Why does “the battery run down”? Computational Modeling in Parkinson’s Disease: Towards an Understanding of the Pathophysiology of Bradykinesia

What follows is a review I wrote with Ajay Pillai and Sule Tinaz as a post-baccalaureate fellow in Mark Hallett’s lab at NIH, which we submitted as a journal club review to The Journal of Neuroscience. It wasn’t accepted, so I thought I would post it here. In this review, we summarize the findings of a 2013 J neuro paper by Baraduc and colleagues, and relate their study to recent developments in our understanding of bradykinesia, or slowness of movement, one of the cardinal symptoms of Parkinson’s disease. Further, we extend the authors’ discussion by relating their model and findings to another feature of bradykinesia known as the “sequence effect.” Finally, we discuss another model of motor control, Dynamical Systems Theory, and its potential use in elucidating the pathophysiology of the sequence effect and bradykinesia.

Why does “the battery run down”? Computational Modeling in Parkinson’s Disease: Towards an Understanding of the Pathophysiology of Bradykinesia

Patrick Malone, Ajay Pillai, and Sule Tinaz

How organisms coordinate multiple end effectors, muscles, and neural activity to produce purposeful motor behavior has been the central question of motor control theories. The Optimal Control Theory (OCT) provides a computational framework to understand motor control. The theory posits that organisms learn to generate goal-directed movements that optimize cost (e.g., speed, accuracy). The models employ a two-factor cost function that encodes both the feature to be optimized (e.g., speed) and another factor that needs to be regularized (e.g., motor command representing the neural input to the system). More recent versions of OCT-based approaches also incorporate feedback into the model in which the current state of the system is informed by its previous states (Diedrichsen et al., 2010).

Research in this area has focused on computational characterization of visually guided reaching movements (Shadmehr and Krakauer, 2008). It has long been known that movement speed inversely scales with the accuracy requirements of the task (Fitts, 1954). Bradykinesia, the cardinal motor feature of Parkinson’s disease (PD), is characterized by slowness of movement caused by problems in scaling speed to movement distance (Hallett and Khoshbin, 1980). Scaling deficits could be due to a higher accuracy cost for these patients, however this view has been challenged in recent years. In response, the energetic cost has been introduced as another variable in the cost/benefit models and is thought to be a major determinant of movement speed (Mazzoni et al., 2007).

Mazzoni and colleagues provided evidence of a higher sensitivity to movement energy cost in patients with PD during a reaching task. Patients were able to move as fast as controls without compromising endpoint accuracy, but required more attempts to reach the speed requirements. The authors concluded that bradykinesia in PD was determined primarily by low motor energy and a shift in the cost/benefit ratio of energy expenditure.

Baraduc and colleagues (2013) expanded on this view in their paper in The Journal of Neuroscience. An optimal control framework was employed to model discrete reaching movements of varying distances in controls and PD patients off and on subthalamic nucleus deep brain stimulation (DBS). The hypothesis was that bradykinesia in PD reflects a downward shift in the motor vigor allocated to each movement. Subjects were instructed to move the handle to the target as quickly and accurately as possible. The authors used the experimentally derived duration for each movement to calculate trajectories that minimized the neuromuscular cost. The timing and value of peak velocity and peak acceleration predicted by the model was compared to experimentally observed values.

The minimum-effort model correctly described the experimental data for both groups (Baraduc et al., 2013, their Fig. 5 and Table 3). PD patients displayed slower movement characteristics than controls, including a longer reaction time and movement duration and decreased peak velocity and acceleration, all of which were more pronounced in the off-DBS state. The acceleration at 100 ms after movement initiation was also examined. While acceleration increased as a function of movement extent in controls, it plateaued in PD patients.

If the same model accurately accounts for reaching movements in controls and PD patients, why is there decrease in the motor command as evidenced by decreases in movement speed and acceleration? The answer lies in the motor command range available to each subject. The range of motor commands corresponds to the range from baseline to the maximum activation of a population of motoneurons. In PD patients, this motor command range was abnormally narrow across all movement amplitudes (Baraduc et al., 2013, their Fig. 6B). This finding implies that a preset motor envelope for motor commands governs the kinematics of discrete movements. The kinematics in turn determines the movement duration. The constraint of a common motor range for all movements, regardless of amplitude, results in a scaling of movement duration with movement extent. PD patients possess an abnormally narrow motor range, which leads to bradykinesia.

