Linear Identification of Nonlinear Wrist Neuromechanics in Stroke

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Linear Identification of Nonlinear Wrist

Neuromechanics in Stroke

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Linear Identification of Nonlinear Wrist

Neuromechanics in Stroke

Proefschrift

ter verkrijging van de graad van doctor aan de Technische Universtiteit Delft,

op gezag van de Rector Magnificus prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties,

in het openbaar te verdedigen op woensdag 20 mei 2015 om 15:00 uur

door

Asbjørn KLOMP

Meet- en Regeltechnisch Ingenieur

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promotoren: Prof. dr. F.C.T. van der Helm en Prof. dr. J.H. Arendzen en

copromotoren: Dr. ir. E. de Vlugt en Dr. C.G.M. Meskers

Samenstelling promotiecommissie: Rector Magnificus,

Prof. dr. F.C.T. van der Helm, Prof. dr. J.H. Arendzen, Dr. ir. E. de Vlugt, Dr. C.G.M. Meskers,

Technische Universiteit Delft, voorzitter Technische Universiteit Delft, promotor Leids Universitair Medisch Centrum, promotor Technische Universiteit Delft, copromotor VU Medisch Centrum, copromotor Onafhankelijke leden:

Prof. dr. ir. J. de Schutter, Prof. dr. A.C.H. Geurts, Prof. dr. ir. J. Harlaar, Prof. dr. H.E.J. Veeger, Prof. dr. ir. E.R. Valstar,

Koninklijke Universiteit Leuven

Radboud Universitair Medisch Centrum VU Medisch Centrum

VU Medisch Centrum, Technische Universiteit Delft Leids Universitair Medisch Centrum, reservelid Dr. ir. J.H. de Groot van het Leids Universitair Medisch Centrum, heeft evenzo als begeleider in belangrijke mate aan de totstandkoming van het proefschrift bijgedra-gen.

The studies presented in this thesis were supported by ZonMW (grant 89000001), Het Revalidatiefonds, Revalidatie Nederland and De Nederlandse Vereniging van Re-validatieartsen.

Title: Linear Identification of Nonlinear Wrist Neuromechanics in Stroke Author: Asbjørn Klomp

Printing: GVO drukkers & vormgevers B.V. c

2015, A. Klomp

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Summary

Background

In many stroke patients, a motor cortex lesion alters motor control. Initially, paresis is most prominent, but then over time, joint stiffening and hyperreflexia may occur. How these different disorders develop over time is still unknown due to high system complexity. Secondary changes in the corticospinal tract, peripheral biomechanics and spinal reflexive system, may also occur.

This thesis is part of the EXPLICIT-Stroke study (see Chapters 1, 2 and 3), a randomized, controlled trial that researches the effect of early therapy on post stroke recovery of the upper limb. Amongst other measurements, the EXPLICIT-Stroke study investigates post-stroke changes of brain function and corticospinal tract with fMRI and TMS, respectively. The work in this thesis aims to identify post stroke changes in peripheral biomechanics and the spinal reflexes of the wrist: wrist joint neuromechanics.

Neuromechanics play an important role in the functioning of a joint. Inputs to the neuromechanical system are: neural input originating from supraspinal regions and externally applied rotation/torque. Neuromechanics therefore rep-resent the translation from supraspinal input to muscle contraction and result-ant joint rotation, torque and/or stiffness, and also describe the relationship between external perturbation and joint response. Joint impedance, the dy-namic relationship between joint angle and resultant joint torque, was used to investigate joint neuromechanics.

Neuromechanics can be split into: dynamics of passive soft tissues, vol-untary muscle contraction and reflexive muscle contraction. Knowledge of changes in the underlying properties yields insight into the complex devel-opment of movement disorders and can eventually lead to targeted therapy. Measurement of impedance is achieved by external (motorised) angular

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per-turbation of the joint whilst measuring the joint torque response. This is commonly supported by measurement of muscle activation: Electromyography (EMG).

Joint neuromechanics are highly nonlinear. Although many nonlinear neu-romechanical properties are known from literature, the effects of these non-linear properties on joint impedance, and thus their functional and clinical relevance, have generally not been quantified. Commonly known examples of nonlinearity are increased resistance against movement in extreme angles of the range of motion and increased joint stiffness with muscle contraction. Due to nonlinearity, linearly observed neuromechanics depend on input, i.e., de-pend on measurement conditions. In line with the previous examples, joint stiffness depends on muscle contraction and joint angle. Therefore, under-standing nonlinearity is essential for interpretation of joint impedance.

Linear modelling and system identification methods allow for estimation of neuromechanical parameters. Use of these linear methods restricts measure-ment to small deviations in joint angle, angular velocity and muscle contrac-tion. As normal movement often includes large deviations in angle, angular velocity and muscle contraction, such measurements do not describe the full range of interest in joint neuromechanics. Furthermore, comparison of sub-jects requires that they are measured in the same angles, angular velocities and contraction levels, such that observed differences between subjects are due to differences in neuromechanical properties, and not due to nonlinearity. For example, high joint stiffness in Chapter 9, was hypothesized to be caused by co-activation of the antagonistic muscle pair, i.e., the nonlinear system under a different contraction level (active state), and not caused by different peripheral neuromechanical properties.

Aim

The aim of this thesis was to:

1. Estimate parameters that expose reflexive and non-reflexive contribu-tions to joint impedance, in healthy subjects and stroke patients, using available techniques, in order to improve understanding of post stroke movement disorders.

2. Quantify the effects of nonlinearity on joint impedance in healthy sub-jects and stroke patients, by use of linear methods and systematically varying measurement conditions.

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Chapters 2 and 3: The EXPLICIT-Stroke protocol

A measurement protocol was developed that assesses passive tissue, active muscle and reflexive joint properties after stroke (see Chapter 2 and 3). The protocol includes tests that assess properties comparable to clinical measures, such as the Range of Motion and Ashworth score, but also tests that assess underlying neuromechanical properties: inertia, damping, stiffness, reflex gain, reflex time delay and eigenfrequency of muscle activation dynamics (described by a first order low pass filter). The protocol is described in detail in Chapter 2. Passive tissue and voluntary and reflexive muscle activation, contributing to movement disorder around the wrist after stroke, were measured in a reliable and comprehensive way (see Chapter 3) and were responsive to clinical status. Results of the extensive measurement protocol revealed the necessity to apply multiple measurement conditions in the research of underlying mechan-isms of post stroke movement disorders.

