Intersegmental coordination patterns are differently affected in Parkinson’s disease and cerebellar ataxia

Abstract

The law of intersegmental coordination (Borghese et al. 1996) may be altered in pathological conditions. Here we investigated the contribution of the basal ganglia (BG) and the cerebellum to lower limb intersegmental coordination by inspecting the plane’s orientation and other parameters pertinent to this law in patients with idiopathic Parkinson’s disease (PD) or cerebellar ataxia (CA). We also applied a mathematical model that successfully accounts for the intersegmental law of coordination observed in control subjects (Barliya et al. 2009). In the present study, we compared the planarity index (PI), covariation plane (CVP) orientation, and CVP orientation predicted by the model in 11 PD patients, 8 CA patients, and two groups of healthy subjects matched for age, height, weight, and gender to each patient group (Ctrl_PD and Ctrl_CA). Controls were instructed to alter their gait speed to match those of their respective patient group. PD patients were examined after overnight withdrawal of anti-parkinsonian medications (PD-off-med) and then on medication (PD-on-med). PI was above 96% in all gait conditions in all groups suggesting that the law of intersegmental coordination is preserved in both BG and cerebellar pathology. However, the measured and predicted CVP orientations rotated in PD-on-med and PD-off-med compared with Ctrl_PD and in CA vs. Ctrl_CA. These rotations caused by PD and CA were in opposite directions suggesting differences in the roles of the BG and cerebellum in intersegmental coordination during human locomotion.

NEW & NOTEWORTHY Kinematic and muscular synergies may have a role in overcoming motor redundancies, which may be reflected in intersegmental covariation. Basal ganglia and cerebellar networks were suggested to be involved in crafting and modulating synergies. We thus compared intersegmental coordination in Parkinson’s disease and cerebellar disease patients and found opposite effects in some aspects. Further research integrating muscle activities as well as biomechanical and neural control modeling are needed to account for these findings.

INTRODUCTION

The control of movements in humans involves an excess of kinematic and kinetic degrees of freedom across the neural and musculoskeletal levels of the sensorimotor control hierarchy. This motor redundancy is referred to as the excess degrees of freedom problem (Bernstein 1967; Latash et al. 2007). Although such redundancies may allow adaptive and flexible control, dimension reduction might be needed to reduce the complexities associated with the control of multijoint movements.

One way to overcome motor redundancies is to use a modular control scheme based on the adaptive control of kinematic, kinetic, or muscular synergies. The employment of a modular control structure may operate at one or more hierarchical levels including those of individual muscles or joints, thus creating muscular or kinematic synergies, respectively. Modular control might also operate at different neural levels involving motor-neurons and interneurons, spinal segments, and cortical/subcortical circuits (Flash and Bizzi 2016; Lacquaniti et al. 2013; Tresch and Jarc 2009; Zelik et al. 2014).

In recent years the powerful idea of controlling movements through muscle synergies activation rather than individual muscles has received support from many neurophysiological studies conducted in frogs (d’Avella et al. 2003), cats (Yakovenko et al. 2011), primates (Overduin et al. 2015), and humans (Ivanenko et al. 2006). Synergies composed of several muscles, particularly those acting on proximally situated limb segments, may suggest not only how movements of individual limb or body segments are generated, but also how they may give rise to kinematic synergies and well-coordinated movements of several segments. Flexible and modifiable muscle synergies might be crafted by the nervous system to generate a variety of movements within different actions, tasks, and contexts. In the context of human locomotion, the shape of muscle activation patterns remains stable but their timing and spatial weights dictating the activations of various muscles to stabilize posture or to move one or more joints may vary with gait speed, direction, loading, and unloading (Lacquaniti et al. 2012). There is also a strong consensus that the cerebellum (CBL) plays a key role in the timing of muscles’ activities, both during simple single-joint and complex multijoint movements involving several muscle groups and synergies (Hallett et al. 1975; Holmes 1939; Ivry et al. 2002; Vinueza Veloz et al. 2015).

Neurophysiological studies have indicated that the basal ganglia (BG) and CBL are both neuroanatomically and neurophysiologically well poised to have higher level influences on how the motor cortex organizes movements. Crafting or modifying synergies may well be one of the functions of these subcortical systems. Examining how gait synergies are affected by diseases of these structures can therefore reveal their role in overcoming the complexities associated with controlling multijoint movements, as well as taking advantage of the considerable redundancy existing at the muscular and kinematic levels.

The coordination between the movements of leg segments during locomotion has been shown to follow the law of planar covariation, whereby lower limb elevation angles form a loop that fits on the so-called intersegmental covariation plane (CVP) (Borghese et al. 1996). The elevation angle of a limb segment is represented by the angle between the limb segment projected onto the sagittal plane and the vertical axis. In the case of the leg there exist three elevation angles: thigh, shank, and foot pertaining to the hip, knee, and ankle joints, respectively (see Fig. 1). The law of covariation is invariant to gait type, e.g., running and walking backward (Ivanenko et al. 2007). It holds for both walking along straight and curved paths (Courtine and Schieppati 2004) and is also invariant to different visual feedback conditions (Courtine and Schieppati 2004). This law may therefore represent a solution to the motor redundancy problem (Bernstein 1967) in the context of locomotion, serving to reduce the number of kinematic degrees of freedom existing for the individual limb from three to two (Lacquaniti et al. 1999). Hence, during human locomotion, kinematic synergies resulting from particular modes of time-dependent activations of muscle synergies can be detected by inspecting the 2D time-dependent paths emerging within the CVP from the coordinated rotations of the ankle, knee, and hip joints. Being two-dimensional, rather than a three-dimensional path that weaves through 3D space, it reflects the existence of coordinated patterns of lower limb segment rotations during human locomotion.

Fig. 1.

Elevation angles but not anatomical angles show planar covariation. This figure shows data from a healthy subject walking straight ahead, eyes open. A shows the time course of the three elevation angles: thigh, shank, and foot, of one gait cycle from heel strike to heel strike in one representative healthy subject. The dotted lines represent the raw data points and the continuous lines represent the curve fit function using a Fourier series up to the third harmonics from which the phase and amplitude parameters for the oscillators-based model were derived (see Eq. 6 in the methods section). B shows the same data represented in three dimensions whereby each data point comprises the elevation angle of each segment at a given point in time. The position of heel strike in the three-dimensional covariation loop in B is at the top right point and progression in time is counterclockwise. The units of all axes are degrees. C is equivalent to B but with a rotated viewing angle to demonstrate the high degree of planarity in the statistical structure of the data. D to F are equivalent to A to C only for the anatomical angles hip, knee and ankle. In contrast to elevation angles, there is no planar covariation of anatomical angles. In subplots B, C, E, and F, the u₃ parameter is a unit vector orthogonal to the covariation plane. G and H demonstrate the distinction between elevation and anatomical angles. Note that anatomical angles are defined relative to the limb segment proximal and distal to the anatomical joint and, in contrast to elevation angles, without any relation to neither gravity nor the direction of locomotion.

In addition to the planarity property of the intersegmental CVP, other features relating to the coordination of intralimb elevation angles have been described. One such feature is the orientation of the CVP, which is defined by the 3rd eigenvector (u₃) obtained from a principal component analysis (PCA) of the time courses of the three elevation angles. This unit vector represents the vector orthogonal to the CVP and thus the CVP’s orientation in the elevation angles configuration space. The vector’s three coordinates can be viewed as the direction cosines of the vector in the direction of the three semiaxes: thigh (u_3t), shank (u_3s), and foot (u_3f) (see Fig. 1). The orientation of the CVP varies among different gaits (Ivanenko et al. 2007) and is modified with increasing gait speed in a way that reduces energy expenditure (Bianchi et al. 1998a, 1998b), with the component showing the largest change being the u_3t component. In contrast, analysis of the direction of the 1st eigenvector (u₁), which corresponds to the long axis of the covariation loop, shows no effect of gait speed on any of the u₁ components (Bianchi et al. 1998b). Previous studies have shown that the u_3t values in healthy and pathological populations range between 0° and 23° (see Table 1). Furthermore, the magnitude of u_3t is positively correlated with the phase shift between the shank and foot elevation angles (Bianchi et al. 1998a, 1998b).

