Computer Modeling in Basal Ganglia Disorders

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From: Current Clinical Neurology: Atypical Parkinsonian DisordersEdited by: I. Litvan © Humana Press Inc., Totowa, NJ

7Computer Modeling in Basal Ganglia Disorders

José Luis Contreras-Vidal

1. INTRODUCTION

The last two decades have witnessed an increasing interest in the use of computational modelingand mathematical analysis as tools to unravel the complex neural mechanisms and computationalalgorithms underlying the function of the basal ganglia and related structures under normal and neu-rological conditions (1–3). Computational modeling of basal ganglia disorders has until recentlybeen focused on Parkinson’s disease (PD), and to a smaller scale, Huntington’s disease (HD) (4–6).However, with the advent of large-scale neural network models of frontal, parietal, basal ganglia, andcerebellar network dynamics (7–9), it is now possible to use these models as a window to studyneurological disorders that involve more distributed pathology such as in atypical parkinsonian dis-orders (APDs). Importantly, computational models may also be used for bridging data across scalesto reduce the gap between electrophysiology and human brain imaging (10), to integrate data in allareas of neurobiology and across modalities (11), and to guide the design of novel experiments andintervention programs (e.g., optimization of pharmacotherapy in PD) (12).

This chapter aims to present the paradigm of computational modeling as applied to the study ofPD and APDs so that it can be understood for those approaching it for the first time. Therefore,mathematical details are kept to a minimum; however, references to detailed mathematical treat-ments are given. The brain, in its intact state, is a very complex dynamical system both structurallyand functionally, and many questions remain unanswered. However, theoretical and computationalneuroscience approaches may prove to be a very valuable tool for the neuroscientist and the neurolo-gist in understanding how the brain works in health and disease.

The Modeling ParadigmComputational models of brain and neurological disorders vary widely in the focus and scale of

the modeling, their degrees of simulated biological realism, and the mathematical approach used(13). A combination of “top-down” and “bottom-up” approaches to computational modeling in neu-roscience is depicted in Fig. 1, which shows the series of steps that need to be taken to study braindisorders computationally. One first has to measure the behavioral operating characteristics (BOCs),such as movement kinematics, average firing rates of homogenous cell populations, or neurotrans-mitter levels under intact conditions. The next step is to construct a mathematical model based on thebehavioral, anatomical, neurophysiological, and pharmacological data concerned with the produc-tion of the BOCs. The specified model should be capable of reproducing the measured behavior. Themodeled output is compared with the initial BOCs, leading to model refinement and further computersimulations until a reasonable match between the measured and the modeled BOC can be achieved.

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Although models are usually developed to demonstrate the biological plausibility of a particularpreexisting hypothesis, or to show how computational algorithms may be implemented in neuralnetworks, the same models can be used to generate and test new ideas by analyzing the emergentproperties of the model—model properties that cannot be explained by the operation or the wiring ofindividual model components alone. Moreover, by lesioning the intact structural components of themodel, manipulating its dynamic mechanisms, or altering its inputs, it is possible to characterize theneuropathology of the disease and the associated changes in the behavior. It is then also possible totest the effect of surgical or pharmacological interventions to counteract the effects of lesions ordisease (2,12). Thus, computational modeling of neurological disorders involves a succession ofmodeling cycles to first account for neural mechanisms underlying the normative data, followed bythe characterization and simulation of diseased mechanisms and abnormal behavior.

Modeling PD and APDsAlthough a comprehensive review of the literature on modeling of basal ganglia function in health

and disease is not possible because of space limitations, the reader is referred to the reviews of Beiseret al. (1), Ruppin et al. (2), and Gillies and Arbuthnott (3) for a detailed account. These efforts havefocused on explaining the roles of the basal ganglia in procedural learning (14–17), action selection(18–20), serial order (21–23), and movement planning and control (24–27). Unfortunately, althoughthese models have provided insights on the abnormal mechanisms underlying PD, few efforts havebeen put forward on modeling APDs. Thus, one goal of this chapter is to describe how existingmodels of cortical, basal ganglia, and cerebellar dynamics can be used to model and simulate APDs.In the next section, we briefly review the neuropathology in APDs. The reader is referred to Chapters 1,4, 8, and 18–20 of this book for detailed reviews and discussion of the underlying neuropathology.

Neuropathology of the APDsIt is widely recognized that the differential diagnosis of APDs presents some difficult problems.

First, clinical diagnostic criteria are often suboptimal or partially validated (28); and second, the

Fig. 1. The paradigm of neural network modeling.

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usefulness of routine brain-imaging techniques, such as magnetic resonance imaging (MRI), is stilldebatable because of issues such as specificity, sensitivity, variations in technical parameters, and theexperience of radiologists and neurologists (29). Nevertheless, modern MRI methodologies are use-ful to differentiate PD from APDs, as brain MRI in PD is grossly normal. Moreover, MRI studiessuggest specific regional brain markers associated with the underlying pathology in APDs, such asmultiple system atrophy (MSA), progressive supranuclear palsy (PSP), and corticobasal degenera-tion (CBD). Importantly, as these data can be used as a starting point for modeling purposes (Fig. 1),we briefly summarize the MRI findings.