Chapters 4, 6 and 7: Linear Identification of Joint Nonlinearity Throughout Chapters 4, 6 and 7, nonlinearity of joint neuromechanics was systematically investigated. Neuromechanical parameters were estimated us-ing linear system identification methods in combination with linear math-ematical models. Due to nonlinearity, a single linear model cannot describe neuromechanical behaviour for all inputs (external and supraspinal). Nonlin-ear properties of the neuromechanical system were investigated by variation in measurement condition, i.e., perturbation angle, angular velocity and reques-ted joint torque. It was hypothesized that changes in model parameters with measurement condition were an indication of, and could be used to investigate, joint nonlinearity.

Linearly estimated neuromechanical parameters were shown to be highly sensitive to applied perturbation amplitude (Chapter 4), angular velocity (Chapter 6) and Inter Stimulus Interval (ISI, the waiting time between con-secutive perturbations, see Chapter 7).

Variation in measurement conditions mainly resulted in changes in estim-ated joint damping, stiffness and reflex gain. Estimestim-ated variation in damping with measurement condition was shown in line with the force-velocity relation-ship of muscle fibres. The reflex gain was low, yet it was repeatably estimated. Effects of perturbation velocity and ISI on reflex gain were existing, the former in line with the nonlinear response of muscle spindles, the latter in line with Post Activation Depression (see Chapter 7 and 9). Large effects of requested

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joint torque (supraspinal originating muscle activation) on estimated para-meters were evident in our measurements.

Chapter 5: Reflex Gain Reduction due the Refractory Period of Motor Neurons

In Chapter 5 it was shown that the reduction in reflex gain with increasing perturbation amplitude could largely be explained by the inability of a linear model to describe a nonlinear reflexive pathway. It was shown that linear models for the reflexive pathway were only able to produce responses similar to the reflex response when using perturbations of short duration, coinciding with the duration of the short latency response. The reflexive response is known to consist of multiple consecutive activation volleys, the short latency response (M1) and the long latency response (M2) being the first two. For angular perturbations with longer duration than the applied 22ms, we indicated that the refractory period, the period of low muscle activation between M1 and M2, largely explained a decrease in reflex gain.

Chapter 8: Multisine and Ramp and Hold perturbations

In Chapters 4 to 7 and 9, nonlinearity was investigated by application of angular-controlled Ramp and Hold (RaH) perturbations. These perturbations allow for control of joint angle and angular velocity. In the EXPLICIT-Stroke protocol (Chapters 2 and 3), force-controlled multisine (MS) perturbations were used. MS force perturbations are generally combined with an angle task (keep the handle in a specific position) and are generally more familiar to the subject (for example similar to resisting perturbations of a bumpy road on the handle bars when cycling). Highly different linear model parameters were expected to result from both perturbation types, i.e, MS and RaH, and the difference between angle and torque controlled perturbations, with nonlinear-ity of joint neuromechanics in mind. Markedly, it was shown that MS and RaH signals with highly different time domain representations (but identical power spectrum) resulted in similar linear model parameters. Both perturba-tion types were applied as angle-controlled perturbaperturba-tions with the same force-offset task.

Chapter 9: Nonlinearity in Stroke Patients

In the final chapter of the main body of this thesis, the role of nonlinearity in post stroke movement disorders was investigated by application of the same

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linear analysis strategy as was used in Chapters 4 to 7. Fourteen patients and 10 healthy controls were measured using angular-controlled RaH perturba-tions. Dependency of the linear model parameters to measurement conditions was used to investigate nonlinearity. All patients had enhanced joint imped-ance as assessed by a modified Ashworth score (mAs ≥ 1). Twelve patients had a low mAs of 1 and two patients had a mAs of 2, due to stringent inclusion criteria, such as the ability to perform the task.

Two groups of patients were identified based on a large variance in estim-ated joint stiffness and reflex gain. One group was similar to the control sub-jects group while the other behaved differently. Joint impedance of patients in the former group was hypothesized to be similar to that of the healthy subjects, as careful alignment of comparable measurement conditions resul-ted in equal performance/behaviour. Patients in the latter deviating group were hypothesized to differ from healthy subjects by a high base activation and (subsequent) co-contraction of the antagonistic muscle pair, resulting in a high joint stiffness and reflex gains, which are known to occur with muscle contraction. This would imply that all measured patients, with a generally low mAs, did not differ from healthy subjects in terms of peripheral neuromecha-nics, but only in supraspinal drive to the joint.

Conclusion

A measurement protocol was developed that measures many properties of joint neuromechanics and is capable of identifying passive soft tissue, muscle contraction and reflexive properties (Chapters 2 and 3). Due to nonlinearity, it was hypothesized that the linearly estimated properties were dependent on the chosen measurement conditions. In Chapters 4 to 8, joint neuromechanics were shown to be highly nonlinear and the effect of nonlinearity on joint impedance could be quantified. In the final chapter, it was hypothesized that stroke patients with a generally low mAs score were not different from healthy controls in their joint neuromechanics. Differences between stroke patients and healthy subjects are however likely to emerge from differences in supraspinal muscle activation (Chapter 9). Nonlinearity dictates that when using linear methods it needs to be considered that estimated parameters are a direct result of the applied measurement conditions.

Results of this thesis support the development of nonlinear models that allow measurement over a larger functional domain. When nonlinear models are not available, a measurement protocol should include many measurement conditions to gain insight into the many aspects of joint neuromechanics.

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Chapter

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General Introduction

1.1 General

A stroke or cerebrovascular accident (CVA) is a loss of brain function caused by blood flow disruption, either in the form of a blood vessel blockage (ischaemic stroke) or rupture (haemorrhagic stroke) [1]. In 2002, approximately 15 million people suffered from a stroke worldwide, of which 5 million suffered from permanent disability [2]. In the acute phase after stroke a motor cortex lesion often produces a flaccid paralysis. In the chronic phase, secondary changes are believed to contribute to muscle over-activity and joint stiffening [3, 4].

A signal originating from the motor cortex, travelling via the corticospinal tract and peripheral nerves, will be converted to joint torque by muscles. The conversion from neural signal to joint torque will also be determined by passive soft tissues, such as ligaments and connective tissues, and other neural signals originating from the peripheral nervous system, i.e., reflexive pathways. Any system that is part of the conversion of brain action to joint movement has a role in the translation of stroke to movement disorder, be it altered or not. The primary lesion of the brain may affect each of these components due to disuse or altered supraspinal drive.

