A dynamic model of cross-coupling between accommodation and convergence: simulations of step and frequency responses

The near triad consists of an increase in accommodation, vergence, and pupillary constriction. All three motor systems exhibit phasic and tonic responses. The tonic response adapts readily to phasic efforts of accommodation and vergence. Cross-coupling between accommodation and vergence provides a means of dynamically adjusting the tonic set points of the two motor systems to a common near or far working distance. Accommodative vergence cross-links play a dominant role in coordinating proximal changes in accommodation and convergence. The magnitude of cross-link interactions can be modified by imbalanced strength of tonic adaptation by accommodation and vergence. Reducing adaptation of tonic accommodation increases the AC/A ratio and decreases the CA/C ratio. Reducing adaptation of tonic vergence has the opposite effect. A model is able to predict these and other interactions simply by reducing the decay time constant of one of the two motor systems. For example, reducing the time constant for tonic accommodation results in an increased AC/A ratio and decreased CA/C ratio. Reducing the time constant for tonic vergence has the opposite effect. The model predicts transient step responses by accommodative vergence when the AC/A ratio is low and transient step responses of vergence accommodation when the CA/C ratio is low. It also predicts a reciprocal relationship between the AC/A and CA/C ratios. When one cross-link ratio is high the other cross-link ratio is low. Simulated frequency responses predict the low frequency roll off of low AC/A and low CA/C ratios. The step and frequency responses of cross-link ratios are shown to be the same for proximal (perceived distance) and retinal (blur and disparity) stimuli. The model suggests that physiological variations of tonic decay time constants may play an important role in determining clinically abnormal values of AC/A and CA/C ratios.