After looking at the several database scheme suggested by both Amandas and Jacob, I found myself confused and/or unhappy. By studying the three schemes mentioned above, one can conclude the following: They all take into consideration important and relevant aspects. However, we can also conclude the following about each of them:
- Amanda A.: The proposed schema reflects the organization already implemented in the Web pages for BMW. Since the BMW Web hierarchy was built based on the needs to store at least 7 brain models (as far as I remember), it contains several neat and useful ideas. For example, it was from the experience of placing the models out there that the need for example runs together with a step-by-step tutorial became obvious. As we can see from Amanda A.'s diagram, this is an important branch of her schema.
- Amanda B.: The proposed schema is hard to read, since it was thought of in a time where we used to think of having the bibliographical data inside BMW. By taking the reference part out, we are left with few tables that actually reflect the core of what should be our BMW schema. However, once more, these tables are hard to read, since they have several bibliographical pointers.
- Jacob: This schema appears to be quite complete, however the relations between the core tables are hard to follow. The "Link" table, in my point of view, complicates the connectivity of the proposed schema. From another perspective, Jacob's schema provides a low-level view of Amanda B.'s schema. As we can see, in all three scheme, the core tables are almost the same: Model, Simulation/Experiment, Module/Computer Model.
With this in mind, I decided to provide a cleaner and better schema, based on all the above scheme. By doing so, I come up with the schema depicted in below. If it is cleaner or better than the already proposed scheme, it is left for the future. However, I agree that it is not complete and definitive. I just want to highlight important aspects that we all have been considering. I also do not explicitly consider low level information such as postscript versions, cell types, etc.
The yellow balls in the end of the links mean a 1 to Many relationship. For instance, a model can relate to several other models.
As it can be seen, pointers to references are left blank. The idea represented in the diagram above trys to explain data related solely to BMW and not to an assumed existing bibliographical database.
For a better understanding of the proposed schema. I will try to explain it next in a few words.
I considered that the core BMW tables would be: Simulation, Model, and Module (more less according to a hand-written document I had from one of our previous meetings, probably compiled by one of the Amandas).
Simulation: describes a particular simulation/experiment with a particular model. In this case, Simulation has to address the following data:
* Inputs: points to a table containing the parameters (see Jacob's schema) and empirical data (the training and the test sets).
* Outputs: points to a table containing textual and/or visual data produced by the simulation.
* Description: textual and/or visual description of the simulation specifics.
* Experimental Data (1 to Many): specific experimental data the simulation is trying to explain.
* Predictions: specific predictions the simulation is giving us.
Model: describes the overall model
* Author (1 to Many): possible link to the bibliographical database
* Module (1 to Many): a model can be composed by several modules. In Java, each module could correspond to a class.
* Run (1 to 1): points to a table containing the model's binary code. The Run table also contains the manual of how to successfuly run the executable (the user's guide), together with a pointer to example runs (1 to Many).
* Model Documentation (1 to 1): points to a table containing the description of the model (textual or visual), as well as its mathematical formalization. Here I am assuming that the description of the model also contains its assumptions.
* Model Evaluation (1 to 1): points to a table containing the model's drawbacks, achivements, open questions, and predictions. The predictions in this case would contain all the predictions of the model.
* Related Model (1 to Many): points to a table containing the description/critiques of other related models, as well as the assumptions used in the current model that were extracted from the related model.
* Experimental Data (1 to Many): points to a table containing the description (visual or textual) of the relevant data. This table would be also the one linking BMW to the Time-Series Database.
Module: part of a model (as pointed out by one of the Amandas, it may be subunits of code, e.g., java classes, or a whole program, e.g., genesis), together with its documentation.
Below, I will try to apply the schema depicted above to chapter 5 of Crowley's thesis. Again, I leave to you the judgement of how well I did it. I should remind you all that I don't consider myself a database expert (I hope this can be used as a disclaimer). I also want to point out that the data pertaining to "Related Model" and "Experimental Data" the way it is represented below needs more work to be conformant to the schema provided above.
