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Spinal mechanisms may provide a combination of intermittent and continuous control of human posture: predictions from a biologically based neuromusculoskeletal model.

Elias LA, Watanabe RN, Kohn AF - PLoS Comput. Biol. (2014)

Bottom Line: Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface.These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control.Another finding was the occurrence of the so-called "paradoxical" behaviour of muscle fibre lengths as a function of postural sway.

View Article: PubMed Central - PubMed

Affiliation: Biomedical Engineering Laboratory, Escola Polit├ęcnica, University of Sao Paulo, Sao Paulo, Brazil.

ABSTRACT
Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called "paradoxical" behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.

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Overview of the postural control model.(A) Schematic view of the Spinal-Like Controller (SLC) and the biomechanics of the human upright standing. Mathematical models of spinal  motor neurons (MNs) and interneurons (INs) make up the motor nuclei associated with the Triceps Surae (TS) and Tibialis Anterior (TA) muscles. MNs from the TS motor nuclei receive constant intensity descending commands during the maintenance of upright stance. Proprioceptive feedback is provided by Ia, II and Ib afferents from muscle spindles and Golgi tendon organs (GTOs). The information carried through these afferents is fed back to the spinal cord representing fundamental pathways (or neuronal circuits) involved in the postural control task, such as Ia monosynaptic excitation, Ib di-synaptic inhibition, group II di-synaptic excitation, and reciprocal inhibition from antagonistic Ia afferents. Activity from Gamma motor neurons (-MNs) set the sensitivities of the muscle spindles. Ankle joint torque () that drives the body biomechanics (to compensate for the gravitational toppling torque) is given by the sum of the torques produced by the muscles () and the passive ankle joint torque, represented by the passive ankle joint stiffness () and viscosity (). The body angle () is the resultant output of the inverted pendulum acted on by gravity and by . It indirectly (by means of Equations 8 and 9) defines moment arms () and musculotendon (MTU) lengths (), which are used to define the dynamics of both MTUs and muscle receptors (see dashed lines). Additionally,  is fed back without delay to account for the intrinsic passive joint impedance (stiffness and viscosity). (B) Hill-type model used to represent the viscoelastic and contractile properties of the MTUs. Muscle fibres are represented by parallel passive elements (muscle fibre stiffness, , and viscosity, ) and two contractile elements (CE) representing the contractile properties of type-I and type-II muscle fibres. A pinnation angle () is adopted to represent the angle between the muscle fibres and the aponeurosis. In addition, a mass () is used to increase the computational stability. Passive properties of tendon and distal aponeurosis are represented by a lumped non-linear stiffness (). Muscle spindle is placed parallel to the muscle fibres, while the GTO is in series with the tendon. (C) Inverted pendulum model used to represent the body biomechanics during the upright quiet stance. Arrows indicate the positive direction of each variable (see the description of each variable in the text).
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pcbi-1003944-g009: Overview of the postural control model.(A) Schematic view of the Spinal-Like Controller (SLC) and the biomechanics of the human upright standing. Mathematical models of spinal motor neurons (MNs) and interneurons (INs) make up the motor nuclei associated with the Triceps Surae (TS) and Tibialis Anterior (TA) muscles. MNs from the TS motor nuclei receive constant intensity descending commands during the maintenance of upright stance. Proprioceptive feedback is provided by Ia, II and Ib afferents from muscle spindles and Golgi tendon organs (GTOs). The information carried through these afferents is fed back to the spinal cord representing fundamental pathways (or neuronal circuits) involved in the postural control task, such as Ia monosynaptic excitation, Ib di-synaptic inhibition, group II di-synaptic excitation, and reciprocal inhibition from antagonistic Ia afferents. Activity from Gamma motor neurons (-MNs) set the sensitivities of the muscle spindles. Ankle joint torque () that drives the body biomechanics (to compensate for the gravitational toppling torque) is given by the sum of the torques produced by the muscles () and the passive ankle joint torque, represented by the passive ankle joint stiffness () and viscosity (). The body angle () is the resultant output of the inverted pendulum acted on by gravity and by . It indirectly (by means of Equations 8 and 9) defines moment arms () and musculotendon (MTU) lengths (), which are used to define the dynamics of both MTUs and muscle receptors (see dashed lines). Additionally, is fed back without delay to account for the intrinsic passive joint impedance (stiffness and viscosity). (B) Hill-type model used to represent the viscoelastic and contractile properties of the MTUs. Muscle fibres are represented by parallel passive elements (muscle fibre stiffness, , and viscosity, ) and two contractile elements (CE) representing the contractile properties of type-I and type-II muscle fibres. A pinnation angle () is adopted to represent the angle between the muscle fibres and the aponeurosis. In addition, a mass () is used to increase the computational stability. Passive properties of tendon and distal aponeurosis are represented by a lumped non-linear stiffness (). Muscle spindle is placed parallel to the muscle fibres, while the GTO is in series with the tendon. (C) Inverted pendulum model used to represent the body biomechanics during the upright quiet stance. Arrows indicate the positive direction of each variable (see the description of each variable in the text).

