Motor unit populations in healthy and diseased muscles.

The importance of the motor unit as a basic element in the production of force or movement was recognized by Sherrington.[1] Since Sherrington's time, numerous studies have been concerned with different aspects of the structure and function of motor units, but there remains one aspect for which, in humans, relatively little is known: the number of motor units in individual muscles. in this article, we discuss why this situation exists and how the deficiency may be remedied by a straightforward physiological approach. As determined by this methodology, the sizes of motor unit populations in different human muscles are given together with the effects of aging. Finally, we show how the numbers of motor units may change in various types of neuromuscular disorders.

Motor Unit Estimation in Nonhuman Species

In mammalian muscles, there are two anatomical techniques that may be used to obtain reliable determinations of the numbers of motor units. The original method is, first, to dispose of the muscle afferent fibers by dividing the dorsal roots distal to their ganglia and allowing the fibers to degenerate over the new few days. The nerve to a particular muscle (the "motor" nerve) can then be dissected out and the number of fibers counted. The fibers with large and small diameters will correspond to [alpha]- and [gamma]-motor axons, respectively, and the number of [alpha]-motor axons will equal the number of motor units in the muscle.

A more recent technique makes use of the phenomenon of retrograde axonal transport, whereby molecules or larger particles may be taken up by the motor axon and conveyed to the motoneuron somata in the spinal cord and brain stem. The substance first used for this purpose, and still the most frequency used, is horseradish peroxidase (HRP). When conjugated with wheat germ agglutinin and injected into a muscle belly, HRP enters the motor nerve terminals and is then transported; after 24 hours or more, the HRP-containing motoneurons are stained with tetramethylbenzidine and counted in transverse sections of the spinal cord.[2] Because HRP may diffuse from the injected muscle belly to neighboring muscle bellies, a simple and more accurate version of the technique is to place the central stump of the divided motor nerve in a solution containing HRP and to allow uptake to occur.

Anatomical Estimates of Motor Units in Human Muscle

Axon-counting can be successfully applied to the muscles of the face and orbit because the largest axons of the 3rd, 4th, 6th, and 7th cranial nerves are exclusively motor. These small muscles are found to have large numbers of small motor units; for example, the lateral rectus muscle of the eye contains approximately 3,000 motor units.[3] For limb muscles, however, a considerable proportion of the large-diameter axons in the motor nerves are sensory, originating in muscle spindles and tendon organs. If this proportion were known and constant from one muscle to another, this complication would be unimportant. Unfortunately, the extensive studies of Boyd and Davey[4] in the cat hind limb make it clear that the ratio of sensory to motor axons can vary significantly from one muscle to another, for example, from 40% to 70%. There is a further problem in human studies, in that the distinction between "large" and "small" fibers is not always obvious because the axon diameters in some motor nerves show unimodal, rather than bimodal, distributions. The study by Feinstein and colleagues[3] is subject to such caveats; these authors assumed that 60% of large axons were [alpha]-motor, on the basis of axon counts in a patient who died from poliomyelitis. The values obtained by Feinstein et al[3] are shown in Table 1, and it should be noted that no more than one or two motor nerves were examined for each of the muscles in the table. This restriction adds further uncertainty, because the richness of the motor innervation varies considerably among individuals, judging by the range of values found for motor nerve roots5 and by the results of our own investigations.

Table 1. Numbers of Motor Units in
Human Muscles Estimated by Axon
Counts(3a)
Muscle                    No. of Units
External rectus           2,970
Platysma                 1,096
First lumbrical              96(b)
First dorsal interosseus    119
Brachioradialis             333(b)
Tibialis anterior           445
Medial gastrocnemius        579
(a) Feinstein and colleagues assumed that 60% of
large axons were [alpha]-motor, on the basis of
axon counts in a patient who died from poliomyelitis.
The values they obtained are shown
in Tab. 1, and it should be noted that no more
than one or two motor nerves were examined
for each of the muscles in the table.
(b) Mean of two values; other values are single
estimates.