Enjoy!
Alex
Table SIMULATION:
Model: links to table MODEL below
Description:
Simple Saccades
In our model, saccades are terminated by sufficient activation of the central superior colliculus buildup cells representing the rostral pole of the SC (Munoz and Wurtz 1993; Optican 1994). Thus, the accuracy of a simple saccade generated by the model is determined by the performance of the buildup neurons as a saccade is occurring and by the control it exerts upon the saccade generating circuitry in the superior colliculus and brainstem when the activation in the buildup neurons reaches the rostral pole (see section four for a more complete description). To test our model's ability to accurately terminate saccades, we had the model generate simple saccades with no fixation signal present and compared the actual location of the model "fovea" to the desired location.
Inputs:
In a neural network model with as many neuronal arrays with weight constants, time constants and ranges of firing rates, it is possible to obtain almost any range of behavior desired. For our model, we utilized neurophysiological data where available, but to fill in the gaps, as it were, we used saccadic latency times for express saccades (no fixation, or gap size of 200 msec) and for voluntary saccades with fixation. Express saccades occur approximately 100 msec after the presentation of the saccade stimulus (Fischer and Boch 1983; Fischer and Ramsperger 1984; Sommer 1994; Baro, Hughes et al. 1995). Normal saccades take 160 msec to 300 msec to occur when a fixation signal is present until the visual stimulus is presented (overlap task, i.e., gap is 0 msec) (Braun, Weber et al. 1992).
In "establishing" parameters in our model for which we had little, or no biological data, we settled on an express saccade latency of 100 msec and a normal saccade with fixation latency of 200 msec. We then tuned model parameters to obtain these values.
Outputs:
Simple Saccades
The largest errors generated during saccades in this experiment occurred with the smallest saccades because the activation in the buildup cells had not reached the level required to terminate, i.e., the "eye" was moving so slowly that the saccade had not terminated at the end of the experiment, even though the more normally behaving saccades generated by the model had sufficient time to complete.
Figure 5.3.1 Saccade Error
Displays the foveal error as a percentage of the saccade amplitude. Smaller saccades produce a higher error (maximum 9.5% error), whereas the largest saccades that can be generated by our model slightly overshot the fovea (-.77% error). We suggest that the two smallest saccades would have activated the smooth pursuit system in animals, not the saccade system.
Experimental Data:
MacAvoy et al. (1991)
Predictions:
We suggest that these small saccades, would instead have
activated the smooth pursuit neurons in FEF, not the saccade neurons as
in our model. We base this suggestion upon the findings of MacAvoy et al.
(1991) that microstimulation of neurons ventral to the small saccade region
in FEF generate smooth-pursuit eye movements. Thus, the FEF neurons closest
to the fovea control smooth pursuit eye movements, not saccadic eye movements.
Table SIMULATION:
Model: links to table MODEL below
Description:
Another benchmark of our model under normal conditions is the latency of saccade generation overall and the various latencies of the different brain regions involved in saccadic eye movements. There is general agreement that there are two types of simple saccades: express, or reflexive, saccades and "normal" saccades. Express saccades occur approximately 100 msec after the presentation of the saccade stimulus (Fischer and Boch 1983; Fischer and Ramsperger 1984; Sommer 1994; Baro, Hughes et al. 1995), but only when no fixation signal has been present for 150 msec or more. This is called the gap task, as there is a gap between the time when the fixation signal disappears and when the stimulus to which the animal is to saccade appears.
Normal saccades take 160 msec to 300 msec to occur when a fixation signal is present until the visual stimulus is presented (overlap task, i.e., gap is 0 msec) (Braun, Weber et al. 1992).