Table 1.

Summary of literature on the orientation of the covariation plane in studies with adult humans

Author-Date	u3t, o	Comments
Borgheseet al. 1996	9.2–18.3	HA, n = 6
Bianchi et al. 1998b	0–22.9	HA, n = 24
Courtine and Schieppati 2004	11.5–20.1	HA, Straight and turning, n = 6
Maclellan and McFadyen 2010	14.3	HA ~0.4%, n = 10
Ivanenko et al. 2008	~20	HA, n = 8
Grasso et al. 2000	12.6	HA, 38.4 knees and trunk flexed, n = 5
Grasso et al. 1999	14.3–20.6	PD-on-med, n = 5
	15.5–22.3	PD-off-med, n = 5
	5.7–17.2	17.2 DBS on, 5.7 DBS off, n = 1
MacLellan et al. 2011	~7	CA, n = 8
	~9	HA, n = 8
Martino et al. 2014	~8.6	CA, n = 19
	~17.2	HA, n = 20
Dan et al. 2000	6.0–14.0	Spastic paraparesis, n = 1
	1.0–5.0	HA, n = 7
Leurs et al. 2012	0–17.2	Prosthetic limb, n = 7
	8.0–22.3	HA, n = 10
MacLellan et al. 2013	~11	Nonparetic limb, stroke, n = 6
	~12	Paretic limb, stroke, n = 6

HA, healthy adults, CA, cerebellar ataxia, PD-on-med, Parkinson’s disease on medication, PD-off-med, Parkinson’s disease off medication.

^*P < 0.05.

This body of research relating to planar covariation under different experimental conditions (Courtine and Schieppati 2004; Grasso et al. 1999; Ivanenko et al. 2007; Lacquaniti et al. 2002; Leurs et al. 2012; Noble and Prentice 2008; Sylos-Labini et al. 2013), as well as research in nonhuman species (Courtine et al. 2005; Ogihara et al. 2012, 2014), suggests that, in contrast to anatomical angles, elevation angles have particular importance in the control of lower limb movements and may represent a more parsimonious control variable. Two lines of evidence support this notion. First, classic physiological research performed in the 1970s and 80s showed that although joint afferents encode parameters relating to the anatomical angle, joint position sense, and kinesthesia depend on additional receptors and mechanisms (McCloskey 1978; Matthews 1982). Second, psychophysical studies suggest that the reference frame for position sense is more closely associated with body segment elevation angles rather than with anatomical angles (Soechting and Ross 1984).

A mathematical model assuming that lower leg movements can be adequately described using simple oscillatory movements of the three leg segments was shown to successfully account for the intersegmental patterns of coordination. It also showed that using the amplitudes and phases of the first harmonics of the elevation angles, one can successfully describe the conditions needed to comply with the planar constraint and predict the eccentricity of the covariation loop and the orientation of the plane (u_3t) (Barliya et al. 2009).

The gait disorders of Parkinson’s disease (PD) and cerebellar ataxia (CA) are clinically distinguishable and are likely to be comprised of features directly related to disease pathophysiology and features that emerge from physiological compensatory mechanisms, which may initially be adaptive but may become maladaptive. Here we aimed to test whether and in what ways certain aspects of intersegmental coordination are modulated by Parkinson’s disease and cerebellar disease and thus gain insight into the possible roles of the BG and CBL in controlling human locomotion. In this context, we challenged the subjects with complex gait conditions: walking in a circle and walking with eyes closed. Walking along a curved path requires control in the lateral plane as well as the sagittal plane in the heading direction. The preservation of gait coordination with this additional complexity thus represents a major computational challenge for the central nervous system (Courtine and Schieppati 2004). Although the law of intersegmental coordination was reported to be preserved in the absence of visual feedback in either straight-ahead or curved locomotion in both healthy adults (Courtine and Schieppati 2003) and healthy children (Hallemans and Aerts 2009), people with CA have reduced capability to make normally directed error corrections when walking along curved trajectories (Goodworth et al. 2012). Furthermore, PD patients, depicting normal gait during straight ahead walking, may have reduced stride length when walking along a curved trajectory (Guglielmetti et al. 2009). Here we aimed to characterize the abnormal patterns of intersegmental coordination observed in PD and in CA and the effect of visual feedback availability and gait complexity on these patterns. We compared PD (as a model of BG pathology) and CA (as a model of cerebellar pathology) to explore the functional implications of BG–cerebellar communications, identify divergent effects of BG and cerebellar dysfunction and thus, in the context of intersegmental coordination, determine possible contributions of the BG and cerebellum (CBL) to the CVP constraint.

By inspecting the pattern of intersegmental of coordination, we aimed to determine whether BG or cerebellar dysfunction perturb the planar covariation constraint or modulate the normal patterns of intersegmental coordination, observed in control subjects. Through such analysis, we also wished to examine the possible connection between a synergies-based control scheme at the kinetic level and the planar covariation observed at the kinematic level in the context of solving the redundancy problems in locomotion. Such analysis may subserve future studies aimed at examining the proposed roles of cortical and subcortical circuitry, including the basal ganglia and the cerebellum, in the control of muscle synergies (Lacquaniti et al. 2013; Tresch and Jarc 2009).

METHODS

Participants

We performed instrumented gait analysis in 11 subjects with PD (all treated with levodopa), 8 subjects with CA (3 idiopathic, 3 spinocerebellar ataxia SCA-6, 1 SCA-15, and 1 with olivo-ponto-cerebellar ataxia), 12 healthy subjects matched for PD (Ctrl_PD), and 8 healthy subjects matched for CA (Ctrl_CA) (see Table 2). Both PD and CA subjects were referred by movement disorders neurologists. Control subjects were matched to their respective patients for age, gender, weight, and height (Table 2). Furthermore, control subjects were instructed to walk at a slower pace than their usual to match for gait speed.

Table 2.

Demographics and clinical characteristics of participants with PD and healthy participants matched for PD

	Ctrl_PD (n = 12)	PD (n = 11)	Ctrl CA (n = 8)	CA (n = 8)
Age, yr	63 ± 9 (43–80)	64 ± 9 (46–81)	57 ± 7 (47–64)	58 ± 7 (48–68)
Gender	12 M	11 M	2 M, 6 F	2 M, 6 F
Height, cm	174 ± 6 (165–183)	177 ± 5 (168–185)	170 ± 11 (150–183)	169 ± 11 (154–185)
Weight, kg	80 ± 11 (62–99)	82 ± 8 (68–94)	75 ± 13 (64–99)	75 ± 13 (64–100)
Duration of disease, yr		8 ± 4 (2–12)		5 ± 3 (2–9)
Motor UPDRS, PD-off-med		34 ± 9 (22–47)
Motor UPDRS, PD-on-med		24 ± 8 (14.5–40.5)
H & Y, off-medication		2.3 ± 0.4 (2.0–3.0)
H & Y, on-medication		2.0 ± 0.2 (2.0–2.5)
SARA score				13.9 ± 3 (9–18)

Values are displayed as mean ± SD (range). PD, Parkinson’s disease, Ctrl_PD, control subjects matched for Parkinson's disease, CA, cerebellar ataxia, Ctrl_CA, control subjects matched for CA, M, male, F, Female, UPDRS, Unified Parkinson’s Disease Rating Scale (maximum score = 108), H & Y, Hoehn and Yahr stage (maximum score = 5), PD-on-med, Parkinson’s disease on medication, PD-off-med, Parkinson’s disease off medication, SARA, Scale for the Assessment and Rating of Ataxia (maximum score = 40).

Neither patients nor healthy subjects had any prior history of neurological diseases other than PD or CA in the case of patients and none had musculoskeletal or neurological impairment that could contribute to postural instability or movement dysfunction, including severely flexed posture. All subjects were ambulatory and able to stand without an assisting device for the experiment.