Physiological Estimates of Motors Units in Human Muscles: Methodology

If the mean dimension of some physiological property of motor units were known, then it should be possible to determine the number of motor units by comparing the dimension with that obtained from the whole muscle. In theory, either the compound action potentials or the tensions generated by the motor units could be used for this purpose, and both have been. Measurements of tension have the advantage that the contributions of individual motor units are transmitted with little distortion to the tendon of insertion, whereas the sizes of motor unit potentials will be affected by the positions of the muscle fibers within the muscle belly relative to the recording electrodes. On the other hand, tension measurements require a rather elaborate experimental setup and occupy considerable time; in contrast, the potentials of single motor units can be rapidly and easily recorded and then compared with the maximum compound action potential (M-wave) of the muscle.

In our laboratory, we have found that the simplest method to obtain a sample of motor unit potentials is to gradually increase the intensity of an

electrical stimulus delivered to the motor nerve, starting from a subthreshold value.[6] The recordings are made with electrodes attached to the skin overlying the muscle. The stigmatic electrode, commonly referred to as the active recording electrode, is usually placed over the end-plate zone of the muscle, with the reference electrode situated remotely[7]; for the biceps brachii and vastus medialis muscles, however, bipolar configurations are needed to reduce the shock artifact to a manageable size. The muscles, and the electrode placements that have been used in their investigation, are shown in Figure 1. The responses grow in discrete steps as the stimulus intensity is raised; the first such response can be seen to be "all-or-nothing" in nature. Each increment in the response is assumed to result from the excitation of an additional motor unit, and, when a sufficient number have been obtained, the mean peak-to-peak amplitude, or voltage-time area, is calculated and divided into the corresponding value for the maximum M-wave. The maximum M-wave is determined by noting when increases in stimulus intensity no longer produce enlargement of the response.

In practice, there are a number of potential problems in motor unit estimation, of which the most serious is "alternation." This term describes the fluctuation in response amplitude that may take place as stimuli of the same intensity are repeated. Alternation is due to axons with similar thresholds firing in different combinations. To take the simplest case, if the stimulus intensity reaches the thresholds of two motor axons, there will be occasions when each axon will independency discharge as well as occasions when the two axons will discharge together. Thus, three possible responses (one for each axon and one for the axons combined) are generated by two motor axons, and one of these responses will therefore be "fictive" during the motor unit estimating procedure. Up to a certain value, higher stimulus intensities produce more opportunity for alternation because of the normal distribution of axon thresholds; the larger the stimulus, the greater the number of axons with overlapping thresholds.

Because alternation produces fictive motor unit responses, its effect is to overestimate the number of motor units in a muscle. The theoretical basis of alternation has been discussed at some length by Brown,[8] who devised two means of dealing with alternation. One method, multiple-point stimulation, involves stimulating the motor nerve and collecting only one to three motor unit potentials before moving the stimulating electrodes to a new site and repeating the process; the potentials from several such collections, are then pooled, and their average amplitude is determined.[9] A second method for eliminating alternation is to average the surface-recorded motor unit potentials, using an intramuscular needle electrode to select the activity of a particular unit, which, in turn, triggers the averaging system.[10]

A second problem in motor unit estimation concerns the subjective component of the original technique, in which the stimulus intensity is adjusted manually by the investigator. Thus, the more slowly the intensity is increased, the larger will be the number of stimuli presented at any given intensity and die greater will be the opportunity for alternation to occur; spuriously high motor unit estimates will result. Subjectivity is also involved in the decision by the investigator as to whether an increment has appeared in the response. Finally, there is the inevitable question of the adequacy of the sample of motor unit potentials used in the calculation of motor unit numbers. The sizes of the motor unit potentials will be affected not only by the positions of the muscle fibers relative to the recording electrodes, but also by the numbers of fibers within the unit.

Studies of nonhuman mammalian muscles, using the glycogen-depletion technique, have revealed a hundredfold variation in the numbers of muscle

fibers in different motor units,[11] and the measurements of motor unit tension and of potential amplitude suggest that the same wide range is true of human muscles.[6,12] If the sample of motor units is biased toward large units, the mean potential size will be increased and the number of motor units will be underestimated. By comparing the amplitudes of the first and last putative motor unit potentials in the sample, we have been able to show that the stimulation technique does not select motor units that are larger or smaller than average; the same conclusion was reached using an impulse conclusion technique.[6] A nonsystematic deviation in the sizes of the motor units sampled can only be diminished by increasing the size of the sample, but this is difficult to achieve with the original technique, partly because the amplification has to be reduced to accommodate the responses on the viewing screen, a maneuver that leads to less visible separation of the increments. As noted previously, the increase in alternation, as the stimulus intensity is raised, constitutes a further problem.