Inputs:
In a neural network model with as many neuronal arrays with weight constants, time constants and ranges of firing rates, it is possible to obtain almost any range of behavior desired. For our model, we utilized neurophysiological data where available, but to fill in the gaps, as it were, we used saccadic latency times for express saccades (no fixation, or gap size of 200 msec) and for voluntary saccades with fixation. Express saccades occur approximately 100 msec after the presentation of the saccade stimulus (Fischer and Boch 1983; Fischer and Ramsperger 1984; Sommer 1994; Baro, Hughes et al. 1995). Normal saccades take 160 msec to 300 msec to occur when a fixation signal is present until the visual stimulus is presented (overlap task, i.e., gap is 0 msec) (Braun, Weber et al. 1992).
In "establishing" parameters in our model for which we had little, or no biological data, we settled on an express saccade latency of 100 msec and a normal saccade with fixation latency of 200 msec. We then tuned model parameters to obtain these values.
Outputs:
Figure 5.3.2 below shows the saccadic velocity profile
for both the gap task and the overlap task as generated by our model. What
we found is that our model generates an "express" saccade 100
msec after the saccade stimulus is presented. When fixation is present
until the visual stimulus is presented (overlap task), it takes 195 msec
to generate a saccade.
|
|
(a) |
(b) |
Figure 5.3.2 Simple Saccades with no fixation and with fixation (overlap task)
Without fixation (a), an "express" saccade occurs about 100 msec after the onset of the saccade target. In (b), with fixation offset at the same time as target onset, the saccade latency is 195 msec.
In the gap task, the presence of fixation less than 200 msec before the presentation of the saccade stimulus still affects the generation of express saccades (Fischer and Ramsperger 1984). We simulated this experiment by removing the fixation signal 100, 150 and 200 msec before the presentation of the saccade stimulus to see how the saccade latency was affected. Figure 5.3.3 below shows the latencies for the 100 msec (Figure 5.3.3.a) and 200 msec (Figure 5.3.3.b) cases. The saccade latency varied from 135 msec in the 100 msec gap test, to 117.5 msec in the 150 msec gap test, to 107.5 msec in the 200 msec gap test. We then extended this experiment to testing saccade latency for gaps every 25 msec between 0 msec (overlap task) to 250 msec. Table 5.3.4 shows the results of this experiment.
What we found in this experiment was a fairly quick decrease
in saccade latency in the first 100 msec of gap from 200 msec latency with
no gap to 135 msec with 100 msec of gap. There was a much more gradual
decrease in saccade latency from 100 msec of gap to 200 msec of gap where
the saccade latency remained essentially constant through the maximum gap
tested. In Fischer and Ramsperger (1984), they found with a gap of 200
msec, that the average of all express saccades (30,00 total saccades) was
103.7 msec from target onset with a standard deviation of 10.8 msec. Additionally,
though they do not include the data, they varied the gap from 150 msec
to 250 msec and still found the peak of express saccades around 100 msec
or slightly longer with a standard deviation of about 10 msec. Our model
has an express saccade latency of 107.5 msec with a gap duration of 200
msec and the range of latencies for gap durations of 150 msec to 250 msec
is 117.5 msec to 105 msec, which is within the standard deviation of the
data of Fischer and Ramsperger.
|
|
(a) |
(b) |
Figure 5.3.3 Gap task with 100 msec gap (a) and 200 msec gap (b).
Saccade latency changes with a change in gap size. Saccade latency with 100 msec gap is 135 msec (a) and is 107.5 msec with a gap duration of 200 msec.
In experiments with trained monkeys, Fischer and Boch
(1983) found "fast-regular" saccades occurring with latencies
of 140 msec with a gap duration of 150 msec or more when express saccades
did not occur. As they decreased the gap duration down to zero, they found
the regular saccade latency linearly increasing to 200 msec. With larger
gap durations, express saccades occurred more frequently. When the gap
was 200 msec or more, express saccades occurred more than 70% of the time.
