the protein. Denaturation is irreversible. A
simple example of protein denaturation is the cooking of an egg
white. (F. Despa, 2005)
Slide 15
The process of protein denaturation and aggregation can be
modeled as a statistical process Rate of protein unfolding similar
to the Arrhenius equation As the temperature increases, a protein
is unable to remain in its normal, folded conformation and begins
to transition into its unfolded state. At the melting temperature
of the protein, it can unfold and refold at the same rate. The
protein can also reach its denatured state by transitioning
irreversibly from its unfolded state If the rate of conversion from
the unfolded state to the denatured state is faster than the
transition from the unfolded state to the refolded state, then the
rate of denaturation becomes independent of the rate of
irreversible unfolding and refolding. K (F. Despa, 2005) Percent
denaturation equation:Rate of unfolding and refolding:
Slide 16
The kinetics of protein denaturation is affected by so many
different factors: density, solvent, bond strengths, interactions
with surrounding molecules. Since every protein is different, then
clearly each protein should have a different rate of denaturation.
How, then, is it possible that the rate of protein denaturation
follows a single, Arrhenius- like equation? 2 hypotheses: 1.Cell
denaturation depends on an infinite number of different processes
that, when combine, behaves like a single Arrhenius process.
2.Lethal burn injury is dominated by only a few molecular processes
i.e., there are one or two key structures that are critical to cell
survival in a burn injury. The relative stability of a variety of
different types of tissues was investigated by F. Despa et al. to
determine if cell denaturation is dependent on only a few molecular
processes. (F. Despa, 2005)
Slide 17
Table.1:Percent denaturation of proteins and cellular
components after 20 seconds exposure to varying temperatures
(40-66C) Table 2: Percent denaturation of proteins and cellular
components at 80 C as a function of time.
Slide 18
As can be seen from the graphs, most of proteins in the study
denature at around 60 C. The lipid bilayer and the membrane bound
ATPases, the Na+/K+ pump (NKP) and Ca2+ pump (PMCP), are the first
to denature. As a result of these findings, this study suggests
that alteration of the plasma membrane and its components as a
result of high temperatures is likely to be the most significant
cause of tissue necrosis. (F. Despa, 2005)
http://academic.brooklyn.cuny.edu/biology/bio4fv/page/cotrans.htm
Slide 19
Heating therapies that intentionally incite protein
denaturation are being used in a variety of medical fields Most of
these therapies are refined by trial and error Developing
theoretical models Reduces need for extensive clinical trials Makes
therapies more effective
Slide 20
Determine rate of denaturation As a function of temperature As
a function of mechanical load Determine the values of
thermophysical properties Specific Heat Thermal Conductivity
Thermal Diffusivity
Slide 21
Target of many heating therapies Triple-helix structure
Moderate heating Induces reversible local unfolding Breaking of a
few hydrogen bonds Regains shape upon cooling Severe heating
Time-dependent irreversible changes Breaking of many hydrogen bonds
Random, coiled structure Shrinks upon heating
Slide 22
Quickly heat collagen to a specific temperature Measure
shrinkage over time isothermally Equation: is the shrinkage, K(T)
is the specific reaction rate, is the time
Slide 23
Denaturation of Collagen Via Heating: An Irreversible Rate
Process Wright
Slide 24
Actually developing a working mathematical model is beyond the
scope of this project Requires fairly extensive empirical
validation and assigning meaningful values to constants Our
proposal for animal testing fell through, so we were unable to
gather our own data on this front Solve: For temperatures, then
plug that result into the Arrhenius Both equations must be
integrated numerically. As the reaction proceeds heat is absorbed
and released by the proteins folding and unfolding. An initial heat
distribution resulting from point exposure to a high temperature
object Heat diffusion as experienced by a particular skin surface
model.