Computer-based Methods

The various problems in estimating the number of motor units have not been completely solved, but good progress has nevertheless been made. One major step has been the elimination of possible observer bias by automating the estimating technique. In the system used by Daube,[13] a computer software program holds the stimulus intensity at a given level and analyzes the fluctuation in the responses due to the excitation of varying numbers of motor axons with overlapping thresholds. The assumption underlying this method is that, on a random basis, there will be a greater chance of a single axon responding than of two axons, whereas responses due to three or more axons discharging in unison will occur even less frequency. Under these conditions, the response amplitudes would be expected to occur in a Poisson distribution; a distribution of this type is known to characterize the amplitudes of the miniature end-plate potentials,[14] caused by the spontaneous release of packets of acetylcholine (ACh) from motor nerve terminals. However, although the ACh content of the synaptic vesicles is probably fairly uniform, the numbers of muscle fibers in individual motor units show a hundredfold variation. For this reason, a "large" potential increment could indicate either several small motor units joining together or the response of a single large unit. Despite this objection, the technique used by Daube has given results that are in keeping with other values for healthy muscles, and it has proven to be of value for the detection of muscle denervation.[13]

The computer program developed in our own laboratory[15] is based on the original "manual" technique; that is, the stimulus intensity is gradually increased (in 0.05-mA steps), and increments in the response are sought. The decision as to whether an increment has appeared is made by comparing the fast Fourier transforms of the last response and those of other response templates held in the computer memory. At the end of the collection period, the response templates are ranked in order of increasing voltage-time areas, and each is subtracted from the next largest; the difference is assumed to correspond to a motor unit potential. The problem of alternation is dealt with in two ways. First, a given increment is not used in the calculation of motor unit number unless it occurs on at least three occasions as the stimulus intensity is lowered slightly and then raised again. Second, at the end of the collection period, the computer program compares each increment with every other one in the sample; matching increments are attributed to alternation and are corrected for in the calculation of motor unit number. Other differences from the manual technique are that the size of the sample of motor units is larger (eg, 20 units as opposed to 10) and that the voltage-time area of the response, rather than the peak-to-peak amplitude, is used. An example of a motor unit estimate, derived in this way in the thenar muscles of a 30-year-old healthy subject, is given in Figure 2. in this example, the mean motor unit potential area was 0.265 mV.ms and that of the maximum M-wave was 77 mV.ms, giving an estimate of 290 motor units. A feature of the software program is that the configurations of the putative motor unit potentials can be visualized by subtracting each response template from the next largest; the individual motor unit potentials are then displayed in a montage (Fig. 2, left). Under normal circumstances, 20 such potentials are obtained; any instance of alternation causes one of the identical responses to be deleted and results in a blank panel within the montage. The software program also enables the configuration of the summated motor unit potentials in the sample to be compared with that of the maximum M-wave (Fig. 2, bottom right); a high degree of overlap (percentage of fit) gives confidence in the adequacy of the sample.

Once the electrodes are in place, an automated motor unit estimate takes 3 to 5 minutes to obtain. In the electromyography (EMG) clinic, a normal result is not repeated, but second estimates are obtained if the initial value is borderline or diminished. In research studies, it is recommended that the mean value of three estimates be used; altering the duration of the stimulus pulse or moving the stimulating electrodes slightly ensures that some of the units sampled will differ in the three trials.

The automated technique can be applied with little difficulty to most subjects, though experience is required in obtaining optimum position of the stimulating and recording electrodes in some situations. In a minority of cases, it is impossible to gain a satisfactory estimate because of background EMG activity, as in those subjects who are unable to relax or who have prominent F-waves or H-reflexes; in some patients, tremor or fasciculations can disrupt the estimating process.

Motor Unit Estimates in Healthy Subjects

Table 2 shows the estimated numbers of motor units, obtained with the automated technique, in a sample of healthy male and female subjects. To eliminate the possible effects of aging on motor unit estimates, only data for subjects below the age of 60 years are shown in the table.