Multiple system atrophy of the parkinsonian type (MSA-P) appears to be characterized byputaminal atrophy, T2-hypointensity, and “slit-like” marginal hyperintensity (29–32), whereas MSAof the cerebellar type (MSA-C) usually is accompanied by atrophy of the lower brainstem, pons,middle cerebellar peduncles, and vermis, as well as signal abnormalities in the pontine and the middlecerebellar peduncles (30,31,33,34). Mild-to-moderate cortical atrophy is also common to both MSA-P and MSA-C (29,35).

PSP is usually characterized by widespread cell loss and gliosis in the globus pallidus, subtha-lamic nucleus, red nucleus, substantia nigra, dentate nucleus, and brainstem, and often cortical atro-phy and lateral ventricle dilatation (29). These patients also show decreased 18F-flurodopa in bothanterior and posterior putamen and caudate nucleus, and an anterior–posterior hypometabolic gradi-ent (36). On the other hand, CBD may be differentiated by the presence of asymmetric frontoparietaland midbrain atrophy (29).

Interestingly, cortical atrophy in APDs, particularly in cases involving damage of frontoparietalnetworks, is consistent with reports of ideomotor apraxia, which can also be seen in PD patients whentheir pathology is coincident with cortical atrophy (36–39). In particular, patients with PD and PSP,who showed ideomotor apraxia, had the greatest deficits in movement accuracy, spatial and temporalcoupling, and multijoint coordination (38). However, as has been noted elsewhere, it remains to beseen if the kinematic deficits observed in this patients are characteristic of apraxia or are caused byelementary motor deficits (40). Given the pathological heterogeneity seen in patients with APDs, andeven in PD, it seems that computer modeling would be a useful tool to study how damage to fronto-parietal networks and their interaction with a dysfunctional basal ganglia and/or cerebellar systemsmay increase the kinematic abnormalities beyond some threshold that would result in the genesis oflimb apraxia.

MODELING STUDIES

In this section we present two examples of computational models of basal ganglia disorders. Thefirst example presents a model formulated as a control problem to investigate akinesia and bradyki-nesia in PD, whereas the second example, formulated as a large-scale, dynamic neural network modelinvolving frontoparietal, basal ganglia, and cerebellar networks, investigates the effects of PD andPSP on limb apraxia.

Modeling Hypokinetic Disorders in PDContreras-Vidal and Stelmach proposed a neural network model of the sensorimotor cortico-

striato-pallido-thalamo-cortical system to explain some movement deficits (the “BOCs” in the mod-eling cycle) seen in PD patients (24). This model, originally specified as a set of nonlinear differentialequations, proposed the concept of basal ganglia gating of thalamo-cortical pathways involved inmovement preparation (or priming), movement initiation and execution, and movement termination(Fig. 2A). In this model, three routes for cortical control of the basal ganglia output exist: activationof the “direct pathway” opens the gate by disinhibition of the thalamic neurons (route 1), whereasactivation of both a slower indirect (through GPe, route 2) pathway and a faster direct cortical (route 3)pathway closes the gate through inhibition of thalamo-cortical neurons.

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In this theoretical framework, activation of pathway 1 would result in activation of thalamo-corti-cal motor circuits leading to initiation and modulation of movement, whereas activation of pathway 2would lead to breaking of ongoing movement. Activation of pathway 3 would facilitate rapid move-ment switching, or prevent the release of movement. The model postulated a role of the pallidaloutput for generating an analog gating signal (at the thalamus) that modulated a (hypothesized) cor-tical system that vectorially computed the difference between a target position vector and the presentlimb position vector, the so-called Vector-Integration-To-Endpoint (VITE) model (Fig. 2B) (41).

In this computational model, the basal ganglia output had the role of gating the onset, timing, andthe rate of change of the difference vector (DV), therefore controlling movement parameters suchas movement initiation, speed, and size. Moreover, the proposed basal ganglia gating functionallows three control modes: preparation for action or priming (gate is closed), initiation of action(gate starts to open), and termination of action (gate starts to close). Simulations of this model dem-onstrated a single mechanism for akinesia, bradykinesia, and hypometria, and a correlation betweendegree of striatal dopamine depletion and the severity of the PD signs.

In the terminology of control theory, it can been shown that the sensorimotor cortico-basal ganglianetwork of Contreras-Vidal and Stelmach (24) can be approximated as a proportional + derivativecontroller (Equation 1) with time-varying position (Gp; Equation 2) and velocity (Gv; Equation 3)gains. The system described by the second-order differential equation (1) represents the motion ofthe endpoint (P) toward the target (T) under the initial position and velocity conditions P = P0 anddP0/dt = 0, respectively.