Mentions: The model proposed in this study encompasses four main subsystems (neuronal controller, muscles, proprioceptors, and body biomechanics) that were interconnected to represent the NMS system involved in the control of human upright stance. An overview of this large-scale model is depicted in Figure 9. It is worth mentioning that the model is aimed to study body sway in the sagittal plane during unperturbed stance. In this condition, the posture control task relies mainly on afferent and efferent activities associated with the muscles around the ankle joint (ankle strategy) [9]. Figure 9A shows a schematic view of the neuronal circuitry composed of groups of spinal MNs and INs (see mathematical description below), referred to as the SLC (Spinal-Like Controller). MNs were assembled in motor nuclei associated to the TS (i.e., SO, MG, and LG) and TA muscles, which is the most relevant antagonist group of muscles involved in postural control during ankle strategy [9], [29], [36]. Stochastic descending commands represented part of the synaptic inputs from the brain that drive the spinal MNs during the maintenance of upright standing. Musculotendon units (MTUs) were represented by Hill-type models (see mathematical description below), which were driven by the spike trains from the spinal MNs (Figure 9B). Muscle spindles were placed in parallel with the muscle fibres and received commands from Gamma motor neurons (-MNs), while GTOs were placed in series with the tendon. Proprioceptive feedback was provided by Ia, II and Ib axons mediating: i) monosynaptic Ia excitation; ii) di-synaptic Ib inhibition; iii) di-synaptic II excitation; and iv) reciprocal inhibition from antagonistic Ia afferents. These are fundamental pathways frequently associated with different motor tasks, including upright standing [58]. An inverted pendulum was adopted to represent the body biomechanics (Figure 9C), which is a first approximation for unperturbed quiet standing [4], [5], [10], [11], [20], [25], [26]. In the following sections, the mathematical details concerning each of these models will be provided.


Spinal mechanisms may provide a combination of intermittent and continuous control of human posture: predictions from a biologically based neuromusculoskeletal model.

Elias LA, Watanabe RN, Kohn AF - PLoS Comput. Biol. (2014)

Overview of the postural control model.(A) Schematic view of the Spinal-Like Controller (SLC) and the biomechanics of the human upright standing. Mathematical models of spinal  motor neurons (MNs) and interneurons (INs) make up the motor nuclei associated with the Triceps Surae (TS) and Tibialis Anterior (TA) muscles. MNs from the TS motor nuclei receive constant intensity descending commands during the maintenance of upright stance. Proprioceptive feedback is provided by Ia, II and Ib afferents from muscle spindles and Golgi tendon organs (GTOs). The information carried through these afferents is fed back to the spinal cord representing fundamental pathways (or neuronal circuits) involved in the postural control task, such as Ia monosynaptic excitation, Ib di-synaptic inhibition, group II di-synaptic excitation, and reciprocal inhibition from antagonistic Ia afferents. Activity from Gamma motor neurons (-MNs) set the sensitivities of the muscle spindles. Ankle joint torque () that drives the body biomechanics (to compensate for the gravitational toppling torque) is given by the sum of the torques produced by the muscles () and the passive ankle joint torque, represented by the passive ankle joint stiffness () and viscosity (). The body angle () is the resultant output of the inverted pendulum acted on by gravity and by . It indirectly (by means of Equations 8 and 9) defines moment arms () and musculotendon (MTU) lengths (), which are used to define the dynamics of both MTUs and muscle receptors (see dashed lines). Additionally,  is fed back without delay to account for the intrinsic passive joint impedance (stiffness and viscosity). (B) Hill-type model used to represent the viscoelastic and contractile properties of the MTUs. Muscle fibres are represented by parallel passive elements (muscle fibre stiffness, , and viscosity, ) and two contractile elements (CE) representing the contractile properties of type-I and type-II muscle fibres. A pinnation angle () is adopted to represent the angle between the muscle fibres and the aponeurosis. In addition, a mass () is used to increase the computational stability. Passive properties of tendon and distal aponeurosis are represented by a lumped non-linear stiffness (). Muscle spindle is placed parallel to the muscle fibres, while the GTO is in series with the tendon. (C) Inverted pendulum model used to represent the body biomechanics during the upright quiet stance. Arrows indicate the positive direction of each variable (see the description of each variable in the text).
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Related In: Results  -  Collection

