Abeta Fibers Mediate Cutaneous Reflexes During Human Walking

B.M.H. van Wezel,1 B.G.M. van Engelen,2 F.J.M. Gabreëls,3 A.A.W.M. Gabreëls-Festen,2 and J. Duysens1,4

 1Department of Medical Physics and Biophysics, University of Nijmegen, NL-6525 EZ Nijmegen;  2Institute of Neurology and  3Department of Child Neurology, University Hospital Nijmegen, NL-6500 HB Nijmegen; and  4SMK Research, NL-6500 GM Nijmegen, The Netherlands


    ABSTRACT
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

van Wezel, B.M.H., B.G.M. van Engelen, F.J.M. Gabreëls, A.A.W.M. Gabreëls-Festen, and J. Duysens. Abeta Fibers Mediate Cutaneous Reflexes During Human Walking. J. Neurophysiol. 83: 2980-2986, 2000. During human gait, transmission of cutaneous reflexes from the foot is controlled specifically according to the phase of the step cycle. These reflex responses can be evoked by nonnociceptive stimuli, and therefore it is thought that the large-myelinated and low-threshold Abeta afferent fibers mediate these reflexes. At present, this hypothesis is not yet verified. To test whether Abeta fibers are involved the reflex responses were studied in patients with a sensory polyneuropathy who suffer from a predominant loss of large-myelinated Abeta fibers. The sural nerve of both patients and healthy control subjects was stimulated electrically at a nonnociceptive intensity during the early and late swing phases while they walked on a treadmill. The responses were studied by recording electromyographic (EMG) activity of the biceps femoris (BF) and tibialis anterior (TA) of the stimulated leg. In both phases, large facilitatory responses were observed in the BF of the healthy subjects. These facilitations were reduced significantly in the BF of the patients, indicating that Abeta fibers mediate these reflexes. In TA similar results were obtained. The absolute response magnitude across the two phases was significantly smaller for the patients than for the healthy subjects. The TA responses for the healthy subjects were on average facilitatory during early swing and suppressive during end swing. Both facilitations and suppressions were considerably smaller for the patients, indicating that both types of responses are mediated by Abeta fibers. It is concluded that low-threshold Abeta sensory fibers mediate these reflexes during human gait. The low threshold and the precise phase-dependent control of these responses suggest that these responses are important in the regulation of gait. The loss of such reflex activity may be related to the gait impairments of these patients.


    INTRODUCTION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

Somatosensory feedback from muscles, joints, and skin is essential in the normal execution of human gait. One important source of afferent input during gait comes from the skin of the foot. A nonnociceptive electrical stimulus applied to the sural, posterior tibial, or superficial peroneal nerves can elicit both facilitatory and suppressive reflex responses with latencies of ~50, 80, and 100 ms (Duysens et al. 1990; Tax et al. 1995; Van Wezel et al. 1997; Yang and Stein 1990). The reflex responses at a latency of ~80 ms are observed in a wide variety of muscles in both legs. The amplitude of these responses is modulated according to the phase of the step cycle (De Serres et al. 1995; Duysens et al. 1990-1992, 1995, 1996; Tax et al. 1995; Van Wezel et al. 1997; Yang and Stein 1990; Zehr et al. 1997, 1998b). This phase-dependent modulation depends on the muscle (Duysens et al. 1996; Tax et al. 1995; Van Wezel et al. 1997), the leg (Tax et al. 1995; Van Wezel et al. 1997), and the location of the stimulus (Van Wezel et al. 1997; Zehr et al. 1997).

The large-myelinated and low-threshold Abeta afferent fibers may be involved because nonnociceptive stimulation is sufficient to evoke these reflex responses. However, at present this hypothesis has not yet been verified. In fact, although the small-myelinated Adelta fibers mostly transmit nociceptive information, these also can transmit nonnociceptive information (Adriaensen et al. 1983; Handwerker and Kobal 1993; Millan 1999). Moreover, reflex responses after a nonnociceptive stimulus often are observed in periods of the step cycle when muscles are inactive (Duysens et al. 1996; Tax et al. 1995; Van Wezel et al. 1997; Zehr et al. 1997, 1998b), a condition that requires Adelta -fiber activation to elicit responses under static conditions (Ertekin et al. 1975; Rossi et al. 1996). Hence, at present it remains unclear whether Abeta fibers mediate cutaneous reflexes during human gait.

