Biomedical Engineering Reference
In-Depth Information
FIgURE 5.1:
Illustration of the mechanisms of population vector approach.
N
B
∑
=
n
P
(
V
,
t
)
=
w
(
V
,
t
)
,
(5.3)
n
B
n
1
n
The population vector can therefore be thought of as a local linear model, where the con-
tributions of each neuron are weighted appropriately from the trajectory. It should be noted here
that the PVA approach includes several assumptions whose appropriateness in the context of neural
physiology and motor control will only be briefly considered here (see Ref. [
23
] for a full discus-
sion). First, each cell is considered independently in their contribution to the kinematic trajectory.
The formulation does not consider feedback of the neuronal firing patterns; a feature found in real
interconnected neural architectures. Second, neuronal firing counts are linearly combined to repro-
duce the trajectory. At this moment it is unclear how the neural activation of nonlinear functions
can create arbitrarily complex movement trajectories. The PV model determines the movement
direction from neural activity, but the reconstruction of hand trajectory also requires the estimation
of the speed. Georgopoulos et al [
1
] directly used the magnitude of the population vector, |
P
(
n
)|,
for estimating the instantaneous speed, and Moran and Schwartz [
24
] extended the PVA model to
include the hand speed. Then, the trajectory of the hand position was reconstructed by a time series
of population vectors that were connected tip to tail as time progresses.
