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Anatomical pathology of Parkinson’s disease
The basal ganglia, innervated by the dopaminergic system, is the most seriously aected brain area in PD.
The recognized cause of PD is the death of dopaminergic neurons in the substantia nigra pars compacta (SNc) region of basal ganglia in the midbrain [25]. Secretion of neuro-mediator dopamine (DA) in this region leads to decreased inhibition of motor system, releasing it for activation. The outcome of DA loss is increased eort to move [16].
There are ve major pathways in the brain connecting other brain areas with the basal ganglia. These are known as the motor, oculo-motor, associative, limbic, and orbitofrontal circuits, with names indicating the main projection area of each circuit. All of them are aected by PD, and their disruption explains many of the symptoms of the disease since these circuits are involved in a wide variety of functions including movement, attention and learning. The pathological characteristic of PD of cell death in the SNc that plays an important role in reward and movement, aecting up to 70% of the cells by the time when patient’s death occurs [34].
Normally, the basal ganglia exert a constant inhibitory inuence on a wide range of motor systems, preventing them from becoming active at inappropriate times. When a decision is made to perform a particular action, inhibition is reduced for the required motor system, thereby releasing it for activation. Dopamine (DA) acts to facilitate this release of inhibition, so high levels of DA tend to promote motor activity, while low levels of DA, such as occur in PD, demand greater exertion of eort for any given movement.
Thus, the net eect of DA depletion produces hypokinesia (decreased bodily movement), an overall
reduction in motor output. Drugs that are used to treat PD, conversely, may produce excessive DA activity, allowing motor systems to be activated at inappropriate times and thereby producing dyskinesia (involuntary muscle movements).
The motor symptoms of the PD result from the death of DA neurons in the SNc. In the absence of dopamine, D1-receptors in the basal ganglia don’t stimulate the GABAergic neurons, which favor the direct pathway, and thus not increasing movement. This sets o the indirect pathway that results in inhibition of upper motor neurons and less movement. In the presence of DA, D2-receptors in the basal ganglia inhibit these GABAergic neurons, which reduces the indirect pathways inhibitory eect. The antagonistic functions of the direct and indirect pathways are modulated by the SNc, which produces dopamine.
In the presence of DA, regardless of its source, D1-receptors in the BG stimulate the GABAergic neurons, favoring the direct pathway, and thus increasing movement. The GABAergic neurons of the indirect pathway are stimulated by excitatory neurotransmitters acetylcholine and glutamate. This sets o the indirect pathway that ultimately results in inhibition of upper motor neurons, and less movement.
In the presence of dopamine, D2-receptors in the basal ganglia inhibit these GABAergic neurons, which reduces the indirect pathway’s inhibitory eect.
DA, therefore, increases the excitatory eect of the direct pathway (causing movement) and reduces the inhibitory eect of the indirect pathway (preventing full inhibition of movement). Through these mechanisms, the body is able to maintain balance between excitation and inhibition
of motion. Lack of balance in this delicate system leads to pathology such as Parkinson’s disease. During PD, the direct pathway is less able to function (so no movement is initiated) and the indirect pathway is in overdrive (causing too much inhibition of movement).
Models of neuron circuitry with implied Parkinson’s disease
Considering the functioning of basal ganglia aected by Parkinson’s disease, the researchers had made numerous models that simulate PD either only in brain structures or applied to a certain task. But most of the models are limited to BG and relations between its nuclei. These models result in ring rates of neurons or other intrinsic parameters of system as their aim is to identify the source of abnormal oscillations in BG, related to PD. Human movements governed by lower structures that receive signals from BG are as well perturbed by PD and this impacts the daily life of aected people. Therefore, despite interesting ways of modeling BG and PD, these works are not suciently connected to consequences of PD on the human movements and especially on the walk.
Nevertheless, the models of subcortical structures (sometimes including motor cortex) vary in complexity, tting their research purpose. The models that look for the origin of parkinsonian tremor [23, 22] result as ring rates of neurons, which, for the control purpose, need to be transformed into commands for lower structures. Other models are more applicable and simulate handwriting [19], object lifting [35], and walking [36].
In the considered models, PD simulation is applied through special dopamine level parameter or tting the parameters to experimental data of parkinsonian patients. In the following, we describe these six representative models of brain structures including basal ganglia aected by PD.
PD tremor model
In the work [23], the authors have searched a source of PD tremor in Basal Ganglia-Thalamo-Cortical circuit, simplied to conductance-based model of 3 biological neurons. Fig. 1.4 shows the said network.
There are one GPe and one STN neurons and a feedback neuron, represented by a blank box. PD was simulated by using such synaptic strengths that result in tremor-like activity of the model. The model result in Hodgkin-Huxley neuron activity that has to be non-trivially further transformed in control commands for motor network.
PD-related BG oscillations model
In the work [22], the authors have evaluated several computational models of BG with experimental data presented in the paper [37]. It states that for generation of abnormal oscillations only cortex-STN-GPe connections are essential. As a result, they identied two models (Fig. 1.5): a resonance model and a feedback model that both could maintain abnormal beta oscillations. As of results, both models are similarly close to experimental data.
The most important thing is that the MATLAB source code for models is available http://modeldb. yale.edu/184491, which simplies the utilization of this model as a controller for abnormal gait. PD was simulated with increased synaptic weights values, obtained from parkinsonian monkeys’ models. As in previous work, resulting neuron ring rated of this model have to be transformed into motor commands.
PD walk estimation model
In article [36], authors present a computational model of altered gait velocity patterns in PD based on 2 investigations of FoG, as patients at ON and OFF dopaminergic medication walked through a doorway with variable width.