Therefore the present study investigated whether Abeta fibers contribute to cutaneous reflexes from the foot during human gait on patients who suffered from a clinically established sensory polyneuropathy with a predominant loss of large-myelinated low-threshold Abeta sensory fibers. Hence, reduced or absent reflexes during gait of these patients would indicate that Abeta fibers are involved. The responses to electrical stimulation of the sural nerve were studied in the biceps femoris (BF) and tibialis anterior (TA) of the stimulated leg during walking of these patients. The BF was chosen because this muscle usually exhibits large facilitatory responses to sural nerve stimulation during human gait (Duysens et al. 1996; Tax et al. 1995; Van Wezel et al. 1997) and therefore primarily will provide information about changes in the amplitude of reflex responses during gait of patients with sensory polyneuropathy. The TA was chosen because stimulation of the sural nerve elicits reflex responses at ~80 ms in TA, which are on average facilitatory during early swing, whereas these are suppressive during late swing (Duysens et al. 1996; Tax et al. 1995; Van Wezel et al. 1997; Yang and Stein 1990). In principle, it is possible that these responses are mediated by fibers with different activation thresholds. In that case, these two types of responses should be affected differently in patients with a sensory polyneuropathy. The responses in this muscle therefore will provide information about potential differences in the excitatory and inhibitory reflex pathways and their phase-dependent control during gait of patients with sensory polyneuropathy.


    METHODS
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INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

The methods in this study were mostly identical to those which have been described in detail elsewhere (Duysens et al. 1996; Tax et al. 1995; Van Wezel et al. 1997). The essentials will be described in the following text, together with some specific procedures.

Patients and methods

Experiments were performed on a group of 7 patients (5 male, 2 female) with a predominant sensory polyneuropathy (aged between 13 and 80). The selection of patients was based on clinical investigation that indicated a relatively specific loss of sensory afferents and not motor efferents and that sensory deficits were restricted largely to the loss of large-myelinated Abeta and not Adelta fibers.

In all patients, tactile sensory impairment (vibration/position) was evident in the feet and lower legs during clinical investigation. Romberg test was impaired in all patients. In none of the patients could a sensory evoked potential be observed during clinical electrophysiological investigation of the sural nerve, suggesting loss of large-myelinated Abeta fibers. No abnormal acute pain sensation (pin prick) was observed in four of the patients, suggesting no severe loss of small myelinated Adelta fibers. A predominant loss of large-myelinated Abeta afferents, although the small myelinated Adelta fibers were less affected (see RESULTS), was evident in three patients for whom a sural nerve biopsy was available (taken previously for clinical diagnosis). In six patients, no responses were observed after ankle taps. In five patients, no responses were observed after patella taps. During clinical examination no signs of weakness were observed in six patients and weakness only in the feet of one patient, indicating no severe motor impairments in the muscles that were measured in the present study (BF and TA). Clinical electrophysiological investigation on the peroneal nerve confirmed this because in all patients a motor-evoked potential could be elicited, suggesting no severe loss of motoneurons.

For comparison, 10 normal healthy subjects (aged between 19 and 60) with no known history of neurological or motor disorder participated in this study. In addition, two patients with a predominant motor polyneuropathy (aged 17 and 70) participated to investigate the possibility that any reflex impairments during the walking experiments were due to motor components. All subjects had given informed consent. The experiments were carried out in conformity with the declaration of Helsinki for experiments on humans.

Experimental setup

All subjects were asked to walk on a treadmill while wearing a safety-harness that was fastened to an emergency brake at the ceiling. A second emergency brake was attached close to the subject on the handrail of the treadmill so that the subject could stop the treadmill at any moment. Very thin insole foot-switch systems (designed in collaboration with Algra Fotometaal B. V., Wormerveer, The Netherlands) were used to detect foot contact. Bipolar electromyographic (EMG) activity was recorded in both legs by means of surface electrodes over the long head of the BF and the TA muscles. The EMG signals were (pre-)amplified (by a total factor that was generally in the order of 104-105), high-pass filtered (cutoff frequency at 3 Hz), full-wave rectified and then low-pass filtered (cutoff frequency at 300 Hz). These signals were sampled along with the foot-switch signals and a digital code referring to the stimulus condition. The data were sampled at 500 Hz and stored on hard disk for each trial.

