The reasons why stroke patients expend so much energy to walk slowly.

Abstract

The energy consumed per covered distance (C) is increased in hemiparetic stroke adults during walking.
To ascertain if increased C in stroke patients is a result of increased mechanical work, of decreased efficiency of work production by muscles or of slow walking speed.
C and mechanical work were computed in 20 patients walking on a force measuring treadmill at speeds ranging from 1 km h(-1) to their own maximum speed (WS(MAX)). Works done by healthy and pathological limbs were computed separately.
For hemiparetic patients, C was around 1.7 times greater than normal. When these patients had a slower WS(MAX), they had greater C and mechanical work (r=-0.44 and -0.57, respectively). The increased C was related to the external work performed to lift the center of body mass when the healthy limb was supporting the body weight (r=0.77).
The increase of C in stroke patients is more pronounced when WS(MAX) is slow. Moreover, this increase is related to increased mechanical work done by muscles and is not related to slow walking speed or decreased efficiency. As in healthy subjects, C and external work presented optimum speeds, indicating a preserved pendular mechanism of walking.

Full text

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The reasons why stroke patients expend so much energy to walk slowly
G. Stoquarta,b,*, C. Detrembleura, T.M. Lejeunea,b
aUniversite ´ Catholique de Louvain, Institute of Neuroscience (IoNS), Belgium
bUniversite ´ Catholique de Louvain, Cliniques Universitaires Saint-Luc, Belgium
1. Introduction
Spastic hemiparetic stroke patients expend up to two times
more energy to walk than healthy subjects, and that limits their
activities and participation. Though it is obvious that those
patients walk at slow speeds (for review, Waters [1]), the relation
between energy consumption and walking speed remains partly
unknown. In healthy subjects, since the energy consumed per unit
of time increases as a quadratic function of walking speed (power,
W kg?1), the energy per covered distance (energy cost, C,
J kg?1m?1) fits a well-known U-shaped curve [2]. This curve
presents
minimum
values
(?4.5 km h?1). When speed varies from this optimum, C progressive-
ly increases [3].
In stroke patients walking at various speeds on a treadmill,
Reisman et al. [4] have shown that energy cost of stroke patients
decreased with increasing walking speed. Average maximum
walking speed of all patients was 68.2 ? 28.9% higher than
spontaneous one. It corroborates the hypothesis of authors [5] who
believe that increased energy cost in stroke patients is explained by
their very slow walking speed [1]. A normal energy consumption
around
spontaneous
speeds
would then be reached if patients were able to walk as fast as healthy
subjects.
However, in addition to slow walking speed, the increased
energy cost could be related either to the increased mechanical
work done by muscles, or the decreased efficiency of production of
this work. Detrembleur et al. [6] found, in nine stroke patients
compared to controls walking at same speeds, that increased
energy cost was proportional to increased mechanical work.
Therefore, the aim of the present study is two-fold: first, to
study more deeply the relationships between energetics and
mechanics to understand the origin of increased C in stroke
patients; second, to evaluate the effects of walking speed on
mechanics and energetics.
2. Methods
2.1. Study population
Twenty post-stroke chronic (more than 6 months) hemiparetic patients (age:
50 ? 12 years; weight 78 ? 18 kg; height: 173 ? 11 cm) were enrolled in the
present study. Inclusion criteria included the ability to walk independently on a
treadmill without any assistive device, at a minimum of two different speeds
(?1 km h?1), for a time allowing metabolic measurement (around 3 min at each
speed). After giving their informed consent, all patients participated freely in the
study, which was approved by the ethical board of the university. A clinical
examination was carried out by the same examiner, including Stroke Impairment
Assessment Set (SIAS, 0-76) [7], and the 10-m walking test on level ground to
evaluate their spontaneous walking speed (WSspont). Patients’ results were
compared to reference data from our lab, obtained in 12 healthy subjects [8]
Gait & Posture 36 (2012) 409–413
A R T I C L E
I N F O
Article history:
Received 29 August 2011
Received in revised form 6 March 2012
Accepted 27 March 2012
Keywords:
Stroke
Walking
Energetics
Mechanics
Treadmill test
A B S T R A C T
Background: The energy consumed per covered distance (C) is increased in hemiparetic stroke adults
during walking.