PD subjects had no history suggesting atypical parkinsonism, as defined by Hughes et al. (1992), and had a Hoehn and Yahr score (Hoehn and Yahr 1967) of 2 to 2.5 on-medication and 2 to 3 off-medication. All subjects signed a written, informed consent in accordance with the Oregon Health and Science University Internal Review Board regulations for human subjects’ studies, which approved the protocol for this study, and with the Helsinki Declaration.

Disease severity of motor dysfunction in the PD group was rated using the motor part (part III) of the Unified PD Rating Scale (UPDRS) (Fahn et al. 1987). PD patients first performed the tasks on the morning after abstaining from levodopa treatment overnight (washout period ≥12 h) (PD-off-med) and then repeated on the same day after taking a normal dose of their PD medications and a rest period of at least 1 h (PD-on-med). Patients were considered PD-on-med when they reported feeling the effect of the medications and after objectively confirming motor improvement by the motor part of the UPDRS.

Severity of the CA patients was measured by the Scale for the Assessment and Rating of Ataxia (SARA) (Schmitz-Hübsch et al. 2006).

Experimental Apparatus and Instrumentation

Subjects were instrumented with reflective markers that were positioned according to the standard convention. The positions of the markers were recorded with a sampling frequency of 60 Hz in three dimensions with an eight-camera video system (Hi-Res, Motion Analysis System, Santa Rosa, CA).

Subjects performed two locomotion tasks as follows:

• Straight-ahead walking: Patients and control subjects were instructed to walk straight toward the other side of the room (~10–14 m long). They performed 10 trials eyes-open (EO) followed by 10 trials eyes-closed (EC). The subjects initiated gait 1–2 m before entering the recording volume and stopped 2–3 m after exiting the volume to ensure steady-state walking.

• Circular walking: Patients and control subjects walked around a circle outlined on the floor (diameter 1.2 m). They executed one full turn, stopped at the starting point, turned around 180°, and then walked one full turn in the other direction. This was repeated five times both clockwise (CW) and counterclockwise (CCW), i.e., 10 revolutions around the circle. To encourage an erect posture, subjects were asked to try to maintain the head in a straight-ahead position without staring at the floor. All subjects started with EO condition and then repeated the same number of trials with EC. The starting point in the room (initial start position) was changed across subjects to avoid the use of auditory cues as a reference.

All tasks were performed with arms crossed to avoid obscuring leg markers with the arms. In the EC condition for circular walking, the subjects were asked to stop when they thought they had completed a full revolution. They were not given any feedback on their position until they stopped (unless they went so far off track that they needed to be stopped to avoid hitting a wall). For further details on the experimental procedures, please see Paquette et al. (2011).

Healthy controls (Ctrl_PD and Ctrl_CA) first executed straight-ahead and circular walking (10 trials with eyes-open and 10 trials with eyes-closed) at their self-selected speed (not analyzed in the current paper), without receiving any instruction on their speed, and then at a slower speed. The number of steps and the time taken to complete each trial was monitored and subjects were instructed to walk faster or slower and/or to take shorter or longer strides as appropriate to match the healthy control subjects’ speed to that of the patient.

Data Preprocessing

The body center of mass was defined as the arithmetic mean of the four hip marker coordinates from the left and right, anterior and posterior iliac spines. Data were interpolated using a cubic spline to remove high frequency noise and smoothed by fitting to a second order Fourier series to remove the effect of lateral sway, which is more significant at slower speeds as in the current experiment.

The direction of locomotion was defined according to the first time derivative of the position of the body center in the horizontal plane. For each time point, the direction of locomotion and the position of the body center were used to map the leg markers from an extrinsic room-referenced coordinate frame to an intrinsic body-referenced frame (subtracting the body center’s coordinates from the markers’ coordinates and rotating according to the direction of locomotion).

Limb segments were defined according to the following pairs of joint markers: 1) thigh, greater trochanter (hip) to the lateral femoral epicondyle (knee); 2) shank, knee to lateral malleolus (ankle); and 3) foot, ankle to hallux (great toe). Elevation angles were defined as the angle between the limb segment projected onto the sagittal plane and the vertical axis, namely gravity (Borghese et al. 1996). In addition, the pelvis elevation angle (the elevation angle of the vector orthogonal to the plane of the pelvis as defined by the superior iliac spine pelvic markers) and the trunk elevation angle (the elevation angle of the trunk segment as defined by the midpelvic point and the midshoulder point) were calculated.

An automatic algorithm using a combination of local minima and zero-crossings for the position and time derivatives of position of heel and toe markers was used to determine the time points of heel strikes to parse the data into individual gait cycles, as based on previous studies (Borghese et al. 1996; Ivanenko et al. 2007).

Calculation and Definition of Basic Gait Parameters

For each gait cycle, the following basic gait parameters were calculated: 1) gait speed: the time derivative of the horizontal position of the body center; 2) stride length: distance between two consecutive heel strikes; 3) gait cycle duration: time elapsed between two consecutive heel strikes of the same leg; 4) stance width: the distance between the midpoints between the heel and toe of both legs during double stance in the frontal plane (i.e., perpendicular to the direction of gait).

Statistical Analysis

Gait cycles of each leg from straight-ahead path trials were designated as “straight-ahead” and in a circular path as “inside” or “outside” according to the leg and the direction of the gait path. There were six experimental conditions: 1) eyes-open, straight-ahead (EO-sa), 2) eyes-open, inside (EO-ins), 3) eyes-open, outside (EO-out), 4) eyes-closed, straight-ahead (EC-sa), 5) eyes-closed, inside (EC-ins), and 6) eyes-closed, outside (EC-out). Data for each subject were averaged across cycles and trials for each of the six task conditions. The MATLAB toolbox “CircStat” for circular statistics (Berens 2009) was used for angular data assuming a von Mises distribution of the data, which is equivalent to normal distribution for angular data:

$$f\left(x\text{|}\mu ,\kappa \right)=\frac{e^{\kappa \text{cos}\left(x-\mu \right)}}{2\pi I_o\left(\kappa \right)}$$

where I₀(x) is the modified Bessel function of order 0.

Statistical analysis was performed using the linear mixed model command (LMM, based on the generalized linear model) in IBM SPSS Statistics 19. First analysis was performed on data from the eyes-open, straight-ahead (EO-sa) experimental condition only. Group was defined as a fixed effect and was tested separately for 1) PD-off-med vs. Ctrl_PD, 2) PD-on-med vs. Ctrl_PD and 3) CA vs. Ctrl_CA. Additionally, the analysis was repeated including the data from all the experimental conditions with the factors vision (eyes-open or closed) and leg direction (straight-ahead, inside, or outside) defined as repeated variables, again with group as the main effect (fixed effects design).

To test for a possible effect of disease severity on the magnitude of CVP rotation, we performed linear regression analysis on u_3t vs. disease severity scores (UPDRS for PD and SARA for CA), after averaging across trials per subject per conditions.

Calculation and Definition of Intersegmental Coordination Parameters

Intersegmental coordination parameters were calculated by PCA on elevation angles for each gait cycle separately to obtain three principal components with corresponding variabilities V₁, V₂, and V₃ and eigenvectors u₁, u₂, and u₃, as originally described by Borghese et al. (1996) and Bianchi et al. (1998b). We calculated the planarity index (PI), a measure of the extent of planarity as defined by Eq. 1 below.

The pattern of intersegmental coordination of each limb in the sagittal plane was described by the temporal covariations among the elevation angles of the thigh, shank, and foot segments. The statistical structure underlying the distribution of these geometrical configurations was investigated by computing the covariance matrix A of the ensemble of time-varying angles ($\vartheta$) for each individual gait cycle, the dimensions of $\vartheta$ being three times the number of time points in the gait cycle. The three eigenvectors u₁ to u₃ of A, rank-ordered on the basis of the corresponding eigenvalues, correspond to the orthogonal directions of maximum variance in the sample scatter. The best-fitting plane of angular covariation, from here on the CVP, is formed by the first two eigenvectors u₁ to u₂. The third eigenvector (u₃) is the normal to the plane and defines the plane orientation in the position-space of the elevation angles. For each (j^th) eigenvector, the parameters correspond to the direction cosines with the positive semiaxis of the thigh (u_jt), shank (u_js), and foot (u_jf) angular coordinates, as originally described by Borghese et al. (1996).

$$p{c}_j=u_j\left(\begin{array}{c}{\vartheta }_t\\ {\vartheta }_s\\ {\vartheta }_f\end{array}\right)$$

Planarity index of the elevation and anatomical angles.