The EXPLICIT-Stroke1 project aims to understand brain plasticity and functional changes in the initial stages after stroke. Brain plasticity and cor-ticospinal tract integrity are investigated with fMRI and TMS, respectively. This thesis contributes to the development of a measurement method that allows for longitudinal tracking of passive and contractile tissues, muscle ac-tivation and the reflexive pathway, that together with the CNS determine joint movement. The term neuromechanics will be used throughout to de-scribe these biomechanical and peripheral neurological properties. Considered inputs to the neuromechanical system are external perturbations to the joint

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and muscle activation originating from supraspinal regions.

Knowledge of the changes that occur in underlying neuromechanical prop-erties is required to understand patient specific development of movement disorders. This information is therefore critical for the alignment of patient specific therapy. Fast identification of altered joint neuromechanics will allow for early targeted therapy and may yield long term improvement in joint func-tionality. But neuromechanical properties are difficult to assess in the clinic. Currently applied clinical measurement methods are manual and lack sensit-ivity to differentiate between neuromechanical components, i.e., passive and contractile tissues, muscle activation and the reflexive pathway contributions. Lack of knowledge of the underlying neuromechanical cause may result in improper therapy.

A new measurement and actuating device, the Wristalyzer, was implemen-ted to allow for sensitive measurement of neuromechanics. Alignment of a motor and joint axis allows for control over an input (torque/angle) to the joint as well as accurate measurement of the (torque/angle) response. Using specific task instructions the supraspinal originating muscle activation can, to some extent, be controlled. Besides neuromechanical properties, descript-ive parameters from the clinic such as the range of motion (ROM), maximal voluntary contraction (MVC) and/or an Ashworth score for spasticity, can be obtained.

The main consideration in assessment of joint neuromechanics is nonlin-earity. The neuromechanical system is the dynamical relationship that trans-forms joint inputs (perturbations and neural drive) into outputs (responses). The term ’dynamics’ implies that the system response is based on current as well as past inputs. Nonlinearity implies that the properties of this dynamical system will depend on the current state the system is in and/or the input to the system, i.e., applied perturbation and supraspinal drive.

In a linear system, joint neuromechanical properties, such as joint stiffness and the reflex gain, would be constant, regardless of measurement conditions. In reality this is not the case. For example, a reflexive threshold is known to exist: reflex gains will be near zero for low slow movement, and with increasing 1_{The EXPLICIT-Stroke project is a multi-centre randomized controlled trial in the Netherlands,} which researches the effect of early therapy on post stroke recovery of the upper limb. The wrist joint was researched as wrist joint dexterity is known to be a good predictor of the extent of functional recovery post stroke [5]. The measurement methods applied to assess relevant post stroke changes were functional magnetic resonance imaging (fMRI) for brain function and plasticity, transcranial magnetic stimulation (TMS) for corticospinal tract integrity (and plasticity), neuromechanics (for biomechanical and peripheral neural changes), kinematics (for compensation strategies) and a set of tests comparable to current clinical measures. Detailed project design is treated in the publication by Kwakkel et al. [5].

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1.1. General Flexion Extension Joint tor que Joint angle Linear fit

Figure 1.1: Measured resistance torque of a passive wrist joint slowly moving from flexion to extension and back. A linear fit of the response of the nonlinear system has been plotted that represents the data well for the centre angles. The slope of the curve in this plot represents stiffness, and difference in torque between the two lines is originates from the hysteresis caused by viscosity (and velocity).

movement velocity the linear reflex gain is expected to increase sharply. An-other well known nonlinearity is the increase in joint stiffness by contraction. If a subject is asked to stiffen a joint, opposing muscle pairs will be activated (co-contraction), causing both muscles to stiffen, whilst the opposing forces from both muscles can keep the joint in place. Many less trivial nonlinearities exist and will be treated throughout this thesis.

Analysis of a nonlinear system is sometimes done by using nonlinear mod-els but more often by using a linear representation of the nonlinear system. Current state of the art neuromechanical analysis is based on linear neuro-mechanical modelling and identification methods. These linear methods allow for identification of reflexive and non-reflexive components simultaneously and sensitively, yet they impose strict requirements.

A linear model can only describe the data well if the system behaves near-linear in the range perturbed. For example, passive joint resistance is often close to linear (can be described by a stiffness and viscosity) around the centre angles, yet in the extreme angles stiffness quickly increases and a single stiff-ness would not suffice in modelling passive soft tissue stiffstiff-ness throughout the full ROM (see Fig. 1.1). Unfortunately, joint neuromechanics, and in particu-lar muscle contractile properties and reflexive feedback responses, are highly nonlinear.

Gaining an understanding of joint nonlinearity is therefore essential for the proper interpretation of results based on linear methods. Nonlinear models will allow joint property assessment in a larger, more functional, range. It should not be forgotten that nonlinearity is also part of (normal) joint functioning.

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Being able to model nonlinear mechanisms will allow us to assess properties such as the reflexive threshold mentioned earlier, which may be affected in the post-stroke patient and may contribute to altered joint functioning.

A high level of control is necessary to repeatably identify nonlinearity of joint dynamics, which has been achieved throughout this thesis by use of an-gular controlled joint perturbations (i.e., with fixed/controlled perturbation angle and angular velocity). This thesis therefore often refers to joint imped-ance, being the dynamical relationship between angular perturbation (input) and observed resistance torque (output).

Many nonlinear properties are known from literature and are often based on animal testing and electromyography (EMG). EMG is used to measure muscle activity. How these properties translate to joint impedance is often unknown. However, using knowledge from literature in combination with a local linear view of carefully chosen neuromechanical system states, allows for a stepwise investigation of the effects of well known nonlinear properties on joint functioning.

This is a first step towards understanding which nonlinear properties mat-ter in joint functioning, and how they can be modelled.

1.2 Physiology

The conversion of brain action to joint function is determined by multiple biological systems. The direct contributors to joint movement and/or torque are the supraspinal regions, corticospinal tract (together the central nervous system (CNS)), reflexive feedback, passive soft tissues and muscle contrac-tion. Reflexive feedback partly consists of efferent forward neural pathways that activate the muscle as well as the afferent neural pathways that provide information from proprioceptive sensors. A simplified overview of relevant in-formation flow is depicted in Fig. 1.2.