The electrical stimulus (a train of 5 rectangular pulses of 1-ms duration given at 200 Hz) was applied by a custom-made constant-current stimulator through a bipolar stimulation electrode (with poles of 0.5 cm and an interpole distance of 2.0 cm) that usually was positioned over the left sural nerve (approximately halfway between the lateral malleolus and the Achilles tendon), firmly pressed with elastic straps. In one patient, the electrode was positioned over the right sural nerve because his left sural nerve was taken for a biopsy for clinical diagnosis. For each subject, the exact position of the stimulation electrode was determined so that an electrical stimulus evoked a clear sensation along the innervation area of the sural nerve (lateral side of the foot).

Stimulus stability

Both voltage and current of the stimulus appeared to be quite constant for the two phases. The maximum deviation from the mean of all stimuli was <2.5% for the voltage and <1.5% for the current. However, this does not rule out the possibility that the nerve itself might receive a variable input due to changes in the ankle positions during the course of a step cycle. In previous publications, it was discussed that this possibility did not play a large role (Duysens et al. 1995, 1996). Furthermore the stability was also verified in one subject by measuring the compound sensory action potentials of the sural nerve for several ankle positions under stationary conditions (Van Wezel et al. 1997). In addition, the responses of the ipsilateral tibialis anterior muscle in this study agree with those of other groups (see RESULTS), including those that have controlled for the stimulation by using mixed nerve stimulation and monitoring of the M waves (De Serres et al. 1995; Yang and Stein 1990; Zehr et al. 1997). Hence there are no indications that there is a large phase-dependent variation of the stimulus delivered to the nerve.

Experimental protocol

Before each experimental run, during quiet standing, the perception threshold (PT) was determined by gradually increasing (to above PT) and decreasing (to below PT) the stimulus amplitude. During the experiment, the electrical stimuli were delivered to the sural nerve during the early and end swing phases at an intensity of two PT. During the same phases, control values (i.e., no stimulus) of the EMG also were measured. Every stimulus condition was presented >= 10 times in an experimental run. All trials occurred in random order. The successive stimulus conditions were separated by a random interval in the range of 3.5-6.5 s. Hence, two stimuli always were separated by at least two step cycles without a stimulus. At the end of each experimental run the perception threshold was determined once more. It was slightly lowered (8% on average) as compared with the measurement taken immediately before the experimental run.

Data analysis

The overall effect after nerve stimulation was obtained by averaging the 10 trials of each stimulus condition and subsequently by subtracting the average EMG control trials from the corresponding average EMG stimulus trials ("pure" responses or "subtractions"). To quantify these responses, the average EMG value was calculated within a time window around the responses (Duysens et al. 1991, 1996; Tax et al. 1995; Van Wezel et al. 1997; Yang and Stein 1990). When a muscle showed little or no responses, no adequate window could be set. In that case, an average window was used, calculated from the time windows used to measure responses in (in order of priority) other muscles or the average of other subjects (cf. Tax et al. 1995).

For each trial, the EMG was averaged within the applicable window. Then the average and standard error were calculated for corresponding stimulus conditions (n = 10 trials per condition). The resulting data underwent an amplitude normalization with respect to the maximum control value in the step cycle so that a proper intersubject comparison could be made. The statistical significance of the observed reflex responses was tested using the Wilcoxon signed-rank test (significance level P < 0.05).


    RESULTS
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Unperturbed treadmill walking

Gait on the treadmill of the patients with sensory polyneuropathy clearly was impaired. During a short walking period, the patients were asked to determine the speed at which they walked most comfortably. This preferred walking speed was generally slower for the patients than for the healthy subjects. On average, the most comfortable belt speed for the patients was 2.4 ± 0.6 (SD) km/h, whereas healthy subjects usually are studied at 4 km/h (De Serres et al. 1995; Duysens et al. 1990, 1996; Van Wezel et al. 1997; Yang and Stein 1990; Zehr et al. 1997, 1998b). To exclude possible influence of walking speed on the results, the healthy subjects, used as controls in this study, also were investigated at 2.5 km/h.