Fig. 2. (A) Three pathways for control of pallidal output by cortical areas. B) Block diagram of the cortico-basal ganglia-thalamo-cortical network of Contreras-Vidal and Stelmach (24). The basal ganglia output (GPi)gates activity at the ventro-lateral thalamus (VLo), thus modulating cortico-cortical communication in the “vec-tor integration model” that progressively moves the endeffector (PPV) to the target location (TPV). The basalganglia gating allows priming and controls the speed of change from limb present position (PPV) to targetposition (TPV). Filled circles imply inhibitory connections, whereas arrows imply excitatory connections.

d2

dt2

P = Gv

ddt

P – Gp

P – T (1)

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where α represents an integration rate and G0 is a scaling constant and t is the time in sec. Thesystem given by Equations 1–3 is based on the experimentally testable assumption that pallidal sig-nals modulate the ventro-lateral thalamus (VLo) such that the pattern of thalamic output has a sigmoi-dal shape or is gradually increasing as a function of time as in Equation 4. This assumption impliesthat either a compact set of pallidal neurons progressively decrease their firing rate as a function oftime before movement onset, therefore gradually disinhibiting the motor thalamus, or an increasingnumber of (inhibitory) pallidal cells, controlling the prime movers, are depressed as the movementunfolds.

Gp

= αG0

t1 + t (2)

Figure 3 shows the mean cumulative distributions of onsets (decreases and increases) for GPi neu-rons prior to movement onset obtained from a set of neurophysiological studies published between1978 and 1998 (Table 1) in which information about the timing of internal globus pallidus (GPi)neurons was available. The plot shows a gradual buildup or decrease of the mean cumulative distribu-tion of neurons whose activations were either enhanced or depressed prior to movement onset. Overall,increases in GPi activity were predominant (48% and 26% for increases and decreases, respectively). Itis likely that the small percentage of GPi depressions prior to movement onset reflects the focusedactivation of prime mover muscles required to produce an arm movement. Interestingly, the meancumulative distribution shows an increasing number of GPi neurons that are depressed, which supportsthe foregoing model’s assumption.

Computer simulations of the set of equations (1–4) show that smaller-than-normal position andvelocity gains can lead to bradykinesia (Fig. 4). Therefore, it is hypothesized that a function of basalganglia networks is to compute these time-varying position and velocity gains. Low gains wouldprevent appropriate opening of the pallidal gate leading to poor activation of thalamo-cortical path-ways involved in movement, whereas high gains may lead to excess or unstable movement. Interest-ingly, Suri and colleagues also used a dynamical linear model to model basal ganglia function andtheir simulations suggested that low gains in the direct and indirect pathways resulted in PD motordeficits (26).

In addition, reduced movement amplitudes may be caused by premature resetting of these gainsthat prevent movement completion. Indeed, we have shown that smaller-than-normal (in durationand size) pallido-thalamic signals produced by dopamine depletion in the basal ganglia can repro-duce micrographic handwriting (12).

Modeling Abnormal Kinematics During Pointing Movement and Errors in Praxisin PD and APDs

To study the kinematic aspects of movement in basal ganglia disorders, we have performed com-puter simulations of the finger-to-nose task and a “bread-slicing gestural task”; the latter task is usedcommonly in testing for ideomotor apraxia (38). These two tasks require the integration and transfor-mation of sensory information into motor commands for movement, and therefore successful taskcompletion depends on accurate spatial and temporal organization of movement.

Gv

= 1 + t

1 + t2

– α (3)

(4) VLo

= G0

t1 + t

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Table 1Cumulative Distribution of Onsets for GPi Cells

Initial Timing of Discharge (%) Prior to:

–150 ms –100 ms –50 ms 0 ms EMG cells

Ref Location � � � � � � � � � � #

42a C (m. N) 7 0 27 0 40 7 53 13 20 0 1543b NAc — — — — 2 2 — — 7 7 3544d DL EP 22 14 45 29 48 31 53 34 37 24 11445 NA — — — — — — 38 26 11 14 3646e VL — — 10f 4 — — 29 12 2 1 4147g VL (m. 2) — — 19 3 81 14 84 15 37 7 6848h DL EP 57 16 57 16 63 18 66 19 NA NA 2849i DL/VL — — 17 17 25 53 62 91 NA NA 18

Mean % 10.8 3.8 21.9 8.6 32.4 15.6 48.1 26.3 14.3 6.63 —Total 355

�, increase;�, decrease; C, centered; DL, dorsolateral; EMG, onset of first muscle activity in primemovers; EP, entopenduncular nucleus (GPi-like structure in felines); GPi, internal globus pallidus; m., mon-key; NA, data not available; VL, ventrolateral. All times with respect to movement onset, except EMG data.Notes: a biphasic stimulation trains (from Fig. 8), b EMG recordings were made at separate times from thesingle-cell recordings; c recording was done from “full extent of GP” and percentages of discharges weredivided equally in increases and decreases; d estimated from Fig. 9 (61%: �, 39%: �); e for VisStep task(71% [29%] GPi increased [decreased] their discharge overall); f estimated from Fig. 5, by counting num-ber of samples during time interval and dividing by the maximum number of conditions (four); g dataestimated from Fig. 6C (85%: �, 15%: �); h estimated from Fig. 4 (assumes uniform distributions of 78%activations in EP); i data estimated from Fig. 3B.

