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Misalignment of the eyes (strabismus) is commonly treated by surgical manipulation of the extraocular muscles. The high failure rate of such surgery has led to the application of engineering methods in diagnosis and surgical planning. Computer models of orbital statics can now aid in diagnosis, and can help predict the outcome of surgery. Methods have been developed to collect biophysical data to customize the models for particular patients. Such biomechanical models will become increasingly important in clinical practice. Nevertheless, the heuristics employed by expert strabismus surgeons will not soon be reduced to algorithms Knowledge engineering methods are needed to explicate and disseminate the reasoning of experts in their own terms. Such an expert system could make use of a biomechanical model to explore hypotheses, much as human experts do now. Such a hybrid system might effectively advise surgeons on how to treat individual cases.