Walking is an energy-cheap activity, its energy requirement being only about 50% above that of resting metabolism in healthy individuals (23). Margaria (17), in a classic energy expenditure study of walking and running at different speeds, had suggested that the energy spent per unit of distance covered as a parameter for measuring the walking economy. Later, Schmidt-Nielsen (24) called this parameter the cost of transport (CT). In healthy individuals, the CT reaches a minimum at an intermediate speed (approximately 2 J·kg−1·m−1 at 4.5 km·h−1), often called the optimal walking speed (OWS), which is very close to the self-selected walking speed (SSWS) (23).
In patients with chronic heart failure (CHF), who have cardiopulmonary and muscular limitations that reduce their ability to exercise, walking speed may influence quality of life (14). Moreover, the 6-min walking distance is inversely associated with the New York Heart Association functional class and has been shown to be an independent predictor of hospitalization and mortality in CHF patients (14). Despite the importance of walking speed, little is known about the CT and SSWS in patients with CHF. Beneke and Meyer (4) have shown the effect of a 3-wk exercise program on performance and walking economy in 16 male patients with CHF. Exercise training resulted in improvement in walking economy and SSWS. Because exercise performance of patients with CHF is markedly influenced by the ventilatory responses (22), we hypothesized that, contrary to what happens in healthy individuals, SSWS could be determined by the work of breathing instead of the CT in patients with CHF, and the present study was conducted to test this hypothesis.
Seventeen patients with a previous history of stable symptomatic CHF due to left ventricular systolic dysfunction (left ventricular ejection fraction <45%) and 17 healthy controls participated in the study. Patients with angina, diabetes, uncontrolled hypertension, renal or pulmonary disease, recent myocardial infarction (previous 3 months), decompensated heart failure, neuromuscular disease, and smokers were not included. The control group included individuals matched for age and sex, with a normal medical history and physical examination, as well as with normal resting and exercise ECG. The protocol was approved by the Hospital de Clínicas de Porto Alegre Ethics Committee, and all individuals signed an informed consent form.
In this cross-sectional study, each participant was submitted to an incremental cardiopulmonary exercise test and, at least 48 h after, to a walking cost test. On the first visit, leg length (m) was measured from trochanter to the ground, with shoes (3). Weight was measured in both visits.
Cardiopulmonary exercise protocol.
Maximal incremental test was performed on a treadmill (INBRAMED 10200, Porto Alegre, Brazil) using a ramp protocol, as previously described (11). Gas exchange variables were measured breath-by-breath by a validated system (Metalyzer 3B, CPX System; Cortex, Leipzig, Germany). In short, peak oxygen uptake (V˙O2peak) was defined as the highest value achieved during the test for 20 s. Minute ventilation to carbon dioxide output slope was determined by linear regression using all points of the test. Heart rate was continuously recorded from a 12-lead ECG.
Walking transport cost protocol.
Initially, resting oxygen uptake (V˙O2) was measured in orthostasis, during 5 min. Then the subjects were asked to walk in a comfortable speed—one that could be sustained for a prolonged period, without getting tired—on a 15-m corridor, three times, and this was defined as the SSWS on the ground. At least 30 min after, participants were taken to the treadmill laboratory to perform the walking cost tests (20). Initially, the SSWS on the ground was set on the treadmill. Because the SSWS on the ground may differ from the SSWS on the treadmill (10), the individuals walked for a couple of min and could adjust the speed to attain what was called the SSWS. The walking cost tests were performed at five different speeds: the SSWS, two speeds below (−0.5 and −1.0 km·h−1), and two speeds above (+0.5 and +1.0 km·h−1). The subjects were required to walk for 5 min at each speed. The speed ordering was randomized, and gas exchange was measured throughout the tests. Between each speed, the subjects were allowed to rest until the oxygen consumption levels were close to those at rest (usually 5 to 6 min).
Walking transport cost analysis.
The mean V˙O2 (mL·kg−1·min−1) measured during the last 2 min of walking at each speed was used to calculate the walking cost, after subtracting the V˙O2 in orthostasis. To convert the walking cost to joules per kilogram per second, this value was divided by 60, and, adjusting for the respiratory quotient, the energetic equivalent was obtained (8). Subsequently, this value was divided by the walking speed (m·s−1) to determine the walking transport cost in joules per kilogram per meter (8).
