Simple Prototype Of Sensorimotor Function And Its Formalization Modeling

A sensorimotor system can be schematized as a circuit of information flow (see arrows in Fig. 16-2). Starting from the external physical world, information is flowing via sensors into an individual and its brain for information processing and back to the outside world via actuators. If performance of the individual were always absolutely accurate, we would have to assume that the brain is able to exactly represent internally the outside world (this would entail for us researchers a disadvantage: we would be unable to infer from the outside how the brain is doing this job). Phylogenesis has optimized over millions of years the information pickup via the sensors, the internal information processing, and the actuators. Yet, human performance in reality usually is not perfect. This is mainly due to information loss at the level of the sensors and to the noise that arises there and internally (Fig. 16-2). We consider this fact a great chance for our enterprise, because from comparisons between input and output (by means of a systems analysis) and some knowledge about sensor characteristics and internal signals we can derive a notion of how the brain proceeds in the internal reconstruction of the outside world. Before we proceed and specify this point, however, we take a snapshot from the 'waiter on the ship' scenario illustrated in Figure 16-1 in order to formalize and simplify it for our model.

We choose from the scenario a moment where the waiter produces a voluntary body lean in the presence of external perturbations (omitting locomotion and the beer). Thus the function considered in the following is stance control (task: make a 2° forward body lean in space despite external perturbations). The perturbations would be support-surface motion (swaying deck), external contact forces (pushing crowd), and gravity. Let us make the following assumptions (compare Fig. 16-3): (a) Only small body and deck angular motions are considered (i.e. rotations of a few degrees), so that gravity is continuously pressing the person's feet firmly onto the support (we then can suppose that the waiter is continuously in a working mode of stance control and can omit situations where a heel or forefoot lift-off in response to very strong stimuli would force him to switch to an emergency mode). Using small signals has furthermore the advantage that saturations and dead stops are avoided. (b) We restrict the motion to the anterior-posterior, a-p, rotational plane. (c) With the small rotations ('small signal approach'), we have to consider essentially body rotations about the ankle joints and can neglect very small hip and knee bending, i.e., we have a situation of an inverted pendulum where two segments (body consisting of head, trunk, and legs versus foot and its support) are inter-connected by the ankle joint. (d) An ideal actuator produces torque in the ankle joint to move the body.

Figure 16-3. Inverted pendulum model of 'waiter on the ship' scenario. Body (head, trunk, leg) is connected to foot and its support by ankle joint, which allows anterior-posterior body rotations. Ankle torque (7ank) results from summation of active muscle torque and passive torque (due to viscous-elastic muscle properties; box BIOM., for biomechanics). The torque accelerates the body and thus affects body-in-space position, BS. BS excursion leads to further body acceleration (via box F, and gravity torque, Tgrav,), as does a pull stimulus on the body ('external torque', Text). Body-to-foot depends on BS and foot-in-space (FS; tilt) in the form of BF= BS - FS. COP, Centre Of Pressure. Full lines: angular positions; dashed lines: torques; dotted lines: sensory inputs. (Modified from Maurer et al., 2006).

Figure 16-3. Inverted pendulum model of 'waiter on the ship' scenario. Body (head, trunk, leg) is connected to foot and its support by ankle joint, which allows anterior-posterior body rotations. Ankle torque (7ank) results from summation of active muscle torque and passive torque (due to viscous-elastic muscle properties; box BIOM., for biomechanics). The torque accelerates the body and thus affects body-in-space position, BS. BS excursion leads to further body acceleration (via box F, and gravity torque, Tgrav,), as does a pull stimulus on the body ('external torque', Text). Body-to-foot depends on BS and foot-in-space (FS; tilt) in the form of BF= BS - FS. COP, Centre Of Pressure. Full lines: angular positions; dashed lines: torques; dotted lines: sensory inputs. (Modified from Maurer et al., 2006).

With these assumptions, we have the very simple situation depicted in Figure 16-3 in the form of a wiring diagram. When we now fill anthropometric data (body weight, height of centre of mass, COM, above ankle joint) of the subject as well as transfer functions into the boxes 'Body Inertia' and 'F' (for the calculation of 'gravity torque') and add the external perturbations 'support tilt' (Foot-in-Space, FS, TILT) and 'body pull' (External Torque), we could try to produce simulations that mimic the dynamics of the pendulum in response to the voluntary lean and the external perturbations. But this would always end with its 'fall'. The reason is that the pendulum is inherently instable and that gravity and other external stimuli tend to accelerate it. Therefore, we need a sensory feedback system that tries to compensate for gravity and to counteract the external perturbations. For this system we have to choose appropriate receptor systems.

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