Computational model of BG is based on Reinforcement Learning (« Critic » module), GEN decisions, coupled with a CPG model that mimics spinal rhythm (Fig. 1.9). The Critic module computes the value for the view vector. As a model of the CPG network, the authors used network of coupled non-linear oscillators, modeled using adaptive Hopf oscillators (see Section 2.1.3). The number of Hopf oscillators used to train the hip (!h) and knee angles (!k1 and !k2) are 2 and 3 respectively. Phase dierence within- CPGs is maintained by local while across-CPGs is maintained by global. s modulate the intrinsic CPG rhythm to output the learned joint angles.
Feedback signals of motor control
As for the sensory feedback from muscles and environment, we tend to use biologically plausible signals to control human gait on spinal level. Only one of used receptor signals originates in brain. It is vestibular signal from inner ear that is integrated in sensory pathways through brainstem [56] (Fig. 2.1).
The other signals are muscle and cutaneous proprioceptive sensors. They measure inner state of the organism. Simulated in this work sensors reacting to state of the muscles are aerents of type Ia, Ib, and II [14].
Ia-type aerents are muscle spindle stretch receptors that react to muscle length changes and are fast adapting thus providing muscle stretch velocity signal to CPGs and brain. Each Ia sensory neuron react to positive contraction velocity of its muscle. Which means that Ia sensor indirectly measures opposite muscle’s activation velocity. Ia sensor excite its own motoneuron to limit joint’s angular velocity.
Ib-type aerents are Golgi tendon organs that sense the force generated by muscle and sent it to CPGs and brain. II -type aerents measure muscle’s length and are non-adapting providing CPGs and brain with in2.1.
All presented sensors besides of providing feedback to motor controllers, participate in unconditional motor reexes as well [57]. The problem of separation of these motor actions between CPGs and independent nervous loops is open and is adverted in this thesis.
Models of central pattern generators
Despite the origination of CPG theory in biology from locomotion experiments, we cannot easily model the network of interneurons to control the locomotion. The biological model of CPG is not established yet and is under active investigation [42, 58, 44, 59]. The researchers have developed a number of models of dierent levels to mimic CPG’s specic features.
Our model of central pattern generator
Our gait controller utilizes mesoscopic CPG model. The mesoscopic neuron models provide more complex behavior than microscopic, while are easier to tune. On the other hand, they are still close to biology, apart from macroscopic models. Previously, our CPG model has been used to generate patterns for humanoid robot locomotion [53, 82, 74] and more recently for better understanding of robot-human handshake interaction [72, 86]. The model is supported by two neurophysiological studies [41, 87] and combines their propositions in multi-layered multi-pattern CPG model. An important feature of using a CPG as a controller, is its ability to produce repeated patterns without descending signals from brain. This is conrmed in our simulations showing our model of CPG is able to produce stable gait during whole simulation without using input from upper structures.
Overall CPG architecture
This architecture is based on the work of Rybak et al. [41] for a two-level CPG that separates the timing and activation of the locomotion cycle. Fig. 2.2a shows the general CPG scheme with two layers plus motoneurons and aerents with half-center architecture. Oscillations are generated at the top rhythm generator (RG) layer and then passed to pattern formation (PF) layer, which innervates motoneurons (MN). Our CPG model has similar layers (Fig. 2.2b). Additionally, the model explicitly includes upper controller and feedback sensory neurons (SN) that shape the activity of the CPG neurons. These neurons are of two types: proprioceptors of muscle feedback (type-Ia, Ib, and II ) and exteroceptors of environment (body angle, foot/ground force).
Table of contents :
1 Healthy and decient gait
1.1 Classication of gaits
1.2 Motor control
1.2.1 Basal ganglia
1.3 Parkinson’s disease
1.3.1 Anatomical pathology of Parkinson’s disease
1.3.2 Models of neuron circuitry with implied Parkinson’s disease
1.4 Conclusion
2 Central pattern generators
2.0.1 Spinal cord and descending control
2.0.2 Feedback signals of motor control
2.1 Models of central pattern generators
2.1.1 Microscopic models
2.1.2 Mesoscopic models
2.1.3 Macroscopic models
2.2 Application of CPG models
2.3 Our model of central pattern generator
2.3.1 Overall CPG architecture
2.3.2 Rhythm Generator layer
2.3.3 The other layers
2.4 Controller architecture
2.5 Equilibrium control
2.5.1 Reex controller
2.5.2 Arm control
2.6 Conclusion
3 Musculoskeletal model of human body
3.1 GAIT2DE, a simple musculoskeletal model
3.2 Musculoskeletal model in OpenSim
3.3 Modications to the musculoskeletal model
3.3.1 Simplications of the model
3.3.2 Extensions to the model
3.4 Connecting controller to the model
3.4.1 Implementation of the platform
3.4.2 Biological feedback
3.5 Conclusion
4 Simulated gait analysis
4.1 Gait cycle
4.2 Experimental data
4.3 Optimization of controller parameters
4.3.1 Parameter optimization methods
4.3.2 Target functions
4.4 Correlation gait evaluation criterion
4.4.1 Cross-correlation
4.5 Conclusion
5 Results of neuro-musculoskeletal simulations
5.1 CPG control of a single joint
5.1.1 Movement with constant speed
5.1.2 Movement with variable speed
5.2 Joint-targeted CPG controller
5.2.1 Walking with constant speed
5.2.2 Walking with variable speed
5.3 Muscle-targeted CPG controller
5.3.1 Simulation with GAIT2DE model
5.3.2 Simulation with OpenSim model
5.3.3 Disrupted gait
5.4 Phase-targeted CPG controller
5.5 Balance controller
5.6 Conclusion
Bibliography