Objective: To ascertain if increased C in stroke patients is a result of increased mechanical work, of
decreased efficiency of work production by muscles or of slow walking speed.
Methods: C and mechanical work were computed in 20 patients walking on a force measuring treadmill
at speeds ranging from 1 km h?1to their own maximum speed (WSMAX). Works done by healthy and
pathological limbs were computed separately.
Results: For hemiparetic patients, C was around 1.7 times greater than normal. When these patients had
a slower WSMAX, they had greater C and mechanical work (r = ?0.44 and ?0.57, respectively). The
increased C was related to the external work performed to lift the center of body mass when the healthy
limb was supporting the body weight (r = 0.77).
Conclusions: The increase of C in stroke patients is more pronounced when WSMAXis slow. Moreover, this
increase is related to increased mechanical work done by muscles and is not related to slow walking
speed or decreased efficiency. As in healthy subjects, C and external work presented optimum speeds,
indicating a preserved pendular mechanism of walking.
? 2012 Elsevier B.V. All rights reserved.
* Corresponding author at: Cliniques Universitaires Saint-Luc, 10 Avenue
Hippocrate, B-1200 Brussels, Belgium. Tel.: +32 2 764 16 49; fax: +32 2 764 90 63.
E-mail address: Gaetan.Stoquart@uclouvain.be (G. Stoquart).
Contents lists available at SciVerse ScienceDirect
Gait & Posture
jo u rn al h om ep age: ww w.els evier.c o m/lo c ate/g aitp os t
0966-6362/$ – see front matter ? 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.gaitpost.2012.03.019

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(age: 23 ? 2 years; weight: 58 ? 10 kg; height: 167 ? 7 cm), knowing that age is
not a major determinant of walking energetics [9].
2.2. Gait analysis
Gait was assessed by a three-dimensional analysis, including simultaneous
mechanical and energetic measurements. Data were acquired simultaneously on a
force measuring treadmill (Mercury LTmed, HP Cosmos, Germany) [10].
Total positive mechanical work done by muscles during walking, Wtot, is
computed as:
Wtot¼ Wintþ Wext
where Wintis the internal work, i.e. mechanical work performed to move body
segments relative to the center of body mass (COMb), and Wextis the external work,
i.e. mechanical work performed to move the COMbrelative to the surroundings.
Wtotwas computed following the method described by Willems et al. [11], and
adapted to pathological walking [12]. Wintwas computed from the kinematics (Elite
system, BTS, Italy). Wextwas computed from measurement of 3D ground reaction
forces (GRF) recorded by four strain gauges located under each corner of the
treadmill [10]. Positive works done by muscles during walking to accelerate the
COMbmainly in forward direction (Wk), and to increase potential energy of the
COMb (Wp), were respectively computed from kinetic and potential energy
variations of the COMb, during one gait cycle. Wextwas computed from variations of
the sum of these two energy curves. The recovery, R, quantifies the amount of
energy-saving transfer between potential and kinetic energies, reflecting the
efficiency of pendulum-like mechanism of walking. It was calculated as:
R ¼ 100 ?Wkþ Wp? Wext
Wkþ Wp
Wextwas divided in two parts: the one done by the healthy limb (Wext-HL) and the
one done by the pathological limb (Wext-PL). Wext-HL corresponds to the work
performed during the second single stance when the healthy foot was the sole on
the ground, and during the first double stance when the healthy foot was in the rear
and pushed the body up and forward. Wext-PLcorresponds to the work performed
during the first single stance and the second double stance.
Metabolic cost of walking was determined by patient’s oxygen consumption
(VO2) and carbon dioxide production (VCO2) measured during steady state periods
of 2 min, at each speed. The energy expended above resting value was divided by
walking speed to obtain the net energy cost of walking (C, J kg?1m?1). Respiratory
exchange ratio (RER), computed as the ratio between VCO2and VO2, was always less
than 1.