When possible, patients were asked to walk without any support devices. However, four of the seven patients needed support from the side bars of the treadmill. When they were asked to release the side bars, they usually staggered for a few steps and then grasped the side bars again to prevent falling. The patients who walked without support tended to have a shorter average step-cycle duration (1,159 ± 63 ms across patients, n = 3) than the healthy subjects (1,327 ± 122 ms across subjects, n = 10), whereas the patients who did walk with support of the side bars tended to have a longer average step-cycle duration (1,568 ± 50 ms across patients, n = 4). The variability of the step-cycle duration was on average almost four times larger for the patients who walked without support (SD 8.1% of the average step cycle) than for the healthy subjects (SD 2.1% of the average step cycle). The patients who walked with support also had an increased variability of the step-cycle duration (SD 3.5% of the average step cycle).

Reflex responses to sural nerve stimulation

The sural nerve was stimulated at an intensity of two times perception threshold (2 PT). At this intensity both patients and healthy subjects felt a tactile, nonnociceptive irradiation to the lateral side of the foot, which is the innervation area of the sural nerve. During gait the stimulus was applied during the early and late swing phases. To obtain the average net effect after stimulation of the sural nerve, for both stimulus and control (i.e., no stimulus) conditions, the 10 trials of the two stimulus phases were averaged and the average control trials were subsequently subtracted from the corresponding average stimulus trials (Fig. 1A).



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Fig. 1. Subtracted electromyographic (EMG) data after sural nerve stimulation during walking. A: subtraction technique. EMG activity of biceps femoris (BF) measured when no stimulus is given (control, middle) is subtracted from the EMG activity measured when a stimulus is given (stimulated, top). The resulting subtracted data provides the net effect of the stimulus (subtracted, bottom). B: BF subtraction traces are shown for 3 subjects: a healthy subject (top), a patient with a predominant motor neuropathy (middle), and a patient with a predominant sensory polyneuropathy (bottom). In A and B, all traces are averages of 10 trials. Vertical solid lines indicate the time of stimulation, whereas the vertical dotted lines refer to a delay of 100 ms with respect to the onset of stimulation. Time calibration 100 ms; EMG calibration normalized.

Figure 1B shows the subtracted responses of the BF for a healthy subject, a patient with a predominant motor polyneuropathy, and a patient with a predominant sensory polyneuropathy. The stimuli were presented during the end swing period, a phase in which the BF was active during unperturbed gait in all subjects. In the healthy subject a large facilitatory reflex response is observed at a latency of ~80-90 ms (Fig. 1B, top). When the same experiment was performed on two patients with predominant motor polyneuropathy, the responses were similar to those observed in the healthy subject (example in Fig. 1B, middle). In contrast, the responses in a patient with a predominant sensory polyneuropathy were much smaller or even absent (Fig. 1B, bottom).

To quantify the responses a time window was set around the responses, in which the mean EMG value is calculated. On average for all subjects, this time window started at 85 ± 7 ms and ended at 112 ± 10 ms. Subsequently, for all stimulus conditions (i.e., for early- and late-swing phases and for both control and stimulus conditions), both the average and the standard error were calculated for these window-averaged trials (n = 10 trials per stimulus condition). The data of the individual subjects were normalized to the maximum control EMG value in the step cycle (see METHODS). The resulting values were subsequently averaged for both patients and healthy subjects (Fig. 2).



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Fig. 2. Sural nerve reflexes during walking. Average subtracted responses (± SE) of BF (top) and TA (bottom) for the healthy subjects (left) and the patients with sensory polyneuropathy (right) in both early and late swing. Data are normalized with respect to the maximum background locomotor activity of each muscle (see METHODS).

Consistent with previous results (Duysens et al. 1996; Tax et al. 1995; Van Wezel et al. 1997), large responses were observed in BF for the healthy subjects, with no statistically significant phase-dependent effect in the early and late swing phases. For the patient group, the responses in BF were considerably smaller and on average no significant responses were observed (Fig. 2). The difference between healthy subjects and patients was statistically significant (Wilcoxon rank sum test: P < 0.01).

Similar results were obtained for the responses in the TA muscle. For the healthy subjects, the well-known "reflex reversal" (Duysens et al. 1990; Tax et al. 1995; Van Wezel et al. 1997; Yang and Stein 1990) was observed from facilitatory responses during early swing to suppressive responses during late swing. This modulation tended to be similar in the patients with sensory polyneuropathy, although the responses were smaller. Both the facilitatory responses during early swing and the suppressive responses during late swing were smaller for the patients than for the healthy subjects (Fig. 2). For the absolute response magnitude across the two phases, the difference between healthy subjects and patients was statistically significant (Wilcoxon rank sum test: P < 0.01).