Froude number, quadratic equation, and prediction of the OWS.
We used a standardized method to predict OWS based on the similarity theory, which states that two geometrically similar bodies will behave similarly if they have the same Froude number (Fr), defined as follows:
where s is the speed (m·s−1), g is the acceleration of gravity (9.81 m·s−2), and L is the leg length (m) (3,19,23). Farley and Ferris (12) found that humans and other animals choose walking instead of running if their speed leads to a Fr less than 0.5. However, when subjects are walking at OWS, their Fr is close to 0.25.
We also used the quadratic equation to predict the OWS (9). This quadratic equation has the mathematical reasoning that the experimental CT (CTexp) is given as follows:
The relationship between walking speed and CT can be approximated by a U-shape quadratic equation, meaning that there is a specific walking speed corresponding to the minimum CT. The relationship between walking speed and CT can be mathematically described as the following equation:
where a–c are the constants determined by the least squares with the actually observed CT values at each walking speed and s is the walking speed. Therefore, a differential equation of the original quadratic equation of each experimental condition could be described as follows:
The OWS was then determined at the speed when CT equals 0. That is, the OWSexp could be observed as follows:
Based on the Fr equation and the quadratic equation, we also calculated a rehabilitation index (RI) to assist in the rehabilitation of individuals with walking limitations, whether physical or metabolic. We assumed that the rehabilitation procedure should target an increase in walking speed, with the goal of bringing the patients’ walking speed closer to the OWS. We suggest that, should a gas analyzer be available, the following equation may be used to precisely calculate the experimental rehabilitation goal (RIexp) based on the quadratic equation:
Otherwise, if a gas analyzer is not available, we can estimate a theoretical rehabilitation goal (RItheor) based on the Fr equation:
For both RI, the closer to 100% this result gets, the closer to OWS will the subject be.
All values are expressed as mean ± SE, unless indicated. Based on the results of a previous study (4), we estimated a sample size of at least 12 individuals per group to detect a difference in CT of 20%, with a power of 80% and an alpha of 0.05. Comparisons between patient and control characteristics were carried out by unpaired t-test. To compare data of walking speed, walking cost, and V˙ E/V˙CO2, repeated-measures ANOVA was used. When appropriate, multiple comparisons were made with the Bonferroni correction.
Table 1 shows that CHF patients and controls were well matched for age and sex distribution. Patients with CHF had moderate reduction of left ventricular systolic function and mild impairment in functional capacity. SSWS was lower in patients with CHF (P = 0.002), and the CT was higher in this group (P = 0.05). All CHF patients were studied under currently recommended medical therapy. As expected, V˙O2peak was significantly higher in the control group (P = 0.001). The V˙ E/V˙CO2 slope was higher in CHF patients (P = 0.049). Peak heart rate was higher on the control group (0.009). RIexp and RItheor were significantly lower in controls (P = 0.001 and 0.002). Controls presented higher RI, indicating that these subjects are walking closer to their OWS than CHF patients. As expected, controls presented the lowest CT at the SSWS (P = 0.05).
Walking transport cost protocol.
Figure 1 shows the CT in CHF patients and controls. As expected, controls presented the lowest CT at the SSWS. In contrast, CHF patients presented the lowest CT at speeds above their SSWS. On average, the SSWS of CHF patients was 0.75 ± 0.14 m·s−1; their two speeds below were 0.46 ± 0.03 and 0.60 ± 0.03 m·s−1; their speeds above were 0.87 ± 0.04 and 1.01 ± 0.03 m·s−1. The controls’ SSWS was 0.97 ± 0.07 m·s−1, and their two speeds below were 0.71 ± 0.06 and 0.84 ± 0.07 m·s−1; their speeds above were 1.11 ± 0.07 and 1.28 ± 0.08 m·s−1. The lowest CT in CHF patients occurred at an absolute speed of 0.87 ± 0.04 m·s−1, which is similar to the OWS of the controls (0.97 ± 0.07 m·s−1). Both groups presented the lowest V˙ E/V˙CO2 at the SSWS. In contrast, CHF patients presented the lowest CT at speeds above their SSWS (ANOVA, P = 0.001).