We calculated the PI, a measure of the extent of planarity, according to the equation below:

$$PI=\frac{V_1+V_2}{V_1+V_2+V_3}\times 100\%$$ (1)

This variable represents a measure of the compliance with the law of planar covariation.

Percentage variance of the second principal component.

$$PVPC2=\frac{V_2}{V_1+V_2+V_3}\times 100\%$$ (2)

This variable represents a measure of the energy of the elevation angles in the second principal component and correlates with the width of the covariation loop.

Eccentricity.

This refers to the extent of stretch of the covariation loop projected onto the covariation plane when approximated to an ellipse. A value of 1 is a straight line and 0 is a circle.

$$e=\sqrt{1-\frac{V_2^2}{V_1^2}}$$ (3)

V₁ is the 1st eigenvalue and V₂ is the 2nd eigenvalue.

This variable also correlates with the width of the covariation loop.

Shape.

The perimeter divided by the square root of the area as defined by Hallemans and Aerts (2009).

$$Shape=\frac{Perimeter}{\sqrt{Area}}$$

$$Perimeter=\sum \sqrt{{\left(x_{i+1}-x_i\right)}^2+{\left(y_{i+1}-y_i\right)}^2}$$

$$\begin{array}{l}Area=\sum \frac{1}{2}\cdot \left[\sqrt{{\left(x_i-\overline{x}\right)}^2+{\left(y_i-\overline{y}\right)}^2}\right]\\ \hspace{1em}\hspace{0.17em}\hspace{1em}\hspace{1em}\hspace{0.17em}\cdot \left[\sqrt{{\left(x_{i+1}-\overline{x}\right)}^2+{\left(y_{i+1}-\overline{y}\right)}^2}\right]\cdot \text{sin}\left(\vartheta \right)\end{array}$$

$$\vartheta =atan\left[\frac{\sqrt{{\left(x_{i+1}-\overline{x}\right)}^2+{\left(y_{i+1}-\overline{y}\right)}^2}}{\sqrt{{\left(x_i-\overline{x}\right)}^2+{\left(y_i-\overline{y}\right)}^2}}\right]$$ (4)

This variable represents a measure of the noise or variability of the data.

Orientation of the CVP (u_3t).

The thigh coordinate of the unit direction vector u₃ (the 3rd eigenvector derived by PCA).

$$u_3=\left(\begin{array}{c}{u}_{3t}\\ u_{3s}\\ u_{3f}\end{array}\right)$$ (5)

This variable has been shown to vary with gait speed, gait type, and bodily expression of emotion.

Shank-foot phase shift.

The phase of the fundamental harmonic of the shank elevation angle minus the phase of the fundamental harmonic of the foot elevation angle (derived from the 3rd order Fourier decomposition; see Eq. 6). The nomenclature is as such: ${\phi }_{1s}-{\phi }_{1f}$.

This variable has been shown to relate to u_3t.

Shank-foot correlation.

Pearson correlation between the shank and foot elevation angle time courses.

This variable may be of relevance to dimension reduction.

The A_1sA_1f product.

The product of the amplitudes of the first harmonics of the shank and foot elevation angles.

This variable represents the second component of the predicted orientation of the plane.

The predicted orientation of the plane (u_{3t_p}).

This was calculated according to the oscillators-based mathematical model; see Eq. 6 from Barliya et al. (2009):

First the elevation angles are decomposed into a 3rd order Fourier series as such:

$$\begin{array}{l}{\vartheta }_i\left(t\right)=a_{0i}+A_{1\text{i}}sin\left({\omega }_{i}t+{\phi }_{1i}\right)+A_{2i}sin\left(2{\omega }_{i}t+{\phi }_{2i}\right)\\ \hspace{1em}\hspace{0.17em}\hspace{1em}\hspace{0.17em}\hspace{1em}+A_{3i}sin\left(3{\omega }_{i}t+{\phi }_{3i}\right)\end{array}$$ (6)

where $\omega$ is the fundamental frequency, and there are three harmonics, one for each elevation angle: thigh, shank, and foot. Each harmonic has an amplitude and phase ($A_{1t}$ and ${\phi }_{1t}$ for thigh, $A_{1s}$ and ${\phi }_{1s}$ for shank, and $A_{1f}$ and ${\phi }_{1f}$ for foot).

Then the expression for each elevation angle is expressed as a 1st order cosine curve using the phase and the amplitudes of the first term (the fundamental), as such:

$${\vartheta }_t\left(t\right)=a_x+A_{1t}\sin \left({\omega }_{t}t+{\phi }_{1t}\right)$$

$${\vartheta }_s\left(t\right)=a_y+A_{1s}\text{sin}\left({\omega }_{s}t+{\phi }_{1s}\right)$$

$${\vartheta }_f\left(t\right)={\text{a}}_{\text{z}}+{\text{A}}_{1\text{f}}\text{sin}\left({\text{ω}}_f\text{t}+{\phi }_{1f}\right)$$

According to the Barliya et al. (2009) model, the expression for the predicted u₃ is thus:

$$u{3}_p=\left[\begin{array}{c}-A_{1s}{A}_{1f}sin\left({\phi }_{1s}-{\phi }_{1f}\right)\\ A_{1t}{A}_{1f}sin\left({\phi }_{1t}-{\phi }_{1f}\right)\\ -A_{1t}{A}_{1s}sin\left({\phi }_{1t}-{\phi }_{1s}\right)\end{array}\right]$$ (7)

This variable is of interest in testing the validity of the oscillators model in PD and CA.

Model error.

The angle subtended between the predicted and the actual u₃.

Predicted eccentricity.

Predicted eccentricity was also calculated according to the oscillators-based mathematical model; see Barliya et al. (2009):

$$e_p=\sqrt{1-\frac{si{n}^2\left({\phi }_{1t}-{\phi }_{1s}\right)}{4A_{1t}{}^2{A}_{1s}{}^2}}$$ (8)

Eccentricity error.

$$e_{err}=\frac{e_p-e}{e}\times 100\%$$ (9)

RESULTS

Clinical characteristics for patients vs. their respective control groups are presented in Table 2. P-values are not displayed, but all values (using t-test for parametric data and χ² for categorical data) were all nonsignificant for age, gender, height, and weight comparing each patient group with their respective controls.

Basic Gait Parameters

As intended by the design of the experiment, the gait speed and stride length of the control subjects matched their respective patient groups with the exception of PD-on-med (faster gait speed) and CA (shorter stride length) (see Table 3 and Fig. 2. Gait cycle duration was longer in both control groups (above 1.27 s) when compared with their respective control groups (less than 1.19 s), P < 0.001 for CA and PD-off-med and P < 0.01 for PD-on-med (see Table 3 and Fig. 2) Stance width was narrower in PD (on and off medication) and wider in CA than in their respective controls.

Table 3.

Global gait kinematics

	Ctrl_PD	PD-off-med	PD-on-med	Ctrl_CA	CA
Speed, m/s	0.54 ± 0.14	0.57 ± 0.14	0.60 ± 0.17*	0.48 ± 0.12	0.48 ± 0.10
Stride length, m	0.96 ± 0.22	0.94 ± 0.22	1.00 ± 0.23	0.86 ± 0.18	0.72 ± 0.17**
Cycle duration, s	1.27 ± 0.15	1.17 ± 0.17***	1.19 ± 0.20**	1.28 ± 0.18	1.14 ± 0.14***
Stance width, mm	168 ± 18	156 ± 18***	145 ± 19, P < 10−7***	156 ± 19	200 ± 44, P < 10−5***

Values are displayed as mean ± SD. Ctrl_PD, control subjects matched for Parkinson's disease, PD-off-med, Parkinson’s disease in off-medication, PD-on-med, Parkinson’s disease in on-medication, Ctrl_CA, control subjects matched for CA, CA, cerebellar ataxia.

