Neuroscience 273 (2014) 189–198
VARIABILITY, FREQUENCY COMPOSITION, AND COMPLEXITY OF SUBMAXIMAL ISOMETRIC KNEE EXTENSION FORCE FROM SUBACUTE TO CHRONIC STROKE J. W. CHOW * AND D. S. STOKIC Center for Neuroscience and Neurological Recovery, Methodist Rehabilitation Center, Jackson, MS, USA
Key words: force steadiness, spectral analysis, sample entropy, knee extensors, hemiparesis.
Abstract—We examined changes in the variability, frequency composition, and complexity of force signal from subacute to chronic stage of stroke during maintenance of isometric knee extension and compared these parameters between chronic stroke and healthy subjects. The sample included 15 healthy (65 ± 8 years) and 23 chronic stroke subjects (65 ± 14 years, 6–112 months post-stroke) of whom 10 (64 ± 15 years) were also examined 11–22 days post-stroke (subacute stage). The subjects performed isometric knee extension at 10%, 20%, 30%, and 50% of peak torque for 10 s (two trials each). Coeﬃcient of variation (CV) was used as a measure of force variability. The median frequency and relative power in the 0–3, 4–6, and 8–12 Hz bands were obtained through a power spectrum analysis of the force signal. The signal complexity was quantiﬁed using the sample entropy (SampEn). The longitudinal analysis revealed a signiﬁcant decrease in CV from subacute to chronic stage across all contraction levels (P < 0.001) but no signiﬁcant changes in the frequency and entropy parameters. Comparison between the chronic stroke and control subjects revealed no signiﬁcant diﬀerence in CV across the force levels (P > 0.05) but signiﬁcantly decreased median frequency (P < 0.01), with the relative power increased in 0–3 Hz band and decreased in 4–6 and 8–12 Hz bands in both paretic and non-paretic legs (P < 0.001). SampEn was also signiﬁcantly decreased in chronic stroke, bilaterally (P < 0.001). These results indicate a shift toward lower frequencies and a less complex physiological process underlying force control in chronic stroke. The overall results suggest the improvement in force variability from subacute to chronic stroke but without normalization in the frequency composition and complexity of the force signal. Thus, disordered structure of the force signal remains a marker of impaired motor control long after stroke occurrence despite apparent recovery in force variability. Ó 2014 IBRO. Published by Elsevier Ltd. All rights reserved.
INTRODUCTION The ability to produce a steady force is impaired in stroke patients. Lodha et al. (2010) reported a signiﬁcantly greater force variability (coeﬃcient of variation (CV)) in the paretic wrist/ﬁnger extensors for nine stroke subjects (4 months to 12 years post-onset) compared to nine controls at 5%, 25%, and 50% of the maximum voluntary contraction (MVC). The greatest diﬀerence between stroke and control subjects was found for bilateral tasks at 5% and 50% of MVC (Lodha et al., 2012). Chow and Stokic (2011) examined 33 subjects within a month of stroke on the isometric knee extension task at 10%, 20%, 30%, and 50% of MVC and reported signiﬁcantly increased CV in both paretic and non-paretic legs of stroke subjects compared to controls across all force levels. In addition to simple measures of force variability (CV), nonlinear analytic approaches allow examination of the structure of force signal and provide an insight into underlying physiological processes (Schiﬀman et al., 2006). The structure of a time series includes both time (complexity analysis) and frequency (power spectrum analysis) domains. Approximate entropy, a measure of complexity structure of the force signal, was signiﬁcantly decreased in stroke subjects during a constant wrist/ﬁnger extension task, particularly at higher force levels (Lodha et al., 2010). These investigators ascribed the less complex force signal to the lack of motor adaptability associated with relatively ﬁxed or stereotypic patterns in motor coordination and abnormal movement synergies in chronic stroke. Chow and Stokic (2013) performed a power spectrum analysis on force signals during a constant knee extension task in subacute stroke and reported a shift from 4–12 Hz to 0–3 Hz. A shift toward lower frequencies within the 0–1 Hz band has also been reported in chronic stroke in an isometric grip task (Lodha et al., 2013). The predominance of lower frequencies in the power spectrum and decreased entropy during constant-force tasks have been found in Down syndrome (Heﬀernan et al., 2009) and Parkinson’s disease (Vaillancourt et al., 2001), suggesting disordered structure of the force signal across
