CLASSIFICATION OF HUMAN MUSCLE STRETCH-RECEPTOR AFFERENTS - A BAYESIAN-APPROACH

1. A sample of 124 human muscle afferents originating from the finger extensor muscles were recorded from the radial nerve in the upper arm. A method is described to formalize the classification of units in muscle spindle primary and secondary afferents and Golgi tendon organ afferents on the basis of a few, nonrigorous assumptions. The classification was based on experimental data that largely have been described in a series of previous papers, although some additional data were collected in the present study. 2. The units were subjected to five tests providing identification data: twitch contraction test, ramp-and-hold stretch, small-amplitude sinusoidal stretches superimposed on ramp stretch, stretch sensitization, and isometric contraction/relaxation. From these five tests the following eight response features were extracted: response to maximal isometric twitch contractions, type of stretch sensitization, correlation between discharge rate and contractile force, response to sudden isometric relaxation, presence or absence of an initial burst, deceleration response, prompt silencing at slow muscle shortening, and driving by small-amplitude sinusoidal stretches. 3. A Bayesian decision procedure was adopted to classify the units on the basis of the eight discriminators. As a first step, units were provisionally classified into muscle spindle primary and secondary afferents, and Golgi tendon organ afferents, by intuitively weighing their responses to the identification tests. Prior probabilities were estimated on the basis of the provisional classification. The eight response features were analyzed and tabulated for all afferents, and the likelihood functions of the tests were directly calculated on the basis of these data. 4. With the use of the prior probabilities and likelihood functions inferred from the experimental data, the probabilities were calculated according to Bayes' theorem that each individual unit was a muscle spindle primary afferent, a secondary afferent, and a Golgi tendon organ afferent. The units were then classified on the basis of their highest probability. It was found that, on average, units were correctly allocated to a receptor type with a probability of 0.95 and correctly excluded with a probability of 0.98. These figures were obtained when all eight discriminators were taken into account but allowance was made for interdependence between some of them. 5. To evaluate the sensitivity of the resultant classification on errors in prior probabilities and likelihood functions, similar calculations were carried out with the use of three different sets of prior probabilities and likelihood functions. By comparing resultant classifications obtained with these sets, it was shown that the classification was practically insensitive to pronounced modifications of the prior probabilities. Moreover, it was largely insensitive to moderate modifications of the likelihood functions, as long as a reasonable number of tests features were considered. 6. It was concluded that a reliable classification of muscle proprioceptors can be obtained when no more than four of five response features are available, even if each one has but moderate discriminative power. 7. The Bayesian approach thus offers considerable advantages over the traditional procedure with the use of intuitive weighing of nonconclusive test outcomes and subjectively estimated balance of evidence. These advantages include reproducibility and easy reassessment of the classification of individual units as well as the possibility to communicate exactly how afferents are classified.