2.3. Protocol
All patients were accustomed to the treadmill prior to the study. Then the study
started, all patients walking at 1 km h?1. Speed was then increased by steps of 0.5 or
1 km h?1, up to the maximum speed (WSMAX) that the patient could reach. They
walked for at least 2 min in metabolic steady state at each speed. Kinematic,
mechanical and energetic data were acquired at the same time. Acquisitions
stopped either because of breathlessness, fatigue or leg pain [13], or because RER
became greater than 1.
2.4. Statistical analysis
Because the range of walking speeds explored was different in each patient and
different from healthy subjects (see Section 3), variables were difficult to compare
between patients and healthy subjects and to submit to statistical analysis. To
overcome this problem, each variable (X) was transformed in Xi, which corresponds
to the ‘‘mean’’ increase in one patient in comparison to healthy subjects mean value,
through all walking speeds assessed in this patient (Fig. 1). It was computed as:
Xi¼
where XP(RWSMAX
respectively. XPiand XHSiwere the mean values for each patient and for the 12
healthy subjects over the range of speeds explored (WSMAX? 1) for each patient. If
the mean value of X of a patient and of healthy subjects were identical over the
range of speeds explored for the patient, then Xi= 0. Negative and positive values of
Xicorresponded, respectively, to lower and greater patients’ values in comparison
to healthy subjects mean value. A paired t-test between XPi and XHSi allowed
determining if the difference was significant between patients and healthy subjects.
Pearson correlations were computed to explore relationships between mechanics,
energetics and WSMAX. Pearson and Spearman correlations were computed to
explore relationships between WSMAXand WSspont, and between WSMAXand SIAS,
respectively.
RWSMAX
1
XP
WSMAX? 1?
RWSMAX
XP: blue area) and XHS(RWSMAX
1
XHS
WSMAX? 1¼ XPi? XHSi
11
XHS: hatched area) were the values
of X recorded at each explored speed in each patient and in all healthy subjects,
3. Results
The maximal walking speed on the treadmill (WSMAX) and the
spontaneous walking speed adopted overground (WSspont) varied
from patient to patient, ranging from 1.7 to 5.5 km h?1and from
2.1 to 5.1 km h?1, respectively. However, both speeds were well
correlated
(r = 0.81,
p < 0.0001),
(3.5 ? 1.1 km h?1) and WSspont(3.4 ? 0.8 km h?1) were similar. They
and
mean
WSMAX
Fig. 1. Method for computation of Xi. The variable (X, in J kg?1m?1) is presented as a
function of walking speed (in km h?1). The white curve and the gray area represent
the mean value of X for the 12 healthy subjects and one standard deviation around
this mean value, from 1 to 4 km h?1. The blue curve represents X of one stroke
patient. The hatched area, i.e. the area under the curve of healthy subjects
RWSMAX
1
former was then subtracted from the latter to compute Xi. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
this article.)
1
XHS
XP
?
?
, were divided by the range of speed of the patient (WSMAX? 1). The
, and the cyan area, i.e. the area under the curve of the patient.
RWSMAX
?
?
Table 1
Results in energy cost and mechanical work.