*Corresponding author. Address: Methodist Rehabilitation Center, 1350 East Woodrow Wilson Drive, Jackson, MS 39216, USA. Tel: +1-601-364-3402; fax: +1-601-364-3305. E-mail address: [email protected]
(J. W. Chow). Abbreviations: ANOVA, analysis of variance; CV, coeﬃcient of variation; FFT, Fast Fourier Transform; FM, Fugl-Meyer scale; MVC, maximum voluntary contraction; RMI, Rivermead Mobility Index; SampEn, Sample entropy; SD, standard deviation. http://dx.doi.org/10.1016/j.neuroscience.2014.05.018 0306-4522/Ó 2014 IBRO. Published by Elsevier Ltd. All rights reserved. 189
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198
diﬀerent neurological disorders. In healthy subjects, 0–3 Hz band during a constant-force task has been associated with visuomotor processing (Freund and Hefter, 1993; Slifkin et al., 2000; Vaillancourt et al., 2001), 4–6 Hz band with long-latency stretch reﬂexes (Marsden, 1978; McAuley and Marsden, 2000), and 8–12 Hz band with short-latency stretch reﬂexes (Marsden, 1978; McAuley and Marsden, 2000). Our previous ﬁndings (Chow and Stokic, 2013) raise a question whether the increased force variability and altered force frequency characteristics observed in the subacute stage of stroke carry over into the chronic stage. Also it is unknown whether decreased complexity of the force signal in chronic stroke reported for the wrist/ﬁnger extensors (Lodha et al., 2010) also applies to the knee extensors. Therefore, the ﬁrst aim of this study was to examine changes in the variability, frequency composition, and complexity of the force signal from the subacute (within the ﬁrst month of stroke) to the chronic stage of stroke (at least 6 months post-stroke) during an isometric knee extension task. We hypothesized some degree of normalization of CV, frequency composition, and complexity of the force signal over time (hypothesis 1). Because the force structure of an isometric knee extension has not been previously investigated in chronic stroke, our second aim was to compare variability, frequency composition, and complexity of the force signal between persons with chronic stroke and healthy controls. Based on the previous ﬁndings (Lodha et al., 2010, 2013; Chow and Stokic, 2013), we hypothesized that chronic stroke subjects would show an increase in force variability, a shift toward lower frequencies in the power spectrum, and a decrease in complexity of the force signal in both the paretic and non-paretic legs compared to controls (hypothesis 2). Since the associations between force parameters and clinical measures of motor recovery were not directly related to the tested hypotheses, these correlations were explored in secondary analyses.
EXPERIMENTAL PROCEDURES Subjects Twenty-three community-dwelling persons with chronic stroke were included in this study (Table 1). The inclusion criteria were at least 6 months post-stroke, single unilateral stroke or multiple strokes on the same side, unimpaired vision (able to see a line on a monitor), able to extend both knees against gravity in the seated position, and able to follow simple instructions. Those with clinical evidence of visual (hemianopia) or perceptual (neglect) deﬁcits, heart diseases, uncontrolled hypertension, normal pressure hydrocephalus, knee pain, or artiﬁcial knee replacement were excluded. The control group included 15 subjects (age 65 ± 8 years, height 177 ± 11 cm, body mass 82 ± 14 kg, 11 men) with normal or corrected-to-normal vision and no reported orthopedic or neurological disorders at the time of testing. The age diﬀerence between the two groups was not signiﬁcant (unpaired t-test, P = 0.63). All subjects signed the informed consent approved by the institutional review board. Prior to force tasks, stroke subjects were
assessed by the same physical therapist on the lower extremity motor section of the Fugl-Meyer (FM) scale (range 0–34, Fugl-Meyer et al., 1975), modiﬁed Ashworth scale (range 1–5, Bohannon and Smith, 1987), and Rivermead Mobility Index (RMI) (maximum 15, Collen et al., 1991; Hsieh et al., 2000) (not collected in two subjects because the therapist was not available). Ten stroke subjects were tested twice – within the ﬁrst month of stroke just prior to discharge from in-patient rehabilitation and then at 6–8 months post-stroke (Table 1). They received outpatient physical and occupational therapy for up to 3 months after the inpatient discharge.