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pcbi-1003944-g009: Overview of the postural control model.(A) Schematic view of the Spinal-Like Controller (SLC) and the biomechanics of the human upright standing. Mathematical models of spinal motor neurons (MNs) and interneurons (INs) make up the motor nuclei associated with the Triceps Surae (TS) and Tibialis Anterior (TA) muscles. MNs from the TS motor nuclei receive constant intensity descending commands during the maintenance of upright stance. Proprioceptive feedback is provided by Ia, II and Ib afferents from muscle spindles and Golgi tendon organs (GTOs). The information carried through these afferents is fed back to the spinal cord representing fundamental pathways (or neuronal circuits) involved in the postural control task, such as Ia monosynaptic excitation, Ib di-synaptic inhibition, group II di-synaptic excitation, and reciprocal inhibition from antagonistic Ia afferents. Activity from Gamma motor neurons (-MNs) set the sensitivities of the muscle spindles. Ankle joint torque () that drives the body biomechanics (to compensate for the gravitational toppling torque) is given by the sum of the torques produced by the muscles () and the passive ankle joint torque, represented by the passive ankle joint stiffness () and viscosity (). The body angle () is the resultant output of the inverted pendulum acted on by gravity and by . It indirectly (by means of Equations 8 and 9) defines moment arms () and musculotendon (MTU) lengths (), which are used to define the dynamics of both MTUs and muscle receptors (see dashed lines). Additionally, is fed back without delay to account for the intrinsic passive joint impedance (stiffness and viscosity). (B) Hill-type model used to represent the viscoelastic and contractile properties of the MTUs. Muscle fibres are represented by parallel passive elements (muscle fibre stiffness, , and viscosity, ) and two contractile elements (CE) representing the contractile properties of type-I and type-II muscle fibres. A pinnation angle () is adopted to represent the angle between the muscle fibres and the aponeurosis. In addition, a mass () is used to increase the computational stability. Passive properties of tendon and distal aponeurosis are represented by a lumped non-linear stiffness (). Muscle spindle is placed parallel to the muscle fibres, while the GTO is in series with the tendon. (C) Inverted pendulum model used to represent the body biomechanics during the upright quiet stance. Arrows indicate the positive direction of each variable (see the description of each variable in the text).
Mentions: The model proposed in this study encompasses four main subsystems (neuronal controller, muscles, proprioceptors, and body biomechanics) that were interconnected to represent the NMS system involved in the control of human upright stance. An overview of this large-scale model is depicted in Figure 9. It is worth mentioning that the model is aimed to study body sway in the sagittal plane during unperturbed stance. In this condition, the posture control task relies mainly on afferent and efferent activities associated with the muscles around the ankle joint (ankle strategy) [9]. Figure 9A shows a schematic view of the neuronal circuitry composed of groups of spinal MNs and INs (see mathematical description below), referred to as the SLC (Spinal-Like Controller). MNs were assembled in motor nuclei associated to the TS (i.e., SO, MG, and LG) and TA muscles, which is the most relevant antagonist group of muscles involved in postural control during ankle strategy [9], [29], [36]. Stochastic descending commands represented part of the synaptic inputs from the brain that drive the spinal MNs during the maintenance of upright standing. Musculotendon units (MTUs) were represented by Hill-type models (see mathematical description below), which were driven by the spike trains from the spinal MNs (Figure 9B). Muscle spindles were placed in parallel with the muscle fibres and received commands from Gamma motor neurons (-MNs), while GTOs were placed in series with the tendon. Proprioceptive feedback was provided by Ia, II and Ib axons mediating: i) monosynaptic Ia excitation; ii) di-synaptic Ib inhibition; iii) di-synaptic II excitation; and iv) reciprocal inhibition from antagonistic Ia afferents. These are fundamental pathways frequently associated with different motor tasks, including upright standing [58]. An inverted pendulum was adopted to represent the body biomechanics (Figure 9C), which is a first approximation for unperturbed quiet standing [4], [5], [10], [11], [20], [25], [26]. In the following sections, the mathematical details concerning each of these models will be provided.

Bottom Line: Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface.These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control.Another finding was the occurrence of the so-called "paradoxical" behaviour of muscle fibre lengths as a function of postural sway.

View Article: PubMed Central - PubMed

Affiliation: Biomedical Engineering Laboratory, Escola Polit├ęcnica, University of Sao Paulo, Sao Paulo, Brazil.

ABSTRACT
Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called "paradoxical" behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.

Show MeSH
Related in: MedlinePlus