^*P < 0.05,

^**P < 0.01,

^***P < 0.001.

The P values for both PD-off-med and PD-on-med refer to Ctrl_PD.

Fig. 2.

Basic gait parameters. Speed is well matched for all groups apart from PD-on-med where the matched controls walked slightly too slowly. Stride length is shorter in CA than CA controls, cycle duration was shorter for all patient groups than their controls, and stance width was narrower in PD-off-med and PD-on-med but wider in CA. Bars represent the means and error bars represent the standard deviations. CA, cerebellar ataxia; Ctrl_CA, control subjects matched for CA; Ctrl_PD, control subjects matched for Parkinson's disease; PD-off-med, Parkinson’s disease in off-medication state; PD-on-med, Parkinson’s disease in on-medication state. The P-values relate to the comparison between each patient group and their respective control group, namely: PD-off-med vs. Ctrl_PD, PD-on-med vs. Ctrl_PD and CA vs. Ctrl_CA.

Intersegmental Coordination

The findings relating to intersegmental coordination and the oscillators-based mathematical model are summarized in Table 4 and Figs. 4, 5, and 6. The mean PI of elevation angles was above 97.7% for all groups with the exception of CA: 96.1% vs. 97.7% for Ctrl_CA, P < 0.001. The PI of anatomical angles was smaller than the PI of elevation angles (95.1 to 95.7%) for all groups. Thus, the law of planar intersegmental coordination was found to be essentially preserved across all groups. Only in CA, there was a reduced PI for the CA group, which may be reflected by the reduced correlation between the shank and foot (Hicheur et al. 2006); see Fig. 3. However, in the PD-off-med and PD-on-med groups, there was also reduced shank-foot correlation (smaller effect size than in CA, but statistically significant), which did not correspond to any reduction in planarity.

Table 4.

Intersegmental coordination parameters

	Ctrl_PD	PD-off-med	PD-on-med	Ctrl_CA	CA
PI elevation angles, %	98.1 ± 1.4	98.0 ± 1.4	98.0 ± 1.4	97.7 ± 1.2	96.1 ± 2.6***
PI anatomical angles, %	95.7 ± 1.0	95.7 ± 1.0	95.1 ± 1.6*	95.4 ± 1.4	95.7 ± 1.2**
Percentage variance PC2, %	12.9 ± 2.0	13.9 ± 1.5**	13.6 ± 1.5*	12.4 ± 2.2	16.7 ± 4.7, P < 10−7***
Eccentricity, %	98.7 ± 0.5	98.5 ± 0.5**	98.6 ± 0.4	98.8 ± 0.6	96.0 ± 9.3, P < 10−5***
Shape	1.8 ± 0.2	1.7 ± 0.2**	1.8 ± 0.3	1.9 ± 0.4	2.0 ± 0.4
u3t, °	17.3 ± 4.1	18.9 ± 6.8*	19.5 ± 4.8**	17.8 ± 5.4	1.7 ± 16.7, P < 10−5***
Shank-foot phase shift, °	33.2 ± 12.8	38.7 ± 11.1**	37.0 ± 10.9*	31.3 ± 9.6	21.2 ± 22.8**
u3t_p, °	28.8 ± 7.0	32.2 ± 7.9**	30.9 ± 7.9	29.2 ± 6.9	13.3 ± 13.4, P < 10−6***
Shank-foot correlation, °	0.92 ± 0.04	0.91 ± 0.04**	0.92 ± 0.03*	0.92 ± 0.04	0.80 ± 0.20**
A1 sA1f product	0.11 ± 0.01	0.12 ± 0.01	0.12 ± 0.01	0.09 ± 0.01	0.07 ± 0.01**
u3t_p, °	28.8 ± 7.0	32.2 ± 7.9**	30.9 ± 7.9	29.2 ± 6.9	13.3 ± 13.4, P < 10−6***
Error, °	1.6 ± 0.1	1.6 ± 0.1	1.7 ± 0.2	1.5 ± 0.1	1.5 ± 0.1
Predicted eccentricity, %	95.0 ± 1.0	95.0 ± 1.0	93.0 ± 0.7*	98.8 ± 0.3	98.3 ± 0.2
Eccentricity error, %	−5.44 ± 8.04	−4.74 ± 6.80	−7.03 ± 9.31*	−1.83 ± 5.85	4.55 ± 24.4

Ctrl_PD, control subjects matched for Parkinson's disease, PD-off-med, Parkinson’s disease off-medication, PD-on-med, Parkinson’s disease on-medication, Ctrl_CA, control subjects matched for CA, CA, cerebellar ataxia. PI, Planarity index; PC2, 2nd principal component, u3t, Orientation of the CVP, u3t_p, Predicted orientation of the covariation plane.

^*P < 0.05,

^**P < 0.01,

^***P < 0.001.

Fig. 4.

Parameters relating to predicted and actual plane orientation. The orientation of the CVP and parameters relating to the oscillators-based mathematical model predicting the CVP orientation. There is a large rotation effect in CA and a smaller rotation effect in PD in the opposite direction. Parameters relating to the mathematical model show group differences accordingly. In particular, there may be a scaling element as well as a phase shift element as reflected by the A_1sA_1f product to the CVP rotation effect in CA. The model error is less than 2° for all groups (P > 0.05). CA, cerebellar ataxia; Ctrl_CA, control subjects matched for CA; Ctrl_PD, control subjects matched for Parkinson's disease; CVP, covariation plane; PD-off-med, Parkinson’s disease in off-medication state; PD-on-med, Parkinson’s disease in on-medication state. The P-values relate to the comparison between each patient group and their respective control group, namely: PD-off-med vs. Ctrl_PD, PD-on-med vs. Ctrl_PD and CA vs. Ctrl_CA.

Fig. 5.

Illustration of the relationship between the elevation angle time courses and the covariation loop orientation of representative subjects from each subject group. A: PD-off-med, straight ahead, eyes open. B: Ctrl_PD, straight ahead, eyes open. C: CA, straight ahead, eyes open. D: Ctrl_CA, straight ahead, eyes open. CA, cerebellar ataxia; Ctrl_CA, control subjects matched for CA; Ctrl_PD, control subjects matched for Parkinson's disease; PD-off-med, Parkinson’s disease in off-medication state. The dotted lines in the top subplot for each subject represent the raw data points and the continuous lines represent the curve fit function using a Fourier series up to the third harmonics from which the phase and amplitude parameters for the oscillators-based model were derived (see Eq. 6 in the methods section).

Fig. 6.

The distribution of the orientation of the CVP and parameters relating to the oscillators-based mathematical model predicting the CVP orientation. Each curve represents the group-level distribution of the mean values per subject per condition pooled across subjects and conditions (A) and for the eyes open, straight ahead condition only (B), i.e., not from individual gait cycles. Each curve in C represents the distribution of the data from one subject for all gait cycles across all conditions without averaging. The curves in all the subplots represent the von Mises fit to the histogram data which is equivalent to the normal distribution for angular data, with the exception of the bottom-left subplot (A_1sA_1f product) which assumes a normal distribution. CA, cerebellar ataxia; Ctrl_CA, control subjects matched for CA; Ctrl_PD, control subjects matched for Parkinson's disease; CVP, covariation plane; PD-off-med, Parkinson’s disease in off-medication state; PD-on-med, Parkinson’s disease in on-medication state.

Fig. 3.

Planarity index, shank-foot correlation, and covariation loop width. The law of intersegmental coordination is essentially preserved across all groups. Only in CA there is a reduced planarity index for the CA group which may be reflected by the reduced shank-foot correlation. Increased covariation loop width is reflected by an increase in the percentage variance of the 2nd principal component and a decrease in eccentricity. The contour of the covariation loop is “smoother” in PD-off-med as reflected by the lower “shape” parameter and less regular in CA (not significant). Bars represent the means and error bars represent the standard deviations. CA, cerebellar ataxia; Ctrl_CA, control subjects matched for CA; Ctrl_PD, control subjects matched for Parkinson's disease; PI, planarity index; PD-off-med, Parkinson’s disease in off-medication state; PD-on-med, Parkinson’s disease in on-medication state. The P-values relate to the comparison between each patient group and their respective control group, namely: PD-off-med vs. Ctrl_PD, PD-on-med vs. Ctrl_PD and CA vs. Ctrl_CA.