The major new finding of this study is that, as opposed to healthy individuals who choose an SSWS that results in the lowest CT, CHF patients choose an SSWS that results in a higher CT but with a lower ventilatory cost. To the best of our knowledge, this is the first study that has demonstrated the importance of the ventilatory cost in the choice of SSWS for CHF patients.
Most of the literature on the influence of CT in the SSWS has evaluated young, healthy individuals (18). As found in our control group, these studies have consistently shown that the SSWS corresponds to the lowest CT. In older healthy individuals (older than 70 yr), the walking CT is higher than the younger subjects, whereas the SSWS is lower (1,15,21). The findings of our healthy individuals extend previous observations and suggest that the influence of the CT on the choice of the SSWS is not influenced by age.
Margaria (16) described walking as an inverted pendulum. In this model, the potential energy and kinetic energy continuously exchange, resulting in a total mechanical energy (total energy is the sum of potential energy and kinetic energy), with a smaller change over the stride with respect to the two components taken separately. The so-called energy recovery quantifies the ability to save mechanical energy by using a pendulum-like paradigm (6). Although in ideal pendulums, the energy exchange is complete (recovery is 100%), the path of the center of mass of the body in walking resembles the motion of a pendulum, with losses associated both with deviation from an ideal system and with the transition from one swing to the next (2). However, the real energy recovery is moderately high (above 60%) and depends on stride length and walking speeds. This maximal recovery of energy is associated with the most economical speed (23).
In contrast to the healthy individuals, our CHF patients chose an SSWS with a higher CT but with a lower ventilatory cost. The mechanisms responsible for this choice are not readily apparent from our data. However, a possible explanation for these patients’ SSWS is the ventilatory efficiency, because it is well established that CHF patients have an abnormal ventilatory response to exercise due primarily to alterations in breathing pattern and excessive hyperventilation when compared with healthy subjects (13,22,26). Thus, despite a higher CT, our patients chose an SSWS that resulted in lower ventilatory cost.
Interventions may improve walking speed in CHF, with potential effect in the SSWS. Several controlled clinical trials have repeatedly shown that different medical interventions, including medications and device implantation (5,7), improve the 6-min walking speed. Nonpharmacologic interventions, such as aerobic exercise training, also improve walking speed (25). Likewise, inspiratory muscle training may increase the 6-min walk test and ventilatory efficiency (11). Beneke and Meyer (4) evaluated CHF patients before and after a 3-wk training program, which included cycle ergometer and treadmill exercises, as well as flexibility, muscular movement coordination, and isometric contractions of small muscle groups. This resulted in significant walking economy and improvement in SSWS.
To assist in the management of these patients, both clinically and on training, we propose on this study a measure that we called the RI. Both the theoretical and the experimental RI values were closer to 100% in the control group, which may indicate that these subjects are walking closer to their OWS. With this finding, we suggest that the theoretical RI may be a simple and easy method for everyday use to establish a goal for cardiac rehabilitation in CHF.
Some limitations of the present study should be pointed out. A possible difference between the ground and the treadmill SSWS may have influenced the results. However, this difference is known, as cited in the Methods section. Our patients had only mild reduction in function capacity; therefore, our findings may not be generalized to patients with more advanced CHF. However, with contemporary management, most patients in heart failure clinics have similar profile.
In conclusion, contrary to what happens with healthy subjects, where the SSWS has the lowest CT, CHF patients choose an SSWS with a higher CT but with lower ventilatory cost. These findings suggest that interventions that enhance ventilatory efficiency may increase the patients’ SSWS and improve their quality of life.
This study was supported by a grant from the Hospital de Clínicas de Porto Alegre Fund for the Incentive of Research, Porto Alegre, Brazil. P. Figueiredo and P.A. Ribeiro received scholarships from the Brazilian Coordination for the Development of Superior Education Personnel (CAPES), Brasília, Brazil. J.P. Ribeiro is an established investigator of the Brazilian Research Council (CNPq), Brasília, Brazil.
All authors report no potential conflict of interests related to the content of the manuscript.
The results of this study do not constitute endorsement by the American College of Sports Medicine.
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