Thus, it seems that express saccades are a separate mechanism from normal
saccades and that conditions must be just right for their generation, or
a normal saccade, with latency inversely related to gap duration, is generated
instead. Thus, even though we tuned our model to a single latency express
saccade with no fixation and to a normal saccade with a gap size of 0 msec,
our model is able to reproduce the available for a range of gap sizes from
0 through 250 msec.
|
Saccade Latency |
0 |
200 |
25 |
180 |
50 |
162.5 |
75 |
147.5 |
100 |
135 |
125 |
127.5 |
150 |
117.5 |
175 |
110 |
200 |
107.5 |
225 |
105 |
250 |
105 |
Table 5.3.4 Model saccade latency for gap tasks from 0 msec gap to 250 msec gap
Experimental Data:
Fischer and Boch 1983;
Fischer and Ramsperger 1984;
Sommer 1994;
Baro, Hughes et al. 1995;
Braun, Weber et al. 1992;
Predictions:
Table SIMULATION:
Model: links to table MODEL below
Description:
We now want to examine the latencies of different regions in our model with available data to see how well some of the individual components perform. Segraves and Park (1987) found that 58% of the FEF neurons they examined reached a peak in activity within 40 msec (mean time of 13 msec) of the start of eye movements in a saccade. Additionally, Munoz and Wurtz (1995) found that SC neurons fire within 40 msec of saccade eye movements.
Inputs:
In a neural network model with as many neuronal arrays with weight constants, time constants and ranges of firing rates, it is possible to obtain almost any range of behavior desired. For our model, we utilized neurophysiological data where available, but to fill in the gaps, as it were, we used saccadic latency times for express saccades (no fixation, or gap size of 200 msec) and for voluntary saccades with fixation. Express saccades occur approximately 100 msec after the presentation of the saccade stimulus (Fischer and Boch 1983; Fischer and Ramsperger 1984; Sommer 1994; Baro, Hughes et al. 1995). Normal saccades take 160 msec to 300 msec to occur when a fixation signal is present until the visual stimulus is presented (overlap task, i.e., gap is 0 msec) (Braun, Weber et al. 1992).
In "establishing" parameters in our model for which we had little, or no biological data, we settled on an express saccade latency of 100 msec and a normal saccade with fixation latency of 200 msec. We then tuned model parameters to obtain these values.
Outputs:
In our model, with a simple saccade with no fixation,
we found that the peak in firing of the FEF saccade-related neurons (FEFsac)
occurred 10 msec prior to saccade onset (see Figure 5.3.5b). Additionally,
the SRBNs in the superior colliculus began firing 40 msec prior to the
initiation of the saccade (Figure 5.3.5.c).
(a) |
|
(b) |
FEF (a)and SC saccade-related neuronal firing (b) for simple saccade with no fixation (a) and (b) show the firing profile for FEF and SC saccade-related burst neurons, respectively. (c) show saccade velocity. |
(c) |
|
Experimental Data:
Fischer and Boch 1983;
Fischer and Ramsperger 1984;
Sommer 1994;
Baro, Hughes et al. 1995;
Braun, Weber et al. 1992;
Munoz and Wurtz 1995;
Predictions:
Table: MODEL
Title: Model of a Forebrain Mechanism for Controlling the Initiation of Voluntary Saccadic Eye Movements
Author: Michael Gregory Crowley (this could actually be a link to the authors table in the bibliographic database).
Version: 1.1 (?)
Keywords: Saccades, Basal Ganglia, Superior Colliculus, ...
Simulator: NSL (pointer to NSL and program guide)
Module: Source code and documentation
Run: Executable together with example runs.