Patients
Healthy subjects
WSMAX
Ci
C
Wtot
Wext
Wint
Wp
Wk
Wext-HL
Wext-PL
R
J kg?1m?1
J kg?1m?1
J kg?1m?1
J kg?1m?1
J kg?1m?1
J kg?1m?1
J kg?1m?1
J kg?1m?1
%
4.3 ? 1.2*
0.69 ? 0.13*
0.43 ? 0.12*
0.28 ? 0.05*
0.55 ? 0.11*
0.18 ? 0.06 (p = 0.283)
0.35 ? 0.13*
0.33 ? 0.14*
45 ? 6 (p = 0.306)
2.3 ? 0.2
0.47 ? 0.02
0.28 ? 0.00
0.18 ? 0.02
0.35 ? 0.02
0.19 ? 0.05
0.21 ? 0.01
0.21 ? 0.01
44 ? 11
r = ?0.44, p = 0.05
r = ?0.57, p = 0.008
r = ?0.62, p = 0.004
r = ?0.09, p = 0.7
r = ?0.49, p = 0.03
r = ?0.21, p = 0.37
r = ?0.40, p = 0.03
r = ?0.50, p = 0.03
r = 0.42, p = 0.07
r = 0.77, p < 0.001
r = 0.69, p < 0.001
r = ?0.06, p = 0.78
r = 0.66, p = 0.001
r = 0.102, p = 0.668
r = 0.77, p < 0.001
r = ?0.01, p = 0.97
r = 0.50, p = 0.024
Data in columns ‘‘Patients’’ and ‘‘Healthy subjects’’ were computed as XPiand XHSi, respectively. The column ‘‘WSMAX’’ shows correlation coefficient values (r) and p-values for
the relationship between WSMAXand each variable, when computed as Xi(see Section 2). The column ‘‘Ci’’ shows r and p-values for the relationship between Ciand each
variable, when computed as Xi.
*Indicates data statistically different between patients and healthy subjects (p < 0.001 for all data).
G. Stoquart et al. / Gait & Posture 36 (2012) 409–413
410

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were lower than usual spontaneous walking speeds in healthy
subjects (4.5 km h?1). Neurological impairments correlated signifi-
cantly with WSMAX (r = 0.63, p = 0.003) and WSspont (r = 0.62,
p = 0.002). The median value [range] of SIAS was 58 [36–73].
Mean results (?sd) for all variables, computed as XPiand XHSi(see
Section 2), are presented in Table 1. Energy cost and representative
data (C, Wtot, Wp, and Wext-HL) are also presented in Fig. 2A as a
function of walking speed. Most mechanical and energetic data were
statistically greater in patients than in healthy subjects (p < 0.001).
Only Wkand R were not increased in comparison to normal data
(p = 0.283 and 0.306, respectively). Mean Ciof all patients corre-
sponded to 2.0 J kg?1m?1, indicating that C was on average
2.0 J kg?1m?1greater in patients than in healthy subjects, what
corresponds to 1.7 times normal values. Mean Wtot-iand Wext-HLiwere
0.22 and 0.14 J kg?1m?1. Mean Wint-iand Wext-PLiwere 0.10 and
0.12 J kg?1m?1, respectively.
In Fig. 2B, all variables decreased with increasing WSMAX,
indicating that faster walking patients had mechanical and
energetic data (including Wext) closer to normal than slower
walking patients. A regression line was fitted through data and
confirmed a significant but moderate relationship for all variables.
In Fig. 3, Ciincreased as a function of Wtot-i, Wp-iand Wext-HLi. It
means that increased C was mainly explained by an increase of
mechanical work mainly done by the healthy leg, to lift the COMb.
On the contrary, Ciwas not explained by Wint-i, by Wk-i, and by
Wext-PLi. R was only slightly related to Ci.
4. Discussion
The present study confirms that stroke patients expend more
energy to walk than healthy subjects. The increased C was not
explained by their slow walking speed. Indeed, C was greater in
patients than in healthy subjects walking at a comparable slow
speed. This change of C was related to an increase of the
mechanical work, mainly done by the healthy leg to lift the center
of body mass, but poorly related to the efficiency of work
production, confirming previous results [6,14].
In stroke patients, many studies have documented the
increased C, but few have found relationships between C and
other gait variables. C is often related to neurological impairments
in stroke patients or to spontaneous or maximal walking speeds
[1]. Increased mechanical work could be explained by typical joint
deformities (equinus, hip flessum, . . .) or altered pattern of
movement (hip hiking, stiff-knee gait, . . .). In the present study,
Ciwas only poorly correlated to SIAS (r = ?0.26, p = 0.27), what
could be due to high and similar values of SIAS, which were
explained by strict inclusion criteria.