Fig. 3. Mean cumulative (SE) distributions of activations and depressions of GPi activity obtained from setof studies in Table 1.

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Figure 5 depicts a schematic diagram of frontal, parietal, basal ganglia, and cerebellar networkspostulated to be engaged in the learning and updating of sensorimotor transformations for reaching tovisual or proprioceptive targets. The model is based on an extension of the computational models ofBullock et al. (9) and Burnod et al. (8), and recent imaging and behavioral experiments (50–53) thatsuggest distinct roles for fronto-parietal, basal ganglia, and cerebellar networks. In the model, visualand/or proprioceptive signals about target location and end-effector position are used to code aninternal representation for target (T) and arm (Eff), presumably in posterior parietal cortex (PPC).These internal representations are compared to compute a spatial difference vector (DVs) as in thecortical “vector integration model” depicted in Fig. 2B. The DV’s outflow must be transformed intoa joint rotation vector (DVm) in order to guide the end-effector to the target. This spatial direction-to-joint rotation transformation is an inverse kinematic transformation and computationally, it can belearned through certain amount of simultaneous exposure to patterned proprioceptive and visualstimulation under conditions of self-produced movement—referred to as “motor babbling” (8,9).

The cortical network just described is complemented by two subcortical networks connected intwo distinct, parallel, lateral loops, namely, a frontostriatal network and a parieto-cerebellar system.The former provides a learned bias term that rotates the frame of reference for movement, whereasthe latter provides a correction term that is added to the direction vector whenever the actual directionof movement deviates from the desired one. The frontostriatal network is modeled as an adaptivesearch element that performs search and action selection using reinforcement learning (15). Thissystem uses an explicit error (dopamine) signal to drive the selection and the reinforcement/punish-ment mechanisms used for learning new procedural skills. It searches and evaluates candidatevisuomotor actions that would lead to acquisition of a spatial target. The cerebellar component ismodeled as an adaptive error-correcting module that continuously provides a compensatory signal todrive the visuomotor error (provided by the climbing fibers) to zero (7).

Fig. 4. Simulations of normal (thick lines) and Parkinson’s disease (thin lines) movement control. Jointposition (ramp trajectories) and velocity (bell-shaped trajectories) for three different position and velocity gainsettings are shown (α = 10; G0 = 10; normal: Gp = Gv = 1.0; PD1: Gp = Gv = 0.6; PD2: Gp = Gv = 0.2).Reducing the gain resulted in slower movement (bradykinesia).

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Simulating the Finger-to-Nose Test in Control, PD, and APDThe model summarized in the previous discussion was implemented in Matlab Simulink (follow-

ing the mathematical equations in refs. 8 and 9) to investigate the effects of PD and APDs in thespatial and temporal characteristics of repetitive pointing movement to the nose (a kinesthetic target).Figure 6 depicts the movement trajectories and the joint angles for a simulated arm with three joints(shoulder, elbow, wrist). The simulation assumed horizontal movements at the nose level, and there-fore the paths are shown as two-dimensional plots. As expected, in the virtual control subject, thefinger-to-nose trajectories were slightly curved and showed high spatial and temporal accuracy. Thejoint excursions reflected the repetitive nature of the task with most of the movement performed byelbow flexion/extension followed by the shoulder and to a lesser degree by the wrist.

To simulate PD, the gain of the basal ganglia gating signal was decreased by 30% with respect tothat in the intact system. In addition, Gaussian noise (N(0,1)*30) was added to the internal represen-tation of the hand to account for kinesthetic deficits reported in PD patients (degradation of thekinesthetic representation of the spatial location of the nose would have had the same effect) (54).Computer simulations of the PD network showed decreased movement smoothness and increasedspatial and temporal movement variability. Moreover, the joint rotations were slower and progres-sively decreased in amplitude. Thus, the simulation is consistent with reports of deficits in the pro-duction of multiarticulated repetitive movement in PD.

Following the observations of cortical atrophy in frontal and parietal areas in APD summarized insubheading Neuropathology of the APDs, we modeled this disease in two steps: First, we added noise(uniform distribution between 0 and 1.5) to the adaptive synaptic weights of the frontoparietal net-work in the intact (“control”) system; second, we pruned the synaptic weights by randomly setting50% of the weights to zero; and third, the gain of the basal ganglia gating signal was reduced to 50%of the control value. Simulation of the APD network model showed that the movement trajectories

Fig. 5. Diagram of hypothesized networks involved in sensorimotor transformation for reaching. See text fordescription.

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Fig. 6. Simulations of the finger-to-nose test in normal, PD, and APD models. Movement trajectories andjoint angles are shown. See videoclip for real-time simulation.

were severely affected. The virtual subject showed misreaching to the nose and produced movementpaths that varied widely in space. This was reflected in the joint excursions, which were character-ized by noisy and asymmetrical flexion and extension ranges, as well as some periods of joint immo-bility. Thus, simulation of APD had the largest effect on the spatial and temporal aspects of movementcoordination.