In the EXPLICIT-Stroke project, research into brain function and plas-ticity and corticospinal tract integrity is covered by functional magnetic res-onance imaging (fMRI) and transcranial magnetic stimulation (TMS) based studies. This thesis focuses on the study of peripheral joint neuromechanics. In this section the relevant neuromechanical properties will be grouped into passive soft tissue, contractile (muscle) and reflexive feedback properties. The neuromechanical system includes supraspinal originating neural drive as an input to the neuromechanical system.

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1.2. Physiology

Sensory feedback Neural drive

Figure 1.2: Simplified schematic of the forward pathway (blue) consisting of neural drive from supra-spinal regions (depicted motor cortex) to the muscle (red), and the reflexive feedback pathway to the spinal cord (green) and back to the muscle (same line, blue)

1.2.1 Muscle Activation and Contraction

A muscle is the actuator of the joint. It is activated through either a forward pathway (the neural pathway from the brain to the muscle) or via one of sev-eral reflexive feedback pathways (see Fig. 1.2). The muscle consists of multiple muscle fibres. Each muscle fibre is activated by neural input, via a synapse connecting the neuron to the muscle fibre, i.e., the neuromuscular junction. Action potentials travel over the neuron, end up at the synapse and induce cal-cium release from the sarcoplasmic reticulum within the muscle fibre. Muscle fibres can be split up into myofibrils, which consist of a serial connection of sar-comeres. Sarcomeres are composed of the sliding or contractile actin and my-osin filaments [6]. Calcium allows for the connection between actin and mymy-osin filaments (also called cross-bridges) which generates force. The filaments are being pulled alongside each other by cross-bridges which continuously release and reconnect, a cycle referred to as cross-bridge turnover. An optimal over-lap between the sliding filaments yields maximum output tension, as shown in the force-length relationship (see Fig. 1.3). A further dependency on stretch velocity is shown in the same figure by the force-velocity relationship [7, 8] (Fig. 1.3).

When a muscle contracts, the number of cross-bridges connecting the con-tractile filaments increases, which results in an increase of stiffness. This is

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Muscle velocity Mu s c le te n s io n Muscle length

Figure 1.3: Simplified representation of the force-length and force-velocity relationships of the muscle, as shown by Rack and Westbury [9] and Joyce et al. [7], respectively, on isolated muscle fibres. The force length relationship represents the muscle force at zero velocity (isometric), the force velo-city relationship is determined at a fixed length. Both relationships are determined under constant activation

clearly shown by co-contraction, i.e., simultaneous activation of an opposing (/antagonistic) muscle pair. As joint torque from the antagonistic muscles is opposing, the resultant torque will be zero and therefore no movement res-ults. Contrary to inflicted joint torque, joint stiffness will be summed up. This additional stiffness component is attributed to the cross-bridge connections between filaments. As cross-bridges are continuously releasing and reconnect-ing, this stiffness slowly reduces over time. A long duration non-zero resist-ance muscle force remains after returning to an initial position, which has been named ’force enhancement’ [10]. The cross-bridge re-attachments during move-ment may cause additional viscosity: a continuous resistance against/during slow movement [11].

1.2.2 Passive soft tissue

Passive soft tissue is defined as all tissue that does not generate force from neural input, e.g., connective tissues, ligaments, but also skin. Skeletal muscles consist of bundles of muscle fibres (or fascicles) with surrounding connect-ive tissue called epimysium for the full muscle and perimysium for the fibre bundle. Each individual fibre is also covered by a layer of connective tissue: endomysium. These connective tissues come together at the muscle endings and form tendinous tissues.

Connective tissues distribute forces within the muscle, and their elasticity adds to the stiffness of the muscle. The high resistances that determine the extreme angles of the ROM are normally determined by passive resistance.

Research into muscle fibres has indicated that a truly passive muscle fibre behaves mostly elastic, rather than viscous [12, 13], yet viscous (or damped)

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1.2. Physiology

behaviour is present when measuring the wrist joint impedance [13], poten-tially because of movement of fluids in and around the muscle.

1.2.3 Supraspinal input and reflexes

As previously mentioned, muscle activation can stem from either a forward or feedback action of the nervous system. Reflexive feedback action is caused by systems other than those supraspinal, even though its sensitivity has been shown to be adaptable to the task at hand. Sensory organs that induce reflex-ive action include, but are not limited to, organs sensitreflex-ive to joint posture, movement and force, balance, skin temperature, touch and pain.

Fast reflexive corrections require a short neural pathway and little pro-cessing of neural information. Such signals will only be processed by the spinal cord. Other reflexive signals may also travel through the subcortical regions (e.g., thalamus, brainstem), which are responsible for basic functionings such as inter joint movement patterns. The travel to and from the subcortical re-gions will require significant more time [14].

The reflex loop transforms position, movement and/or tension as observed by proprioceptive sensors/receptors into muscle activation. Joint angle and velocity are sensed by muscle spindles [15], which are placed parallel to muscle fibres, and forces are sensed by Golgi tendon organs [16], which are placed in series with the muscle fibre (i.e., in the tendon). Spindle and Golgi receptors feed back information in the form of action potentials over afferent nerve fibres from dendrite to axon, made possible by polarisation of the neuron. Afferent implies direction towards the spinal cord. A synapse is the physical interconnection between neurons and other neurons or cells. There, the neural signal can be transferred by release of neurotransmitter. Muscle fibres may be innervated via a single synapse, i.e., monosynaptic, resulting in an activation of the same muscle the signal originated from (the agonist muscle). Alternatively, signals can travel via interneurons to other muscles (polysynaptic reflexes) and/or to supraspinal regions. Muscles may be activated or relaxed, referred to as reciprocal excitation or inhibition, respectively.

From receptor to muscle, the sensitivity of the reflex loop can be altered by numerous physiological systems:

1. The fusimotor system, refers to the gamma efferent motor neuron. The gamma motor neuron keeps spindle receptors under tension and is known to fire together with the alpha motor neuron activating the muscle, i.e. alpha-gamma co-activation [17–19]. Therefore, while the muscle contracts and fibres shorten, the muscle spindle does not go slack. With the ability

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to adjust spindle length, the gamma motor neuron can adjust muscle spindle sensitivity.

