Introduction

The Romberg test, a classic neurology test to assess proprioceptive deficits, was proposed in 1836 by Professor Moritz Heinrich Romberg and consists of the patient keeping an unperturbed upright stance, while the neurologist compares the amount of sway with the patient’s eyes closed to that with the patient’s eyes open. Romberg’s ingenious solution for measuring sway was to attach a feather to the patient’s head in a vertical position, and to measure the trajectory traced by the feather on a soot-covered wooden plate suspended over the patient’s head [1]. This operation is much easier nowadays [2]: a force plate gives the coordinates of the center of pressure (COP) on its surface, by way of simple calculation [3]. The COP under the soles of the foot is defined as the point of location of the vertical ground reaction force vector - the sum of all pressures exerted on the surface of the plate through the foot soles for the purpose of keeping balance while standing upright. Sampling the recording several times per second the COP path appears rather smooth, and a growing number of parameters measurable from its coordinates have been proposed to permit and support diagnostic assessment [4].

In addition to the well-known parameters to describe trajectory (sway path, sway area, standard deviation of the oscillations) or express the distribution of the COP positions sampled during the test (the smallest ellipse containing the mean COP and 95% of the sampled points), other “structural” parameters have been proposed to show the “structure” of the sway which results from a combination of anticipatory commands and low frequency feedback controls [5].

An important contribution to the analysis of balance control has come from the harmonic analysis of both frontal and sagittal plane sway [6]. The idea comes from the Fourier theory, which allows the time variation of the coordinates of a stationary oscillatory movement to be transformed into the sum of elementary sinusoidal oscillations with a specific amplitude, frequency, and phase. Without going into the details of the mathematical process [7], it is worth noting that the presence of “harmonics” – the name given to the individual sinusoidal oscillations – suggests a repeatable phenomenon responsible for those specific oscillations, and that the intensity of those oscillations is directly proportional to their amplitude.

Balance while standing is intrinsically unstable: the center of mass is slightly under the umbilicus (about 55% of subject height from the ground), placing it well above the ankle axis. The system of balance control in humans solves the biomechanical problem of keeping the body in an intrinsically unstable position by modulating the pressure exerted on the ground through the soles of the feet. This system must also control the many body segments which pivot around the joints and hinges connecting the skeleton.

To maintain a so-called “stable” upright stance, humans need to correct any oscillations via a combination of proprioceptive input and the motor control patterns adaptively learned and continuously updated based on the body’s anthropometrics. The study of human balance control mechanisms has received a tremendous boost from the studies performed to design bipedal humanoid robots capable of walking and standing while performing different tasks. The combination of actuators across the joints (agonists and antagonist as muscles) was immediately adopted by researchers, together with overall control mechanisms involving feed-forward [8] and feedback functions [9].

By observing the structure of the human skeleton and the distribution of skeletal muscles, researchers recognized that a good model for understanding the behaviour of balance keeping was the inverted pendulum [10, 11], and a multi-segmented one at that, where segments are interconnected by the specific joints. More recently, however, the single segment pendulum has been suggested as a better option [12]. The oscillations of a pendulum depend solely on its length: the longer the pendulum arm, the lower its frequency of oscillation (Figure 1). The mathematics of the pendulum is shown in (Table 1).

Figure 1: A Metronome: an inverted pendulum whose arm length can be adjusted to provide the required oscillation frequency

Table 1: Frequency of an oscillating pendulum.

From our experience the differences of harmonics’ frequencies due to the subject stature seem much smaller than the ones coming from the sole mathematics. We suppose that the viscoelastic properties of muscles and joints account for a much smaller variability, and we propose to use a normalized stature to the mean values reported, for example, by NASA for the 50th percentile of the American Males/Females (Figure 2).

Figure 2: Normalized height (US 50^th percentile population) (From NASA document retrieved on April 10, 2023 @ https://msis.jsc.nasa.gov/sections/section03.htm)

Previous observations, presented in deeper detail in the next paragraph – see, for example [13], – have shown the sway of standing humans to occur at frequencies under 1 Hz.