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Simulating the Bread-Slicing Gesture in Control, PD, and APDRecent clinical studies suggest that apraxia may be explained in terms of damage to a fronto-

parietal network involved in reaching and prehension (38). According to Rothi, ideomotor apraxia ischaracterized by “impairment in the timing, sequencing, and spatial organization of gestural move-ments” (55). Studies involving patients with PD and APDs, including PSP and CBD, indicate thatcombined involvement of basal ganglia and cortical networks may underlie the presence of apraxia inthese patients (37,38). Moreover, in a group of studies by Leiguarda and colleagues, they found thatpatients with PD, PSP, and CBD, who tested positive for apraxia in the clinical test, showed largerkinematic abnormalities than those patients who do not show apraxia on clinical examination. How-ever, as discussed initially by Roy, it is still a matter of debate whether these kinematic abnormalitiesare a result of an apraxia-like impairment or to basic motor control deficits (40). For example, do thebasic motor control deficits seen in these clinical populations explain the abnormal kinematic deficitsseen in patients with ideomotor apraxia?

In the computer simulations that follow we focus on production errors, which are associated withdeficits in the programming and execution of gestural movements, like the bread-slicing task. Simu-lations of higher-order content errors would require modeling of frontal areas related to ideational orconceptual processing, which are not included in the current model. In the model simulations, it isassumed that the planning and control components are disturbed because of the pathology in fronto-parietal networks.

Figure 7 shows the performance in the ‘bread slicing’ task in a normal virtual subject (Control),and after simulated PD and APD. Both diseases were simulated as in subheading ModelingHypokinetic Disorders in PD. In the control simulation the slicing gesture, depicted as a continuousdark line, reflected a tight, curvilinear trajectory, which was primarily a result of the repetitive, peri-odic, shoulder rotations. Elbow and wrist joint angles also showed sustained, periodic patterns albeitof smaller amplitude. Simulation of the parkinsonian network resulted in reduced spatial and tempo-ral accuracy of the slicing movement. This was accompanied by slower and asymmetrical joint oscil-lations that were maximal for the shoulder joint, but considerably reduced for the wrist joint. In fact,as the slicing gesture was generated, the wrist joint was progressively rotated from ~18° to ~38° (seegeometry of the arm in top panel of Fig. 7). Simulation of PSP resulted in large production errors asevidenced by distorted spatial trajectories, some of which left the spatial area for the simulated breadsurface. The profiles of the joint angles also resemble those reported in recent studies (see e.g., Fig. 5in ref. 38). For example, the angular changes of virtual patients with PD and APDs are smaller,irregular, and distorted compared to the simulated control subject.

CONCLUSIONSModels of basal ganglia disorders have been advanced in the last two decades. These models have

mostly focused on PD, in part because of the computational burden of simulating large-scale modelsthat include multiple brain areas. However, recent computational work on frontal, parietal, cerebel-lar, and basal ganglia dynamics involved in sensorimotor transformations for reaching provide awindow to study widespread pathologies as those seen in APDs. These models can inform the experi-mentalist about the various potential sources of movement variability in various types of tasks (simplevs sequential, pantomime vs real tool use, kinesthetic vs visual cueing, etc.). Moreover, simulatedlesions and interventions can be used to test hypotheses and guide new experiments.

For example, we modeled the pharmacokinetics and the pharmacodynamics using a neural net-work model parameterized by the measurements of the handwriting kinematics of PD patients (12).Other mathematical treatments of the dose–effect relationship of levodopa and motor behavior treatthe motor control system as a black-box system and do not provide insights on the mechanisms,although they may still be useful for therapy optimization purposes (56). On the other hand, a bio-logically inspired, albeit highly simplified neural network model of cortico-basal ganglia dynamics

Computer Models of Atypical Parkinsonism 105

during normal and neurological conditions would be valuable to assess which parameters might be mostamenable to therapeutic intervention, including individual optimization of pharmacological therapy,while at the same time informing about abnormal mechanisms.

Limitations of Current Models of Basal Ganglia DisordersAPDs are caused by various diseases, therefore involving a complex neuropathophysiology and a

wide spectrum of abnormal behavioral signs. Currently, there is no mathematical or conceptual modelthat can explain all the symptoms based on abnormal mechanisms within the basal ganglia, cerebel-lum, and/or cortical areas. This limitation is partially because of the necessary simplification of theneurobiology required to make the model computationally or mathematically tractable for formalinvestigation. Thus, it is likely that some aspect of any proposed model may be wrong; however, thelikelihood of this happening can be minimized by developing a step-by-step reconstruction of thesystem under study, with each step required to account for additional sources of neural or motor

Fig. 7. Simulations of the bread-slicing gesture commonly used to test ideomotor apraxia in basal gangliadisorders. Simulations show movement trajectories and joint angles (shoulder, elbow, and wrist) for normal,PD, and APD simulations. See videoclip on accompanying DVD for real-time simulation.