2. Presynaptic inhibition, by depolarisation of the primary afferent neuron2 [20, 21]), will reduce the transmission of action potentials over the affer-ent neuron. It has been shown by excitation of specific afferaffer-ent neurons that inhibition of the reflexive pathway occurs [22].

3. The motor motor neuron pool is the collective set of motor neurons that innervate (activate) a muscle. Persistent inward currents in the dendritic regions result in the continued firing of the post synaptic motor neuron pool after short excitation [23–25]. This initially excitatory mechanism allows for increased responses to small reflexive input and is highly de-pendent on controllable chemicals.

Although afferent reflexive signals contain representations of muscle stretch, stretch velocity and muscle torque, this is not true for the motor unit response. The afferent signal is significantly transformed/processed in the CNS. When measuring a collective set of motor units with electromyography (EMG) sev-eral consecutive activation volleys may be observed, where the first two are known as the M1-M2 response [26, 27]. The first volley (M1) appears approx-imately 25ms after excitation onset and is therefore, given axonal transmission speed, accepted to be a monosynaptic reflex response. It has been suggested that the reduced activity period between M1 and M2 would be caused by synchronous firing [28, 29], or actually synchronized refraction, of the motor neurons.

1.3 Current Neuromechanical Analysis

The individual assessment of reflexive and non-reflexive components in joint neuromechanics is essential so that patient specific therapy can be given. In the case of increased reflexive activity (hyperreflexia), botulinum toxin or baclofen can be used to weaken the overly active, but paretic, muscle. In case of in-creased passive soft tissue stiffness, stretching of the stiffened tissue is often included in therapy. Tailored therapy at an early stage relies on sensitive as-sessment of individual changes in reflexive and non-reflexive components.

The use of measurement robotics, such as the Wristalyzer, allows for the sensitive analysis of joint neuromechanics. Using task instruction the neural drive can to some extent be controlled. By careful control of perturbations, 2_{Although primary afferent depolarisation is generally abbreviated to PAD, the abbreviation} PAD has been reserved for Post Activation Depression in this thesis.

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1.3. Current Neuromechanical Analysis

an input to the neuromechanical system can be applied, generally angle or torque, and a response of the system can be measured.

This allows for sensitive measurement of clinical measures such as the ROM, or the Ashworth score (a spasticity test). Such measurements associate a value to combined neuromechanical dynamics; passive soft tissue, muscle contraction and reflex properties. Such aggregate outcome parameters are of functional value (e.g., is the patient able to move as freely as a healthy sub-ject?), but may not be sufficient for identification of an underlying cause.

Current individual assessment of reflexive and non-reflexive contributions is achieved by task instruction, velocity of perturbation, assessment of Elec-tromyography (EMG) or temporal differentiation, that is:

1. by asking a subject to relax, reflexes reduce (i.e., due to the fusimotor system)

2. by applying low velocity perturbations, no reflexive activity will be ob-served due to motor unit firing thresholds and

3. by measurement EMG, the time delay in reflexes and the MU-firing threshold can be investigated without having to differentiate between torques originating from the three different origins - passive soft tissues, active muscle and reflexes.

4. by using short perturbations, reflexive contributions can be differentiated from non-reflexive contributions, as reflexes are delayed and result in a long lasting muscle activation. This requires the non-reflexive system to be in a measurable or known steady state.

There are however strong limitations to the above. As hinted at in these items, the allocation of observed joint torque to the three underlying components, passive soft tissues, muscle contraction and reflexes, can not be done simultan-eously using such methods. Interpretation of EMG amplitude does not supply a solution, as it is strongly depends on location of the electrodes. Besides, EMG measures muscle activation, and muscle contraction is dynamical, i.e., responds over time. Therefore, proper investigation of reflexive action using EMG requires the joint to be in steady state at time of the reflexive action (see last item).

System identification methods are considered to be a strong way forward as they can be used to individually assess reflexive and non-reflexive joint torques due to knowledge of the physiological model structure: the reflexive pathway is dynamically different from passive soft tissues and (constant) muscle contrac-tion. A so called ’grey box’ modelling and identification strategy that includes a predefined neuromechanical structure and with free parameters can be used

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to gain insight in the contribution of individual elements to the measured data. Model structures have historically been mass-spring-damper models at first [30], and have later been expanded to include a reflexive pathway [31–34]. The mass-spring-damper component of the models captures all properties of the muscles and passive soft tissues in three parameters. Mass is the com-bined mass of all that is moved with joint movement, likely mostly determined by weight of the hand and the muscle. The spring, or stiffness, component, rep-resents the combined stiffness of the muscle and parallel passive soft tissues. As stated previously, connected cross bridges between contractile filaments add to muscle stiffness. Thus, with increasing muscle activation, joint stiffness in-creases. Damping, i.e., viscosity, describes the torque dependent on movement velocity, which is believed to originate in movement of fluids in and around the muscle.

The reflexive pathway model currently used by our group includes: 1. Reflex gains describing the linear contributions of joint angle (muscle

stretch), angular velocity (muscle stretch velocity) and tendon force, to joint torque, in line with literature on muscle spindle and Golgi tendon organ feedback,

2. A low-pass filter that describes the activation dynamics of the muscle, and

3. A time delay representing the transport delay of afferent and efferent neural signals.

It has been shown that these models describe the data well when using small amplitude perturbations, both in rest or under constant (co-)contraction. These restrictions are in place due to joint nonlinearity, which will be treated in section 1.5. In short, nonlinearity implies that a linear model cannot be con-structed that describes joint impedance for any input. For example, as stated in section 1.1 and Fig. 1.1, a linear stiffness and viscosity, i.e., spring-damper, model can describe low velocity impedance well around the centre angles, but no single stiffness can be used for the full ROM.

Under the restrictions of linearisation, these linear models still allow for an accurate simultaneous discrimination of reflexive and non-reflexive (contract-ile and connective tissue) contributions to joint impedance. This is of high relevance for the clinic as therapeutic strategies can be tailored accordingly.

Implications of limitations of linear methods are significant. The compar-ison between subjects requires measurement in the same neuromechanical sys-tem state, in joint measurement largely determined by joint angle and angu-lar velocity. Other internal states can be difficult to identify. For example,

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1.4. Problem Statement

although the joint of a spastic patient and a healthy control can be observed in the same angle, the patient may have a altered muscle stiffness and thus a different pre-tension on the spindle/GTO receptors. This of course does not imply that the receptor properties have changed, but when analysing the reflex gain, a researcher may end up with that conclusion.