Model Documentation:
Model Formalization: Appendix A
Model Description:
In section three, we discussed cortical circuitry involved in the generation of saccadic eye movements:
These cortical brain regions all play a role in the processing of visual information and providing the results of their processing to the subcortical regions superior colliculus and basal ganglia. In section four, we discussed the superior colliculus and its crucial role in not only the generation of express saccades (<100 msec latency), but also in voluntary saccade eye movements. It also seems most likely that the superior colliculus is actively involved in terminated saccades through a feedback loop with the brainstem (section four). However, the cortical regions mentioned above do not have any inhibitory connections onto the superior colliculus, thus, other than an excitatory connection from foveal-responsive neurons in the frontal eye fields (FEFfovea, equations FEF3 in appendix A), the cortex has no way to keep the superior colliculus from generating a saccade when it receives sufficient cortical excitation. This inhibitory task falls to the basal ganglia and the inhibitory connections it maintains with the superior colliculus. In the rest of this section, we discuss the basal ganglia and the role it plays in controlling the burst of activity in the saccade-related burst neurons in the SC signaling an impending saccade. In section six, we will present a second role of for the basal ganglia in saccadic motor control through its projections to mediodorsal thalamus-the same neurons active in the cortico-thalamic memory loops discussed in section three.
Our saccade model is based upon the hypothesis that the BG has two primary roles in the control of saccadic eye movements:
1. Maintain inhibition of a planned voluntary saccade until a GO signal is established by prefrontal cortex. This concept has been established in the literature through a number of experiments we will describe in this section. We call this our motor inhibition circuit.
2. Provide a remapping signal to parietal and prefrontal cortex, through thalamic projections, that is a learned estimate of the future sensory state based upon the execution of the planned motor command. This remapping signal begins prior to the initiation of the eye movement for the currently planned saccade and by doing so, allows cortical planning centers to "preplan" the next saccade while the current saccade is executed. This results in an improvement in the ability to perform sequences of movements. We term this our sensory remapping circuit.
Our use of the basal ganglia to inhibit a planned motor command prior to its execution was also used by Dominey and Arbib (1992) in their saccadic model. However, our proposal of a remapping of sensory information is different from the work of Berns and Sejnowski and Dominey, Arbib and Joseph who suggest that the BG is involved in selecting from competing streams of information to determine the next appropriate action. We see the BG not as selecting which movement is to be executed, but as providing future sensory state information to cortical planning centers for planning future actions.
Our remapping proposal requires that the basal ganglia be exposed to the sequence of tasks, e.g., a double saccade, repetitively so that it can modulate its performance to provide this "feedforward" remapping signal to the cortex. Monkeys, and in particular humans, are able to perform sequences of tasks without any training, but initially the "sequence" is little more than a string of individual movements. It is only through repetition that movement sequences, like a tennis serve, become fluid. This is the behavior that we propose is influenced by the remapping we suggest is performed by the basal ganglia.
To support our two assumptions on the roles of the basal
ganglia, we describe experimental data on specific brain regions shown
to exist in an "oculomotor loop" with the basal ganglia and show
results generated by our model that simulate both normal (this section)
and abnormal (section 6) oculomotor functioning.
The basal ganglia consist of five subcortical nuclei: the caudate nucleus (CD), putamen, globus pallidus, subthalamic nucleus, and substantia nigra. The neostriatum, or striatum, consists of both the caudate nucleus and putamen as they develop from the same telencephalic structure. The neostriatum receives nearly all of the input to the basal ganglia, receiving topographically organized afferents from all four lobes of the cerebral cortex, including sensory, motor, association, and limbic areas (Alexander, DeLong et al. 1986; Alexander, Crutcher et al. 1990; Gerfen 1992; Parent and Hazrati 1993). However, it projects back only to frontal cortex, through the thalamus.
The striatum projects to its output nuclei (substantia nigra pars reticulata and internal globus pallidus) via a direct and indirect path. The indirect path includes the GPe and STN and excites the BG output nuclei, whereas the direct path contains GABA neurons which inhibit the tonically firing SNr neurons. Lastly, the SNr projects back to prefrontal cortex through the thalamus (Carpenter, Nakano et al. 1976; Goldman-Rakic and Porrino 1985; Ilinsky, Jouandet et al. 1985; Selemon and Goldman-Rakic 1988) as well as projecting to the superior colliculus.