Increased covariation loop width was observed both in PD and CA, with the effect size and statistical significance being much greater for CA, as reflected by an increase in the percentage variance of the second principal component [PD-off-med (P < 0.01), PD-on-med (P < 0.05), CA (P < 10⁻⁷)], and a decrease in eccentricity [PD-off-med, (P < 0.01), CA (P < 10⁻⁵)]. Eccentricity value approaches 1 (or 100%) as the ellipse approaches a line and width decreases and approaches 0 as the ellipse approaches a circle. The contour of the covariation loop is “smoother” in PD-off-med as reflected by the lower “shape” parameter (P < 0.01), but less smooth in CA (not significant). Predicted eccentricity was smaller in PD-on-med than controls and the eccentricity error was negative in PD-on-med vs. controls (see Table 4 and Fig. 3).

With respect to the orientation of the CVP, which reflects kinematic synergies, and parameters relating to the oscillators-based mathematical model predicting the CVP orientation, there was a large rotation effect in CA (1.7 ± 6.7°) vs. Crl_CA (17.8 ± 5.4°, P < 10⁻⁵) and a smaller rotation effect in PD in the opposite direction (PD-off-med: 18.9 ± 6.8°, PD-on-med: 19.5 ± 4.8°, Ctrl_PD: 17.3 ± 4.1°, P < 0.05). The shank-foot phase shift differed between subject groups consistently with the prediction of the mathematical model; however, the A_1sA_1f product only differed between the CA and Ctrl_CA groups. Lastly, the reliability of the mathematical model was also reflected in low model error values: less than 2° for all groups (P > 0.5) (see Fig. 4).

The oscillators-based model based on Fourier analysis predicts that the orientation of the plane is mostly determined by the phase lag between the shank and foot elevation angles (Barliya et al. 2009). Consistent with this, more positive u_3t (seen in both PD-off-med vs. Ctrl_PD and PD-on-med vs. Ctrl_PD) was associated with an increased shank-foot phase lag (namely, the shank led the foot to a greater extent): PD-off-med: 38.7 ± 11.1°, P < 0.01, and PD-on-med: 37.0 ± 10.9°, P < 0.05, vs. Ctrl_PD: 33.2 ± 12.8°. Less positive u_3t (seen in CA vs. Ctrl_CA) was associated with a reduced shank-foot phase lag (the shank led the foot by a smaller amount): 21.2 ± 22.8° in CA vs. 31.3 ± 9.6° in Ctrl_CA, P < 0.01.

Furthermore, the plane orientation as predicted by the mathematical model was more positive in the u_3t direction in PD vs. Ctrl_PD but only significantly for PD-off-med: 32.2 ± 7.9 vs. 28.8 ± 7.0, P < 0.01 and less positive in CA vs. Ctrl_CA: 13.3 ± 13.4 vs. 29.2 ± 6.9, P < 10⁻⁶. Thus, the direction of change in the predicted orientation of the plane was consistent with the change in the actual orientation of the plane.

We also compared the product of the amplitudes of the first harmonic of the shank and foot elevation angles, which comprises the other component of the predicted u_3t term in the mathematical model (see Eq. 7 in Calculation and definition of intersegmental coordination parameters in the methods section above. The effect of CA and PD was consistent with the direction of change of u_3t but was statistically significant only for CA vs. Ctrl_CA: 0.07 ± 0.01 vs. 0.09 ± 0.01, P < 0.01 (see Table 4 and Fig. 4).

Individual elevation angle time courses and covariation loop plots from gait cycles for representative subjects from each subject group are shown in Fig. 5 and data distributions on both the group and the individual levels are shown in Fig. 6.

The effect of disease severity was pronounced in CA (P < 0.001) with increasing disease severity being associated with a lower or more negative u_3t thus diverging away from the CA control group. In the case of PD there was a disease severity effect in both the on- and off-medication states but this effect resulted in a change in u_3t such that subjects with more severe clinical disease severity scores in fact have u_3t values closer to the PD control group. On the other hand, this relationship between u_3t and severity appears to be less pronounced for PD-off-med than PD-on-med (P < 0.01 for PD-off-med and P < 0.001 PD-on-med). These findings are shown graphically in Fig. 7.

Fig. 7.

Relationship between disease severity, speed, and CVP orientation. Scatter plots and linear regression analysis of 1) 1st row: CVP orientation (u3t) vs. clinical score of disease severity (UPDRS part III for PD and SARA for CA), 2) 2nd row: CVP orientation (u3t) vs. gait speed for control groups only and 3) 3rd row gait speed vs. disease severity for patient groups only. One regression is performed per subject group on the pooled data from all conditions: inside, straight ahead and outside in separate subplots and eyes open and eyes closed overlaid. The inserted table shows the slope of the regression and the P-value. CA, cerebellar ataxia; Ctrl_CA, control subjects matched for CA; Ctrl_PD, control subjects matched for Parkinson's disease; CVP, covariation plane; PD, Parkinson's disease; PD-off-med, Parkinson’s disease in off-medication state; PD-on-med, Parkinson’s disease in on-medication state; SARA, Scale for the Assessment and Rating of Ataxia; UPDRS, Unified PD Rating Scale.

Lastly, even though speed was well controlled for, given that speed has been shown to affect CVP orientation and that inherently there was a certain range of speeds for each subject group, we explored whether gait speed differences may explain the findings by comparing our data set visually with that of Bianchi et al. (1998b). They showed that at low speeds there was minimal or no correlation between gait speed and CVP orientation. By superimposing our data on an adapted figure from Bianchi et al. (1998b) we show that the gait speeds of the data set in the present study corresponded to these low gait speeds where there was no correlation with CVP orientation (see Fig. 8).

Fig. 8.

Correlation between gait speed and CVP orientation. At low speeds there is minimal or no correlation between gait speed and CVP orientation. We show here our data (unfilled circles, with color code according to subject group as shown in the key) superimposed on an adapted figure from Bianchi et al. (1998b). Over the whole range of gait speeds in the Bianchi data set (filled black circles) there is a negative correlation between gait speed and u_3t (blue regression line). At lower speeds, however, energy expended is independent of plane orientation in both data sets. Note that the units of the y-axis scale are radians, 0.5 radians is ~29°. CA, cerebellar ataxia; Ctrl_CA, control subjects matched for CA; Ctrl_PD, control subjects matched for Parkinson's disease; CVP, covariation plane; PDOFF, Parkinson’s disease in off-medication state; PDON, Parkinson’s disease in on-medication state.

DISCUSSION

The three main findings presented here are 1) the law of planarity was essentially preserved in BG and CBL pathology as reflected by the high planarity indices in the PD and CA groups, 2) PD and CA were associated with opposite effects on the patterns of intersegmental coordination as reflected by the orientation of the CVP, and 3) the oscillators-based model of locomotor control successfully predicted CVP orientation.

Intersegmental Coordination and CVP Features

CVP planarity.

Regarding planarity, despite a small but statistically significant smaller PI in CA vs. Ctrl_CA, we report high PI values (>96%, similar to previously reported results in the literature) in all subject groups, thus supporting the ubiquity and robustness of the planar covariation of intralimb elevation angles, even in the presence of BG and cerebellar pathologies. The robustness of this law shown here, together with supporting empirical evidence emerging from the use of physiological (Ivanenko et al. 2008) and computational approaches (Hoellinger et al. 2013), adds further support to the notion that elevation angles may represent key variables subserving central nervous encoding of human locomotion (Ivanenko et al. 2008).

Comparing the properties of the CVP and the predicted model of “normalcy” to those observed in pathological conditions provides an opportunity to derive information on the contribution of different neural structures to the control of intralimb coordination. Our results, showing preservation of the law of planarity in patients with damaged BG or CBL, are consistent with earlier findings demonstrating that rhythmical leg movements are generated by central pattern generators (CPGs), dispersed over several spinal segments (Guertin 2009).