1.4 Problem Statement

The general methodological aim in joint neuromechanical assessment is to identify the reflexive and non-reflexive contribution to joint impedance simul-taneously, such that their roles in movement disorders can be quantified. We apply state of the art linear system identification methods, which although strong in the differentiation, are subjected to restrictions imposed by lin-earisation criteria. These restrictions include small deviations from a specific state the system is in and constant muscle activation. In normal functioning of joints, large variation in joint angle, angular velocity and contraction level, are common. Therefore, linearisation restrict measurement to a limited functional range.

Furthermore, lack of knowledge of the effect of nonlinearity of joint neuro-mechanics is likely to be a potential source of misinterpretation. This is due to the lack of knowledge of the state of the neuromechanical system, and is expected to invalidate comparisons between patients and healthy subjects.

1.5 Joint nonlinearity

It has been established that muscles, passive soft tissues and reflexive feedback are all nonlinear. The severity of nonlinearity and effect of nonlinearity on neuromechanical properties is however still unknown, both in healthy subjects and stroke patients.

In stroke patients, altered joint neuromechanics are known to contribute to observed movement disorders. High joint rigidity and altered posture, may be caused by stiffening of passive soft tissues or increased reflexive sensitivity. Whether any of the following nonlinear properties have altered in subjects suffering from post stroke movement disorders, is mostly unknown.

In this section current known nonlinear properties of physiological systems will be treated. Many can be identified in literature, but only ones that are believed to be relevant to this thesis are listed.

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1.5.1 Muscle Mechanics

The force-length relationship is related to muscle filament overlap [35–37]. Around the rest angle of the joint there exist an optimal angle in which the highest number of cross-bridges can bind to binding sites. At any other angle the amount of sites reduces and therefore the force output of the muscle will reduce. The optimal length of a muscle will move with muscle activation [38]. The force-velocity relationship describes the ability of cross-bridges to pull whilst being shortened or stretched [7, 8, 12, 39, 40]. When being stretched the muscle force increases only a little, but when being shortened the cross-bridges can hardly generate force.

Resistant muscle force is known to show a sudden yield when being stretched for large amplitudes [41], or actually longer durations [42]. This is referred to as short-range-stiffness; an initial resistance that is cause by stretching attached cross-bridges. However, for larger amplitudes these connections release/are pulled apart and the drop in resistance can be observed. It has recently been shown that this is also measurable on joint level.

1.5.2 Reflex Gain Sensitivity and Modulation

As mentioned before, the reflexive sensitivity can be modulated by the fusimo-tor system, by pre-synaptic inhibition and/or by altered mofusimo-tor neuron pool sensitivity. Such adjustments in reflexive sensitivity are highly nonlinear and are likely to contribute to post stroke spasticity [43], as the origin of such mod-ulations lies within supraspinal regions. Short or long term synaptic plasticity (adaptation of the synapse between neurones) may last anywhere between seconds or minutes, respectively and can be either excitatory (facilitating) or inhibitory and either presynaptic or postsynaptic [44]. Although of interest, the different origins of such inhibitory and/or excitatory functions will be impossible to differentiate between using only joint torque, angle and EMG data.

Post activation depression (PAD, [45]) is an decreased reflexive sensitiv-ity after previous excitation of the pathway. This effect has been observed in the monosynaptic reflex [46, 47] and has been related to presynaptic neuro-transmitter release dynamics [48]. A synapse between afferent axon en efferent motoneuron is a chemical process in which neurotransmitter is released. Hypo-thetically, the neurotransmitter may temporarily run out, i.e., need a recovery time, resulting in lower sensitivity directly after excitation of the synapse. PAD recovery times are generally in the order of three seconds for the wrist [49]. Decreased Post Activation Depression (PAD) has been observed in

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spas-1.6. Aim

tic patients and has been hypothesized to contribute to the reduced ability to initiate movement [48].

According to Henneman’s size principle, smaller, slower efferent motoneur-ons are known more likely to be active with increasing contraction [50], and are connected to slow-twitch muscle fibres. Therefore, the more neural drive, the more fast-twitch fibres are recruited and the higher the sensitivity to neural input of the muscle. Slow-twitch muscle fibres are also less susceptible to fa-tigue, but can produce less force than fast-twitch fibres [51]. The motor unit membrane is known to contain firing threshold. This minimum excitation level of the reflexive system can easily be seen [52]. The motoneuron size principle may contribute to an observable nonlinear dependency on reflexive input, but will also affect supra-spinal originating neural drive.

1.6 Aim

Although many nonlinear properties can be identified in literature, it is un-known which nonlinearities are functionally important and affect joint meas-urement. Furthermore, although it has been hypothesized, it is unknown if neuromechanical properties have altered in stroke patients to an extent that yields altered joint impedance. Assessment of nonlinearity can be a tool to gain insight into altered properties of neuromechanical reflexive and non-reflexive components.

The aim of this thesis was to:

1. Estimate parameters that determine reflexive and non- reflexive contri-butions to joint impedance, in healthy subjects and stroke patients, using currently available techniques, in order to improve understanding of post stroke movement disorders.

2. Quantify the effects of nonlinearity on joint impedance in healthy sub-jects and stroke patients, by use of linear methods.

Knowledge of nonlinear joint impedance, and its underlying properties and associated nonlinear dynamics, will help interpret results from linear analyses, and is a first step towards nonlinear models that enable measurement over a larger, more functional domain. Change in specific nonlinear properties (see section 1.5), may also contribute to understanding movement disorders.

1.7 Approach

The assessment of relevant joint neuromechanics is aimed to be a compre-hensive set of tests that together form a picture of the subject measured. It

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will require functional outcome measures, such as the ROM and MVC, but also assessment of underlying causes in terms of passive soft tissue, muscle contraction and reflex properties will be included. Individual assessment of these contributors to joint impedance will be achieved by combination of task instruction and careful design of perturbation type.

Identification of joint nonlinearity often relies on prior knowledge of the type of nonlinearity. For example, a static nonlinearity (instantaneous non-linear function) on the input or output of a system can be captured by a Wiener or Hammerstein model. Although some methods of nonlinear system identification are available, our aim to identify presence of a large range of nonlinearities in the first place encourages a simplified method.