It has been demonstrated that although the classic free oscillating pendulum depends exclusively on the height of the center of mass, the human pendulum-like model should be adjusted to consider the viscoelastic properties of the antagonist muscles [14, 15] which stabilize all the joints responsible for the multisegmented pendulum-like behavior of the human body.

At the end of the design phase of the balance force plate (ArgoPlusMK1 by Fremslife Genoa, Italy), a sample of normal subjects was tested to give the reference values for all parameters. Testing involved the subjects standing in an upright position with feet together, with closed and open eyes, for a recording time of 40 seconds and a sampling rate of 100 Hz, and the normal ranges (mean ± 2 std. dev.) were calculated for all parameters, including the harmonic spectral power, in 16 sub-bands, 8 on the frontal and 8 on the sagittal plane. The sample consisted of 195 healthy young volunteers, 119 of whom were elite athletes [16] and was subsequently extended to a total of 1212 normofunctional individuals. Since then we have collected several thousand test results during our routine clinical practice, investigations which included a specific test to explore the feasibility of using the Romberg test as a screening tool for balance deficits [17], and we noticed the as-yet unreported relationship between the harmonic analysis and the position of what could perhaps be described as an irritative focus. It was only during a recent discussion of the topic that the co-authors of this paper came to exchange experiences and comments which led to the definition of the present medical hypothesis.

The typical distribution of the harmonic spectral power over 8 bands was calculated from the observed characteristics of the sample of 1212 normofunctional individuals (Table 2 and Figures 2 and 3). While developing the normal parameters from this population, the normal harmonic spectrum values were also extrapolated.

Table 2: The sample.

Figure 3: The normalized sway harmonic power in norm functional individuals.

Figure 4: The absolute sway harmonic power values in normofunctional individuals.

The selected bands (Table 3 and Figure 5) were defined based on the hypothesis of a possible correlation to body segments, according to the inverted pendulum logic.

Table 3: Sub-band distribution of the total calculated total harmonic power (mm²/Hz).

Figure 5: Correspondence between skeletal segments, frequencies, and spectral bands.

A large body of literature – for example [18–29] –claims that postural sway is modified by musculoskeletal pain, although we have also found a paper demonstrating that the most widely used balance parameters (mean sway velocity and sway area) are not affected by such pain [30].We believe that force plate parameters are not always reliable, therefore it is crucial to select those which are most appropriate [31]. We also believe that harmonic analysis can constitute a reliable tool for detecting the presence and position of a focusresponsible for generating nociceptive interferences – even those under the pain perception threshold.

The assumption of the authors presented in this manuscript is that the frequency of a peak in the harmonic analysis of the recording performed with closed eyes is closely correlated to the position of the irritative focus which causes that specific sway anomaly. It is worth noting that such a focus may be accompanied by pain or be a residual compensation of an old injury requiring rehabilitation or re-education. This hypothesis, however, should be further explored to provide a more specific and reliable correlation.Several technical/ operational requirements must be met to permit an analysis of the oscillation harmonics from the sequence of COP positions:

a) To calculate the COP coordinates, the signals from the load cells should be sampled and filtered (a second order Butterworth filter with a 10 Hz cut-off frequency is recommended) to provide reliable information.

b) The filtered COP coordinate output must be at a frequency higher than the one expected in the oscillation by at least one order of magnitude [32]. Its resolution depends on this frequency: the higher the better.

c) The recording time should be as long as possible (the lowest detectable frequency is inversely proportional to the acquisition interval) as a compromise between the achievement of a steady state and the onset of fatigue in dysfunctional subjects, or attention loss in healthy subjects who find the task easy to complete [33].

d) Testing should be done under normal environmental conditions [34].

e) The subject should assume a normal standing position on the force plate [35].

Materials and Methods

Measurements were performed using the Force Plate ArgoPlusMK1 (Fremslife – Genova Italy). The main characteristics of the device are given in (Table 4).

Table 4: ArgoPlusMK1 Characteristics.