During the experiments, four of the seven patients with a sensory polyneuropathy needed support from the side bars of the treadmill. This did not play a large role because three patients did not use support from the side bars, and in these three patients, the amplitude of the reflex responses also were reduced significantly. Furthermore the two patients with a motor neuropathy also used the side bar for support. These two patients exhibited reflexes that were normal compared with the healthy subjects.

In three patients, a sural nerve biopsy that was taken for clinical purposes showed a predominant loss of large-myelinated Abeta fibers. Normally, the histogram of myelinated fiber density versus fiber diameter in the sural nerve is bimodal: one group of thick fibers (Abeta fibers; low-activation threshold) is clustering around a diameter of 9 µm; another group of thin fibers (Adelta fibers; higher threshold) has a peak of approximately 3-4 µm with an overlap between both groups (Fig. 3, ). In these three patients, there was a significant difference of 50% in the remaining amount of Abeta as compared with Adelta fibers (Fig. 3, ). The density of large diameter fibers (range 6-14 µm) was on average 10 ± 7% of the normal density. In contrast, the density of small diameter fibers (range 1-6 µm) was 77 ± 13% of the normal density. The reflexes in BF of these three patients were on average 9 ± 4% of the magnitude of the reflexes of the healthy subjects (Fig. 4).



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Fig. 3. Morphometry of the sural nerve. Histograms of myelinated fiber density vs. fiber diameter in the sural nerve (determined on sural nerve biopsies) of 3 patients with a sensory polyneuropathy () and age-matched normal distribution ().



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Fig. 4. Relation between remaining amount of sensory fibers and reflex amplitude. Percentage of remaining Adelta fibers, Abeta fibers, and reflex amplitude of the BF of the patients (n = 3) as compared with the BF of the healthy subjects (n = 10). Data for Adelta fibers (1-6 µm) and Abeta fibers (6-14 µm) are based on morphometry of sural nerve biopsies. The reflex amplitude was averaged for the 2 stimulus phases.


    DISCUSSION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
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Abeta fibers mediate cutaneous reflexes during walking

This study showed that reflexes at a latency of ~80 ms evoked by nonnociceptive stimulation of the sural nerve were significantly smaller for patients with a sensory polyneuropathy than for healthy subjects during gait. Clinical investigation of these patients revealed severe sensory deficits for tactile perception (vibration and position), suggesting functional loss of ascending Abeta fibers. In contrast, acute pain perception (pin prick) was less affected, indicating a higher degree of functionally intact ascending Adelta fibers. This fitted well with both sural nerve clinical electrophysiology and morphometry indicating a selective loss of large-myelinated Abeta fibers. A sural nerve biopsy, which was available for three patients, showed a distinct difference between the loss of large-myelinated Abeta fibers (reduction to 10%) and the loss of small myelinated Adelta fibers (reduction to 77%). A large decrease in the amplitude of the reflexes in BF of these three patients was observed (reduction to 9%). Hence the present results provide direct experimental evidence that Abeta fibers mediate reflexes at ~80 ms during human gait.

This is compatible with other studies that indicated that nonnociceptive stimulation is sufficient under static conditions in active muscles (Aniss et al. 1992; Burke et al. 1991; Kukulka 1994; Meinck et al. 1981; Rossi et al. 1996). An average conduction velocity of ~45 m/s was reported for the reflex afferents involved, suggesting contribution from Abeta fibers (Rossi et al. 1996). In contrast, nociceptive stimuli are usually necessary to evoke reflex responses in inactive muscles under stationary conditions (Ertekin et al. 1975; Rossi et al. 1996). For these reflexes, Adelta fibers are believed widely to be involved because of the close relation between the amplitude of these responses and subjective pain score (Chan and Dallaire 1989; Willer 1977; Willer et al. 1984) and because of the observed conduction velocity of the reflex afferents involved (~10-25 m/s, Ertekin et al. 1975; ~27 m/s, Rossi et al. 1996).