Despite the fact that other authors have studied mechanical
work in various diseases and in healthy subjects (for example
[15,16]), this is the first time, to our knowledge, that the total
mechanical work done by muscles was measured at several speeds
in stroke patients. Allen et al. [17] showed that plantarflexor
moment and knee extensor moment were enhanced in the healthy
leg of stroke patients. These moments can possibly lead to an
elevation of the COMb. In myelomeningocele patients, McDowell
et al. [18] showed a good relationship between energy cost and
mechanical work estimated from vertical excursion of the sacrum,
also studied by Bennett et al. [19]. In amputees, Tesio et al. [12]
found an increase of mechanical work done by the healthy leg in
comparison to the pathological one.
Fig. 2. Main results. Each of the four panels A presents the data of patients and
healthy subjects for one of the following variables: C, Wtot, Wp, and Wext-HL, as a
function of the walking speed. The white curve and the gray area represent the
mean value of the 12 healthy subjects and one standard deviation around this mean
value, respectively. The curve and the area were fitted through values of all subjects,
from 1 to 6 km h?1. Each blue curve represents the data of one stroke patient. Each
curve was fitted through all data recorded at all explored walking speeds for the
specific patient. A faster WSMAXis denoted by a darker curve. The panels B present
the data of patients for all variables (Xi) as a function of WSMAX. Each black circle
corresponds to the data of one patient. A regression line was computed to describe
the relationship between each variable and the WSMAX. (For interpretation of the
references to color in this figure legend, the reader is referred to the web version of
this article.)
G. Stoquart et al. / Gait & Posture 36 (2012) 409–413
411

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Interestingly, the knowledge of this increase could lead to
specific treatments aiming at reducing mechanical work. For
example, Massaad et al. [20] trained stroke patients to decrease
vertical displacements of their COMb, which resulted in lower
mechanical work and energy cost. In hemiparetic patients walking
with stiff-knee [21,22], C and mechanical work were lowered after
botulinum toxin injections decreasing the stiff-knee.
Treadmill walking is comparable to overground walking in
stroke patients, on a kinematic and electromyographic point of
view [23]. In the present study, seven patients with slow WSMAX
did not reach their WSspont. Similarly, Eng et al. [24] found that
comfortable walking speed on treadmill was only 60% of WSspontin
12 stroke patients. In the present study, although patients were
accustomed to the assessment [25], it could be due to fatigue
induced by the duration of exercise (up to 25 min).
WSMAXcould also be limited by the fitness of patients. Because
of increased C, patients had to decrease their walking speed to
maintain their energy expenditure at levels adapted to their
fitness. The maximal oxygen consumption (VO2-max) was not
measured. However, O2power at WSMAX, when expressed per unit
of time (14.5 ? 3.0 ml kg?1min?1), was close to low VO2-maxvalues
found in stroke patients by several authors [26–28]. This decreased
exercise capacity has many possible origins (for review, Ivey [26]).
Exercise programs have become recommended among stroke
patients [29]: if their cardio-vascular fitness increased, patients with
slow WSMAXwould probably attain higher walking speeds.
Thirteen patients with medium to fast WSMAX presented
optimum speeds at which C and Wextwere minimized. In ten of
these patients, optimum speeds were similar to WSspont, as in
healthy subjects [3,30]. Reisman et al. [4] found a similar trend in
11 (among 16) stroke patients walking on a treadmill. However,
she did not find minimum values around optimal speeds.
5. Conclusion
The energy cost increase is mainly due to mechanical work done
by the healthy limb, mainly to lift the COMb. Future studies should
examine kinematics and kinetics to explain the mechanical work
increase. This could allow targeted treatment to improve energy
cost of stroke patients, and then their walking ability.
Acknowledgments
This study was sponsored by the Association Nationale d’Aide
aux personnes Handicape ´es (ANAH-Rotary Belgium and Luxem-
burg), the Fondation du patrimoine (Universite ´ catholique de
Louvain, Brussels) and the Fonds National de la Recherche
Scientifique (FNRS).
Conflict of interest statement
Authors disclose any financial and personal relationship with
other people that could inappropriately influence their work.
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