Experimental setup and protocol With the subject in a seated position, knee extension torques were collected using a Biodex System 3 isokinetic dynamometer (Biodex Medical Systems, Inc., New York, NY, USA) and a custom-built ampliﬁer connected directly to the torque sensor of the dynamometer (overall sensitivity 57.5 mV/Nm). Torque signals from the dynamometer were fed to a 17-in. LCD monitor that was mounted on a swing arm and an EvaRT data acquisition system (Motion Analysis Corp., Santa Rosa, CA, USA, sample rate 1200 Hz, 12-bit analog-to-digital resolution). Before practice trials, the monitor was positioned according to individual preferences, usually 40–50 cm directly in front of the head. Both legs of stroke patients were tested in a random order and only the self-reported dominant (preferred ball kicking) leg in controls. The warm-up included ﬁve repetitions of maximum isokinetic knee extension-ﬂexion at 210°/s and 60°/s. The subject then performed three to four trials of maximum isometric knee extension (90° angle, 3–4 s each, 1-min pause). The largest force (proportional to the largest torque because of the constant moment arm) was used as the MVC. After several practice trials, the subject was asked to extend the knee, match the displayed torque signal (a horizontal line) with a designated target force marked on the monitor (10%, 20%, 30%, or 50% of MVC), and maintain the force for 10 s, as accurately and steadily as possible. The four force levels were presented in a random order and two trials per level were completed with a 30–60-s rest in between.
Data analyses MVC torques were smoothed using a sliding average of 600 data points (0.5-s window). Torques during constant-force trials were ﬁltered using a second-order Butterworth low-pass ﬁlter with 30-Hz cutoﬀ. The CV, calculated as the ratio between standard deviation (SD) and mean torque (CV = SD/mean 100%), was used to quantify force variability (steadiness). Only the middle 8 s of each 10-s trial were analyzed to exclude the ramp up and down portions of the force signal. Out of two trials collected at each force level, the one with a lower CV was used for statistical analysis. The ratio of paretic
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198 Table 1. Subject characteristics
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Mean SD
Chronic postinjury (months)
Subacute postinjury (days)
Lower extremity Fugl-Meyer*
Rivermead Mobility Index*
F F M F F F M M M M M M F M M M F M F M F M F
64 88 79 53 77 57 56 61 58 75 80 43 53 75 82 73 62 87 55 56 39 50 62
163 157 178 165 155 163 180 175 183 170 191 173 165 173 175 183 157 173 165 179 160 168 152
55 55 80 59 64 68 75 80 98 75 94 90 78 81 71 120 86 75 88 83 81 91 55
112 16 12 14 12 14 51 15 13 18 12 14 6 7 6 7 6 6 7 6 8 6 8
n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a n/a 16 12 11 14 14 15 17 14 12 22
L L R R R L R R L L L L L L L L R L R R L R L
n/a 28 34 34 24 17 18 12 29 21 25 27 29 33 (n/a) 34 (30) 32 (31) 24 (19) 32 (30) 17 (22) 19 (16) 29 (28) 20 (14) 34 (30)
n/a 15 15 15 15 13 7 14 14 11 14 15 13 13 (n/a) 15 (13) 13 (14) 9 (5) 14 (13) 15 (13) 13 (13) 15 (15) 12 (11) 15 (15)
0.60 0.57 0.69 1.06 0.98 0.28 0.38 0.74 0.68 0.71 0.80 0.97 0.75 0.79 0.79 0.85 0.57 1.01 0.52 0.79 0.76 0.43 0.88
26.0 (27.4) 6.7 (6.7)
13.4 (13.4) 2.1 (1.9)
0.73 (0.76) 0.21 (0.19)
(0.55) (0.80) (0.78) (0.66) (0.85) (0.55) (0.14) (0.92) (0.55) (0.62)
Abbreviations: M, male; F, female; R, right; L, left; MVC, maximum voluntary contraction; n/a, not available/not applicable. * Values for subacute stage in parentheses, if applicable.