Studies that used the spatial facilitation technique suggested that nociceptive Adelta and nonnociceptive Abeta fibers converge on common interneurons (Behrends et al. 1983; Rossi et al. 1996). Hence it is not unlikely that at least part of the pathways is common for the nonnociceptive and the nociceptive reflexes. On the other hand, during gait, there is evidence that the two types of input, nonnociceptive and nociceptive, use largely different reflex pathways. After nonnociceptive stimulation of the sural nerve during the midswing phase, facilitatory reflex responses were observed in TA, which induced dorsiflexion movements of the ankle (Duysens et al. 1992). In contrast, a nociceptive stimulus to the same nerve elicited suppressive reflex responses with the same latency accompanied by ankle plantar flexion (Duysens et al. 1992). This indicates entirely different reflexes and behavioral reactions after nonnociceptive and nociceptive stimulation during human walking. Combined with the present results, this suggests that during gait the presently described reflex responses would be mediated solely by Abeta fibers and not by Adelta fibers, and therefore a purely nocifensive role for these reflexes during gait in terms of a flexion reflex can be excluded.

The phase-dependent reflex reversal in TA from facilitation in early swing to suppression during end swing is in agreement with previous studies (Duysens et al. 1996; Tax et al. 1995; Van Wezel et al. 1997). In the patients, both the facilitations and the suppressions were reduced indicating that both types of responses are mediated by Abeta fibers. This is important because the TA reflex reversal often is used as one of the characteristic features of the phase-dependent modulation of cutaneous reflexes (De Serres et al. 1995; Duysens et al. 1992, 1996; Jones and Yang 1994; Tax et al. 1995; Van Wezel et al. 1997; Yang and Stein 1990).

Functional considerations

Just as cutaneous afferents are known to play a role in the control of posture (Do et al. 1990; Thoumie and Do 1996; Wu and Chang 1997), Abeta fibers may provide low-threshold sensory information during gait. For example, during the stance phase of walking, activity from low-threshold cutaneous mechanoreceptors (Sinkjaer et al. 1994) could provide information about phase transitions [as was observed in cats (Duysens 1977)] or irregularities on the ground surface. Furthermore when the foot strikes an object during the swing phase, the so-called stumbling reaction can be evoked in humans (Eng et al. 1994; Schillings et al. 1996, 1999). Low-threshold cutaneous reflexes could participate in these corrective responses, as has been proposed previously (cats: Drew and Rossignol 1987; Forssberg 1979; humans: Zehr et al. 1997).

If such information is processed through reflexes such as described in the present study, then one would expect abnormalities in the walking patterns if the reflexes are abnormal. A relation between abnormal cutaneous reflexes from the foot and impaired gait was observed in patients with other forms of neurological disorders, such as patients suffering from an incomplete spinal-cord injury (Jones and Yang 1994) or a stroke (Zehr et al. 1998a). Because descending control clearly is affected in those patients, these studies could point to supraspinal or even transcortical involvement in these reflexes (see also Christensen et al. 1999; Nielsen et al. 1997). Nevertheless in those patients, the causal relation between abnormal reflexes and abnormal gait is hard to establish because the neural pathways that are affected are not precisely known. The present study, in contrast, describes a population of patients in which the primary cause of abnormal reflexes during gait is the neurological disorder itself (loss of large-myelinated afferent fibers). This (partial) deafferentation may be comparable to studies on cats which show that deafferentation of the limbs cause abnormalities in the gait patterns (Giuliani and Smith 1987; Goldberger 1977, 1988a,b; Grillner and Zangger 1984; Rasmussen et al. 1986; Wetzel et al. 1976). Hence, the combination of gait impairments such as described in the present study (and by Lajoie et al. 1996) and the loss of reflex activity mediated by low-threshold Abeta fibers would support the possibility that the loss of sensory input, in part channeled and processed through cutaneous reflex pathways, is one of the contributing factors causing abnormalities in human walking.


    ACKNOWLEDGMENTS

The authors thank I. Gommans for participating in the experiments, A. M. Schillings for critically reading the manuscript, G. Windau for software development, and A. M. van Dreumel and J.W.C. Kleijnen for technical assistance.

This work was supported by the Prinses Beatrix Fonds in The Netherlands.


    FOOTNOTES

Address for reprint requests: B.M.H. Van Wezel, Dept. of Medical Physics and Biophysics, University of Nijmegen, Geert Grooteplein 21, 6525 EZ Nijmegen, The Netherlands.

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Received 26 July 1999; accepted in final form 10 February 2000.


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