CVP orientation.

The second finding was that the effects of PD and CA on the observed patterns of intersegmental coordination, as reflected by the orientations of the CVP, give rise to rotations of the CVP orientations in opposite directions in PD vs. cerebellar patients, with respect to the orientation observed in control subjects. This finding suggests functional differences between the roles of the CBL vs. the BG in modulating the waveforms and durations of the latent kinematic synergies operating during human locomotion. Our results suggest that 1) cerebellar networks have a greater influence than the BG networks on the kinematic intersegmental coordination patterns and 2) the two networks may in some aspects have opposite influences on the motor system.

The Oscillators-Based Model of Locomotor Control

The CVP orientation is predicted by the oscillators-based model of locomotor control (Barliya et al. 2009), as well as its two components: 1) the phase shift between the shank and foot segment oscillators and 2) the product of the amplitudes of the first harmonics of the shank and foot elevation angles (see Eq. 7). Both of these components differed among the subject groups and these effects were consistent with observed changes in the actual orientation of the covariation plane. The only significant group effect on phase shift and product was for CA vs. Ctrl_CA. In the cerebellar patients, we observed a smaller phase shift between the shank and foot, with the foot being rotated earlier with respect to the shank in CA vs. controls. The CA foot amplitude was also smaller in magnitude, which is consistent with the findings of Serrao and colleagues (Serrao et al. 2012; Serrao and Conte 2016) which showed a smaller range of motion of the ankle joints in CA vs. control subjects. In PD the CVP orientation rotated in opposite direction compared with controls with a larger difference between the shank and foot phases. Our observations and their interpretation in view of the mathematical model of Barliya et al. (2009) support the usefulness and validity of applying this model, which predicts the orientation of the covariation plane in ataxic (CA) and in parkinsonian (PD) gaits. In addition, it shows that the rotation effect in CA (and possibly also in PD) is mediated not only by the phase shift between the shank and foot elevation angles, but also by a gain factor reflected in the product of the amplitudes of the first harmonics of the motion of the shank and foot elevation angles. The change in CVP orientation independently of gait speed between the subject groups, which is reported here, complements the findings that plane orientation changes with emotional state (Barliya et al. 2013), beyond changes related to speed modification. Together, the results reported here support the fundamental role of phase relationships of elevation angles in gait control, which are likely to emerge from the fine-tuning of the coupling between spinal CPGs controlling muscle synergies, leading to appropriate coordination between the oscillatory time courses of proximal elevation angles, needed to create kinematic synergies.

In particular, here we provide evidence that the phase shift between the shank and foot segment oscillators is altered by PD and CA in a manner that is independent of gait speed. This supports the notion that supraspinal loops involving the BG and the CBL play a role in modulating gait patterns as reflected in intersegmental coordination patterns and elevation angle phase shifts. The mechanisms underlying the control of these phases and intersegmental coordination patterns are not yet understood although some clues can be derived from earlier studies quantifying muscle activations and joint rotation kinematic patterns.

We propose that the CBL modulates spinal CPG phase relationships affecting the intersegmental coordination patterns and, in particular, the CVP orientation. Consistent with this interpretation are the observations made by Martino et al. (2014, 2015) who have recorded and analyzed muscle activation patterns in ataxic patients (Martino et al. 2014) and healthy subjects during regular gait or gait performed in several unstable conditions (Martino et al. 2015). Their observations regarding the change in CVP orientation were similar to ours and to observations made in healthy subjects walking in unstable conditions. Additionally, their findings showed that in CA and unstable conditions the variations of the EMG waveforms were accounted for by four control modules (synergies) characterized by temporal widening of the muscle activation patterns. Their interpretation of these findings were that the nervous system adopts a strategy of prolonging the basic muscle activity temporal patterns to cope with the instability resulting from cerebellar pathology. Prolonging muscle activation patterns may affect the shape and phases between the different waveforms representing the oscillatory movements of the different limb segments as schematized by the Barliya et al. (2009) model, leading to deviations of the CVP orientation from those found in healthy subjects.

Regarding previous literature on intersegmental coordination in PD the reported effect on CVP orientation is sparse and somewhat inconsistent. Grasso et al. (1999) found a rotation of the CVP with less positive u_3t in PD patients treated with D1-D2 receptor agonist treatment (n = 5, ~18.9° off treatment and ~17.5° on). In contrast, DBS of the globus pallidus internus resulted in more positive u_3t (n = 3 subjects, but was reported only for 1 subject, 5.7° with the DBS therapy turned off and 17.2° when turned on) (Grasso et al. 1999) (see Table 1. With respect to CA, MacLellan et al. (2011) showed a similar value for u_3t (~7°) in CA although their healthy controls (also matched for gait speed) had only slightly higher values (~9°). Martino et al. (2014) also showed similar deviations in the value of u_3t compared with ours: ~8.6° in CA vs. ~17.2° in controls.

With respect to the BG, our results suggest that the BG may play a modulatory role, albeit to a lesser extent than the CBL, and that spatial modulation of locomotor patterns, to a lesser extent than temporal control, may reflect the supraspinal modulatory effect of the BG on kinematic and muscle synergies. Previous work focusing on decomposing muscle activations into basic modules has shown that neuromechanical control in PD tends to be less complex and that the motor module activation profiles differ between PD and healthy controls (Rodriguez et al. 2013). Rodriguez et al. (2013) also reported a reduced number of modules in PD patients compared with healthy controls. While currently we cannot associate between these reported observations concerning muscle activation modules and our observations concerning intersegmental kinematic coordination patterns in PD, future work should try to bridge the gap between these different levels of analysis.

An additional aspect of intersegmental coordination that differed between patients vs. controls was the width of the covariation loop as reflected by the percentage variance of the second principal component and loop eccentricity. Both patient groups showed increased width of the covariation loop compared with controls, with the effects’ size and significance (in comparison to the respective controls) in decreasing order as follows: CA, PD-off-med, then PD-on-med (see Fig. 3 and Table 4). Cheron et al. (2001) showed that the planarity property of intersegmental coordination and the “mature” orientation of the plane emerges over a relatively short period of time from the first independent steps of a toddler. In contrast, the width of the covariation loop continues to mature throughout childhood and adolescence. The authors suggest that the development of the mature pattern of intersegmental coordination is mediated by the maturation of the CBL and cerebellar networks. Our results regarding the width of the covariation loop lend further support to this hypothesis, namely that with cerebellar disease the pattern of CPG activity returns to the more immature state.

Consideration of Energetics/Metabolic Cost

Our results together with previous analysis of energy expenditure as a function of speed indicate that any change in CVP orientation at speeds below 1.1 m/s does not have any effect on energy expenditure. From Fig. 4 it can be seen that when our data are overlaid on the figure from Bianchi et al. (1998b) the energy contour lines at gait speeds up to 1.1 m/s are orthogonal to the x-axis (gait speed). Furthermore, inspection of Fig. 4 reveals that the gait speed-plane orientation association becomes weaker at lower gait speeds with a broadening of the distribution of u_3t. It is also possible that there is a ceiling effect on gait speed and/or plane orientation in patients, whereby the maximum gait speed and u_3t are reached earlier. This may be due to neuronal or biomechanical factors or a combination of the two.

Alternative variables including subject-specific factors may need to be taken into account to explain the broad distributions of u_3t despite a relatively narrow range in gait velocity. For example, it has been shown that the emotional valence of locomotion (i.e., bodily expressed emotion in gait) can affect CVP orientation beyond the effect of gait speed, whereby anger and sadness are associated with both speed-dependent and speed-independent CVP rotation in the direction of lower speed (i.e., increased shank-foot phase shift and increased u_3t) (Barliya et al. 2013).

While in the current study the range of walking speeds was limited, increasing gait speed is accompanied with reduced u_3t, which was shown to allow a reduction in the increased energy costs associated with faster walking (Bianchi et al. 1998b). Since higher activity energy expenditure per step count was reported in CA (Mähler et al. 2014) and the increase in the duration of EMG bursts in CA is also likely to lead to increased metabolic costs (Martino et al. 2014), the plane orientation rotation effect in CA is likely to be compensatory and adaptive.