to non-paretic MVC torque was used as an index of strength asymmetry (MVC asymmetry, Table 1). The Fast Fourier Transform (FFT) function in Matlab (MathWorks, Inc., Natick, MA, USA) was used to obtain the power spectrum of the torque signals. The time constant was 8 s and the frequency bin resolution was 0.125 Hz (1200 Hz/9600 samples). We focused on the power between 0 and 12 Hz because the remaining power in the 12–20-Hz and 20–30-Hz bands accounted for only 1.08 ± 2.29% and 0.22 ± 0.51% of the total power, respectively, consistently across all subjects, limbs and force levels. Parameters extracted from the power spectrum of each trial were the median frequency (the frequency that divides the 0–12-Hz spectrum into two equal areas) and relative proportion of power in the 0–3 Hz (low-frequency band), 4–6 Hz (mid-frequency band) and 8–12 Hz (high-frequency band). The latter were computed as the ratio (%) between the integral of the power spectrum in each respective band and the integral of the power spectrum in the 0–12-Hz band (Kouzaki et al., 2004; Dewhurst et al., 2007; Muceli et al., 2011). Unlike the FFT analysis, the entropy analysis is sensitive to the sampling rate. To ensure our ﬁndings are comparable to the literature, the torque signals were down-sampled to 100 Hz before entropy computation. For assessing the complexity of knee extension force in the time domain, we chose sample entropy (SampEn) (Richman and Moorman, 2000) over the more commonly used approximate entropy (Pincus, 1991) because
SampEn has greater relative consistency and is less dependent on the dataset length (Richman and Moorman, 2000). SampEn (m, r, N) is the negative natural logarithm of the conditional probability that a dataset of length N, having repeated itself within a tolerance r for m points, will also repeat itself for m + 1 points, without allowing self matches (Lake et al., 2002). The analysis was completed using a Matlab program downloaded from the open source PhysioNet (www.physionet.org/) with N = 800, m = 3, and r = 0.2 SD of the time series (Lake et al., 2002; Simmons et al., 2012). SampEn values range from 0 (less complex) to 2 (random noise). Statistical analysis For hypothesis 1 (subacute to chronic comparison), Friedman’s non-parametric 2-way analysis of variance (ANOVA) by ranks (two Time points in columns and four Force Levels in rows) was performed on each force outcome (i.e., comparison of Time eﬀects without testing for Force Level eﬀects or interactions). Prior to testing hypothesis 2, we ﬁrst determined if the outcomes signiﬁcantly diﬀered between the 10 subjects studied twice and 13 subjects studied in the chronic stage only because the time from stroke occurrence to evaluation was borderline signiﬁcant between the two groups (7 ± 1 vs. 24 ± 29 months, unequal variance t-test, P = 0.051). Unpaired t-test and 2 Group 4 Force Level ANOVA with adjustment per Levene’s and Mauchly’s tests were used, as appropriate. No
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198
signiﬁcant diﬀerences were found for FM motor score, RMI, MVC torque, and MVC asymmetry (t-tests P P 0.353). Also, there were no signiﬁcant main eﬀects of Group (P P 0.087) or Group Force Level interactions (P P 0.289) for the CV, frequency, and entropy parameters in either leg. This justiﬁed the pooling of all data for testing hypothesis 2. For this, the paretic and non-paretic legs were separately compared to the control leg using a 2 (Leg: paretic/non-paretic, control) 4 (Force Level: 10%, 20%, 30%, 50% MVC) ANOVA with repeated measures on the second factor and Greenhouse–Geisser correction (Mauchly’s test of sphericity, P 6 0.05) for each force outcome. Because the emphasis was on between-leg comparisons and interactions, the signiﬁcant main eﬀect of Force Level was ignored to reduce the number of statistical tests (Chow and Stokic, 2013). In secondary analyses, associations between the MVC asymmetry, FM motor score, and RMI on the one side and the frequency and entropy parameters on the other side (paretic leg only) were explored at each contraction level using both linear and non-linear models. The relative spectral power in 0–3-Hz band was best ﬁtted against FM score with an adjungated hyperbolic function [Y = a/(X b) + c, where a, b, and c are constants], whereas the relative spectral power in the other two frequency bands and FM score was best ﬁtted with an exponential growth function [Y = d exp(e X), where d and e are constants]. Considering the number of statistical tests performed, the P-value was set at a more stringent level of 0.01.
