Biomedical Engineering Reference
In-Depth Information
2
Thermal Dose Models:
Irreversible Alterations in Tissues
2.1 Introduction ...............................................................................................................................23
2.2 Irreversible Thermal Alterations in Tissues ......................................................................... 24
Low Temperature Tissue Effects • Higher Temperature Tissue Effects • Healing Processes
2.3 Physical Chemical Models: Arrhenius Formulation ............................................................26
Chemical Thermodynamics Basis for the Arrhenius Model • Arrhenius Process Functional
Behavior and Determination of Process Coefficients • Example Thermal Damage Processes
2.4 Comparative Measures for Thermal Histories: Thermal Dose Concept ...........................32
Foundation of the Thermal Dose Concept • Example Process Calculations
2.5 Applications in Thermal Models .............................................................................................32
Apoptosis/Necrosis Example Prediction • Alterations in Structural Proteins: Muscle and
Collagen Thermal Damage Examples • Example Multiple Damage Numerical Model
2.6 Summary .....................................................................................................................................38
References ...............................................................................................................................................38
John A. Pearce
University of Texas at Austin
2.1 Introduction
discussion of thermal dose units, cumulative equivalent minutes
(CEM) as typically used in hyperthermia studies, which derive
from Relative Reaction Rates—more properly, relative reaction
times—follows. Thermal dose units effectively normalize dif-
ferent thermal histories to a common basis for comparison. The
typical assessment criterion in hyperthermia work is to regard a
CEM value in excess of a defined threshold number of minutes
as evidence of an effective treatment, or an estimate of a treat-
ment physical boundary. CEM values do not,
per se
, provide a
prediction of an outcome in the tissues of interest.
The underlying physical principles of the two descriptions are
the same; however, their physical significance is quite different.
In thermal damage analyses Arrhenius calculations can be used
to estimate the volume fraction of damaged tissue constituent, or
the probability of observing a particular discrete damage event
in an ensemble of experiments.
(1)
In contrast, thermal dose units
constitute a normalizing method for thermal histories: a par-
ticular thermal exposure is scaled into an equivalent exposure
time at the reference temperature, typically 43°C. It is therefore
fair to describe thermal dose units as comparative rather than
predictive.
Irreversible thermal alterations in tissues result from dena-
turation of native state tissue enzymes, proteins, and related
structures, such as cell membranes, micro tubules, and the
like. Mathematical description of these processes, while
somewhat cumbersome, yields valuable insight into experi-
mentally observed tissue changes and is a worthwhile under-
taking. Predictions of temperature alone are just not adequate
since the time of exposure is a defining parameter: hour-long
hyperthermia treatments at moderate temperatures exhibit
different thermal alteration processes than minutes-long treat-
ments at higher temperatures in ablation procedures. This
chapter reviews thermal damage processes in tissues, their
physical-chemical thermodynamic governing relations, and
useful approximations that have been used to describe them.
Specific modeling approaches that have proven useful are also
discussed.
We begin with the classical Arrhenius formulation, the
Theory of Absolute Reaction Rates, which is designed to predict
the “yield” of a reaction (i.e., the fraction of product formed). A
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