The globus pallidus is divided into the internal and external segments (Ct and Crutcher 1991). The substantia nigra consists of the pars reticulata, which is similar to the globus pallidus, and the pars compacta, comprised mostly of dopamine-containing neurons. The internal segment of the globus pallidus (GPi) and the substantia nigra pars reticulata are the output structures of the BG. These two regions are very similar and can be considered as a single structure like the caudate nucleus and putamen of the striatum.
Activity in the direct path causes a reduction in the
inhibitory activity of the BG output; activity in the direct path causes
an increase in the inhibitory activity of the BG output. See Figure 5.2.1
below.
Figure 5.2.1 Simplified BG Circuitry
Gray lines are inhibitory and black lines are excitatory connections between regions. Cortical input to the direct path through the BG causes inhibition of its output regions (GPi/SNr) which decreases the inhibitory outflow from the BG. However, cortical input to the indirect path causes an excitation of the BG output regions producing an increase in inhibitory output from the BG. (Excerpted from Alexander, Crutcher et al. 1990).
The subthalamic nucleus (STN) receives excitatory direct input from motor and somatomotor cortical areas (Hartmann-von Monakow, Akert et al. 1978; Rinvik, Grofova et al. 1979; Afsharpour 1985; Canteras, Shammah-Lagnado et al. 1990), as well as tonically inhibitory input from the striatum through the external globus pallidus (GPe). Both of these sets of inputs have been found to be highly organized (Ryan and Clark 1992; Wichmann et al. 1994). STN projects to the output structures of the basal ganglia with the excitatory neurotransmitter glutamate (Kitai and Kita 1987; Steriade, Pare et al. 1988; Nakanishi, Kita et al. 1991). Hikosaka et al. (1993) found cells in STN that began firing when the monkey began fixating a central spot and continued firing until the end of the trial, or until a saccade was initiated. Thus, it is generally believed that the STN is involved in increasing the output of the BG and consequently increasing the inhibition of the BG onto the thalamus and superior colliculus.
The substantia nigra pars reticulata, the oculomotor output nuclei of the basal ganglia, has GABAergic projection neurons that provide inhibitory connections to both the thalamus and superior colliculus. The SC projection terminates predominantly on the large neurons in the intermediate layers of SC. These SC neurons project to the brainstem pathway controlling eye and head movements. Studies have shown that the SNr-SC pathway is involved in gaze shifting, gaze fixation and saccadic eye movements (Hikosaka and Wurtz 1980; Hikosaka and Wurtz 1983; Hikosaka and Wurtz 1983; Hikosaka and Wurtz 1983; Hikosaka and Wurtz 1983; Chevalier, Vacher et al. 1985; Hikosaka and Wurtz 1985). We will describe the thalamic projections in more detail in section 5.3.
Our model deals specifically with the saccadic oculomotor system. For this reason, we will not include the internal globus pallidus or the putamen, as these brain regions seem to be more involved in skeletomotor control.
The BG motor inhibition circuit output is represented by the inhibitory projection from SNr to the superior colliculus saccade-related burst neurons (Hikosaka and Wurtz 1983). The basal ganglia appears to control the timing of voluntary saccades by maintaining a tonic level of inhibition on SC that is released when a saccade is to be performed. In our model, we use both the direct and indirect paths of the basal ganglia to execute this function. The indirect path, when active, causes an increase in the inhibitory outflow of the BG. Based on the experimental data presented above on the STN (Hikosaka et al. 1993), the cortical fixation system (PFCfixation, section 3.4) projects to caudate neurons projecting to the indirect path (CDindscburst, Appendix C, equations BG1). When fixation is to be maintained, the basal ganglia increases its inhibition onto the superior colliculus, allowing only reflexive saccades to seemingly important stimuli in the peripheral visual field to be generated; all voluntary saccades are inhibited. This fixation signal is a diffuse signal that is shared by all caudate neurons projecting to the indirect path.