RESULTS All stroke subjects were ambulatory (RMI P 7) at the chronic stage with FM motor scores from 12 to 34 on the paretic side (Table 1). Ashworth scores in the paretic knee extensors were 1 in all but one case (score of 2), indicating no clinical hypertonia. The MVC torques were signiﬁcantly lower (P < 0.001, unpaired t-test) in the paretic leg (99 ± 45 Nm) compared to either the non-paretic (138 ± 51 Nm) or control leg (164 ± 57 Nm). The diﬀerence remained signiﬁcant (P < 0.001) after MVC torque was normalized to the body mass (paretic leg 1.25 ± 0.45 Nm/kg, non-paretic leg 1.74 ± 0.47 Nm/kg, control 1.98 ± 0.58 Nm/kg). The 10 stroke subjects assessed longitudinally showed motor improvements from the subacute to chronic stage that approached signiﬁcance (FM motor score 24.4 ± 6.7 to 27.4 ± 6.7, paired t-test, P = 0.063; RMI 12.4 ± 3.0 to 13.4 ± 1.9, P = 0.081; paretic MVC torque 93 ± 50 to 110 ± 40 Nm, P = 0.102; non-paretic MVC torque 142 ± 54 to 150 ± 52 Nm, P = 0.401; MVC asymmetry 0.64 ± 0.22 to 0.76 ± 0.19, P = 0.102). As to hypothesis 1, the only signiﬁcant change from the subacute to chronic stage was a decrease in CV in the paretic leg (P < 0.001) with a similar trend in the non-paretic leg (P = 0.028) (Figs. 1 and 2). The average decrease in CV across all force levels in the paretic leg was from 5.4 ± 3.6% at subacute stage to 3.9 ± 3.7% at chronic stage (Fig. 2). The corresponding values for the non-paretic leg were 2.3 ± 1.0% and
Fig. 1. Representative torque and power spectrum proﬁles for the paretic and non-paretic legs of a stroke subject and the dominant leg of a control subject at diﬀerent force levels illustrating the shift toward lower frequencies and decreased complexity in the force structure after stroke. Dashed lines indicate target forces. Note the same 20-Nm range in torque plots and variable ranges in power spectrum plots. Abbreviations: CV, coeﬃcient of variation; SampEn, sample entropy; MF, median frequency (Hz), B1: 0–3 Hz band, B2: 4–6 Hz band, B3: 8–12 Hz band. The sum of B1, B2, and B3 is less than 100% because of the gaps between adjacent frequency bands.
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198
Fig. 2. Comparison of coeﬃcients of variations and diﬀerent frequency and entropy parameters across four force levels between the subacute stage (ﬁlled symbols) and chronic stage (unﬁlled symbols) of stroke for the paretic (black) and non-paretic (gray) legs (n = 10). The error bars indicate standard deviations. ⁄Signiﬁcant diﬀerence between the paretic and non-paretic leg (P < 0.001).