[TABULAR DATA 2 OMITTED]

In examining the values for the thenar and hypothenar muscles in Table 2, account must be taken of the number of muscles in each group. With the recording electrodes positioned as in Figure 1, stimulation of the ulnar nerve at the wrist will evoke responses in four muscles under the stigmatic recording electrode--the abductor, flexor, and opponens digiti minimi and the palmaris brevis. Similarly, stimulation of the median nerve at the wrist will activate the abductor pollicis brevis and opponens pollicis muscles, together with part of the flexor pollicis brevis muscle. Therefore, if the hypothenar and thenar muscle values in Table 2 are divided by 4 and 2.5, respectively, the intrinsic muscles of the human hand are seen to have roughly 100 motor units each--an estimate in agreement with the anatomically derived results of Feinstein et al[3] for the first dorsal interosseus and lumbrical muscles (Tab. 1.) The thenar muscle results obtained with the automated system are also close to those determined by Lee et al,[16] who, using motor conduction velocities as a guide, counted the numbers of axons with diameters greater than 8.3 Km in the recurrent branch of the median nerve and assumed that 50% of these axons were X-motor. Their value of 203 motor nerve fibers may be compared with the mean estimate of 240 motor units obtained with the present computer-based system.

Initially, it may appear surprising that a small muscle in the hand has almost as many motor units as the biceps brachii, a much larger muscle (Tab. 2). It could be argued, however, that the biceps brachii muscle, in flexing the elbow and supinating the forearm, does not require the same fine gradations of force and speed of movement as a muscle operating the thumb or one of the fingers.

The large scatter of results, as reflected in the standard deviations around the means for the different muscles, also deserves comment. Part of this scatter is due to the considerable variation in the sizes of motor units, and therefore of the motor unit potentials, in a given subject. Another methodological error comes from one of the steps used in the calculation of motor unit number, in which the voltage-time area of the average motor unit potential is divided into that of the maximum M-wave. Like any other division, this step will have the effect of converting a normal distribution into a distribution that is skewed toward high values. Of equal importance, however, is the existence of differences among subjects, such that some appear to be endowed with more plentiful muscle innervation than others. It is our impression that the richness of innervation is widespread throughout the body; it is not clear from animal studies whether the differences among subjects would result from corresponding changes in neuronal proliferation or in programmed cell death during embryo-genesis. Earlier investigations, using the "manual" estimating technique, revealed that the extent of the motor unit population had been determined by birth, because the estimates in neonates were similar to those in older children and adults (Alan J McComas, unpublished observations). In contrast, the fiber-type destinies of the motor units do not appear to be resolved until 8 to 10 months after birth.[17]

Influence of Aging on Motor Unit Populations

In the elderly, there are varying degrees of atrophy in many tissues and organs, and the skeletal muscles are not excepted. Not surprisingly, there is a commensurate loss of strength, [18] and muscle contractions become slower. Because the numbers of muscle fibers are reduced[19] and surviving fibers often show evidence of fiber-type grouping or grouped atrophy, it is reasonable to suspect that denervation may have occurred. This possibility has now been explored using the automated motor unit estimating system, and the results are shown in Figure 3. In this figure, the results for a proximal muscle, the biceps brachii, have been compared with those for small muscles in the hand and foot. In keeping with the findings of an earlier study using the manual estimating technique,[20] the distal muscles (thenar and extensor digitorum brevis) show losses of motor units with increasing age. The respective declines become statistically significant in the 60- to 79-year-old subjects and are still more marked in the oldest individuals (80-98 years). In contrast, the numbers of motor units appear to be well maintained in the biceps brachii muscle, even in the oldest age group (see, however, Doherty et al[21]). Without examining other muscles, it is not possible to say whether these results are indicative of a greater susceptibility of distal muscles to denervation in aging; if this is indeed the case, the situation in aging would resemble that found in generalized peripheral neuropathies due to other causes, such as diabetes, renal failure, and vincristine toxicity.

Even though motor units are lost with age, the increased sizes of the compound action potentials of the surviving units[20] indicate that a proportion of the elderly motoneurons are able to undertake collateral reinnervation and to diminish the loss of strength that would otherwise occur. Although the topic remains somewhat controversial, there are histochemical studies of muscle fibers that give no indication that aging affects motor units of one type more than another.[19]

It is a reasonable hypothesis that maintenance of motor unit populations is a prerequisite for avoiding some of the hazards confronting the elderly, such as bronchopneumonia and accidents due to loss of mobility. Further, if the richness of muscle innervation is genetically determined, then future studies in the elderly would be expected to show correlations between motor unit estimates and parental longevity.