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variability. Moreover, manipulations of model components, such as simulated lesions or deep brainstimulation paradigms, are also oversimplifications of the processes occurring in the brain in responseto such events.

We hope that computational models of basal ganglia disorders will be developed further to helpelucidate and account for the complexity of the clinical symptoms seen in PD and APDs, in such away that these models can guide further theoretical and applied research and foster interactionsbetween clinicians, modelers, and neuroscientists.

FUTURE DIRECTIONS

A controversial question in apraxia research is the relevance of ideomotor apraxia for real-lifeaction (57). Earlier reports suggested that patients with apraxia may use single objects appropriatelyeven when they are unable to pantomime their use (58,59), whereas other have found the same typesof spatiotemporal errors in both object pantomime and during tool use (58) or reported that subjectswith ideomotor apraxia, assessed by gesture pantomime, had more errors with tools while eating thanmatched controls (61). The large-scale neural network presented in this chapter may help to elucidateany potential relationship of ideomotor apraxia to skilled tool use in naturalistic situations. Extensionof the large-scale neural network model to include visual and tactile signals produced by the sight andon-line interaction with the object would be critical to answer this question. Another important direc-tion for future work relates to the integration of stored movement primitives (so-called gesture en-grams) and dynamic movement features required to produce and distinguish a given gesture fromothers. Although the simulations of the “slicing” gesture in anapraxic neural network model pre-sented in this chapter were based on degraded sensorimotor transformations for movement, it shouldalso be possible to evaluate the effects of disruptions in the on-line sequential (dynamic) processesunderlying the repetitive nature of the slicing task, which were intact in the present simulations.Finally, the hypothetical effects of neuromotor noise in different model components could also beassessed through neural network simulations.

ACKNOWLEDGMENTS

The author thanks Shihua Wen, University of Maryland’s Department of Mathematics, for run-ning the simulations shown in Figs. 6 and 7. The author’s computational work summarized herein hasbeen supported in part by INSERM and the National Institutes of Health.

FIGURES

Figures were generated in Matlab and filtered using Abobe Illustrator.

MEDIA

Procedure Used to Generate the MPEG Files:In the CD disk, there are six mpeg files, the file names represent the simulated tasks, which are

described below. The frames in format .avi were generated by the computational model written inMatLab's Simulink. The .avi files are generated by a shareware named "HyperCam" produced byHypererionics Technology (www.hperionics.com). The mpeg files were obtained using the freewardsoftward "avi2meg" written by USH (www.ush.de). All the movies are recorded at a rate of 30 framesper second.

Description of Movies:Finger-to-nose Control (duration: 1:48): Simulation shows the end-pont trajectories during the

finger-to-nose task. A three segments arm is shown. These segments are linked by the shoulder,elbow, and wrist joints. This simulation of an intact (Control) network shows almost linear trajectories.

Computer Models of Atypical Parkinsonism 107

Finger-to-nose PD: This movie shows the performance of the computer model after simulatingsevere PD. In this simulation, the movement becomes slower, discrete, and noisy. Moreover, some ofthe targeted movements do not reach the nose.

Finger-to-nose APD: This movie shows the finger-to-nose simulations after damage to the fronto-parietal network involved in sensorimotor trnsformations for reaching, which simulated APD. Theend-point trajectories become irregular, coarse, fragmented, and dyscoordinated.

Slicing Control: This clip shows a simulation of the "bread slicing" gesture as seen from directlyabove. The rectangle represents the loaf of bread. Note that there were not constrains on the way thevirtual arm was supposed to produce the gesture. Note that during the repetitive movement the wristjoint was initially slightly flexed, but gradually became extended. This illustrates the fact that in aredundant arm there are many possible arm configurations that can be used to move the end point toa spatial target or along a given spatial trajectory.

Slicing PD: The PD simulation shows reduced range of motion for all joints, discontinuous move-ments, and a difficulty in generating the repetitive slicing gesture. In this particular simulation, thewrist is in the extended position from the onset of the movement.

Slicing APD: This video shows the slicing gesture task after simulated APD. This simulationshows production errors as the arm fails to move the end point along the desired slicing trajectory.This resulted in highly disrupted spatial and temporal organization.

REFERENCES

1. Beiser DG, Hua SE, Houk JC. Network models of the basal ganglia. Curr Opin Neurobiol 1997;7:185–190.2. Ruppin E, Reggia JA, Glanzman D. Understanding brain and cognitive disorders: the computational perspective. Prog

Brain Res 1999;121:ix–xv.3. Gillies A, Arbuthnott G. Computational models of the basal ganglia. Mov Disord 2000;15:762–770.4. Amos A. A computational model of information processing in the frontal cortex and basal ganglia. J Cogn Neurosci

2000;12:505–519.5. Lorincz A. Static and dynamic state feedback control model of basal ganglia-thalamocortical loops. Int J Neural Syst