A linear analysis method near specifically chosen system states has there-fore been applied. As previously pointed out, a single linear model will not be able to describe a nonlinear system throughout its full range of potential operation. Changes of estimated parameters with measurement condition will imply nonlinearity (if the model structure is correct). The strengths of such an approach are simplicity of the model structure and ease of interpretation. This will directly allow for a greater understanding of the linear results and is a first step towards nonlinear models, equalling measurement over a larger functional domain.

The shape of change in parameter with measurement condition, in combin-ation with knowledge of underlying neuromechanical properties from literat-ure, will allow for an explanation to be formed. This comes with the risk that multiple explanations may exist for similar changes of in observed nonlinear dynamics, and further investigation may be needed before accurate conclu-sions can be made.

In this approach, joint perturbations are to be varied carefully and system-atically, to allow for comparison between subjects. The space of all possible perturbation types has been explored by variations in amplitude, velocity and inter stimulus interval, the latter to identify effects of previous perturbation. This was followed by a study into the effects of multisine perturbations and ramp and hold perturbations on linearly estimated parameters. Both of these perturbation types are often used in assessment of joint neuromechanics (e.g., [34, 53]). As contraction level is a strong modulator of muscle properties, it has been altered in each of these studies.

Variations in linearly estimated parameters will first be measured on healthy subjects, to investigate which nonlinear properties are present more promin-ently. Resulting conditions of interest will then be used for identification of nonlinear dynamics in post stroke patients.

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1.7. Approach Post-stroke wrist neuromechanics Post-stroke wrist nonlinearity Wrist nonlinearity Amplitude Velocity Multisine v.s. Ramp and Hold

Inter stimulus interval

Linear models & EMG 2 & 3 4 5 6 7 8 4 - 8 9

Figure 1.4: Thesis content with chapter numbers

A very general thesis outline has been given in Fig. 1.4 and can be described by the following:

• A protocol was developed to addresses therapeutically-relevant wrist joint properties in post stroke movement disorders. The methodology or ’line of thought’ of the protocol is given in Chapter 2, the reliability of the protocol and its sensitivity to variations in movement disorders is treated in Chapter 3).

• The investigations into the effects of nonlinear dynamics on linearly es-timated neuromechanical parameters is given in Chapter 4 to 8. Effects of amplitude (Chapter 4), velocity (Chapter 6), inter stimulus interval (Chapter 7) and multisine v.s. ramp and hold perturbations (Chapter 8) were individually assessed, for multiple levels of voluntary contraction. Chapter 5 shows, on the data of Chapter 4, how well linear models can describe electromyographically measured responses.

• Post-stroke patients were subsequently measured to identify potential changes in earlier determined nonlinear dynamics, that may contribute to movement disorders (Chapter 9).

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Chapter

2

The EXPLICIT-Stroke

Neuromechanical Assessment Protocol

2.1 Introduction

Movement disorders after stroke may have a major impact on daily life. Al-most two thirds of the stroke survivors suffer from sustained deterioration of arm-hand function which threatens physical independency [1]. Besides cortical and corticospinal tract integrity, functional movement and motor deficits are largely determined by joint neuromechanics.

In the acute phase after stroke, mechanical behaviour at joint level is charac-terized by flaccidity and paresis, while in the sub acute phase, signs of muscle over-activity and joint stiffening become more prominent [2, 3]. Although this is a common recovery pattern, several different phenotypes may develop in the chronic phase [4]. These phenotypes will be the result of a complex and varying interplay between neurological and biomechanical changes over time. A better understanding of the interplay and changing contributions of aforementioned neuromechanical processes to movement disorders is needed to address the full functional recovery potential. The EXPLICIT-Stroke (EXplaining PLas-tICITy after stroke) study was designed to explore the functional impact of the time-dependent changes in cortical neuroplasticity and neuromechanics, as well as the adaptive compensation strategies that are applied to cope with ischaemic brain lesion related motor deficits [5].

Current clinical assessment of joint neuromechanics is restricted to ordinal rating scales such as the Medical Research Council scale for muscle force, go-niometry for impaired range of motion (ROM) and Ashworth score for spas-ticity. The latter however, is incapable of discriminating between the pos-sible neural and/or mechanical sources of increased joint resistance [4, 6, 7].

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The use of robotics (e.g., a wrist manipulator) to evoke controlled force and torque perturbations, electromyography (EMG) to record muscle activity and neuromuscular modelling potentially allows for an individual assessment of neurological and biomechanical joint properties [6, 8–11].

Nonlinear dynamics of the neuromuscular system greatly influence joint behaviour, yet their role has not been fully recognised. For example, the stretching of tissue yields nonlinear force curves: twice as much stretching does not result in twice as much resistance of the joint [12]. Another example is the sensitivity of the stretch reflexes, which may be modulated at spinal cord level [13]. While linear mass-spring-damper-like concepts are far easier to apply and are regularly used to simplify mechanical behaviour, they do not comprehensively describe biomechanical properties of the joint under differ-ent environmdiffer-ental conditions (tasks and loadings). Using prior knowledge of nonlinearities, the joint can be conditioned such that the nonlinear dynamics of the neuromuscular system can be accounted for, or even parametrized.

In this paper we present the methodological aspects on how to individually address the different properties of the (nonlinear) neurological and biomech-anical components of wrist joint behaviour in during flexion-extension move-ment. This resulted in a comprehensive and clinically applicable assessment protocol. Longitudinal measurements with this specific protocol, within a lon-gitudinal measurement framework such as the EXPLICIT-Stroke study, will enhance our knowledge of primary and secondary changes in neuromechanics when functional changes are observed.