Motor Unit Estimates in Patients With Neuromuscular Disorders

In patients attending the EMG clinic with suspected neuromuscular problems, the primary function of the estimating technique is to establish whether muscle denervation is present, and if so, its severity. In addition, the relative sizes of the putative motor unit potentials will give some indication of the degree of collateral reinnervation that has taken place. Thus, if enlarged motor unit potentials are present, the denervating process must have been present for several weeks at least; in patients with slowly progressive disorders, collateral reinnervation can provide such good functional compensation that 80% to 90% of the motor units may be lost before weakness and muscle atrophy supervene.[22] Finally, in patients in whom the diagnosis is known, serial motor unit estimates may be used to study the progress of the condition. In our laboratory, we have used this approach to monitor patients with peripheral neuropathies and those with different types of motoneuron disorders. in the next sections, we briefly present results in amyotrophic lateral sclerosis (ALS), spinal muscular atrophy, post-polio syndrome, and peripheral neuropathy.

Amyotrophic Lateral Sclerosis

In this condition, familiarly known as Lou Gehrig's disease, there is a progressive loss of [alpha]-motoneurons in the spinal cord and brain stem, which ultimately results in muscle paralysis and death. The condition is familial in a small percentage of cases, and multiple factors may be responsible in others. The disease is increasingly common with advancing age, and the mean life expectancy, from the time of diagnosis, is approximately 3 years.

In 123 patients with this condition investigated in our laboratory, a total of 373 muscles were examined by the manual motor unit estimating technique[23]; other patients have since been tested with the automated system. One of the most striking findings was the very advanced denervation found in some of the muscles at the time of diagnosis; presumably, the condition had been masked by compensatory collateral reinnervation. Plots of motor unit number against mean motor unit potential amplitude suggest that, in most muscles, the amount of collateral reinnervation is directly proportional to the availability of denervated muscle fibers. Thus, surviving motoneurons may ultimately supply, on average, seven times their normal complement of muscle fibers, and some neurons will exceed this ratio. Scanning EMG examinations in humans[24] and glycogen-depletion studies in animals[25] Suggest that the collateral reinnervation process does not extend beyond the original territorial boundaries of the motor unit, but rather captures fibers from other motor units within that territory. In the late stage of the disease, however, the failing motoneurons gradually relinquish their complements of muscle fibers.[26]

One of the most interesting questions in ALS is how rapidly the motor units are lost, and this has been answered in our laboratory by repeated investigations of individual muscles. Our results show that, once a motoneuron pool is affected, the degenerative process proceeds quickly, such that on average, half the neurons have ceased to function within 6 months Fig. 4). With the increasing application of experimental therapies in ALS, automated motor unit estimation may be expected to fulfill an important role by measuring outcome.

Spinal Muscular Atrophy

In this condition, as in ALS, there is a loss of [alpha]-motoneurons, which is probably due to a genetic fault in the majority of cases. The condition may be present in infancy, with death supervening in months or years. At the other extreme, the condition may not manifest itself before adulthood, and may then progress slowly, often with a normal life expectancy for the patient.

Motor unit estimates are diminished in spinal muscular atrophy, though usually not to the same extent as in ALS, and collateral reinnervation is prominent. One of the most fascinating findings in adolescents and adults is that the numbers of functioning motor units usually do not decrease.[27] This surprising result implies that the depletion of motoneurons is already present at birth, due either to reduced neuronal proliferation or to excessive cell death during embryogenesis. The onset of symptoms in later life is presumably due to the gradual shedding of muscle fibers as motoneurons begin to fall.

Post-polio Syndrome

It is now widely recognized that patients who recovered fully or partially from acute poliomyelitis 20 to 40 years previously, may in later life develop a syndrome of increasing muscle weakness and wasting, usually with fatigue and muscle soreness.28 It is not only of physiological interest but also of prognostic importance to understand the nature of any changes that might be affecting the motor units during this period of declining function. With this consideration in mind, we have estimated motor unit populations in a total of 40 patients with post-polio syndrome; most patients were examined with the manual technique, often on more than one occasion, but more recently the automated technique has been used.