1997;8:339–357.6. Wickens JR, Kotter R, Alexander ME. Effects of local connectivity on striatal function: stimulation and analysis of a

model. Synapse 1995;20:281–298.7. Contreras-Vidal JL, Grossberg S, Bullock D. A neural model of cerebellar learning for arm movement control: cortico-

spino-cerebellar dynamics. Learn Mem 1997;3:475–502.8. Burnod Y, Grandguillaume P, Otto I, Ferraina S, Johnson PB, Caminiti R. Visuomotor transformations underlying arm

movements toward visual targets: a neural network model of cerebral cortical operations. J Neurosci 1992;12:1435–1453.9. Bullock D, Grossberg S, Guenther FH. A self-organizing neural model of motor equivalent reaching and tool use by a

multijoint arm. J Cogn Neurosci 1993;5:408–435.10. Tagamets MA, Horwitz B. Interpreting PET and fMRI measures of functional neural activity: the effects of synaptic

inhibition on cortical activation in human imaging studies. Brain Res Bull 2001;54:267–273.11. Horwitz B, Poeppel D. How can EEG/MEG and fMRI/PET data be combined? Hum Brain Mapp 2002;17:1–3.12. Contreras-Vidal JL, Poluha P, Teulings HL, Stelmach GE. Neural dynamics of short and medium-term motor control

effects of levodopa therapy in Parkinson’s disease. Artif Int Med 1998;13:57–79.13. Bower JM. Modeling the nervous system. TINS 1992;15:411–412.14. Schultz W, Dayan P, Montague R. A neural substrate of prediction and reward. Science 1997;275:1593–1599.15. Contreras-Vidal JL, Schultz W. A predictive reinforcement model of dopamine neurons for learning approach behav-

ior. J Comput Neurosci 1999;6:191–214.16. Nakahara H, Doya K, Hikosaka O. Parallel cortico-basal ganglia mechanisms for acquisition and execution of

visuomotor sequences—A computational approach. J Cogn Neurosci 2001;13:626–647.17. Suri R, Schultz W. Learning of sequential movements by neural network model with dopamine-like reinforcement

signal. Exp Brain Res 1998;121:350–354.18. Contreras-Vidal, JL. The gating functions of the basal ganglia in movement control. In: JA Reggia, E Ruppin, DL

Glanzman (eds.). Progress in Brain Research. Disorders of Brain, Behavior and Cognition: the NeurocomputationalPerspective. Amsterdam: Elsevier, 1999:261–276.

19. Humphries MD, Gurney KN. The role of intra-thalamic and thalamocortical circuits in action selection. Network2002;13:131–156.

108 Contreras-Vidal

20. Gurney K, Prescott TJ, Redgrave P. A computational model of action selection in the basal ganglia. II. Analysis andsimulation of behaviour. Biol Cybern 2001;84:411–423.

21. Beiser D, Houk J. Model of cortical-basal ganglia ganglionic processing: encoding the serial order of sensory events.J Neurophysiol 1998;79:3168–3188.

22. Fukai T. Sequence generation in arbitrary temporal patterns from theta-nested gamma oscillations: a model of the basalganglia-thalamo-cortical loops. Neural Netw 1999;12:975–987.

23. Berns GS, Sejnowski TJ. A computational model of how the basal ganglia produce sequences. J Cogn Neurosci1998;10:108–121.

24. Contreras-Vidal JL, Stelmach GE. A neural model of basal ganglia–thalamocortical relations in normal and Parkinso-nian movement. Biol Cybern 1995;73:467–476.

25. Connolly CI, Burns JB, Jog MS. A dynamical-systems model for Parkinson’s disease. Biol Cybern 2000;83:47–59.26. Suri RE, Albani C, Glattfelder AH. A dynamic model of motor basal ganglia functions. Biol Cybern 1997;76:451–458.27. Borrett DS, Yeap TH, Kwan HC. Neural networks and Parkinson’s disease. Can J Neurol Sci 1993;20:107–113.28. Litvan I. Recent advances in atypical parkinsonian disorders. Curr Opin Neurol 1999;12:441–446.29. Yekhlef F, Ballan G, Macia F, Delmer O, Sourgen C, Tison F. Routine MRI for the differential diagnosis of Parkinson’s

disease, MSA, PSP, and CBD. J Neural Transm 2003;110:151–169.30. Schrag A, Kingsley D, Phatouros C, et al. Clinical usefulness of magnetic resonance imaging in multiple system atro-

phy. J Neurol Neurosurg Psychiatry 1998;65:65–71.31. Schrag A, Good CD, Miszkiel K, et al. Differentiation of atypical parkinsonian syndromes with routine MRI. Neurol-

ogy 2000;54:697–702.32. Kraft E, Schwarz J, Trenkwalder C, Vogl T, Pfluger T, Oertel WH. The combination of hypointense and hyperintense

signal changes on T2-weighted magnetic resonance maging sequences: a specific marker of multiple system atrophy?Arch Neurol 1999;56:225–228.

33. Savoiardo M, Strada L, Girotti F, Zimmerman RA, Grisoli M, Testa D, Petrillo R. Olivopontocerebellar atrophy: MRdiagnosis and relationship to multisystem atrophy. Radiology 1990;174:693–669.