The Sway Harmonic analysis was calculated from the recorded stabilogram values (X, Y coordinates vs. time) using the NonParametric Welch FFT algorithm [36].From the 4,000 recorded values (40 seconds at 100 Hz) the FFT provides 300 values at 0.012207 Hz interval having excluded the values under 0.1 Hz as non-significant.

The spectrum graph is therefore given with 300 values on the logarithmic scale to give a good visual resolution in the frequency range up to 1 Hz. Dataset were selected among the ones recorded on subjects occasionally visiting the Physiotherapy wards for musculoskeletal rehabilitation. Patients gave their written consent to the anonymous publication of the evidence collected. Full data set may be made available on request.

Results

The following examples are being reported to support the hypothesis of a correlation among the harmonics’ frequencies and their originating focuses.

Application example 1 – Treatment of a musculoskeletal condition

Spectral analysis of the instrumented Romberg test performed on a 79-year-old female patient (155 cm tall, weighing 70 Kg) who had undergone total right hip arthroplasty and was complaining of persistent hip pain while standing (Figure 6).

Figure 6: Spectral analysis of the instrumented Romberg test performed on a 79-year-old female patient. Green plot = latero-lateral sway; red plot = antero-posterior sway. Horizontal axis shows frequencies, whilev ertical axis shows harmonic power (mm²/Hz). Note that graphs (a) and (d) are identical (harmonic power vs frequency in the closed eyes recording prior to treatment)

Gait functionality was impaired. Harmonic analysis indicated the likelihood of a proprioceptive interference, as demonstrated by the difference between graphs (a) (closed eyes recording) and (b) (open eyes recording) caused by nociceptive stimuli and demonstrated the effect of a rehabilitative treatment: graphs (d) and (c) show the closed eyes recordings before and approximately 45 minutes after an effective rehabilitation treatment (laser acupuncture with Libralux by Fremslife (Genoa – Italy)).

Application example 2 – Treatment of a central deficit

The high frequency harmonics of neurological interest can also be seen, and a differential “ex-adjuvantibus” diagnosis can be made to support the treatment program (Figure 7).

Figure 7: Harmonic plot of a patient following a traumatic event with suspicion of cerebellar injury.

Although his vision compensated the closed eyes sway [please see (b) vs. (a) graphs –note that in (b) the vertical axis has top values over 100 mm²/Hz, while in (a) they are under 20] the graphs showed a significant dysfunction. Besides the high frequency harmonics that are strongly suggesting a cerebellar involvement, the harmonics at 0.1 Hz are consistent with a latero-lateral cervical condition (cervicothoracic hinge) with a latero-lateral harmonic at coccygeal level (0.35 Hz) which may be compensatory. These harmonics are still visible following treatment, albeit at a reduced level (2.5÷3 mm²/Hz instead of 7.5÷11).

The patient was tested again 25 minutes after treatment (closed eyes only), significantly reducing the high frequency harmonics [(c) vs. (b) graphs] to almost normal levels. The antero-posterior harmonics at 0.07, 0.11,0.15 and 0.25 Hz disappeared.

A patient was examined following a traumatic event with suspicion of a cerebellar injury, undergoing Romberg testing on the ArgoPlusMK1 device. Although his vision appeared well compensated, the closed eyes sway was consistent with significant dysfunction. Although the likelihood was of a centrally originated dysfunction, the patient was undergoing rehabilitation treatment at the time (laser acupuncture with Libralux by Fremslife (Genoa – Italy)). The patient was tested again 25 minutes after treatment (closed eyes only), showing that the laser acupuncture treatment had significantly abated the high frequency harmonics to an almost normal level. Unfortunately the patient’s symptoms returned three days after treatment, confirming the need for further neurological investigations. It is to remark that the major harmonics at frequencies under 0.05 Hz are non-significant because the minimum detectable frequency is reciprocal to the recording time (40 sec and, therefore, 1/40 = 0.025 Hz).

Application example 3 – Compensation of an old injury

Harmonic analysis is also able to show the presence of interference due to an old, apparently compensated injury. While functionality in bending, walking, and performing life activities was not impaired, and the subject gave no medical history prior to the test, harmonic analysis (Figure 8) suggested the presence of a dysfunction.