We propose that the input to this BG circuit is the motor command from FEF and a "go" signal received from prefrontal cortex (PFCgo, Appendix A, equations PFC2). Thus, the BG inhibition on SC is released when there is sufficient cortical excitation of the direct path of the basal ganglia to override the tonic inhibition of the substantia nigra pars reticulata (SNr). Also, we suggest that tonic levels of dopamine in the striatum act in a manner to facilitate the firing of the striatal burst cells once the cortical excitation has reached a certain threshold. This is similar in concept to that used by the Dominey and Arbib (1992) saccade model.
The indirect-path caudate neurons have an inhibitory connection to inhibitory neurons in GPe (GPEscburst, Appendix C, equations BG5), which have their own inhibitory projections to the subthalamic nucleus (STNscburst, Appendix C, equations BG6). The subthalamic nucleus neurons have excitatory connections to the burst neurons in SNr (SNRscburst, Appendix C, equations BG8) completing the indirect path (see figure 5.2.2).
Figure 5.2.2 Model layers for motor inhibition basal
ganglia circuit and its inputs and outputs
We use the direct path through the BG to decrease its inhibition onto SC. The saccade-related burst neurons in FEF (FEFsac, section 3.3 discussion, Appendix A, equations FEF2) and prefrontal neurons that provide a go (PFCgo, Appendix A, equations PFC2) signal indicating that it is time to perform a saccade, project to the caudate direct path projection neurons (CDdirscburst, Appendix C, equations BG2). These caudate neurons project directly to the burst neurons in SNr (SNRscburst, Appendix C, equations BG8), the same neurons receiving excitation from the indirect path. It is the balance of activity between the indirect path and direct path projections onto SNr that determines its level of output at a given spatiotopic location.
Thus, there is a push-pull arrangement through the basal ganglia that allows for either an increase, or decrease, in inhibition from tonic levels. The inhibitory SNr burst neurons project to the saccade-related burst cells in the superior colliculus. We describe each type of neuron in our model BG in more detail below and show their connections in figure 5.2.1.
Wilson et al. (1981) found that the GABAergic inhibitory projection neurons in the BG rarely fire more than 40 spikes per second, which is the maximum firing rate for our model neurons. Wilson, Chang et al. (1990) found that the tonically active giant aspiny interneurons fire with a frequency less than 20 Hz. In our model, we have set the maximum firing rate of the BG interneurons to be 10 Hz, this ensures that their activity does not overwhelm the behavior of the MSN projection neurons.
Below we present a more detailed discussion of the types of neurons we have modeled for the BG motor inhibition circuit. In section six we present the sensory remapping circuit, the commonalties it has with the motor inhibition circuit and also the differences.
Caudate Burst Cells (CDscburst) are typically quiet and are tonically inhibited by the TAN cholinergic interneurons. They receive excitatory input from cortex (LIP, PFC, and FEF) and the thalamus. One set of cells projects to SNr (direct path, CDdirscburst, Appendix C, equations BG2) and the other set of cells project to GPe (indirect path, CDindscburst, Appendix C, equations BG1). They also receive afferents from the SNc dopaminergic cells described below. See Appendix C, equations BG1 and BG2 for the mathematical description of these neurons, for both the indirect and direct paths, respectively.
Caudate Tonically Active Cells (CDsctan) are cholinergic interneurons that fire tonically. They are inhibited by the non-dopaminergic aspiny interneurons in caudate (CDscinh, see below) and by the SNc dopaminergic neurons (SNCdop, see below). These cells are active throughout the striatum and act similarly to the burst neurons projecting to both the direct and indirect paths. See Appendix C, equations BG4 for the mathematical description of these neurons.
