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 Fuzzy
pharmacology is a term coined to represent the application of
fuzzy logic and fuzzy set theory to pharmacological problems.
Fuzzy logic is the science of reasoning, thinking and
inference that recognizes and uses the real world phenomenon
that everything is a matter of degree. It is an extension of
binary logic that is able to deal with complex systems because
it does not require crisp definitions and distinctions for the
system components. In pharmacology, fuzzy modeling has been
used for the mechanical control of drug delivery in surgical
settings, and work has begun evaluating its use in other
pharmacokinetic and pharmacodynamic applications. Fuzzy
pharmacology is an emerging field that, based on these initial
explorations, warrants further investigation.
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Predicting outcomes of
pharmacotherapy is difficult because of the many sources of
pharmacokinetic and pharmacodynamic variation. Several of
these sources of variation have been recognized for many
years: for example, age, gender, weight, disease state,
genetic polymorphisms and concomitant medications
[1]. More recently, additional sources have been proposed,
including individual variability in drug transporters across
biological barriers and in endogenous ligand activity
[2]. Thus, modeling to predict outcomes in pharmacology is
complex. Traditionally, medical science has used statistical
and mathematical approaches for modeling. In general, the
pharmacological system is described in mathematical terms,
where variables are associated with the outcome of interest in
terms of equations with identified parameters (e.g. rate
constants). Parameter values are estimated with statistical
error values attached to describe variability. Approaches that
are conceptually different from this traditional approach have
evolved in the field of engineering when confronted with very
complex systems. We propose that the approach of fuzzy logic
modeling might be particularly suitable for pharmacological
problems.
What is fuzzy logic?
Fuzzy logic is the science of reasoning, thinking and
inference that recognizes and uses the real world phenomenon
that everything is a matter of degree. In the simplest terms,
fuzzy logic theory is an extension of binary logic theory that
does not require crisp definitions and distinctions. Instead
of assuming everything must be defined crisply into black or
white categories (binary view), it is recognized that most
things in the world fall somewhere in between black and white,
that is, varying shades of gray (fuzzy view). Fuzzy logic is a
methodology that captures and uses the concept of fuzziness in
a computationally effective manner. This concept was developed
>36 years ago when Lofti Zadeh, originally an engineer and
systems scientist, expressed the concern that as the
complexity of a system increased, the information afforded by
traditional mathematical models rapidly declined
[3,4] . He felt this was due to the way in which the
variables in the system were represented and manipulated in a
binary manner: variables (e.g. drug response) would be defined
in discrete terms (i.e. poor or good). Using a fuzzy approach
the transition between terms can be gradual, and the binary,
all or none, options become the extreme ends of a continuum.
The fuzzy view of the world was put into operation for
computational purposes through the use of fuzzy sets
[3].
Fuzzy sets
Variables, variable terms, and definitions can be thought
of in terms of sets and set theory. In traditional set theory,
using a binary view, something either belongs to a set or does
not, depending on whether it fits the definition for that set.
In other words, it has a degree of membership (µ) to the set
either equal to one (µ = 1) or equal to zero (µ = 0). In fuzzy
set theory, something can partially belong to a set. A value
for a variable might partially belong to a set and have a
degree of membership anywhere between zero and one (i.e. 0
µ
1), and thus it can partially belong to several sets with the
total membership adding to one ( Box 1).
Although often represented as trapezoidal, fuzzy sets can have
different shapes including triangular, sigmoidal, bell shaped
or irregular
[4]. Recently, the concept of Type II fuzzy sets has been
introduced, in which the borders of the fuzzy sets are
represented as upper and lower boundaries rather than as one
line, in order to better express fuzziness
[5]. It is fuzzy sets, their definitions and relationships
that form the basis of fuzzy system modeling.
Fuzziness versus probability
It is important to distinguish between the concepts of
fuzzy logic and probability. Probability calculus is a tool
for estimating the likelihood that something is true or will
happen. It is a way of handling and expressing randomness. The
concept centers around an all-or-none event once again, a
binary concept where the event can be defined as an entity
having a particular characteristic (i.e. the entity either
does or does not have that characteristic). This is very
different from fuzziness, which does not try to estimate the
likelihood that the entity does or does not have that
particular characteristic but rather assesses how much the
entity is compatible with the meaning of the word we
associated to define that characteristic. For example, an
individual patient can have both a partially 'good' response
to a medication (i.e. to a degree of 0.7), and a partially
'not good' response (i.e. to a degree of 0.3). This is
different from a patient having a 70% probability of having a
good response to a medication. In this case, patients will
either have a 'good' response (70% of patients) or a 'not
good' response (30% of patients). At some point the
determination is made whether the response was good or not and
the probability estimate is no longer required.
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BioMedNet Magazine
25th September - 8th October 2002 |
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