Similarly it has been shown that walking economy is poorer in PD, i.e., there is greater energy expenditure (Christiansen et al. 2009; Gallo et al. 2013; Maggioni et al. 2012). This may, at least in part, be related to the characteristic bent posture in PD and the increased muscle tone associated with parkinsonian rigidity. Indeed, Grasso et al. (2000) showed higher amounts of EMG activity in healthy controls walking with a bent posture together with an increase in the u_3t from 12.6 to 38.4°, but to our knowledge a similar study has not been performed in PD subjects. PD symptoms may reflect energy-saving strategies to compensate for energy imbalance due to impaired mitochondrial function (Amano et al. 2015), but the direction of rotation of the CVP in PD observed in the present study is in the direction of reduced energy efficiency and thus may be either a direct result of PD pathophysiology or a maladaptive compensatory mechanism. Another factor that may affect the energetic expenditure in PD is movement vigor, reported to be affected in PD (Mazzoni et al. 2007). While the interplay between energy expenditure and vigor has been studied earlier by analyzing end-effector motion (Mazzoni et al. 2007), it has not been studied yet in the context of multijoint movements and remains to be investigated in future studies.

Cerebellar-Basal Ganglia Respective Functional Roles and Interactions

Given that in this paper we have focused on analyzing the movement kinematics rather than kinetics or muscular activation patterns, it is hard to infer the possible roles of the BG and CBL in modulating the activities of muscles within different muscular synergies. Thach (2014) has reviewed different possible functions of the CBL in movement initiation or the formation of muscle synergies. The role of the CBL in compensating for accounting for intersegmental interaction torques was examined by Bastian et al. (1996) and by Ghez and Sainburg (1995). Currently available understanding concerning the formation and the number of muscular synergies underlying human locomotion in healthy subjects vs. movement disorders was discussed in a recent review by Ting et al. (2015). However, based on the findings presented here, it is too early to speculate about the possible roles of the BG vs. CBL in the formation, temporal recruitment, and scaling of different muscle synergies, nor will it be possible here to infer the respective roles of the BG vs. the CBL in controlling either kinematic or muscular synergies or both.

Another relevant topic in view of the recent interest in muscle synergies is the interactions between the cerebellar and basal ganglia loops in controlling human locomotion. Basal ganglia and cerebellar interactions were thought to occur throughout the multiple cortical areas to which they both project (Doya 2000), but over the last decade this view has been challenged based on neuroanatomical evidence in nonhuman primates of dense reciprocal connections between the two structures (Bostan et al. 2013). It has been speculated that abnormal activity at one node can percolate throughout the entire network to cause dysfunction at other nodes in the network (Bostan and Strick 2018; Bostan et al. 2018) which may be compensatory or maladaptive (Bostan and Strick 2018). The implications of these connections on a functional level both in health and disease are yet to be fully understood. The CBL and BG have opposing effects on downstream influences of on cortical excitability (Doya 2000; Hallett 2006; Liepert et al. 2004; Tamburin et al. 2004), CA and PD have opposite effects on cerebellar activity in human functional imaging studies (Catalan et al. 1999; Nakamura et al. 2015; Stefanescu et al. 2015; Yu et al. 2007); muscle tone, increased in PD (Berardelli et al. 1983; Cantello et al. 1991, 1995) and possibly reduced in CA (at least acutely) (Holmes 1939; King 1948); and muscle force/movement speed is bradykinetic in PD (Berardelli et al. 1983, 2001) and hyperkinetic in CA (Manto et al. 2012).

Concerning the possible role of the CBL in motor timing it is worthwhile to mention the importance of the different types of cerebellar oscillations, a topic that is reviewed in Cheron et al. (2016). This review highlighted the importance of the subthreshold oscillations of the inferior olive (IO) as described in the seminal paper by Llinás (2009). The IO definitely determines the oscillatory behavior of the Purkinje cells in the cerebellar cortex and the output of the deep cerebellar nuclei (DCN) to the red nucleus and the thalamus. Here it is also relevant to mention that, in a recent study, a dynamic recurrent neural network (DRNN) based on mimicking the natural oscillatory behavior of human locomotion was developed (Hoellinger et al. 2013). The network took the first three harmonics of the sagittal elevation angles of the thigh, shank, and foot of each lower limb to reproduce the planar covariation in both legs at different walking speeds. This study reinforced the present oscillatory approach and showed that the proportion of inhibitory connections (inherently presented both in the BG and in the CBL networks) consistently increased with the number of neuronal units and the related performance of the DRNN.

Here, we propose an additional opposing functional reciprocity of the CBL and the BG: the top-down control of phase patterns of intralimb intersegmental elevation angles and thus their movement patterns. Another interesting finding of the current study is with respect to disease severity. In CA there was a greater CVP rotation with increasing disease severity, but in PD the magnitude of rotation of the CVP compared with controls in fact decreased with increasing disease severity (see Fig. 3). Both the disease and disease severity effects were much weaker in PD than in CA. While investigating further the possibly different roles of the BG and CBL in controlling the intersegmental phases it is interesting to note that the DCN input to the thalamus is excitatory while the input of the internal part of the globus pallidus (GPi) to the thalamus is inhibitory. This could possibly facilitate the control of the oscillatory phase implicated in the final emergence of the planar covariation of lower limb coordination. Another important topic is the role of CBL in PD, since there is evidence that cerebellar pathways may serve a compensatory role (Appel-Cresswell et al. 2010; Bezard et al. 2003; Holschneider et al. 2007).

In this context, it could also be suggested that interventional studies, involving for example noninvasive neuromodulatory brain stimulations targeted to the CBL in PD and CA patients, would allow the purported role of the CBL in tuning and modulating intersegmental coordination, as reflected by changes in the loop width and orientation, to be directly tested. Furthermore, given that the degree and the direction of connectivity between the CBL and BG changes with age (Hausman et al. 2018), PD (Festini et al. 2015; Kwak et al. 2010), and dopamine treatment (Festini et al. 2015; Kwak et al. 2010), it remains to be determined whether and how CBL-BG connectivity correlates with the shape and the orientation of the CVP.

One potential limitation of this study is that, to avoid obscuring the body markers, all subjects walked with their arms crossed. This was at the cost of the gait being less natural, especially for the non-PD groups. An additional potential confound is that, to control for gait speed, healthy controls walked at a pace that was slower than their natural pace but patients walked at their comfortable pace. Lastly, since kinematic and biomechanical parameters were matched between the patient groups and their appropriate control groups but not across each other, and PD subjects’ comfortable walking pace was faster than that of CA subjects, PD and CA subjects should not be directly compared.

Parameters of intersegmental coordination may serve as quantitative biomarkers for the diagnosis, prognosis, and follow-up of either or both PD and CA as well as other brain disorders that effect cerebellar function and motor control. Further studies incorporating neurophysiological signals into the analysis, e.g., EMG data, and biomechanical and computational models that include considerations of phase and amplitude variables and muscles’ viscoelastic properties, are needed to test how biomechanical, neuromuscular, and gait control mechanisms affect and modulate CVP orientation.

GRANTS

This work was supported by the European Union Seventh Framework Programme (KoRoibot Grant 611909 and VERE grant 257695), the National Institutes of Health National Institute of Aging R37 (grant number AG006457), and the Computational Neuroscience (CRCNS) from the United States–Israel Binational Science Foundation (grant number 2016740).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

S. D. I-K., A. B., C. P., E. F., R. I., F. B. H. and T. F. conceived and designed research; C. P. and E. F. performed experiments; S. D. I-K. and A. B. analyzed data; S. D. I-K., R. I. and T. F. interpreted results of experiments; S. D. I-K. prepared figures; S. D. I-K. drafted manuscript; S. D. I-K., A. B., C. P., E. F., R. I., F. B. H. and T. F. edited and revised manuscript; S. D. I-K., A. B., C. P., E. F., R. I., F. B. H. and T. F. approved final version of manuscript.