1.8 ± 0.7%, respectively. Changes in the spectral frequency and entropy parameters were not signiﬁcant (P P 0.174). In the chronic stage (hypothesis 2), all force variables (P 6 0.002) except CV (P P 0.119) were signiﬁcantly diﬀerent when paretic or non-paretic leg was compared with control (Fig. 3). Speciﬁcally, both legs of stroke subjects showed signiﬁcantly decreased median frequency, increased relative power in 0–3-Hz band, decreased relative power in 3–6 and 8–12-Hz bands, and decreased SampEn. In the paretic leg, signiﬁcant Leg x Force Level interactions were found for the relative power in 0–3 and 8–12-Hz bands as well as SampEn (P 6 0.006), whereas in the non-paretic leg the only signiﬁcant Leg Force Level interaction was for the relative power in 8–12-Hz band (P = 0.007). The interaction plots (Fig. 3) indicate that, with increasing force level, there was a smaller rate of decrease in the relative power in 0–3-Hz band and a smaller rate of increase in the relative power in 8–12-Hz band and SampEn in the paretic than control leg. Only the rate of increase in the relative power in 8–12-Hz band was smaller in the non-paretic than control leg.
In terms of correlations with the force parameters in the paretic leg, MVC asymmetry did not correlate with the CV, frequency, or entropy measures (P P 0.093). However, signiﬁcant non-linear correlations were found between FM motor score and the relative power in 0–3 and 4–6-Hz bands at 20–50% force level (P 6 0.005, Fig. 4). A signiﬁcant correlation was also found between FM score and the relative power in 8–12-Hz band at the 30% force level (P = 0.006). The signiﬁcant correlation between RMI and the relative power in 8–12-Hz band at 10% MVC (r = -0.56, P = 0.006) was conﬁrmed to be due to two outliers.
DISCUSSION In this study, we examined whether increased variability and altered structure of the isometric force signal found in knee extensors within a month of stroke (Chow and Stokic, 2013) are still present at 6 months or later and how that relates to motor recovery. For this, we longitudinally followed-up a subset of stroke subjects from the subacute to chronic stage (hypothesis 1) and compared in a cross-section study chronic stroke to healthy subjects
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198
Fig. 3. Comparison of coeﬃcients of variations and diﬀerent frequency and entropy parameters across four force levels between chronic stroke and healthy subjects. The paretic or non-paretic leg of stroke subjects was compared to controls using a 2 (Leg) 4 (Force Level, FL) ANOVA. P-values in parenthesis refer to signiﬁcant main eﬀects of Leg and signiﬁcant Leg FL interactions (P 6 0.01). The error bars indicate standard deviations.
(hypothesis 2). The obtained results provide converging evidence of some normalization in force variability (CV) but without concurrent normalization in the structure of force signal (relative power distribution, complexity). Thus, behind less variable force in the chronic stage of stroke still remain greater concentration of power in the low-frequency band (0–3 Hz) and less complex force signal (decreased SampEn) as signatures of the persisting motor impairment. The results also suggest diﬀerent mechanisms underlying the recovery of force variability, force structure, and gross motor function after stroke. Force variability and structure from subacute to chronic stroke Stroke results in variable motor impairments with major recovery taking place within the ﬁrst 6 months (Jorgensen et al., 1995; Gilman, 2006; Kwakkel et al., 2006). Our subjects showed improvements in all clinical outcomes but the diﬀerence did not reach statistical significance. This is likely due to a combination of factors, including a bias in recruiting less impaired subjects to comply with the task demand in the subacute phase, shallow slope of improvement from 1 to 6 months in initially less impaired subjects (Buurke et al., 2008; Verheyden
et al., 2008), ceiling eﬀect of some of the selected clinical measures (Gladstone et al., 2002; Kwakkel et al., 2006), and a relatively small sample size. Nevertheless, our subjects attained typical recovery over the ﬁrst 6 months given the initial impairment (Buurke et al., 2008; Verheyden et al., 2008). The hypothesis that the force variability, frequency composition, and complexity would normalize over the ﬁrst 6 months of stroke was only supported for the force variability. Because force ﬂuctuation is inﬂuenced by discharge variability of active motor units (Enoka et al., 2003), and the discharge patterns of motor units are disrupted after stroke due to impaired descending and aﬀerent input to the segmental network (Dietz et al., 1986; Gemperline et al., 1995; Campanini et al., 2009), improved force variability from subacute to chronic stage may be associated with cortical reorganization during recovery from stroke (Gerloﬀ et al., 2006). However, the recovery of force variability within the ﬁrst 6 months of stroke was not associated with a broadening of the force frequency proﬁle and greater force complexity. Computer simulations of motor-unit activity suggest that manipulation of recruitment and rate coding alone could not adequately describe the frequency composition of force ﬂuctuation favoring instead the interaction of multiple