In keeping with the variations in disability from one patient to another, the motor unit populations differ widely. In severely affected upper and lower extremities, there may be total denervation, whereas in those limbs that appeared to escape the onslaught of the disease, the full complements of motor units may be present. Substantial losses of units can often be demonstrated in muscles thought to have been spared. As in ALS and spinal muscular atrophy, it is the remarkable ability of the surviving motoneurons to undertake collateral reinnervation that enables contractile force and muscle bulk to be maintained.

Why, then, do patients with post-polio syndrome become weaker in later life? One obvious possibility is that there is a further loss of motoneuronal function due to normal or accelerated aging. To test this possibility, we examined motor unit populations in the same muscles of patients with post-polio syndrome over a 2-year period. In the majority of muscles, it was not possible to demonstrate any reduction in motor unit number, though the potential error associated with the motor unit estimating technique would not have permitted small changes to be detected. In an attempt to overcome this problem, the results were pooled for six muscles in each patient. In the few patients who were deteriorating rapidly, however, losses of motor units and reductions in excitable muscle mass could be demonstrated. The tentative answer to the earlier question, then, is that motoneuron function does decline in the post-polio syndrome, albeit very slowly. The comprehensive studies of Dalakas et al[29] Suggest that there is a period of attrition, during which muscle fibers are relinguished, before the entire motor unit is destroyed.

Peripheral Neuropathies

As would be expected, motor unit estimation is a valuable test for the diagnosis and assessment of peripheral neuropathy, and as such is used routinely in patients suspected of having nerve entrapments. In patients with generalized peripheral neuropathies, motor unit estimation brings to light interesting differences in the susceptibility of muscles to denervation. Not only are distal muscles affected more than proximal muscles, but the distal muscles differ among themselves in their degrees of involvement. Thus, the thenar and extensor digitorum brevis muscles invariably have more denervation, in relation to their original motor unit populations, than the hypothenar and plantar muscles. Why these differences exist is not clear. They cannot be related to axonal length or to the proportions of motor units with the various muscle fiber types, because these variables are similar among the muscles considered, nor is usage likely to be a factor. Figure 5 shows the reduced number of motor units estimated in the extensor digitorum brevis muscle of a 31-year-old man with a history of increasing weakness over several years. The estimate of 29 units was well below the lower limit of the normal range (ie, 75 units) and provided part of the EMG evidence for the presence of a peripheral neuropathy.

A further use of motor unit estimation is to follow the progress of patients with peripheral neuropathies. This is most easily done in those patients with axonal forms of neuropathy, because in demyelinating disorders, the temporal dispersion of the evoked motor unit responses makes motor unit estimation rather unreliable. Figure 6 shows consecutive motor unit estimates in the thenar and extensor digitorum brevis muscles of a patient treated with vincristine for a malignancy. The toxicity of the drug denervated the thenar and extensor digitorum brevis muscles almost completely. After the treatment was stopped, however, both muscles regained their innervation over a period of many months. Reinnervation was almost complete in the thenar muscles, whereas fewer than half of the motor axons were able to regenerate successfully in the extensor digitorum brevis muscle.

Summary

The introduction of motor unit estimation more than 20 years ago has added to our knowledge of the sizes of the motoneuron pools serving muscles in the human upper and lower extremities. With the recent advent of automated methods, it is anticipated that motor unit estimation will be used increasingly in the EMG clinic for the diagnosis and assessment of patients with muscle denervation. The results of such studies cannot help but increase our understanding of the pathophysiology of such disorders and may provide a rational basis for evaluating new therapies. Further modification and refinements of the automated methodology may be anticipated as more academic laboratories begin to use this neurophysiological approach for the study of neuromuscular disorders.

Acknowledgment

We thank Jane Butler for her technical support.

References

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AJ McComas, MB, FRCP(C), is Professor and Chair, Department of Biomedical Sciences (Room 4N83), McMaster Health Sciences Centre, McMaster University, 1200 Main St W, Hamilton, Ontario, Canada L8N 3Z5. Address all correspondence to Mr McComas.

V Galea, MSc, is Assistant Professor, School of Occupational and Physical Therapy, McMaster Univer

H de Bruin, PhD, is Associate Professor, Department of Medicine, McMaster University.

This work was approved by the Ethics Committee of McMaster University.

This work was supported by the Muscular Dystrophy Association of Canada and by the DeGroote Foundation.