What reduces the motor command range in PD? A possible mechanism is explained by an emerging view of the role of basal ganglia (BG) and dopamine in motor control. Recent evidence suggests that the BG and its dopaminergic innervations regulate movement energy or response ‘vigor’ (Niv et al., 2007). The OCT is particularly suited to model this view of BG function. Within this framework, the BG are assigned the role of computing the “cost-to-go function” by estimating the value of the desired state and the cost of the movement. These computations are strongly influenced by dopamine. Dopamine has long been known as the critical neurotransmitter in reinforcement learning by encoding a reward prediction error via phasic spiking activity of dopaminergic neurons, and relaying this information to the striatum to promote the choice of efficient actions to maximize reward in subsequent trials.

Recent evidence suggests that dopamine’s role in motor behavior is not limited to its phasic release in discrete choice tasks (Niv et al., 2007). The tonic levels of dopamine have been shown to energize the behavior and increase the motor response vigor in a more sustained fashion. Niv et al. (2007) proposed a model to account for the response vigor in free-operant behavioral tasks by utilizing the average rate of reward (reported by tonic dopamine levels) that represents the “opportunity cost”. If the average rate of reward is high (high opportunity cost), then every second to receive the reward becomes costly. Therefore, one should move faster. Conversely, if the opportunity cost is low as a result of reduced dopamine levels, then there would be no urgency to move faster.

According to this model, one could predict that in PD, dopamine depletion might reduce the reported opportunity cost and lead to slower responses as a result. Indeed, a study of saccadic eye movements demonstrated that the hyperbolic cost function of reward valuation accounts for the kinematics of saccades (Shadmehr et al., 2010). The authors found that the duration of the movement is equivalent to a delay of reward.

Taken together, the findings implicate aberrant encoding of reward as a possible mechanism of bradykinesia. Specifically, dopamine depletion leads to a decreased valuation of the average rate of reward that subsequently slows the pace of actions. As Niv and Rivlin-Etzion (2007) pointed out in their Journal Club article, bradykinesia may be caused by a distorted value of time. To test this conjecture, it is crucial that any model of motor control in PD account for movement over time. It would be important to apply the authors’ modeling to another feature of bradykinesia that manifests during sequential movements known as the “sequence effect (SE).”

In the clinical setting, bradykinesia is assessed during repetitive sequential movements. The amplitude and speed of the movements become smaller with each repetition. This phenomenon is known as the SE. Patients often find the SE most disabling and report feeling as if their “battery is running down.” SE is common in daily activities such as handwriting (micrographia), gait (shuffling with smaller steps) and speech (hypophonia). Deficits in motor energy and scaling the movement vigor are thought to play a role in the underlying pathophysiology (Hallett 2003). Moreover, the SE occurs even under optimal dopaminergic conditions. It seems that optimal tonic dopamine levels can invigorate motor behavior in discrete tasks, but fail to do so in sequential tasks. Low phasic dopamine levels may play an important role here by failing to provide the BG with cues to promote the maintenance of efficient motor response with each repetition. Of note, cues such as visual feedback reverse the SE (Morris et al., 2008). One possible mechanism is that visual feedback produces a large phasic burst of dopamine that facilitates activity in the BG. An alternative, but not mutually exclusive explanation would be that visual feedback directly facilitates the implementation of motor commands by the premotor and primary cortices.

It is somewhat puzzling that both the amplitude and speed of the movement decrease with each repetition. According to the cost/benefit model, one would expect deterioration in one aspect in order to maintain the other (e.g., slowing down in order to maintain the letter size). It is conceivable that the SE is a result of abnormally high motor cost that accumulates over time with each repetition. This hypothesis could be readily explored with the authors’ model by computing the motor range of each sequential movement. A decreasing motor range with each consecutive movement would be consistent with an accumulating motor cost.

Alternatively, the Dynamical Systems Theory may also provide a useful framework to understand the neural basis of SE. In this theory, motor patterns are viewed as emergent properties of biological systems and express themselves in a context dependent fashion. Using mathematical tools from non-linear dynamics, rhythmic/cyclic movements have been successfully modeled within this framework. More recent approaches have also combined optimization and dynamic models (Schaal et al., 2007), and unified both discrete and rhythmic movement generation (Huys et al., 2008, Fink et al., 2009). A comprehensive model that captures the dynamic nature of bradykinesia, specifically the SE, and the range of motor vigor deficits in various contexts would further our understanding of the neural basis of motor abnormalities in PD.



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