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198
Fig. 4. Correlations between paretic Fugl-Meyer (FM) lower extremity motor score and relative spectral power in the 0–3, 3–6, and 8–12-Hz frequency bands (left to right) for the paretic leg of stroke subjects at diﬀerent force levels. The FM motor score was nonlinearly (adjungated hyperbolic or exponential growth functions) correlated with selected relative power in diﬀerent frequency bands. Values given in each plot of signiﬁcant correlation are the coeﬃcient of determination (R2) and associated P-value. The horizontal dashed lines are upper (0–3-Hz band) and lower (4–6-Hz and 8–12-Hz bands) bounds of the 95% conﬁdence intervals for control subjects.
features of motor-unit activity (Taylor et al., 2003). Thus, physiological mechanisms underlying partial normalization of the isometric force structure warrant further investigations. Force variability and structure in chronic stroke The hypothesis of a greater CV, a shift toward lower frequencies in the power spectrum, and a decrease in complexity of the force signal in the chronic stroke compared with control subjects was supported for the latter two parts only. Although the average CV across all force levels was somewhat higher in both the paretic (3.01 ± 2.70%) and non-paretic (2.03 ± 0.98%) legs compared to controls (1.98 ± 0.81%), the diﬀerences were not statistically signiﬁcant (P P 0.119). These
non-signiﬁcant diﬀerences in CV may be ascribed in part to the overall improved motor function after stroke, but large variances and skewness in the stroke data should also be considered, especially in the paretic leg (skewness range 2.9–4.2, mean > median). The shift in spectral power toward the low-frequency band observed in subacute stroke (Chow and Stokic, 2013) still persists in the chronic stage, but some normalization in CV likely led to disappearance of the previously reported nonlinear correlation between the CV and relative spectral power in diﬀerent frequency bands. The combined ﬁndings suggest that a shift in spectral power toward lower frequencies remains a marker of disordered motor control long after stroke. Similar changes in force frequency composition have also been found in Parkinson’s disease (Vaillancourt et al., 2001) and Down
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198
syndrome (Heﬀernan et al., 2009). Mechanisms proposed to explain this shift include the inability to adequately control force output when processing visual information and producing motor corrections in Parkinson’s disease (Vaillancourt et al., 2001), greater closed-loop sensorimotor corrective processing in Down syndrome (Heﬀernan et al., 2009), and deﬁcits in engaging additional control processes in higher frequency modulation of force in developing children (Deutsch and Newell, 2004) and older adults (Vaillancourt and Newell, 2003). It remains unknown to which extent these mechanisms explaining the downshift in force frequency apply to stroke. Our ﬁnding of decreased complexity of the force signal during isometric knee extension agrees with those reported during wrist/ﬁnger extension in chronic stroke (Lodha et al., 2010). Decreased complexity of an isometric force has also been reported in Down syndrome (Heﬀernan et al., 2009), Parkinson’s disease (Vaillancourt et al., 2001), and children with heavy prenatal alcohol exposure (Simmons et al., 2012). In our task, visual feedback was used to match the generated force with the target force (constantly update and reduce the diﬀerence). In the case of adequate visuomotor integration, the structure of the resulting force signal is complex and irregular, which becomes more regular if visuomotor integration is impaired (Simmons et al., 2012), as commonly seen after stroke (Rowe et al., 2009). Thus, impaired visuomotor integration may be responsible for less complex force signal after stroke, which warrants further investigations. Force structure and contraction intensity in chronic stroke Similar to the subacute stroke (Chow and Stokic, 2013), a signiﬁcant shift in