Caudate Non-dopaminergic Interneuron Cells (CDscinh) are normally quiet. They are activated by the FEF saccadic motor command (FEFsac, Appendix A, equations FEF2) and by the go signal from PFC (PFCgo, Appendix A, equations PFC2). When this input exceeds a certain threshold, these cells will fire and inhibit the tonically active interneurons (CDsctan, appendix C, equations BG4). These cells are active throughout the striatum and act similarly to the burst neurons projecting to both the direct and indirect paths. See Appendix C, equations BG3 for the mathematical description of these neurons.
GPe Burst Cells (GPEscburst) are tonically active and receive inhibition from the caudate burst cells. These inhibitory cells project to the STN burst cells (STNscburst, see below). See Appendix C, equations BG5 for the mathematical description of these neurons.
STN Burst Cells (STNscburst) are tonically active neurons receiving tonic inhibition from the GPe burst cells (GPEscburst). They provide excitatory input to the substantia nigra pars reticulata (SNRscburst, see below). See Appendix C, equations BG6 for the mathematical description of these neurons.
SNc Dopaminergic Cells (SNCdop) project to the burst cells (CDindscburst and CDdirscburst) and tonically active cells in the caudate (CDsctan). They receive excitatory afferents from limbic cortex about primary reward related events. See Appendix C, equations BG7 for the mathematical description of these neurons.
SNr Burst Cells (SNRscburst) are inhibitory neurons that are tonically active receiving inhibition from the caudate burst cells (CDdirscburst) and excitation from the STN burst cells (STNscburst). These cells project to the superior colliculus (SCsac, Appendix B, equations SC2) and are responsible for inhibiting the execution of a saccade motor command until deactivated by a corticostriatal "go" signal through the striatum (from PFCgo, Appendix A, equations PFC2). See Appendix C, equations BG8 for the mathematical description of these neurons.
Drawbacks:
Open Questions:
Accomplishments:
In "establishing" parameters in our model for which we had little, or no biological data, we settled on an express saccade latency of 100 msec and a normal saccade with fixation latency of 200 msec. We then tuned model parameters to obtain these values.We present a number of experiments that show not only that we achieved these two latencies, but that the model generates a range of behavior that also matches biological data.
We have seen that the overall performance of our saccade model matches actual saccade data fairly well.
Predictions:
The basal ganglia serves as both a brake and a gas pedal on the oculomotor circuit activated by cortical activity (described in section three) and implemented by the superior colliculus and brainstem (section four). The basal ganglia implements the voluntary fixation control of cortex onto superior colliculus through increased inhibitory outflow towards SC caused by an increase in activity of the indirect path. This fixation control path makes it more difficult to produce saccades even when direct electrical stimulation is applied to SC or FEF.
The basal ganglia also implements a facilitation of voluntary saccades through a decrease in its inhibition upon SC by increased activity in the BG's direct path. This facilitation makes it more likely that desired saccades occur, and through the use of a go signal from prefrontal cortex (PFCgo, Appendix A, equations PFC2), the basal ganglia controls the timing of the voluntary saccade as well. Without the basal ganglia, there is no mechanism, other than a foveal stimulus from the frontal eye fields, to control saccade initiation. This is exactly the behavior seen when GABA antagonists are applied to the substantia nigra pars reticulata causing a reduction in its activity (Hikosaka and Wurtz 1985).
Related Model:
Dominey and Arbib 1992;
Experimental Data:
Hikosaka and Wurtz 1985;
Hikosaka et al. 1993;
Wilson et al. 1981;
Wilson, Chang et al. 1990;
Hartmann-von Monakow, Akert et al. 1978;
Rinvik, Grofova et al. 1979;
Afsharpour 1985;
Canteras, Shammah-Lagnado et al. 1990;
Ryan and Clark 1992;
Wichmann et al. 1994;
Kitai and Kita 1987;
Steriade, Pare et al. 1988;
Nakanishi, Kita et al. 1991;
Carpenter, Nakano et al. 1976;
Goldman-Rakic and Porrino 1985;
Ilinsky, Jouandet et al. 1985;
Selemon and Goldman-Rakic 1988;