Biomedical Engineering Reference
In-Depth Information
at the skin surface. A surface Ω value of 0.53 corresponded to
first-degree, 1.0 to second-degree, and 10 4 to third-degree burns
by their definition. We will look more closely at this particular
process in a later section.
The Arrhenius model is based on the kinetic model of rela-
tive reaction rates that the Swedish scientist Svante Arrhenius
first formulated and described in 1889, (23) which was extended
to the theory of absolute reaction rates in later studies. That
original work was published in German, and is well described
by Johnson et al. (24) in their first chapter. Henriques and Moritz,
unfortunately, did not fully employ the rate process description
as a prediction of the extent of damage, and left the result in
terms of Ω alone, evaluated at the surface of the skin.
Historically, the kinetic model was thoroughly studied in
the context of protein denaturation in vitro —a dominant pro-
cess in tissue thermal damage. The review by Eyring and Stearn
in 1939 (25) (see Table 2.2) effectively summarizes much of the
early work. Perhaps the first rigorous application of Arrhenius
analysis to the skin burn problem was by Fugitt in 1955. (26)
Successful models of thermal radiation (i.e., “flash”) skin burns
were a matter of great interest in the decades immediately fol-
lowing the initial development of nuclear weapons. In this dis-
cussion the underlying formulation for the Arrhenius model is
briefly reviewed from the physical chemistry point of view, and
cast into a form that can readily be compared to quantitative
measures of thermal alteration in tissues, such as histologic
section, relative fluorescence intensity, relative birefringence
intensity, or vital stain assay.
2.2.3 Healing processes
The two major healing pathways are: (1) a “repair in place”
mechanism, wherein the tissue is rebuilt into its original com-
position, architectural structure, and function with little to no
observable scarring, and (2) replacement of the damaged tissue
by fibroblastic scar with concomitant loss of function. (5) In cer-
tain cases the damaged tissues may be replaced with metaplastic
structures that include nonfibroblastic scarring or tissues of a
type not native to the damaged region.
Healing processes begin with the autolytic enzymatic break-
down of injured cells—heat-fixed tissues do not undergo these
changes and do not participate in healing. Heat-fixed tissues
maintain their in situ appearance for the first several days to a
week while the coagulative necrotic tissues fade out and assume
a ghost-like appearance. After about a week, heat-fixed tissues
gradually fade to the appearance of coagulative necrosis and
become brittle. The adjacent zone of coagulative necrosis is
eventually phagocytized and replaced by scar tissue, and a layer
of histocytes forms a barrier around the heat-fixed tissue as a
foreign body reaction. (5) The isolated foreign body can remain
stable for extended times.
2.3 physical Chemical Models:
arrhenius Formulation
Arrhenius models of irreversible thermal alterations in tissues
were first introduced in a seminal series of papers by Henriques
and Moritz in 1947. (19 -22) In their work skin burns were created
in pig skin by flowing water over the surface at constant tem-
perature, and the relative damage was calculated in the form of a
dimensionless parameter, Ω:
2.3.1 Chemical thermodynamics Basis
for the arrhenius Model
For a first-order unimolecular reaction, the rate of disappearance
of the reactant is described by a Bernoulli differential equation:
E
RT ()
a
τ
(2 .1)
Ωτ=
()
Ae
dt
dC
dt
0
=−
kC
(2.2)
where τ = the duration of the exposure (s), A = the frequency
factor (s −1 ), E a = the activation energy (J/mole), R = the universal
gas constant, 8.3143 (J mole −1 K −1 ), T = temperature (K), and t the
time (s). Ω was calculated based on the temperature and expo-
sure time of the flowing water and represents the thermal history
where C = the concentration of reactant, and k = the velocity
of the reaction (s −1 ). Physically, the reactant is described as sur-
mounting an energy barrier to form an “activated” complex,
C *, in quasi-equilibrium with the normal inactivated state. The
TABLE 2.2
Arrhenius Parameters for Selected Proteins and Enzymes from Erying and Stearn
Process Parameters
Protein/Enzyme
A (s −1 )
E a (J mole −1 )
@ T (°C)
Δ S * (J mole −1 K −1 )
Insulin
1.177 × 10 18
1.49 × 10 5
80
99.63
Egg albumin
7.51 × 10 81
5.53 × 10 5
65
1321.5
Hemoglobin
170 × 10 46
3.165 × 10 5
60.5
639.2
Pancreatic proteinase
5.074 × 10 21
1.585 × 10 5
50
170.0
Pancreatic lipase
5.503 × 10 27
1.899 × 10 5
50
285.5
Hydrated invertase
1.931 × 10 53
3.615 × 10 5
55
774.4
Source: Eyring H, Stearn AE, Chemical Reviews , 24, 1939.
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