## Overview Of The Favite Model

I will not burden the reader with the mathematical equations available in Bullock et al. (1998) and Cisek et al. (1998). I will instead sketch out the general ideas of the model with rather broad strokes. In essence, the FAVITE model is a circuit which generates a kinematic movement command online through internal feedback and superimposes dynamics compensation upon it (see Figure 11.1). Unlike many traditional control schemes from robotics, no "desired trajectory" is prepared and optimized before movement begins. Instead, only a desired target is specified and then the arm moved toward it by gradually reducing a Difference Vector (DV), computed as the difference between the current and desired limb positions (what may be called a "motor error"). In this sense, FAVITE operates like a kinematic transcortical servo, except that the reduction of the DV can be voluntarily controlled and its speed independently gated. During DV reduction, a descending positional command controlling the resting length of muscles is shifted from an initial to a final position. However, unlike equilibrium point models (Bizzi, Accornero, Chap-ple, & Hogan, 1984; Bizzi, Hogan, Mussa-Ivaldi, & Giszter, 1992; Feldman, 1974; Feldman, 1986), the descending command is not purely positional, but also combines dynamics compensation for inertial and static forces.

The model, in essence, consists of seven hypotheses regarding the organization of movement control. These are:

1. A representation of current limb position (called the Perceived Position Vector, or PPV) exists in anterior area 5 and is computed on the basis of efference copy from area 4 and feedback from primary muscle spindles routed through area 2.

2. A voluntary arm movement involves the reduction of a Difference Vector (DV), which is computed in posterior area 5 as the difference between the PPV and a Target Position Vector (TPV), which represents the target position. The DV may be activated, or "primed," before the movement is released.

rostral -caudal area 4 c s area 5

FIGURE 11.1 The FAVITE model. Thick lines highlight the kinematic feedback control aspects of the model, with thin lines representing additional compensatory circuitry. GO — scaleable gating signal; DVV — Desired Velocity Vector; OPV — Outflow Position Vector; OFPV — Outflow Force + Position Vector; SFV — Static Force Vector; IFV — Inertial Force Vector; PPV — Perceived Position Vector; DV — Difference Vector; TPV — Target Position Vector; CBM-cerebellum y d — gamma-dynamic motoneuron; y s — gamma-static motorneuron; a — alpha motoneuron; Ia — type-Ia afferent fiber; II — type-II afferent fiber; c.s. — central sulcus; i.p.s. — intraparietal sulcus. The symbol + represents excitation, - represents inhibition, x represents multiplicative gating, and +J represents integration over time. (From Bullock, D., Cisek, P., and Grossberg, S., Cerebral Cortex, 8, 48, 1998. With permission.)

FIGURE 11.1 The FAVITE model. Thick lines highlight the kinematic feedback control aspects of the model, with thin lines representing additional compensatory circuitry. GO — scaleable gating signal; DVV — Desired Velocity Vector; OPV — Outflow Position Vector; OFPV — Outflow Force + Position Vector; SFV — Static Force Vector; IFV — Inertial Force Vector; PPV — Perceived Position Vector; DV — Difference Vector; TPV — Target Position Vector; CBM-cerebellum y d — gamma-dynamic motoneuron; y s — gamma-static motorneuron; a — alpha motoneuron; Ia — type-Ia afferent fiber; II — type-II afferent fiber; c.s. — central sulcus; i.p.s. — intraparietal sulcus. The symbol + represents excitation, - represents inhibition, x represents multiplicative gating, and +J represents integration over time. (From Bullock, D., Cisek, P., and Grossberg, S., Cerebral Cortex, 8, 48, 1998. With permission.)

3. The DV projects to a Desired Velocity Vector (DVV) in area 4 "phasic movement-time" cells,* where it is scaled by a GO signal arriving from the basal ganglia. The GO signal controls the onset time and the speed of movement. The DVV serves as a velocity command which controls changes in the descending positional command from area 4 (see hypothesis 4 below) and also projects to spinal gamma-dynamic motor neurons.

4. In area 4, an Outflow Position Vector (OPV) projects a positional command to alpha- and gamma-static motor neurons. The OPV also serves at the source of the efference copy signal to the PPV (see hypothesis 1 above). During voluntary movement, the OPV gradually integrates the DVV command over time, shifting the hand toward the target. As the hand approaches the target, the DV in area 5 and the DVV in area 4 are both reduced to baseline, at which point the OPV integration ends and movement ceases.

* The classification of area 4 cells used here is based on Kalaska et al. (1989). © 2002 CRC Press LLC

5. The descending command to alpha motor neurons is augmented by an Outflow Force + Position Vector (OFPV) in area 4 "phasic-tonic" cells, which superimposes static and dynamic load compensation upon the shifting OPV command. Two kinds of compensation signals are described in Bullock et al. (1998): a transient Inertial Force Vector (IFV), which provides force pulses for launching and braking the limb and a sustained Static Force Vector (SFV), which compensates for gravity and other static loads. Although in the mathematical implementation of the FAVITE model, these signals were generated via peripheral feedback (for the sake of mathematical simplicity), we actually prefer to conceive of them as being supplied by a forward dynamics model, possibly implemented in the cerebellum (Bullock & Grossberg, 1991; Ito, 1984; Kawato & Gomi, 1992; Miall & Wolpert, 1996; Vilis & Hore, 1980).

6. A reciprocal connection from the area 5 PPV to the area 4 OPV enables the descending command to track any movements imposed by external forces and keeps muscle spindles loaded and in their range of optimal sensitivity.

7. In different movement contexts, the strength of some of the circuit connections may be varied to modify the operating characteristics of the system. For example, during fast movements, peripheral sensitivity can be reduced to shift the system from a feedback controller toward a feedforward controller.

The first six of these hypotheses are described in detail by Bullock et al. (1998), where evidence for them is reviewed. The seventh hypothesis is discussed by Cisek et al. (1998) in the context of various proprioceptive illusions induced by muscle tendon vibration, as well as movements in the presence of elastic loads and Coriolis forces. In this chapter, I will focus primarily on the first two hypotheses, those concerned with the computations proposed to occur in the posterior parietal cortex.

Below, I attempt to bring together diverse sources of experimental data on the functional role of the parietal cortex. Perhaps some of this data is being inappropriately forced into my particular perspective. The parietal cortex is a complex brain region, with many functional roles. Its study is made difficult by a lack of consensus on what regions in the human are homologous with those in the monkey, and even by a lack of a consistent nomenclature for specific recording sites. Therefore, the following discussion should merely be taken as well-intentioned speculation.

0 0