spectral power from the low- to high-frequency band with increasing contraction was observed in controls, but not in chronic stroke (Fig. 3d–f). Inadequate modulation of spectral power with increasing contraction has been explained by the failure to reorganize the sensorimotor output to meet the task demands (Deutsch and Newell, 2001) and by fewer degrees of freedom available to the motor system for executing motor tasks (Latash, 2012). From the physiological perspective, selective functional loss of the large, high-threshold motor units (Lukacs et al., 2008) or reduced number of recruited motor units in the paretic muscles (Li et al., 2011) may account for impaired modulation of force spectrum at stronger contractions after stroke. To gain further insights, future studies should investigate the association between cortical/ muscle activity and force signals in the frequency domain. Although our results agree with Lodha et al. (2010) in terms of a decreased complexity of force signal during an isometric task in chronic stroke, there appears to be disagreement as to how the complexity is modulated with the contraction intensity. Lodha et al. (2010) reported a steady decrease in complexity of the wrist/ﬁnger extension force from 5% to 50% MVC, but the opposite was observed here for the knee extension force. Decreased complexity of index ﬁnger and thumb forces with increasing force was also found in Parkinson’s patients (Vaillancourt et al., 2001). However, inconsistent ﬁndings
were often reported in healthy individuals (Slifkin and Newell, 1999; Sosnoﬀ and Newell, 2007; Sosnoﬀ et al., 2007; Prodoehl and Vaillancourt, 2010). It has been suggested that force complexity should be the greatest at moderate contraction levels (e.g., around 35% of MVC) because both motor unit recruitment and rate coding strategies could be simultaneously exploited making many degrees of freedom available for a task execution (Lodha et al., 2010). Relationship between clinical and force outcomes In addition to examining group diﬀerences between the stroke and healthy subjects, we also explored associations between the degree of clinical recovery and the force parameters in the paretic leg. The results revealed several signiﬁcant nonlinear correlations between the FM lower extremity motor score and the relative spectral power in diﬀerent frequency bands. These plots (Fig. 4) indicate that the stroke data points are uniformly outside the control limits across the broad range of incomplete motor recovery and that the frequency composition of the force signal tends to normalize when the gross motor recovery is nearly complete (FM score 34) . This re-aﬃrms the notion that the shift in spectral power toward lower frequencies may be considered a marker of residual motor impairment in chronic stroke. Because our sample was biased toward higher level stroke subjects who initially required inpatient rehabilitation, future studies should explore this link further by including both more and less impaired subjects than studied here. Study limitations The results pertain to the chronic stroke population who achieved better motor recovery. Our sample was comparable to other studied chronic samples in terms of the isometric knee extension strength (Severinsen et al., 2011), FM motor scores (Wong et al., 2013; Sawacha et al., 2013), and RMI (Globas et al., 2012). Any selection bias was unintentional and introduced by the study eligibility criteria. Therefore, our results cannot be generalized to lower level stroke patients including those non-ambulatory. Although patients with clinical evidence of visual (hemianopia) and perceptual (hemineglect) deﬁcits were excluded, they still might have some deﬁcit in visual processing (McIntosh, 2003; Khan et al., 2008; Rowe et al., 2009). Conclusion Force variability during an isometric knee extension is not impaired among subjects who achieve relatively good motor recovery after 6 months of stroke. However, improved force variability is not accompanied by the normalization of spectral power and greater complexity of the force signal. Thus, impaired structure of the isometric force produced by knee extensors remains a marker of disordered motor control after stroke despite recovery in force variability and overall motor functions.
J. W. Chow, D. S. Stokic / Neuroscience 273 (2014) 189–198 Acknowledgments—This work was supported by the Wilson Research Foundation, Jackson, MS, USA. The authors are grateful to Mark Hemleben, Robert Hirko, Heather Maloney, Jennifer Sivak, and L. Anthony Smith for their assistance with this study.
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(Accepted 10 May 2014) (Available online 16 May 2014)