2.2 Methods

2.2.1 Line of thought

Assessment of neurological and biomechanical contributors to movement dis-orders after stroke should result in structure specific parameters that are potentially modifiable by therapeutic intervention. Treatment is commonly aimed at muscle activation or strength in case of paresis, reduction of reflex sensitivity or neural input in case of hyperreflexia or the stretching of pass-ive tissue in case of joint stiffening. Therefore, we define the neuromechanical system on a therapeutically attainable level into passive, active and reflexive torque components:

• Passive: all joint resistance observed when no neural input is fed to the muscles

• Active: muscle torque generation from contraction due to neural input (supraspinal and reflexive)

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2.2. Methods Passive tissue viscoelasticity (Supra-) spinal Input Active muscle viscoelasticity Inertia Active muscle (Motor Units) Reflexive fb (M. Spindle) Reflexive fb (GTO) WA (torque) Input Internal Torques Wrist torque Wrist rotation EMG Spinal cord

Figure 2.1: Simplified graphical model of the components of the wrist joint, depicted with active, passive and reflexive elements, corresponding with areas for target therapy. Dotted lines indicate non-invasively measurable connections, EMG (left), torque (centre) and rotation (right). Rotation includes angle and rotational velocity

• Reflexive: active muscle torque solely due to proprioceptive feedback The interconnection between passive, active and reflexive contributors is rep-resented in Fig. 2.1. By differentiating the contributions of each of these ele-ments to joint level mechanics, their individual roles in movement disorders can be better defined, allowing for targeted therapy.

In order to characterize the phenotype of post-stroke patients properly, the neuromechanical system needs to be sufficiently triggered i.e., different con-ditions need to be applied. Passive, active and reflexive components will be dependent on the state of the wrist (i.e., joint torque, joint angle and muscle activity) and the externally applied loading. The state represents the cur-rent operating point of the system and subsequently its dynamical properties, observed at endpoint level in torque (and angle). A haptic wrist manipulator combined with electromyographic (EMG) measurement is an easy-to-use com-bination of tools that allows for applying angle or torque controlled perturb-ations and the subsequent assessment of changes in joint state. The different modes in combination with task instruction enable us to impose a desired state. Properties of passive, active and reflexive contributors can be estimated from the measured in- and output data. When torque is the input, angular displacement is the output and vice-versa. Output signals including EMG, as a representative of active muscle state, may also be used to inform the subject on actual task performance.

For analysis, we define two different approaches. The first approach will be referred to as signal analysis. This approach aims to induce large variations regarding the role of model components by applying specific conditions to the system. Slow movements will exclude reflexive activity, while the amount of

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voluntary contraction can be modulated, and therefore controlled, by proper task instruction. This gives contributor-specific tests that aim to assess pass-ive, active or reflexive contributors individually. The second approach, referred to as system identification, is based on the fact that reflexive resistance is dy-namically different from passive or active resistance. Differentiation between the feedback pathways can be done using torque-angle correlation analysis, keeping the closed loop configuration of reflexive (neural) and muscular (mech-anical) components into account. Both approaches make it possible to express system performance in terms of its underlying properties, yet conditions are significantly different. System identification methods are not yet sophisticated enough to perform well over a nonlinear domain, and additional signal ana-lysis methods are still needed. Furthermore, limit behaviour, such as ROM or maximal voluntary contraction (MVC), is easier to assess using basic signal analysis. The following subsections describe a listing of interesting outcomes that together result in a comprehensive set for assessment of joint neurome-chanics. These outcomes were used as a basis for the protocol discussed in the following section, i.e., ‘The EXPLICIT-Stroke protocol’.

Signal analysis

Passive tests (slow movement while instructed to ”do nothing”) Of func-tional interest are the ROM and the resistance that subjects experience when their joint is moved passively through the ROM. The equilibrium angle of the joint, or rest angle represents a stiffness balance between agonist and ant-agonistic muscles. Passive tests aim to assess the passive joint structures in subjects, as given in Fig. 2.1. For the assessment of the passive structures, sub-jects are instructed to do nothing. Movement of the wrist at a slow velocity then results in stretching of passive tissues, while minimizing the contribution of active muscle contraction and reflexive activity. The resulting joint torque will be the result of the stiffness and viscosity arising from predominantly passive contractile and non-contractile tissue. EMG measurements should be used to check for interfering muscle activation during measurement and for data analysis. The following outcomes can be listed for passive tasks:

• responsive range of motion • stiffness and damping

• rest angle (angle of joint flexion-extension torque equilibrium)

In stroke patients, relative to controls, we expect restrictions in ROM, higher joint stiffness and a rest angle that tends towards flexion [2].

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2.2. Methods

Active tests (slow movement while instructed to ‘move / push / resist’)

These tests address the ability of the patient to actively generate torque at the joint level, preferably in a controlled manner (Fig 2.1). Applied torque levels should exceed resistance of passive tissue or antagonistic muscles. A subject’s ability to generate this particular torque level can be easily tested (also in the clinic) by asking them to flex or extend maximally (i.e., the active ROM). Alternative active tests are performed in a standard position (i.e., the rest angle) or during imposed slow movement to minimize reflex activity. Subjects are provided with visual feedback on their actual task performance. Joint angle (relating to overlap of muscle filaments and muscle moment arm, tissue strain) and joint velocity (relating to cross-bridge turnover dynamics and tissue viscosity) also contribute to the potential production of joint torque [14]. Applying an active and a passive test in similar test conditions, defined in terms of joint angle and angular velocity, allows for subtraction of torques generated by the passive structures from the data, under the assumption that the active muscle does not influence stiffness/viscosity values of surrounding passive structures. From these measurements the following outcomes can be listed for active tasks:

• self induced ROM

• control over joint torque build-up (i.e., quality of motor control) • maximally attainable torque

• angular/velocity dependent joint torque production

In stroke patients, relative to controls, we expect a smaller self induced ROM, a lower maximally attainable joint torque and less control over joint torque. Furthermore, it is expected that angular-dependency of torque production increases, with an optimum angle (e.g., muscle filament overlap) tending more towards flexion [15].

Reflexive tests (fast movement) Reflexive tests are aimed to assess the re-flexive pathways, as given in Fig. 2.1. Higher reflex activity is known to be triggered by high joint angular velocity [11] and together with reflexive time delay (loop-time) it is considered to play an important role in reflex loop sta-bility. To measure the reflexes we commonly use EMG recordings together with controlled, repeated perturbations. This will deliver reproducible data on reflexively triggered muscle activity (e.g., short and long latency reflexes). Perturbations are to be applied at random intervals to minimize anticipation (as subjects can influence their reflexive sensitivity, i.e., reflex modulation). Note however that active components should also be considered when

Linear Identification of Nonlinear Wrist Neuromechanics in Stroke

Linear Identification of Nonlinear Wrist

Neuromechanics in Stroke

Linear Identification of Nonlinear Wrist

Neuromechanics in Stroke

Contents

Summary

1

General Introduction

2

The EXPLICIT-Stroke

Neuromechanical Assessment Protocol