Harmonic analysis of the closed eyes recording shows an undampened antero-posterior harmonic (blue oval) pertaining to a sagittal compromise at the lumbar level, fully compensated by the patient’s vision (small blue oval) at the cost of a cervical compensation (brown oval). The red oval in the closed eyes test shows a latero-lateral cervical oscillation corresponding to some “noise” in the region of the knee joint.

The harmonic analysis of the closed eyes recording showed an undampened antero-posterior harmonic (blue oval) pertaining to a sagittal compromission at the lumbar level, fully compensated by the patient’s vision (small blue oval) at the cost of a cervical compensation (brown oval).

The red oval in the closed eye test showed a latero-lateral cervical oscillation corresponding to some “noise” in the region of the knee joint. Following specific questions on his medical history, the patient reported a motorbike accident (3 years previously) in which he suffered an injury to the lumbar spine, treated with 6 months’ immobilization (corset) of the lumbosacral spine. It could be concluded that the rehabilitation process did not restore full mobility of the spine.

Application example 4 – Acute orthopedic injury

A patient presented with a fracture to the humeral head due to a bicycle accident (Figure 9). The fracture was clearly shown by the harmonic analysis of the closed eyes recording. Note the compensation at the thoracolumbar hinge.

Figure 9: Orthopedic injury following a bicycle accident.

Application example 5 – Musculoskeletal pain interference

A 65-year-old cyclist was unable to practice more than 20 minutes due to unbearable monolateral hip joint pain. Harmonic analysis clearly showed interference well compensated by visual input (Figure 10), while the Romberg test showed visually compensated musculoskeletal interference. The frequency of the main harmonic (0.35 Hz) in the latero-lateral oscillation during the closed eyes recording suggested a monolateral lumbosacral origin (hip joint).

Figure 10: The Romberg test shows a visually compensated musculoskeletal interference. The frequency of the main harmonic (0.35 Hz) suggests a monolateral lumbosacral origin (hip joint).

Application example 6 – Postural instability

An 83-year-old woman complained of postural instability. The Romberg test suggested a possible patellofemoral syndrome and following physiotherapy treatment with a Vibra device (Vibra 3.0 by AD SWISS MEDTECH SA – CH), the patient reported a significant improvement, confirmed by a second measurement 15 days after physiotherapy treatment (Figure 11).

Figure 11: Reduction of latero-lateral postural stability, probably due to a monolateral patellofemoral syndrome, treated and measured before and after a rehabilitation program. The harmonic at 0.4 Hz was strongly reduced.

Discussion

Postural control requires maintenance of an unperturbed upright stance. This ability involves spinal and brain stem structures, as well as cortical areas which are fundamental for adjusting the motor commands from the peripheral receptors, such as the condition of the body and environmental changes [37]. Proprioceptive signals play an important role in postural control, due to the low proprioceptive threshold linked to body sway [38,39]. The muscle spindles play a key role in this context, conveying information about changes in muscle length and speed of contraction: indeed, lengthening of the muscle activates the receptors and the consequent transmission of the action potential through the afferent fibers and to the alpha motoneurons and interneurons, conveying the proprioceptive information to the sensorimotor cortex and to the cerebellum [40]. Both physiological and pathological conditions alter the proprioceptive system with a possible consequent increase in body sway, impaired balance, and a higher risk of falling [41]. In fact, the ability to detect and compensate for body sway by adjusting leg muscle length via rotation around the ankle joint is an important component of postural control [42].

Painful conditions may interfere with postural control, irrespective of the underlying pathology. Although the exact mechanisms are still unclear, one possible explanation may be the loss of proprioception consequent to a painful stimulus [43], indeed the activation of nociceptive fibers Aδ and C which convey the signal at a spinal level may lead to a reflex excitation of ϒ-motoneurons and to a consequent hypersensitivity of muscle spindles [44]. While this has only been demonstrated in animal models, with experimentally induced pain in humans not appearing to induce changes in muscle spindle activity [45,46], there is a probable link between pain and proprioceptive deficits in the central nervous system (CNS), in both the motor and somatosensory cortex [47,48].