34. Savoiardo M, Grisoli M, Girotti F, Testa D, Caraceni T. MRI in sporadic olivopontocerebellar atrophy and striatonigraldegeneration. Neurology 1997;48:790–792.

35. Horimoto Y, Aiba I, Yasuda T, et al.Cerebral atrophy in multiple system atrophy by MRI. J Neurol Sci 2000;173:109–112.36. Fahn S, Green PE, Ford B, Bressman SB. Handbook of Movement Disorders. London: Blackwell Science, 1997.37. Leiguarda RC, Marsden CD. Limb apraxias: higher-order disorders of sensorimotor integration. Brain 2000;123:860–79.38. Leiguarda R, Merello M, Balej J, Starkstein S, Nogues M, Marsden CD. Disruption of spatial organization and interjoint

coordination in Parkinson’s disease, progressive supranuclear palsy, and multiple system atrophy. Mov Disord2000;15:627–640.

39. Litvan I. Progressive supranuclear palsy and corticobasal degeneration. Baillieres Clin Neurol 1997;6:167–185.40. Roy EA. Apraxia in diseases of the basal ganglia. Mov Disord 2000;15:598–600.41. Bullock D, Grossberg S. Neural dynamics of planned arm movements: emergent invariants and speed-accuracy proper-

ties during trajectory formation. Psychol Rev 1988;95:49–90.42. Anderson ME, Horak FB. Influence of the globus pallidus on arm movements in monkeys. III. Timing of movement-

related information. J Neurophysiol 1985;54:433–448.43. Brotchie P, Iansek R, Horne MK. Motor function of the monkey globus pallidus. 1. Neuronal discharge and parameters

of movement. Brain. 1991;114:1667–1683.44. Cheruel F, Dormont JF, Amalric M, Schmied A, Farin D. The role of putamen and pallidum in motor initiation in the

cat. I. Timing of movement-related single-unit activity. Exp Brain Res 1994;100:250–266.45. Georgopoulos AP, DeLong MR, Crutcher MD. Relations between parameters of step-tracking movements and single

cell discharge in the globus pallidus and subthalamic nucleus of the behaving monkey. J Neurosci 1983;3:1586–1598.46. Mink JW, Thach WT. Basal ganglia motor control. I. Nonexclusive relation of pallidal discharge to five movement

modes. J Neurophysiol 1991;65:273–300.47. Nambu A, Yoshida S, Jinnai K. Movement-related activity of thalamic neurons with input from the globus pallidus and

projection to the motor cortex in the monkey. Exp Brain Res 1991;84:279–284.48. Neafsey EJ, Hull CD, Buchwald NA. Preparation for movement in the cat. II. Unit activity in the basal ganglia and

thalamus. Electroencephalogr Clin Neurophysiol 1978;44:714–723.49. Turner RS, Anderson ME. Pallidal discharge related to the kinematics of reaching movements in two dimensions.

J Neurophysiol 1997;77:1051–1074.50. Contreras-Vidal JL, Buch ER. Effects of Parkinson’s disease on visuomotor adaptation. Exp Brain Res 2003;150:25–32.51. Buch ER, Young S, Contreras-Vidal JL. Visuomotor adaptation in normal aging. Learn Mem 2003;10:55–63.52. Inoue K, Kawashima R, Satoh K, et al. A PET study of visuomotor learning under optical rotation. Neuroimage

2000;11:505–516.53. Balslev D, Nielsen FA, Frutiger SA, et al. Cluster analysis of activity-time series in motor learning. Hum Brain Mapp

2002;15:135–45.

Computer Models of Atypical Parkinsonism 109

54. Klockgether T, Borutta M, Rapp H, Spieker S, Dichgans J. A defect of kinesthesia in Parkinson’s disease. Mov Disord1995;10:460–465.

55. Rothi LJG, Ochipa C, Heilman KM. A cognitive neuropsychological model of limb praxis. Cogn Neuropsychol1991;8:443–458.

56. Hacisalihzade SS, Mansour M, Albani C. Optimization of symptomatic therapy in Parkinson’s disease. IEEE TransBiomed Eng 1989;36:363–372.

57. Buxbaum LJ. Ideomotor apraxia: A call to Action. Neurocase 2001;7:445–458.58. Poizner H, Mack L, Verfaellie M, Rothi LJ, Heilman KM. Three-dimensional computer graphic analysis of apraxia.

Neural representations of learned movement. Brain 1990;113:85–101.59. Liepmann H. The left hemisphere and action. London, Ontario: University of Western Ontario, 1905.60. De Rensi E, Motti F, Nichelli P. Imitating gestures. A quantitative approach to ideomotor apraxia. Arch Neurol

1980;37:6–10.61. Foundas AL, Macauley BL, Raymer AM, Maher LM, Heilman KM, Gonzalez Rothi, LJ. Ecological implications of

limb apraxia: evidence from mealtime behavior. J Int Neuropsychol Soc 1995;1:62–66.